Ice, Cloud, and Land Elevation Satellite 2 (ICESat-2) for ... · ICESat-2 Algorithm Theoretical...

ICESat-2AlgorithmTheoreticalBasisDocumentforLand-VegetationAlong-TrackProducts(ATL08)

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Released15September20191

Ice, Cloud, and Land Elevation Satellite 2 (ICESat-2) 1 2

Algorithm Theoretical Basis Document (ATBD) 3 4

for 5 6

Land - Vegetation Along-Track Products (ATL08) 7 8

9

10

Contributions by Land/Vegetation SDT Team Members 11and ICESat-2 Project Science Office 12

(Amy Neuenschwander, Katherine Pitts, Benjamin Jelley, John Robbins, 13Brad Klotz, Sorin Popescu, Ross Nelson, David Harding, Dylan Pederson, 14

and Ryan Sheridan) 15 16

17

ATBD prepared by 18

Amy Neuenschwander and 19

Katherine Pitts 20

21

15 September 2019 22

23

24

Contentreviewed:technicalapproach,assumptions,scientificsoundness,25

maturity,scientificutilityofthedataproduct26

27 28


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ATL08algorithmandproductchangehistory2930ATBDVersion Change2016Nov Productsegmentsizechangedfrom250signalphotonsto

100musingfive20msegmentsfromATL03(Sec2)2016Nov Filteredsignalclassificationflagremovedfrom

classed_pc_flag(Sec2.3.2)2016Nov DRAGANNsignalflagadded(Sec2.3.4)2016Nov Donotreportsegmentstatisticsiftoofewgroundphotons

withinsegment(Sec4.15(3))2016Nov Productparametersadded:h_canopy_uncertainty,

landsat_flag,d_flag,delta_time_beg,delta_time_end,night_flag,msw_flag(Sec2)

2017May Revisedregionboundariestobeseparatedbycontinent(Sec2)

2017May AlternativeDRAGANNparametercalculationadded(Sec1.1.1)

2017May Setcanopyflag=0whenL-kmsegmentisoverAntarcticaorGreenlandregions(Sec4.4(1))

2017May Changeinitialcanopyfiltersearchradiusfrom3mto15m(Sec4.9(6))

2017May Productparametersremoved:h_rel_ph,terrain_thresh2017May Productparametersadded:segment_id,segment_id_beg,

segment_id_end,dem_flag,surf_type(Sec2)2017July Urbanflagadded(Sec2.4.17)2017July Dynamicpointspreadfunctionadded(Sec4.11(6))2017July MethodologyforprocessingL-kmsegmentswithbuffer

added(Sec4.1(2),Sec4.17)2017July RevisedalternativeDRAGANNmethodology(seeboldedtext

inSec1.1.1)2017July Addedpost-DRAGANNfilteringmethodology(Sec4.7)2017July UpdatedSNRtobeestimatedfromsupersetofATL03and

DRAGANNfoundsignalusedforprocessingATL08(Sec2.5.17)

2017September MoredetailsaddedtoDRAGANNdescription(Sec4.3),andcorrectionstoDRAGANNimplementation(Sec3.1.1,Sec4.3(9))

2017September AddedAppendixA–verydetailedDRAGANNdescription2017September RevisedalternativeDRAGANNmethodology(seeboldedtext

inSec1.1.1)2017September ClarifiedSNRcalculation(Sec2.5.17,Sec4.3(18))2017September Addedcloudflagfilteringoption(SecError!Reference

sourcenotfound.)


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2017September Addedtopofcanopymediansurfacefilter(Sec3.5(a),Sec4.10(3),Sec4.12(1-3))

2017September Modified500canopyphotonsegmentfilter(Sec3.5(c),Sec4.12(6))

2017November Addedsolar_azimuth,solar_elevation,andn_seg_phtoReferenceDatagroup;parameterswerealreadyinproduct(Sec2.4)

2017November Specifiednumberofgroundphotonsthresholdforrelativecanopyproductcalculations(Sec4.16(2));nonumberofgroundphotonsthresholdforabsolutecanopyheights(Sec4.16.1(1))

2017November ChangedtheATL03signalusedinsupersetfromallATL03signal(signal_conf_phflags1-4)tothemedium-highconfidenceflags(signal_conf_phflags3-4)(Sec3.1,Sec4.3(17))

2017November RemovedDateparameterfromTable2.4sinceUTCdateisinfilemetadata

2018March Clarifiedthatcloudflagfilteringoptionshouldbeturnedoffbydefault(SecError!Referencesourcenotfound.)

2018March Changedh_diff_refQAthresholdfrom10mto25m(Table5.2)

2018March Addedabsolutecanopyheightquartiles,canopy_h_quartile_abs(Laterremoved)

2018March Removedpsf_flagfrommainproduct;psf_flagwillonlybeaQAQCalert(Sec5.2)

2018March AddedanAsmoothfilterbasedonthereferenceDEMvalue(Sec4.6(4-5))

2018March Changedreliefcalculationto95th–5thsignalphotonheights.(Sec4.6(6))

2018March AdjustedtheAsmoothsmoothingmethodology(Sec4.6(8))2018March RecalculatetheAsmoothsurfaceafterfilteringoutlyingnoise

fromsignal,thendetrendsignalheightdata(Sec4.7(3-4))2018March AddedoptiontorunalternativeDRAGANNprocessagainin

highnoisecases(Sec4.3.2)2018March ChangedgloballandcoverreferencetoMODISGlobal

Mosaicsproduct(Sec2.4.14)2018March Adjustedthetopofcanopymedianfilterthresholdsbasedon

SNR(Sec4.12(1-2))2018March AddedafinalphotonclassificationQAcheck(Sec4.14,Table

5.2)2018March Addedslopeadjustedterrainparameters(Laterremoved)2018June Replacedslopeadjustedterrainparameterswithterrainbest

fitparameter(Sec2.1.14,4.15(2.e))


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2018June Clarifiedsourceforwatermask(Sec2.4.15)2018June Clarifiedsourceforurbanmask(Sec2.4.17)2018June Addedexpansiontotheterrain_slopecalculation(Sec4.15)2018June Removedcanopy_d_quartile2018June Removedcanopy_quartile_heightsand

canopy_quartile_heights_abs,replacedwithcanopy_h_metrics(Secs2.2.3,4.16(6),4.16.1(5))

2018***draft1 Delta_timespecifiedasmid-segmenttime,ratherthanmeansegmenttime(Sec2.4.5)

2018***draft1 QA/QCproductstobereportedonaperorbitbasis,ratherthanperregion(Sec5.2)

2018***draft1 Addedmoredetailtolandsat_flagdescription(Sec2.2.23)2018***draft1 Addedpsf_flagbackintoATL08product,asitisalsoneeded

fortheQAproduct(Sec2.5.12)2018***draft1 Specifiedthatthesigma_hvaluereportedhereisthemeanof

theATL03reportedsigma_hvalues(Sec2.5.7)2018***draft1 Removedn_photonsfromallsubgroups2018***draft1 Betterdefinedtheinterpolationandsmoothingmethods

usedthroughout:• Error!Referencesourcenotfound.(3):

Interpolation–nearest• 4.6(5):Interpolation–PCHIP• 4.6(8):Smoothing–movingaverage• 4.7(3):Interpolation–PCHIP• 4.7(3):Smoothing–movingaverage• 4.8(3):Smoothing–movingaverage• 4.8(4):Interpolation–linear• 4.8(5):Smoothing–movingaverage• 4.8(6):Interpolation–linear• 4.8(7):Smoothing–movingaverage• 4.8(8):Smoothing–Savitzky-Golay• 4.8(9):Interpolation–linear• 4.8(14):Interpolation–PCHIP• 4.10(10):Interpolation–linear• 4.11(all):Smoothing–movingaverage• 4.10(6.b):Interpolation–linear• 4.12(1.a):Interpolation–linear• 4.12(1.c):Smoothing–lowess• 4.12(4):Interpolation–PCHIP• 4.12(7):Interpolation–PCHIP• 4.12(9):Smoothing–movingaverage• 4.15(2.e.i.1):Interpolation–linear


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2018***draft1 Addedref_elevandref_azimuthbackin(itwasmistakenlyremovedinapreviousversion;Secs2.5.3,2.5.4)

2018***draft1 Clarifiedwordingofh_canopy_quaddefinition(Sec2.2.17)2018***draft1 Updatedsegment_snowcoverdescriptiontomatchthe

ATL09snow_iceparameteritreferences(Sec2.4.16)andaddedproductreferencetoTable4.2

2018***draft1 Addedph_ndx_beg(Sec2.5.21);parameterwasalreadyonproduct

2018***draft1 Addeddem_removal_flagforQApurposes(Sec2.4.11;Table5.2)

2018***draft2 ReformattedQA/QCtrendingandtriggeralertlistintoatableforbetterclarification(Table5.3)

2018***draft2 Replacedn_photonsinTable5.2withn_te_photons,n_ca_photons,andn_toc_photons

2018***draft2 Removedbeam_numberfromTable2.5.Beamnumberandweak/strongdesignationwithingtxgroupattributes.

2018***draft2 Clarifiedcalculationofh_te_best_fit(Sec4.15(2.e))2018***draft2 Changedh_canopyandh_canopy_abstobe98thpercentile

height(Table2.2,Sec2.2.5,Sec2.2.6,Sec4.16(4),Sec4.16.1(3))

2018***draft2 Separatedh_canopy_metrics_absfromh_canopy_metrics(Table2.2,Sec2.2.3,Sec4.16.1(5))

2018October Removed99thpercentilefromh_canopy_metricsandh_canopy_metrics_abs(Table2.2,Sec2.2.3,Sec2.2.4,Sec4.16(4),Sec4.16.1(5))

2018December RenamedandrewordedSection1.1.1tobetterindicatethattheDRAGANNpreprocessingstepisnotoptional

2018December SpecifiedthatDRAGANNshouldusealong-tracktime,andaddedtimerescalingstep(Sec4.3(1-4))

2018December AddedDRAGANNchangesmadetobettercapturesparsecanopyincasesoflownoiserates(Sec4.3,AppendixA)

2018December MadecorrectionstoDRAGANNdescriptionregardingthedeterminationofthenoiseGaussian(Sec3.1.1,Sec4.3)

2018December Removedh_median_canopyandh_median_canopy_abs,astheyareequivalenttocanopy_h_metrics(50)andcanopy_h_metrics_abs(50)(Table2.2,Sec4.16(5),Sec4.16.1(4))

2018December Removedtherequirementthat>5%groundphotonsrequiredtocalculaterelativecanopyheightparameters(Table2.2,Sec4.16(2))

2018December Addedcanopyrelativeheightconfidenceflag(canopy_rh_conf)basedonthepercentageofgroundandcanopyphotonsinasegment(Table2.2,Sec4.16(2))


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2018December AddedATL09layer_flagtoATL08output(Table2.5,Table4.2)

2019February AdjustedcloudfilteringtobebasedonATL09backscatteranalysisratherthancloudflags(Sec4.1)

2019March5 UpdatedATL09-basedproductdescriptionsreportedonATL08product(Secs2.5.13,2.5.14,2.5.15,1.1.1)

2019March5 Updatedcloud-basedlowsignalfiltermethodology,andmovedtofirststepofATL08processing(Sec4.1)

2019March13 Replacecanopy_closurewithnewlandsat_percparameter(Table2.2,Sec2.2.24)

2019March13 ChangeATL08productoutputregionstomatchATL03regions(Sec2),butkeepATL08regionsinternallyandreportinnewparameteratl08_regions(Table2.4,Sec2.4.19)

2019March13 AddmethodologyforhandlingshortATL08processingsegmentsattheendofanATL03granule(Sec4.2),andoutputdistancetheprocessingsegmentlengthisextendedintonewparameterlast_seg_extend(Table2.4,Sec2.4.20)

2019March13 AddpreprocessingstepforremovingatmosphericandoceantidecorrectionsfromATL03heights(Laterremoved)

2019March27 RemovepreprocessingstepforremovingatmosphericandoceantidecorrectionsfromATL03heights,sincethosevaluesarenowremovedfromtheATL03photonheights.

2019March27 ReplacedATL03regionfigurewithcorrectedversion(Figure2.2)

2019March27 Specifiedthatatleast50classedphotonsarerequiredtocreatethe100mlandandcanopyproducts(Secs2,4.15(1),4.16(1))

2019March27 Clarifiedthatanynon-extendedsegmentswouldreportaland_seg_extendvalueof0(Sec4.2,Sec2.4.20)

2019April30 FixedtheerrorinEqn1.4forthesigmatopovalue2019May13 Specifiedforcloudflagcarry-overfromATL09thatATL08

willreportthehighestcloudflagifan08segmentstraddlestwo09segments.(Section2.5)

2019May13 Changedparametercloud_flag_asrtocloud_flag_atmsincethecloud_flag_asrislikelynottoworkoverlandduetovaryingsurfacereflectance(Sec,2.5)

2019May13 AddATL09parametercloud_fold_flagtotheATL08dataproductforfutureqa/qcchecksforlowclouds.(Secs,2.5)

2019May13 Clarificationonthecalculationofgradientforslopethatfeedsintothecalculationofthepointspreadfunction(Sec4.11)


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2019July1 ChangedLandsatcanopycoverpercentageto3%(fromoriginalvalueof5%)

31 32


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Contents33

ListofTables.................................................................................................................................................14 34

ListofFigures...............................................................................................................................................15 35

1 INTRODUCTION................................................................................................................................17 36

1.1. Background.................................................................................................................................18 37

1.2 PhotonCountingLidar..........................................................................................................20 38

1.3 TheICESat-2concept.............................................................................................................22 39

1.4 HeightRetrievalfromATLAS.............................................................................................25 40

1.5 AccuracyExpectedfromATLAS........................................................................................26 41

1.6 AdditionalPotentialHeightErrorsfromATLAS.......................................................28 42

1.7 DenseCanopyCases...............................................................................................................29 43

1.8 SparseCanopyCases..............................................................................................................29 44

2. ATL08:DATAPRODUCT...............................................................................................................31 45

2.1 Subgroup:LandParameters...............................................................................................34 46

2.1.1 Georeferenced_segment_number_beg..................................................................35 47

2.1.2 Georeferenced_segment_number_end..................................................................35 48

2.1.3 Segment_terrain_height_mean.................................................................................36 49

2.1.4 Segment_terrain_height_med....................................................................................36 50

2.1.5 Segment_terrain_height_min.....................................................................................36 51

2.1.6 Segment_terrain_height_max....................................................................................37 52

2.1.7 Segment_terrain_height_mode.................................................................................37 53

2.1.8 Segment_terrain_height_skew..................................................................................37 54

2.1.9 Segment_number_terrain_photons........................................................................37 55

2.1.10 Segmentheight_interp.................................................................................................38 56

2.1.11 Segmenth_te_std.............................................................................................................38 57


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2.1.12 Segment_terrain_height_uncertainty....................................................................38 58

2.1.13 Segment_terrain_slope.................................................................................................38 59

2.1.14 Segment_terrain_height_best_fit..............................................................................39 60

2.2 Subgroup:VegetationParameters...................................................................................39 61



2.2.3 Canopy_height_metrics_abs.......................................................................................42 64

2.2.4 Canopy_height_metrics................................................................................................43 65

2.2.5 Absolute_segment_canopy_height..........................................................................43 66

2.2.6 Segment_canopy_height..............................................................................................43 67

2.2.7 Absolute_segment_mean_canopy............................................................................44 68

2.2.8 Segment_mean_canopy................................................................................................44 69

2.2.9 Segment_dif_canopy......................................................................................................44 70

2.2.10 Absolute_segment_min_canopy...............................................................................44 71

2.2.11 Segment_min_canopy....................................................................................................44 72

2.2.12 Absolute_segment_max_canopy...............................................................................44 73

2.2.13 Segment_max_canopy...................................................................................................45 74

2.2.14 Segment_canopy_height_uncertainty....................................................................45 75

2.2.15 Segment_canopy_openness........................................................................................46 76

2.2.16 Segment_top_of_canopy_roughness.......................................................................46 77

2.2.17 Segment_canopy_quadratic_height........................................................................46 78

2.2.18 Segment_number_canopy_photons........................................................................46 79

2.2.19 Segment_number_top_canopy_photons...............................................................47 80

2.2.20 Centroid_height................................................................................................................47 81

2.2.21 Segment_rel_canopy_conf...........................................................................................47 82

2.2.22 Canopy_flag........................................................................................................................47 83


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2.2.23 Landsat_flag.......................................................................................................................47 84

2.2.24 Landsat_perc.....................................................................................................................48 85

2.3 Subgroup:Photons..................................................................................................................48 86

2.3.1 Indices_of_classed_photons.......................................................................................49 87

2.3.2 Photon_class......................................................................................................................49 88

2.3.3 Georeferenced_segment_number...........................................................................49 89

2.3.4 DRAGANN_flag.................................................................................................................49 90

2.4 Subgroup:Referencedata....................................................................................................49 91



2.4.3 Segment_latitude.............................................................................................................52 94

2.4.4 Segment_longitude.........................................................................................................52 95

2.4.5 Delta_time...........................................................................................................................52 96

2.4.6 Delta_time_beg.................................................................................................................52 97

2.4.7 Delta_time_end.................................................................................................................52 98

2.4.8 Night_Flag...........................................................................................................................52 99

2.4.9 Segment_reference_DTM.............................................................................................53 100

2.4.10 Segment_reference_DEM_source.............................................................................53 101

2.4.11 Segment_reference_DEM_removal_flag................................................................53 102

2.4.12 Segment_terrain_difference.......................................................................................53 103

2.4.13 Segment_terrainflag.....................................................................................................53 104

2.4.14 Segment_landcover........................................................................................................53 105

2.4.15 Segment_watermask.....................................................................................................54 106

2.4.16 Segment_snowcover......................................................................................................54 107

2.4.17 Urban_flag...........................................................................................................................54 108

2.4.18 Surface_type......................................................................................................................55 109


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2.4.19 ATL08_region....................................................................................................................55 110

2.4.20 Last_segment_extend....................................................................................................55 111

2.5 Subgroup:Beamdata.............................................................................................................56 112



2.5.3 Beam_coelevation...........................................................................................................59 115

2.5.4 Beam_azimuth..................................................................................................................59 116

2.5.5 ATLAS_Pointing_Angle.................................................................................................59 117

2.5.6 Reference_ground_track..............................................................................................59 118

2.5.7 Sigma_h................................................................................................................................59 119

2.5.8 Sigma_along.......................................................................................................................60 120

2.5.9 Sigma_across.....................................................................................................................60 121

2.5.10 Sigma_topo.........................................................................................................................60 122

2.5.11 Sigma_ATLAS_LAND......................................................................................................60 123

2.5.12 PSF_flag................................................................................................................................60 124

2.5.13 Layer_flag............................................................................................................................61 125

2.5.14 Cloud_flag_atm.................................................................................................................61 126

2.5.15 MSW......................................................................................................................................61 127

2.5.16 CloudFoldFlag.................................................................................................................62 128

2.5.17 Computed_Apparent_Surface_Reflectance.........................................................62 129

2.5.18 Signal_to_Noise_Ratio...................................................................................................62 130

2.5.19 Solar_Azimuth...................................................................................................................62 131

2.5.20 Solar_Elevation.................................................................................................................62 132

2.5.21 Number_of_segment_photons...................................................................................62 133

2.5.22 Photon_Index_Begin......................................................................................................62 134

3 ALGORITHMMETHODOLOGY....................................................................................................64 135


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3.1 NoiseFiltering...........................................................................................................................64 136

3.1.1 DRAGANN...........................................................................................................................65 137

3.2 SurfaceFinding.........................................................................................................................69 138

3.2.1 De-trendingtheSignalPhotons...............................................................................71 139

3.2.2 CanopyDetermination.................................................................................................71 140

3.2.3 VariableWindowDetermination............................................................................73 141

3.2.4 Computedescriptivestatistics.................................................................................74 142

3.2.5 GroundFindingFilter(Iterativemedianfiltering).........................................76 143

3.3 TopofCanopyFindingFilter..............................................................................................78 144

3.4 ClassifyingthePhotons.........................................................................................................78 145

3.5 RefiningthePhotonLabels.................................................................................................79 146

3.6 CanopyHeightDetermination...........................................................................................83 147

3.7 LinkScaleforDataproducts...............................................................................................83 148

4. ALGORITHMIMPLEMENTATION.............................................................................................85 149

4.1 Cloudbasedfiltering...............................................................................................................88 150

4.2 PreparingATL03dataforinputtoATL08algorithm.............................................90 151

4.3 NoisefilteringviaDRAGANN.............................................................................................91 152

4.3.1 DRAGANNQualityAssurance...................................................................................94 153

4.3.2 PreprocessingtodynamicallydetermineaDRAGANNparameter.........94 154

4.3.3 IterativeDRAGANNprocessing...............................................................................97 155

4.4 IsCanopyPresent....................................................................................................................98 156

4.5 ComputeFilteringWindow.................................................................................................98 157

4.6 De-trendData.............................................................................................................................99 158

4.7 Filteroutliernoisefromsignal........................................................................................100 159

4.8 Findingtheinitialgroundestimate...............................................................................100 160

4.9 Findthetopofthecanopy(ifcanopy_flag=1).......................................................102 161


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4.10 Computestatisticsonde-trendeddata.......................................................................103 162

4.11 RefineGroundEstimates....................................................................................................104 163

4.12 CanopyPhotonFiltering.....................................................................................................106 164

4.13 ComputeindividualCanopyHeights............................................................................108 165

4.14 FinalphotonclassificationQAcheck............................................................................109 166

4.15 ComputesegmentparametersfortheLandProducts.........................................109 167

4.16 ComputesegmentparametersfortheCanopyProducts....................................112 168

4.16.1 CanopyProductscalculatedwithabsoluteheights......................................114 169

4.17 Recordfinalproductwithoutbuffer.............................................................................114 170

5 DATAPRODUCTVALIDATIONSTRATEGY........................................................................115 171

5.1 ValidationData........................................................................................................................115 172

5.2 InternalQCMonitoring.......................................................................................................118 173

6 REFERENCES....................................................................................................................................125 174

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ListofTables176

Table2.1.SummarytableoflandparametersonATL08........................................................34 177

Table2.2.SummarytableofcanopyparametersonATL08.................................................40 178

Table2.3.SummarytableforphotonparametersfortheATL08product.....................48 179

Table2.4.SummarytableforreferenceparametersfortheATL08product................50 180

Table2.5.SummarytableforbeamparametersfortheATL08product........................56 181

Table3.1.Standarddeviationrangesutilizedtoqualifythespreadofphotonswithin182movingwindow...........................................................................................................................................75 183

Table4.1.InputparameterstoATL08classificationalgorithm..........................................85 184

Table4.2.AdditionalexternalparametersreferencedinATL08product.....................86 185

Table5.1.Airbornelidardataverticalheight(Zaccuracy)requirementsfor186validationdata...........................................................................................................................................115 187

Table5.2.ATL08parametermonitoring......................................................................................118 188

Table5.3.QA/QCtrendingandtriggers........................................................................................123 189

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ListofFigures191

Figure1.1.Variousmodalitiesoflidardetection.AdaptedfromHarding,2009.........21 192

Figure1.2.Schematicof6-beamconfigurationforICESat-2mission.Thelaser193energywillbesplitinto3laserbeampairs–eachpairhavingaweakspot(1X)anda194strongspot(4X)..........................................................................................................................................23 195

Figure1.3.Illustrationofoff-nadirpointingscenarios.Overland(greenregions)in196themid-latitudes,ICESat-2willbepointedawayfromtherepeatgroundtracksto197increasethedensityofmeasurementsoverterrestrialsurfaces........................................24 198

Figure1.4.Illustrationofthepointspreadfunction,alsoreferredtoasZnoise,fora199seriesofphotonsaboutasurface.......................................................................................................27 200

Figure2.1.HDF5datastructureforATL08products..............................................................32 201

Figure2.2.ATL03granuleregions;graphicfromATL03ATBD(Neumannetal.).....33 202

Figure2.3.ATL08productregions....................................................................................................34 203

Figure2.4.Illustrationofcanopyphotons(reddots)interactioninavegetatedarea.204Relativecanopyheights,Hi,arecomputedbydifferencingthecanopyphotonheight205fromaninterpolatedterrainsurface................................................................................................40 206

Figure3.1.Combinationofnoisefilteringalgorithmstocreateasupersetofinput207dataforsurfacefindingalgorithms...................................................................................................65 208

Figure3.2.Histogramofthenumberofphotonswithinasearchradius.This209histogramisusedtodeterminethethresholdfortheDRAGANNapproach.................67 210

Figure3.3.OutputfromDRAGANNfiltering.Signalphotonsareshownasblue.......69 211

Figure3.4.Flowchartofoverallsurfacefindingmethod........................................................70 212

Figure3.5.PlotofSignalPhotons(black)from2014MABELflightoverAlaskaand213de-trendedphotons(red)......................................................................................................................71 214

Figure3.6.ShapeParameterforvariablewindowsize...........................................................74 215

Figure3.7.Illustrationofthestandarddeviationscalculatedforeachmoving216windowtoidentifytheamountofspreadofsignalphotonswithinagivenwindow.217.............................................................................................................................................................................76 218

Figure3.8.ThreeiterationsofthegroundfindingconceptforL-kmsegmentswith219canopy..............................................................................................................................................................77 220


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Figure3.9.Exampleoftheintermediategroundandtopofcanopysurfaces221calculatedfromMABELflightdataoverAlaskaduringJuly2014.....................................80 222

Figure3.10.ExampleofclassifiedphotonsfromMABELdatacollectedinAlaska2232014.Redphotonsarephotonsclassifiedasterrain.Greenphotonsareclassifiedas224topofcanopy.Canopyphotons(shownasblue)areconsideredasphotonslying225betweentheterrainsurfaceandtopofcanopy...........................................................................81 226



Figure5.1.ExampleofL-kmsegmentclassificationsandinterpolatedground235surface...........................................................................................................................................................122 236

237


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1 INTRODUCTION 238

This document describes the theoretical basis and implementation of the239

processingalgorithmsanddataparametersforLevel3landandvegetationheights240

forthenon-polarregionsoftheEarth.TheATL08productcontainsheightsforboth241

terrain and canopy in the along-track direction as well as other descriptive242

parametersderivedfromthemeasurements.Atthemostbasiclevel,aderivedsurface243

heightfromtheATLASinstrumentatagiventimeisprovidedrelativetotheWGS-84244

ellipsoid.HeightestimatesfromATL08canbecomparedwithothergeodeticdataand245

usedas input tohigher-level ICESat-2products,namelyATL13andATL18.ATL13246

will provide estimates of inland water-related heights and associated descriptive247

parameters.ATL18willconsistofgriddedmapsforterrainandcanopyfeatures.248

TheATL08productwillprovideestimatesofterrainheights,canopyheights,249

andcanopycover at fine spatial scales in the along-trackdirection.Along-track is250

defined as the direction of travel of the ICESat-2 satellite in the velocity vector.251

