A novel sigma coordinate system to simulate abrupt changes of underwater terrain in a hydrodynamic model: application to Lake Mead, USA

摘要

The sigma (SIG) coordinate system in ocean circulation simulation models results inevitably in horizontal pressure gradient error. This problem also emerges in models of deep lakes or reservoirs with the same characteristics of underwater terrain mutation. SIG coordinates reflect vertical relative stratification but cannot be used to calculate horizontal pressure gradient force in places with drastic topographic changes; this results in vertical water temperature and circulation errors. In deep lakes or reservoirs, differences in water density caused by the temperature difference between upper and lower water bodies is the primary cause of thermal stratification phenomena. Lake Mead was used as a case study on steep topography based on Environmental Fluid Dynamics Code (EFDC) model in this study. SIG coordinates result in close agreement between the calibrated temperature time series at the top and middle water layers, but disparity in the bottom water layer. The error emerges in the horizontal pressure gradient error due to the SIG coordinate transformation. Neither increasing the vertical resolution nor adjusting the horizontal viscosity coefficient resolve this error. We test the sigma-zed (SGZ) coordinate which combines Z coordinate and SIG coordinate as a replacement for the SIG coordinate to find that they effectively reduce the model’s runtime and simulation efficiency. The vertical temperature distribution in SGZ coordinate mode is more accurate than the distribution in SIG coordinate mode. The Navier-Stokes horizontal gradient and advection diffusion equation results under SIG coordinates are very sensitive to the pressure gradient. The replacement also enhances resolution near the thermocline, facilitates reclosing of the water bottom and the equal sigma surface, lends significant advantages in terms of vertical temperature in the simulation for local deep water with steep terrain, and shortens runtime for 0.14?h. SGZ mixed coordinates are recommended in the simulation of deep lakes or reservoirs wherein the underwater topography is large (with abundant continuous deep trenches or reefs).