Predicting total organic carbon loads in river using a mass-conserving LSTM integrated with QUAL2E kinetics

The increasing complexity of water pollution and its impact on aquatic ecosystems necessitates the accurate prediction of water pollutant loads for effective river management. Total Organic Carbon (TOC), a key indicator of organic pollution levels, is central to assessing ecosystem health and informing water treatment strategies. However, conventional process-based modeling methods, while capable of providing precise water quality predictions, require extensive input data and significant computational resources, limiting their practical application. Consequently, alternative modeling approaches, particularly those leveraging artificial intelligence, have been explored. Recent advancements in deep learning have improved predictive modeling in environmental sciences. These approaches have showed effectiveness in hydrological applications, such as streamflow forecasting, by capturing complex nonlinear relationships within environmental systems. Despite these advancements, a notable limitation of these models is their difficulty in maintaining physical consistency, specifically in adhering to the principle of mass balance—a fundamental concept in both hydrology and water quality modeling. In this study, we evaluate a Mass-Conserving Long Short-Term Memory network integrated with QUAL2E kinetics (MC-LSTM-QUAL2E) to predict TOC loads in river systems. By incorporating representations of decay and reaeration processes within a mass-conserving neural network framework, this model combines data-driven prediction capabilities with the requirements of physical consistency. A key component of this framework is the trash cell, designed to simulate TOC transformations based on QUAL2E dynamics. Within the trash cell, TOC decay and reaeration are modeled using parameters k_decay​ and k_reaeration​, which are determined by environmental variables such as temperature, pH, dissolved oxygen, total nitrogen, and total phosphorus. The QUAL2E module updates the trash state at each timestep to account for TOC losses due to decay and gains from reaeration, ensuring mass conservation.  The MC-LSTM-QUAL2E model was compared to a conventional LSTM model using environmental variables, including temperature, pH, dissolved oxygen, and nutrient levels, as inputs. The analysis used data from 2012 to 2020, with the period from 2012 to 2017 designated for training and 2018 to 2020 for tests. Model performance was assessed using metrics such as Nash-Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency (KGE), Root Mean Square Error-observations standard deviation Ratio (RSR), and Percent Bias (PBIAS). By maintaining mass balance and incorporating QUAL2E dynamics, the model provides reliable predictions of TOC loads in river systems and offers insights into associated biochemical and hydrological processes.