Geostatistical Analysis and Copula-Based Data Merging Algorithms for a Stochastic Quantification of Precipitation Fields
Dr. Barbara Haese and Prof. Dr. Harald Kunstmann

Project within the DFG Research Unit 2131 "Data Assimilation for Improved Characterization of Fluxes across Compartmental interfaces”

For the improved understanding of the regional water cycle the knowledge of the spatio-temporal distribution of precipitation is of crucial importance. Surface precipitation fields are central information for determining state variables and parameters of the coupled soil-vegetation-atmosphere system. Precipitation fields retrieved from atmospheric models still suffer from large errors in reproducing its detailed spatio-temporal distribution in sufficient quality for subsequent hydrological applications. Precipitation fields conditioned on observations usually have higher reliability.

Our project Geostatistical Analysis and Copula-Based Data Merging Algorithms for a Stochastic Quantification of Precipitation Fields will provide precipitation fields derived from three different measurement types: gauge (point), microwave link (line) and radar (patterns). Uncertainties caused by restricted areal and temporal coverage and by the specific measurement processes are derived and quantified. Rain gauges provide high-quality direct point information, albeit their spatial representativeness is often little. Microwave links e.g. from commercial cellular operators can be used to estimate line integrals of near-surface rainfall information and the wide use of cellular communication provides a high resolution built-in sensor network. Radar observations provide spatial pattern information, but the transformation of radar observables to rain intensity carries large uncertainties.

This project combines these data sources while preserving the particular advantages of point, line integrated, and pattern information. The investigations are performed using hydro-meteorological data originating both from the virtual reality generated by the fully coupled subsurface-surface-atmospheric model framework TerrSysMP (ParFlow-CLM-COSMO) (pseudo-observations are derived by application of suitable error models) and later from observed precipitation.

The main objective is the development of new Copula-based algorithms to reconstruct optimal rainfall fields from different types of precipitation information (point, line, patterns).

In the overall context of the Research Unit it is the provision of ensembles of spatio-temporally consistent rainfall fields (i.e. including the respective uncertainty) as stochastic input for data assimilation.

These objectives will be achieved by a comprehensive multivariate geostatistical analysis of rainfall characteristics from virtual reality and the analysis of dependence structures between different types of rainfall information and different hydrometeorological variables. Ensembles of precipitation fields will be generated from the derived Copula-models, based on the identified dependence structures i.e. the conditional Copula functions and the marginal distributions. As the framework of the virtual reality allows to set up precipitation observation networks with full freedom to their configuration, the sensitivities of the developed approaches will be studied and strategies for optimal configurations will be proposed. The virtual reality provides the unique possibility to study and evaluate the Copula-based data merging algorithms against this known reference.