Predicting Weather and Climate with Computers: Numerical Weather Prediction (NWP)

Meteo 415Fall 2012

ENIAC University of Pennsylvania, 1945~ 5000 +/- per secondFirst one-day numerical weather forecast, 1950 NOAA IBM Supercomputer~4 teraflops/second

A round planet in a parallel beamof solar radiation will have strong temperature gradients from the equator to the polesTemperature gradients create pressure gradients which drive atmospheric motions

Earth system: Atmosphere, hydrosphere, biosphere, cryosphere, geosphereFluxes of terrestrial energy and mass (water)

Observations to initialize the model

Making the ForecastF at future time=F now+Change in F between now and future timeNeed partial differential equation describing rate of change of FForecast a quantity F (temp, pressure, humidity, wind) at point xInitialization, or initial conditions (some from satellite)

The Equations of Atmospheric MotionConservation of MomentumConservation of EnergyConservation of MassConservation of Constituent qEquation of StateMaterial Derivative

Constructing an NWP modelGrid-point model: Cover 3-D domain with grid of points, solve forecast equations at grid points.Examples: Eta, WRF (Weather Research and Forecast)

Spectral model: atmospheric variables presumed to be wave-like functions (such as sines and cosines). Spectral models are more attune with wave-like motions in real atmosphere, so they save computational time. Long-range (beyond 4-day) forecasts usually come from spectral modelsConstructing an NWP modelExamples: GFS (Global Forecast System), European

Atmospheric Numerical ModelsBasic LimitsInitial Conditions (resolution)Boundary Conditions (forces)Physics (inexact, empirical relationships)Round-off errors (computational)Chaos (systemic)

Models Limits

Atmospheric Numerical ModelsStarting the ModelStart with first guess fieldUsually a 6 hour forecast from same modelAdvantages:On same grid domain with the parameters neededReasonable assumption errors accumulate with timeComputational short-cutsAdjust with Observations - window of opportunity - discern good v bad reports - automate the process

The WRF Initialization

Reminder on WRF Initialization

Other Data Sources

SST Effects from Satellite

Snow/Ice Effects from Satellite

Terrain Definition in GSI

Better Resolution in Vertical

Non-Hydrostatic Effects in Mts

Global Model Initial Conditions

Satellite Input Quality AssuranceIR derived winds: 700-1000mb [7048 accepted]Water Vapor derived winds: 300-700mb [1847 accepted]IR derived winds: 150-300mb [4653 accepted]

Estimating Model Radiance

Shortcomings of Model EstimatesRadiative transfer law approximations are applied. Radiances from several different satellite channels are used together to produce one temperature sounding. The derived soundings essentially are layer averages in layers defined by the absorber weighting functions for the observed radiation wavelengths. These are interpolated to much thinner model layers to compare against model fields, or they are interpolated to standard sounding levels and model data are also interpolated to standard sounding levels for comparison.

Shortcomings of Model EstimatesErrors in various packagesAnalysis SchemesObservational (instrument)Representativeness*Model physics*Example: Satellite microwave soundings (actually, radiances) over the ocean. These are the only source of temperature profiles in cloudy regions! Resolving only 3 or 4 thick tropospheric levels, they vertically smear out model-resolved tropopause folds and sloping frontal zones. If use of this data degrades the background fields, then the data should be rejected.

Data ReliabilityAscertaining what to keep and throw away

Data ReliabilityAscertaining what to keep and throw away The No Surprise Snowstorm Jan 25, 2000

Data ReliabilityKnown error distributions for GOES in 4DAS

Challenges of Using Satellite DataAny radiation that's sensed comes from a deep layer of the atmosphere, so vertical resolution is coarser than model vertical resolution This will improve greatly when interferometers replace radiometers. This is not scheduled on GOES until at least GOES-S The proper conversion of satellite radiances to temperatures requires knowing the emissivity at the bottom of the layer being sensed. This presents problems over land, so data over land are only reliable for channels sensing the upper troposphere and stratosphere

Atmospheric Numerical ModelsThe Pitfalls of Data AssimilationSUMMARYData Void regions (particularly the oceans)Bad First Guess FieldsGood Data rejectedAnalysis Assumptions

Typical Model Forecast Presentation: 4-panel prog

Typical Model Forecast Presentation: 4-panel prog

700-mb (~10,000 ft) relative humidity (>70% and >90% shaded green)

A good forecast

Simulating tomorrows satellite and radar imageryAfter-the-fact test caseSnowstorm of February 11-13, 2006(26.9 Central Park)February 11-13, 2006

Simulating tomorrows satellite and radar imageryWRF simulation,12 km domain

Clouds are defined using WRF cloud ice (kg/kg) and cloud liquid water (kg/kg)

Comparison of the water vapor image computed using WRF and the radiative transfer model (left) with the observed (by GOES-12) (below)

References

The COMET Program: www.meted.ucar.edu/WeatherVentures, Inc.: www.weatherventures.com/University of Pennsylvania: www.library.upenn.edu/exhibits/rbm/mauchly/jwm0-1.html

ReferencesFixing Errant Data with Complex Quality ControlCollins, W.G., 1997: The use of complex quality control for the detection and correction of rough errors in rawinsonde heights and temperatures: A new algorithm at NCEP/EMC. NCEP Office Note 419, 49 pp. Julian, P.R., 1989: Quality control of the aircraft file at the NMC. Part I. NCEP Office Note 358, 13 pp. [Note - NCEP office notes are scheduled to be available online within a few months of publication of this module] References on Many Aspects of How 3D-VAR Works in the Global Data Assimilation SystemDerber, J. C., D.F. Parrish, and S. J. Lord, 1991: The new global operational analysis system at the National Meteorological Center. Wea. and Forecasting, 6, 538-547.

ReferencesDerber, J. C. and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126, 2287-2299. McNally, A.P., J.C. Derber, W.-S. Wu, and B.B. Katz, 2000: The use of TOVS level-1B radiances in the NCEP SSI analysis system. Quart. J. Roy. Meteor. Soc., 126, 689-724. Parrish, D. F. and J. C. Derber, 1992: The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev., 120, 1747-1763.

Spatial Patterns of Model Error Used in 3D-VAR AnalysisDerber, J. C. and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 51A, 195-221

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