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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. - PowerPoint PPT Presentation
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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 ()– 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= -g)– 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 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
Model Initialization: The 1st step
Model Initialization: The 1st step
Model Initialization: The 1st step
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+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)}/ 2x
Numerical Integration: The 2nd step
Numerical Integration: The 2nd step
[ T(x,t+t) – T(x,t-t)]/ 2t = -U(t) { T (x+x, t) – T (x-x, t)/ 2x}
- 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
Numerical Integration: The 2nd step
[ T(x,t+t) – T(x,t-t)]/ 2t = -U(t) { T (x+x, t) – T (x-x, t)/ 2x}
- 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
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 ……
WRF FORECAST!
Use this for Ques. # 8 homework assignment
X = 100km
t = 1 hour
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