SHW Ch. 4 - Computer Models

• Numerical Weather Prediction (NWP):

  • British researcher Lewis F. Richardson wrote a manuscript during World War I (1914-1918) suggesting a method of "numerical forecasting; it was published in 1922, where he determined that it would take 6000 people, using mechanical hand calculators, working simultaneously to generate a 12 to 24 hour set of forecast maps.

  • Hungarian mathematician John von Neumann working at Princeton University (1948), wrote the first computer forecast model; it took a few hours to create 12, 24 & 36 hour forecasts of the 500 mb height and vorticity fields.

  • Four steps of NWP (Figure 4.3):

    • 1) ANALYSIS - objectively analyze the data over an analysis grid; Figure 4.4, 4.5 & 4.6

    • 2) INITIALIZATION - rewrite or redescribe the analysis so that the data is compatible with being input to the equations used by the forecast model; Figure 4.7 & 4.8

    • 3) PREDICTION - run the computer model in short time steps, first using the Primitive Equations:

      • Equation of Continuity: air cannot be created or destroyed

      • Hydrostatic Equation: relates the change in pressure to the change in height

      • Poisson's Equation: relates the temperature and pressure and a quantity called potential temperature (a conservative property; can be used as a "tracer" of air parcels)

      • Specific Humidity (Mixing Ratio): moisture parameterization

      • In the equations for the accelerations of the westerly, southerly and vertical components of the wind, those terms are solved from the Coriolis term, the pressure gradient term and the friction term

      • Equations for derived fields such as divergence and vorticity

      • Grid spacing and time steps can lead to computational instability

      • "Fudge Factors" are applied to "stabilize" a model

    • 4) POST PROCESS - generate products such as forecast weather maps, from the computer-model output, and "clean up" for cosmetic purposes) any erroneous contours or data; create MOS forecast

      (SHW Ch. 4 - Computer Models Continued)

• Model Problems & Limitations:

  • relatively small amount of observational data (most not made at the locations of the grid points); lack of data over polar regions and oceans

  • errors in the observational data

  • boundary errors in non-hemispheric and non-global models

  • loss of most mesoscale features (thunderstorms, tornadoes, and sometimes small tropical storms) that are too small and "slip through the cracks" in the grid

  • parameterizing topography, both large and small mountain ranges

  • parameterizing snowcover

  • parameterizing physical processes (i.e., inexact equations, and assumptions, some of which can be way off)

  • parameterizing convection ("convective feedback")

  • parameterizing land-sea interactions, especially at coastal boundaries

  • CHAOS !! Countless, small, unpredictable atmospheric fluctuations that can become dominant (i.e., amplify) as the forecast is extended into time. (A denser observing network and a "perfect" model cannot overcome chaos!)

• Ensemble Forecasting:

  • a model is run repeatedly for the same case, but with slightly different initial conditions or slight changes in the model's formulation; or,

  • several models are run for the same case to create an "ensemble member", from which a "consensus forecast" can be derived

  • "spaghetti plot:" pre-selected 500 mb heights (usually two levels) are selected from each "member" of an ensemble and drawn on a chart; often the chart will look like a plate of "spaghetti" as one goes farther out in time and the various solutions diverge; the more the "scatter" the less the confidence in the result.