QPF and Numerical Modeling Basics

1. QPF and Numerical Modeling Basics Tom Hopson

2. Utility of a Three-Tier Forecast System SEASONAL OUTLOOK: Long term planning of agriculture, water resource management & disaster mitigation especially if high probability of anomalous season (e.g., flood/drought) 30 DAY FORECAST: Broad-scale planning schedules for planting, harvesting, pesticide & fertilizer application and water resource management (e.g., irrigation/hydro-power determination). Major disaster mitigation resource allocation. 1-10 DAY FORECAST: Detailed agriculture, water resource and disaster planning. E.g., fine tuning of reservoir level, planting and harvesting.

3. forecast products for hydrologic applications • Seasonal -- ECMWF System 3 - based on: 1) long predictability of ocean circulation, 2) variability in tropical SSTs impacts global atmospheric circulation - coupled atmosphere-ocean model integrations - out to 7 month lead-times, integrated 1Xmonth - 41 member ensembles, 1.125X1.125 degrees (TL159L62), 130km • Monthly forecasts -- ECMWF - “fills in the gaps” -- atmosphere retains some memory with ocean variability impacting atmospheric circulation - coupled ocean-atmospheric modeling after 10 days - 15 to 32 day lead-times, integrated 1Xweek - 51 member ensemble, 1.125X1.125 degrees (TL159L62), 130km • Medium-range -- ECMWF EPS - atmospheric initial value problem, SST’s persisted - 6hr - 15 day lead-time forecasts, integrated 2Xdaily - 51 member ensembles, 0.5X0.5 deg (TL255L40), 80km • Short-range -- RIMES - 26-member Country Regional Integrated Multi-hazard Early Warning System (RIMES) WRF Precipitation Forecasts - 3hr - 5 day lead-time, integrated 2X daily - 9km resolution

4. Motivation for Generating Ensemble Discharge Forecasts (from ensemble weather forecasts) • Greater accuracy of ensemble mean forecast (half the error variance of single forecast) • Likelihood of extremes • Non-Gaussian forecast PDF’s • Ensemble spread as a representation of forecast uncertainty Motivation for generating ensemble forecasts (weather or hydrologic): => a well-calibrated ensemble forecast provides a prognosis of its own uncertainty or level of confidence

5. What is a Model? • Take the equations that describe atmospheric processes. • Convert them to a form where they can be programmed into a large computer. • Solve them so that this software representation of the atmosphere evolves within the computer. • This is called a “model” of the atmosphere

6. What do we mean by “solve the equations” • The equations describe how the atmosphere changes with time. • For example, one equation would be

8. So – “solving” the equation would be to estimate the terms on the right side, add them up, and obtain the rate of change of temperature

9. How theModel Forecasts Model-calculated T changes X X Temperature X X X X T now (observed) Time 

10. This equation is solved for a three-dimensional “matrix” of points (or a grid) that covers the atmosphere from the surface to some level near the top of the atmosphere. • Here is a 2-dimensional slice through the grid……..

11. 100 millibars ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… Altitude  Computational levels Grid points Ground East-West Distance 

12. X X X Grid-point spacing

13. Similar Equations Would be Solved for • East-west wind component • North-south wind component • Specific humidity (or RH) • Pressure • Cloud water • Rain/snow water

14. Two Types of Models • Global – grid covers the entire atmosphere of Earth (global models) • Limited-area – grid covers a region of the atmosphere such as continent or a state or a city (limited area models)

15. “Nested” grids • Grids can be telescoped, or nested, to zoom in on a small area Large grid-point spacing – say 90 km 30 km 10 km

16. Uses of Atmospheric Models • Daily weather prediction (let models run into the future for 1-10 days) • Climate prediction (let models run for years) - “what-if” experiments, e.g., what will happen if we double the CO2? - simply let the model run forward • Research – Study the model solution when you don’t have good observations of real atmosphere

17. The Model Setup

18. NumericalWeatherPrediction(NWP) ModelFundamentals:Areview (Plus1/2slideonclimatemodels) WilliamR.Bua,UCAR/COMET NCARISPSummercolloquiumonAfricanWeatherandClimate 27July2011

