PROVIDING DISTRIBUTED PROVIDING DISTRIBUTED FORECASTS OF FORECASTS OF PRECIPITATION USING A PRECIPITATION USING A STATISTICAL NOWCAST STATISTICAL NOWCAST SCHEME SCHEME Neil I. Fox and Chris K. Neil I. Fox and Chris K. Wikle Wikle University of Missouri- University of Missouri- Columbia Columbia
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PROVIDING DISTRIBUTED FORECASTS OF PRECIPITATION USING A STATISTICAL NOWCAST SCHEME Neil I. Fox and Chris K. Wikle University of Missouri- Columbia.
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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
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
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
• 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
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