 AREA 1  Data assimilation and NWP improvements
High resolution atmospheric forecast models have become indispensable tools for operational weather forecasting. Weather radar systems, on the other hand, are today indispensable tools for monitoring weather developments in real time and for forecasting, particularly the severe weather events, a couple of hours in advance. In synthesis, weather radar data are potentially important for input to the forecast models, when the required forecasting leadtime is within the catchments time of concentration. For several reasons, this potential has been only very marginally exploited so far. Recent developments in processing and quality control of radar information as well as developments in data assimilation techniques have now reached such an advanced level, however, that it may be rather premature to suggest that the central objective of the present project could be a breakthrough in the quantitative utilisation of weather radar information for numerical weather prediction.
For high resolution model integration, it has generally been seen, and also indicated by geostrophic adjustment theory, that it is most vital to accurately determine the 3dimensional wind fields. The standard atmospheric observing system for winds is the radiosonde network. The horizontal resolution of the radiosonde network, with a mean distance between the stations of 500 km over Europe, is very poor, especially when atmospheric models with a gridresolution of the order of 10 km are sought. Generally, the potential data sources for atmospheric winds are automated aircraft reports, satellites and radar winds. The radar winds are quite problematic since only the velocity component along the radar beam is measured at full resolution. Other problems with radar winds are the inconsistencies between the vertical components of the radar radial winds and modelled vertical velocities and a Doppler velocity folding. An impressive early demonstration of the potential of assimilation of radar radial winds is given by Kapitza (1991) .
In order to correctly link radar data and NWP methods, the preprocessing phase will be explored. The main task will be the extraction of parameters suitable for ingestion in numerical procedures. Doppler radar data will be processed in order to extract wind field information convenient to ingest in NWP procedure or to be used in forecast validation exercise. The quality control of radar information before their ingestion in NWP procedure is therefore a critical aspect in the operational application. Activities will be addressed to increase the reliability of Doppler information.
Radar reflectivity (precipitation) data are another potentially important input data to numerical weather prediction. The main difficulty here is that precipitation is not a state variable of the forecast models but rather an output variable of very complicated and nonlinear model processes, i.e. convection, condensation and precipitation. It remains unclear which assimilation technique has the best chances to assimilate the information inherent in the radar data. Therefore a multitude of assimilation techniques will be tested and compared in the present project. Variational techniques (Daley, 1991 , Lorenc, 1986 ) have theoretical advantages since they allow for complicated relationships between observed quantities and model state variables. This is very important for a rational use of radar radial wind vector and precipitation information. On the other hand, the calculation cost may be prohibitive, at least for nowcasting and very shortrange forecasting purposes. A newly developed variational assimilation system will be applied to radar observations within the project. As an alternative, continuous assimilation based on nudging will also be applied. The main advantage of nudging is its conceptual simplicity and its low computation cost. Also, for nowcasting and very shortrange forecasting purposes, a mesoscale analysis scheme based on a simplified spatial interpolation will be applied.
The structure of forecast errors is strongly linked to the actual state of the atmosphere, for example, in connection with instability processes leading to development of extreme weather events. Operational data assimilation techniques generally, however, apply stationary forecast error statistics in the process of mixing forecast and observed information. Online estimation of forecast error statistics will be applied in CARPE DIEM, in order to improve data assimilation for the forecasting of extreme weather events like flooding.
The assessment of the uncertainty of NWP is currently based upon the so called "ensemble forecasting". This technique implies that the largest forecasting errors are essentially due to the uncertainty in the initial conditions (which are estimated on the basis of scattered observations) while the NWP model is implicitly assumed as perfect. Nonetheless, when data assimilation are envisaged to be used in order to improve model performances and reducing model divergence, it is essential to evaluate the "model uncertainty" (which derives from the discretisation of the equations and from the used parameterisations), because the largest improvements are obtained if the relative uncertainty between model and assimilated data can be specified.
In fact, in the absence of model error, errors in a forecast would result exclusively from errors in the initial data. In that case the atmospheric data assimilation problem could be solved by applying model fitting techniques. If, on the other hand, model error is significant (as has been suggested by a number of studies: see Boer, 1984 ; Bloom and Schubert, 1990 ) then its effect on forecast error must somehow be accounted for when forecast and observations are combined into an analysis.
Several techniques have been proposed for NWP model uncertainty assessment, such as the ones based upon model adjoint or based upon Maximum Likelihood and Simplified Kalman Filters (ML/SKF) approach ( Dee, 1991 ; 1995 ).
Within the frame of CARPE DIEM, the ML/SKF approach will be implemented and tested versus and a another estimation technique based upon imposing the KF optimality conditions in terms of independence in time of the innovation process (IIP) (Mehra, 1970 and Todini 1978 ).
References:
 Kapitza, H., 1991: Numerical experiments with the adjoint of a nonhydrostatic mesoscale model. Mon. Wea. Rev., 119, 29933011.
 Daley, R., 1991: Atmospheric data analysis. Cambridge University Press, Cambridge, UK, 460 pp.
 Lorenc, A., 1986: Analysis methods for numerical weather prediction. Q. J. R. Meteor. Soc., 112, 11771194.
 Boer, G.J., 1984: A spectral analysis of predictability and error in an operational forecast system. Mon. Wea. Rev. 112,11831197.
 Bloom, S.C. and Schubert, S., 1990: The influence of Monte Carlo estimates of model error growth on the GLA OI assimilation system. Int. Symp. on Assimilation of observations in meteorology and oceanography. WMO. pp.467470.
 Dee, D.P., 1991: Simplification of the Kalman filter for meteorological data assimilation, Q.J.R. Meteorol. Soc. 117,365384.
 Dee, D.P., 1995: Online estimation of error covariance parameters for atmospheric data assimilation, Mon. Wea. Rev. 123,11281145.
 Mehra, R.K., 1970: On the identification of variances and adaptive Kalman filtering. IEEE Trans. Automat. Contr. Vol. AC15,175184.
 Todini, E., 1978: Mutually interactive stateparameter (MISP) estimation. In ChaoLin Chu (ed) Applications of Kalman Filter to Hydrology, Hydraulics, and Water Resources. Stochastic Hydraulics Program Dept. Civil Eng. University of Pittsburgh (Penn).
