Meteorology 415Meteorology 415

October 2010October 2010

Numerical GuidanceNumerical Guidance

Skill dependent on:Skill dependent on: Initial ConditionsInitial Conditions ResolutionResolution Model PhysicsModel Physics ParameterizationParameterization Computational PowerComputational Power Boundary valuesBoundary values

Statistical GuidanceStatistical Guidance

There are several techniques that may be used beside multiple There are several techniques that may be used beside multiple linear regression to generate statistical relationships between linear regression to generate statistical relationships between predictor and predictand. These includepredictor and predictand. These include

Kalman FiltersKalman Filters

Neural NetworksNeural Networks

Artificial IntelligenceArtificial Intelligence

Fuzzy Logic Fuzzy Logic

Remember that Poor Model Performance translates into Poor Remember that Poor Model Performance translates into Poor MOS GuidanceMOS Guidance

Numerical GuidanceNumerical Guidance

Perfect Prog TechniquePerfect Prog Technique

The development of a Perfect-Prog can The development of a Perfect-Prog can make use of the NCEP reanalysis make use of the NCEP reanalysis database which provides long and database which provides long and stable time series of atmospheric stable time series of atmospheric analyses, which are necessary for analyses, which are necessary for building reliable regression building reliable regression equations equations based solelybased solely on past on past observations.observations.

OutlineOutline

MOS BasicsMOS BasicsWhat is MOS? What is MOS? MOS PropertiesMOS PropertiesPredictand DefinitionsPredictand DefinitionsEquation DevelopmentEquation DevelopmentGuidance post-processingGuidance post-processingMOS IssuesMOS Issues

Future WorkFuture WorkNew Packages - UMOS (Canadian)New Packages - UMOS (Canadian)Gridded MOSGridded MOS

Model Output Statistics (MOS)Model Output Statistics (MOS)MOS relates observations of the MOS relates observations of the weather element to be predicted weather element to be predicted ((PREDICTANDSPREDICTANDS) to appropriate variables ) to appropriate variables ((PREDICTORSPREDICTORS) via a statistical method) via a statistical method

Predictors can include:Predictors can include: NWP model output interpolated to NWP model output interpolated to observing siteobserving site Prior observationsPrior observations Geoclimatic data – terrain, normals, Geoclimatic data – terrain, normals, lat/lon, etc.lat/lon, etc.Current statistical method: Multiple Current statistical method: Multiple Linear Regression (forward selection)Linear Regression (forward selection)

MOS PropertiesMOS Properties Mathematically simple, yet powerful Mathematically simple, yet powerful techniquetechnique Produces probability forecasts from a Produces probability forecasts from a single run of the underlying NWP model single run of the underlying NWP model outputoutput Can use other mathematical approaches Can use other mathematical approaches such as logistic regression or neural such as logistic regression or neural networksnetworks Can develop guidance for elements Can develop guidance for elements not directly forecast by models; e.g. not directly forecast by models; e.g. thunderstormsthunderstorms

MOS Guidance ProductionMOS Guidance Production1.1. Model runs on NCEP IBM mainframeModel runs on NCEP IBM mainframe

2.2. Predictors are collected from model Predictors are collected from model fields, “constants” files, etc.fields, “constants” files, etc.

3.3. Equations are evaluatedEquations are evaluated

4.4. Guidance is post-processedGuidance is post-processed Checks are made for meteorological and Checks are made for meteorological and

statistical consistencystatistical consistency Categorical forecasts are generatedCategorical forecasts are generated

5.5. Final products disseminated to the Final products disseminated to the worldworld

MOS GuidanceMOS Guidance GFS (MAV) 4 times daily GFS (MAV) 4 times daily (00,06,12,18Z)(00,06,12,18Z) GFS Ext. (MEX) once daily (00Z)GFS Ext. (MEX) once daily (00Z) Eta/NAM (MET) 2 times daily Eta/NAM (MET) 2 times daily (00,12Z)(00,12Z) Variety of formats: text bulletins, Variety of formats: text bulletins, GRIB and BUFR messages, GRIB and BUFR messages, graphics … graphics …

