1. Progea S.r.l Bologna & SMHI CARPE DIEM 6TH PROJECT MEETING JUNE 24 HELSINKI WP 4: Assessment of Nwp Model Uncertainty Including Models Errors Dott.ssa Riccardo Sara

2. Progea S.r.l Bologna & SMHI METHODOLOGY Carpe Diem 6th Project Meeting June 24 Helsinki Aim: to estimate relative weight of background error covariance P and observations error covariance R matrices into HIRLAM variational assimilation system HIRVDA Spatially distribuited observations for each level Hirlam domain Estimations of variogram parameters for each time step analysis with Kriging and ML method in order to estimate innovation covariance matrix from the innovation values Amplification or a de-amplification of factor “alpha” is used to approach the optimal interpolation

3. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki ALGORITHM OF KRIGING METHOD We have a set of innovation vector z * i   interpolating weights  ij   covariance of innovation  ij  variogram could be esponential, gaussian or more and it is function of distance h between measures

4. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki Background errors Observations errors Innovation MODELLING ERRORS Errors must be unbiased and gaussian Observation and background errors are mutually uncorrelated

5. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki MAXIMUM LIKELIHOOD METHOD In observation space we estimate covariance innovation with a covariogram based on the exponential variogram Parameters p (nugget), w (range), a(scale) are estimated with ML tecnique to find the minimum of the gaussiam pdf or maximum of the logaritmic function

6. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki WEIGHT FACTOR The weight factor “alpha” is defined as follows It describes how the observation errors variance weights respect background errors in HIRVDA 3D-var data assimilation process

7. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki APPLICATIONS Spatially distribuited observations in Hirlam domain GeopotentialTemperature Meteorological data provided by HIRVDA 3D-var data assimilation process of HIRLAM (SMHI) August 1-10 2003 Wind

8. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki Estimations of variogram parameters with ML tecnique in order to estimate innovation covariance matrix from the innovation values Weight factor “alpha”

9. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki CONCLUSIONS Set algorithm ML to estimate covariance parameters Calculation of weigth factors for optimal interpolation Application for some types of observations (ex. geopotential and temperature) …FUTURE HIRLAM simulations to text weigth factors Application of covariance information in kalman filter

10. Progea S.r.l Bologna & SMHI Carpe Diem 6th Project Meeting June 24 Helsinki REFERENCES [1] Dee, D.P., 1991: Simplification of the Kalman filter for meteorological data assimilation, Q.J.R. Meteorol. Soc. 117,365-384. [2] Dee, D.P., 1995: On-line estimation of error covariance parameters for atmospheric data assimilation, Mon. Wea. Rev. 123,1128-1145. [3] Todini, Ferraresi, 1996: Influence of parameter estimation uncertainty in Kriging, J. Hydrol.175,555-566. [4] Todini E., Pellegrini F. (1999). A Maximum Likelihood estimator for semi- variogram parameters in Kriging. In J. Gomez-Hernandez, A Soares, R. Froidevaux (eds.) GeoENVII – Geostatistics for Environmental Applications. Kluwer Academic Publishers. pp. 187-198. [5] Todini, 2001: Influence of parameter estimation uncertainty in Kriging. Part1 and Part2, Hydrol. Earth System Sci. 5, 215-232.