Models of daily rainfall cross-correlation for the United Kingdom

Automated easy-to-use tools capable of generating spatial-temporal weather scenarios for the present day or downscaled future climate projections are highly desirable. Such tools would greatly support the analysis of hazard, risk and reliability of systems such as urban infrastructure, river catchments and water resources. However, the automatic parameterization of such models to the properties of a selected scenario requires the characterization of both point and spatial statistics. Whilst point statistics, such as the mean daily rainfall, may be described by a map, spatial properties such as cross-correlation vary according to a pair of sample points, and should ideally be available for every possible pair of locations. For such properties simple automatic representations are needed for any pair of locations. To address this need simple empirical models are developed of the lag-zero cross-correlation-distance (XCD) properties of United Kingdom daily rainfall. Following error and consistency checking, daily rainfall timeseries for the period 1961-1990 from 143 raingauges are used to calculate observed XCD properties. A three parameter double exponential expression is then fitted to appropriate data partitions assuming isotropic and piecewise-homogeneous XCD properties. Three models are developed: 1) a national aseasonal model; 2) a national model partitioned by calendar month; and 3) a regional model partitioned by nine UK climatic regions and by calendar month. These models provide estimates of lag-zero cross-correlation properties of any two locations in the UK. These cross-correlation models can facilitate the development of automated spatial rainfall modelling tools. This is demonstrated through implementation of the regional model into a spatial modelling framework and by application to two simulation domains (both ∼10,000 km²), one in north-west England and one in south-east England. The required point statistics are generally well simulated and a good match is found between simulated and observed XCD properties. The models developed here are straightforward to implement, incorporate correction of data errors, are pre-calculated for computational efficiency, provide smoothing of sample variability arising from sporadic coverage of observations and are repeatable. They may be used to parameterise spatial rainfall models in the UK and the methodology is likely to be easily adaptable to other regions of the world.