A Likelihood Approach for Modeling Spatial and Temporal Patterns of Storms Using Radar and Land Data

Abstract

While the existing spatiotemporal approaches provide an estimation of the rainfall over geographical areas, they in effect provide only for an interpolation of the data. The proposed approach introduces the concept of the construction of the likelihood function of the repartition of rain over a territory using historical storm data, both radar and land data. Radar imaging and gauges data are used to build a likelihood model for the estimation and reproduction of spatial and temporal patterns of storms over catchment areas. A novel aspect of the approach is the reduction of the two dimensioned spatial characteristics of storm rainfall fields to a univariate model representation of a storm crossing the geographical area. The study and characterization of radar tracked storms over the catchment area, along with the use of land gauges data for estimation and validation, provide for the spatiotemporal analysis of the storm rainfall, with both time and space variables being univariate. This reduction in dimensionality is a departure from traditional methods where interpolation is the major approach. It allows for the construction of a probability model to explain rainfall statistics at any location. The reproduction of rainfall data for water management studies is done through the storm models. Weather can be considered infinite in its variation, and it is doubtful that any mathematical model would accurately predict rainfall. Weather prediction and its physics are ignored and the emphasis is on the development of a statistical model. Radar imaging is used to process a large amount of information from which statistics are extracted for the construction of the likelihood model. Historical trajectories of storms are looked at as a logical explanation in time for the accumulation of rainfall levels. Along with storms strengths, they provide the essential variables for the dissection and reconstruction of the rainfall process over the catchment area. This reduction of the problem dimensionality is key, taking the problem of rainfall distribution estimation into a new direction. Rather than limit the inputs of a numerical simulation of water flows to interpolated data, a probability model is used to reproduce the rainfall data. A probability based model allows for the variation of the input parameters and for a probabilistic assessment of the outputs. Accurate estimation of the spatiotemporal heterogeneity of rainfall is important in a catchment simulation.