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Numerical Weather Prediction (NWP): The basics

Numerical Weather Prediction (NWP): The basics. Mathematical computer models that predict the weather Contain the 7 fundamental equations of meteorology Equations explain how the atmosphere behaves Equations initialized with observations. Numerical Weather Prediction (NWP): The basics.

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Numerical Weather Prediction (NWP): The basics

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  1. Numerical Weather Prediction (NWP): The basics • Mathematical computer models that predict the weather • Contain the 7 fundamental equations of meteorology • Equations explain how the atmosphere behaves • Equations initialized with observations

  2. Numerical Weather Prediction (NWP): The basics • Seven Fundamental Variables: • Temperature (T) • Pressure (p) • Specific humidity (q) • Density (r) • East/west wind component (u) • South/north wind component (v) • Vertical wind component (w)

  3. Numerical Weather Prediction (NWP): The basics • Seven Fundamental Equations: • Temperature equation (dT/dt=) • ADVECTION/DIABATIC/ADIABATIC • Three equations of motion (dV/dt=) • HORIZONTAL MOTIONS: PGF/COR/FR • VERTICAL MOTIONS • Hydrostatic Equation (dp/dz= -rg) • Continuity equation (du/dx + dv/dy + dw/dz=0) • Water vapor equation (dq/dt=)

  4. Model Initialization: The 1st step • Model uses previous run’s forecast as “first guess” • Today’s 12z ETA is initialized first with the 00z’s 12-hr forecast • First guess gets modified by real observations Q: Why not go right with the real obs? • Irregularly-spaced obs are ‘way out’ of “dynamic balance” • Dynamic Balance: Occurs when the mass and wind field are in balance to allow for quasi-geostrophic/hydrostatic processes

  5. Model Initialization: The 1st step

  6. Model Initialization: The 1st step

  7. Model Initialization: The 1st step -BUOYS -ASOS -SHIPS

  8. Model Initialization: The 1st step

  9. Model Initialization: The 1st step Surface Data

  10. Model Initialization: The 1st step Surface Data

  11. Model Initialization: The 1st step Surface Data

  12. Model Initialization: The 1st step Upper Air Data

  13. Numerically integrate into the future Use finite difference approximations Numerical Integration: The 2nd step

  14. Numerical Integration: The 2nd step • Example: Temperature Forecast 1) dT/dt =[ T(x,t+Dt) – T(x,t-Dt)] /2Dt dT/dt = ADV + DIAB + ADIAB Let’s only consider ADVECTION in U direction 2) –U dT/dx = -U(t) { T(x+Dx,t) – T (x-Dx,t)}/ 2Dx

  15. Numerical Integration: The 2nd step

  16. Numerical Integration: The 2nd step [ T(x,t+Dt) – T(x,t-Dt)]/ 2Dt = -U(t) { T (x+Dx, t) – T (x-Dx, t)/ 2Dx} - Solve for T (x, t+Dt): The future temperature at grid point x T ( x, t+Dt) = T (x, t-Dt) – U (t) { T (x+Dx, t) – T ( x-Dx, t} Dt/Dx

  17. Numerical Integration: The 2nd step

  18. Numerical Integration: The 2nd step

  19. Numerical Integration: The 2nd step • At the end of the time integration ….. • Have future values (aka. forecasts) of the fundamental variables at each grid point! • Keep integrating in time until model run is complete • Contour your results and you have ……

  20. ETA FORECAST

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