Introduction
Following the initial introduction of the ULTIMATE-QUICKEST implementation for advective transport in EFDC+, we further explore this feature by focusing on its enhancement to model performance over the original upwind differencing in simulating constituent transport. This blog focuses on the overall computational cost, providing a detailed analysis of advective transport computations and total model runtime. The mitigation of numerical issues, including artificial diffusion as well as over- and undershoot, is addressed in our white paper.
Model Performance Efficiency
The 3D Lake Mendota Eutrophication model is used to demonstrate the practical advantages of the QUICKEST algorithm, focusing on the computation efficiency in real-world applications. Lake Mendota is a eutrophic freshwater lake located in Madison, Wisconsin, with a surface area of approximately 3,940 hectares. The lake has an average depth of 12.8 m, and its maximum depth reaches about 25.3 m. The primary hydrological inflows and outflows occur through the Yahara River.
Figure 1 illustrates the model grid, locations of the boundary conditions, and the bottom elevation. The model domain is discretized using a uniform grid of 1405 cells, each with a resolution of 170 m × 170 m. The vertical layering uses SGZ uniform layers option varying from 3 to 30 layers. The model simulates two algal groups: cyanobacteria and diatoms. Nutrient constituents include organic carbon, nitrogen, phosphorus, and silica, each represented by their respective sub-classes: refractory particulate, labile particulate, and dissolved fractions. The total number of water quality constituents simulated is 18. The simulation period covers one year, from January 7, 2012, to December 28, 2012. Two model runs were conducted using the original upwind scheme implemented in EFDC+ and the new ULTIMATE-QUICKEST option, respectively:
- Run01 – Upwind Difference with Anti-Diffusion Correction and Flux Limitation
- Run02 – ULTIMATE-QUICKEST
Figures 2a and 2b compare the time series of temperature at different water depths at the BUOY point obtained from the two model runs. Minor differences between the Upwind and ULTIMATE-QUICKEST schemes are observed; however, overall, both schemes show good agreement with the observed data.
Regarding computational efficiency, Figure 3 summarizes the reduction in computation time achieved by ULTIMATE-QUICKEST relative to the Upwind scheme across five real-world model applications, for both advective transport time and total model run time. The ULTIMATE-QUICKEST method significantly reduces the time spent on advective transport — by roughly 40–62% depending on the model — which in turn lowers the total model run time by up to approximately 34%. The efficiency gains become more pronounced as the number of simulated constituents increases. Additionally, 3D models exhibit greater reductions in computation time compared to 2D models, as they include advective transport in the vertical direction.
Conclusions
The enhancement in computational time of the ULTIMATE-QUICKEST scheme is evaluated using different real-world models’ applications. The results and analysis demonstrate that ULTIMATE-QUICKEST effectively improves computational efficiency as the algorithm significantly reduces the time required for the advective transport calculations during the simulation.
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