Parametersfortheterrainandcanopywillbeprovidedatafixedstep-sizeof100m252

alongthegroundtrackreferredtoasasegment.Afixedsegmentsizeof100mwas253

chosentoprovidecontinuityofdataparametersontheATL08dataproduct.Froman254

analysisperspective,itisdifficultandcumbersometoattempttorelatecanopycover255

overvariablelengths.Furthermore,asegmentsizeof100mwillfacilitateasimpler256

combinationofalong-trackdatatocreatethegriddedproducts.257

Weanticipatethatthesignalreturnedfromtheweakbeamwillbesufficiently258

weak andmay prohibit the determination of both a terrain and canopy segment259

height,particularlyoverareasofdensevegetation.However,inmorearidregionswe260

anticipateproducingaterrainheightforboththeweakandstrongbeams.261

Inthisdocument,section1providesabackgroundoflidarintheecosystem262

communityaswellasdescribingphotoncountingsystemsandhowtheydifferfrom263

discrete return lidar systems. Section 2 provides an overview of the Land and264


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Vegetation parameters and how they are defined on the data product. Section 3265

describesthebasicmethodologythatwillbeusedtoderivetheparametersforATL08.266

Section4describestheprocessingsteps,inputdata,andproceduretoderivethedata267

parameters. Section 5 will describe the test data and specific tests that NASA’s268

implementation of the algorithm should pass in order to determine a successful269

implementationofthealgorithm.270

271

1.1. Background272

TheEarth’s landsurface is a complexmosaicof geomorphicunits and land273

covertypesresultinginlargevariationsinterrainheight,slope,roughness,vegetation274

heightand reflectance,oftenwith thevariationsoccurringoververy small spatial275

scales.Documentationoftheselandscapepropertiesisafirststepinunderstanding276

theinterplaybetweentheformativeprocessesandresponsetochangingconditions.277

Characterizationofthelandscapeisalsonecessarytoestablishboundaryconditions278

for models which are sensitive to these properties, such as predictive models of279

atmosphericchangethatdependon land-atmosphere interactions.Topography,or280

landsurfaceheight,isanimportantcomponentformanyheightapplications,bothto281

thescientificandcommercialsectors.Themostaccurateglobalterrainproductwas282

produced by the Shuttle Radar Topography Mission (SRTM) launched in 2000;283

however, elevation data are limited to non-polar regions. The accuracy of SRTM284

derivedelevationsrangefrom5–10m,dependingupontheamountoftopography285

andvegetationcoveroveraparticulararea.ICESat-2willprovideaglobaldistribution286

ofgeodeticmeasurements(ofboththeterrainsurfaceandrelativecanopyheights)287

whichwillprovideasignificantbenefittosocietythroughavarietyofapplications288

including sea level change monitoring, forest structural mapping and biomass289

estimation,andimprovedglobaldigitalterrainmodels.290

Inadditiontoproducingaglobalterrainproduct,monitoringtheamountand291


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distribution of above ground vegetation and carbon pools enables improved292

characterizationof theglobal carbonbudget. Forestsplaya significant role in the293

terrestrial carbon cycle as carbon pools. Events, such as management activities294

(Krankinaet al. 2012)anddisturbances can release carbonstored in forest above295

groundbiomass(AGB)intotheatmosphereascarbondioxide,agreenhousegasthat296

contributestoclimatechange(Ahmedetal.2013).Whilecarbonstocks innations297

withcontinuousnationalforestinventories(NFIs)areknown,complicationswithNFI298

carbonstockestimatesexist, including:(1)ground-basedinventorymeasurements299

are time consuming, expensive, and difficult to collect at large-scales (Houghton300

2005; Ahmed et al. 2013); (2) asynchronously collected data; (3) extended time301

betweenrepeatmeasurements(Houghton2005);and(4)thelackofinformationon302

thespatialdistributionofforestAGB,requiredformonitoringsourcesandsinksof303

carbon(Houghton2005).Airbornelidarhasbeenusedforsmallstudiestocapture304

canopyheightandinthosestudiescanopyheightvariationformultipleforesttypes305

ismeasuredtoapproximately7mstandarddeviation(Halletal.,2011).306

Althoughthespatialextentandchangestoforestscanbemappedwithexisting307

satelliteremotesensingdata,thelackofinformationonforestverticalstructureand308

biomasslimitstheknowledgeofbiomass/biomasschangewithintheglobalcarbon309

budget.Basedontheglobalcarbonbudgetfor2015(Quereetal.,2015),thelargest310

remaining uncertainties about the Earth’s carbon budget are in its terrestrial311

components, the global residual terrestrial carbon sink, estimated at 3.0 ± 0.8312

GtC/yearforthelastdecade(2005-2014).Similarly,carbonemissionsfromland-use313

changes, including deforestation, afforestation, logging, forest degradation and314

shiftingcultivationareestimatedat0.9±0.5GtC/year.Byprovidinginformationon315

vegetation canopyheightgloballywithahigher spatial resolution thanpreviously316

afforded by other spaceborne sensors, the ICESat-2 mission can contribute317

significantlytoreducinguncertaintiesassociatedwithforestvegetationcarbon.318


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AlthoughICESat-2isnotpositionedtoprovideglobalbiomassestimatesdue319

to its profiling configuration and somewhat limited detection capabilities, it is320

anticipatedthatthedataproductsforvegetationwillbecomplementarytoongoing321

biomassandvegetationmappingefforts.SynergisticuseofICESat-2datawithother322

space-based mapping systems is one solution for extended use of ICESat-2 data.323

PossibilitiesincludeNASA’sGlobalEcosystemsDynamicsInvestigation(GEDI)lidar324

plannedtoflyonboardtheInternationalSpaceStation(ISS)orimagingsensors,such325

asLandsat8,orNASA/ISRO–NISARradarmission.326

327

1.2 PhotonCountingLidar328

Ratherthanusingananalog,fullwaveformsystemsimilartowhatwasutilized329

ontheICESat/GLASmission,ICESat-2willemployaphotoncountinglidar.Photon330

countinglidarhasbeenusedsuccessfullyforrangingforseveraldecadesinboththe331

science and defense communities. Photon counting lidar systems operate on the332

concept that a low power laser pulse is transmitted and the detectors used are333

sensitiveatthesinglephotonlevel.Duetothistypeofdetector,anyreturnedphoton334

whetherfromthereflectedsignalorsolarbackgroundcantriggeraneventwithinthe335

detector.Adiscussionregardingdiscriminatingbetweensignalandbackgroundnoise336

photonsisdiscussedlaterinthisdocument.Aquestionofinteresttotheecosystem337

community is to understand where within the canopy is the photon likely to be338

reflected.Figure1.1 isanexampleof threedifferent laserdetectormodalities: full339

waveform,discretereturn,andphotoncounting.Fullwaveformsensorsrecordthe340

entiretemporalprofileofthereflectedlaserenergythroughthecanopy.Incontrast,341

discrete return systems have timing hardware that record the time when the342

amplitudeofthereflectedsignalenergyexceedsacertainthresholdamount.Aphoton343

counting system, however, will record the arrival time associated with a single344

photon detection that can occur anywhere within the vertical distribution of the345

reflectedsignal.Ifaphotoncountinglidarsystemweretodwelloverasurfacefora346


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significantnumberofshots(i.e.hundredsormore),theverticaldistributionofthe347

reflectedphotonswillresemblea fullwaveform.Thus,whilean individualphoton348

could be reflected from anywhere within the vertical canopy, the probability349

distribution function (PDF) of that reflected photon would be the full waveform.350

Furthermore, the probability of detecting the top of the tree is not as great as351

detecting reflective surfaces positioned deeper into the canopywhere the bulkof352

leavesandbranchesarelocated.Asonemightimagine,thePDFwilldifferaccording353

tocanopystructureandvegetationphysiology.Forexample,thePDFofaconifertree354

willlookdifferentthanbroadleaftrees.355

356

Figure 1.1. Various modalities of lidar detection. Adapted from Harding, 2009. 357

Acautionarynote,thephotoncountingPDFthatisillustratedinFigure1.1is358

merelyanillustrationifenoughphotons(i.e.hundredsofphotonsormore)wereto359

bereflectedfromatarget.Inreality,duetothespacecraftspeed,ATLASwillrecord0360

–4photonspertransmitlaserpulseovervegetation.361

362


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1.3 TheICESat-2concept363

The Advanced Topographic Laser Altimeter System (ATLAS) instrument364

designed for ICESat-2willutilizeadifferent technology than theGLAS instrument365

usedforICESat.Insteadofusingahigh-energy,single-beamlaseranddigitizingthe366

entire temporal profile of returned laser energy, ATLAS will use a multi-beam,367

micropulselaser(sometimesreferredtoasphoton-counting).Thetraveltimeofeach368

detectedphotonisusedtodeterminearangetothesurfacewhich,whencombined369

withsatelliteattitudeandpointinginformation,canbegeolocatedintoauniqueXYZ370

locationonorneartheEarth’ssurface.Formore informationonhowthephotons371

fromICESat-2aregeolocated,refertoATL03ATBD.TheXYZpositionsfromATLAS372

are subsequently used to derive surface and vegetation properties. The ATLAS373

instrumentwilloperateat532nminthegreenrangeof theelectromagnetic(EM)374

spectrumandwillhavealaserrepetitionrateof10kHz.Thecombinationofthelaser375

repetition rate and satellite velocity will result in one outgoing laser pulse376

approximatelyevery70cmontheEarth’ssurfaceandeachspotonthesurfaceis~13377

mindiameter.Eachtransmittedlaserpulseissplitbyadiffractiveopticalelementin378

ATLAS togenerate six individualbeams, arranged in threepairs (Figure1.2).The379

beamswithineachpairhavedifferenttransmitenergies(‘weak’and‘strong’,withan380

energyratioofapproximately1:4)tocompensateforvaryingsurfacereflectance.The381

beampairsareseparatedby~3.3kmintheacross-trackdirectionandthestrongand382

weakbeamsareseparatedby~2.5kminthealong-trackdirection.AsICESat-2moves383

alongitsorbit,theATLASbeamsdescribesixtracksontheEarth’ssurface;thearray384

isrotatedslightlywithrespecttothesatellite’sflightdirectionsothattracksforthe385

fore and aft beams in each column produce pairs of tracks – each separated by386

approximately90m.387


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388

389Figure 1.2. Schematic of 6-beam configuration for ICESat-2 mission. The laser energy will 390

be split into 3 laser beam pairs – each pair having a weak spot (1X) and a strong spot (4X). 391

Themotivation behind thismulti-beam design is its capability to compute392

cross-track slopes on a per-orbit basis, which contributes to an improved393

understandingoficedynamics.Previously,slopemeasurementsoftheterrainwere394

determinedviarepeat-trackandcrossoveranalysis.Thelaserbeamconfigurationas395

proposedforICESat-2isalsobeneficialforterrestrialecosystemscomparedtoGLAS396

asitenablesadenserspatialsamplinginthenon-polarregions.Toachieveaspatial397

samplinggoalofnomorethan2kmbetweenequatorialgroundtracks,ICESat-2will398

2.5 km* 3.305 km*

Weak (1)

Strong (4)

Strong (4)

Weak (1)

Strong (4)

Weak (1)


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be off-nadir pointed a maximum of 1.8 degrees from the reference ground track399

duringtheentiremission.400

401

Figure 1.3. Illustration of off-nadir pointing scenarios. Over land (green regions) in the 402

mid-latitudes, ICESat-2 will be pointed away from the repeat ground tracks to increase the 403

density of measurements over terrestrial surfaces. 404

ICESat-2 is designed to densely sample the Earth’s surface, permitting405

scientists to measure and quantitatively characterize vegetation across vast406

expanses, e.g., nations, continents, globally. ICESat-2 will acquire synoptic407

measurements of vegetation canopy height, density, the vertical distribution of408

photosyntheticallyactivematerial,leadingtoimprovedestimatesofforestbiomass,409

carbon,andvolume.Inaddition,theorbitaldensity,i.e.,thenumberoforbitsperunit410

area, at theendof the threeyearmissionwill facilitate theproductionof gridded411

globalproducts.ICESat-2willprovidethemeansbywhichanaccurate“snapshot”of412

globalbiomassandcarbonmaybeconstructedforthemissionperiod.413

414


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1.4 HeightRetrievalfromATLAS415

LightfromtheATLASlasersreachestheearth’ssurfaceasflatdisksofdown-416

traveling photons approximately 50 cm in vertical extent and spread over417

approximately14mhorizontally.Uponhittingtheearth’ssurface, thephotonsare418

reflected and scattered in every direction and a handful of photons return to the419

ATLAS telescope’s focalplane. The number of photon events per laser pulse is a420

functionofoutgoinglaserenergy,surfacereflectance,solarconditions,andscattering421

andattenuationintheatmosphere.Forhighlyreflectivesurfaces(suchaslandice)422

and clear skies, approximately 10 signal photons from a single strong beam are423

expectedtoberecordedbytheATLASinstrumentforagiventransmitlaserpulse.424

Overvegetatedlandwherethesurfacereflectanceisconsiderablylessthansnowor425

ice surfaces,we expect to see fewer returned photons from the surface.Whereas426

snow and ice surfaces have high reflectance at 532 nm (typical Lambertian427

reflectancebetween0.8and0.98(Martino,GSFCinternalreport,2010)),canopyand428

terrainsurfaceshavemuchlowerreflectance(typicallyaround0.3forsoiland0.1for429

vegetation)at532nm.Asaconsequenceweexpecttosee1/3to1/9asmanyphotons430

returned from terrestrial surfaces as from ice and snow surfaces. For vegetated431

surfaces,thenumberofreflectedsignalphotoneventspertransmittedlaserpulseis432

estimatedtorangebetween0to4photons.433

Thetimemeasuredfromthedetectedphotoneventsareusedtocomputea434

range,ordistance,fromthesatellite.Combinedwiththeprecisepointingandattitude435

informationaboutthesatellite,therangecanbegeolocatedintoaXYZpoint(known436

as a geolocated photon) above the WGS-84 reference ellipsoid. In addition to437

recording photons from the reflected signal, the ATLAS instrument will detect438

backgroundphotons fromsunlightwhicharecontinuallyenteringthetelescope.A439

primary objective of the ICESat-2 data processing software is to correctly440

discriminate between signal photons and background photons. Some of this441

processingoccursattheATL03levelandsomeofitalsooccurswithinthesoftware442


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forATL08.AtATL03,thisdiscriminationisdonethroughaseriesofthreestepsof443

progressivelyfinerresolutionwithsomeprocessingoccurringonboardthesatellite444

priortodownlinkoftherawdata.TheATL03dataproductproducesaclassification445

betweensignalandbackground(i.e.noise)photons,andfurtherdiscussiononthat446

classificationprocess canbe read in theATL03ATBD. Inaddition, all geophysical447

corrections (e.g. ocean tide, solid earth tide models, etc.) are not applied to the448

position of the individual geolocated photons at the ATL03 level, but they are449

providedonthedataproduct if thereexistsaneedtoapplythem.Thus,allof the450

heightsprocessedintheATL08algorithmconsistsoftheATL03heightswithrespect451

totheWGS-84ellipsoid.452

453

1.5 AccuracyExpectedfromATLAS454

Thereareavarietyofelementsthatcontributetotheelevationaccuracythat455

are expected from ATLAS and the derived data products. Elevation accuracy is a456

composite of ranging precision of the instrument, radial orbital uncertainty,457

geolocationknowledge,forwardscatteringintheatmosphere,andtroposphericpath458

delayuncertainty.TherangingprecisionseenbyATLASwillbeafunctionofthelaser459

pulsewidth,thesurfaceareapotentiallyilluminatedbythelaser,anduncertaintyin460

thetimingelectronics.Therequirementonradialorbitaluncertaintyisspecifiedto461

belessthan4cmandtroposphericpathdelayuncertaintyisestimatedtobe3cm.In462

the case of ATLAS, the ranging precision for flat surfaces, is expected to have a463

standarddeviationofapproximately25cm.Thecompositeofeachoftheerrorscan464

alsobethoughtofasthespreadofphotonsaboutasurface(seeFigure1.4)andis465

referredtoasthepointspreadfunctionorZnoise.466


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467

Figure 1.4. Illustration of the point spread function, also referred to as Znoise, for a series 468

of photons about a surface. 469

The estimates of 𝜎"#$%&, 𝜎&#()(*)+,#,, 𝜎-(#./#0*1/&&,#%23, 𝜎)(%2&%23 , 𝑎𝑛𝑑𝜎&%8%23 470

foraphotonwillberepresentedontheATL03dataproductasthefinalgeolocated471

accuracy in theX,Y, andZ (orheight)direction. In reality, theseparametershave472

differenttemporalandspatialscales,howeveruntilICESat-2isonorbit,itisuncertain473

howtheseparameterswillvaryovertime.Assuch,Equation1.1maychangeoncethe474

temporal aspects of these parameters are better understood. For a preliminary475

quantificationoftheuncertainties,Equation1.1isvalidtoincorporatetheinstrument476

relatedfactors.477

𝜎9 = ;𝜎"#$%&< + 𝜎&#()< + 𝜎-(#./#0*1/&&,#%23< + 𝜎)(%2&%23< + 𝜎&%8%23< Eqn.1.1478

479

Although𝜎9 ontheATL03productrepresentsthebestunderstandingofthe480

uncertainty for each geolocated photon, it does not incorporate the uncertainty481

associatedwithlocalslopeofthetopography.Theslopecomponenttothegeolocation482

uncertaintyisafunctionofboththegeolocationknowledgeofthepointing(whichis483

requiredtobelessthan6.5m)multipliedbythetangentofthesurfaceslope.Inacase484

offlattopography(<=1degreeslope),𝜎9<=25cm,whereasinthecaseofa10degree485

surfaceslope,𝜎9 =119cm.Theuncertaintyassociatedwiththe localslopewillbe486

combinedwith𝜎9 toproducetheterm𝜎>&?/*@ABC .487

𝜎>&?/*@ABC = ;𝜎9< + 𝜎&()(< Eqn.1.2488


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𝜎&()( = Eqn.1.3489

Ultimately,theuncertaintythatwillbereportedonthedataproductATL08490

willincludethe𝜎>&?/*@ABC termandthelocalrmsvaluesofheightscomputedwithin491

each data parameter segment. For example, calculations of terrain height will be492

made on photons classified as terrain photons (this process is described in the493

followingsections).Theuncertaintyoftheterrainheightforasegmentisdescribed494

inEquation1.4,where the rootmeansquare termof𝜎>&?/*@ABC and rmsof terrain495

heightsarenormalizedbythenumberofterrainphotonsforthatgivensegment.496

𝜎>DEFGHIJKIBL = ;𝜎>&?/*@ABC< + 𝜎9#8*HIJKIBL_NOAHH

< Eqn.1.4497

498

1.6 AdditionalPotentialHeightErrorsfromATLAS499

Some additional potential height errors in theATL08 terrain and vegetation500

productcancomefromavarietyofsourcesincluding:501

a. Vertical sampling error. ATLAS height estimates are based on a502

randomsamplingof thesurfaceheightdistribution.Photonsmay503

bereflectedfromanywherewithinthePDFofthereflectingsurface;504

more specifically, anywhere fromwithin the canopy. A detailed505

lookatthepotentialeffectofverticalsamplingerrorisprovidedin506

NeuenschwanderandMagruder(2016).507

b. Background noise. Random noise photons are mixed with the508

signalphotonssoclassifiedphotonswillincluderandomoutliers.509

c. Complex topography. The along-track product may not always510

represent complex surfaces, particularly if the density of ground511

photonsdoesnotsupportanaccuraterepresentation.512


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d. Vegetation. Dense vegetation may preclude reflected photon513

eventsfromreachingtheunderlyinggroundsurface.Anincorrect514

estimationoftheunderlyinggroundsurfacewillsubsequentlylead515

toanincorrectcanopyheightdetermination.516

e. Misidentified photons. The product from ATL03 combinedwith517

additionalnoise filteringmaynot identify thecorrectphotonsas518

signalphotons.519

520

1.7 DenseCanopyCases521

Although the height accuracy produced from ICESat-2 is anticipated to be522

superior to other global height products (e.g. SRTM), for certain biomes photon523

countinglidardataasitwillbecollectedbytheATLASinstrumentpresentachallenge524

forextractingboth the terrainandcanopyheights,particularly forareasofdense525

vegetation.Duetotherelativelylowlaserpower,weanticipatethatthealong-track526

signal fromATLASmay lose ground signal under dense forest (e.g. >96% canopy527

closure)andinsituationswherecloudcoverobscurestheterrestrialsignal.Inareas528

havingdensevegetation,itislikelythatonlyahandfulofphotonswillbereturned529

fromthegroundsurfacewiththemajorityofreflectionsoccurringfromthecanopy.530

Apossiblesourceoferrorcanoccurwithboththecanopyheightestimatesandthe531

terrainheightsifthevegetationisparticularlydenseandthegroundphotonswere532

notcorrectlyidentified.533

534

1.8 SparseCanopyCases535

Conversely, sparse canopy cases also pose a challenge to vegetation height536

retrievals. In these cases, expected reflected photon events from sparse trees or537

shrubsmaybedifficulttodiscriminatebetweensolarbackgroundnoisephotons.The538


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algorithms being developed for ATL08 operate under the assumption that signal539

photonsareclosetogetherandnoisephotonswillbemoreisolatedinnature.Thus,540

signal(inthiscasecanopy)photonsmaybeincorrectlyidentifiedassolarbackground541

noise on the data product. Due to the nature of the photon counting processing,542

canopyphotonsidentifiedinareasthathaveextremelylowcanopycover<15%will543

befilteredoutandreassignedasnoisephotons.544

545


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2. ATL08:DATAPRODUCT546

TheATL08productwillprovideestimatesof terrainheight, canopyheight,547

andcanopycoveratfinespatialscalesinthealong-trackdirection.Inaccordancewith548

the HDF-driven structure of the ICESat-2 products, the ATL08 product will549

characterize each of the six Ground Tracks (GT) associated with each Reference550

GroundTrack(RGT)foreachcycleandorbitnumber.Eachgroundtrackgrouphasa551

distinct beam number, distance from the reference track, and transmit energy552

strength,andallbeamswillbeprocessedindependentlyusingthesamesequenceof553

stepsdescribedwithinATL08.Eachgroundtrackgroup(GT)ontheATL08product554

contains subgroups for land and canopy heights segments as well as beam and555

referenceparametersusefulintheATL08processing.Inaddition,thelabeledphotons556

thatareusedtodeterminethedataparameterswillbeindexedbacktotheATL03557

productssuchthattheyareavailableforfurther,independentanalysis.Alayoutof558

theATL08HDFproductisshowninFigure2.1.ThesixGTsarenumberedfromleftto559

right,regardlessofsatelliteorientation.560


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561

Figure 2.1. HDF5 data structure for ATL08 products 562

563

Foreachdataparameter,terrainsurfaceelevationandcanopyheightswillbe564

providedatafixedsegmentsizeof100metersalongthegroundtrack.Basedonthe565

satellitevelocityandtheexpectednumberofreflectedphotonsforlandsurfaces,each566

segmentshouldhavemorethan100signalphotons,butinsomeinstancestheremay567

belessthan100signalphotonspersegment.Ifasegmenthaslessthan50classed568

(i.e., labeled byATL08 as ground, canopy, or top of canopy) photonswe feel this569

wouldnotaccuratelyrepresentthesurface.Thus,aninvalidvaluewillbereportedin570

allheightfields.Intheeventthattherearemorethan50classedphotons,butaterrain571

heightcannotbedeterminedduetoaninsufficientnumberofgroundphotons,(e.g.572


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lackofphotonspenetratingthroughdensecanopy),theonlyreportedterrainheight573

willbetheinterpolatedsurfaceheight.574

TheATL08productwillbeproducedpergranulebasedontheATL03defined575

regions(seeFigure2.2).Thus,theATL08file/nameconventionschemewillmatch576

thefile/namingconventionforATL03–inattemptforreducingcomplexitytoallow577

userstoexaminebothdataproducts.578

579

Figure 2.2. ATL03 granule regions; graphic from ATL03 ATBD (Neumann et al.). 580

The ATL08 product additionally has its own internal regions, which are581

roughly assigned by continent, as shown by Figure 2.3. For the regions covering582

Antarctica(regions7,8,9,10)andGreenland(region11),theATL08algorithmwill583

assumethatnocanopyispresent.TheseinternalATL08regionswillbenotedinthe584

ATL08product(seeparameteratl08_regioninSection2.4.19).Notethattheregions585

foreachICESat-2productarenotthesame.586


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587

Figure 2.3. ATL08 product regions. 588

589

2.1 Subgroup:LandParameters590

ATL08terrainheightparametersaredefinedintermsoftheabsoluteheight591

abovethereferenceellipsoid.592

Table 2.1. Summary table of land parameters on ATL08. 593

Group Datatype Description Sourcesegment_id_beg Integer Firstalong-tracksegment_id

numberin100-msegmentATL03

segment_id_end Integer

Lastalong-tracksegment_idnumberin100-msegment

ATL03

h_te_mean Float Meanterrainheightforsegment

computed

h_te_median Float Medianterrainheightforsegment

computed

h_te_min Float Minimumterrainheightforsegment

computed

h_te_max Float Maximumterrainheightforsegment

computed

h_te_mode Float Modeofterrainheightforsegment

computed


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h_te_skew Float Skewofterrainheightforsegment

computed

n_te_photons Integer Numberofgroundphotonsinsegment

computed

h_te_interp Float Interpolatedterrainsurfaceheightatmid-pointofsegment

computed

h_te_std Float Standarddeviationofgroundheightsabouttheinterpolatedgroundsurface

computed

h_te_uncertainty Float Uncertaintyofgroundheightestimates.Includesallknownuncertaintiessuchasgeolocation,pointingangle,timing,radialorbiterrors,etc.