Samples of EachSamples of Each

GFS (MAV)GFS (MAV)

Samples of EachSamples of Each

GFS EXT (MEX)GFS EXT (MEX)

Samples of EachSamples of Each

NAM (MET)NAM (MET)

Statistical GuidanceStatistical Guidance

Most common approachMost common approach

Statistical ApproachStatistical Approach

Statistical GuidanceStatistical Guidance

Statistical GuidanceStatistical Guidance

Predictand StrategiesPredictand Strategies

Predictands always come from Predictands always come from meteorological data and a variety of meteorological data and a variety of sources:sources: Point observations (ASOS, AWOS, Co-Point observations (ASOS, AWOS, Co-op sites)op sites) Satellite data (e.g., SCP data)Satellite data (e.g., SCP data) Lightning data (NLDN)Lightning data (NLDN) Radar data (WSR-88D)Radar data (WSR-88D)It is very important to quality control It is very important to quality control predictands before performing a predictands before performing a regression analysisregression analysis……

Predictand StrategiesPredictand Strategies

1.(Quasi-)Continuous Predictands: best 1.(Quasi-)Continuous Predictands: best for variables with a relatively smooth for variables with a relatively smooth distributiondistribution

Temperature, dew point, wind (u and v Temperature, dew point, wind (u and v components, wind speed)components, wind speed)

Quasi-continuous because temperature, dew point Quasi-continuous because temperature, dew point available usually only to the nearest degree C, available usually only to the nearest degree C, wind direction to the nearest 10 degrees, wind wind direction to the nearest 10 degrees, wind speed to the nearest m/s.speed to the nearest m/s.

2. Categorical Predictands: 2. Categorical Predictands: observations are reported as categoriesobservations are reported as categories

Sky Cover (CLR, FEW, SCT, BKN, OVC)Sky Cover (CLR, FEW, SCT, BKN, OVC)

Predictand StrategiesPredictand Strategies3. “Transformed” Predictands: predictand values 3. “Transformed” Predictands: predictand values have been changed from their original valueshave been changed from their original values

Categorize (quasi-)continuous observations such as ceiling Categorize (quasi-)continuous observations such as ceiling heightheight

Binary predictands such as PoP (precip amount Binary predictands such as PoP (precip amount >> 0.01”) 0.01”) Non-numeric observations can also be categorized or Non-numeric observations can also be categorized or

“binned”, like obstruction to vision (FOG, HAZE, MIST, “binned”, like obstruction to vision (FOG, HAZE, MIST, Blowing, none)Blowing, none)

Operational requirements (e.g., average sky cover/P-type Operational requirements (e.g., average sky cover/P-type over a time period, or getting 24-h precip amounts from 6-h over a time period, or getting 24-h precip amounts from 6-h precip obs)precip obs)

4. Conditional Predictands: predictand is 4. Conditional Predictands: predictand is conditional upon another event occurringconditional upon another event occurring

PQPF: Conditional on PoPPQPF: Conditional on PoP PTYPE: Conditional on precipitation occurringPTYPE: Conditional on precipitation occurring

MOS PredictandsMOS PredictandsTemperatureTemperature

Spot temperature (every 3 h)Spot temperature (every 3 h) Spot dew point (every 3 h)Spot dew point (every 3 h) Daytime maximum temperature [0700 – 1900 LST] Daytime maximum temperature [0700 – 1900 LST]

(every 24 h)(every 24 h) Nighttime minimum temperature [1900 – 0800 LST] Nighttime minimum temperature [1900 – 0800 LST]

(every 24 h)(every 24 h)

WindWind U- and V- wind components (every 3 h)U- and V- wind components (every 3 h) Wind speed (every 3 h)Wind speed (every 3 h)

Sky CoverSky Cover Clear, few, scattered, broken, overcast [binary/MECE] Clear, few, scattered, broken, overcast [binary/MECE]

(every 3 h)(every 3 h)

