PROVIDING DISTRIBUTED PROVIDING DISTRIBUTED FORECASTS OF FORECASTS OF

PRECIPITATION USING A PRECIPITATION USING A STATISTICAL NOWCAST STATISTICAL NOWCAST

SCHEMESCHEME

Neil I. Fox and Chris K. Wikle Neil I. Fox and Chris K. Wikle

University of Missouri- University of Missouri- ColumbiaColumbia

ReasoningReasoning

• Need realistic representation of Need realistic representation of uncertainty in precipitation forecastsuncertainty in precipitation forecasts

• Previous methods too deterministic Previous methods too deterministic (no measure of uncertainty) or too (no measure of uncertainty) or too probabilistic (stochastic)probabilistic (stochastic)

• This methodology allows for the This methodology allows for the integration of some real physics with a integration of some real physics with a realistic statistical formulation that realistic statistical formulation that can provide genuine information on can provide genuine information on forecast uncertaintyforecast uncertainty

What I’ll show todayWhat I’ll show today

• Not much theoryNot much theory

• The future of nowcastingThe future of nowcasting

• Examples of productsExamples of products

• The future of this nowcasting methodThe future of this nowcasting method

Nowcasting techniques - Nowcasting techniques - currentcurrent• Extrapolation techniquesExtrapolation techniques

– Mostly linear extrapolationMostly linear extrapolation– Do not account for developmentDo not account for development

• Modeling approachesModeling approaches– Forecasts motion and developmentForecasts motion and development– Lack of knowledge of:Lack of knowledge of:

•Storm scale dynamics (model accuracy)Storm scale dynamics (model accuracy)

•Atmospheric environment (observation Atmospheric environment (observation limitation)limitation)

Limitations of Current Limitations of Current NowcastingNowcasting• Only good for very short periodsOnly good for very short periods

• Poor at simulating developmentPoor at simulating development– Predict position but not characteristics of Predict position but not characteristics of

stormsstorms– No estimation of forecast rainfall No estimation of forecast rainfall

• Tend to smooth high intensity featuresTend to smooth high intensity features

• Little or no indication of forecast Little or no indication of forecast uncertaintyuncertainty

• Computationally intensiveComputationally intensive

Nowcast formulationNowcast formulation

where s and r are spatial locations in the domain of interest, ks(r; θs) is a redistribution kernel that describes how the process at time t is redistributed in space at time t+1. η represents the noise and γ is a growth / stationarity parameter

)()();(k)(1s1sdrryrsy

ttst

Stochastic integro-difference equationContinuous in spaceDiscrete in time

The nowcast field (yt+1) is related to the current field (yt) by

Model implementation: Model implementation: MCMCMCMC

• Markov Chain Monte-CarloMarkov Chain Monte-Carlo

• Gibbs samplerGibbs sampler

Things this can doThings this can do

• Full spatial variance fieldFull spatial variance field– Where do we have least confidence in the Where do we have least confidence in the

forecastforecast– Quantitative uncertainty for defined points Quantitative uncertainty for defined points

and areas (i.e. catchment QPF uncertainty)and areas (i.e. catchment QPF uncertainty)

• Incorporation of physicsIncorporation of physics– γγ (growth/decay) conditioned on (growth/decay) conditioned on

convergenceconvergence– Spatial kernel conditioned on windsSpatial kernel conditioned on winds

Advantages of Statistical Advantages of Statistical ApproachApproach

• Provide full distribution of forecasts Provide full distribution of forecasts allowing realistic assessment of allowing realistic assessment of uncertaintyuncertainty

• Avoid detailed physical modeling of Avoid detailed physical modeling of atmosphereatmosphere

• Can ‘train’ systemCan ‘train’ system

• Can incorporate further observations Can incorporate further observations to constrain equation parametersto constrain equation parameters

ExampleExample

• Nowcast of supercell motion from Nowcast of supercell motion from 11/03/0011/03/00

• Sydney, Australia (to prove we can Sydney, Australia (to prove we can cope with any hemisphere)cope with any hemisphere)