computedfromEquation1.4

terrain_slope Float Slopeofterrainwithinsegment

computed

h_te_best_fit Float Bestfitterrainelevationatthe100msegmentmid-pointlocation

computed

594

2.1.1 Georeferenced_segment_number_beg595

(parameter=segment_id_beg).Thefirstalong-tracksegment_idineach100-m596

segment.Each100-msegmentconsistsof fivesequential20-msegmentsprovided597

fromtheATL03product,whicharelabeledassegment_id.Thesegment_idisaseven598

digitnumberthatuniquelyidentifieseachalongtracksegment,andiswrittenatthe599

along-track geolocation segment rate (i.e. ~20m along track). The four digit RGT600

numbercanbecombinedwiththesevendigitsegment_idnumbertouniquelydefine601

anyalong-tracksegmentnumber.Valuesaresequential,with0000001referringto602

thefirstsegmentaftertheequatorialcrossingoftheascendingnode.603

2.1.2 Georeferenced_segment_number_end604

(parameter=segment_id_end).Thelastalong-tracksegment_idineach100-m605





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2.1.3 Segment_terrain_height_mean613

(parameter = h_te_mean). Estimated mean of the terrain height above the614

referenceellipsoidderivedfromclassifiedgroundphotonswithinthe100msegment.615

Ifaterrainheightcannotbedirectlydeterminedwithinthesegment(i.e.therearenot616

asufficientnumberofgroundphotons),onlytheinterpolatedterrainheightwillbe617

reported.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledaseither618

canopyorgroundintheATL08processing).Thisparameterwillbederivedfromonly619

classifiedgroundphotons.620

2.1.4 Segment_terrain_height_med621

(parameter = h_te_median). Median terrain height above the reference622

ellipsoidderivedfromtheclassifiedgroundphotonswithinthe100msegment. If623

therearenotasufficientnumberofgroundphotons,aninvalidvaluewillbereported624

–no interpolation will be done. Required input data is classified point cloud (i.e.625

photonslabeledaseithercanopyorgroundintheATL08processing).Thisparameter626

willbederivedfromonlyclassifiedgroundphotons.627

2.1.5 Segment_terrain_height_min628

(parameter=h_te_min).Minimumterrainheightabovethereferenceellipsoid629

derivedfromtheclassifiedgroundphotonswithinthe100msegment.Ifthereare630

not a sufficient number of groundphotons, an invalid valuewill be reported –no631

interpolationwillbedone.Requiredinputdataisclassifiedpointcloud(i.e.photons632

labeledaseithercanopyorgroundintheATL08processing).Thisparameterwillbe633

derivedfromonlyclassifiedgroundphotons.634


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2.1.6 Segment_terrain_height_max635

(parameter = h_te_max). Maximum terrain height above the reference636

ellipsoidderivedfromtheclassifiedgroundphotonswithinthe100msegment. If637

therearenotasufficientnumberofgroundphotons,aninvalidvaluewillbereported638

–no interpolationwill be done. Required input data is classified point cloud (i.e.639

photonslabeledaseithercanopyorgroundintheATL08processing).Thisparameter640

willbederivedfromonlyclassifiedgroundphotons.641

2.1.7 Segment_terrain_height_mode642

(parameter=h_te_mode).Modeoftheclassifiedgroundphotonheightsabove643

thereferenceellipsoidwithinthe100msegment.Iftherearenotasufficientnumber644

ofgroundphotons,aninvalidvaluewillbereported–nointerpolationwillbedone.645

Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledaseithercanopyor646

groundintheATL08processing).Thisparameterwillbederivedfromonlyclassified647

groundphotons.648

2.1.8 Segment_terrain_height_skew649

(parameter=h_te_skew).Theskewoftheclassifiedgroundphotonswithinthe650

100msegment. If therearenotasufficientnumberofgroundphotons,an invalid651

valuewillbereported–nointerpolationwillbedone.Requiredinputdataisclassified652

pointcloud(i.e.photonslabeledaseithercanopyorgroundintheATL08processing).653

Thisparameterwillbederivedfromonlyclassifiedgroundphotons.654

2.1.9 Segment_number_terrain_photons655

(parameter=n_te_photons).Numberofterrainphotonsidentifiedinsegment.656


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2.1.10 Segmentheight_interp657

(parameter = h_te_interp). Interpolated terrain surface height above the658

referenceellipsoid fromATL08processingat themid-pointof each segment.This659

interpolatedsurfaceistheFINALGROUNDestimate(describedinsection4.9).660

2.1.11 Segmenth_te_std661

(parameter = h_te_std). Standard deviations of terrain points about the662

interpolatedgroundsurfacewithin the segment.Providesan indicationof surface663

roughness.664

2.1.12 Segment_terrain_height_uncertainty665

(parameter=h_te_uncertainty).Uncertaintyofthemeanterrainheightforthe666

segment. This uncertainty incorporates all systematic uncertainties (e.g. timing,667

orbits,geolocation,etc.)aswellasuncertaintyfromerrorsofidentifiedphotons.This668

parameterisdescribedinSection1,Equation1.4.Iftherearenotasufficientnumber669

ofgroundphotons,aninvalidvaluewillbereported–nointerpolationwillbedone.670


groundintheATL08processing).Thisparameterwillbederivedfromonlyclassified672

ground photons. The 𝜎*,38,2&1?/**term in Equation 1.4 represents the standard673

deviationoftheterrainheightresidualsabouttheFINALGROUNDestimate.674

2.1.13 Segment_terrain_slope675

(parameter=terrain_slope). Slopeof terrainwithineachsegment.Slope is676

computedfromalinearfitoftheterrainphotons.Itestimatestherise[m]inrelief677

overeachsegment[100m];e.g.,iftheslopevalueis0.04,thereisa4mriseoverthe678

100msegment.Requiredinputdataaretheclassifiedterrainphotons.679


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2.1.14 Segment_terrain_height_best_fit680

(parameter = h_te_best_fit). The best fit terrain elevation at the mid-point681

locationofeach100msegment.Themid-segmentterrainelevationisdeterminedby682

selectingthebestofthreefits–linear,3rdorderand4thorderpolynomials–tothe683

terrainphotonsandinterpolatingtheelevationatthemid-pointlocationofthe100684

m segment. For the linear fit, a slope correction andweighting is applied to each685

groundphotonbasedonthedistancetotheslopeheightatthecenterofthesegment.686

687

2.2 Subgroup:VegetationParameters688

CanopyparameterswillbereportedontheATL08dataproductintermsofboth689

theabsoluteheightabovethereferenceellipsoidaswellastherelativeheightabove690

anestimatedground.Therelativecanopyheight,Hi,iscomputedastheheightfrom691

an identified canopy photonminus the interpolated ground surface for the same692

horizontalgeolocation(seeFigure2.3).Thus,eachidentifiedsignalphotonabovean693

interpolated surface (including a buffer distance based on the instrument point694

spreadfunction)isbydefaultconsideredacanopyphoton.Canopyparameterswill695

only be computed for segmentswheremore than 5% of the classed photons are696

classifiedascanopyphotons.697

698


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699

Figure 2.4. Illustration of canopy photons (red dots) interaction in a vegetated area. 700

Relative canopy heights, Hi, are computed by differencing the canopy photon height from 701

an interpolated terrain surface. 702

Table 2.2. Summary table of canopy parameters on ATL08. 703

Group Datatype

Description Source

segment_id_beg Integer Firstalong-tracksegment_idnumberin100-msegment

ATL03

segment_id_end Integer Lastalong-tracksegment_idnumberin100-msegment

ATL03

canopy_h_metrics_abs Float Absolute(H##)canopyheightmetricscalculatedatthefollowingpercentiles:25,50,60,70,75,80,85,90,95.

computed

canopy_h_metrics Float Relative(RH##)canopyheightmetricscalculatedatthefollowingpercentiles:25,50,60,70,75,80,85,90,95.

computed

h_canopy_abs Float 98%heightofalltheindividualabsolutecanopyheightsforsegment.

computed

h_canopy Float 98%heightofalltheindividualrelativecanopyheightsforsegment.

computed

h_mean_canopy_abs Float Meanofindividualabsolutecanopyheightswithinsegment

computed


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h_mean_canopy Float Meanofindividualrelativecanopyheightswithinsegment

computed

h_dif_canopy Float Differencebetweenh_canopyandcanopy_h_metrics(50)

computed

h_min_canopy_abs Float Minimumofindividualabsolutecanopyheightswithinsegment

computed

h_min_canopy Float Minimumofindividualrelativecanopyheightswithinsegment

computed

h_max_canopy_abs Float Maximumofindividualabsolutecanopyheightswithinsegment.ShouldbeequivalenttoH100

computed

h_max_canopy Float Maximumofindividualrelativecanopyheightswithinsegment.ShouldbeequivalenttoRH100

computed

h_canopy_uncertainty Float Uncertaintyoftherelativecanopyheight(h_canopy)

computed

canopy_openness Float STDofrelativeheightsforallphotonsclassifiedascanopyphotonswithinthesegmenttoprovideinferenceofcanopyopenness

computed

toc_roughness Float STDofrelativeheightsofallphotonsclassifiedastopofcanopywithinthesegment

computed

h_canopy_quad Float Quadraticmeancanopyheight computedn_ca_photons Integer4 Numberofcanopyphotonswithin100

msegmentcomputed

n_toc_photons Integer4 Numberoftopofcanopyphotonswithin100msegment

computed

centroid_height Float Absoluteheightabovereferenceellipsoidassociatedwiththecentroidofallsignalphotons

computed

canopy_rh_conf Integer Canopyrelativeheightconfidenceflagbasedonpercentageofgroundandcanopyphotonswithinasegment:0(<5%canopy),1(>5%canopy,<5%ground),2(>5%canopy,>5%ground)

computed

canopy_flag Integer FlagindicatingthatcanopywasdetectedusingtheLandsatTreeCoverContinuousFieldsdataproduct

computed

landsat_flag Integer FlagindicatingthatLandsatTreeCoverContinuousFieldsdataproducthadmorethan50%values>100forL-kmsegment

computed

landsat_perc Float Averagepercentagevalueofthevalid(value<=100)LandsatTreeCover


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ContinuousFieldsproductforeach100msegment

704



















2.2.3 Canopy_height_metrics_abs723

(parameter = canopy_h_metrics_abs). The absoluteheightmetrics (H##) of724

classifiedcanopyphotonsabovetheellipsoid.Theheightmetricsaresortedbasedon725

acumulativedistributionandcalculatedatthefollowingpercentiles:25,50,60,70,726

75,80,85,90,95.Theseheightmetricsareoftenusedintheliteraturetocharacterize727

vertical structure of vegetation. One important distinction of these canopy height728


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metricscomparedtothosederivedfromotherlidarsystems(e.g.,LVISorGEDI)is729

thattheICESat-2canopyheightmetricsareheightsabovethegroundsurface.These730

metrics do not include the groundphotons. Required input data are the absolute731

canopyheightsofallcanopyphotons.732

2.2.4 Canopy_height_metrics733

(parameter=canopy_h_metrics).Relativeheightmetricsabovetheestimated734

terrainsurface(RH##)ofclassifiedcanopyphotons.Theheightmetricsaresorted735

basedonacumulativedistributionandcalculatedatthefollowingpercentiles: 25,736

50,60,70,75,80,85,90,95.Theseheightmetricsareoftenusedintheliteratureto737

characterize vertical structure of vegetation. One important distinction of these738

canopyheightmetricscomparedtothosederivedfromotherlidarsystems(e.g.,LVIS739

orGEDI) is that the ICESat-2 canopyheightmetricsareheightsabove theground740

surface.Thesemetricsdonotincludethegroundphotons.Requiredinputdataare741

relativecanopyheightsabovetheestimatedterrainsurfaceforallcanopyphotons.742

2.2.5 Absolute_segment_canopy_height743

(parameter = h_canopy_abs). The absolute 98%height of classified canopy744

photon heights above the ellipsoid. The absolute height from classified canopy745

photonsaresortedintoacumulativedistribution,andtheheightassociatedwiththe746

98%heightisreported.747

2.2.6 Segment_canopy_height748

(parameter=h_canopy).Therelative98%heightofclassifiedcanopyphoton749

heights above the estimated terrain surface. Relative canopy heights have been750

computed by differencing the canopy photon height from the estimated terrain751

surface in the ATL08 processing. The relative canopy heights are sorted into a752

cumulativedistribution,andtheheightassociatedwiththe98%heightisreported.753


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2.2.7 Absolute_segment_mean_canopy754

(parameter=h_mean_canopy_abs).Theabsolutemeancanopyheightforthe755

segment. Absolute canopy heights are the photons heights above the reference756

ellipsoid.Theseheightsareaveraged.757

2.2.8 Segment_mean_canopy758

(parameter = h_mean_canopy). The mean canopy height for the segment.759

Relative canopy heights have been computed by differencing the canopy photon760

heightfromtheestimatedterrainsurfaceintheATL08processing.Theseheightsare761

averaged.762

2.2.9 Segment_dif_canopy763

(parameter=h_dif_canopy).Differencebetweenh_canopyand764

canopy_h_metrics(50).Thisparameterisonemetricusedtodescribethevertical765

distributionofthecanopywithinthesegment.766

2.2.10 Absolute_segment_min_canopy767

(parameter=h_min_canopy_abs).Theminimumabsolutecanopyheightfor768

the segment. Required input data is classified point cloud (i.e. photons labeled as769

eithercanopyorgroundintheATL08processing).770

2.2.11 Segment_min_canopy771

(parameter=h_min_canopy). Theminimumrelative canopyheight for the772

segment.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledaseither773

canopyorgroundintheATL08processing).774

2.2.12 Absolute_segment_max_canopy775

(parameter=h_max_canopy_abs).Themaximumabsolutecanopyheightfor776

thesegment.ThisproductisequivalenttoH100metricreportedintheliterature.This777

parameter,however,hasthepotentialforerrorasrandomsolarbackgroundnoise778


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maynothavebeenfullyrejected.Itisrecommendedthath_canopyorh_canopy_abs779

(i.e., the 98% canopy height) be considered as the top of canopy measurement.780


groundintheATL08processing).782

2.2.13 Segment_max_canopy783

(parameter=h_max_canopy). Themaximumrelativecanopyheight for the784

segment.ThisproductisequivalenttoRH100metricreportedintheliterature.This785

parameter,however,hasthepotentialforerrorasrandomsolarbackgroundnoise786

maynothavebeenfullyrejected.Itisrecommendedthath_canopyorh_canopy_abs787

(i.e., the 98% canopy height) be considered as the top of canopy measurement.788



2.2.14 Segment_canopy_height_uncertainty791

(parameter = h_canopy_uncertainty). Uncertainty of the relative canopy792

height for the segment. This uncertainty incorporates all systematic uncertainties793

(e.g.timing,orbits,geolocation,etc.)aswellasuncertaintyfromerrorsofidentified794

photons.Thisparameter isdescribed inSection1,Equation1.4. If therearenota795

sufficient number of ground photons, an invalid value will be reported –no796

interpolationwillbedone.Inthecaseforcanopyheightuncertainty,theparameter797

𝜎*,38,2&1?/**iscomprisedofboththeterrainuncertaintywithinthesegmentbutalso798

thetopofcanopyresiduals.Requiredinputdataisclassifiedpointcloud(i.e.photons799

labeledaseithertopofcanopyorgroundintheATL08processing).Thisparameter800

will be derived from only classified top of canopy photons. The canopy height801

uncertaintyisderivedfromEquation1.4,shownbelowasEquation1.5,represents802

thestandarddeviationoftheterrainpointsandthestandarddeviationofthetopof803

canopyheightphotons.804

𝜎>DEFGHIJKIBL_1+ = Eqn1.5805


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806

2.2.15 Segment_canopy_openness807

(parameter = canopy_openness). Standard deviation of relative canopy808

heightswithineachsegment.Thisparameterwillpotentiallyprovideanindicatorof809

canopy openness as a greater standard deviation of heights indicates greater810

penetrationofthelaserenergyintothecanopy.Requiredinputdataisclassifiedpoint811

cloud(i.e.photonslabeledaseithercanopyorgroundintheATL08processing).812

2.2.16 Segment_top_of_canopy_roughness813

(parameter = toc_roughness). Standard deviation of relative top of canopy814

heightswithineachsegment.Thisparameterwillpotentiallyprovideanindicatorof815

canopyvariability.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeled816

asthetopofthecanopyintheATL08processing).817

2.2.17 Segment_canopy_quadratic_height818

(parameter=h_canopy_quad).Thequadraticmeanrelativeheightofclassified819

canopyphotons.Thequadraticmeanheightiscomputedas:820

𝑞𝑚ℎ = S Tℎ%<

𝑛_𝑐𝑎_𝑝ℎ𝑜𝑡𝑜𝑛𝑠

2_1/_)+(&(2*

%Z[

821

2.2.18 Segment_number_canopy_photons822

(parameter=n_ca_photons).Numberofcanopyphotonswithineachsegment.823




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2.2.19 Segment_number_top_canopy_photons826

(parameter=n_toc_photons).Numberoftopofcanopyphotonswithineach827

segment.Requiredinputdataisclassifiedpointcloud(i.e.photonslabeledastopof828

canopyintheATL08processing).829

2.2.20 Centroid_height830

(parameter= centroid_height). Optical centroidof allphotons classifiedas831

eithercanopyorgroundpointswithinasegment.Theheightsusedinthiscalculation832

areabsoluteheightsabovethereferenceellipsoid.Thisparameterisequivalenttothe833

centroidheightproducedonICESatGLA14.834

2.2.21 Segment_rel_canopy_conf835

(parameter=canopy_rh_conf).Canopyrelativeheightconfidenceflagbased836

onpercentageofgroundphotonsandpercentageofcanopyphotons,relativetothe837

totalclassified(groundandcanopy)photonswithinasegment:0(<5%canopy),1838

(>5%canopyand<5%ground),2(>5%canopyand>5%ground).Thisisameasure839

basedonthequantity,notthequality,oftheclassifiedphotonsineachsegment.840

2.2.22 Canopy_flag841

(parameter=canopy_flag).Flagindicatingthatcanopywasdetectedusingthe842

LandsatContinuousCoverproductfortheL-kmsegment.Currently,ifmorethan5%843

of the Landsat CC pixels along the profile have canopy in them, we make the844

assumptioncanopyispresentalongtheentireL-kmsegment.845

2.2.23 Landsat_flag846

(parameter=landsat_flag).Flagindicatingthatmorethan50%oftheLandsat847

Tree Cover Continuous Fields product have values >100 (indicatingwater, cloud,848

shadow,orfilledvalues)fortheL-kmsegment.Canopyisassumedpresentalongthe849

L-kmsegmentiflandsat_flagis1.850


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2.2.24 Landsat_perc851

(parameter= landsat_perc). Averagepercentagevalueof thevalid(value<=852

100)LandsatTreeCoverContinuousFieldsproductpixelsthatoverlapwithineach853

100msegment.854

855

856

2.3 Subgroup:Photons857

The subgroup for photons contains the classified photons thatwere used to858

generatetheparameterswithinthelandorcanopysubgroups.Eachphotonthatis859

identifiedasbeinglikelysignalwillbeclassifiedas:0=noise,1=ground,2=canopy,860

or3=topofcanopy.Theindexvaluesforeachclassifiedphotonwillbeprovidedsuch861

thattheycanbeextractedfromtheATL03dataproductforindependentevaluation.862

Table 2.3. Summary table for photon parameters for the ATL08 product. 863

Group DataType Description Sourceclassed_PC_indx Float Indicesofphotonstracking

backtoATL03thatsurfacefindingsoftwareidentifiedandusedwithinthecreationofthedataproducts.

ATL03

classed_PC_flag Integer Classificationflagforeachphotonaseithernoise,ground,canopy,ortopofcanopy.

computed

ph_segment_id Integer Georeferencedbinnumber(20-m)associatedwitheachphoton

ATL03

d_flag Integer FlagindicatingwhetherDRAGANNlabeledthephotonasnoiseorsignal

computed

864


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2.3.1 Indices_of_classed_photons865

(parameter=classed_PC_indx).IndicesofphotonstrackingbacktoATL03that866

surfacefindingsoftwareidentifiedandusedwithinthecreationofthedataproducts867

foragivensegment.868

2.3.2 Photon_class869

(parameter = classed_PC_flag).Classification flags for a given segment. 0 =870

noise, 1 = ground, 2 = canopy, 3 = top of canopy. The final ground and canopy871

classificationareflags1-3.Thefullcanopyisthecombinationofflags2and3.872

2.3.3 Georeferenced_segment_number873

(parameter=ph_segment_id).Thesegment_idassociatedwitheveryphotonin874

each100-msegment.Each100-msegmentconsistsoffivesequential20-msegments875

providedfromtheATL03product,whicharelabeledassegment_id.Thesegment_id876

is a seven digit number that uniquely identifies each along track segment, and is877

writtenatthealong-trackgeolocationsegmentrate(i.e.~20malongtrack).Thefour878

digit RGT number can be combined with the seven digit segment_id number to879

uniquely define any along-track segment number. Values are sequential, with880

0000001referringtothefirstsegmentaftertheequatorialcrossingoftheascending881

node.882

2.3.4 DRAGANN_flag883

(parameter=d_flag).FlagindicatingthelabelingofDRAGANNnoisefilteringfor884

agivenphoton.0=noise,1=signal.885

886

2.4 Subgroup:Referencedata887

Thereferencedatasubgroupcontainsparametersand informationthatare888

useful for determining the terrain and canopy heights that are reported on the889


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product.Inadditiontopositionandtiminginformation,theseparametersincludethe890

referenceDEMheight,referencelandcovertype,andflagsindicatingwaterorsnow.891

Table 2.4. Summary table for reference parameters for the ATL08 product. 892

Group DataType

Description Source


ATL03


ATL03

latitude Float Centerlatitudeofsignalphotonswithineachsegment

ATL03

longitude Float Centerlongitudeofsignalphotonswithineachsegment

ATL03

delta_time Float Mid-segmentGPStimeinsecondspastanepoch.Theepochisprovidedinthemetadataatthefilelevel

ATL03

delta_time_beg Float Deltatimeofthefirstphotoninthesegment

ATL03

delta_time_end Float Deltatimeofthelastphotoninthesegment

ATL03

night_flag Integer Flagindicatingwhetherthemeasurementswereacquiredduringnighttimeconditions

computed

dem_h Float4 ReferenceDEMelevation externaldem_flag SourceofreferenceDEM externaldem_removal_flag Integer Qualitycheckflagtoindicate

>20%photonsremovedduetolargedistancefromdem_h

computed

h_dif_ref Float4 Differencebetweenh_te_mediananddem_h

computed

terrain_flg Integer TerrainflagqualitychecktoindicateadeviationfromthereferenceDTM

computed

segment_landcover Integer4 Referencelandcoverforsegmentderivedfrombestgloballandcoverproductavailable

external

segment_watermask Integer4 Watermaskindicatinginlandwaterproducedfrombestsourcesavailable

external


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segment_snowcover Integer4 Dailysnowcovermaskderivedfrombestsources

external

urban_flag Integer Flagindicatingsegmentislocatedinanurbanarea

external

surf_type Integer1 Flagsdescribingsurfacetypes:0=nottype,1=istype.Orderofarrayisland,ocean,seaice,landice,inlandwater.

