Improved Thermal Predictions in CE-QUAL-W2

Recent modifications to the transport scheme within the two-dimensional hydrodynamic and water quality model CEQUAL-W2 have resulted in a significant improvement in the prediction of temperature distributions by reducing numerical diffusion. These changes allow for a more accurate description of wind effects in the model. This paper briefly describes the modifications to CE-QUAL-W2 and presents results of two simulations both with and without the improvements to the transport algorithm. Introduction CE-QUAL-W2 is a two-dimensional, laterally averaged, hydrodynamic and water quality model (WES,1986) widely applied by the U. S. Army Corps of Engineers, universities, and the private sector. The experience gained through numerous applications of the model has led to the identification of a number of potential model improvements. One improvement recently addressed is the removal of excessive numerical diffusion generated by the original upwind advective transport scheme. The reduction in numerical diffusion was of primary importance because of difficulties encountered when modeling temperature dynamics. In order to calibrate temperature profiles, previous applications have relied mainly on a wind sheltering coefficient ranging from 0 to 1 which is applied to reduce the observed winds. 1Ray Chapman & Associates, 1725 MacArthur Place. Vicksburg, MS 39180 2Hydrologist, U. S. Army Engineer waterways Experiment station, 3909 Halls Ferry Rd., vicksburg, MS 39180 158 IMPROVED THERMAL PREDICTIONS 159 For example, the DeGray Lake application (Martin, 1978) used a wind sheltering coefficient of 0.3 throughout the summer stratification period. Since the wind shear formulation in CE-QUAL-W2 is a function of the square of the wind speed, wind shear was reduced by over 90%. The ef~e'?ts ,!f numerical diffusion. were overcome by essentially el1m1nat1ng one of the most 1mportant physical processes responsible for vertical temperature distribution wind shear. The problems associated with upwind numerical diffusion have been reduced by implementing 1) the explicit thirdorder QUICKEST advective transport scheme (Leonard, 1979) in both the horizontal and vertical dimensions, and 2) options for time-weighted implicit vertical advection. The purpose of this paper is to briefly describe improvements to the transport scheme and present comparisons of model applications with and without the improved transport scheme. Transport Modifications A modification of the third-order QUICKEST finite difference scheme has been implemented in both the horizontal and vert~cal dimensions (Chapman, 1988). A nonuniform grid verS10n was developed using a three-point Lagrangian interpolation function (Henrici, 1964) to estimate constituent values at grid cell interfaces. Specifically advective multipliers for each of three upstream weighted grid cells have been derived in terms of cell lengths and the local cell interface velocity. An advantage of this technique is that time varying and time invariant contributions to the interpolation functions can be segregated so that multiple constituents can be transported with a minimum of computational effort. An option for implicit vertical transport set up for a variable grid size has also been implemented. This option employs a fully implicit diffusion algorithm and a timeweighted, central difference, implicit advection scheme. A unique feature of the implicit vertical advection option is that the explicit part of the time-weighted scheme is QUICKEST which increases overall accuracy. In addition the implicit vertical transport relaxes the stability re: quirements allowing for larger timesteps which the model automatically calculates and adjusts during a simUlation. Demonstration Simulations Two simUlations are presented to demonstrate the improvement .in ~hermal predictions using the new transport algor1thm 1n CE-QUAL-W2. These test simUlations revisit exis~1n9 application. of DeGray Lake, Arkansas and Oahe Published in Hydraulic Engineering: Saving a Threatened Resource—In Search of Solutions: Proceedings of the Hydraulic Engineering sessions at Water Forum ’92. Baltimore, Maryland, August 2–6, 1992. Published by American Society of Civil Engineers. 160 HYDRAULIC ENGINEERING Lake, S?uth Dakota, both of which are Corps of Engineer reservo1rs. The details concerning the physical setting and computational set-up of the applications can be found in Martin (1987) and Cole et al. (1992) for Degray and Oahe Lakes, respectively. Verification years for the two sites are used to contrast the model predictions obtained using the new transport scheme and the original upwind difference method. Results of the DeGray and Oahe Lake simulation with and without the new transport scheme are presented in Figures 1 and 2. The upper series of temperature profiles used QUICKEST transport horizontally and fully implicit transport vertically with a wind sheltering coefficient of 0.9 throughout the simulation. The lower series used the original upwind differencing scheme with the same wind sheltering coefficient. The differences for both applications are dramatic showing very clearly why previous applications resorted to the use of wind sheltering coefficients in order to reduce the amount of vertical m1x1ng. Resul ts from the other two vertical transport options (fully explicit QUICKEST and time-weighted) yielded similar reductions in numerical diffusion. Conclusions Although previous applications of CE-QUAL-W2 have produced reasonable temperature predictions, the results were obtained at the expense of correctly specifying wind shear, one of the most important physical processes involved in temperature dynamics. The reduction in numerical diffusion accomplished by the new transport scheme allows for a more realistic specification of wind inputs into the model thus improving the models predictive capabilities. IMPROVED THERMAL PREDICTIONS