QPF and Numerical QPF and Numerical Modeling BasicsModeling Basics

Tom HopsonTom Hopson

Utility of a Three-Tier Forecast Utility of a Three-Tier Forecast SystemSystem

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.

forecast products for hydrologic forecast products for hydrologic applicationsapplications

Seasonal -- ECMWF System 3Seasonal -- ECMWF System 3- based on: 1) long predictability of ocean circulation, 2) variability in tropical - based on: 1) long predictability of ocean circulation, 2) variability in tropical

SSTs impacts global atmospheric circulationSSTs impacts global atmospheric circulation- coupled atmosphere-ocean model integrations- coupled atmosphere-ocean model integrations- out to 7 month lead-times, integrated 1Xmonth- out to 7 month lead-times, integrated 1Xmonth- 41 member ensembles, 1.125X1.125 degrees (TL159L62), 130km- 41 member ensembles, 1.125X1.125 degrees (TL159L62), 130km

Monthly forecasts -- ECMWFMonthly forecasts -- ECMWF- “fills in the gaps” -- atmosphere retains some memory with ocean variability - “fills in the gaps” -- atmosphere retains some memory with ocean variability impacting impacting atmospheric circulationatmospheric circulation- coupled ocean-atmospheric modeling after 10 days- coupled ocean-atmospheric modeling after 10 days- 15 to 32 day lead-times, integrated 1Xweek- 15 to 32 day lead-times, integrated 1Xweek- 51 member ensemble, 1.125X1.125 degrees (TL159L62), 130km- 51 member ensemble, 1.125X1.125 degrees (TL159L62), 130km

Medium-range -- ECMWF EPSMedium-range -- ECMWF EPS- atmospheric initial value problem, SST’s persisted- atmospheric initial value problem, SST’s persisted- 6hr - 15 day lead-time forecasts, integrated 2Xdaily- 6hr - 15 day lead-time forecasts, integrated 2Xdaily- 51 member ensembles, 0.5X0.5 deg (TL255L40), 80km- 51 member ensembles, 0.5X0.5 deg (TL255L40), 80km

Short-range -- RIMESShort-range -- RIMES- 26-member Country Regional Integrated Multi-hazard Early Warning - 26-member Country Regional Integrated Multi-hazard Early Warning System System (RIMES) WRF Precipitation Forecasts(RIMES) WRF Precipitation Forecasts- 3hr - 5 day lead-time, integrated 2X daily- 3hr - 5 day lead-time, integrated 2X daily- 9km resolution- 9km resolution

1)1) Greater accuracy of ensemble mean forecast (half Greater accuracy of ensemble mean forecast (half the error variance of single forecast)the error variance of single forecast)

2)2) Likelihood of extremesLikelihood of extremes

3)3) Non-Gaussian forecast PDF’sNon-Gaussian forecast PDF’s

4)4) Ensemble spread as a representation of forecast Ensemble spread as a representation of forecast uncertaintyuncertainty

Motivation for Generating Ensemble Discharge Forecasts (from ensemble weather forecasts)

Motivation for generating ensemble forecasts (weather or hydrologic):=> a well-calibrated ensemble forecast provides a prognosis of its own uncertainty

or level of confidence

What is a Model?What is a Model?

Take the equations that describe Take the equations that describe atmospheric processes.atmospheric processes.

Convert them to a form where they can Convert them to a form where they can be programmed into a large computer.be programmed into a large computer.

Solve them so that this software Solve them so that this software representation of the atmosphere representation of the atmosphere evolves within the computer.evolves within the computer.

This is called a “model” of the This is called a “model” of the atmosphereatmosphere

What do we mean by “solve the What do we mean by “solve the equations”equations”

The equations describe how the The equations describe how the atmosphere changes with time.atmosphere changes with time.

For example, one equation would beFor example, one equation would be

advection

oncondensati nevaporatio

convectionconduction

IR(loss)IR(gain) solar

time

Tchange

So – “solving” the equation would be So – “solving” the equation would be to estimate the terms on the right to estimate the terms on the right side, add them up, and obtain the side, add them up, and obtain the

rate of change of temperaturerate of change of temperature

How theHow the Model ForecastsModel Forecasts

Time

Tem

per

atu

re

T now (observed)

X

X

Model-calculated T changes

XX

XX

This equation is solved for a This equation is solved for a three-three-dimensionaldimensional “matrix” of points (or a “matrix” of points (or a grid) that covers the atmosphere grid) that covers the atmosphere from the surface to some level near from the surface to some level near the top of the atmosphere.the top of the atmosphere.

Here is a 2-dimensional slice Here is a 2-dimensional slice through the grid……..through the grid……..

