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