1. Role of Statistics in Climate Sciences
Boulder, NCAR, November 29-30, 2001
MADDEN SYMPOSIUM
Role of Statistics in Climate Sciences

2. Overview Randomness as a conceptual model Randomized parameterizations
Estimation in dynamical systems

3. Stochasticity in climate:
ubiquity of non-linear components creates variability indistinguishable from (the mathematical construct of) statistical noise.

5. Randomized Parameterization

6. Randomized Parameterization

7. Randomized Parameterization

8. Randomized Parameterization
The role of statistics here is to
first suggest a suitable distribution S
then to condition the free parameters in a manner consistent with empirical evidence and dynamical wisdom.
The parameters often include parameters like means, variances and lag correlations.
As a result of such a „randomized parameterization“ the statistics of the state variables may change.

9. Randomized Parameterization
Example:
Energy Balance Model, with albedo nonlinearly dependent on the state variable (temperature)
albedo
temperature
Transmissivity parameterized as constant
temperature
years

10. Randomized Parameterization
Transmissivity as constant + Gaussian noise
temperature
Randomized Parameterization
years

11. Randomized Parameterization
Problem: high-frequency variations of wind speed and its effect on ocean waves 6 3
1 hour
Randomized Parameterization

12. Randomized Parameterization
Problem: high-frequency variations of wind speed and its effect on ocean waves
Randomized Parameterization
 3 days

14. Estimation in dynamical systems

15. Estimation in dynamical systems

16. Estimation in dynamical systems
Simulation of water level along the North Sea coast in 20 x 20 km2 boxes. Simulated box-mean water level differs from water level along the shore line.

17. Estimation in dynamical systems
POPs

18. Estimation in dynamical systems
POPs of equatorial velocity potential at 200 hPa
Estimation in dynamical systems
0o oE o oW o

19. Estimation in dynamical systems
POP coefficients (= index of MJO) in 1985
Estimation in dynamical systems
days

20. Estimation in dynamical systems
Propagation of velocity potential and OLR pattern in winter
Estimation in dynamical systems

21. Estimation in dynamical systems
Propagation of velocity potential and OLR pattern in summer
Estimation in dynamical systems

22. Estimation in dynamical systems
Forecasting with recduced POP model
Estimation in dynamical systems
Logintudinal location of minimum of velocity potential

23. Estimation in dynamical systems
Skill of forecasting with POP model
correlation skill score
Estimation in dynamical systems
days

24. Purpose of statistics: Combination of dynamical knowledge and limited empirical evidence to build consistent descriptions of reality