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

2. 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.

3. 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

4. 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

5. 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

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

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

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

9. 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.

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

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

12. WRF FORECAST
in the E-Wall

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

14. 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