MOS PredictandsMOS Predictands

PoP/QPFPoP/QPF PoP: accumulation of 0.01” of liquid-equivalent PoP: accumulation of 0.01” of liquid-equivalent

precipitation in a {6/12/24} h period [binary]precipitation in a {6/12/24} h period [binary] QPF: accumulation of QPF: accumulation of

{0.10”/0.25”/0.50”/1.00”/2.00”*} CONDITIONAL on {0.10”/0.25”/0.50”/1.00”/2.00”*} CONDITIONAL on accumulation of 0.01” [binary/conditional]accumulation of 0.01” [binary/conditional]

6 h and 12 h guidance every 6 h; 24 h guidance 6 h and 12 h guidance every 6 h; 24 h guidance every 12 hevery 12 h

2.00” category not available for 6 h guidance2.00” category not available for 6 h guidance

ThunderstormsThunderstorms 1+ lightning strike in gridbox (size varies) [binary]1+ lightning strike in gridbox (size varies) [binary]

SevereSevere 1+ severe weather report (define) in gridbox [binary]1+ severe weather report (define) in gridbox [binary]

MOS PredictandsMOS PredictandsCeiling HeightCeiling Height

CH < 200 ft, 200-400 ft, 500-900 ft, 1000-1900 CH < 200 ft, 200-400 ft, 500-900 ft, 1000-1900 ft, 2000-3000 ft, 3100-6500 ft, 6600-12000 ft, > ft, 2000-3000 ft, 3100-6500 ft, 6600-12000 ft, > 12000 ft [binary/MECE- Mutually Exclusive and 12000 ft [binary/MECE- Mutually Exclusive and Collectively ExhaustivCollectively Exhaustivee]]

VisibilityVisibility Visibility < ½ mile, < 1 mile, < 2 miles, < 3 miles, Visibility < ½ mile, < 1 mile, < 2 miles, < 3 miles,

<< 5 miles, 5 miles, << 6 miles [binary] 6 miles [binary]

Obstruction to VisionObstruction to Vision Observed fog (fog w/ vis < 5/8 mi), mist (fog w/ Observed fog (fog w/ vis < 5/8 mi), mist (fog w/

vis vis >> 5/8 mi), haze (includes smoke and dust), 5/8 mi), haze (includes smoke and dust), blowing phenomena, or none [binary]blowing phenomena, or none [binary]

MOS PredictandsMOS Predictands

Precipitation TypePrecipitation Type Pure snow (S); freezing rain/drizzle, ice pellets, Pure snow (S); freezing rain/drizzle, ice pellets,

or anything mixed with these (Z); pure or anything mixed with these (Z); pure rain/drizzle or rain mixed with snow (R)rain/drizzle or rain mixed with snow (R)

Conditional on precipitation occurringConditional on precipitation occurring

Precipitation Characteristics (PoPC)Precipitation Characteristics (PoPC) Observed drizzle, steady precip, or showery Observed drizzle, steady precip, or showery

precipprecip Conditional on precipitation occurringConditional on precipitation occurring

Precipitation Occurrence (PoPO)Precipitation Occurrence (PoPO) Observed precipitation Observed precipitation on the houron the hour – does NOT – does NOT

have to accumulatehave to accumulate

StratificationStratification

Goal: To achieve maximum homogeneity in Goal: To achieve maximum homogeneity in the developmental datasets, while keeping the developmental datasets, while keeping their size large enough for a stable their size large enough for a stable regressionregression

MOS equations are developed for two seasonal MOS equations are developed for two seasonal stratifications:stratifications: COOL SEASON: October 1 – March 31COOL SEASON: October 1 – March 31 WARM SEASON: April 1 – September 30WARM SEASON: April 1 – September 30**EXCEPT Thunderstorms 3 seasonsEXCEPT Thunderstorms 3 seasons

(Oct. 16 – Mar. 15, Mar. 16 – Jun. 30, July 1 – Oct. (Oct. 16 – Mar. 15, Mar. 16 – Jun. 30, July 1 – Oct. 15)15)