Ground

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

100 millibars

Grid points

Co

mp

uta

tio

nal

lev

els

East-West Distance

Alt

itu

de

X X X

Grid-point spacing

Similar Equations Would be Similar Equations Would be Solved forSolved for

East-west wind componentEast-west wind component North-south wind componentNorth-south wind component Specific humidity (or RH)Specific humidity (or RH) PressurePressure Cloud waterCloud water Rain/snow waterRain/snow water

Two Types of ModelsTwo Types of Models

Global – grid covers the entire Global – grid covers the entire atmosphere of Earth (global models)atmosphere of Earth (global models)

Limited-area – grid covers a region of the Limited-area – grid covers a region of the atmosphere such as continent or a state atmosphere such as continent or a state or a city (limited area models)or a city (limited area models)

““Nested” gridsNested” grids Grids can be telescoped, or nested, to Grids can be telescoped, or nested, to

zoom in on a small areazoom in on a small area

Large grid-point spacing – say 90 km

30 km

10 km

Uses of Atmospheric Models Uses of Atmospheric Models

Daily weather prediction (let models run into Daily weather prediction (let models run into the future for 1-10 days) the future for 1-10 days)

Climate prediction (let models run for years)Climate prediction (let models run for years)- “what-if” experiments, e.g., what will - “what-if” experiments, e.g., what will happen if we double the COhappen if we double the CO22??

- simply let the model run forward - simply let the model run forward Research – Study the model solution when you Research – Study the model solution when you

don’t have good observations of real don’t have good observations of real atmosphereatmosphere

The Model SetupThe Model Setup

Numerical Weather Prediction (NWP)Model Fundamentals: A review(Plus 1/2 slide on climate models)

William R. Bua, UCAR/COMET

NCAR ISP Summer colloquium on African Weather and Climate27 July 2011

Outline

• What is the land-ocean-atmosphere system andits connection to weather and climate?

• What is in an NWP system?

• What are the shortcomings of NWP models?

• Ensemble Forecast Systems: Mitgating theshortcomings of NWP models

• Conservation of momentum,heat, moisture

• Conservation of mass

• Hydrostatic approximation

• Dynamical equations arecoupled to– The earth’s land/ocean surface

(friction/ turbulence, surfaceevaporation/ evapotranspirationand precipitation)

– Sub-grid scale physical/diabaticprocesses (radiation, evaporation/condensation, water phasechanges in precip processes,cloud/radiation interaction, etc.)

The Land-Ocean-Atmosphere SystemEquations of Motion (Eulerian/Pressure coordinate form)

Simplified Equations

– Outgoing terrestrial radiation

• Microphysics– Condensation/evaporation/

sublimation– Collision/coalescence, mixed

phase processes, phasechanges

• Convection (shallow *and*deep)

• Turbulent processes• Land surface processes

– Vegetation, soil moisture,snow, surface energybalance and fluxes

topography

Precipitationmicrophysics

Land and

Vegetation, soil moisture,surface energy balance/fluxes

Incomingshortwaverad. Shortwave

scattering

Reflection

The Land-Ocean-Atmosphere SystemParameterized Land/Atmosphere Physical Processes

• Radiation processes– Incoming solar radiation

Convection

Longwave Radiation

Longwave Rad.

Climate and Weather Prediction ModelsGeneral Circulation(Climate) models

• Interested in climate details (means,anomalies, standard deviations) at long

time scales

• Long, lower resolution runs– Climate drift must be corrected

• Physical processes are simplified

• Slowly varying processes must beaccounted for

– A fully coupled system

– For multi-decadal climate change• Interactive vegetation adapts to

changing climate

• Carbon cycle/slowly varyingatmospheric chemistry

Numerical WeatherPrediction (NWP) Models

• Interested in short time scalesand weather details

• Short, high resolution runs– Climate drift not important,

especially for short range

• Physical processes are morerealistic (e.g. microphysics)

• Atmosphere/land coupling; slowprocesses held fixed

– Fixed ocean (SSTs)/sea ice

– Fixed vegetation

– Fixed atmospheric composition/greenhouse gases

NWP MODELS: DYNAMICS

NWP Models: Dynamics

• Horizontal coordinatesystem– Equations computed

either by

– Breaking down thehorizontal direction intogrid points and takingdifferences from point topoint …. or

– Breaking down the largescale flow into a seriesof increasingly smallsine and cosine wavesand plugging those intothe equations to do thecalculations

…+

= Shortest wave

NWP Models: Dynamics• Numerical problems

decrease with improvedhorizontal resolution– 2-point wave: poor

depiction, disperses withoutadvecting

– 7-point wave: betterdepiction, disperses andadvects

– 20-point wave: well-depictedand forecasted

NWP Models: Dynamics• Vertical coordinate

– Upper left: terrain-following sigma

– Second: step-mountain

– Third: hybrid sigma-isentropic (theta)

– Fourth: hybrid sigma-pressure (transition topressure complete atabout 100-hPa)

