Effects of dimensionality on the performance of hydrodynamic models for stratified lakes and reservoirs

Abstract

Abstract. Numerical models are an important tool for simulating temperature, hydrodynamics, and water quality in lakes and reservoirs. Existing models differ in dimensionality by considering spatial variations of simulated parameters (e.g., flow velocity and water temperature) in one (1D), two (2D) or three (3D) spatial dimensions. The different approaches are based on different levels of simplification in the description of hydrodynamic processes and result in different demands on computational power. The aim of this study is to compare three models with different dimensionalities and to analyze differences between model results in relation to model simplifications. We analyze simulations of thermal stratification, flow velocity and substance transport by density currents in a medium-sized drinking-water reservoir in the subtropical zone, using three widely used open-source models: GLM (1D), CE-QUAL-W2 (2D) and Delft3D (3D). The models were operated with identical initial and boundary conditions over a 1-year period. Their performance was assessed by comparing model results with measurements of temperature, flow velocity and turbulence. Our results show that all models were capable of simulating the seasonal changes in water temperature and stratification. Flow velocities, only available for the 2D and 3D approaches, were more challenging to reproduce, but 3D simulations showed closer agreement with observations. With increasing dimensionality, the quality of the simulations also increased in terms of error, correlation and variance. None of the models provided good agreement with observations in terms of mixed layer depth, which also affects the spreading of inflowing water as density currents and the results of water quality models that build on outputs of the hydrodynamic models.

Lake Water Temperature Modeling in an Era of Climate Change: Data Sources, Models, and Future Prospects

“…A typical application is to use 1D lake models in projecting climate change effects on lake systems (e.g., Ayala et al., 2020; Fenocchi et al., 2018; U. G. Kobler & Schmid, 2019; Magee & Wu, 2017; Moras et al., 2019; Piccolroaz & Toffolon, 2018; Robertson & Ragotzkie, 1990; Woolway, Jennings, et al., 2021; Wood et al., 2023), as, due to low computational costs, they can project long‐term effects in a low time frame. Their application for climate change projections is especially advisable as 1D lake models can sufficiently replicate the dynamics of lake systems regarding stratification, ice formation and mixing compared with higher dimensional models (Ishikawa et al., 2022), and upscaling is technically feasible due to low computational demands. 1D lake models are also frequently used to evaluate the effect of meteorological extreme events on in‐lake mixing and heat transport (e.g., Bueche et al., 2017; Mesman et al., 2021; Perga et al., 2018; Shinohara et al., 2023).…”

“…Although this approach is still sometimes recommended (Yu et al., 2022), it can be highly inefficient in terms of both time needed and effects obtained. Nonetheless, manual calibration is frequently used for computationally demanding, 2D (Diogo et al., 2008; Ishikawa et al., 2022; Zouabi‐Aloui et al., 2015) and 3D (Castelletti et al., 2010; Hodges & Dallimore, 2001; Hui et al., 2018; B. Martin et al., 2013; Missaghi & Hondzo, 2010; Preston et al., 2014; Soulignac et al., 2017) thermo‐hydrodynamic lake or reservoir models. The other approach is using gradient, or second‐order derivative‐based algorithms (Battiti, 1992; Levenberg, 1944), which are often fast and accurate in finding the local optimum.…”

“…The choice of the best model to use depends upon the processes that are investigated and the morphological characteristics of the lake at hand and is often constrained by the type and quality of available data. In this respect, we refer the interested reader to the study by Ishikawa et al (2022) for a detailed comparison among models with different dimensions (from 1D to 3D) in relation to their ability in simulating, among others, thermal stratification in a medium-sized drinking-water reservoir. Here, we provide a description of each category of model along with references to the most relevant literature on the topic, with a particular focus on 0D and 1D models passing through 0.5D models.…”

Modular Compositional Learning Improves 1D Hydrodynamic Lake Model Performance by Merging Process‐Based Modeling With Deep Learning

“…Lake hydrodynamic models may be used to understand how warming air temperatures will alter lake thermal structure (Woolway et al., 2021) and linked biogeochemical conditions such as dissolved oxygen concentrations (Jane et al., 2022). Due to their low computational costs but sufficient replication of lake mixing dynamics (Ishikawa et al., 2022), one‐dimensional hydrodynamic lake models are commonly employed to project changes in water temperature (Moore et al., 2021), when it is reasonable to neglect horizontal mixing and focus only on resolving the vertical transport.…”

Mechanistic Modeling of the Variability of Methane Emissions from an Artificial Reservoir

“…Models of this type have been previously used to estimate CH 4 and CO 2 emissions from natural lakes with high residence time [27][28][29][30][31][32][33]. However, artificial water bodies are often characterized by significant horizontal heterogeneity in the distribution of both physical and biogeochemical variables, presenting a challenge for 1D models to successfully reproduce surface energy and mass exchange [34]. Therefore, one of the objectives of this study is to assess the applicability of a 1D (vertical) approach to simulate the concentration and fluxes of methane in reservoirs using the LAKE model.…”