Kalman filtering at HNMS

1. Kalman filtering at HNMS Petroula Louka Hellenic National Meteorological Service louka@hnms.gr

2. Kalman filter method • The main goal is the estimation of the bias yt as a function of the forecasting model direct output (mt): • The coefficients (xi,t) are the parameters that have to be estimated by the filter and vt the Gaussian non systematic error. • The state vector of the filter is the one formed by the coefficients 11th COSMO General Meeting

3. Kalman filter method (cont) • The observation matrix takes the form: • The system and observation equations, are: • The variance matrices of the system equation, Wt, and the observation equation, Vt, are estimated based on the sample of the last 7 values of and : 11th COSMO General Meeting

4. NWP products at HNMS • COSMO runs with a resolution of ~7km. • SKIRON runs with similar resolution. • It is a non-hydrostatic model similar to COSMO. • It is based on Eta/NCEP model further developed by the University of Athens. • ECMWF deterministic forecasts at 25km resolution. • In order to fulfill the demands of the Forecasting Centre, Kalman filtering is applied, operationally, to NWPs (at the nearest model location): • 2m maximum and minimum temperature forecasts, and • 10m maximum wind speed COSMO forecasts (still at a pilot stage). 11th COSMO General Meeting

5. Statistical analysis • Statistical analysis of maximum and minimum values of 2m temperature (modeled and filtered) of all three models for the whole 2008 divided by season for all available observation stations. • Statistical analysis of maximum 10m wind for summer 2009. 11th COSMO General Meeting

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10. Preliminary results for wind 11th COSMO General Meeting

11. Applications • Wind power applications – ANEMOS European project • Galanis G., Louka P., Katsafados P., Pytharoulis I., and Kallos G.: Applications of Kalman filters based on non-linear functions to numerical weather predictions. Ann. Geophys., 2006, 24, 2451-2460. • Louka P., Galanis G., Siebert N., Kariniotakis G., Katsafados P. Pytharoulis I., Kallos G.: Improvements in wind speed forecasts for wind power prediction purposes using Kalman filtering. J. Wind Eng. Ind. Aerodyn., 2008, 96, 2348-2362. 11th COSMO General Meeting

12. Remarks • Kalman filtering fulfills its scope removing the systematic bias from the modelled data. • Even when applied to temperature forecasts of a global model it seems to “correct” them adequately providing similar values with those of the filtered regional forecasts. • When considering wind, a non-linear Kalman filter (order of 3) is applied. Although, it is still in a pilot stage, this operational use seems to perform quite well. 11th COSMO General Meeting

13. How can Kalman filter applications fulfill the requirements of the forecasters? • Kalman filtering performs well, when the error is systematic. How, can it be improved when a “large” change in the weather occurs? • How can we increase the accuracy of filtered data for more than 2 days ahead? 11th COSMO General Meeting

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15. Preliminary results for wind 11th COSMO General Meeting