OutlineStatistical structure of rainfallModelling the errors in a nowcastTemporal development Radar reflectivity to rain rate conversionTrackingNowcast ensemblesRadar only nowcastsRadar + NWP blending ProductsEnsembles for end usersExpected rainfall ensemble meanProbability of exceeding various thresholdsMeteogramsProductsDevelopmentsConclusions

15-min rainfall over the UK 1000 km (15 min)

Adelaide Radar 250 km (10 min)

Auckland 10 km (2 min)15 km x 7.5 km box, 100 m resolution

Variability as a function of scaleModelling1000 km domain, eastern half of the HRRR region

Nowcast skill as a function of scale and lead time

Widespread rain in Sydney

Chart2

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0.98999913020.98000100250.96000020160.8936960760.53702808370.0529050601

0.98503626450.97015199240.94060435750.8448600540.39354599430.0121687458

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0.97029644240.94119488840.88473655740.71378851080.15487844970.0001480784

0.96543234640.93173587980.866861340.67478353760.11349833520.0000340597

0.9605926340.92237193420.84934727350.63790999120.0831740770.0000078341

0.95577718310.91310209620.83218706120.60305139970.06095179350.0000018019

0.95098587210.90392542020.81537355380.5700976560.04466681520.0000004145

0.94621857990.89484096970.79889974650.53894466960.03273282480.0000000953

0.94147518620.8858478180.7827587760.50949403810.02398733420.0000000219

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0.90893059810.8253761960.67854332150.34379818940.00272252250

0.9043741290.81708116520.66483403230.32501133730.00199512440

0.89984050150.80886949950.65140172550.30725109280.0014620710

0.8953296010.80074036110.6382408050.29046135690.00107143780

0.89084131380.79269292040.62534578780.2745890960.00078517320

0.88637552620.78472635660.61271130150.25958417490.00057539220

0.88193212570.77683985670.60033208230.24539919760.00042166010

0.8775110.76903261610.5882029730.23198935850.00030900180

0.87311203730.76130383840.57631892010.21931230.00022644330

0.86873512670.75365273480.56467497260.20732797930.00016594260

0.86438015750.74607852480.55326627950.19599854190.00012160640

0.86004701980.73858043560.54208808760.18528820160.00008911590

0.85573560410.73115770220.53113573980.17516312780.00006530610

0.85144580150.72380956730.52040467340.16559133870.00004785770

0.84717750370.71653528120.50989041730.15654260.00003507120

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0.83870499170.70220529390.48949490340.13990150730.00001883420

0.83450056360.69514813070.47960514840.13225658950.00001380210

500 km

250 km

100 km

50 km

20 km

10 km

Lead Time (hours)

Correlation

Skill vs Lead Time

cascade_autocor

0.99498757676.3617537504

0.98995251.5910437.9932856438

0.979796109.892450361618.8019307256

0.94535547.99992339346.8291808291

0.73282220.9658865391.2345541728

0.2300119.15768958140.2611301256

-0.154348

500 km250 km100 km50 km20 km10 km

Time576251.59104109.892450361647.999923393420.9658865399.1576895814

10.16666666670.9949870.989950.9797960.9453550.7328220.230011

20.33333333330.98999913020.98000100250.96000020160.8936960760.53702808370.0529050601

30.50.98503626450.97015199240.94060435750.8448600540.39354599430.0121687458

40.66666666670.98009827770.96040196490.92160038710.79869267630.28839916270.0027989454

50.83333333330.97518504510.95074992520.90298037290.7550481150.21134525120.0006437882

610.97029644240.94119488840.88473655740.71378851080.15487844970.0001480784

71.16666666670.96543234640.93173587980.866861340.67478353760.11349833520.0000340597

81.33333333330.9605926340.92237193420.84934727350.63790999120.0831740770.0000078341

91.50.95577718310.91310209620.83218706120.60305139970.06095179350.0000018019

101.66666666670.95098587210.90392542020.81537355380.5700976560.04466681520.0000004145

111.83333333330.94621857990.89484096970.79889974650.53894466960.03273282480.0000000953

1220.94147518620.8858478180.7827587760.50949403810.02398733420.0000000219

132.16666666670.93675557110.87694504740.76694391770.48165273640.01757844620.000000005

142.33333333330.93205961540.86813174970.75144858280.45533282260.01288187210.0000000012

152.50.92738720060.85940702560.73626631570.43045116050.00944011930.0000000003

162.66666666670.92273820850.8507699850.7213907910.40692915680.00691792710.0000000001