Pooling DataPooling Data Generally, this means Generally, this means REGIONALIZATION: collecting nearby REGIONALIZATION: collecting nearby stations with similar climatologiesstations with similar climatologies Particularly important for forecasting Particularly important for forecasting RARE EVENTS:RARE EVENTS:QPF Probability of 2”+ in 12 hoursQPF Probability of 2”+ in 12 hoursCeiling Height < 200 ft; Visibility < ½ mileCeiling Height < 200 ft; Visibility < ½ mile

Regionalization allows for guidance Regionalization allows for guidance to be produced at sites with poor, to be produced at sites with poor, unreliable, or non-existent observation unreliable, or non-existent observation systemssystems All MOS equations are regional except All MOS equations are regional except

temperature and windtemperature and wind

Example of RegionsExample of Regions

GFS MOS GFS MOS PoP/QPF PoP/QPF Region Map,Region Map,Cool SeasonCool Season

• Note that Note that each element each element has its own has its own regions, regions, which usually which usually differ by differ by seasonseason

TransformTransformPoint Binary PredictorPoint Binary Predictor

FCST: F24 MEAN RH PREDICTOR CUTOFF = 70%INTERPOLATE; STATION RH ≥ 70% , SET BINARY = 1;

BINARY = 0, OTHERWISE

96 86 89 94

87 73 76 90

76 60 69 92

64 54 68 93RH ≥70% ; BINARY AT KBHM = 1

•KBHM

(71%)

TransformTransformGrid Binary PredictorGrid Binary Predictor

FCST: F24 MEAN RH PREDICTOR CUTOFF = 70%WHERE RH ≥ 70% , SET GRIDPOINT VALUE = 1, OTHERWISE = 0

INTERPOLATE TO STATIONS

1 1 1 1

1 1 1 1

1 0 0 1

0 0 0 10 < VALUE AT KBHM < 1

•KBHM

(0.21)

Binary PredictandsBinary Predictands

If the predictand is BINARY, MOS If the predictand is BINARY, MOS equations yield estimates of event equations yield estimates of event PROBABILITIES…PROBABILITIES…MOS Probabilities are:MOS Probabilities are: Unbiased – the average of the probabilities over a Unbiased – the average of the probabilities over a

period of time equals the long-term relative frequency of period of time equals the long-term relative frequency of the eventthe event

Reliable – conditionally (“piece-wise”) unbiased over Reliable – conditionally (“piece-wise”) unbiased over the range of probabilitiesthe range of probabilities

Reflective of predictability of the event – range of Reflective of predictability of the event – range of probabilities narrows and approaches relative frequency probabilities narrows and approaches relative frequency of event as predictability decreases, for example, with of event as predictability decreases, for example, with increasing projections or with rare eventsincreasing projections or with rare events

Post-Processing MOS GuidancePost-Processing MOS Guidance

Meteorological consistencies – Meteorological consistencies – SOME checksSOME checks T T >> Td; min T Td; min T << T T << max T; dir = 0 if wind speed = 0 max T; dir = 0 if wind speed = 0 BUT no checks between PTYPE and T, between PoP BUT no checks between PTYPE and T, between PoP

and sky coverand sky cover

Statistical consistencies – again, SOME checksStatistical consistencies – again, SOME checks Conditional probabilities made unconditionalConditional probabilities made unconditional Truncation (no probabilities < 0, > 1)Truncation (no probabilities < 0, > 1) Normalization (for MECE elements like sky cover)Normalization (for MECE elements like sky cover) Monotonicity enforced (for elements like QPF)Monotonicity enforced (for elements like QPF) BUT temporal coherence is only partially checkedBUT temporal coherence is only partially checked

Generation of “best categories”Generation of “best categories”

Unconditional Probabilities from Unconditional Probabilities from ConditionalConditional

If event B is conditioned upon If event B is conditioned upon A occurring:A occurring: Prob(B|A)=Prob(B)/Prob(A) Prob(B|A)=Prob(B)/Prob(A) Prob(B) = Prob(A) × Prob(B|A) Prob(B) = Prob(A) × Prob(B|A)

Example: Example:

Let A = event of Let A = event of >> .01 in., .01 in., and B = event of and B = event of >> .25 in., then .25 in., then if:if:Prob (A) = .70, and Prob (A) = .70, and Prob (B|A) = .35, Prob (B|A) = .35,

U

A

B

then then Prob (B) = .70 × .35 = .245Prob (B) = .70 × .35 = .245

Truncating ProbabilitiesTruncating Probabilities

0 0 << Prob (A) Prob (A) << 1.0 1.0Applied to PoP’s and Applied to PoP’s and thunderstorm thunderstorm probabilitiesprobabilitiesIf Prob(A) < 0, ProbIf Prob(A) < 0, Probadjadj (A)=0 (A)=0 If Prob(A) > 1, ProbIf Prob(A) > 1, Probadjadj (A)=1.(A)=1.

Normalizing MECE ProbabilitiesNormalizing MECE ProbabilitiesSum of probabilities for Sum of probabilities for exclusive and exhaustive exclusive and exhaustive categories must equal categories must equal 1.01.0If Prob (A) < 0, then If Prob (A) < 0, then sum of Prob (B) and sum of Prob (B) and Prob (C) = D, and is > Prob (C) = D, and is > 1.0.1.0.Set: ProbSet: Probadjadj (A) = 0, (A) = 0,

ProbProbadjadj (B) = Prob (B) / (B) = Prob (B) /

D,D,ProbProbadjadj (C) = Prob (C) / (C) = Prob (C) /

DD

Monotonic Categorical Monotonic Categorical ProbabilitiesProbabilities

If event B is a subset of If event B is a subset of event A, then:event A, then: Prob (B) should be Prob (B) should be << Prob (A).Prob (A).Example: B is Example: B is >> 0.25 in; A 0.25 in; A is is >> 0.10 in 0.10 inThen, if Prob (B) > Prob Then, if Prob (B) > Prob (A)(A)set Probset Probadjadj (B) = Prob (A). (B) = Prob (A).Now, if event C is a subset Now, if event C is a subset of event B, e.g., C is of event B, e.g., C is >> 0.50 0.50 in, and if Prob (C) > Prob in, and if Prob (C) > Prob (B),(B),set Probset Probadjadj (C) = Prob (B) (C) = Prob (B)

Temporal Coherence of Temporal Coherence of ProbabilitiesProbabilities

Event A is Event A is >> 0.01 in. 0.01 in. occurring from 12Z-18Zoccurring from 12Z-18ZEvent B is Event B is >> 0.01 in. 0.01 in. occurring from 18Z-00Zoccurring from 18Z-00Z A A B is B is >> 0.01 in. 0.01 in. occurring from 12Z-00Zoccurring from 12Z-00ZThen P(AThen P(AB) = P(A) + B) = P(A) + P(B) – P(AP(B) – P(AB)B)

Thus, P(AThus, P(AB) should B) should be:be:<< P(A) + P(B) and P(A) + P(B) and>> maximum of P(A), maximum of P(A), P(B)P(B)

A BC

0

20

40

60

80

0.01" 0.10" 0.25" 0.50" 1.00" 2.00"PRECIPITATION AMOUNT EQUAL TO OR EXCEEDING

FORECAST

THRESHOLD

MOS Best Category SelectionMOS Best Category SelectionP

RO

BA

BIL

ITY

(%

)

THRESHOLD

EXCEEDED?

TO MOS GUIDANCE MESSAGES

An example with QPF…An example with QPF…

Other Possible Post-ProcessingOther Possible Post-Processing

Computing the Expected ValueComputing the Expected Value used for estimating precipitation amountused for estimating precipitation amount

Fitting probabilities with a distributionFitting probabilities with a distribution Weibull distribution used to estimate median or Weibull distribution used to estimate median or

other percentiles of precipitation amountother percentiles of precipitation amount

Reconciling meteorological Reconciling meteorological inconsistenciesinconsistencies

Not always straightforward or easy to doNot always straightforward or easy to do Inconsistencies are minimized somewhat by use Inconsistencies are minimized somewhat by use

of NWP model in development and application of of NWP model in development and application of forecast equationsforecast equations

