Correlation and covariance of runoff revisited

The spatio-temporal covariance function, besides being a basic descriptor of variability, serves as the basic tool for interpolation and consistent mapping of runoff and its statistical descriptors. It is also the background for the uncertainty measures of spatio-temporal data assimilation procedures. The problem of determining the spatial covariance of runoff by considering the structure of the river network and the related drainage basin support has been dealt with by . This approach is further elaborated to apply to a spatio-temporal runoff process. Three features of runoff covariance needed special attention for the elaboration of a theoretical model: – The degree of intermittency of the runoff process giving rise to different structure of the autocorrelation function between drainage basins. – The role of temporal support for explaining the changes in the autocorrelation function with changing duration of averaging. – The role of spatial support (basin area) for explaining the scatter in spatial correlation. The theoretical findings were tested on a data set of 35 runoff time series of 23 years from the French part of Moselle River. The estimated spatio-temporal correlations correspond with the observed values for large basins along river branches with a slight overestimation and also for small headwaters with low and moderate autocorrelation. However, the method was unable to correctly predict the low correlation of small headwaters with very high temporal autocorrelation caused by local features.