NWP Model: Dynamics• Topography

– Only as good as the resolution ofthe model

– Can choose representation oftopo in each grid box

• Envelope: valleys and passesfilled, blocking effect enhanced

• Silhouette: averages tallestfeatures, more valley details

• Mean: averages all features, trimsmtns, diminishes mtn blocking

– Standard deviation of topo ingrid box used for physicalprocesses

• Land/sea mask depends onresolution also

NWP Model: Non-hydrostatic Dynamics

• Add an equation for vertical accelerations (below)

• Use in high-res models (< about 5-10 km)– Will result in mesoscale details of convective systems,

including outflow boundaries and cold pools

– Requires sophisticated physics, esp. for precipitation

– Costs more to run, usually small domain and short-rangeforecast only

T-storms, mtn. waves ↑ for warmmoist air

weight ofprecip. “pulling

relative to env. on the air”

NSSL-WRFNCEP-WRF

1-km Simulated Radar Reflectivity

Actual radarvalid at about

same time

NWP MODELS: PHYSICS

NWP Models: Radiation (SW)• Actual SW scatter/

reflection/ abspt.btw. TOA and sfc.– Blue vs. brown

lines

• RRTM model:– UV (3 bands, 0.2-

0.4 μm)

– Visible (2 bands,0.44 – 0.76 μm)

– Near IR (9 bands,0.778 – 12.2 μm)

… 12.2

NWP Models: Radiation (LW)

• Long (IR) wave radiation absorption/reemission in realatmosphere (actual spectrum shown, with absorptionbands labeled with gaseous absorber)– Many absorption lines in evidence

• RRTM scheme breaks LW spectrum into 16 bands forcalculations from about 4 μm to 400 μm wavelength

NWP Models: Radiation and Clouds

• Real atmosphere

• Clouds reflect,scatter, and absorbSW radiation; someSW reaches surface

• Clouds absorb andreemit LW radiation

• Cloud layers, cloudfraction, water phase(liquid and/or ice), cloudoverlap all should beaddressed in NWPmodels

–

–

–

–

–

Very small scales (mm - μm)

Condensation/evaporation/sublimation

Collision/coalescence (rain)

Aggregation (snow, riming)

Bergeron process (ice crystals grow

preferentially in mixed phase clouds)

– Fall rates depend on precip. type

• Models– Bulk processes based on forecast T,

RH, vertical motion

– Precipitation sometimes assumed tofall out instantaneously

NWP Models: Precip. Microphysics

• Actual atmosphere

• Convection: Real atmosphere– Conditional instability drives updrafts

(small scale, <1 km)

– Moisture condenses latentheating, clds./precip.

– Downdrafts from precip. evap.cooling and precip. drag

– End result: PBL cools/dries, freeatmosphere warms/moistens

• Conv. Param., NWP models– Can’t resolve thunderstorms;

unresolved updrafts taken into acct.

– Impact on model variables estimated

• Convective trigger

• Vertical exch. of heat/moisture/momentum at grid scale

– Shallow conv. treated separately

NWP Models: Convection

NWP Models: Surface Processes

• Surface water balance– Precipitation minus evaporation

as input• Evaporation controlled by soil

moisture, vegetation, and localweather conditions (wind, RH,PAR)

• Surface energy balance– Incoming minus outgoing

energy fluxes

– Sfc. water and energy balancescoupled via evaporation

SH LE 0G LWSWnet LW

NWP Models: Turbulent Processes• Observed planetary boundary

layer from surface upward:– Contact and surface layers– Mixed layer (day) or stable BL with

overlying residual layer (night)– Capping inversion (night) or

entrainment zone (day)

• NWP version (sub-grid scale):– Contact layer: Fluxes depend on

wind, moisture, temperature forecasts– Surface layer = constant flux layer– Mixed and residual layer mixing

depends on wind shear, lapse rate,diffusion coefficient

– PBL top• Found using forecast stability• Moisture/momentum/heat exchange w/

free atmosphere modeled, sometimes w/shallow convection

• Free atmosphere sub-gridscale mixing/turbulence

– Rate determined by lapse rateand horizontal/ vertical windshear

– Aviation concerns where windshears are strong

• Typically near jet stream

• NWP– Lapse rate and adjacent layer

and grid box wind shears used tomix air

– Richardson number used asproxy

NWP Models: Turbulent Processes

gravity wave drag– Depends on stability of flow

over topo, angle of windrelative to topo, topo variability

– More stable: More blocking,less gravity wave breaking

• NWP:– Uses resolved topo height and

sub-grid scale topo standarddeviation

– Forecast stability partitionsflow between gravity wavedrag and mountain blocking

NWP Models: Turbulent Processes• Mountain blocking and

Blocked flow around mtn.

Gravity wave-inducing flow over mtn.