Interpolation of daily rainfall networks using simulated radar fields for realistic hydrological modelling of spatial rain field ensembles

- Daily gauges are not able to reveal the rainfall spatial structure.
- Radar wetted area ratio is the most significant radar image statistic influencing the rainfall spatial structure.
- The gauge wetness ratio is related to the radar wetted area ratio through a transition probability matrix.
- The range and anisotropy ratio of the spatial correlogram exhibit negative dependence.
- The inter-quartile range of simulated daily rainfall narrows near the control gauges.

SummaryGiven a record of daily rainfall over a network of gauges, this paper describes a method of linking the Gauge Wetness Ratio (GWR) on a given day to the joint distribution of the parameters of the anisotropic correlogram defining the spatial statistics of simulated radar-rainfall fields. We generate a large number of Gaussian random fields by sampling from the correlogram parameters conditioned on the GWR and then conditionally merge these fields to the gauge observations transformed into the Gaussian domain. Availability of such a tool allows better spatially distributed hydrological modelling, because good quality ensemble spatial information is required for such work, as it yields uncertainty of the fields so generated. To achieve these ends, correlograms of many Gaussianised daily accumulations of radar images were developed using the Fast Fourier Transform to generate their sample power spectra. Empirical correlograms were fitted using a 2D exponential distribution to yield the 3 key parameters of the correlogram: the range, the anisotropy ratio and the direction of the major axis. It was found that the range follows a Gamma distribution while the anisotropy parameters follow a Loglogistic one; a t5 copula was adequate to capture the bivariate negative dependence structure between the range and ratio. The Radar Wetted Area Ratio (RWAR) drives the parameters of the correlogram, and its link with GWR is modelled by a transition probability matrix. We take each of the generated Gaussian random fields and conditionally merge it with Gaussianised rainfall values at the gauge locations using Ordinary Kriging. The method produces realistic simulated radar images, on a grid chosen to suit the data, which match the gauge observations at their locations. Ensemble simulations of 1000 samples were used to derive the median and the inter-quartile range of the fields; these were found to narrow near the control gauge locations, as expected, emphasising the value of high density gauge networks. Ongoing research is looking towards integration of the presented methodology with a stochastic daily rainfall generator for useful spatial rainfall simulation over catchments with gauged records.