Inferring shallow storage properties from the analysis of percolation theory of streamflow elasticity

The recent application of a new percolation theory of the water balance to streamflow elasticity yielded predictions that were substantially in agreement with four major worldwide or continental datasets for, e.g., the median values of the elasticity in various climate zones. By comparing the deviations of streamflow elasticity data from the predicted median value with what would be expected from typical annual changes in storage, it was also possible to infer the important role of changes in the storage in the water balance and in the precipitation elasticity of streamflow. Since the global-scale data for the world's largest river drainages did, overall, generate the smallest deviations from the predicted median values of the streamflow elasticity, it was suggested that the reason for the difference may be traced to the difficulty of generating storage changes of the same sign in all regions of river drainages of an area of 100,000 km² and larger. Here, the potential of this hypothesis to explain the scaling of elasticity deviations with basin area in terms of the Gaussian statistics is investigated. Our results confirm that both the maximum annual basin storage changes and the maximum deviations from the predicted median values of the elasticity scale with negative ½ power of the basin area, in accord with storage changes that are uncorrelated in space at sufficiently large spatial scales. Furthermore, for the large basins that are the focus of the present study, Gaussian statistics can account reasonably well for the distribution of streamflow elasticity about the mean, although the mean is displaced slightly from the median in a predictable way.