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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