# Zusammenfassung 1. Phase - Summary of progress report

# Statistical-dynamical methods for scale dependent model evaluation and short term precipitation forecasting (STAMPF)

## Summary 2. PHASE

### Summary of progress report

The central goals of the project STAMPF are to introduce new dynamical and statistical parameters as well as error measures for a scale dependent model evaluation of high resolution precipitation forecasts of the non-hydrostatic Lokal Modell (LM, COSMO-EU, COSMO-DE) of the German Weather Service (DWD). The Dynamic State Index (DSI), information entropy and a scaling exponent are used to assess the performance of non-hydrostatic models with horizontal grid-resolutions of 7 km up to 2.8 km and time resolutions of hours up to 15 minutes. Complementary, to evaluate the various forecast data, an improved model-independent precipitation analysis is performed, using cloud classes derived from Meteosat-8 data. Additionally a high density Berlin precipitation network is applied to analyse especially convectively induced precipitation events in a spatial resolution of 500 m and a temporal resolution of 5 minutes.

For the model independent Freie Univeristät Berlin (FUB) precipitation analysis for Germany the statistical interpolation procedure, introduced in the first phase of the project, is improved further. Time dependent cloud weighting factors with a spatial-temporal resolution of 2.8 km and one hour, derived from Meteosat-8 (MSG-1) data are used. The result of this newly performed precipitation analysis demonstrates that orographically induced precipitation is better analysed by using hourly varying weighting factors. Especially the diurnal cycle of convective cloud types is integrated showing the importance of temporal varying weighting factors. Furthermore, in the frame of the General Observation Period (GOP) an interpolated precipitation analysis with a horizontal resolution of 500 m and temporal resolution of 5 minutes is established, using the Berlin network of 71 stations. These high density precipitation data, which are listed on the GOP-homepage can be applied to investigate the fundamental physical processes, which accompany the life cycle of convective precipitation events. An important result concerning the statistical investigation of the FUB-500m-analysis demonstrates that strong local rainfall is better indicated by the Pareto-exponent and not in terms of simple mean values. Moreover, the result of our FUB-500m-analysis of the year 2002, dominated by two severe convective cells can serve as an example of the limitation of deterministic numerical weather predictions in such small scales.

The DSI field variable, introduced in the first part of the project is now analysed in a more general way to improve the dynamical understanding of precipitation processes in the atmosphere. As a new result the analysis of the vertical structure of the DSI gives a relation to the IPV-Thinking, introduced by Hoskins (1985). The relationship between the isentropic PV-Thinking (IPV) and the DSI-concept results in the definition of the DSI, which is proportional to the advection of Pi² under non-stationary, adiabatic conditions. In this context the high correlation of DSI and precipitation reflects the interaction of characteristic PV-anomalies in the lower and upper troposphere which regarding to the IPV-Thinking explains cyclogenetic processes. A recent application of the DSI concerning the visualisation of storm tracks and the evolution of severe winterstorms and hurricanes can be found by Weber and Névir (2007). Moreover, this relation gives a dynamical explanation of the elongated structure of frontal rain bands. This feature is shown in a case study of the winterstorm Kyrill. The related total precipitation field, based on COSMO-DE forecast data, corresponds very well with the filament-like structure of the DSI-pattern and with the corresponding radar image of the DWD.

As an advanced step the DSI is not only correlated with modelled precipitation but also with observed precipitation as well as cloud types. In general, the absolute value of the DSI shows high correlations with hourly LM and COSMO-DE forecast data and slightly less correlations with the FUB precipitation analysis. Considering the direct correlation between modelled and observed precipitation of 70%, one half of the area mean precipitation of Germany can be dynamically explained by the absolute value of the DSI. The statistical evaluation of clouds with the index reveals a |DSI|-threshold, which is used to introduce a novel precipitation activity index of clouds. For example, the cumulonimbus cloud has the greatest precipitation activity, but the lowest probability of occurrence. This result agrees with findings of Peters and Christensen (2006), which showed that rain comes in rare cloudburst rather than as continuous drizzle. Thus, the precipitation activity index of clouds attributes a quantitative measure to the clouds and may open the possibility to introduce the cloud information in the data assimilation approach to initialise convective-scale events.

For scale-dependent evaluation of LM forecast data the predictability of the gridscale and convective part of rainfall is analysed, using the mean absolute error (MAE). Thereby the model independent FUB-analysis data are separated in convective and stratiform precipitation, based on WMO-data and weighting factors derived from Meteosat-8 cloud data. An interesting result is that the error of the convective precipitation increases twice as much in comparison to the stratiform part. Thus, the error of the total precipitation is dominated by the convective part. This is in agreement with the fact that errors in the small scales grow very rapidly with high doubling times. These errors move upstream in the spectrum and finally also decontaminate the large scale (Lorenz, 1993). A similar outcome is obtained for the COSMO-DE data, concerning the total rainfall. In this context another evaluation proposed in the project is the information entropy. Generally, this information entropy increases with longer forecast times similar to the MAE. A characteristic feature are the greater entropy values of the LM-precipitation compared to the observed rainfall, with a nearly constant difference in the forecast range from 3 to 24 hours. That means that the model behaves more randomly or too "Gaussian" and that the probability distributions of the observational data are more powerlaw distributed. In summary, this scale-dependent evaluation using these new error measures quantifies the uncertainties of precipitation forecasts performed by state of the art non-hydrostatic NWP models.