Scaling of Canadian low flows

Scaling properties of Canadian low flows, namely annual minimum mean 1-, 5- and 7-day flows, are evaluated across Canada and in its sub-climatic regions. Across the entire country, the log relationship between the kth product moments (PMs, EQ_i^k]) of low flows and drainage area (A_i) can be represented by: ln(EQ_i^k])=a_k+b_kln(A_i)and b_k=k, with = 0.86, 0.94 and 0.93 for annual minimum mean 1-, 5- and 7-day flows, respectively. The log linear relationships between the kth probability weighted moments (PWMs, ) and A_i are ln()=c_k+Hln(A_i), in which H is constant and is independent of k. The values of H are 0.87, 0.97, and 0.96 for annual minimum mean 1-, 5- and 7-day flows, respectively, which are almost the same as the values. The coefficients of variation (Cv) are almost independent of drainage area. These results demonstrate that Canadian low flows generally exhibit simple scaling and drainage area alone describes most of the variability in the moments of the low flows. Low flows in each of the sub-climatic regions also obey a simple scaling law. The values of , H and Cv are different in each region, which may stem from physiographical and climatological differences among these regions. The finding lays a basis for applying the index flood method to conduct regional low flow frequency analysis as simple scaling is equivalent to the index flood method.Acknowledgements The authors thank Prof. Thian Yew Gan of University of Alberta, Canada for providing additional pristine data sites for regions 4 and 10. A constructive comments provided by an anonymous reviewer improved the quality of the paper.