Spatial scaling properties of annual streamflow in the United States

The spatial scaling properties of annual average streamflow is examined usi ng records from 1 433 river basins across the continental United States. Th e log-linear relationship In(E[Q(i)(r)]) = a(r) + b(r)In(A(i)) is represent ative throughout the United States, where E[Q(i)(r)] represents the expecta tion 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 per fect linear relationships a(r) = r alpha and b(r) = r beta throughout the c ontinental United States. We conclude that the probability distribution of annual streamflow follows simple scaling relationships in all regions of th e United States. In temperate regions where climate is relatively homogeneo us, 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 o f the moments of annual flow.