1. Predicting Weather and Climate with Computers: Numerical Weather Prediction (NWP)
Meteo 415
Fall 2012

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

3. A round planet in a parallel beam
of solar radiation will have strong temperature gradients from the
equator to the poles
Temperature gradients create pressure gradients which drive atmospheric motions

4. Fluxes of terrestrial energy and mass (water)
Earth system: Atmosphere, hydrosphere, biosphere, cryosphere, geosphere
Fluxes of terrestrial energy and mass (water)

6. Observations to “initialize” the model

7. Change in F between now and future time
Making the Forecast
Forecast a quantity F (temp, pressure, humidity, wind) at point x
F at future time
F now +
Change in F between now and future time =
“Initialization”, or “initial conditions” (some from satellite)
Need partial differential equation describing rate of change of F

8. The Equations of Atmospheric Motion
Conservation of Momentum
Conservation of Energy
Conservation of Mass
Conservation of Constituent q
Equation of State
Material Derivative

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

10. Constructing an NWP model
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 models
Examples: GFS (Global Forecast System), European

11. Atmospheric Numerical Models
Basic Limits
Initial Conditions (resolution)
Boundary Conditions (forces)
Physics (inexact, empirical relationships)
Round-off errors (computational)
Chaos (systemic)

12. Models Limits

13. Atmospheric Numerical Models
Starting the Model
Start with first guess field
Usually a 6 hour forecast from same model
Advantages:
On same grid domain with the parameters needed
Reasonable assumption – errors accumulate with time
Computational short-cuts
Adjust with Observations
- window of opportunity
- discern good v bad reports
- automate the process

14. The WRF Initialization

15. Reminder on WRF Initialization

16. Other Data Sources

17. SST Effects from Satellite

18. Snow/Ice Effects from Satellite

19. Terrain Definition in GSI

20. Better Resolution in Vertical

21. Non-Hydrostatic Effects in Mts

22. Global Model Initial Conditions

23. Satellite Input – Quality Assurance
Water Vapor derived winds: mb
[1847 accepted]
IR derived winds: mb [7048 accepted]
IR derived winds: mb [4653 accepted]

24. Estimating Model Radiance

25. Shortcomings of Model Estimates
Radiative 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.

26. Shortcomings of Model Estimates
Errors in various packages
Analysis Schemes
Observational (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.

27. Data Reliability
Ascertaining what to keep and throw away

28. Data Reliability Ascertaining what to keep and throw away –
The No Surprise Snowstorm – Jan 25, 2000

29. Data Reliability
Known error distributions for GOES in 4DAS

30. Challenges of Using Satellite Data
Any 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

31. Atmospheric Numerical Models
The Pitfalls of Data Assimilation
SUMMARY
Data Void regions (particularly the oceans)
Bad First Guess Fields
Good Data rejected
Analysis Assumptions

32. Typical Model Forecast Presentation: “4-panel prog”

34. Typical Model Forecast Presentation: “4-panel prog”

35. 700-mb (~10,000 ft) relative humidity (>70% and >90% shaded green)

36. A good forecast

37. Simulating tomorrow’s satellite and radar imagery
After-the-fact test case
Snowstorm of February 11-13, 2006
(26.9” Central Park)
February 11-13, 2006

38. Simulating tomorrow’s satellite and radar imagery
WRF simulation,
12 km domain
Clouds are defined using WRF cloud ice (kg/kg) and cloud liquid water (kg/kg)

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

40. References The COMET Program: www.meted.ucar.edu/
WeatherVentures, Inc.:
University of Pennsylvania:

41. Fixing Errant Data with Complex Quality Control
References
Fixing Errant Data with Complex Quality Control
Collins, 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 System
Derber, 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,

42. References
Derber, J. C. and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126,
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,
Parrish, D. F. and J. C. Derber, 1992: The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev., 120,
Spatial Patterns of Model Error Used in 3D-VAR Analysis
Derber, J. C. and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 51A,