19. Outline •Whatistheland-ocean-atmospheresystemand itsconnectiontoweatherandclimate? •WhatisinanNWPsystem? •WhataretheshortcomingsofNWPmodels? •EnsembleForecastSystems:Mitgatingthe shortcomingsofNWPmodels

20. TheLand-Ocean-AtmosphereSystem EquationsofMotion(Eulerian/Pressurecoordinateform) •Conservationofmomentum, heat,moisture •Conservationofmass •Hydrostaticapproximation •Dynamicalequationsare coupledto –Theearth’sland/oceansurface (friction/turbulence,surface evaporation/evapotranspiration andprecipitation) –Sub-gridscalephysical/diabatic processes(radiation,evaporation/ condensation,waterphase changesinprecipprocesses, cloud/radiationinteraction,etc.) SimplifiedEquations

21. TheLand-Ocean-AtmosphereSystem ParameterizedLand/AtmospherePhysicalProcesses •Radiationprocesses –Incomingsolarradiation –Outgoingterrestrialradiation •Microphysics –Condensation/evaporation/ sublimation –Collision/coalescence,mixed Incoming shortwave rad.Shortwave scattering Reflection LongwaveRad. phaseprocesses,phase changes •Convection(shallow*and* deep) Precipitation microphysics Landand Convection LongwaveRadiation •Turbulentprocesses •Landsurfaceprocesses –Vegetation,soilmoisture, snow,surfaceenergy balanceandfluxes topography Vegetation,soilmoisture, surfaceenergybalance/fluxes

22. ClimateandWeatherPredictionModels GeneralCirculation (Climate)models NumericalWeather Prediction(NWP)Models • • Interestedinclimatedetails(means, anomalies,standarddeviations)atlong Interestedinshorttimescales andweatherdetails timescales • • Long,lowerresolutionruns –Climatedriftmustbecorrected Short,highresolutionruns –Climatedriftnotimportant, especiallyforshortrange • • Physicalprocessesaresimplified Physicalprocessesaremore realistic(e.g.microphysics) • • Slowlyvaryingprocessesmustbe accountedfor –Afullycoupledsystem –Formulti-decadalclimatechange •Interactivevegetationadaptsto changingclimate •Carboncycle/slowlyvarying Atmosphere/landcoupling;slow processesheldfixed –Fixedocean(SSTs)/seaice –Fixedvegetation –Fixedatmosphericcomposition/ greenhousegases atmosphericchemistry

23. NWPMODELS:DYNAMICS

24. NWPModels:Dynamics •Horizontalcoordinate system –Equationscomputed eitherby –Breakingdownthe horizontaldirectioninto gridpointsandtaking differencesfrompointto point….or =Shortestwave –Breakingdownthelarge scaleflowintoaseries ofincreasinglysmall sineandcosinewaves andpluggingthoseinto theequationstodothe calculations …+

25. NWPModels:Dynamics •Numericalproblems decreasewithimproved horizontalresolution –2-pointwave:poor depiction,disperseswithout advecting –7-pointwave:better depiction,dispersesand advects –20-pointwave:well-depicted andforecasted

26. NWPModels:Dynamics •Verticalcoordinate –Upperleft:terrain- followingsigma –Second:step- mountain –Third:hybridsigma- isentropic(theta) –Fourth:hybridsigma- pressure(transitionto pressurecompleteat about100-hPa)

27. NWPModel:Dynamics •Topography –Onlyasgoodastheresolutionof themodel –Canchooserepresentationof topoineachgridbox •Envelope:valleysandpasses filled,blockingeffectenhanced •Silhouette:averagestallest features,morevalleydetails •Mean:averagesallfeatures,trims mtns,diminishesmtnblocking –Standarddeviationoftopoin gridboxusedforphysical processes •Land/seamaskdependson resolutionalso

28. NWPModel:Non-hydrostaticDynamics •Addanequationforverticalaccelerations(below) •Useinhigh-resmodels(<about5-10km) –Willresultinmesoscaledetailsofconvectivesystems, includingoutflowboundariesandcoldpools –Requiressophisticatedphysics,esp.forprecipitation –Costsmoretorun,usuallysmalldomainandshort-range forecastonly T-storms,mtn.waves↑forwarm moistair weightof precip.“pulling relativetoenv.ontheair”

