Search

Lake thermal dynamics have been considerably impacted by climate change, with potential adverse effects on aquatic ecosystems. To better understand the potential impacts of future climate change on lake thermal dynamics and related processes, the use of mathematical models is essential. In this study, we provide a comprehensive review of lake water temperature modeling. We begin by discussing the physical concepts that regulate thermal dynamics in lakes, which serve as a primer for the description of process‐based models. We then provide an overview of different sources of observational water temperature data, including in situ monitoring and satellite Earth observations, used in the field of lake water temperature modeling. We classify and review the various lake water temperature models available, and then discuss model performance, including commonly used performance metrics and optimization methods. Finally, we analyze emerging modeling approaches, including forecasting, digital twins, combining process‐based modeling with deep learning, evaluating structural model differences through ensemble modeling, adapted water management, and coupling of climate and lake models. This review is aimed at a diverse group of professionals working in the fields of limnology and hydrology, including ecologists, biologists, physicists, engineers, and remote sensing researchers from the private and public sectors who are interested in understanding lake water temperature modeling and its potential applications. Plain Language Summary: Lake thermal dynamics are fundamental in controlling mixing processes and have significant implications for biological and geochemical processes. Consequently, the impacts of climate change on these dynamics can have severe consequences for the health of lakes and their aquatic ecosystems. In this context, mathematical models are essential for understanding the potential effects of future climate change on lake thermal dynamics and related processes. This manuscript offers a comprehensive review of lake water temperature modeling. It covers the fundamental physical concepts that govern thermal dynamics in lakes and provides an overview of various sources of observational water temperature data, including in situ monitoring and satellite data used in these models. The study evaluates different types of lake water temperature models, including statistical, process‐based, and hybrid models. It explores emerging modeling approaches such as forecasting, digital twins, combining process‐based modeling with deep learning, ensemble modeling, and climate‐lake models coupling. Model performance is also discussed, highlighting suggested evaluation metrics and providing a comprehensive analysis of the state‐of‐the‐art optimization methods to assess model accuracy. This review targets researchers in limnology, hydrology, ecology, biology, physics, engineering, and remote sensing from the private and public sectors interested in lake water temperature modeling and its applications. Key Points: Lake thermal dynamics are central in shaping mixing processes and the health of aquatic ecosystems, and climate change alters these dynamicsMathematical models are essential to understand past and project future climate change impacts on lake thermal dynamicsThis study reviews lake water temperature modeling, covering concepts, data sources, and model evaluation for applications across disciplines [ABSTRACT FROM AUTHOR]

Hybrid Knowledge‐Guided Machine Learning (KGML) models, which are deep learning models that utilize scientific theory and process‐based model simulations, have shown improved performance over their process‐based counterparts for the simulation of water temperature and hydrodynamics. We highlight the modular compositional learning (MCL) methodology as a novel design choice for the development of hybrid KGML models in which the model is decomposed into modular sub‐components that can be process‐based models and/or deep learning models. We develop a hybrid MCL model that integrates a deep learning model into a modularized, process‐based model. To achieve this, we first train individual deep learning models with the output of the process‐based models. In a second step, we fine‐tune one deep learning model with observed field data. In this study, we replaced process‐based calculations of vertical diffusive transport with deep learning. Finally, this fine‐tuned deep learning model is integrated into the process‐based model, creating the hybrid MCL model with improved overall projections for water temperature dynamics compared to the original process‐based model. We further compare the performance of the hybrid MCL model with the process‐based model and two alternative deep learning models and highlight how the hybrid MCL model has the best performance for projecting water temperature, Schmidt stability, buoyancy frequency, and depths of different isotherms. Modular compositional learning can be applied to existing modularized, process‐based model structures to make the projections more robust and improve model performance by letting deep learning estimate uncertain process calculations. Plain Language Summary: Lake models based on physical processes are powerful tools for investigating how lakes and reservoirs respond to local weather and for projecting lake responses to long‐term climate change. Historically, physical processes are the basis for designing these models. Due to an abundance of long‐term and high‐frequency data, deep learning models are used more frequently, although they do not reflect our domain expertise about hydrodynamics and heat transport. Recently, the modeling community has been focusing on merging models based on physical processes with deep learning. We are highlighting a novel methodology, modular compositional learning (MCL), that merges different modeling types in a modularized framework. Our resulting hybrid model outperformed the original model based on physical processes as well as alternative deep learning models regarding the simulation of various lake variables related to water temperature, and showed physically valid results. We are further showing various ways on how MCL can improve future lake model development and applications. Key Points: Deep learning models were pretrained on process‐based lake water temperature model output and fine‐tuned on observed high‐frequency dataFine‐tuned deep learning model was integrated into process‐based model creating the hybrid modelHybrid model outperformed process‐based model and two alternative deep learning models in projecting hydrodynamic lake characteristics [ABSTRACT FROM AUTHOR]