DMRT-ML Studies on

Remote Sensing of Ice Sheet Subsurface Temperatures

Mustafa Aksoy and Joel T. Johnson02/25/2014

DMRT-ML• Dense Media Radiative Transfer Multi-Layer (DMRT-ML):

A Physically based numerical model designed to compute the thermal microwave emission of a given snowpack (Picard et al, Geosci. Model Dev. Discuss. 2012)

Snow/Ice medium is assumed to be a stack of plane-parallel layers containing of isotropic/homogeneous background material containing spherical particle inhomogeneities

Scattering and Extinction coefficients are computed as a function of particle radius and medium density (density determines fractional volume for air/ice mixture)

Finally Radiative Transfer Equation is solved numerically using Discrete Ordinate Method (DISORT)

DMRT-ML• DMRT-ML Method has been validated with External Data

Optical Radius of the particles (Grain Size) should be multiplied by 2.8-3.5 to be suitable as DMRT-ML input. For example, for a study where the actual grain size is 1mm, 3mm should be entered in DMRT-ML simulations.

• DMRT-ML inputs:Thickness of each layerDensity in each layer (determines fractional volume of scatterers)Grain size in each layerTemperatrure in each layerStickiness in each layer (not used here)Medium type in each layer (ice or air treated as background)Particle distribution type in each layer (using mono-disperse default)Basal Layer material (soil with given soil moisture, fixed epsilon, or ice plus rough or flat)Downwelling Tb due to AtmosphereRadiometer frequency

• DMRT-ML outputs:Brightness temperature as a function of angle and polarization

Theory• Temperature Profile Model (Jezek et al, submitted to TGRS):

Z=H (total thickness) at surface and 0 at base of glacierM=surface accumulation rate

We can simplify the Model by defining new parameters:

Simplified Model:

1

2

Hk

ML

d ck

GLC2

L

zerfC

L

HerfCTzT s

Theory

• Density Model (Drinkwater paper, Annals of Glaciology, 2004) in kg/m^3

(note z=0 at surface in above equation: lower density at surface increasing with depth)

• Ice Dielectric Constant Model (DMRT-ML default):Matzler&Wegmuller

• Grain Size Model (Prof Jezek’s suggestions):A=0.25+0.75*z/10; % mm (z=0 at surface and in meters)A(z>10)=1; % These are now air pores of 1 mm sizeA(z>100)=0; % No scattering at depths > 100 m

ze 0165.0564.0916.01000

DMRT-ML SimulationsAssumptions

• Ice Temperature Profile: Jezek Formula with different L,C and H values• Surface Temperature: 216oK (-57oC)• Incidence Angle: Normal Incidence• Layer Thickness: 10m• Basal Layer: Flat soil with temperature equal to the temperature of the deepest

layer• Frequency: 100MHz-3GHz • Stickiness: Ice is assumed to be non-sticky• Medium Type: Ice in air for density<458.5kg/m-3, air bubbles in ice for higher

density• Atmospheric Effect: Ignored• Particle Distribution: Default DMRT-ML choice. Mono-disperse distribution.

DMRT-ML SimulationsChange in Ice Parameters (Ice Thickness)

• Fixed M and Grain Size– M = 4cm/yr– Grain size = 1mm

• Other parameters are as given in the assumptions.

• Ice Thickness matters mostly for lower frequencies.

• At high frequencies only upper part of the ice sheet is observed. 0 500 1000 1500 2000 2500 3000

210

215

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245

Frequency(MHz)

Tb(

K)

Tb vs Freq

H=1.5km

H=2kmH=2.5km

H=3km

DMRT-ML SimulationsChange in Ice Parameters (Accumulation Rate)

0 500 1000 1500 2000 2500 3000170

180

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220

230

240

250

Frequency(MHz)

Tb(

K)

Tb vs Freq

L=1km (M=27cm/yr)

L=2km (M=7cm/yr)

L=3km (M=3cm/yr)L=4km (M=2cm/yr)

L=3km (M=1cm/yr)

• Fixed H and Grain Size and changed L

– H = 3000m– Grain size = 3mm

• Other parameters are as given in the assumptions.

• Accumulation rate also matters only for lower frequencies.

• Temperature change due to accumulation rate is low at upper layers.