172.83333333330.91811252190.84221974660.70681581150.38469251310.00506960920

1830.91351002380.83375543820.69253530480.36367099070.00371512110

193.16666666670.90893059810.8253761960.67854332150.34379818940.00272252250

203.33333333330.9043741290.81708116520.66483403230.32501133730.00199512440

213.50.89984050150.80886949950.65140172550.30725109280.0014620710

223.66666666670.8953296010.80074036110.6382408050.29046135690.00107143780

233.83333333330.89084131380.79269292040.62534578780.2745890960.00078517320

2440.88637552620.78472635660.61271130150.25958417490.00057539220

254.16666666670.88193212570.77683985670.60033208230.24539919760.00042166010

264.33333333330.8775110.76903261610.5882029730.23198935850.00030900180

274.50.87311203730.76130383840.57631892010.21931230.00022644330

284.66666666670.86873512670.75365273480.56467497260.20732797930.00016594260

294.83333333330.86438015750.74607852480.55326627950.19599854190.00012160640

3050.86004701980.73858043560.54208808760.18528820160.00008911590

315.16666666670.85573560410.73115770220.53113573980.17516312780.00006530610

325.33333333330.85144580150.72380956730.52040467340.16559133870.00004785770

335.50.84717750370.71653528120.50989041730.15654260.00003507120

345.66666666670.84293060290.70933410160.49958859130.14798832960.00002570090

355.83333333330.83870499170.70220529390.48949490340.13990150730.00001883420

3660.83450056360.69514813070.47960514840.13225658950.00001380210

cascade_autocor

Correlation Length

Scale (km)

Life Time (hours)

Sheet2

500 km

250 km

100 km

50 km

20 km

10 km

Lead Time (hours)

Correlation

Skill vs Lead Time

Sheet3

OutlineStatistical structure of rainfallModelling the errors in a nowcastTemporal development Radar reflectivity to rain rate conversionTrackingNowcast ensemblesRadar only nowcastsRadar + NWP blending ProductsEnsembles for end usersExpected rainfall ensemble meanProbability of exceeding various thresholdsMeteogramsDevelopmentsConclusions

Conceptual model for rainfallRainfall usually has areas of higher intensity rainfall inside areas of lower intensity rainfall, and we get clusters of storms and not just a random pattern of storms- variability over a wide range of scales

The lifetime of a storm increases with the size of the storm as a power law

The simplest model is a multiplicative cascade model (used to model turbulence) for the spatial scaling and a hierarchy of AR(1) models for the Lagrangian temporal evolution so as to reproduce the dynamic scaling of the field Temporal development of rainfall

Multiplicative Cascade Model for TurbulenceLovejoy et al., 1987J. Geophys. Res.Each cascade level evolves in time Rate of development decreases with increasing scaleHierarchy of AR(1) models used for temporal development Temporal development of rainfall

Spectral decomposition of a rainfall fieldTemporal development of rainfall

Radar Z-R error is coherent over scales that are significant for urban hydrologyRadar measurement errorZ - R Error

Space & Time correlations of radar z-r error Villarini et al, WRR 45, W01404 2009Z - R Error

Errors due to observing above ground levelCorrelation as a function of height separation for pairs of radar observations where one observation is at the base scan and the other is below the wet bulb freezing level. Sampling Error

Model of radar ZR and sampling errorsObserved and ensembles for 10-min rainfallRadar measurement errorEnsemble 1Ensemble 2ObservationRadar observation error model includes Z-R and sampling errors due to observing at a height above the ground Modelling QPE Error

Verification of radar error modelReliability of probabilitiesPower specta of observed and perturbed fieldsModelling QPE Error

Other radar observation errors are tricky, depending on the situation and the QC algorithms used Radar measurement errorBeam blockingClutterDaily rainfall accumulation for MelbourneModelling QPE Error

Modelling the tracking errorWe do not have a complete description of tracking errorGenerating fields of U,V error components that are correlated with each other and in space and time is VERY tricky- at least I do not know how to do itNot the most important source of error in the first 6 hours so we can keep it simpleMultiply the radar U,V components by a random number that has a mean of 1 and some (small) variance Modelling Tracking Error

OutlineStatistical structure of rainfallModelling the errors in a nowcastTemporal development Radar reflectivity to rain rate conversionTrackingNowcast ensemblesRadar only nowcastsRadar + NWP blending ProductsEnsembles for end usersExpected rainfall ensemble meanProbability of exceeding various thresholdsMeteogramsDevelopmentsConclusions