MOS Weaknesses / IssuesMOS Weaknesses / Issues

MOS can have trouble with some local MOS can have trouble with some local effects (e.g., cold air damming along effects (e.g., cold air damming along Appalachians, and some other terrain-Appalachians, and some other terrain-induced phenomena)induced phenomena) MOS can have trouble if conditions are MOS can have trouble if conditions are highly unusual, and thus not sampled highly unusual, and thus not sampled adequately in the training sampleadequately in the training sample But, MOS can and has predicted record highs & But, MOS can and has predicted record highs &

lowslows

• MOS typically does not pick up on MOS typically does not pick up on mesoscale-forced featuresmesoscale-forced features

MOS Weaknesses / IssuesMOS Weaknesses / Issues Like the models, MOS has problems with Like the models, MOS has problems with QPF in the warm season (particularly QPF in the warm season (particularly convection near sea breeze fronts along the convection near sea breeze fronts along the Gulf and Atlantic coasts)Gulf and Atlantic coasts) Model changes can impact MOS skillModel changes can impact MOS skill MOS tends toward climatology at extended MOS tends toward climatology at extended projections – due to degraded model accuracy projections – due to degraded model accuracy CHECK THE MODEL…MOS will correct CHECK THE MODEL…MOS will correct many systematic biases, but will not “fix” a many systematic biases, but will not “fix” a bad forecast. GIGO (garbage in, garbage bad forecast. GIGO (garbage in, garbage out).out).

Why do we need Gridded MOS?Why do we need Gridded MOS?

Because forecasters Because forecasters have tohave toproduce products produce products like this for the like this for the NDFD…NDFD…

Traditional MOS GraphicsTraditional MOS Graphics

This is This is better, but better, but still lacks still lacks most of most of the detail the detail in the in the Western Western U.S.U.S.

ObjectivesObjectives

Produce MOS guidance on high-Produce MOS guidance on high-resolution grid (2.5 to 5 km resolution grid (2.5 to 5 km spacing)spacing) Generate guidance with sufficient Generate guidance with sufficient detail for forecast initialization at detail for forecast initialization at WFOsWFOs Generate guidance with a level Generate guidance with a level of accuracy comparable to that of of accuracy comparable to that of the station-oriented guidancethe station-oriented guidance

BCDG AnalysisBCDG Analysis

Method of successive correctionsMethod of successive corrections Land/water gridpoints treated Land/water gridpoints treated differentlydifferently Elevation (“lapse rate”) Elevation (“lapse rate”) adjustmentadjustment

MOS Max Temperature ForecastMOS Max Temperature Forecast

NDFD Max Temperature ForecastNDFD Max Temperature Forecast

Statistical GuidanceStatistical Guidance UMOS – Updateable MOSUMOS – Updateable MOS

Updating concept As described by Ross (1992), a UMOS system is intended to facilitate the rapid and frequent updating of a large number

of MOS equations from a linear statistical model, either MLR or MDA. Both of these techniques use the sums-of-squares-and-cross-products matrix (SSCP), or components of it. The

idea of the updating is to do part of the necessary recalculation of coefficients in near–real time by updating the SSCP matrix, and storing the data in that form rather than as

raw observations.

Weather and ForecastingArticle: pp. 206–222 | Abstract | PDF (560K)The Canadian Updateable Model Output Statistics (UMOS) System: Design and Development TestsLaurence J. Wilson and Marcel ValléeMeteorological Service of Canada, Dorval, Quebec, Canada(Manuscript received April 19, 2001, in final form October 12, 2001)

Statistical GuidanceStatistical Guidance

UMOS – Updateable MOSUMOS – Updateable MOS

Future of Gridded MOSFuture of Gridded MOS

Evaluation (objective & Evaluation (objective & subjective)subjective) Expansion (area & elements)Expansion (area & elements) Improvement –make Improvement –make UpdateableUpdateable Use of remote-sensing Use of remote-sensing observationsobservations