ATL03

atl08_region Integer ATL08region(s)encompassedbyATL03granulebeingprocessed

computed

last_seg_extend Float Thedistance(km)thatthelastATL08processingsegmentinafileiseitherextendedoroverlappedwiththepreviousATL08processingsegment

computed

893

















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2.4.3 Segment_latitude912

(parameter=latitude).Centerlatitudeofsignalphotonswithineachsegment913

2.4.4 Segment_longitude914

(parameter = longitude). Center longitude of signal photons within each915

segment916

2.4.5 Delta_time917

(parameter=delta_time).Mid-segmentGPStimeforthesegmentinseconds918

pastanepoch.Theepochislistedinthemetadataatthefilelevel.919

2.4.6 Delta_time_beg920

(parameter=delta_time_beg).Deltatimeforthefirstphotoninthesegment921

insecondspastanepoch.Theepochislistedinthemetadataatthefilelevel.922

2.4.7 Delta_time_end923

(parameter=delta_time_end).Deltatimeforthelastphotoninthesegment924

insecondspastanepoch.Theepochislistedinthemetadataatthefilelevel.925

2.4.8 Night_Flag926

(parameter = night_flag). Flag indicating the data were acquired in night927

conditions: 0=day,1=night.Night flag is setwhensolarelevation isbelow0.0928

degrees.929


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2.4.9 Segment_reference_DTM930

(parameter=dem_h).Referenceterrainheightvalueforsegmentdetermined931

by the “best” DEM available based on data location. All heights in ICESat-2 are932

referencedtotheWGS84ellipsoidunlessclearlynotedotherwise.DEMistakenfrom933

avarietyofancillarydatasources:GIMP,GMTED,MSS.TheDEMsourceflagindicates934

whichsourcewasused.935

2.4.10 Segment_reference_DEM_source936

(parameter=dem_flag).IndicatessourceofthereferenceDEMheight.Values:937

0=None,1=GIMP,2=GMTED,3=MSS.938

2.4.11 Segment_reference_DEM_removal_flag939

(parameter = dem_removal_flag). Quality check flag to indicate > 20%940

classifiedphotonsremovedfromlandsegmentduetolargedistancefromdem_h.941

2.4.12 Segment_terrain_difference942

(parameter=h_dif_ref).Differencebetweenh_te_mediananddem_h.Sincethe943

meanterrainheightismoresensitivetooutliers,themedianterrainheightwillbe944

evaluatedagainstthereferenceDEM.Thisparameterwillbeusedasaninternaldata945

qualitycheckwiththenotionbeingthatifthedifferenceexceedsathreshold(TBD)a946

terrainqualityflag(terrain_flg)willbetriggered.947

2.4.13 Segment_terrainflag948

(parameter= terrain_flg).Terrain flag to indicate confidence in thederived949

terrain height estimate. If h_dif_ref exceeds a threshold (TBD) the terrain_flg950

parameterwillbesetto1.Otherwise,itis0.951

2.4.14 Segment_landcover952

(parameter=segment_landcover).Segmentlandcoverwillbebasedonbest953

availablegloballandcoverproductusedforreference.Onepotentialsourceisthe0.5954


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kmglobalmosaicsofthestandardMODISlandcoverproduct(Channanetal,2015;955

Friedletal,2010;availableonlineathttp://glcf.umd.edu/data/lc/index.shtml).Here,956

17 classes are defined ranging from evergreen (needle and broadleaf forest),957

deciduous (needle and broadleaf forest), shrublands, woodlands, savanna and958

grasslands,agriculture,tourban.Themostcurrentyearprocessedforthisproductis959

basedonMODISmeasurementsfrom2012.960

2.4.15 Segment_watermask961

(parameter=segment_watermask).Watermask(i.e., flag) indicating inland962

waterasreferencedfromtheGlobalRasterWaterMaskat250mspatialresolution963

(Carrolletal,2009;availableonlineathttp://glcf.umd.edu/data/watermask/).0=964

nowater;1=water.965

2.4.16 Segment_snowcover966

(parameter = segment_snowcover). Daily snowcover mask (i.e., flag)967

indicatingalikelypresenceofsnoworicewithineachsegmentproducedfrombest968

availablesourceusedforreference.Thesnowmaskwillbethesamesnowmaskas969

used for ATL09 Atmospheric Products: NOAA snow-ice flag. 0=ice free water;970

1=snowfreeland;2=snow;3=ice.971

2.4.17 Urban_flag972

(parameter = urban_flag). The urban flag indicates that a segment is likely973

locatedoveranurbanarea.Intheseareas,buildingsmaybemisclassifiedascanopy,974

andthusthecanopyproductsmaybeincorrect.Theurbanflagissourcedfromthe975

“urbanandbuiltup”classificationontheMODISlandcoverproduct(Channanetal,976

2015; Friedl et al, 2010; available online at977

http://glcf.umd.edu/data/lc/index.shtml).0=noturban;1=urban.978


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2.4.18 Surface_type979

(parameter=surf_type).Thesurfacetypeforagivensegmentisdeterminedat980

themajor framerate(every200shots,or~140metersalong-track)and isa two-981

dimensionalarraysurf_type(n,nsurf),wherenisthemajorframenumber,andnsurf982

is thenumberofpossiblesurfacetypessuchthatsurf_type(n,isurf) isset to0or1983

indicating ifsurfacetype isurf ispresent(1)ornot(0),where isurf=1to5(land,984

ocean,seaice,landice,andinlandwater)respectively.985

2.4.19 ATL08_region986

(parameter = atl08_region). The ATL08 regions that encompass the ATL03987

granulebeingprocessedthroughtheATL08algorithm.TheATL08regionsareshown988

by Figure 2.3. In ATL08 regions 11 (Greenland) and 7 – 10 (Antarctica), the989

canopy_flagisautomaticallysettofalseforATL08processing.990

2.4.20 Last_segment_extend991

(parameter= last_seg_extend).Thedistance (km) that the lastATL0810km992

processingsegmentiseitherextendedbeyond10kmorusesdatafromtheprevious993

10kmprocessingsegmenttoallowforenoughdataforprocessingtheATL03photons994

throughtheATL08algorithm.IfthelastportionofanATL03granulebeingprocessed995

wouldresultinasegmentwithlessthan3.4km(170geosegments)worthofdata,996

thatlastportionisaddedtotheprevious10kmprocessingwindowtobeprocessed997

togetherasoneextendedATL08processingsegment.Theresultinglast_seg_extend998

valuewouldbeapositivevalueofdistancebeyond10kmthattheATL08processing999

segmentwasextendedby.IfthelastATL08processingsegmentwouldbelessthan1000

10kmbutgreaterthan3.4km,aportionextendingfromthestartofcurrentATL081001

processingsegmentbackwardsintothepreviousATL08processingsegmentwould1002

beaddedtothecurrentATL08processingsegmenttomakeit10kminlength.The1003

distanceofthisbackwarddatagatheringwouldbereportedinlast_seg_extendasa1004

negativedistancevalue.Onlynew100mATL08segmentproductsgeneratedfrom1005


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thisbackwardextensionwouldbereported.Allothersegmentsthatarenotextended1006

willreportalast_seg_extendvalueof0.1007

1008

2.5 Subgroup:Beamdata1009

Thesubgroupforbeamdatacontainsbasicinformationonthegeometryand1010

pointingaccuracyforeachbeam.1011

Table 2.5. Summary table for beam parameters for the ATL08 product. 1012

Group DataType

Units Description Source


ATL03


ATL03

ref_elev Float ElevationoftheunitpointingvectorforthereferencephotoninthelocalENUframeinradians.TheangleismeasuredfromEast-Northplaneandpositivetowardsup

ATL03

ref_azimith Float AzimuthoftheunitpointingvectorforthereferencephotonintheENUframeinradians.TheangleismeasuredfromNorthandpositivetowardEast.

ATL03

atlas_pa Float Offnadirpointingangleofthespacecraft

ATL03

rgt Integer Thereferencegroundtrack(RGT)isthetrackontheearthatwhichthevectorbisectinglaserbeams3and4is

ATL03


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pointedduringrepeatoperations

sigma_h Float TotalverticaluncertaintyduetoPPDandPOD

ATL03

sigma_along Float Totalalong-trackuncertaintyduetoPPDandPODknowledge

ATL03

sigma_across Float Totalcross-trackuncertaintyduetoPPDandPODknowledge

ATL03

sigma_topo Float Uncertaintyofthegeolocationknowledgeduetolocaltopography(Equation1.3)

computed

sigma_atlas_land Float Totaluncertaintythatincludessigma_hplusthegeolocationuncertaintyduetolocalslopeEquation1.2

computed

psf_flag integer Flagindicatingsigma_atlas_land(akaPSF)ascomputedinEquation1.2exceedsavalueof1m.

computed

layer_flag Integer Cloudflagindicatingpresenceofcloudsorblowingsnow

ATL09

cloud_flag_asr Integer CloudconfidenceflagfromATL09indicatingclearskies

ATL09

msw_flag Integer MultiplescatteringwarningproductproducedonATL09

ATL09

asr Float Apparentsurfacereflectance

ATL09

snr Float Backgroundsignaltonoiselevel

Computed

solar_azimuth Float Theazimuth(indegrees)ofthesunpositionvectorfromthereferencephotonbouncepointpositioninthelocalENUframe.Theangleismeasuredfrom

ATL03g


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NorthandispositivetowardsEast.

solar_elevation Float TheelevationofthesunpositionvectorfromthereferencephotonbouncepointpositioninthelocalENUframe.TheangleismeasuredfromtheEast-NorthplaneandispositiveUp.

ATL03g

n_seg_ph Integer Numberofphotonswithineachlandsegment

computed

ph_ndx_beg Integer Photonindexbegin computed1013


















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2.5.3 Beam_coelevation1032

(parameter=ref_elev).Elevationoftheunitpointingvectorforthereference1033

photon in the localENU frame in radians.Theangle ismeasured fromEast-North1034

planeandpositivetowardsup.1035

2.5.4 Beam_azimuth1036

(parameter = ref_azimuth). Azimuth of the unit pointing vector for the1037

referencephotonintheENUframeinradians.TheangleismeasuredfromNorthand1038

positivetowardEast.1039

2.5.5 ATLAS_Pointing_Angle1040

(parameter=atlas_pa).Offnadirpointingangle(inradians)ofthesatelliteto1041

increasespatialsamplinginthenon-polarregions.1042

2.5.6 Reference_ground_track1043

(parameter=rgt).Thereferencegroundtrack(RGT)isthetrackontheearth1044

atwhich thevectorbisecting laserbeams3and4 (orGT2LandGT2R) ispointed1045

duringrepeatoperations.EachRGTspansthepartofanorbitbetweentwoascending1046

equatorcrossingsandarenumberedsequentially. TheICESat-2missionhas13871047

RGTs,numberedfrom0001xxto1387xx.Thelasttwodigitsrefertothecyclenumber.1048

2.5.7 Sigma_h1049

(parameter=sigma_h).TotalverticaluncertaintyduetoPPD(PrecisePointing1050

Determination), POD (Precise Orbit Determination), and geolocation errors.1051

Specifically, this parameter includes radialorbit error,𝜎"#$%& , tropospheric errors,1052

𝜎D#(),forwardscatteringerrors,𝜎-(#./#0*1/&&,#%23 ,instrumenttimingerrors,𝜎&%8%23,1053

and off-nadir pointing geolocation errors. The component parameters are pulled1054


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fromATL03andATL09.Sigma_histherootsumofsquaresofthesetermsasdetailed1055

inEquation1.1.Thesigma_hreportedhereisthemeanofthesigma_hvaluesreported1056

withinthefiveATL03geosegmentsthatareusedtocreatethe100mATL08segment.1057

2.5.8 Sigma_along1058

(parameter=sigma_along).Totalalong-trackuncertaintyduetoPPDandPOD1059

knowledge.ThisparameterispulledfromATL03.1060

2.5.9 Sigma_across1061

(parameter = sigma_across). Total cross-track uncertainty due to PPD and1062

PODknowledge.ThisparameterispulledfromATL03.1063

2.5.10 Sigma_topo1064

(parameter=sigma_topo).Uncertaintyinthegeolocationduetolocalsurface1065

slope as described in Equation 1.3. The local slope is multiplied by the 6.5 m1066

geolocation uncertainty factor that will be used to determine the geolocation1067

uncertainty.Thegeolocationerrorwillbecomputedfroma100msampleduetothe1068

localslopecalculationatthatscale.1069

2.5.11 Sigma_ATLAS_LAND1070

(parameter = sigma_atlas_land). Total vertical geolocation error due to1071

ranging,andlocalsurfaceslope.TheparameteriscomputedforATL08asdescribed1072

inEquation1.2.Thegeolocationerrorwillbecomputedfroma100msampledueto1073

thelocalslopecalculationatthatscale.1074

2.5.12 PSF_flag1075

(parameter = psf_flag). Flag indicating that the point spread function1076

(computedassigma_atlas_land)hasexceeded1m.1077


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2.5.13 Layer_flag1078

(parameter= layer_flag).Flag is a combinationofmultipleATL09 flagsand1079

takesdaytime/nighttime intoconsideration.Avalueof1meanscloudsorblowing1080

snowislikelypresent.Avalueof0indicatesthelikelyabsenceofcloudsorblowing1081

snow.IfnoATL09productisavailableforanATL08segment,aninvalidvaluewillbe1082

reported.1083

2.5.14 Cloud_flag1084

(parameter=cloud_flag_asr).CloudconfidenceflagfromATL09.Flagindicates1085

potential clear skies from ATL09. If no ATL09 product is available for an ATL081086

segment,aninvalidvaluewillbereported.Cloudflags: 1087

0=Highconfidenceclearskies1088

1=Mediumconfidenceclearskies1089

2=Lowconfidenceclearskies1090

3=Lowconfidencecloudyskies1091

4=Mediumconfidencecloudyskies1092

5=Highconfidencecloudyskies1093

2.5.15 MSW1094

(parameter=msw_flag).Multiplescatteringwarningflagwithvaluesfrom-1to1095

5ascomputedintheATL09atmosphericprocessinganddeliveredontheATL09data1096

product.IfnoATL09productisavailableforanATL08segment,aninvalidvaluewill1097

bereported.MSWflags:1098

-1=signaltonoiseratiotoolowtodeterminepresenceof1099

cloudorblowingsnow1100

0=no_scattering1101

1=cloudsat>3km1102

2=cloudsat1-3km1103

3=cloudsat<1km1104


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4=blowingsnowat<0.5opticaldepth1105

5=blowingsnowat>=0.5opticaldepth1106

2.5.16 Computed_Apparent_Surface_Reflectance1107

(parameter = asr). Apparent surface reflectance computed in the ATL091108

atmospheric processing and delivered on the ATL09 data product. If no ATL091109

productisavailableforanATL08segment,aninvalidvaluewillbereported.1110

2.5.17 Signal_to_Noise_Ratio1111

(parameter = snr). The Signal to Noise Ratio of geolocated photons as1112

determinedbytheratioofthesupersetofATL03signalandDRAGANNfoundsignal1113

photonsused forprocessing theATL08segments to thebackgroundphotons (i.e.,1114

noise)withinthesameATL08segments.1115

2.5.18 Solar_Azimuth1116

(parameter=solar_azimuth).Theazimuth(indegrees)ofthesunposition1117

vectorfromthereferencephotonbouncepointpositioninthelocalENUframe.The1118

angleismeasuredfromNorthandispositivetowardsEast.1119

2.5.19 Solar_Elevation1120

(parameter=solar_elevation).Theelevationofthesunpositionvectorfrom1121

thereferencephotonbouncepointpositioninthelocalENUframe.Theangleis1122

measuredfromtheEast-Northplaneandispositiveup.1123

2.5.20 Number_of_segment_photons1124

(parameter=n_seg_ph).Numberofphotonsineachlandsegment.1125

2.5.21 Photon_Index_Begin1126

(parameter=ph_ndx_beg).Index(1-based)withinthephoton-ratedataof1127

thefirstphotonwithinthiseachlandsegment.1128


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1129

1130


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3 ALGORITHMMETHODOLOGY1131

Fortheecosystemcommunity,identificationofthegroundandcanopysurface1132

isbyfarthemostcriticaltask,asmeetingthescienceobjectiveofdeterminingglobal1133

canopy heights hinges upon the ability todetect both the canopy surface and the1134

underlyingtopography.Sinceaspace-basedphotoncountinglasermappingsystem1135

is a relatively new instrument technology for mapping the Earth’s surface, the1136

software to accurately identify and extract both the canopy surface and ground1137

surface is described here. The methodology adopted for ATL08 establishes a1138

frameworktopotentiallyacceptmultipleapproaches forcapturingboththeupper1139

and lower surface of signal photons. Onemethod used is an iterative filtering of1140

photons in thealong-trackdirection.Thismethodhasbeen found topreserve the1141

topographyandcapturecanopyphotons,whilerejectingnoisephotons.Anadvantage1142

of this methodology is that it is self-parameterizing, robust, and works in all1143

ecosystemsifsufficientphotonsfromboththecanopyandgroundareavailable.For1144

processingpurposes,along-trackdatasignalphotonsareparsedintoL-kmsegment1145

oftheorbitwhichisrecommendedtobe10kminlength.1146

1147

3.1 NoiseFiltering 1148

Solar background noise is a significant challenge in the analysis of photon1149

counting laser data. Rangemeasurement data created fromphoton counting lidar1150

detectors typically contain far higher noise levels than themore commonphoton1151

integrating detectors available commercially in the presence of passive, solar1152

background photons. Given the higher detection sensitivity for photon counting1153

devices,abackgroundphotonhasagreaterprobabilityoftriggeringadetectionevent1154

over traditional integralmeasurementsandmaysometimesdominate thedataset.1155

Solar background noise is a function of the surface reflectance, topography, solar1156

elevation, and atmospheric conditions. Prior to running the surface finding1157


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algorithms used for ATL08 data products, the superset of output from the GSFC1158

medium-highconfidenceclassedphotons(ATL03signal_conf_ph:flags3-4)andthe1159

output fromDRAGANNwillbeconsideredas the inputdataset.ATL03 inputdata1160

requirementsincludethelatitude,longitude,height,segmentdeltatime,segmentID,1161

and a preliminary signal classification for each photon. The motivation behind1162

combiningtheresultsfromtwodifferentnoisefilteringmethodsistoensurethatall1163

of the potential signal photons for land surfaceswill be provided as input to the1164

surface finding software. The description of the methodology for the ATL031165

classificationisdescribedseparatelyintheATL03ATBD.Themethodologybehind1166

DRAGANNisdescribedinthefollowingsection.1167

1168

1169

Figure 3.1. Combination of noise filtering algorithms to create a superset of input data for 1170

surface finding algorithms. 1171

1172

3.1.1 DRAGANN1173

The Differential, Regressive, and Gaussian Adaptive Nearest Neighbor1174

(DRAGANN)filteringtechniquewasdevelopedtoidentifyandremovenoisephotons1175

fromthephotoncountingdatapointcloud.DRAGANNutilizesthebasicpremisethat1176

signalphotonswillbecloserinspacethanrandomnoisephotons.Thefirststepofthe1177

filteringistoimplementanadaptivenearestneighborsearch.Byusinganadaptive1178

method, different thresholds can be applied to account for variable amounts of1179


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backgroundnoiseandchangingsurfacereflectancealongthedataprofile.Thissearch1180

findsaneffectiveradiusbycomputingtheprobabilityoffindingPnumberofpoints1181

withinasearcharea.ForMABELandmATLAS,P=20pointswithinthesearcharea1182

was empirically derived but found to be an effective and efficient number of1183

neighbors.1184

Theremaybecases,however,wherethevalueofPneedstobechanged.For1185

example,duringnightacquisitionsitisanticipatedthatthebackgroundnoiseratewill1186

be considerably low. Since DRAGANN is searching for two distributions in1187

neighborhoodsearchingspace,thesoftwarecouldincorrectlyidentifysignalphotons1188

asnoisephotons.TheparameterP,however,canbedetermineddynamically from1189

estimations of the signal and noise rates from the photon cloud. In cases of low1190

background noise (night), P would likely be changed to a value lower than 20.1191

Similarly,incasesofhighamountsofsolarbackground,Pmayneedtobeincreased1192

tobetter capture the signal andavoid classifying small,dense clustersofnoiseas1193

signal.Inthiscase,however,itislikelythatnoisephotonsnearsignalphotonswill1194

alsobemisclassifiedassignal.ThemethodfordynamicallydeterminingaPvalueis1195

explainedfurtherinsection1.1.1.1196

AfterP isdefined, ahistogramof thenumberofneighborswithina search1197

radiusforeachpointisgenerated.Thedistributionofneighborradiusoccurrencesis1198

analyzedtodeterminethenoisethreshold.1199

\]L^LAO

= __L^LAO

Eqn.3.11200

1201

whereNtotalisthetotalnumberofphotonsinthepointcloud,Visthevolumeofthe1202

nearestneighborhoodsearch,andVtotalistheboundingvolumeoftheenclosedpoint1203

cloud.Fora2-dimensionaldataset,Vbecomes1204

1205

𝑉 = 𝜋𝑟< Eqn.3.21206


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1207

wherer is theradius.Agoodpractice is to firstnormalizethedatasetalongeach1208

dimensionbeforerunningtheDRAGANNfilter.Normalizationpreventsthealgorithm1209

from favoringone dimension over the others in the radius search (e.g.,when the1210

latitudeandlongitudeareindegreesandheightisinmeters).1211

1212

1213Figure 3.2. Histogram of the number of photons within a search radius. This histogram is 1214

used to determine the threshold for the DRAGANN approach. 1215

1216

Oncetheradiushasbeencomputed,DRAGANNcountsthenumberofpoints1217

withintheradiusforeachpointandhistogramsthatsetofvalues.Thedistributionof1218

thenumberofpoints,Figure3.2,revealstwodistinctpeaks;anoisepeakandasignal1219

peak.ThemotivationofDRAGANNistoisolatethesignalphotonsbydetermininga1220

thresholdbasedonthenumberofphotonswithinthesearchradius.Thenoisepeak1221

ischaracterizedashavingalargenumberofoccurrencesofphotonswithjustafew1222

neighboringphotonswithinthesearchradius.Thesignalphotonscomprisethebroad1223

secondpeak.Thefirststepindeterminingthethresholdbetweenthenoiseandsignal1224

0 100 200 300 400 500 6000

500

1000

1500

2000

2500

3000

# of points in search radius

# of

occ

uren

ces

Noisepeak

Otherfeatures


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is to implement Gaussian fitting to the number of photons distribution (i.e., the1225

distributionshowninFigure3.2).TheGaussianfunctionhastheform1226

1227

𝑔(𝑥) = 𝑎𝑒 h(ih$)j

<1j Eqn.3.31228

1229

whereaistheamplitudeofthepeak,bisthecenterofthepeak,andcisthestandard1230

deviationofthecurve.Afirstderivativesigncrossingmethodisoneoptiontoidentify1231

peakswithinthedistribution.1232

TodeterminethenoiseandsignalGaussians,uptotenGaussiancurvesarefit1233

to the histogram using an iterative process of fitting and subtracting the max-1234

amplitudepeakcomponentfromthehistogramuntilallpeakshavebeenextracted.1235

Then,thepotentialGaussianspassthrougharejectionprocesstoeliminatethosewith1236

poorstatisticalfitsorotherapparenterrors(GoshtasbyandO’Neill,1994;Chauveet1237

al.2008).AGaussianwithanamplitudelessthan1/5ofthepreviousGaussianand1238

withintwostandarddeviationsofthepreviousGaussianshouldberejected.Oncethe1239

errantGaussiansarerejected,thefinaltworemainingareassumedtorepresentthe1240

noise and signal. These are separated based on the remaining two Gaussian1241

componentswithinthehistogramusingthelogicthattheleftmostGaussianisnoise1242

(lowneighborcounts)andtheotherissignal(highneighborcounts).1243

TheintersectionofthesetwoGaussians(noiseandsignal)determinesadata1244

thresholdvalue.Thethresholdvalueistheparameterusedtodistinguishbetween1245

noisepointsandsignalpointswhenthepointcloudisre-evaluatedforsurfacefinding.1246

Intheeventthatonlyonecurvepassestherejectionprocess,thethresholdissetat1247

1𝜎abovethecenterofthenoisepeak.1248

AnexampleofthenoisefilteredproductfromDRAGANNisshowninFigure1249

3.3.Thesignalphotonsidentifiedinthisprocesswillbecombinedwiththecoarse1250

signalfindingoutputavailableontheATL03dataproduct.1251


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1252

Figure 3.3. Output from DRAGANN filtering. Signal photons are shown as blue. 1253

Figure3.3providesanexampleofalong-track(profiling)heightdatacollected1254

inSeptember2012fromtheMABEL(ICESat-2simulator)overvegetationinNorth1255

Carolina.Thephotonshavebeenfilteredsuchthatthesignalphotonsreturnedfrom1256

vegetationandthegroundsurfaceareremaining.Noisephotonsthatareadjacentto1257

thesignalphotonsarealsoretainedintheinputdataset;however,theseshouldbe1258

classifiedasnoisephotonsduringthesurfacefindingprocess.Itispossiblethatsome1259

additionaloutlyingnoisemayberetainedduringtheDRAGANNprocesswhennoise1260

photonsaredenselygrouped, and thesephotons shouldbe filteredoutbefore the1261

surfacefindingprocess.Estimatesofthegroundsurfaceandcanopyheightcanthen1262

bederivedfromthesignalphotons.1263

1264

3.2 SurfaceFinding1265

Once the signal photons have been determined, the objective is to find the1266

groundandcanopyphotonsfromwithinthepointcloud.Withtheexpectationthat1267

one algorithm may not work everywhere for all biomes, we are employing a1268

frameworkthatwillallowustocombinethesolutionsofmultiplealgorithmsintoone1269


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final composite solution for the ground surface. The composite ground surface1270

solutionwillthenbeutilizedtoclassifytheindividualphotonsasground,canopy,top1271

ofcanopy,ornoise.Currently,theframeworkdescribedhereutilizesonealgorithm1272

for finding the ground surface and canopy surface. Additionalmethods, however,1273

couldbeintegratedintotheframeworkatalatertime.Figure3.4belowdescribesthe1274

framework.1275

1276

1277

1278

Figure 3.4. Flowchart of overall surface finding method. 1279


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1280

3.2.1 De-trendingtheSignalPhotons1281

Animportantstepinthesuccessofthesurfacefindingalgorithmistoremove1282

theeffectof topographyonthe inputdata, thus improvingtheperformanceof the1283

algorithm. This is done by de-trending the input signal photons by subtracting a1284

heavilysmoothed“surface”thatisderivedfromtheinputdata.Essentially,thisisa1285

lowpassfilteroftheoriginaldataandmostoftheanalysistodetectthecanopyand1286

ground will subsequently be implemented on the high pass data. The amount of1287

smoothingthatisimplementedinordertoderivethisfirstsurfaceisdependentupon1288

the relief. For segments where the relief is high, the smoothing window size is1289

decreasedsotopographyisn’tover-filtered.1290

1291

Figure 3.5. Plot of Signal Photons (black) from 2014 MABEL flight over Alaska and de-1292

trended photons (red). 1293

1294

3.2.2 CanopyDetermination1295

Akeyfactorinthesuccessofthesurfacefindingalgorithmisforthesoftware1296

toautomaticallyaccountforthepresenceofcanopyalongagivenL-kmsegment.1297


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Duetothelargevolumeofdata,thisprocesshastooccurinanautomatedfashion,1298

allowingthecorrectmethodologyforextractingthesurfacetobeappliedtothedata.1299

In theabsenceof canopy, the iterative filteringapproach to findinggroundworks1300

extremelywell,butifcanopydoesexist,weneedtoaccommodateforthatfactwhen1301

wearetryingtorecoverthegroundsurface.1302

Currently, theLandsatTreeCoverContinuousFieldsdataset fromthe20001303

epochisusedtosetacanopyflagwithintheATL08algorithm.EachoftheseLandsat1304

Tree Cover tiles contain 30 m pixels indicating the percentage canopy cover for1305

vegetationover5mhighinthatpixelarea.The2000epochisusedoverthenewer1306

2005epochdueto“striping”inthe2005tiles,causedbythefailureofthescanline1307

corrector (SLC) in 2003. The striping artifacts result in inconsistent pixel values1308

across a landscapewhich in turn can result in a tenfold difference in the average1309

canopycoverpercentagecalculatedbetweentheepochsforaflightsegment.Thereis1310

currentlyavailablea2015TreeCoverBetaReleasethatutilizesLandsat8data.This1311

newreleaseofthe2015TreeCoverproductwillreplacethe2000epochforsetting1312

thecanopyflagintheATL08algorithm.TheTreeCoverdataareavailableviaftpat1313

http://glcf.umd.edu/data/landsatTreecover/.1314

For eachL-km segmentof ATLAS data, a comparison ismade between the1315

midpointlocationofthesegmentandthemidpointlocationsoftheWRSLandsattiles1316

tofindtheclosesttilethatencompassestheL-kmsegment.Usingtheclosestfound1317

tile,eachsignalphoton’sX-YlocationisusedtoidentifythecorrespondingLandsat1318

pixel.MultipleinstancesofthesamepixelsfoundfortheL-kmsegmentarediscarded,1319

andthepercentagecanopyvaluesoftheuniquepixelsdeterminedtobeundertheL-1320

km segmentareaveragedtoproduceanaveragecanopycoverpercentage forthat1321

segment.Iftheaveragecanopycoverpercentageforasegmentisover5%(threshold1322

subjecttochangeunderfurthertesting),thentheATL08algorithmwillassumethe1323

presence of canopy and identify both ground and vegetation photons in that1324


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segment’soutput.Else,theATL08algorithmusesasimplifiedcalculationtoidentify1325

onlygroundphotonsinthatsegment.1326

Thecanopyflagdeterminesifthealgorithmwillcalculateonlygroundphotons1327

(canopyflag=0)orbothgroundandvegetationphotons(canopyflag=1)foreachL-1328

kmsegment.1329

ForATL08productregionsoverAntarctica(regions7,8,9,10)andGreenland1330

(region11),thealgorithmwillassumeonlygroundphotons(canopyflag=0)(see1331

Figure2.2).1332

1333

3.2.3 VariableWindowDetermination1334

Themethodforgeneratingabestestimatedterrainsurfacewillvarydepending1335

uponwhethercanopyispresent.L-kmsegmentswithoutcanopyaremucheasierto1336

analyze because the groundphotons are usually continuous. L-km segmentswith1337

canopy,however,requiremorescrutinyasthenumberofsignalphotonsfromground1338

arefewerduetoocclusionbythevegetation.1339

Therearesomecommonelementsforfindingtheterrainsurfaceforbothcases1340

(canopy/nocanopy)andwithbothmethods. Inbothcases,wewilluseavariable1341

windowing span to compute statistics as well as filter and smooth the data. For1342

clarification, thewindowsize is variable foreachL-km segment,but it is constant1343

within the L-km segment. For the surface finding algorithm, we will employ a1344

Savitzky-Golaysmoothing/medianfilteringmethod.Usingthisfilter,wecomputea1345

variablesmoothingparameter(orwindowsize).Itisimportanttoboundthefilter1346

appropriatelyastheoutputfromthemedianfiltercanlosefidelityifthescanisover-1347

filtered.1348


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Wehavedevelopedanempirically-determinedshapefunction,boundbetween1349

