University of Pennsylvania, 1945 (ENIAC museum) First one-day numerical weather forecast, 1950 NCEP IBM Supercomputers ~500 billion calculations/second 2010 NCEP IBM Supercomputers 20 trillion calculations/second 2012 NNCEP IBM Supercomputers 72 trillion calculations/second **Historical Computing Progress** Fig 17.5

The Process of Prediction Change in Y from start to future time Let’s say we want to forecast some quantity (call it Y). You know it’s value to start, call it Y(start) – the “initial condition” Change in Y from start to future time Y(future) = + Y(start) What processes change Y (say Y is temperature)? Computer is programmed with mathematical representations of these processes. Sun or no sun?? Advection Evaporation & condensation Pressure changes Etc, etc, etc After one step forward in time (called a “time step”), the predicted value of Y is used as the new “Y(start)”, and the process is repeated.

Roots of Numerical Weather Prediction Rules (equations) describing how key variables changed -- Newton: F=ma (wind and upward/downward air motions) -- Energy is neither created nor destroyed (temperature) -- Other equations for change of pressure, moisture Vilhelm Bjerknes (early 1900s) -- Suggested solving these equations could forecast the weather Lewis Richardson (WW I) -- Imagined “forecast factory” w/ 1000s human “computers” 3

DYNAMIC WEATHER PREDICTION MODELS “Physical Models” e.g. NMM, GFS SEVEN FUND. EQUATIONS -> Temperature equation -> 3 equations of motion -> Hydrostatic equation -> Continuity equation -> Water vapor equation -> (few other equations) Computer ….. Tool used to solve the mathematical equations

WEATHER PREDICTION MODELS NAM INPUT ? -> Temperature equation -> 3 equations of motion -> Hydrostatic Equation -> Continuity equation -> Water vapor equation DT/dt Temp future – Temp initially = time future – time initial

Where are the eqns. Solved? (NMM for example Model Resolution: Distance between grid points Higher resolution …… VS. Lower resolution

Where are the eqns. Solved? (NMM) Model Resolution: Distance between grid points Higher resolution …… VS. Lower resolution

Higher VS. Lower resolution (WRF/ Increasing resolution ….. Smaller scale features can be forecasted!

Example of how to build an NWP model Fig 17.3 Fig 17.4 Grid-point model: Cover 3D domain with grid of points, solve forecast equations at grid points.

-- Smallest grid “spacing” currently used in operational NWP models: 3 km -- “Sub-grid” scale features (such as t’storms) are not properly represented 10

WEATHER PREDICTION MODELS WRF -> Temperature equation -> 3 equations of motion -> Hydrostatic Equation -> Continuity equation -> Water vapor equation INPUT ? OUTPUT ?

WRF FORECAST in the E-Wall

WEATHER PREDICTION MODELS -> Temperature equation -> 3 equations of motion -> Hydrostatic Equation -> Continuity equation -> Water vapor equation INPUT ? OUTPUT ?

Why do Computer Model Forecasts Go Bad? 1. Observational limitations -- we don’t have observations everywhere, all the time -- observations have errors -- observations have to be interpolated onto the grid for initialization. 2. Atmosphere is a chaotic system -- weather never exactly repeats -- small errors grow rapidly … “sensitive dependence on initial conditions” 3. Computer models are imperfect -- translating the equations into a computer algorithm requires some approximations 14