A Gaussian Random Field Approach for Merging Radar and Ground-Based Rainfall Data on Small Spatial and Temporal Scales

Abstract:

The generation of reliable precipitation products that explicitly account for spatial and temporal structures of precipitation events requires a combination of data with a variety of error structures and temporal resolutions. In-situ measurements are relatively accurate, but available only at sparse and irregularly distributed locations, whereas remote measurements cover areas but suffer from spatially and temporally inhomogeneous systematic errors. Besides gauge measurements are available on coarser spatial and temporal resolution in contrast to remote sensing measurements which are given on a fine spatial and temporal resolution. In our study we use precipitation rates from the composit of two X-band radars in Bonn and Jülich in Germany. Our aim is to formulate a statistical space-time model that aggregates and disaggregates precipitation rates from radar and gauge observations. We model a Gaussian random field as underlying process, where we face the task of dealing with a large non-Gaussian data set. To start the analysis of the unadjusted radar rainfall rates, we follow the work of D. Allcroft and C. Glasbey (2003) and transform the data to a truncated Gaussian distribution. The advantage of the latent variable approach is that it takes account of the occurence of rainfall and the intensity using a single process. We proceed by estimating the empirical correlation from these transformed values with maximum likelihood methods and fit a parametric correlation function that gives rise to a Gaussian random field. Since the transformation gives censored values to dry locations, we simulate values for this area that lie below some threshold and extend the Gaussian field to the whole domain. In order to merge gauge and radar data for precipitation, we first aggregate the data to a scale on which the comparison is reasonable and then disaggregate again back to smaller desirable scales. The disaggregation step consists of calculating the difference between radar aggregate and small scale measurements and the difference between gauge aggregate and derived small scale measurements. Then the spatial structure of the radar anomalies is used to simulate the gauge anomalies on the whole field. In the end we add the simulation to a combined estimator of the radar and gauge aggregates and obtain the small scale merging product.