On a Two-Dimensional Temperature Model: Development and Verification

Government regulators on many rivers have specified acceptable temperatures based upon habitat and biological criteria. These temperature thresholds impose constraints on reservoir operations and can limit water deliveries and power generation. Existing tools based on low-order modeling simplify a river to a simple line with limited spatial distribution of inputs and poorly represent physics of the river processes. The limited spatial extents restrict the usefulness of low-order modeling for such features as agricultural returns, gravel pits, groundwater upwelling, side channel activation, and streamside vegetation. It also imposes limitation on fish habitat assessment and reoperation outside the range of the calibration datasets. This study develops a two-dimensional (2D) temperature module for an existing 2D hydraulic model, SRH-2D version 2. The 2D model incorporates data with both lateral and longitudinal geographic extents rather than lumping results into a point-to-point or uni-directional representation. The objective was to improve the representation of spatial features where low-order models resort to empiricism for a lumped treatment. Better representation of processes leads to increased accuracy and higher confidence. The SRH-2D temperature model utilizes meterological data as inputs (solar radiation, cloud cover, air temperature, dewpoint temperature and wind speed). Physical processes modeled include solar radiation, terrain and vegetation shade, atmospheric radiation, water back radiation, heat exchange between water and river bed, water surface evaporative and conductive losses. The model formulation, along with governing and process equations, is discussed first. The model is then tested and verified with simple cases having analytical solutions. The model is finally verified by applying to flows on the McKay Creek downstream of the McKay Dam.