Simple scaling properties of Canadian annual average streamflow

The spatial scaling properties of Canadian annual average streamflow (abbreviated as AASF) are assessed using both the product moments (PMs) and the probability weighted moments (PWMs) of AASF across the entire country and in its sub-climatic regions. By the PMs, the log relationship between the kth moments of AASF and the drainage area can be almost represented by a perfect straight line across the entire country and in its sub-climatic regions, whose regression parameters are a linear function of the moment order. By the PWMs, the logarithm of the kth PWM is a linear function of the logarithm of drainage area for the entire country and its sub-climatic regions, where its slope (or scale exponent) in a region is constant and is independent of the order. These results indicate that Canadian AASF exhibits simple scaling and drainage area alone may describe most of the variability in the moments of AASF. The third approach, based on the log linearity between quantiles and drainage area, is applied to Region 2, also demonstrate simple scaling of AASF in that region, as concluded from using PMs and PWMs methods, which indicates that all three methods are consistent. The simple scaling results provide a basis for using the index flood method to conduct regional frequency analysis of AASF in Canada.