Flow distribution in selected branches of St. Clair and Detroit rivers

Abstract

St. Clair and Detroit rivers, which are connecting channels between Lake Huron and Lake Erie in the Great Lakes basin, form part of the boundary between the state of Michigan and the province of Ontario. In 13 reaches, this flow divides locally around islands and dikes to form 31 branches. This study develops a set of simple linear regression equations for computing expected flow proportions in branches, generally as a function of the total flow within the reach. The equations are based on 533 acoustic Doppler current profiler measurements of flow obtained between 1996 and 2000. Root-mean-square errors of these regressions range from 0.00323 to 0.0895. In seven upstream reaches where flow is known because of flow specifications at the boundaries of the waterway and continuity constraints, the uncertainties of the flow proportions can be used to directly infer the uncertainties of the corresponding flows. In six downstream reaches, the uncertainties of flows are determined by both the uncertainties of the flow proportions and the uncertainties of the total flow in the reach. For these reaches, Monte Carlo simulations quantify the ratios of total uncertainty to flow proportion uncertainty, which range from 1.0026 to 13.984. To facilitate routine calculation, polynomial regression equations are developed to approximate these ratios as a function of flow. Results provide a mechanism for computing the magnitudes and uncertainties of steady-state flows within selected branches of the connecting channels by specifying inflows at the headwaters of St. Clair River, seven intervening tributaries, and Lake St. Clair.