[551],thatsetsthewindowsize(Sspan)basedonthenumberofphotonswithineach1350

L-kmsegment.1351

𝑆𝑠𝑝𝑎𝑛 = 𝑐𝑒𝑖𝑙[5 + 46 ∗ (1 − 𝑒h/∗?,23&+)] Eqn.3.41352

𝑎 =vwxy[h jz

{z|{}

h<G[[~ ≈ 21𝑥10h� Eqn.3.51353

whereaistheshapeparameterandlengthisthetotalnumberofphotonsintheL-km1354

segment.Theshapeparameter,a,wasdeterminedusingdatacollectedbyMABELand1355

is shown in Figure 3.6. It is possible that themodel of the shape function, or the1356

filtering bounds, will need to be adjusted once ICESat-2/ATLAS is on orbit and1357

collectingdata.1358

1359

Figure 3.6. Shape Parameter for variable window size. 1360

1361

3.2.4 Computedescriptivestatistics1362

Tohelpcharacterizetheinputdataandinitializesomeoftheparametersused1363

inthealgorithm,weemployamovingwindowtocomputedescriptivestatisticson1364

the de-trended data. Themovingwindow’swidth is the smoothing span function1365


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computed in Equation 5 and thewindow slides ¼ of its size to allow of overlap1366

betweenwindows.Bymovingthewindowwithalargeoverlaphelpstoensurethat1367

the approximate ground location is returned. The statistics computed for each1368

windowstepinclude:1369

• Meanheight1370

• Minheight1371

• Maxheight1372

• Standarddeviationofheights1373

1374

Dependentupontheamountofvegetationwithineachwindow,theestimated1375

ground height is estimated using different statistics. A standard deviation of the1376

photon elevations computedwithin eachmovingwindow are used to classify the1377

verticalspreadofphotonsasbelongingtooneoffourclasseswithincreasingamounts1378

ofvariation:open,canopylevel1,canopylevel2,canopylevel3.Thecanopyindices1379

aredefinedinTable3.1.1380

1381

Table 3.1. Standard deviation ranges utilized to qualify the spread of photons within 1382

moving window. 1383

Name Definition LowerLimit UpperLimit

Open Areas with little orno spread in signalphotons determineddue to lowstandarddeviation

N/A Photons fallingwithin1stquartileofStandarddeviation

CanopyLevel1 Areas with smallspread in signalphotons

1stquartile Median


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CanopyLevel2 Areas with amedium amount ofspread

Median 3rdquartile

CanopyLevel3 Areas with highamountofspreadinsignalphotons

3rdquartile N/A

1384

1385

1386

Figure 3.7. Illustration of the standard deviations calculated for each moving window to 1387

identify the amount of spread of signal photons within a given window. 1388

1389

3.2.5 GroundFindingFilter(Iterativemedianfiltering)1390

Acombinationofan iterativemedian filteringandsmoothing filterapproach1391

will be employed to derive the output solution of both the ground and canopy1392

surfaces. The input to this process is the set of de-trended photons. Finding the1393

ground in thepresenceof canopyoftenposesa challengebecauseoften thereare1394

fewergroundphotonsunderneaththecanopy.Thealgorithmadoptedhereusesan1395

iterativemedianfilteringapproachtoretain/eliminatephotonsforgroundfindingin1396


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thepresenceof canopy.Whencanopyexists, a smoothed linewill lay somewhere1397

betweenthecanopytopandtheground.Thisfactisusedtoiterativelylabelpoints1398

abovethesmoothedlineascanopy.Theprocessisrepeatedfivetimestoeliminate1399

canopypointsthatfallabovetheestimatedsurfaceaswellasnoisepointsthatfall1400

belowthegroundsurface.AnexampleofiterativemedianfilteringisshowninFigure1401

3.8.Thefinalmedianfilteredlineisthepreliminarysurfaceestimate.Alimitationof1402

thisapproach,however,isincasesofdensevegetationandfewphotonsreachingthe1403

groundsurface.Intheseinstances,theoutputofthemedianfiltermayliewithinthe1404

canopy.1405

1406

1407 1408

1409Figure 3.8. Three iterations of the ground finding concept for L-km segments with canopy. 1410

1411

4400 4600 4800 5000 5200 5400 5600 5800 6000 6200 64002690

2700

2710

2720

2730

2740

2750

2760

2770

2780

Estimate Lower Bound: Iteration 1

Along-track distance (m)

Elev

atio

n (m

)

Original DataSmoothing InputSmoothed Line

4400 4600 4800 5000 5200 5400 5600 5800 6000 62002690

2700

2710

2720

2730

2740

2750

2760

2770

2780

Estimate Lower Bound: Iteration 2

Along-track Distance (m)

Elev

atio

n (m

)


4600 4800 5000 5200 5400 5600 5800 6000 6200

2700

2710

2720

2730

2740

2750

2760

2770

2780

2790Estimate Lower Bound: Iteration 3

Along-track Distance (m)

Elev

atio

n (m

)



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3.3 TopofCanopyFindingFilter1412

Findingthetopofthecanopysurfaceusesthesamemethodologyasfinding1413

thegroundsurface, exceptnow thede-trendeddataare “flipped”over. The “flip”1414

occursbymultiplyingthephotonsheightsby-1andaddingthemeanofalltheheights1415

backtothedata.Thesameprocedureusedtofindthegroundsurfacecanbeusedto1416

findtheindicesofthetopofcanopypoints.1417

1418

3.4 ClassifyingthePhotons1419

Once a composite groundsurface is determined, photons fallingwithin the1420

point spread function of the surface are labeled as groundphotons.Based on the1421

expectedperformanceofATLAS,thepointspreadfunctionshouldbeapproximately1422

35cmrms.Signalphotonsthatarenotlabeledasgroundandarebelowtheground1423

surface(bufferedwiththepointspreadfunction)areconsiderednoise,butkeepthe1424

signallabel.1425

Thetopofcanopyphotonsthatareidentifiedcanbeusedtogenerateanupper1426

canopysurfacethroughashape-preservingsurfacefittingmethod.Allsignalphotons1427

thatarenotlabeledgroundandlieabovethegroundsurface(bufferedwiththepoint1428

spreadfunction)andbelowtheuppercanopysurfaceareconsideredtobecanopy1429

photons (and thus labeled accordingly). Signal photons that lie above the top of1430

canopysurfaceareconsiderednoise,butkeepthesignallabel. 1431

1432

FLAGS, 0=noise1433

1=ground1434

2=canopy1435

3=TOC(topofcanopy)1436

1437

Thefinalgroundandcanopyclassificationsareflags1–3.Thefullcanopyis1438

thecombinationofflags2and3.1439


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1440

3.5 RefiningthePhotonLabels1441

Duringthefirstiterationofthealgorithm,itispossiblethatsomephotonsare1442

mislabeled;mostlikelythiswouldbenoisephotonsmislabeledascanopy.Toreject1443

thesemislabeledphotons,weapplythreecriteria:1444

a) If top of canopy photons are 2 standard deviations above a1445

smoothedmediantopofcanopysurface1446

b) Iftherearelessthan3canopyindiceswithina15mradius1447

c) If,for500signalphotonsegments,thenumberofcanopyphotons1448

is<5%ofthetotal(whenSNR>1),or<10%ofthetotal(whenSNR1449

<=1).Thisminimumnumberofcanopyindicescriterionimpliesa1450

minimumamountofcanopycoverwithinaregion.1451

There are also instances where the ground points will be redefined. This1452

reassigningofgroundpointsisbasedonhowthefinalgroundsurfaceisdetermined.1453

Following the “iterate” steps in the flowchart shown in Figure 3.4, if there are no1454

canopy indices identified for the L-km segment, the final ground surface is1455

interpolatedfromtheidentifiedgroundphotonsandthenwillundergoafinalround1456

ofmedianfilteringandsmoothing.1457

Ifcanopyphotonsareidentified,thefinalgroundsurfaceisinterpolatedbased1458

uponthelevel/amountofcanopyatthatlocationalongthesegment.Thefinalground1459

surfaceisacompositeofvariousintermediategroundsurfaces,definedthusly:1460

ASmooth heavilysmoothedsurfaceusedtode-trendthesignaldata

Interp_Aground interpolatedgroundsurfacebasedupontheidentifiedground

photons

AgroundSmooth medianfilteredandsmoothedversionofInterp_Aground


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1461

1462

Figure 3.9. Example of the intermediate ground and top of canopy surfaces calculated from 1463

MABEL flight data over Alaska during July 2014. 1464

1465

Duringthefirstroundofgroundsurfacerefinement,wheretherearecanopy1466

photonsidentifiedinthesegment,thegroundsurfaceatthatlocationisdefinedby1467

the smoothed ground surface (AgroundSmooth) value. Else, if there is a location1468

along-trackwherethestandarddeviationoftheground-onlyphotonsisgreaterthan1469

the75%quartileforallsignalphotonstandarddeviations(i.e.,canopylevel3),then1470

thegroundsurfaceatthatlocationisaweightedaveragebetweentheinterpolated1471

groundsurface(Interp_Aground*1/3)andthesmoothedinterpolatedgroundsurface1472

(AgroundSmooth*2/3). For all remaining locations long the segment, the ground1473

surfaceistheaverageoftheinterpolatedgroundsurface(Interp_Aground)andthe1474

heavilysmoothedsurface(Asmooth).1475

The second round of ground surface refinement is simpler than the first.1476

Wheretherearecanopyphotonsidentifiedinthesegment,thegroundsurfaceatthat1477

locationisdefinedbythesmoothedgroundsurface(AgroundSmooth)valueagain.1478


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For all other locations, the ground surface is defined by the interpolated ground1479

surface(Interp_Aground).Thiscompositegroundsurfaceisrunthroughthemedian1480

andsmoothingfiltersagain.1481

Thepseudocodeforthissurfacerefiningprocesscanbefoundinsection4.11.1482

Examples of the ground and canopy photons for several MABEL lines are1483

showninFigures3.10–3.12.1484

1485

Figure 3.10. Example of classified photons from MABEL data collected in Alaska 2014. 1486

Red photons are photons classified as terrain. Green photons are classified as top of canopy. 1487

Canopy photons (shown as blue) are considered as photons lying between the terrain 1488

surface and top of canopy. 1489


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1490





1495


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1496





1501

3.6 CanopyHeightDetermination1502

Once a final ground surface is determined, canopy heights for individual1503

photons are computed by removing the ground surface height for that photon’s1504

latitude/longitude.Theserelativecanopyheightvalueswillbeusedtocomputethe1505

canopystatisticsontheATL08dataproduct.1506

1507

3.7 LinkScaleforDataproducts1508

Thelinkscaleforeachsegmentwithinwhichvaluesforvegetationparameters1509

willbederivedwillbedefinedoverafixeddistanceof100m.Afixedsegmentlength1510

ensuresthatcanopyandterrainmetricsareconsistentbetweensegments,inaddition1511


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toincreasedeaseofuseofthefinalproducts.Asizeof100mwasselectedasitshould1512

provideapproximately140photons(astatisticallysufficientnumber)fromwhichto1513

makethecalculationsforterrainandcanopyheight.1514

1515


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4. ALGORITHMIMPLEMENTATION1516

Prior to running the surface finding algorithms used for ATL08 data products, the 1517

superset of output from the GSFC medium-high confidence classed photons (ATL03 1518

signal_conf_ph: flags 3-4) and the output from DRAGANN will be considered as the input 1519

data set. ATL03 input data requirements include the along-track time, latitude, longitude, 1520

height, and classification for each photon. The motivation behind combining the results 1521

from two different noise filtering methods is to ensure that all of the potential signal 1522

photons for land surfaces will be provided as input to the surface finding software. 1523

Table 4.1. Input parameters to ATL08 classification algorithm. 1524

Name Data Type Long Name

Units Description Source

delta_time DOUBLE GPS elapsed time

seconds Elapsed GPS seconds since start of the granule for a given photon. Use the metadata attribute granule_start_seconds to compute full gps time.

ATL03

lat_ph FLOAT latitude of photon

degrees Latitude of each received photon. Computed from the ECEF Cartesian coordinates of the bounce point.

ATL03

lon_ph FLOAT longitude of photon

degrees Longitude of each received photon. Computed from the ECEF Cartesian coordinates of the bounce point.

ATL03

h_ph FLOAT height of photon

meters Height of each received photon, relative to the WGS-84 ellipsoid.

ATL03

sigma_h FLOAT height uncertainty

m Estimated height uncertainty (1-sigma) for the reference photon.

ATL03

signal_conf_ph

UINT_1_LE

photon signal confidence

counts Confidence level associated with each photon event selected as signal (0-noise. 1- added to allow for buffer but algorithm classifies as background, 2-low, 3-med, 4-high).

ATL03


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segment_id UNIT_32 along-track segment ID number

unitless A seven-digit number uniquely identifying each along-track segment. These are sequential, starting with one for the first segment after an ascending equatorial crossing node.

ATL03

cab_prof FLOAT Calibrated Attenuated Backscatter

unitless Calibrated Attenuated Backscatter from 20 to -1 km with vertical resolution of 30m

ATL09

dem_h FLOAT DEM Height

meters Best available DEM (in priority of GIMP/ANTARCTIC/GMTED/MSS) value at the geolocation point. Height is in meters above the WGS84 Ellipsoid.

ATL09

Landsat tree cover

UINT_8 Landsat Tree Cover Continuous Fields

percentage

Percentage of woody vegetation greater than 5 meters in height across a 30 meter pixel

Global Land Cover Facility (Sexton, 2013)

1525

Table 4.2. Additional external parameters referenced in ATL08 product. 1526

Name Data Type Long Name Units Description Source

atlas_pa Off nadir pointing angle of the spacecraft

ground_track Ground track, as numbered from left to right: 1 = 1L, 2 = 1R, 3 = 2L, 4 = 2R, 5 = 3L, 6 = 3R

dem_h Reference DEM height ANC06

ref_azimuth FLOAT azimuth radians Azimuth of the unit pointing vector for the reference photon in the local ENU frame in radians. The angle is measured from north and positive towards east.

ATL03

ref_elev FLOAT elevation radians Elevation of the unit pointing vector for the reference photon in the local ENU frame in radians. The angle is measured from east-

ATL03


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north plane and positive towards up.

rgt INTEGER_2

reference ground track

unitless The reference ground track (RGT) is the track on the Earth at which a specified unit vector within the observatory is pointed. Under nominal operating conditions, there will be no data collected along the RGT, as the RGT is spanned by GT2L and GT2R. During slews or off-pointing, it is possible that ground tracks may intersect the RGT. The ICESat-2 mission has 1,387 RGTs.

ATL03

sigma_along DOUBLE along-track geolocation uncertainty

meters Estimated Cartesian along-track uncertainty (1-sigma) for the reference photon.

ATL03

sigma_across DOUBLE across-track geolocation uncertainty

meters Estimated Cartesian across-track uncertainty (1-sigma) for the reference photon.

ATL03

surf_type INTEGER_1

surface type unitless Flags describing which surface types this interval is associated with. 0=not type, 1=is type. Order of array is land, ocean, sea ice, land ice, inland water.

ATL03, Section 4

layer_flag Integer Consolidated cloud flag

unitless Flag indicating the presence of clouds or blowing snow with good confidence

ATL09

cloud_flag_asr Integer(3) Cloud probability from ASR

unitless Cloud confidence flag, from 0 to 5, indicating low, med, or high confidence of clear or cloudy sky

ATL09

msw_flag Byte(3) Multiple scattering warning flag

unitless Flag with values from 0 to 5 indicating presence of multiple scattering, which may be due to blowing snow or cloud/aerosol layers.

ATL09

asr Float(3) Apparent surface reflectance

unitless Surface reflectance as modified by atmospheric transmission

ATL09


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snow_ice INTEGER_1

Snow Ice Flag

unitless NOAA snow-ice flag. 0=ice free water; 1=snow free land; 2=snow; 3=ice

ATL09

1527

4.1 Cloudbasedfiltering1528

Itispossibleforthepresenceofcloudstoaffectthenumberofsurfacephoton1529

returnsthroughsignalattenuation,ortocausefalsepositiveclassificationsof1530

groundorcanopyphotonsonlowcloudreturns.Eitherofthesecaseswouldreduce1531

theaccuracyoftheATL08product.ToimprovetheperformanceoftheATL081532

algorithm,ideallyallcloudswouldbeidentifiedpriortoprocessingthroughthe1533

ATL08algorithm.Therewillbeinstances,however,wherelowlyingclouds(e.g.1534

<800mabovethegroundsurface)maybedifficulttoidentify.Currently,ATL081535

providesanATL09derivedcloudflag(layer_flag)onits100mproductand1536

encouragestheusertomakenoteofthepresenceofcloudswhenusingATL081537

output.Unfortunatelyatpresent,areviewofon-orbitdatafromATL03andATL091538

indicatethatthecloudlayerflagisnotbeingsetcorrectlyintheATL09algorithm.1539

Ultimately,thefinalcloudbasedfilteringprocessusedintheATL08algorithmwill1540

mostlikelybederivedfromparameters/flagontheATL09dataproduct.Untilthe1541

ATL09cloudflagsareprovenreliable,however,apreliminarycloudscreening1542

methodispresentedbelow.Thismethodologyutilizesthecalibratedattenuated1543

backscatterontheATL09dataproducttoidentify(andsubsequentlyremovefor1544

processing)cloudsorotherproblematicissues(i.e.incorrectlytelemetered1545

windows).Usingthisnewmethod,telemeteredwindowsidentifiedashavingeither1546

lowornosurfacesignalduetothepresenceofclouds(likelyabovethetelemetered1547

band),aswellasphotonreturnssuspectedtobecloudsinsteadofsurfacereturns,1548

willbeomittedfromtheATL08processing.Thisprocess,however,willnotidentify1549

theextremelylowclouds(i.e.<800m).Thestepsareasfollows:1550

1. MatchuptheATL09calibratedattenuatedbackscatter(cab_prof)columnsto1551

theATL03granulebeingprocessedusingsegmentID.1552


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2. Flipthematchingcab_profverticalcolumnssothattheelevationbinsgo1553

fromlowtohigh.1554

3. ForeachofthematchingATL09cab_profverticalcolumns,performacubic1555

Savitsky-Golaysmoothingfilterwithaspansizeof15verticalbins.Callthis1556

cab_smooth.1557

4. Performthesamesmoothingfilteroneachhorizontalrowofthecab_smooth1558

output,thistimeusingaspansizeof7horizontalbins.Callthis1559

cab_smoother.1560

5. Createalow_signallogicalarraythelengthofthenumberofmatchingATL091561

columnsandsettofalse.1562

6. Foreachcolumnofcab_smoother:1563

a. Setanyvaluesbelow0to0.1564

b. Setalogicalarrayofcab_smootherbinsthatarebelow15kmin1565

elevationtotrue.Callthiscab15.1566

c. UsingtheATL09dem_hvalueforthatcolumn,findtheATL091567

cab_smootherbinsthatare240maboveand240mbelow(~8ATL091568

verticalbinseachdirection)thedem_hvalue.Thebinsfoundherethat1569

arealsowithincab15aredesignatedassfc_bins.1570

d. Findthemaximumpeakvalueofcab_smootherwithinthesfc_bins,if1571

any.Thiswillrepresentthesurfacepeak.1572

e. Findthemaximumvalueofcab_smootherthatishigherinelevation1573

thanthesfc_binsandwithincab15,ifany.Thiswillrepresentthe1574

cloudpeak.1575

f. Ifthereisnosurfacepeak,setthelow_signalflagtotrue.1576

g. Iftherearebothsurfaceandcloudpeakvaluesreturned,determinea1577

surfacepeak/cloudpeakratio.Ifthatratioislessthanorequalto0.4,1578

setlow_signalflagforthatcolumntotrue.1579

7. AftereachmatchingATL09columnofcab_smootherhasbeenanalyzedfor1580

lowsignal,assignthelow_signalflagtoanATL03photonresolutionlogical1581


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arraybymatchinguptheATL03photonsegment_idvaluestotheATL091582

rangeofsegmentIDsforeachATL09cab_profcolumn.1583

8. ForeachATL09cab_profcolumnwherethelow_signalflagwasnotset,check1584

foranyATL03photonsgreaterthan800meters(TBD)inelevationaway1585

(higherorlower)fromtheATL09dem_hvalue.AssignanATL03photon1586

resolutiontoo_far_signalflagtotruewhenthisconditionalismet.1587

9. AlogicalarraymaskiscreatedforanyATL03photonsthathaveeitherthe1588

low_signalflagorthetoo_far_signalflagsettotruesuchthatthosephotons1589

willnotbefurtherprocessedbytheATL08function.1590

1591

4.2 PreparingATL03dataforinputtoATL08algorithm1592

1. BreakupdataintoL-kmsegments.Segmentsequivalentof10kminalong-1593

trackdistanceofanorbitwouldbeappropriate.1594

a. IfthelastportionofanATL03granulebeingprocessedwouldresult1595

inanL-kmsegmentwithlessthan3.4km(170geosegments)worthof1596

data,thatlastportionisaddedtothepreviousL-kmprocessing1597

windowtobeprocessedtogetherasoneextendedL-kmprocessing1598

segment.1599

i. Theresultinglast_seg_extendvaluewouldbereportedasa1600

positivevalueofdistancebeyond10kmthattheATL081601

processingsegmentwasextendedby.1602

b. IfthelastL-kmsegmentwouldbelessthan10kmbutgreaterthan3.41603

km,aportionextendingfromthestartofcurrentL-kmprocessing1604

segmentbackwardsintothepreviousL-kmprocessingsegmentwould1605

beaddedtothecurrentATL08processingsegmenttomakeit10km1606

inlength.Onlynew100mATL08segmentproductsgeneratedfrom1607

thisbackwardextensionwouldbereported.1608


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i. Thedistanceofthisbackwarddatagatheringwouldbe1609

reportedinlast_seg_extendasanegativedistancevalue.1610

c. Allothersegmentsthatarenotextendedwillreportalast_seg_extend1611

valueof0.1612

2. Addabufferof200m(or10segment_id's)tobothendsofeachL-km1613

segment.Thetotalprocessingsegmentlengthis(L-km+2*buffer),butwill1614

bereferredtoasL-kmsegmentsforsimplicity.1615

a. ThefirstL-kmsegmentfromanATL03granulewouldonlyhavea1616

bufferattheend,andthelastL-kmsegmentfromanATL03granule1617

wouldonlyhaveabufferatthebeginning.1618

3. TheinputdataforATL08algorithmisX,Y,Z,T(whereTistime).1619

1620

4.3 NoisefilteringviaDRAGANN1621

DRAGANNwilluseATL03photonswithallsignalclassificationflags(0-4).These1622

willincludebothsignalandnoisephotons.Thissectiongiveabroadoverviewofthe1623

DRAGANNfunction.SeeAppendixAformoredetails.1624

1. Determinetherelativealong-tracktime,ATT,ofeachgeolocatedphoton1625

fromthebeginningofeachL-kmsegment.1626

2. RescaletheATTwithequal-timespacingbetweeneachdataphoton,keeping1627

therelativebeginningandendtimevaluesthesame.1628

3. NormalizetheheightandrescaledATTdatafrom0–1foreachL-km1629

segmentbasedonthemin/maxofeachfield.So,normtime=(time-1630

mintime)/(maxtime-mintime).1631

4. Buildakd-treebasedonnormalizedZandnormalizedandrescaledATT.1632

5. DeterminethesearchradiusstartingwithEquation3.1.P=[determinedby1633

preprocessor;seeSec1.1.1],andVtotal=1.Ntotalisthenumberofphotons1634

withinthedataL-kmsegment.SolveforV.1635

6. NowthatyouknowV,determinetheradiususingEquation3.2.1636


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7. Computethenumberofneighborsforeachphotonusingthissearchradius.1637