29. 1-kmSimulatedRadarReflectivity Actualradar validatabout sametime NCEP-WRF NSSL-WRF

30. NWPMODELS:PHYSICS

31. NWPModels:Radiation(SW) •ActualSWscatter/ reflection/abspt. btw.TOAandsfc. –Bluevs.brown lines •RRTMmodel: –UV(3bands,0.2- 0.4μm) –Visible(2bands, 0.44–0.76μm) –NearIR(9bands, 0.778–12.2μm) …12.2

32. NWPModels:Radiation(LW) •Long(IR)waveradiationabsorption/reemissioninreal atmosphere(actualspectrumshown,withabsorption bandslabeledwithgaseousabsorber) –Manyabsorptionlinesinevidence •RRTMschemebreaksLWspectruminto16bandsfor calculationsfromabout4μmto400μmwavelength

33. NWPModels:RadiationandClouds •Realatmosphere •Cloudsreflect, scatter,andabsorb SWradiation;some SWreachessurface •Cloudsabsorband reemitLWradiation •Cloudlayers,cloud fraction,waterphase (liquidand/orice),cloud overlapallshouldbe addressedinNWP models

34. NWPModels:Precip.Microphysics •Actualatmosphere – – – – – Verysmallscales(mm-μm) Condensation/evaporation/sublimation Collision/coalescence(rain) Aggregation(snow,riming) Bergeronprocess(icecrystalsgrow preferentiallyinmixedphaseclouds) –Fallratesdependonprecip.type •Models –BulkprocessesbasedonforecastT, RH,verticalmotion –Precipitationsometimesassumedto falloutinstantaneously

35. NWPModels:Convection •Convection:Realatmosphere –Conditionalinstabilitydrivesupdrafts (smallscale,<1km) –Moisturecondenseslatent heating,clds./precip. –Downdraftsfromprecip.evap. coolingandprecip.drag –Endresult:PBLcools/dries,free atmospherewarms/moistens •Conv.Param.,NWPmodels –Can’tresolvethunderstorms; unresolvedupdraftstakenintoacct. –Impactonmodelvariablesestimated •Convectivetrigger •Verticalexch.ofheat/moisture/ momentumatgridscale –Shallowconv.treatedseparately

36. NWPModels:SurfaceProcesses •Surfacewaterbalance –Precipitationminusevaporation asinput •Evaporationcontrolledbysoil moisture,vegetation,andlocal weatherconditions(wind,RH, PAR) SWnetLW GLW SHLE0 •Surfaceenergybalance –Incomingminusoutgoing energyfluxes –Sfc.waterandenergybalances coupledviaevaporation

37. NWPModels:TurbulentProcesses •Observedplanetaryboundary layerfromsurfaceupward: –Contactandsurfacelayers –Mixedlayer(day)orstableBLwith overlyingresiduallayer(night) –Cappinginversion(night)or entrainmentzone(day) •NWPversion(sub-gridscale): –Contactlayer:Fluxesdependon wind,moisture,temperatureforecasts –Surfacelayer=constantfluxlayer –Mixedandresiduallayermixing dependsonwindshear,lapserate, diffusioncoefficient –PBLtop •Foundusingforecaststability •Moisture/momentum/heatexchangew/ freeatmospheremodeled,sometimesw/ shallowconvection

38. NWPModels:TurbulentProcesses •Freeatmospheresub-grid scalemixing/turbulence –Ratedeterminedbylapserate andhorizontal/verticalwind shear –Aviationconcernswherewind shearsarestrong •Typicallynearjetstream •NWP –Lapserateandadjacentlayer andgridboxwindshearsusedto mixair –Richardsonnumberusedas proxy

39. NWPModels:TurbulentProcesses •Mountainblockingand gravitywavedrag –Dependsonstabilityofflow Gravitywave-inducingflowovermtn. overtopo,angleofwind relativetotopo,topovariability –Morestable:Moreblocking, lessgravitywavebreaking •NWP: –Usesresolvedtopoheightand sub-gridscaletopostandard deviation –Forecaststabilitypartitions flowbetweengravitywave dragandmountainblocking Blockedflowaroundmtn.