Short Term Ensemble Prediction System- radar only

Estimate the advection field using rainfall fieldsEstimate the AR(1) and cascade parameters using the current observed fieldFor each ensemble memberPerturb the radar analysis with the observation error modelPerturb the advection fieldGenerate a conditional stochastic field for the next 90 minutesModellingSTEPS-nowcast

Beijing Olympics: 1 hr forecast & observationSTEPS-nowcast

Beijing 2008 inter-comparison

Compared STEPS against 5 other international systems during the Beijing Games

STEPS-nowcast

Short Term Ensemble Prediction System- NWP blendDecompose NWP into a cascade Decompose the rainfall field into a cascadeUse radar field to estimate stochastic model parametersCalculate the skill of the NWP at each level in the cascade using the correlation between NWP and radarBlend each level in the radar & NWP cascades using weights that are a function of the forecast error at that scale and lead timeFor each forecast Add noise component to the deterministic blend, the weight of the noise is calculated using the skill of the blended forecastCombine the cascade levels to form a forecastSTEPS-NWP

Blending with NWP calculating the weightsSTEPS-NWP

Nowcast explained variance as a function of scale and lead timeSTEPS-NWP

NWP explained variance as a function of scaleSTEPS-NWP

Weights for nowcast & NWPBlendingSTEPS-NWP

OutlineStatistical structure of rainfallModelling the errors in a nowcastRadar reflectivity to rain rate conversionTrackingTemporal development Nowcast ensemblesRadar only nowcastsRadar + NWP blending ProductsEnsembles for end usersExpected rainfall ensemble meanProbability of exceeding various thresholdsMeteogramsDevelopmentsConclusions

StatusQPE and STEPS-nowcast running on LINUX workstations in operational modeSTEPS-NWP (radar + NWP blend) running on a super computer 16 radars with QPE, 15 QPF domainsGenerating 1000 products (100 Mbytes) per hourUp to 100 clients inside the Bureau being served with products on a busy dayQPE live to the public for capital city radarsPlanning to go live to the public with QPF in May 2011

Products

Rainfall Estimates Melbourne, Sydney, Brisbane, Adelaide 30, 60, 120 min, since 9 AM, daily accumulations blended with rain gauges and updated every 30 min 10 min accumulations radar only with real-time gauge adjustments and updated every 6 or 10 minutesProducts

Rainfall Forecasts: 0 90 minutes4 major cities, 1 km & 6 min resolution, 250 km domain3 Regional forecasts, 2 km & 10 min resolution, 500 km domain30 member ensemble updated every 6,10 minutes30, 60, 90 min accumulations of ensemble mean (expected rain)Probability that rain accumulation will exceed 1,2,5,10,20,50 mm in next 60 minutes

60 min accumulationProbability of rain > 50 mmForecast time series at a pointwith uncertainty shownProducts

Rainfall forecasts: 1 6 hours Melbourne, Sydney, Brisbane 500 km domain, 2 km & 10 min resolution30 member ensemble updated every hour10-min forecasts of rainfall intensity out to 6 hoursProbability products for hourly accumulations for next 6 hoursProbability of rain > 1 mm for 2 & 3 hour lead times, Melbourne Rainfall intensity forecast, 150 min lead time, BrisbaneProducts

Example from east Victoria NWP

Example from east Victoria- STEPS Ensemble member 1

Met Service Canada: Point Mode Paul Joe, 2010

Met Service Canada: Point-Time ModePDF of rainrates at a point for all time lagged nowcastsPaul Joe, 2010

Met Service Canada: POP for a validtime and rainrate thresholdRainrate threshold is 1 mm/h; number of hits exceeding threshold / number of samples (60)Paul Joe, 2010

Probability Probability of 60 min accum > 5 mm

OutlineStatistical structure of rainfallModelling the errors in a nowcastRadar reflectivity to rain rate conversionTrackingTemporal development Nowcast ensemblesRadar only nowcastsRadar + NWP blending ProductsEnsembles for end usersExpected rainfall ensemble meanProbability of exceeding various thresholdsMeteogramsDevelopmentsConclusions

Qualitative severe weather warning

THESPA Calculates the probability of a TITAN cell passing over a point in the next 60 minutes based on the current velocity and cell size and a climatological TITAN tracking error Being developed for aviation applications and use in TIFS

TIFS Operational in most Regional Forecast CentresAutomatic version for aviation is operational Revising the software architecture Graphical and automated text editing feature development

Developments

Development: Closing the gap between NWP & nowcastsStrategic Radar Enhancement Project $48 M project over 7 years, 8 people for three years in CAWCR 4 new radars Radar data assimilation in ACCESSRoll out of a new radar data quality control system for ~50 radarsCharacterise radar errors for use in data assimilation (and QPE)Assimilate radar data (LH nudging, Doppler radial winds, reflectivity) into high res (~2 km) NWP meso-scale models over capital cities

