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 (  ) –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= -  g) –Continuity equation (du/dx + dv/dy + dw/dz=0) –Water vapor equation (dq/dt=)

4. Model Initialization: The 1 st 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 1 st step

9. Surface Data

10. Model Initialization: The 1 st step Surface Data

11. Model Initialization: The 1 st step Surface Data

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

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

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

15. Numerical Integration: The 2 nd step

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

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

18. Numerical Integration: The 2 nd step

20. 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. Numerical Integration: The 2 nd step

22. WRF FORECAST!

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