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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
• 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)
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=)
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 quasigeostrophic/hydrostatic processes
Model Initialization: The 1st step
Model Initialization: The 1st step
Model Initialization: The 1st step
-BUOYS
-ASOS
-SHIPS
Model Initialization: The 1st step
Model Initialization: The 1st step
Surface Data
Model Initialization: The 1st step
Surface Data
Model Initialization: The 1st step
Surface Data
Model Initialization: The 1st step
Upper Air Data
Numerical Integration: The 2nd step
• Numerically integrate into the future
• Use finite difference approximations
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
Numerical Integration: The 2nd step
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
Numerical Integration: The 2nd step
Numerical Integration: The 2nd step
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 ……
ETA FORECAST