Mapping mean monthly runoff pattern using EOF analysis

Abstract

Interpolation of flow patterns, as defined by the variation over the year of the twelve mean monthly discharges, should account both for the auto-correlation in time series and consider the river network, as discharge records are relative to the outlet of the upstream basin. An objective approach of flow pattern mapping along the river implemented within a Geographical Information System (GIS) is presented. Preprocessing of the digital elevation model enables extraction of the main river network (water paths) and basin descriptors, and offers a convenient background for the interpolation scheme. Monthly values are standardised to overcome scale dependence with basin size. Expansion into Empirical Orthogonal Function (EOF) allows interpreting each standardised time series as a linear combination of amplitude functions defined at the regional scale with the weights that need to be interpolated. Empirical dependencies relating these weights to basin characteristics are used for this purpose. Finally, kriging is applied for interpolating the residuals of the weights. The approach has been used for interpolation along a river net of flow patterns of an extensive monthly runoff sample for south-eastern France and has been validated successfully on a sample of eleven stations. Predicted flow patterns have been also introduced into a simple regime classification scheme to derive a map of flow regime in a formal and objective manner.