NUMERICAL WEATHER PREDICTION K. Lagouvardos-V. Kotroni Institute of Environmental Research

1. NUMERICAL WEATHER PREDICTION K. Lagouvardos-V. Kotroni Institute of Environmental Research National Observatory of Athens

2. WHAT IS THE NUMERICAL WEATHER PREDICTION? • A method to forecast weather conditions based on: • Equations describing the flow within the atmosphere as well as many physical processes • Translation into code executed on computers • Application on a specific geographic domain (grid) • Integration in time, based on initial and boundary conditions • Provision of final products (forecasts of wind, temperature, humidity, rain/snow, etc)

3. HISTORY • 1922: L. Richardson, forecast using human calculators • 1950: ΕNIAC forecast for three specific weather events • 1966: world coverage (USA) • 1970: Foundation of the European Center for Medium-range Weather Forecasts (ECMWF) • 1979 : first weather forecast issued by the ECMWF • today: 10 days forecast, horizontal resolution~15 km • 1990: first weather forecasts issued by universities, research centers and private companies.

4. EQUATIONS • Conservation of momentum (Newton’s law) • 3 equations for accelerations of wind (F = Ma) • Conservation of mass • equation for conservation of air (mass continuity) • equation for conservation of water • Conservation of energy • equation for the first law of thermodynamics • Relationship among p, V, and T • equation of state (ideal gas law)

5. NUMERICAL METHODS • Write the governing equations in form of spatial and temporal derivatives and transform them into algebraic equations • Computers can solve these equations, usually using finite difference schemes (expansion in Taylor series) on a grid • All terms are defined and computed on a fixed grid. • Example: 1-D advection equation ∂u / ∂t = -u (∂u / ∂x) ∆x ∆x x-1 x x+1

6. 3-D GRID GRID All atmospheric processes are described within a grid Need for a large number of calculations

7. Physical processes-parameterizations Parameterizations are necessary for the representation of physical processes that are small in size or short in life, complex or poorly known to be explicitly represented

8. Physical processes-parameterizations Parameterizations are necessary for the representation of physical processes that are small in size or short in life, complex or poorly known to be explicitly represented

9. What happens inside the clouds

10. WITHIN THE GRID

11. Constructing the initial conditions

12. Initial conditions: surface obs

13. Initial conditions: buoys

14. Initial conditions: soundings

15. Initial conditions: airplanes

16. Initial conditions: satellites

17. Weather forecasts at NOA Global model (Source: USA) Limited area- Region 1 Region 2

18. Limited area model: area 1

19. Limited area model: area 2

20. Final forecast product

21. Final forecast product

22. Forecast errors Limited knowledge of initial conditions Limited knowledge of physical processes (parameterizations!!!) Result: Forecast errors grow in time

23. Ensemble forecasting It is known that neither the models nor the initial conditions are perfect Problem: deterministic forecastshave limited predictability Possiblesolution:base the final forecast not only on the predictions of one model (deterministic forecast) but on an ensemble of weather model outputs ENSEMBLE FORECASTING Based on perturbing the initial conditions (20-50 perturbed members) provided to individual models, depending on a realistic spectrum of initial errors

24. Ensemble forecasting

25. OTHER APPLICATIONS • Model outputs can be used as an input to: • Wave modeling and ocean circulation • Hydrological modeling for flood forecasting • Fire expansion models • Air-quality models

26. ATMOSPHERIC RESEARCH THEORY OBSERVATIONS MODELS