Spatial scaling properties of annual streamflow in the United States

The spatial scaling properties of annual average streamflow is examined using records from 1 433 river basins across the continental United States. The log-linear relationship In(E[Q(i)(r)]) = a(r) + b(r)In(A(i)) is representative throughout the United States, where E[Q(i)(r)] represents the expectation of the rth moment of annual streamflow at site i, and A(i) represents drainage area. The scaling model parameters a(r) and b(r) follow nearly perfect linear relationships a(r) = r alpha and b(r) = r beta throughout the continental United States. We conclude that the probability distribution of annual streamflow follows simple scaling relationships in all regions of the United States. In temperate regions where climate is relatively homogeneous, scale alone describes most of the variability in the moments of annual streamflow. In the more climatically heterogeneous regions, such as in the Upper Colorado and Missouri river basins, scale alone is a poor predictor of the moments of annual flow.