8. Generateahistogramoftheneighborcountdistribution.Asillustratedin1638

Figure3.2,thenoisepeakisthefirstpeak(usuallywiththehighest1639

amplitude).1640

9. Determinethe10highestpeaksofthehistogram.1641

10. FitGaussianstothe10highestpeaks.Foreachpeak,1642

a. Computetheamplitude,a,whichislocatedatpeakpositionb.1643

b. Determinethewidth,c,bysteppingonebinatatimeawayfromband1644

findingthelasthistogramvaluethatis>½theamplitude,a.1645

c. UsetheamplitudeandwidthtofitaGaussiantothepeakofthe1646

histogram,asdescribedinEquation3.3.1647

d. SubtracttheGaussianfromthehistogram,andmoveontocalculate1648

thenexthighestpeak’sGaussian.1649

e. RejectGaussiansthataretoonear(<2standarddeviations)and1650

amplitudetoolow(<1/5previousamplitude)fromtheprevious1651

signalGaussian.1652

11. RejectanyofthereturnedGaussianswithimaginarycomponents.1653

12. DetermineifthereisanarrownoiseGaussianatthebeginningofthe1654

histogram.Thesetypicallyoccurwhenthereislittlenoise,suchasduring1655

nighttimepasses.1656

a. SearchfortheGaussianwiththehighestamplitude,a,inthefirst5%1657

ofthehistogram1658

b. Checkifthehighestamplitudeis>=1/10ofthemaximumofall1659

Gaussianamplitudes1660

c. Checkifthewidth,c,oftheGaussianwiththehighestamplitudeis<=1661

4bins1662

d. Ifthesethreeconditionsaremet,savethe[a,b,c]valuesas[a0,b0,c0].1663

e. Ifthethreeconditionsarenotmet,searchagainwithinthefirst10%.1664

Repeattheprocess,incrementingthepercentageofhistogram1665


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searchedby5%upto30%.Assoonastheconditionsaremet,save1666

the[a0,b0,c0]valuesandbreakoutofthepercentagehistogramsearch1667

loop.1668

13. Ifanarrownoisepeakwasfound,sorttheremainingGaussiansfromlargest1669

tosmallestarea,estimatedbya*c,thenappend[a0,b0,c0]tothebeginningof1670

thesorted[a,b,c]arrays.Ifanarrownoisepeakwasnotfound,sortall1671

Gaussiansbylargesttosmallestarea.1672

a. Ifanarrownoisepeakwasnotfound,checkinsortedorderifoneof1673

theGaussiansareinthefirst10%ofthehistogram.Ifso,itbecomes1674

thefirstGaussian.1675

b. RejectanyGaussiansthatarefullycontainedwithinanother.1676

c. RejectGaussianswhosecentersarewithin3standarddeviationsof1677

another,unlessonlytwoGaussiansremain1678

14. IftherearetwoormoreGaussiansremaining,theyarereferredtoas1679

Gaussian1andGaussian2,assumedtobethenoiseandsignalGaussians.1680

15. Determinethethresholdvaluethatwilldefinethecutoffbetweennoiseand1681

signal.1682

a. IftheabsolutedifferenceofthetwoGaussiansbecomesnearzero,1683

definedas<1e-8,setthefirstbinindexwherethatoccurs,pastthe1684

firstGaussianpeaklocation,asthethreshold.Thiswouldtypicallybe1685

setifthetwoGaussiansarefarawayfromeachother.1686

b. Else,thethresholdvalueistheintersectionofthetwoGaussians,1687

whichcanbeestimatedasthefirstbinindexpastthefirstGaussian1688

peaklocationwherethereisaminimumabsolutedifferencebetween1689

thetwoGaussians.1690

c. IfthereisonlyoneGaussian,itisassumedtobethenoiseGaussian,1691

andthethresholdissettob+c.1692

16. Labelallphotonshavinganeighborcountabovethethresholdassignal.1693

17. Labelallphotonshavinganeighborcountbelowthethresholdasnoise.1694


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18. Rejectnoisephotons.1695

19. Retainsignalphotonsforfeedingintonextstepofprocessing.1696

20. UseLogicalORtocombineDRAGANNsignalphotonswithATL03medium-1697

highconfidencesignalphotons(flags3-4)asATL08signalphotons.1698

21. Calculateasignaltonoiseratio(SNR)fortheL-kmsegmentbydividingthe1699

numberofATL08signalphotonsbythenumberofnoise(i.e.,all–signal)1700

photons.1701

4.3.1 PreprocessingtodynamicallydetermineaDRAGANNparameter1702

WhileadefaultvalueofP=20wasfoundtoworkwellwhentestingwithMABEL1703

flightdata,furthertestingwithsimulateddatashowedthatP=20isnotsufficientin1704

casesofveryloworveryhighnoise.AdditionaltestingwithrealATL03datahave1705

shownthegroundsignaltobemuchstronger,andthecanopysignaltobemuch1706

weaker,thanoriginallyanticipated.Therefore,apreprocessingstepfordynamically1707

calculatingPandrunningthecoreDRAGANNfunctionisdescribedinthis1708

subsection.ThisassumesL-kmtobe10km(withadditionalL-kmbuffering).1709

1. DefineaDRAGANNprocessingwindowof170segments(~3.4km),1710

andabufferof10segments(~200m).1711

2. ThebufferisappliedtobothsidesofeachDRAGANNprocessing1712

windowtocreatebufferedDRAGANNprocessingwindows1713

(referencedas“bufferedwindow”fortherestofthissection)thatwill1714

overlaptheDRAGANNprocessingwindowsnexttothem.1715

3. ForeachbufferedwindowwithintheL-kmsegment,calculatea1716

histogramofpointswith1melevationbins.1717

4. Foreachbufferedwindowhistogram,calculatethemediancounts.1718

5. Binswithcountsbelowthebufferedwindowmediancountvalueare1719

estimatedtobenoise.Calculatethemeancountofnoisebins.1720

6. Binswithcountsabovethebufferedwindowmediancountvalueare1721

estimatedtobesignal.Calculatethemeancountofsignalbins.1722


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7. Determinethetimeelapsedoverthebufferedwindow.1723

8. Calculateestimatednoiseandsignalratesforeachbufferedwindow1724

bymultiplyingeachwindow’smeancountsofnoisebinsandsignal1725

bins,determinedfromsteps5and6above,by1/(elapsedtime)to1726

returntheratesintermsofpoints/meter[elevation]/second[across].1727

9. Calculateanoiseratioforeachwindowbydividingthenoiserateby1728

thesignalrate.1729

10. If,forallthebufferedwindowsintheL-kmsegment,thenoiserateis1730

lessthan20andthenoiseratioislessthan0.15;ORanynoiserateis1731

0;ORanysignalrateisgreaterthan1000:re-calculatesteps3-91732

usingtheentireL-kmsegment.Continuewiththefollowingsteps1733

usingresultsfromtheoneL-kmwindow(insteadofmultiplebuffered1734

windows).1735

11. Now,determinetheDRAGANNparameter,P,foreachbuffered1736

windowbasedonthefollowingconditionals:1737

a. IfthesignalrateisNaN(i.e.,aninvalidvalue),setthesignal1738

indexarraytoemptyandmoveontothenextbuffered1739

window.1740

b. Ifnoiserate<20||noiseratio<0.15:1741

P=signalrate1742

Ifsignalrateis<5,P=5;ifsignalrate>20,P=201743

c. ElseP=20.1744

12. RunDRAGANNonthebufferedwindowpointsusingthecalculatedP.1745

13. IfDRAGANNfailstofindasignal(i.e.,onlyoneGaussianfound),run1746

DRAGANNagainwithP=10.1747

14. IfDRAGANNstillfailstofindasignal,trytodeterminePasecondtime1748

usingthefollowingconditionals:1749

a. If(noiserate>=20)…1750

&&(signalrate>100)…1751


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&&(signalrate<250),1752

P=(signalrate)/21753

b. Elseifsignalrate>=250,1754

ifnoiserate>=250,1755

P=(noiserate)*1.11756

else,1757

P=2501758

c. Else,P=mean(noiserate,signalrate)1759

15. RunDRAGANNonthebufferedwindowpointsusingthenewly1760

calculatedP.1761

a. Ifstillnosignalpointsarefound,setadragannErrorflag.1762

16. IfsignalpointswerefoundbyDRAGANN,foreachbufferedwindow1763

calculateasignalcheckbydividingthenumberofsignalpointsfound1764

viaDRAGANNbythenumberoftotalpointsinthebufferedwindow.1765

17. IfdragannErrorhasbeenset,ortherearesuspectsignalstatistics,the1766followingsnippetofpseudocodewillcheckthoseconditionalsandtry1767toiterativelyfindabetterPvaluetorunDRAGANNwith:17681769try_count=017701771WhiledragannError…1772||((noiserate>=30)…1773&&(signalcheck>noiseratio)…1774&&(noiseratio>=0.15))…1775||(signalcheck<0.001):17761777ifP<3,1778break1779else,1780P=P*0.751781end17821783iftry_count<21784ClearoutsignalindexresultsfrompreviousDRAGANNrun1785Re-runDRAGANNwithnewPvalue1786Recalculatethesignalcheck1787


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end17881789ifnosignalindexresultsarereturned1790P=P*0.751791end17921793try_count=try_count+117941795end17961797

18. IfnosignalphotonsarefoundbyDRAGANNbecauseonlyone1798

Gaussianwasfound,setthethresholdasb+c(i.e.,onestandard1799

deviationawayfromtheGaussianpeaklocation)forafinalDRAGANN1800

run.Otherwise,setthesignalindexarraytoemptyandmoveontothe1801

nextbufferedwindow.1802

19. AssignthesignalvaluesfoundfromDRAGANNforeachbuffered1803

windowtotheoriginalDRAGANNprocessingwindowrangeofpoints.1804

20. CombinesignalpointsfromeachDRAGANNprocessingwindowback1805

intooneL-kmarrayofsignalpointsforfurtherprocessing.1806

1807

4.3.2 IterativeDRAGANNprocessing1808

ItispossibleinprocessingsegmentswithhighnoiseratesthatDRAGANNwill1809

incorrectlyidentifyclustersofnoiseassignal.Onewaytoreducethesefalsepositive1810

noiseclustersistorunthealternativeDRAGANNprocess(Sec1.1.1)againwiththe1811

inputbeingthesignaloutputphotonsfromthefirstrunthroughalternative1812

DRAGANN.Notethatthismethodologyisstillbeingtested,sobydefaultthisoption1813

shouldnotbeset.1814

1. IfSNR<1(TBD)fromalternativeDRAGANNrun,runalternativeDRAGANN1815

processagainusingtheoutputsignalphotonsfromfirstDRAGANNrunasthe1816

inputtothesecondDRAGANNrun.1817

2. RecalculateSNRbasedonoutputofsecondDRAGANNrun.1818


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1819

4.4 IsCanopyPresent1820

1. IfL-kmsegmentiswithinanATL08regionencompassingAntarctica(regions1821

7,8,9,10)orGreenland(region11),assumenocanopyispresent:canopy1822

flag=0.Else:1823

2. DeterminethecenterLatitude/LongitudepositionfortheL-kmsegment.1824

3. DeterminethecorrespondingtilefromtheLandsatcontinuouscover1825

product.1826

4. ForeachuniqueXYpositionintheATLASsegment,extractthecanopycover1827

valuefromtheLandsatCCproduct1828

5. ComputetheaveragecanopycovervaluefortheL-kmsegment(basedonthe1829

Landsatvalues).1830

6. Ifcanopycover>5%,setcanopyflag=1(assumescanopyispresent)1831

7. Ifcanopycover<=5%,setcanopyflag=0(assumesnocanopyispresent)1832

1833

4.5 ComputeFilteringWindow1834

1. Nextstepistorunasurfacefilterwithavariablewindowsize(variablein1835

thatitwillchangefromL-kmsegmenttoL-kmsegment).Thewindow-sizeis1836

denotedasWindow.1837

2. 𝑊𝑖𝑛𝑑𝑜𝑤 = 𝑐𝑒𝑖𝑙[5 + 46 ∗ (1 − 𝑒h/∗?,23&+)], wherelengthisthenumberof1838

photonsinthesegment.1839

3. 𝑎 =vwxy[h jz

{z|{}

h<G[[~ ≈ 21𝑥10h�, whereaistheshapeparameterforthewindow1840

span. 1841 1842


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4.6 De-trendData1843

1. TheinputdataarethesignalphotonsidentifiedbyDRAGANNandtheATL031844

classification(signal_conf_ph)valuesof3-4.1845

2. Generatearoughsurfacebyconnectingallunique(time)photonstoeach1846

other.Let’scallthissurfaceinterp_A.1847

3. Runamedianfilterthroughinterp_Ausingthewindowsizesetbythe1848

software.Output=Asmooth.1849

4. DefineareferenceDEMlimit(ref_dem_limit)as120m(TBD).1850

5. RemoveanyAsmoothvaluesfurtherthantheref_dem_limitthresholdfrom1851

thereferenceDEM,andinterpolatetheAsmoothsurfacebasedonthe1852

remainingAsmoothvalues.Theinterpolationmethodtouseistheshape1853

preservingpiecewisecubicHermiteinterpolatingpolynomial–hereafter1854

labeledas“pchip”(Fritsch&Carlson,1980).1855

6. ComputetheapproximatereliefoftheL-kmsegmentusingthe95th-5th1856

percentileheightsofthesignalphotons.WearegoingtofilterAsmoothagain1857

andthesmoothingisafunctionoftherelief.1858

7. DefinetheSmoothSizeusingtheconditionalstatementsbelow.The1859

SmoothSizewillbeusedtodetrendthedataaswellastocreatean1860

interpolatedgroundsurfacelater.1861

SmoothSize=2*Window1862

• Ifrelief>=900,SmoothSize=round(SmoothSize/4)1863

• Ifrelief>=400&&<=900,SmoothSize=round(SmoothSize/3)1864

• Ifrelief>=200&&<=400,SmoothSize=round(SmoothSize/2)1865

8. GreatlysmoothAsmoothbyfirstrunningAsmooth10timesthrougha1866

medianfilterthenasmoothingfilterwithamovingaveragemethodonthe1867

result.Boththemedianfilterandthesmoothingfilteruseawindowsizeof1868

SmoothSize.1869


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1870

4.7 Filteroutliernoisefromsignal1871

1. Ifthereareanysignaldatathatare150metersaboveAsmooth,removethem1872

fromthesignaldataset.1873

2. Ifthestandarddeviationofthedetrendedsignalisgreaterthan10meters,1874

removeanysignalvaluefromthesignaldatasetthatis2timesthestandard1875

deviationofthedetrendedsignalbelowAsmooth.1876

3. CalculateanewAsmoothsurfacebyinterpolating(pchipmethod)asurface1877

fromtheremainingsignalphotonsandmedianfilteringusingtheWindow1878

size,thenmedianfilterandsmooth(movingaveragemethod)10timesagain1879

usingtheSmoothSize.1880

4. Detrendthesignalphotonsbysubtractingthesignalheightvaluesfromthe1881

Asmoothsurfaceheightvalues.Usethedetrendedheightsforsurfacefinding.1882

1883

4.8 Findingtheinitialgroundestimate1884

1. Atthispoint,theinitialsignalphotonshavebeennoisefilteredandde-1885

trendedandshouldhavethefollowingformat:X,Y,detrendedZ,T(T=time).1886

Fromthis,theinputdataintothegroundfindingwillbetheATD(alongtrack1887

distance)metric(suchastime)andthedetrendedZheightvalues.1888

2. DefineamedianSpanasWindow*2/3.1889

3. Identifyingthegroundsurfaceisaniterativeprocess.Startbyassumingthat1890

alltheinputsignalheightphotonsaretheground.Thefirstgoalisthecut1891

outthelowerheightexcessphotonsinordertofindalowerboundfor1892

potentialgroundphotons.Thisprocessisdone5timesandanoffsetof41893

metersissubtractedfromtheresultinglowerbound.Thesmoothingfilter1894

usesamovingaverageagain:1895

forj=1:51896


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cutOff=medianfilter(ground,medianSpan)1897

cutOff=smoothfilter(cutOff,Window)1898

ground=ground((cutOff–ground)>-1)1899

end1900

lowerbound=medianfilter(ground,medianSpan*3)1901

middlebound=smoothfilter(lowerbound,Window)1902

lowerbound=smoothfilter(lowerbound,Window)–41903

end;1904

4. Createalinearlyinterpolatedsurfacealongthelowerboundpointsandonly1905

keepinputphotonsabovethatlineaspotentialgroundpoints:1906

top=input(input>interp(lowerbound))1907

5. Thenextgoalistocutoutexcesshigherelevationphotonsinordertofindan1908

upperboundtothegroundphotons.Thisprocessisdone3timesandan1909

offsetof1meterisaddedtotheresultingupperbound.Thesmoothingfilter1910

usesamovingaverage:1911

forj=1:31912

cutOff=medianfilter(top,medianSpan)1913


top=top((cutOff–top)>-1)1915

end1916

upperbound=medianfilter(top,medianSpan)1917

upperbound=smoothfilter(upperbound,Window)+11918

6. Createalinearlyinterpolatedsurfacealongtheupperboundpointsand1919

extractthepointsbetweentheupperandlowerboundsaspotentialground1920

points:1921

ground=input((input>interp(lowerbound))&…1922

(input<interp(upperbound)))1923


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7. Refinetheextractedgroundpointstocutoutmorecanopy,againusingthe1924

movingaveragesmoothing:1925

Forj=1:21926

cutOff=medianfilter(ground,medianSpan)1927


ground=ground((cutOff–ground)>-1)1929

end1930

8. Runthegroundoutputoncemorethroughamedianfilterusingwindowside1931

medianSpanandasmoothingfilterusingwindowsizeWindow,butthistime1932

withtheSavitzky-Golaymethod.1933

9. Finally,linearlyinterpolateasurfacefromthegroundpoints.1934

10. Thefirstestimateofcanopypointsarethoseindicesofpointsthatare1935

between2and150metersabovetheestimatedgroundsurface.Savethese1936

indicesforthenextsectiononfindingthetopofcanopy.1937

11. Theoutputfromthefinaliterationofgroundpointsistemp_interpA–an1938

interpolatedgroundestimate.1939

12. Findgroundindicesthatliewithin+/-0.5moftemp_interpA.1940

13. Applythegroundindicestotheoriginalheights(i.e.,notthede-trendeddata)1941

tolabelgroundphotons.1942

14. Interpolateagroundsurfaceusingthepchipmethodbasedontheground1943

photons.Outputisinterp_Aground.1944

1945

4.9 Findthetopofthecanopy(ifcanopy_flag=1)1946

1. TheinputaretheATDmetric(i.e.,time),andthede-trendedZvaluesindexed1947

bythecanopyindicesextractedfromstep4.8(10).1948

2. Flipthisdataoversothatwecanfindacanopy“surface”bymultiplyingthe1949

de-trendedcanopyheightsby-1.0andaddingthemean(heights).1950


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3. Findingthetopofcanopyisalsoaniterativeprocess.Followthesamesteps1951

describedin4.8(2)–4.8(9),butusethecanopyindexedandflippedZvalues1952

inplaceofthegroundinput.1953

4. Finalretainedphotonsareconsideredtopofcanopyphotons.Usetheindices1954

ofthesephotonstodefinetopofcanopyphotonsintheoriginal(notde-1955

trended)Zvalues.1956

5. Buildakd-treeoncanopyindices.1957

6. Iftherearelessthanthreecanopyindiceswithina15mradius,reassign1958

thesephotonstonoisephotons.1959

1960

4.10 Computestatisticsonde-trendeddata1961

1. Theinputdatahavebeennoisefilteredandde-trendedandshouldhavethe1962

followinginputformat:X,Y,detrendedZ,T.1963

2. Theinputdatawillcontainsignalphotonsaswellasafewnoisephotons1964

nearthesurface.1965

3. Computestatisticsofheightsinthealong-trackdirectionusingasliding1966

window.Usingthewindowsize(window),computeheightstatisticsforall1967

photonsthatfallwithineachwindow.Theseincludemaxheight,median1968

height,meanheight,minheight,andstandarddeviationofallphotonheights.1969

Additionally,ineachwindowcomputethemedianheightandstandard1970

deviationofjusttheinitiallyclassifiedtopofcanopyphotons,andthe1971

standarddeviationofjusttheinitiallyclassifiedgroundphotonheights.1972

Currentlyonlythemediantopofcanopy,andallSTDvariablesarebeing1973

utilized,butit’spossiblethatotherstatisticsmaybeincorporatedas1974

changes/improvementsaremadetothecode.1975

4. Slidethewindow¼ofthewindowspanandrecomputestatisticsalongthe1976

entireL-kmsegment.Thisresultsinonevalueforeachstatisticforeach1977

window.1978


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5. Determinecanopyindexcategoriesforeachwindowbaseduponthetotal1979

distributionofSTDvaluesforallsignalphotonsalongtheL-kmsegment1980

basedonSTDquartiles.1981

6. OpencanopyhaveSTDvaluesfallingwithinthe1stquartile.1982

7. CanopyLevel1hasSTDvaluesfallingfrom1stquartiletomedianSTDvalue.1983

8. CanopyLevel2hasSTDvaluesfallingfrommedianSTDvalueto3rdquartile.1984

9. CanopyLevel3hasSTDvaluesfallingfrom3rdquartiletomaxSTD.1985

10. LinearlyinterpolatethewindowSTDvalues(bothforallphotonsand1986

ground-onlyphotons)backtothenativealong-trackresolutionandcalculate1987

theinterpolatedall-photonSTDquartilestocreateaninterpolatedcanopy1988

levelindex.Thiswillbeusedlaterforinterpolatingagroundsurface.1989

1990

4.11 RefineGroundEstimates1991

1. Smooththeinterpolatedgroundsurface10times.Allfurthergroundsurface1992

smoothingusethemovingaveragemethod:1993

Forj=1:101994

AgroundSmooth=medianfilter(interp_Aground,SmoothSize*5)1995

AgroundSmooth=smoothfilter(AgroundSmooth,SmoothSize)1996

End1997

1998

2. Thisoutput(AgroundSmooth)fromthefiltering/smoothingfunctionisan1999

intermediategroundsolutionanditwillbeusedtoestimatethefinal2000

solution.2001

3. Iftherearenocanopyindicesidentifiedalongtheentiresegment(OR2002

canopy_flag=0)ANDrelief>400m2003

FINALGROUND=medianfilter(Asmooth,SmoothSize)2004

FINALGROUND=smoothfilter(FINALGROUND,SmoothSize)2005


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Else2006

FINALGROUND=AgroundSmooth2007

end2008

4. Iftherearecanopyindicesidentifiedalongthesegment:2009

Ifthereisacanopyphotonidentifiedatalocationalong-trackabovethe2010

groundsurface,thenatthatlocationalong-track2011

FINALGROUND=AgroundSmooth2012

elseifthereisalocationalong-trackwheretheinterpolatedgroundSTDhas2013

aninterpolatedcanopylevel>=32014

FINALGROUND=Interp_Aground*1/3+AgroundSmooth*2/32015

else2016

FINALGROUND=Interp_Aground*1/2+Asmooth*1/22017

end2018

5. Smooththeresultinginterpolatedgroundsurface(FINALGROUND)once2019

usingamedianfilterwithwindowsizeofSmoothSize,thenasmoothingfilter2020

twicewithwindowsizeofSmoothSize.Selectgroundphotonsthatliewithin2021

thepointspreadfunction(PSF)ofFINALGROUND.2022

6. PSFisdeterminedbysigma_atlas_land(Eq.1.2)calculatedatthephoton2023

resolutionandthresholdedbetween0.5to1m.2024

a. Estimatetheterrainslopebytakingthegradientof2025

FINALGROUND.Gradientisreportedatthecenterof2026

((finalground(n+1)-finalground(n-1))/(dist_x(n+1)-dist_x(n-1))/22027

b. Linearlyinterpolatethesigma_hvaluestothephotonresolution.2028

c. Calculatesigma_topo(Eq.1.3)atthephotonresolution.2029

d. Calculatesigma_atlas_landatthephotonresolutionusingthesigma_h2030

andsigma_topovaluesatthephotonresolution.2031

e. SetPSFequaltosigma_atlas_land.2032


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i. AnyPSF<0.5missetto0.5mastheminimumPSF.2033

ii. AnyPSF>1missetto1masthemaximumPSF.Setpsf_flagto2034

true.2035

2036

4.12 CanopyPhotonFiltering2037

1. Thefirstcanopyfilterwillremovephotonsclassifiedastopofcanopythat2038

aresignificantlyaboveasmoothedmediantopofcanopysurface.To2039

calculatethesmoothedmediantopofcanopysurface:2040

a. Linearlyinterpolatethemedianandstandarddeviationcanopy2041

windowstatistics,calculatedfrom4.10(3),tothetopofcanopy2042

photonresolution.Outputvariables:interpMedianC,interpStdC.2043

b. CalculateacanopywindowsizeusingEq.3.4,wherelength=number2044

oftopofcanopyphotons.Outputvariable:winC.2045

c. Createthemedianfilteredandsmoothedtopofcanopysurface,2046

smoothedC,usingalocallyweightedlinearregressionsmoothing2047

method,“lowess”(Cleveland,1979):2048

smoothedC=medianfilter(interpMedianC,winC)2049

2050

ifSNR>1,canopySmoothSpan=winC*2;2051

else,canopySmoothSpan=smoothSpan;2052

2053

smoothedC=smoothfilter(smoothedC,canopySmoothSpan)2054

d. AddthedetrendedheightsbackintothesmoothedCsurface:2055

smoothedC=smoothedC+Asmooth2056

2. SetcanopyheightthresholdsbasedontheinterpolatedtopofcanopySTD:2057


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IfSNR>1,canopySTDthresh=3;else,canopySTDthresh=2;2058

canopy_height_thresh=canopySTDthresh*interpStdC2059

high_cStd=canopy_height_thresh>102060

low_cStd=canopy_height_thresh<32061

canopy_height_thresh(high_cStd)=2062

canopy_height_thresh(high_cStd)/22063

canopy_height_thresh(low_cStd)=32064

3. RelabelasnoiseanytopofcanopyphotonsthatarehigherthansmoothedC+2065

canopy_height_thresh.2066

4. Next,interpolateatopofcanopysurfaceusingtheremainingtopofcanopy2067

photons(herewearetryingtocreateanupperboundoncanopypoints).The2068

interpolationmethodusedispchip.Thisoutputisnamedinterp_Acanopy.2069

5. Photonsfallingbelowinterp_AcanopyandaboveFINALGROUND+PSFare2070

labeledascanopypoints.2071

6. For500signalphotonsegments,ifnumberofallcanopyphotons(i.e.,canopy2072

andtopofcanopy)is:2073

<5%ofthetotal(whenSNR>1),OR2074

<10%ofthetotal(whenSNR<=1),2075

relabelthecanopyphotonsasnoise.2076

7. Interpolate,usingthepchipmethod,anewtopofcanopysurfacefromthe2077

filteredtopofcanopyphotons.Thisoutputisagainnamedinterp_Acanopy.2078

8. Again,labelphotonsthatliebetweeninterp_Acanopyand2079

FINALGROUND+PSFascanopyphotons.2080

9. Sincethecanopypointshavebeenrelabeled,weneedtodoafinal2081

refinementofthegroundsurface:2082

Ifcanopyispresentatanylocationalong-track2083


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FINALGROUND=AgroundSmooth(atthatlocation)2084

