The regional persistence and variability of annual streamflow in the United States

Inference from individual streamflow records can be extremely misleading, e ven for large samples. One is often tempted to trust information available from a streamflow record rather than to exploit regional average statistics of those records. This study documents that regional average streamflow st atistics usually contain much more information about the variability and pe rsistence of streamflow at a particular site than does the individual strea mflow record for that site. Experiments are performed using time series of annual streamflow at 1544 gauging stations across the continental United St ates. We document that 18 broad water resource regions of the United States are homogeneous in terms of the year-to-year persistence of streamflow, wh ereas much smaller regions are required to obtain homogeneity in terms of t he variability of streamflow. Classical homogeneity measures ignore the ser ial correlation of streamflow. Instead, homogeneity is quantified using the sampling properties of at-site estimates of the coefficient of variation C -nu and lag-one correlation rho(1) of annual streamflows. Additional experi ments using the Hurst coefficient reveal that the long-term persistence str ucture of historical annual streamflow series is indistinguishable from the long-term persistence structure of either an AR(1) or ARMA(1,1) process. I f historical flow series are generated from either an AR(1) or ARMA(1,1) pr ocess, then even given 1544 observed time series, we are unable to distingu ish between those two processes.