DMRT-ML SimulationsChange in Ice Parameters (Grain Size)

0 500 1000 1500 2000 2500 3000120

140

160

180

200

220

240

260

Frequency(MHz)

Tb(

K)

Tb vs Freq

GS=0mmGS=1mm

GS=2mm

GS=3mm

GS=4mmGS=5mm

• Fixed H and L– H = 3000 m– L = 3000 m

• Other parameters are as given in the assumptions.

• Grain size doesn’t matter too much below 1GHz.

• λ = 30 cm at 1GHz

DMRT-ML SimulationsContribution of Layers to the Surface Tb

It is possible to approximatelycompute the contribution ofupper n layer to the surfacebrightness temperature bysetting physical temperaturezero at other layers.

At lower frequencies almost alllayers contribute. However forhigher frequencies only upperlayers contribute.

0 50 100 150 200 250

0

500

1000

1500

2000

2500

3000

3500

4000

Cummulative Tb (K)

Dep

th (

m)

M=1cm/year

f=0.5GHzf=0.75GHz

f=1GHz

f=1.25GHz

f=1.5GHz

f=1.75GHzf=2GHz

DMRT-ML SimulationsContribution of Ice Sheet and the Basal Layer

Similarly contribution of the Ice sheet andthe basal layer can be separated.

As frequency increases contribution of thebase diminishes as expected.

Also when the accumulation rate, so theaverage physical temperature increasescontribution of base decreases due toincreased absorption.

228 230 232 234 236 238 240 242 2440

10

20

30

40

50

60

70

Avg Physical Temp (K)

Con

trib

utio

n of

Bas

e (K

)

f=0.5GHz

f=1GHz

f=1.5GHz

f=2GHz

228 230 232 234 236 238 240 242 244160

170

180

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200

210

220

230

240

250

Avg Physical Temp (K)

Con

trib

utio

n of

Ice

(K

)

f=0.5GHz

f=1GHzf=1.5GHz

f=2GHz

DMRT-ML SimulationsRetrieval Studies

• DMRT-ML was run for ~1000 different temperature profile cases changing H,L,C and Grain Size for 100MHz-3GHz frequency band.

H= [1km 1.5km 2km 2.5km 3km]L = [1km 2km 2,5km 3km 3.5km 4km 5km]GS = [0mm 1mm 2mm 3mm 4mm 5mm]C = [0.8 0.9 1 1.1 1.2]xCassumed

• Other Parameters were kept constant as assumed.• ~1000 Tb vs Freq profile were obtained.

• Retrieval1. Take each Tb vs freq profile2. Distort it with a noise N~N(0,1)3. Among original profiles search for the closest one (LSE) to the distorted profile and set it as the

retrieved profile.4. Go back to step 2 and repeat it 100 times (100 trial for each Tb vs freq profile)5. Go back to step 1 and move to the next Tb vs freq profile

DMRT-ML SimulationsRetrieval Studies

• Average Correct Retrieval Percentage 81.17%

• This percentage becomes lower when ice thickness is small and L is large.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

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60

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90

100

% of correct retrieval

# of

cas

es (

out

of 9

85)

% of correct retrieval

DMRT-ML SimulationsRetrieval Studies

• Retrieved physical temperature profiles can be used to calculate the error at temperatures at 10m depth and error in average ice physical temperatures.

• Error at 10m depth– Max=0.07K, Mean=0.00013K, Std=0.0065K (but not much variation among the profile set in 10

m depth temperatures due to fixed surface temperature, std of temperatures at 10m is

0.055K for this 985 cases)

• Error at in Average Physical Temperature– Max=4.69K, Mean=0.0019K, Std=0.34K– Larger errors when Ice thickness increases

10 20 30 40 50 60 70 80 90 100

100

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900

trial

Pro

file

no

Abs Error at 10m

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

10 20 30 40 50 60 70 80 90 100

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900

trial

Pro

file

no

Abs Error in Average Temperature

0.5

1

1.5

2

2.5

3

3.5

4

4.5

DMRT-ML SimulationsRetrieval Studies

• RMS error vs depth can be calculated by averaging error vs depth for all 985x100 cases.

• If the retrieval algorithm guesses the ice thickness wrong, fixed soil temperature (temperature of the last ice layer) of the thinner ice was compared with the extra layers of the thicker ice.

0 500 1000 1500 2000 25000

0.1

0.2

0.3

0.4

0.5

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0.9

depth (m)

RM

S e

rror

Thanks