Seamless rainfall predictionIntegrate rainfall forecasts from 0 10 days lead time into a seamless forecastUse STEPS to blend the forecasts from the various modelsDevelop a portal for convenient access to the rainfall forecasts

Seamless rainfall forecasts

Rainfall portalData source transparent to user AggregationDisaggregation New scienceSTEPS downscaling Blending strategyVerification (esp. transition periods)3-10 day forecasts40-100 km2 x daily1-2 day forecastsACCESS-AACCESS-CAGREPS-RECMWF EPSPME/GOCFGFE5-25 km2-4 x daily1-24 hour forecastsACCESS-AACCESS-CGFE

2-10 km4-8 x daily1-6 hour forecastsACCESS-CSTEPS-NWP1-2 kmhourly10-90 min nowcastsSTEPS-nowcastevery 10 min1 kmDown-scaled and blended using STEPSACCESS-GAGREPS-GECMWF EPSPME/GOCFGFETIGGE? Cross-cutting programs: ESM, CWD, OEB, NMOC

Issues

Limited capacity in the Regional Forecast Centres Head Office support branches to deploy and learn new nowcasting systems, busy with the Next Generation Forecast and Warning System slows the adoption of new algorithms

Focus has been on improving the service adoption of existing nowcasting science through Delivering the products through a range of platforms 3drapic, Google maps, web pagesUsing formats that are carefully designed and that conform to formal geo-spatial standards (eg CF compliant netCDF)Serving the data on a range of platforms (ftp, SOAP, directories)Formalising the use of QPE&F products in the forecast processTraining Developments

ConclusionsNowcasting rainfall is an uncertain business Have incomplete description of the error structure of QPE and QPFHave enough of a description to make useful stochastic ensemble modelsThere is still a lot of work to do to make the stochastic models include more meteorological knowledgeThere is even more work to do to help the end-users make full use of the ensemble members in their decision support systems

This is a rainfall image from the U.K. radar network. The image is 1500 km x 800 km in size and shows a large rainband crossing EnglandThis is a rainfall map from a single radar in Adelaide, Australia. The image is 256 km x 256 km. You see that there are small areas of intense rain inside larger areas of light rain, and looks a lot like the UK mapRadar rainfall measurements of a 15 x 7 km area at 6-second, 100 m resolution and averaged up to 2-minute averages. You can see that there is structure in rainfall down to very small scales. Why does this matter? Because it affects our ability to measure rainfall accurately. If rainfall was smooth at small scales then it would be much easier to measure rainfall and the statistics would not be so sensitive to the scale over which the rainfall is averaged. The power spectrum of rainfall shows that the variability is distributed as a power law over all the scales in the range 1000 km to 1 km. This figure shows the skill of a nowcast when the rainfall map is averaged over different areas and for different lead times. The skill of a nowcast drops of very quickly for the small scales because the rain areas of this size do not last very long, it is very difficult to forecast for an area that is less than 10 km in size. The multiplicative cascade model is able to make patterns that look very much like rainfall so we use it to make our ensembles. It is able to generate most of the spatial structure especially between 1 and 500 km in scale. We break up the rainfall map into a collection of maps where only the patterns of a small range of sizes are allowed. The centre top image is the pattern for 512 1024 km scales, the top right image contains only 256-512 km scales and so on to the smaller scales. We make a nowcast for each of the scales and then add the scales together to get the rainfall forecast. We replace the observed pattern with a statistical pattern during the forecast period, the large scales evolve slowly and the small scales are made to evolve quickly, like rainfall.Radar observation error is a major cause of forecast uncertainty in the first hour and is important for urban flash flooding forecastsThe radar measurement errors are correlated over about 40 km in space and 60 minutes in time so we need to model this error carefullySome errors are due to beam blocking and ground clutter and we are not able to model these errors yetTracking errors are about 15 km per hour and are only important for the longer lead times in widespread rainfall, but can be important in thunderstorms where the storms are quite smallSTEPS was part of the Beijing 2008 WWRP FDPThis is how we blend NWP forecasts with the radar nowcasts using STEPSThis figure shows the skill of a nowcast when the rainfall map is averaged over different areas and for different lead times. The skill of a nowcast drops of very quickly for the small scales because the rain areas of this size do not last very long, it is very difficult to forecast for an area that is less than 10 km in size. Met Service Canada are developing a nowcasting service that is based on STEPS using data that were collected during the Vancouver Winter Olympics Proposal for WIRADA project