Summary 


The hydrodynamic model of Upper Klamath and Agency Lakes, Oregon, was used to run numerical tracer experiments in order to understand the relative effects of wind, lake elevation, and Williamson River inflow on flow and transport (the movement of water and passively transported constituents) through the Williamson River Delta (hereafter referred to as the Delta). This was accomplished by running 384 realizations of the numerical experiment while systematically varying only 1 of the 3 (wind speed, lake elevation, and Williamson River inflow, if wind speed is used) or 4 (east-west wind component, north-south wind component, lake elevation, and Williamson River inflow, if wind speed and direction are used) independent variables at a time. The results of the tracer experiments were quantified and compared by calculating the amount of water on either side of the Delta that left the boundaries of the Delta and was replaced by water from any other part of Upper Klamath or Agency Lakes or the Williamson River in 1 day (the total replacement rate), and the amount of Williamson River water that replaced water on either side of the Delta in 1 day (the partial replacement rate). These calculated total and partial replacement rates were used to develop quantitative relations between transport through the restored areas of the Delta and lake elevation, Williamson River inflow, and wind speed and direction. The quantitative relations took the form of multivariate regression models. The dependent variables of these models were the calculated total and partial replacement rates in the northwest (Tulana) or southeast (Goose Bay) side of the Delta. The independent variables included (1) Williamson River inflow, (2) Upper Klamath Lake elevation, and (3) either wind speed or the magnitude of separate east-west and north-south wind components. 


The results of the tracer experiments and regression models showed that the replacement rate of water increased in Tulana and Goose Bay with increasing lake elevation, Williamson River inflow, and wind speed, although the replacement rate in Tulana had a stronger dependence on wind speed than did the replacement rate in Goose Bay. The fraction of Williamson River inflow passing through either side of the Delta (the partial replacement rate) increased with lake elevation and Williamson River inflow. The dependence of the partial replacement rate on wind speed was different for the two sides of the Delta, such that the partial replacement rate of water in Goose Bay with Williamson River water increased with wind speed, whereas the partial replacement rate of water in Tulana with Williamson River water decreased with wind speed. Thus, stronger wind forcing at the water surface caused more of the Williamson River inflow to pass through Goose Bay than through Tulana. The Goose Bay partial replacement rate increased as the magnitude of the wind component from either the west or north increased, whereas the Tulana partial replacement rate had the opposite dependence. Therefore, westerly to northwesterly winds, which are the prevailing winds during the spring and summer months, result in more of the Williamson River inflow passing through the Goose Bay side of the Delta than through the Tulana side.


The use of the regression models for estimating the total and partial replacement rates was illustrated with two examples in which spring and summer conditions were assumed. In the first example, under the assumed springtime conditions, most of the Williamson River discharge was expected to flow through the Goose Bay side of the Delta. The theoretical time it would take to replace the water in Goose Bay, if the assumed meteorological conditions remained constant, provided an estimate of the residence time in Goose Bay of passively transported larvae. In the second example under the assumed summer conditions, measured summer benthic fluxes of orthophosphate from Tulana soils were used to estimate the steady-state contribution of Tulana soils to the concentration of orthophosphate in the overlying water column. 


The utility of the regression models could be improved by running more experiments at different combinations of flow, lake elevation, and wind. The range of lake elevation used in the tracer experiments was between 4,140.5 and 4,142.5 feet, but exchange between both sides of the Delta and the Williamson River was strongly curtailed at an elevation between 4,140.5 and 4,141.5 feet that could not be precisely determined given the limited number of elevations used. The range of Williamson River inflow used in the tracer experiments was between 530 and 3,531 cubic feet per second. The range of wind conditions considered was limited to winds with a positive east-west component. 


The results presented here provide insight into how movement of water through the Delta responds to hydrology as defined by the lake elevation and Williamson River inflow, and to wind forcing conditions at the lake surface. The regression equations provide a quick and easy-to-use means of making rough estimates of how fast water moves through both sides of the Delta and how the water entering the Delta at the Williamson River might be partitioned between Goose Bay and Tulana under varying conditions. 


First posted March 29, 2012