1. Downscaling Downscaling correction of T2m For Sochi region Inna Rozinkina, Mikhail Chumakov, Sergey Chechin, Mikhail Zaychenko, Denis Blinov, Michail Nikitin, katerina Kazakova

2. Motivation: The significant level of errors of near-surface values, (first - in T2m) in Sochi Region in Sochi Region (first – in mountain cluster) for points (meteogram products) 02.09.2013 2COSMO GM, Sibiu, 2-5 Sept. 2013

3. The 2m temperatures observed at Krasnaya Polyana station in February, 2012 and the COSMO-RU07 model forecasts at the nearest grid point over the same period blue green red The temperatures observed at the station are shown in blue; the temperature forecasts - in green; the averaged forecast - in red; violet the difference between the observed temperature and the averaged forecast is depicted in violet, COSMO General Meeting 2012, Lugano, September, 10-13

4. The big level of T2m errors The big initial values of errors The evident diurnal variation of errors It is possible to use the spectral approach for KF correction (because the duirnal variation of errors)

5. The temperature T observed at the station at time t is represented as The difference D between the observed temperature and the averaged forecast at time t is represented as where Tp is the window width used for expanding the temperature forecasts (4-7 days) and Np is the number of harmonics used (Tp multiplied by (1, 2, or 3)), where Td is the window width used for expanding D (1 day) and Nd is the number of harmonicas used (1, 2, or 3), The forecast at the time t is calculated using the formula COSMO General Meeting 2012, Lugano, September, 10-13

6. Errors of the forecasts from the observations before and after the correction for various filter parameters, feb2012 (mean deviation (upper), and root-mean-square deviation (lower)) COSMO General Meeting 2012, Lugano, September, 10-13

7. Very big level of T2m Errors – What is mean cause? Difference between the real heights of station and model heights The use of vertical gradient (adiabatic) is not universal approach (The cases of inversions are observed)

8. The forecasts of vertical T gradient for points of meteograms can be obtained with use of FieldExtra

9. 907.08.2013Совещание Сочи ГМЦ август 2013

10. Tuning of algorithms of T grad correction The runs of COSMO-Ru07 and COSMO Ru02 were corrected and analyzed The best results were obtained with use the combined T Grad

11. The examples of correction of meteograms data

12. Operational COSMO- coupled postprocessing technology 19.03.2016 CUS 2013: I.Rozinkina and Al. Use of models by forecasters, experiences from the 2012 – 2013 winter 12 Selection of obs.dataFieldextfra Data base FROST (Server) COSMO-RU runs Corrected Meteograms for points Meteograms DESSIMINATION FOR USERS Vert. Grad. Correction vertical gradients of T Corrected meteograms (step1) KF correction GRIB Corrected meteograms (step2)

13. Basic principles 02.09.201313COSMO GM, Sibiu, 2-5 Sept. 2013 T1 T2 T T 1 =Ttrue+g 1 T 2 =Ttrue+g 2 g 1, g 2 -stochastic variable Conditions: Mathematical expectation 1.M(g 1 )=0 2.M(g 2 )=0 Variance 1.D(g 1 )=σ 1 2 2.D(g 2 )=σ 2 2 As a rule, Kalman filter is written as: T cor1 =T 1 +K*(T 2 -T 1 ) K-amplification factor K=P 1 / σ 2 2 P 1 = D(g 1 )* D(g 2 )/(D(g 1 )+D(g 2 )) – variance of estimation Estimation error minimization condition: M{(Ttrue-T cor ) 2 } → 0

14. Basic principles 02.09.201314COSMO GM, Sibiu, 2-5 Sept. 2013 T1T2 T cor1 T 1 =Ttrue+g 1 T 2 =Ttrue+g 2 T 3 =Ttrue+g 3 g i -stochastic variable Conditions: Mathematical expectation 1. M(g i )=0 Variance 2. D(g i )=σ i 2 Kalman filter is written as: T cor2 = T cor1 +K*(T cor1 –T 3 ) K-amplification factor K=P 2 / σ 3 2 P 2 = P 1 *D(g 3 )/(P 1 +D(g 2 )) – variance of estimation When having three or more measurements, recurrent formula for estimation can be obtained T3... T cor2

15. Scheme of COSMO-model (2.2 km) forecast series for Sochi region 02.09.201315COSMO GM, Sibiu, 2-5 Sept. 2013

16. Variance calculation 02.09.201316COSMO GM, Sibiu, 2-5 Sept. 2013 It is supposed that variance of forecast error is equal to value of variance, based on calculation three previous days 00h 15h 00h 15h 6 May 7 May 8 May 9 May obs forecast ∆1=forecast(6May)-obs(6May) ∆2=forecast(7May)-obs(7May) ∆3=forecast(8May)-obs(8May) Obtain variance for 15h forecast from 00h 9 May and systematic error (mathematical expectation)

17. Results of Kalman filter applying to COSMO-Ru 2.2 km T2m forecasts for station Adler. May 2013. RMSE values for T2m 02.09.201317COSMO GM, Sibiu, 2-5 Sept. 2013 Start 00 hStart 06 hStart 12 hStart 18 h Forecast FilteredRef.FilteredRef.FilteredRef.FilteredRef. 03 H1,32,01,32,30,91,41,12,0 06 H1,41,11,41,61,3 1,71,8 09 H1,3 1,62,71,11,51,72,1 12 H1,51,41,31,51,71,91,61,2 15 H1,31,61,11,91,72,11,31,2 18 H1,41,31,71,81,1 1,4 21 H1,11,51,72,01,31,11,21,6 24 H1,71,91,1 1,51,3 Pink – improvement, red – significant improvement, blue – slight worsening

18. Plans 02.09.201318COSMO GM, Sibiu, 2-5 Sept. 2013 Numerical experiments for the whole year are needed for statistics It is required to research the impact of the using order of forecast series The question of using the appropriate number of coefficients for filtering the required estimation according to their variance values is open nowadays It is needed to research the ability of using the averaged value of a lot of used forecasts in Kalman filter algorithm Numerical experiments for testing autoregression algorithm of Kalman filter

19. Conclusions The two-step correction technology of COSMO meteograms was proposed Only the correction with use the forecasts of T Grad (I step) can significant improve the results for forecasts for points The technology for 1 step of correction was developed and now is close to operational implementation The KF correction (II step) significant improve the forecasts for little forecats lead times and specifies of diurnal cycle – in progress

20. Thank you for your attention! 02.09.201320COSMO GM, Sibiu, 2-5 Sept. 2013