• Storm produced localized flooding, F1 Storm produced localized flooding, F1 tornadoes, damaging large hailtornadoes, damaging large hail

• Very complex situationVery complex situation

• Other nowcast systems did okayOther nowcast systems did okay

Products - domainProducts - domain

• Nowcast fieldsNowcast fields– Mean nowcastMean nowcast– to T+60 (10 minute intervals at to T+60 (10 minute intervals at

present)present)

• Variance fieldsVariance fields– UncertaintyUncertainty

Mean nowcast fieldsMean nowcast fields

Indication of uncertainty in Indication of uncertainty in spacespace

How this could appear in How this could appear in opsops

Example validationExample validation

Products - point / catchmentProducts - point / catchment

• Nowcast reflectivityNowcast reflectivity– 10 minute intervals to T+6010 minute intervals to T+60– With varianceWith variance

• Nowcast RainfallNowcast Rainfall– Point or group of pointsPoint or group of points– Mean or median nowcast rainfall or Mean or median nowcast rainfall or

accumulation out to T+60accumulation out to T+60– Cumulative frequency / probability Cumulative frequency / probability

distributionsdistributions

Rainrate distributionRainrate distribution

CumulativCumulative e frequency frequency of of nowcast nowcast rainraterainrate

0 500

50

100

Fre

quen

cy (

%) T+10

0 500

50

100

Fre

quen

cy (

%) T+20

0 500

50

100

Fre

quen

cy (

%) T+30

0 500

50

100

Fre

quen

cy (

%) T+40

0 500

50

100

Fre

quen

cy (

%) T+50

0 500

50

100

Fre

quen

cy (

%)

Rainrate (mm/hr)

T+60

0 500

50

100T+10

0 500

50

100T+20

0 500

50

100T+30

0 500

50

100T+40

0 500

50

100T+50

0 500

50

100

Rainrate (mm/hr)

T+60

0 500

50

100T+10

0 500

50

100T+20

0 500

50

100T+30

0 500

50

100T+40

0 500

50

100T+50

0 500

50

100

Rainrate (mm/hr)

T+60

0 500

50

100T+10

0 500

50

100T+20

0 500

50

100T+30

0 500

50

100T+40

0 500

50

100T+50

0 500

50

100

Rainrate (mm/hr)

T+60

Pixel 1 Pixel 2 Pixel 3 3 pixel aggreg

Cumulative Cumulative frequency frequency of nowcast of nowcast rain rain accumulatiaccumulationon

0 10 20 300

50

100

Fre

quen

cy (

%) T+10

0 10 20 300

50

100

Fre

quen

cy (

%) T+20

0 10 20 300

50

100

Fre

quen

cy (

%) T+30

0 10 20 300

50

100

Fre

quen

cy (

%) T+40

0 10 20 300

50

100

Fre

quen

cy (

%) T+50

0 10 20 300

50

100

Fre

quen

cy (

%)

Rain (mm)

T+60

0 10 20 300

50

100T+10

0 10 20 300

50

100T+20

0 10 20 300

50

100T+30

0 10 20 300

50

100T+40

0 10 20 300

50

100T+50

0 10 20 300

50

100

Rain (mm)

T+60

0 10 20 300

50

100T+10

0 10 20 300

50

100T+20

0 10 20 300

50

100T+30

0 10 20 300

50

100T+40

0 10 20 300

50

100T+50

0 10 20 300

50

100

Rain (mm)

T+60

0 10 20 300

50

100T+10

0 10 20 300

50

100T+20

0 10 20 300

50

100T+30

0 10 20 300

50

100T+40

0 10 20 300

50

100T+50

0 10 20 300

50

100

Rain (mm)

T+60

Pixel 1 Pixel 2 Pixel 3 3 pixel aggreg

In the futureIn the future

• Verification and adjustmentVerification and adjustment

• Incorporation of physicsIncorporation of physics

• Computational efficiencyComputational efficiency

• HydrologyHydrology– lumped model probabilitieslumped model probabilities– distributed probabilistic input distributed probabilistic input