Elseifcanopyisnotpresentatalocationalong-track2085

FINALGROUND=interp_Aground2086

Smooththeresultinginterpolatedgroundsurface(FINALGROUND)once2087

usingamedianfilterwithwindowsizeofSmoothSize,thenamovingaverage2088

smoothingfiltertwicewithwindowsizeofSmoothSize.2089

10. Relabelgroundphotonsbasedonthisnew(andlast)FINALGROUNDsolution2090

+/-arecalculatedPSF(viastepsin4.11(6)).Pointsfallingbelowthebuffer2091

arelabeledasnoise.2092

11. UsingInterp_AcanopyandthislastFINALGROUNDsolution+PSFbuffer,2093

labelallphotonsthatliebetweenthetwoascanopyphotons.2094

12. Repeatthecanopycoverfiltering:For500signalphotonsegments,if2095

numberofallcanopyphotons(i.e.,canopyandtopofcanopy)is:2096

<5%ofthetotal(whenSNR>1),OR2097

<10%ofthetotal(whenSNR<=1),2098

relabelthecanopyphotonsasnoise.Thisisthelastcanopylabelingstep.2099

2100

4.13 ComputeindividualCanopyHeights2101

1. Atthispoint,eachphotonwillhaveitsfinallabelassignedin2102

classed_pc_flag:0=noise,1=ground,2=canopy,3=topofcanopy.2103

2. Foreachindividualphotonlabeledascanopyortopofcanopy,subtracttheZ2104

heightvaluefromtheinterpolatedterrainsurface,FINALGROUND,atthat2105

particularpositioninthealong-trackdirection.2106

3. Therelativeheightforeachindividualcanopyortopofcanopyphotonwill2107

beusedtocalculatecanopyproductsdescribedinSection4.16.Additional2108

canopyproductswillbecalculatedusingtheabsoluteheights,asdescribedin2109


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Section4.16.1.2110

2111

4.14 FinalphotonclassificationQAcheck2112

1. Findanyground,canopy,ortopofcanopyphotonsthathaveelevations2113

furtherthantheref_dem_limitfromthereferenceDEMelevationvalue.2114

Convertthesetothenoiseclassification.2115

2. Findanyrelativeheightsofcanopyortopofcanopyphotonsthataregreater2116

than150mabovetheinterpolatedgroundsurface,FINALGROUND.Convert2117

thesetothenoiseclassification.2118

3. FindanyFINALGROUNDelevationsthatarefurtherthantheref_dem_limit2119

fromthereferenceDEMelevationvalue.ConvertthoseFINALGROUND2120

elevationstoaninvalidvalue,andconvertanyclassifiedphotonsatthesame2121

indicestonoise.2122

4. Ifmorethan50%ofphotonsareremovedinasegment,setph_removal_flag2123

totrue.2124

2125

4.15 ComputesegmentparametersfortheLandProducts2126

1. Foreach100msegment,determinetheclassedphotons(photonsclassified2127

asground,canopy,ortopofcanopy).2128

a. Iftherearefewerthan50classedphotonsina100msegment,donot2129

calculatelandorcanopyproducts.2130

b. Ifthereare50ormoreclassedphotonsina100msegment,extract2131

thegroundphotonstocreatethelandproducts.2132

2. Ifthenumberofgroundphotons>5%ofthetotalnumberofclassedphotons2133

withinthesegment(thiscontrolvalueof5%canbemodifiedonceonorbit):2134

a. Computestatisticsonthegroundphotons:mean,median,min,max,2135

standarddeviation,mode,andskew.Theseheightswillbereported2136


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ontheproductash_te_mean,h_te_median,h_te_min,h_te_max,2137

h_te_mode,andh_te_skewrespectivelydescribedinTable2.1.2138

b. Computethestandarddeviationofthegroundphotonsaboutthe2139

interpolatedterrainsurface,FINALGROUND.Thisvalueisreportedas2140

h_te_stdinTable2.1.2141

c. ComputetheresidualsofthegroundphotonZheightsaboutthe2142

interpolatedterrainsurface,FINALGROUND.Theproductistheroot2143

sumofsquaresofthegroundphotonresidualscombinedwiththe2144

sigma_atlas_landterminTable2.5asdescribedinEquation1.4.This2145

parameterreportedash_te_uncertaintyinTable2.1.2146

d. Computealinearfitonthegroundphotonsandreporttheslope.This2147

parameteristerrain_slopeinTable2.1.2148

e. Calculateabestfitterrainelevationatthemid-pointlocationofthe2149

100msegment:2150

i. Calculateeachterrainphoton’sdistancealong-trackintothe2151

100msegmentusingthecorrespondingATL0320mproducts2152

segment_lengthanddist_ph_along,anddeterminethemid-2153

segmentdistance(expectedtobe50m±0.5m).2154

1. Usethemid-segmentdistancetolinearlyinterpolatea2155

mid-segmenttime(delta_timeinTable2.4).Usethe2156

mid-segmenttimetolinearlyinterpolateothermid-2157

segmentparameters:interpolatedterrainsurface,2158

FINALGROUND,ash_te_interp(Table2.1);latitude2159

andlongitude(Table2.4).2160

ii. Calculatealinearfit,aswellas3rdand4thorderpolynomialfits2161

totheterrainphotonsinthesegment.2162

iii. Createaslope-adjustedandweightedmid-segmentvariable,2163

weightedZ,fromthelinearfit:Useterrain_slopetoapplya2164

slopecorrectiontoeachterrainphotonbysubtractingthe2165


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terrainphotonheightsfromthelinearfit.Determinethemid-2166

segmentlocationofthelinearfit,andaddthatheighttothe2167

slopecorrectedterrainphotons.Applyalinearweightingto2168

eachphotonbasedonitsdistancetothemid-segmentlocation:2169

1/sqrt((photondistancealong–mid-segmentdistance)^2).2170

Calculatetheweightedmid-segmentterrainheight,weightedZ:2171

sum(eachadjustedterrainheight*itsweight)/sum(all2172

weights).2173

iv. Determinewhichofthethreefitsisbestbycalculatingthe2174

meanandstandarddeviationofthefiterrors.Ifoneofthefits2175

hasboththesmallestmeanandstandarddeviations,usethat2176

fit.Else,usethefitwiththesmalleststandarddeviation.If2177

morethanonefithasthesamesmallestmeanand/orstandard2178

deviation,usethefitwiththehigherpolynomial.2179

v. Usethebestfittodefinethemid-segmentelevation.This2180

parameterish_te_best_fitinTable2.1.2181

1. Ifh_te_best_fitisfartherthan3mfromh_te_interp(best2182

fitdiffthreshold),checkif:thereareterrainphotonson2183

bothsidesofthemid-segmentlocation;ortheelevation2184

differencebetweenweightedZandh_te_interpis2185

greaterthanthebestfitdiffthreshold;orthenumberof2186

groundphotonsinthesegmentis<=5%oftotal2187

numberofclassifiedphotonspersegment.Ifanyof2188

thosecasesarepresent,useh_te_interpasthecorrected2189

h_te_best_fit.OtherwiseuseweightedZasthecorrected2190

h_te_best_fit.2191

f. Computethedifferenceofthemediangroundheightfromthe2192

referenceDTMheight.Thisparameterish_dif_refinTable2.4.2193

2194


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3. Ifthenumberofgroundphotonsinthesegment<=5%oftotalnumberof2195

classifiedphotonspersegment,2196

a. Reportaninvalidvalueforterrainproducts:h_te_mean,2197

h_te_median,h_te_min,h_te_max,h_te_mode,h_te_skew,h_te_std,2198

andh_te_uncertaintyrespectivelyasdescribedinTable2.1.2199

b. Ifthenumberofgroundphotonsinthesegmentis<=5%oftotal2200

numberofclassifiedphotonsinthesegment,computeterrain_slope2201

viaalinearfitoftheinterpolatedgroundsurface,FINALGROUND,2202

insteadofthegroundphotons.2203

c. Reportthemid-segmentinterpolatedterrainsurface,FinalGround,as2204

h_te_interpasdescribedinTable2.1,andreporth_te_best_fitasthe2205

h_te_interpvalue.2206

2207

4.16 ComputesegmentparametersfortheCanopyProducts2208

1. Foreach100msegment,determinetheclassedphotons(photonsclassifiedas2209

ground,canopy,ortopofcanopy).2210

a) Iftherearefewerthan50classedphotonsina100msegment,donot2211

calculatelandorcanopyproducts.2212

b) Ifthereare50ormoreclassedphotonsina100msegment,extractall2213

canopyphotons(i.e.,canopyandtopofcanopy;henceforthreferredto2214

as“canopy”unlessotherwisenoted)tocreatethecanopyproducts.2215

2. Onlycomputecanopyheightproductsifthenumberofcanopyphotonsis>2216

5%ofthetotalnumberofclassedphotonswithinthesegment(thiscontrol2217

valueof5%canbemodifiedonceonorbit).2218

a) Ifthenumberofgroundphotons isalso>5%of thetotalnumberof2219

classedphotonswithinthesegment,setcanopy_rh_confto2.2220

b) Ifthenumberofgroundphotonsis<5%ofthetotalnumberofclassed2221

photonswithinthesegment,continuewiththerelativecanopyheight2222

calculations,butsetcanopy_rh_confto1.2223


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c) Ifthenumberofcanopyphotonsis<5%ofthetotalnumberofclassed2224

photons within the segment, regardless of ground percentage, set2225

canopy_rh_confto0andreportaninvalidvalueforeachcanopyheight2226

variable.2227

3. Again, the relative heights (height above the interpolated ground surface,2228

FINALGROUND)havebeencomputedalready.Allparametersderivedinthe2229

sectionarebasedonrelativeheights.2230

4. Sorttheheightsandcomputeacumulativedistributionoftheheights.Select2231

theheightassociatedwiththe98%maximumheight.Thisvalueish_canopy2232

listedinTable2.2.2233

5. Computestatisticsontherelativecanopyheights.Min,Mean,Median,Maxand2234

standard deviation. These values are reported on the product as2235

h_min_canopy, h_mean_canopy, h_max_canopy, and canopy_openness2236

respectivelyinTable2.2.2237

6. Usingthecumulativedistributionofrelativecanopyheights,selecttheheights2238

associatedwiththecanopy_h_metricspercentiledistributions(25,50,60,70,2239

75,80,85,90,95),andreportaslistedinTable2.2.2240

7. Compute the difference between h_canopy and canopy_h_metrics(50). This2241

parameterish_dif_canopyreportedinTable2.2andrepresentsanamountof2242

canopydepth.2243

8. Compute the standarddeviationof allphotons thatwere labeledasTopof2244

Canopy(flag3)inthephotonlabelingportion.Thisvalueisreportedonthe2245

dataproductastoc_roughnesslistedinTable2.2.2246

9. Thequadraticmeanheight,h_canopy_quadiscomputedby2247

𝑞𝑚ℎ = ;∑ +�j

]1/]1/%Z[ 2248

whereNca is the number of canopy photons in the segment and hi are the2249

individualcanopyheights.2250


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2251

4.16.1 CanopyProductscalculatedwithabsoluteheights2252

1. Theabsolutecanopyheightproductsarecalculatedifthenumberofcanopy2253

photonsis>5%ofthetotalnumberofclassedphotonswithinthesegment.2254

Nonumberofgroundphotonsthresholdisappliedforthese.2255

2. Thecentroid_heightparameterinTable2.2isrepresentedbyalltheclassed2256

photonsforthesegment(canopy&ground).Todeterminethecentroid2257

height,computeacumulativedistributionofallabsoluteclassifiedheights2258

andselectthemedianheight.2259

3. Calculateh_canopy_abs,the98thpercentileoftheabsolutecanopyheights.2260

4. Computestatisticsontheabsolutecanopyheights:Min,Mean,Median,and2261

Max.Thesevaluesarereportedontheproductash_min_canopy_abs,2262

h_mean_canopy_abs,andh_max_canopy_abs,respectively,asdescribedin2263

Table2.2.2264

5. Again,usingthecumulativedistributionofabsolutecanopyheights,select2265

theheightsassociatedwiththecanopy_h_metrics_abspercentile2266

distributions(25,50,60,70,75,80,85,90,95),andreportaslistedinTable2267

2.2.2268

4.17 Recordfinalproductwithoutbuffer2269

1. NowthatallproductshavebedeterminedviaprocessingoftheL-km2270

segmentwiththebufferincluded,removetheproductsthatliewithinthe2271

bufferzoneoneachendoftheL-kmsegment.2272

2. RecordthefinalL-kmproductsandmoveontoprocessthenextL-km2273

segment.2274

2275

2276


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5 DATAPRODUCTVALIDATIONSTRATEGY2277

AlthoughtherearenoLevel-1requirementsrelatedtotheaccuracyandprecision2278

oftheATL08dataproducts,wearepresentingamethodologyforvalidatingterrain2279

height, canopy height, and canopy cover once ATL08 data products are created.2280

Parametersfortheterrainandcanopywillbeprovidedatafixedsizeof100malong2281

thegroundtrackreferredtoasasegment.Validationofthedataparametersshould2282

occuratthe100msegmentscaleandresidualsofuncertaintiesarequantified(i.e.2283

averaged)atthe5-kmscale.This5-kmlengthscalewillallowforquantificationof2284

errors and uncertainties at a local scale which should reflect uncertainties as a2285

functionofsurfacetypeandtopography.2286

2287

5.1 ValidationData2288Swathmappingairbornelidaristhepreferredsourceofvalidationdataforthe2289

ICESat-2missionduetothefactthatitiswidelyavailableandtheerrorsassociated2290

with most small-footprint, discrete return data sets are well understood and2291

quantified.Profilingairbornelidarsystems(suchasMABEL)aremorechallengingto2292

useforvalidationduetothelowprobabilityofexactoverlapofflightlinesbetween2293

twoprofilingsystems(e.g.ICESat-2andMABEL).InorderfortheICESat-2validation2294

exercisetobestatisticallyrelevant,theairbornedatashouldmeettherequirements2295

listedinTable5.1.Validationdatasetsshouldpreferablyhaveaminimumaverage2296

pointdensityof5pts/m2. In some instances,however, validationdata setswitha2297

lowerpointdensitythatstillmeettherequirementsinTable5.1maybeutilizedfor2298

validationtoprovidesufficientspatialcoverage.2299

Table 5.1. Airborne lidar data vertical height (Z accuracy) requirements for validation data. 2300

ICESat-2ATL08Parameter Airbornelidar(rms)

Terrainheight <0.3moveropenground(vertical)

<0.5m(horizontal)


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Canopyheight <2mtemperateforest,<3mtropicalforest

Canopycover n/a

2301

Terrainandcanopyheightswillbevalidatedbycomputingtheresidualsbetweenthe2302

ATL08terrainandcanopyheightvalue,respectively,foragiven100msegmentand2303

the terrain height (or canopy height) of the validation data for that same2304

representativedistance.CanopycoverontheATL08dataproductshallbevalidated2305

bycomputingtherelativecanopycover(cc=canopyreturns/totalreturns)forthe2306

samerepresentativedistanceintheairbornelidardata.2307

Itisrecommendedthatthevalidationprocessincludetheuseofancillarydatasets2308

(i.e.Landsat-derivedannualforestchangemaps)toensurethatthevalidationresults2309

arenoterrantlybiasedduetonon-equivalentcontentbetweenthedatasets.2310

Using a synergistic approach, we present two options for acquiring the required2311

validationairbornelidardatasets.2312

2313

Option1:2314

Wewill identifyandutilize freelyavailable,opensourceairbornelidardataas the2315

validation data. Potential repositories of this data include OpenTopo (a NSF2316

repositoryorairbornelidardata),NEON(aNSFrepositoryofecologicalmonitoring2317

in theUnited States), andNASAGSFC (repository ofG-LiHTdata). In addition to2318

small-footprintlidardatasets,NASAMissiondata(i.e.ICESatandGEDI)canalsobe2319

usedinavalidationeffortforlargescalecalculations.2320

2321

Option2:2322


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Option2willincludeOption1aswellastheacquisitionofadditionalairbornelidar2323

datathatwillbenefitmultipleNASAefforts.2324

GEDI:WiththelaunchoftheGlobalEcosystemsDynamicInvestigation2325

(GEDI)missionin2018,therearetremendoussynergisticactivitiesfor2326

datavalidationbetweenboththeICESat-2andGEDImissions.Sincethe2327

GEDI mission, housed on the International Space Station, has a2328

maximumlatitudeof51.6degrees,muchoftheBorealzonewillnotbe2329

mapped byGEDI. The density of GEDI datawill increase as latitude2330

increasesnorthto51.6degrees.SincethedatadensityforGEDIwould2331

be at its highest near 51.6 degrees, we would propose to acquire2332

airborne lidar data in a “GEDI overlap zone” that would ample2333

opportunitytohavesufficientcoverageofbenefittobothICESat-2and2334

GEDIforcalibrationandvalidation.2335

Werecommendtheacquisitionofnewairbornelidarcollectionsthatwillmeetour2336

requirementstobestvalidateICESat-2aswellasbebeneficialfortheGEDImission.2337

Inparticular,wewouldliketoobtaindataoverthefollowingtwoareas:2338

1) Borealforest(asthisforesttypewillNOTbemappedwithGEDI)2339

2) GEDIhighdensityzone(between50to51.6degreesN).Airbornelidardata2340

intheGEDI/ICESat-2overlapzonewillensurecross-calibrationbetween2341

these two critical datasetswhichwill allow for the creation of aglobal,2342

seamless terrain, canopy height, and canopy cover product for the2343

ecosystemcommunity.2344

Inbothcases,wewouldflydatawiththefollowingscenario:2345

Small-footprint,full-waveform,dualwavelength(greenandNIR),highpointdensity2346

(>20pts/m2)and,overlowandhighrelieflocations.Inaddition,thenewlyacquired2347

lidardatamustmeettheerroraccuracieslistedinTable5.1.2348


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Potentialcandidateacquisitionareasinclude:SouthernCanadianRockyMountains2349

(near Banff), Pacific Northwest mountains (Olympic National Park, Mt. Baker-2350

Snoqualmie National Forest), and Sweden/Norway. It is recommended that the2351

airbornelidaracquisitionsoccurduringthesummermonthstoavoidsnowcoverin2352

either2016or2017priortolaunchofICESat-2.2353

2354

5.2 InternalQCMonitoring2355

In addition to the data product validation, internal monitoring of data2356

parameters and variables is required to ensure that the final ATL08 data quality2357

outputistrustworthy.Table5.2listsafewofthecomputedparametersthatshould2358

provide insight into the performance of the surface finding algorithmwithin the2359

ATL08processingchain.2360

Table 5.2. ATL08 parameter monitoring. 2361

Group Description Source Monitor ValidateinField

h_te_median Medianterrainheightforsegment computed Yesagainstairbornelidardata.Theairbornelidardatashouldhaveanabsoluteaccuracyof<30cmrms.

n_te_photonsn_ca_photonsn_toc_photons

Numberofclassed(sumofterrain,canopy,andtopofcanopy)photonsina100msegment

computed Yes.Buildaninternalcounterforthenumberofsegmentsinarow


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wheretherearen’tenoughphotons(currentlyaminimumof50photonsper100msegmentisused)

h_te_interp Interpolatedterrainsurfaceheight,FINALGROUND

computed Differenceh_te_interpandh_te_mediananddetermineifthevalueis>aspecifiedthreshold.2missuggestedasthethresholdvalue.Thisisaninternalchecktoevaluatewhetherthemedianelevationforasegmentisroughlythesameastheinterpolatedsurfaceheight.

h_dif_ref Differencebetweenh_te_medianandref_dem

computed Thisvaluewillbecomputedandflaggedifthedifferenceis>25m.The


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referenceDEMistheonboardDEM.

h_canopy 95%heightofindividualcanopyheightsforsegment

computed Yes,>aspecifiedthreshold(e.g.60m)

Yesagainstairbornelidardata.Thecanopyheightsderivedfromairbornelidardatashouldhavearelativeaccuracy<2mintemperateforest,<3mintropicalforest

h_dif_canopy Differencebetweenh_canopyandcanopy_h_metrics(50)

computed Yes,thisisaninternalchecktomakesurethecalculationsoncanopyheightarenotsuspect

psf_flag FlagissetifcomputedPSFexceeds1m computed Yes,thisisaninternalchecktomakesurethecalculationsarenotsuspect

ph_removal_flag Flagissetifmorethan50%ofclassifiedphotonsinasegmentisremovedduringfinalQAcheck

computed


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dem_removal_flag Flagissetifmorethan20%ofclassifiedphotonsinasegmentisremovedduetoalargedistancefromthereferenceDEM

computed Yes,thiswillcheckifbadresultsareduetobadDEMvaluesorbecausetoomuchnoisewaslabeledassignal

2362


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InadditiontothemonitoringparameterslistedinTable5.2,aplotsuchaswhatis2363

showninFigure5.1wouldbehelpfulforinternalmonitoringandquality2364

assessmentoftheATL08dataproduct.Figure5.1illustratesingraphicalformwhat2365

theinputpointcloudlooklikeinthealong-trackdirection,theclassificationsofeach2366

photon,andtheestimatedgroundsurface(FINALGROUND).2367

2368

Figure 5.1. Example of L-km segment classifications and interpolated ground surface. 2369

2370


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ThefollowingparametersaretobecalculatedandplacedintheQA/QCgrouponthe2371

HDF5datafile,basedonTable5.2oftheATL08ATBD.Statisticsshallbecomputed2372

onaper-granulebasisandreportedonthedataproduct.Ifanyparametermeetsthe2373

QAtriggerconditional,analertwillbesenttotheATL08ATBDteamforproduct2374

review.2375

Table 5.3. QA/QC trending and triggers. 2376

QA/QCtrendingdescription QAtriggerconditional

Percentageofsegmentswith>50classedphotons None

Max,median,andmeanofthenumberofcontiguous

segmentswith<50classedphotons

None

Numberandpercentageofsegmentswithdifferencein

h_te_interp–h_te_medianisgreaterthanaspecified

threshold(2mTBD)

>50segmentsinarow

Max,median,andmeanofh_diff_refoverallsegments None

Percentageofsegmentswhereh_diff_ref>25m Percentage>75%

Percentageofsegmentswheretheh_canopyis>60m None

Max,median,andmeanofh_diff None

NumberandpercentageofLandsatcontinuoustree

coverpixelsperprocessing(L-km)segmentwith

values>100

None

Percentageofsegmentswherepsf_flagisset Percentage>75%


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Percentageofclassifiedphotonsremovedinasegment

duringfinalphotonQAcheck

Percentage>50%

(i.e.,ph_removal_flagis

settotrue)

Percentageofclassifiedphotonsremovedinasegment

duringthereferenceDEMthresholdremovalprocess

Percentage>20%

(i.e.,dem_removal_flagis

settotrue)

2377

2378


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6 REFERENCES2379

2380

Carroll,M.L.,Townshend,J.R.,DiMiceli,C.M.,Noojipady,P.,&Sohlberg,R.A.2381

(2009).Anewglobalrasterwatermaskat250mresolution.InternationalJournalof2382

DigitalEarth,2(4),291–308.http://doi.org/10.1080/175389409029514012383

Channan,S.,K.Collins,andW.R.Emanuel(2014).Globalmosaicsofthestandard2384

MODISlandcovertypedata.UniversityofMarylandandthePacificNorthwest2385

NationalLaboratory,CollegePark,Maryland,USA.2386

Chauve,Adrien,etal.(2008).Processingfull-waveformlidardata:modellingraw2387

signals.Internationalarchivesofphotogrammetry,remotesensingandspatial2388

informationsciences2007,102-107.2389

Cleveland,W.S.(1979).RobustLocallyWeightedRegressionandSmoothing2390

Scatterplots.JournaloftheAmericanStatisticalAssociation,74(368),829–836.2391

http://doi.org/10.2307/22864072392

Friedl,M.A.,D.Sulla-Menashe,B.Tan,A.Schneider,N.Ramankutty,A.SibleyandX.2393

Huang(2010).MODISCollection5globallandcover:Algorithmrefinementsand2394

characterizationofnewdatasets,2001-2012,Collection5.1IGBPLandCover,2395

BostonUniversity,Boston,MA,USA.2396

Fritsch,F.N.,andCarlson,R.E.(1980).MonotonePiecewiseCubicInterpolation.2397

SIAMJournalonNumericalAnalysis,17(2),238–246.2398

http://doi.org/10.1137/07170212399

Goshtasby,A.,andO’Neill,W.D.(1994).CurvefittingbyaSumofGaussians.2400

GraphicalModelsandImageProcessing,56(4),281-288.2401


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GoetzandDubayah(2011).Advancesinremotesensingtechnologyand2402

implicationsformeasuringandmonitoringforestcarbonstocksandchange.Carbon2403

Management,2(3),231-244.doi:10.4155/cmt.11.182404

Hall,F.G.,Bergen,K.,Blair,J.B.,Dubayah,R.,Houghton,R.,Hurtt,G.,Kellndorfer,J.,2405

Lefsky,M.,Ranson,J.,Saatchi,S.,Shugart,H.,Wickland,D.(2011).Characterizing3D2406

vegetationstructurefromspace:Missionrequirements.Remotesensingof2407

environment,115(11),2753-27752408

Harding,D.J.,(2009).Pulsedlaseraltimeterrangingtechniquesandimplicationsfor2409

terrainmapping,inTopographicLaserRangingandScanning:Principlesand2410

Processing,JieShanandCharlesToth,eds.,CRCPress,Taylor&FrancisGroup,173-2411

194.2412

Neuenschwander,A.L.andMagruder,L.A.(2016).Thepotentialimpactofvertical2413

samplinguncertaintyonICESat-2/ATLASterrainandcanopyheightretrievalsfor2414

multipleecosystems.RemoteSensing,8,1039;doi:10.3390/rs81210392415

Neuenschwander,A.L.andPitts,K.(2019).TheATL08LandandVegetationProduct2416

fortheICESat-2Mission.RemoteSensingofEnvironment,221,247-259.2417

https://doi.org/10.1016/j.rse.2018.11.0052418

Neumann,T.,Brenner,A.,Hancock,D.,Robbins,J.,Saba,J.,Harbeck,K.(2018).ICE,2419

CLOUD,andLandElevationSatellite–2(ICESat-2)ProjectAlgorithmTheoretical2420

BasisDocument(ATBD)forGlobalGeolocatedPhotons(ATL03).2421

Olson,D.M.,Dinerstein,E.,Wikramanayake,E.D.,Burgess,N.D.,Powell,G.V.N.,2422

Underwood,E.C.,D'Amico,J.A.,Itoua,I.,Strand,H.E.,Morrison,J.C.,Loucks,C.J.,2423

Allnutt,T.F.,Ricketts,T.H.,Kura,Y.,Lamoreux,J.F.,Wettengel,W.W.,Hedao,P.,2424

Kassem,K.R.(2001).Terrestrialecoregionsoftheworld:anewmapoflifeonEarth.2425

Bioscience,51(11),933-938.2426


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Sexton,J.O.,Song,X.-P.,Feng,M.Noojipady,P.,Anand,A.,Huang,C.,Kim,D.-H.,2427

Collins,K.M.,Channan,S.,DiMiceli,C.,Townshend,J.R.G.(2013).Global,30-m2428

resolutioncontinuousfieldsoftreecover:Landsat-basedrescalingofMODIS2429

VegetationContinuousFieldswithlidar-basedestimationsoferror.International2430

JournalofDigitalEarth,130321031236007.doi:10.1080/17538947.2013.786146.2431

2432


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AppendixA 2433DRAGANNGaussianDeconstruction2434JohnRobbins24352015102124362437UpdatesmadebyKatherinePitts:24382017080824392018121824402441

