Numerical Weather Prediction (NWP): The basics

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 WRF is initialized first with the 6z’s 6-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

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 [ 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

18. Numerical Integration: The 2nd step

19. Numerical Integration: The 2nd step

20. 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 ……

21. WRF FORECAST!

22. Use this for Ques. # 8 homework assignment X = 100km t = 1 hour