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Models of daily rainfall cross-correlation for the United Kingdom

Lookup NU author(s): John Richmond, Dr Vassilis Glenis, Professor Chris Kilsby



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


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.

Publication metadata

Author(s): Burton A, Glenis V, Jones MR, Kilsby CG

Publication type: Article

Publication status: Published

Journal: Environmental Modelling & Software

Year: 2013

Volume: 49

Pages: 22-33

Print publication date: 01/11/2013

Online publication date: 07/08/2013

Acceptance date: 07/06/2013

Date deposited: 01/10/2013

ISSN (print): 1364-8152

ISSN (electronic): 1873-6726

Publisher: Elsevier


DOI: 10.1016/j.envsoft.2013.06.001

Notes: Highlights: • Spatial properties of UK daily rainfall are described with simple models. • An aseasonal national model estimates lag-0 cross-correlation using only distance. • More tailored models specialize by calendar month and for nine climatic regions. • Such properties allow spatial rainfall models to be parameterized easily. • A simple tool for spatial-temporal rainfall modelling is demonstrated.


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Funder referenceFunder name
EP/G013403/1Earth Systems Engineering Platform
EP/G061254/1EPSRC/ARCC projects ARCADIA
NE/G523498/1Postgraduate Research Studentship