Introduction2442

ThisdocumentprovidesaverbaldescriptionofhowtheDRAGANN(Differential,2443Regressive,andGaussianAdaptiveNearestNeighbor)filteringsystemdeconstructs2444ahistogramintoGaussiancomponents,whichcanalsobecallediterativelyfittinga2445sumofGaussianCurves.ThepurposeistoprovideenoughdetailforASAStocreate2446operationalICESat-2coderequiredfortheproductionoftheATL08,Landand2447Vegetationproduct.ThisdocumentcoversthefollowingMatlabfunctionswithin2448DRAGANN:2449

• mainGaussian_dragann2450• findpeaks_dragann2451• peakWidth_dragann2452• checkFit_dragann2453

2454

Componentsofthek-dtreenearest-neighborsearchprocessingandhistogram2455creationwerecoveredinthedocument,DRAGANNk-dTreeInvestigations,andhave2456beendeterminedtofunctionconsistentlywithUTexasDRAGANNMatlabsoftware.2457

2458

HistogramCreation2459

Stepstoproduceahistogramofnearest-neighborcountsfromanormalizedphoton2460cloudsegmenthavebeencompletedandconfirmed.FigureA.1providesanexample2461ofsuchahistogram.Thedevelopment,below,isspecifictothetwo-dimensional2462caseandisprovidedasareview.2463

Thehistogramrepresentsthefrequency(count)ofthenumberofnearbyphotons2464withinaspecifiedradius,asascertainedforeachpointwithinthephotoncloud.The2465radius,R,isestablishedbyfirstnormalizingthephotoncloudintime(x-axis)andin2466height(y-axis),i.e.,bothsetsofcoordinates(time&height)runfrom0to1;thenan2467


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averageradiusforfinding20pointsisdeterminedbasedonformingtheratioof202468tothetotalnumberofthephotonsinthecloud(Ntotal):20/Ntotal.2469

2470

2471

FigureA.1.HistogramforMabeldata,channel43fromSE-AKflightonJuly30,20142472at20:16.2473

Giventhatthetotalareaofthenormalizedphotoncloudis,bydefinition,1,thenthis2474ratiogivestheaveragearea,A,inwhichtofind20points.Acorrespondingradiusis2475foundbythesquarerootofA/π.Asingleequationdescribingtheradius,asa2476functionofthetotalnumberofphotonsinthecloud(rememberingthatthisisdone2477inthecloudnormalized,two-dimensionalspace),isgivenby2478

𝑅 = ;<F ]L^LAO⁄�

(A.1)2479

FortheexampleinFigureA.1,Rwasfoundtobe0.00447122.Thenumberof2480photonsfallingintothisradius,ateachpointinthephotoncloud,isgivenalongthe2481x-axis;acountoftheirnumber(orfrequency)isgivenalongthey-axis.2482

2483

GaussianPeakRemoval24842485


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Atthispoint,thefunction,mainGaussian_dragann,iscalled,whichpassesthe2486histogramandthenumberofpeakstodetect(typicallysetto10).2487

Thisfunctionessentiallyestimates(i.e.,fits)asequenceofGaussiancurves,from2488largertosmaller.ItdeterminesaGaussianfitforthehighesthistogrampeak,then2489removesitbeforedeterminingthefitforthenexthighestpeak,etc.Inconcept,the2490processisaniterativesequential-removalofthetenlargestGaussiancomponents2491withinthehistogram.2492

Intheprocessofsequentialleast-squares,parametersarere-estimatedwheninput2493dataisincrementallyincreasedand/orimproved.Thepresentproblemoperatesin2494aslightlyreverseway:thedatasetisfixed(i.e.,thehistogram),butcomponents2495withinthehistogram(independentGaussiancurvefits)areremovedsequentially2496fromthehistogram.ThepaperbyGoshtasby&O’Neill(1994)outlinestheconcepts.2497

RecallthataGaussiancurveistypicallywrittenas2498

𝑦 = 𝑎 ∙ 𝑒𝑥𝑝(−(𝑥 − 𝑏)< 2𝑐<⁄ ) (A.2)2499

wherea=theheightofthepeak;b=positionofthepeak;andc=widthofthebell2500curve.2501

Thefunction,mainGaussian_dragann,computesthe[a,b,c]valuesfortheten2502highestpeaksfoundinthehistogram.Atinitialization,these[a,b,c]valuesaresetto2503zero.Theprocessbeginsbylocatinghistogrampeaksviathefunction,2504findpeaks_dragann.2505

2506

PeakFinding2507

Asinputarguments,thefindpeaks_dragannfunctionreceivesthehistogramanda2508minimumpeaksizeforconsideration(typicallysettozero,whichmeansallpeaks2509willbefound).Anarrayofindexnumbers(i.e.,the“numberofneighboringpoints”,2510valuesalongx-axisofFigureA.1)forallpeaksisreturnedandplacedintothe2511variablepeaks.2512

Themethodologyforlocatingeachpeakgoeslikethis:Thefunctionfirstcomputes2513thederivativesofthehistogram.InMatlabthereisanintrinsicfunction,calleddiff,2514whichcreatesanarrayofthederivatives.Diffessentiallycomputesthedifferences2515alongsequential,neighboringvalues.“Y=diff(X)calculatesdifferencesbetween2516adjacentelementsofX.”[fromMatlabReferenceGuide]Oncethederivativesare2517computed,thenfindpeaks_dragannentersaloopthatlooksforchangesinthesign2518ofthederivative(positivetonegative).Itskipsanyderivativesthatequalzero.2519

Forthekthderivative,the“next”derivativeissettok+1.Atestismadewherebyif2520thek+1derivativeequalszeroandk+1islessthanthetotalnumberofhistogram2521


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values,thenincrement“next”tok+2(i.e.,findthenextnegativederivative).Thetest2522isiterateduntilthestartofthe“downside”ofthepeakisfound(i.e.,theseiterations2523handlecaseswhenthepeakhasaflattoptoit).2524

Whenasignchange(positivetonegative)isfound,thefunctionthencomputesan2525approximateindexlocation(variablemaximum)ofthepeakvia2526

𝑚𝑎𝑥𝑖𝑚𝑢𝑚 = 𝑟𝑜𝑢𝑛𝑑 y2,i&h�<

} + 𝑘 (A.3)2527

Thesevaluesofmaximumareretainedinthepeaksarray(whichcanbegrownin2528Matlab)andreturnedtothefunctionmainGaussian_dragann.2529

Next,backwithinmainGaussian_dragann,therearetwoteststodeterminewhether2530thefirstorlastelementsofthehistogramarepeaks.Thisisdonesincethe2531findpeaks_dragannfunctionwillnotdetectpeaksatthefirstorlastelements,based2532solelyonderivatives.Thetestsare:2533

If(histogram(1)>histogram(2)&&max(histogram)/histogram(1)<20)then2534insertavalueof1totheveryfirstelementofthepeaksarray(again,Matlabcan2535easily“grow”arrays).Here,max(histogram)isthehighestpeakvalueacrossthe2536wholehistogram.2537

Forthecaseofthelasthistogramvalue(saythereareN-bins),wehave2538

If(histogram(N)>histogram(N-1)&&max(histogram)/histogram(N)<4)then2539insertavalueofNtotheverylastelementofthepeaksarray.2540

Onemoretestismadetodeterminewhetherthereanypeakswereactuallyfound2541forthewholehistogram.Ifnonewerefound,thenthefunction,2542mainGaussian_dragann,merelyexits.2543

2544

IdentifyingandProcessingupontheTenHighestPeaks2545

Thefunction,mainGaussian_dragann,nowbeginsalooptoanalyzethetenhighest2546peaks.Itbeginsthenthloop(wherengoesfrom1to10)bysearchingforthelargest2547peakamongallremainingpeaks.Theindexnumber,aswellasthemagnitudeofthe2548peak,areretainedinavariable,calledmaximum,withdimension2.2549

Ineachpassintheloop,the[a,b,c]values(seeeq.2)areretainedasoutputofthe2550function.Thevaluesofaandbaresetequaltotheindexnumberandpeak2551magnitudesavedinmaximum(1)andmaximum(2),respectively.Thec-valueis2552determinedbycallingthefunction,peakWidth_dragann.2553

DeterminationofGaussianCurveWidth2554


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Thefunction,peakWidth_dragann,receivesthewholehistogramandtheindex2555number(maximum(1))ofthepeakforwhichthevaluecisneeded,asarguments.2556Foraspecificpeak,thefunctionessentiallysearchesforthepointonthehistogram2557thatisabout½thesizeofthepeakandthatisfurthestawayfromthepeakbeing2558investigated(leftandrightofthepeak).Ifthetwosides(leftandright)are2559equidistantfromthepeak,thenthesidewiththesmallestvalueischosen(>½2560peak).2561

Uponentry,itfirstinitializesctozero.Thenitinitializestheindexvaluesleft,xLand2562right,xRasindex-1andindex+1,respectively(thesewillbeusedinaloop,2563describedbelow).Itnextcheckswhetherthenthpeakisthefirstorlastvalueinthe2564histogramandtreatsitasaspecialcase.2565

Atinitialization,firstandlasthistogramvaluesaretreatedasfollows:2566

Iffirstbinofhistogram(peak=1),setleft=1andxL=1.2567

Iflastbinofhistogram,setright=mandxR=m,wheremisthefinalindexofthe2568histogram.2569

Next,asearchismadetotheleftofthepeakforanearbyvaluethatissmallerthan2570thepeakvalue,butlargerthanhalfofthepeakvalue.Awhile-loopdoesthis,with2571thefollowingconditions:(a)left>0,(b)histogramvalueatleftis≥halfofhisto2572valueatpeakand(c)histovalueatleftis≤histovalueatpeak.Whenthese2573conditionsarealltrue,thenxLissettoleftandleftisdecrementedby1,sothatthe2574testcanbemadeagain.Whentheconditionsarenolongermet(i.e.,we’vemovedto2575abininthehistogramwherethevaluedropsbelowhalfofthepeakvalue),thenthe2576programbreaksoutofthewhileloop.2577

Thisisfollowedbyasimilarsearchmadeuponvaluestotherightofthepeak.When2578thesetwowhile-loopsarecomplete,wethenhavetheindexnumbersfromthe2579histogramrepresentingbinsthatareabovehalfthepeakvalue.Thisisshownin2580FigureA.2.2581


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2582

FigureA.2.SchematicrepresentationofahistogramshowingxLandxRparameters2583determinedbythefunctionpeakWidth_dragann.2584

Atestismadetodeterminewhichoftheseisfurthestfromthemiddleofthepeak.In2585FigureA.2,xLisfurthestawayandthevariablexissettoequalxL.Thehistogram2586“height”atx,whichwecallVx,isused(aswellasx)inaninversionofEquationA.22587tosolveforc:2588

𝑐 = �h(ih$)j

<v�y��A } (A.4)2589

Thefunction,peakWidth_dragann,nowreturnsthevalueofcandcontrolreturnsto2590thefunction,mainGaussian_dragann.2591

ThemainGaussian_dragannfunctionthenpicks-upwithatestonwhetherthe2592returnedvalueofciszero.Ifso,thenuseavalueof4,whichisbasedonanapriori2593understandingthatcusuallyfallsbetween4and6.Ifthevalueofcisnotzero,then2594add0.5toc.2595

Atthispoint,wehavethe[a,b,c]valuesoftheGaussianforthenthpeak.Basedon2596thesevalues,theGaussiancurveiscomputed(viaEquationA.2)anditisremoved2597(subtracted)fromthecurrenthistogram(andputintoanewvariablecalled2598newWave).2599

AfteraGaussiancurveisremovedfromthecurrenthistogram,thefollowingpeak2600widthcalculationscouldpotentiallyhaveaVxvaluelessthan1froma.Thiswould2601


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causethewidth,c,tobecalculatedasunrealisticallylarge.Therefore,acheckisput2602inplacetodetermineifa-Vx<1.Ifso,Vxissettoavalueofa-1.2603

NumericOptimizationSteps2604

ThefirstoftheoptimizationstepsutilizesaFullWidthHalfMax(FWHM)approach,2605computedvia2606

𝐹𝑊𝐻𝑀 = 2𝑐√2𝑙𝑛2 (A.5)2607

Aleftrange,Lr,iscomputedbyLr=round(b-FWHM/2).Thistestedtomakesureit2608doesn’tgoofftheleftedgeofthehistogram.Ifso,thenitissetto1.2609

Similarly,arightrange,Rr,iscomputedbyRr=round(b+FWHM/2).Thisisalsotested2610tobesurethatitdoesn’tgoofftherightedgeofthehistogram.Ifso,thenitissetto2611theindexvaluefortheright-mostedgeofthehistogram.2612

Usingthesenewrangevalues,createatemporarysegment(betweenLrandRr)of2613thenewWavehistogram,thisiscallederrorWave.Also,setthreedeltaparameters2614forfurtheroptimization:2615

DeltaC=0.05; DeltaB=0.02; DeltaA=12616

Thetemporarysegment,errorWaveispassedtothefunctioncheckFit_dragann,2617alongwithasetofzerovalueshavingthesamenumberofelementsaserrorWave,2618theresult,atthispoint,issavedintoavariablecalledoldError.Thefunction,2619checkFit_dragann,computesthesumofthesquaresofthedifferencebetweentwo2620histogramsegments(inthiscase,errorWaveandzeroswiththesamenumberof2621elementsaserrorWave).Hence,theresult,oldError,isthesumofthesquaresofthe2622valuesoferrorWave.Thisfunctionisappliedinoptimizationloops,torefinethe2623valuesofbandc,describedbelow.2624

Optimizationoftheb-parameter.Thedo-loopoperatesatamaximumof1000times.2625It’spurposeistorefinethevalueofb,in0.02increments.Itincrementsthevalueof2626bbyDeltaB,totheright,andcomputesanewGaussiancurvebasedonb+∆b,which2627isthenremovedfromthehistogramwiththeresultgoingintothevariable2628newWave.Asbefore,checkFit_draganniscalledbypassingtherange-limitedpartof2629newWave(errorWave)andreturninganewestimateoftheerror(newError)which2630isthencheckedagainstoldErrortodeterminewhichissmaller.IfnewErroris≥2631oldError,thenthevalueofbthatproducedoldErrorisretained,andthetestingloop2632isexited.2633

Optimizationofthec-parameter.Nowthevalueofcisoptimized,firsttotheleft,2634thentotheright.Itisperformedindependentlyof,butsimilarly,totheb-parameter,2635usingdo-loopswithamaximumof1000passes.Theseloopsincrement(toright)or2636decrement(toleft)byavalueof0.05(DeltaC)andusecheckFit_dragannto,again,2637


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checkthequalityofthefit.Theloops(rightandleft)kick-outwhenthefitisfoundto2638besmallest.2639

Thefinal,optimizedGaussiancurveisnowremoved(subtracted)fromthe2640histogram.Afterremoval,astatement“corrects”anyhistogramvaluesthatmay2641dropbelowzero,bysettingthemtozero.Thiscouldhappenduetoanymis-fitofthe2642Gaussian.2643

Thenthloopisconcludedbyexaminingthepeaksremaininginthehistogram2644withoutthepeakjustprocessedbysendingthenth-residualhistogrambackintothe2645functionfindpeaks_dragann.Ifthereturnofpeakindexnumbersfrom2646findpeaks_dragannrevealsmorethan1peakremaining,thentheindexnumbersfor2647peaksthatmeetthesethreecriteriaareretainedinanarrayvariablecalledthese:2648

1. Thepeakmustbelocatedaboveb(n)-2*c(n),and26492. Thepeakmustbelocatedbelowb(n)+2*c(n),and26503. Theheightofthepeakmustbe<a(n)/5.2651

2652

Thepeaksmeetingallthreeofthesecriteriaaretobeeliminatedfromfurther2653consideration.Whatthisaccomplishesiseliminatethenearbypeaksthathaveasize2654lowerthanthepeakjustpreviouslyanalyzed;thus,aftertheirelimination,only2655leavingpeaksthatarefurtherawayfromthepeakjustprocessedandare2656presumably“real”peaks.Thenthiterationendshere,andprocessingbeginswiththe2657revisedhistogram(afterhavingremovedthepeakjustanalyzed).2658

2659

GaussianRejection2660

ThefunctionmainGaussian_dragannreturnsthe[a,b,c]parametersfortheten2661highestpeaksfromtheoriginalhistogram.Theremainingcodeindragannexamines2662eachofthetenGaussianpeaksandeliminatestheonesthatfailtomeetavarietyof2663conditions.Thissectiondetailshowthisisaccomplished.2664

First,anapproximatearea,area1=a*c,iscomputedforeachfoundpeakandb,forall2665tenpeaks,beingtheindexofthepeaks,areconvertedtoanactualvaluevia2666b+min(numptsinrad)-1(callthisallb).2667

Next,arejectionismadeforallpeaksthathaveanycomponentof[a,b,c]thatare2668imaginary(Matlabisrealfunctionisusedtoconfirmthatallthreecomponentsare2669real,inwhichcaseitpasses).2670

Tocheckforanarrownoisepeakatthebeginningofthehistogramincasesoflow2671noiserates,suchasduringnighttimepasses,acheckismadetofirstdetermineifthe2672highestGaussianamplitude,a,withinthefirst5%ofthehistogramis>=1/10*the2673


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maximumamplitudeofallGaussians.Ifso,thatpeak’sGaussianwidth,c,ischecked2674todetermineifitis<=4bins.Ifneitherofthoseconditionsaremetinthefirst5%,2675theconditionsarerecheckedforthefirst10%ofthehistogram.Thisprocessis2676repeatedupto30%ofthehistogram,in5%intervals.Onceanarrownoisepeakis2677found,theprocessbreaksoutoftheincremental5%histogramchecks,andthe2678noisepeakvaluesarereturnedas[a0,b0,c0].2679

Ifanarrownoisepeakwasfound,theremainingpeakareavalues,area1(a*c),then2680passthroughadescendingsort;ifnonarrownoisepeakwasfound,allpeakareasgo2681throughthedescendingsort.Sonow,the[a,allb,c]-valuesaresortedfromlargest2682“area”tosmallest,theseareplacedinarrays[a1,b1,c1].Ifanarrownoisepeakwas2683found,itisthenappendedtothebeginningofthe[a1,b1,c1]arrays,suchthata1=2684[a0a1],b1=[b0b1],c1=[c0c1].2685

Inthecasethatanarrownoisepeakwasnotfound,atestismadetocheckthatat2686leastoneofthepeaksiswithinthefirst10%ofthewholehistogram.Itisdone2687insidealoopthatworksfrompeak1tothenumberofpeaksleftatthispoint.This2688loopfirsttestswhetherthefirst(sorted)peakiswithinthefirst10%ofthe2689histogram;ifso,thenitsimplykicksoutoftheloop.Ifnot,thenitplacestheloop’s2690currentpeakintoaholder(ihold)variable,incrementsthelooptothenextpeakand2691runsthesametestonthesecondpeak,etc.Here’saMatlabcodesnippet:2692

inds = 1:length(a1); 2693for i = 1:length(b1) 2694 if b1(i) <= min(numptsinrad) + 1/10*max(numptsinrad) 2695 if i==1 2696 break; 2697 end 2698 ihold = inds(i); 2699 for j = i:-1:2 2700 inds(j) = inds(j-1); 2701 end 2702 inds(1) = ihold; 2703 break 2704 end 2705end 2706

2707

Thej-loopexpressiongivestheinit_val:step_val:final_val.Thesemi-colonattheend2708ofstatementscausesMatlabtoexecutetheexpressionwithoutprintouttotheuser’s2709screen.Whenthisloopiscomplete,thentheindexes(inds)arere-orderedand2710placedbackintothe[a1,b1,c1]andarea1arrays.2711

Next,areteststorejectanyGaussianpeakthatisentirelyencompassedbyanother2712peak.AMatlabcodesnippethelpstodescribetheprocessing.2713

% reject any gaussian if it is fully contained within another 2714isR = true(1,length(a1)); 2715for i = 1:length(a1) 2716 ai = a1(i); 2717


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bi = b1(i); 2718 ci = c1(i); 2719 aset = (1-(c1/ci).^2); 2720 bset = ((c1/ci).^2*2*bi - 2*b1); 2721 cset = -(2*c1.^2.*log(a1/ai)-b1.^2+(c1/ci).^2*bi^2); 2722 realset = (bset.^2 - 4*aset.*cset >= 0) | (a1 > ai); 2723 isR = isR & realset; 2724end 2725a2 = a1(isR); 2726b2 = b1(isR); 2727c2 = c1(isR); 2728

2729

ThelogicalarrayisRisinitializedtoallbetrue.Thei-do-loopwillrunthroughall2730peaks.Thecomputationsaredoneinarrayformwiththevariablesaset,bset,csetall2731beingarraysoflength(a1).Atthebottomoftheloop,isRremains“true”when2732eitheroftheconditionsintheexpressionforrealsetismet(thesingle“|”isalogical2733“or”).Also,thenomenclature,“.*”and“.^”,denoteelement-by-elementarray2734operations(notmatrixoperations).Uponexitingthei-loop,thearrayvariables2735[a2,b2,c2]aresettothe[a1,b1,c1]thatremainas“true.”[Atthispoint,inourtest2736casefromchannel43ofEast-AKMableflighton20140730@20:16,sixpeaksare2737stillretained:18,433,252,33,44.4and54.]2738

Next,rejectGaussianpeakswhosecenterslaywithin3σofanotherpeak,unlessonly2739twopeaksremain.Thecodesnippetlookslikethis:2740

isR = true(1, length(a2)); 2741for i = 1:length(a2) 2742 ai = a2(i); 2743 bi = b2(i); 2744 ci = c2(i); 2745 realset = (b2 > bi+3*ci | b2 < bi-3*ci | b2 == bi); 2746 realset = realset | a2 > ai; 2747 isR = isR & realset; 2748end 2749if length(a2) == 2 2750 isR = true(1, 2); 2751end 2752a3 = a2(isR); 2753b3 = b2(isR); 2754c3 = c2(isR); 2755

2756

Onceagain,theisRarrayisinitiallysetto“true.”Now,thearray,realset,istested2757twice.Inthefirstline,oneofthreeconditionsmustbetrue.Inthesecondline,if2758realsetistrueora2>ai,thenitremainstrue.Atthispoint,we’vepareddown,from2759tenGaussianpeaks,totwoGaussianpeaks;onerepresentsthenoisepartofthe2760histogram;theotherrepresentsthesignalpart.2761

Iftherearelessthantwopeaksleft,athresholding/histogramerrormessageis2762printedout.IfthelastTryFlagisnotset,DRAGANNendsitsprocessingandanempty2763IDXvalueisreturned.ThelastTryFlagissetinthepreprocessingfunctionwhich2764


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callsDRAGANN,asmultipleDRAGANNrunsmaybetrieduntilsufficientsignalis2765found.2766

Iftherearetwopeaksleft,thensetthearray[a,b,c]tothosetwopeaks.[Atthis2767point,inourtestcasefromchannel43ofEast-AKMableflighton20140730@276820:16,thetwopeaksare:18and433.]2769

2770

GaussianThresholding2771

WiththetwoGaussianpeaksidentifiedasnoiseandsignal,allthatisleftisto2772computethethresholdvaluebetweentheGaussians.2773

Anarrayofxvalsisestablishedrunningfrommin(numptsinrad)to2774max(numptsinrad).Inourexample,xvalshasindicesbetween0and653.Foreach2775ofthesexvals,Gaussiancurves(allGauss)arecomputedforthetwoGaussianpeaks2776[a,b,c]determinedattheendoftheprevioussection.Thiscomputationisperformed2777viaafunctioncalledgaussmakerwhichreceives,asinput,thexvalsarrayandthe2778[a,b,c]parametersforthetwoGaussiancurves.AnarrayofheightsoftheGaussian2779curvesisreturnedbythefunction,computedwithEquationA.2.InMatlab,the2780allGaussarrayhasdimension2x654.Anarray,noiseGaussissettobeequaltothe27811stcolumnofallGauss.2782

Anif-statementcheckswhetherthebarrayhasmorethan1element(i.e.,consisting2783oftwopeaks),ifso,thennextGaussissettothe2ndcolumnofallGauss,anda2784difference,noiseGauss-nextGauss,iscomputed.2785

Thefollowingstepsarerestrictedtobebetweenthetwomainpeaks.First,thefirst2786indexoftheabsolutevalueofthedifferencethatisnear-zero(definedas1e-8)is2787found,ifitexists,andputintothevariablediffNearZero.Thisisexpectedtobefound2788ifthetwoGaussiansarefarawayfromeachotherinthehistogram.2789

Second,thepoint(i.e.,index)isfoundoftheminimumoftheabsolutevalueofthe2790difference;thisindexisputintovariable,signchanges.Thispointiswherethesign2791changesfrompositivetonegativeasonemovesleft-to-right,uptheGaussiancurve2792differences(noiseminusnextwillbepositiveunderthepeakofthenoisecurve,and2793negativeunderthenext(signal)curve).FigureA.3(top)showsthetwoGaussian2794curves.Thebottomplotshowstheirdifferences.2795


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2796

FigureA.3.Top:tworemainingGaussiancurvesrepresentingthenoise(blue)and2797signal(red)portionsofthehistograminF1gureA.1.Bottom:differencenoise–2798signalofthetwoGaussiancurves.Thethresholdisdefinedasthepointwherethe2799signofthedifferenceschange.2800

IfthereisanyvaluestoredindiffNearZero,thatvalueisnowsavedintothevariable2801threshNN.Else,thevalueofthethresholdinsignchangesissavedintothreshNN,2802concludingtheif-statementforbhavingmorethan1element.2803

0

200

400

Gauss

ian V

alu

e

0 100 200 300 400 500 600

number of points inside radius

Noise GaussianSignal Gaussian

−200

0

200

400

Gauss

ian D

iffere

nce

s

0 100 200 300 400 500 600

number of points inside radius

Threshold


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Anelseclause(b!>1),merelysetsthreshNNtob+c,i.e.,1-standarddeviationaway2804frommeanofthe(presumably)noisepeak.2805

Thefinalstepismaskthesignalpartofthehistogramwhereallindicesabovethe2806threshNNindexaresettological1(true).Thisisappliedtothenumptsinradarray,2807whichrepresentsthephotoncloud.Afterapplication,dragannreturnsthecloud2808withpointsinthecloudidentifiedas“signal”points.2809

TheMatlabcodehasafewdebugstatementsthatfollow,alongwithabout40lines2810forplotting.2811

2812

References2813

Goshtasby,A&W.D.O’Neill,CurveFittingbyaSumofGaussians,CVGIP:Graphical2814ModelsandImageProcessing,V.56,No.4,281-288,1994.2815

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