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Model ensembles have several benefits compared to single-model applications but are not frequently used within the lake modelling community. Setting up and running multiple lake models can be challenging and time consuming, despite the many similarities between the existing models (forcing data, hypsograph, etc.). Here we present an R package, LakeEnsemblR, that facilitates running ensembles of five different vertical one-dimensional hydrodynamic lake models (FLake, GLM, GOTM, Simstrat, MyLake). The package requires input in a standardised format and a single configuration file. LakeEnsemblR formats these files to the input required by each model, and provides functions to run and calibrate the models. The outputs of the different models are compiled into a single file, and several post-processing operations are supported. LakeEnsemblR's workflow standardisation can simplify model benchmarking and uncertainty quantification, and improve collaborations between scientists. We showcase the successful application of LakeEnsemblR for two different lakes.

Model ensembles have several benefits compared to single-model applications but are not frequently used within the lake modelling community. Setting up and running multiple lake models can be challenging and time consuming, despite the many similarities between the existing models (forcing data, hypsograph, etc.). Here we present an R package, LakeEnsemblR, that facilitates running ensembles of five different vertical one-dimensional hydrodynamic lake models (FLake, GLM, GOTM, Simstrat, MyLake). The package requires input in a standardised format and a single configuration file. LakeEnsemblR formats these files to the input required by each model, and provides functions to run and calibrate the models. The outputs of the different models are compiled into a single file, and several post-processing operations are supported. LakeEnsemblR's workflow standardisation can simplify model benchmarking and uncertainty quantification, and improve collaborations between scientists. We showcase the successful application of LakeEnsemblR for two different lakes.

Phosphorus (P) loading to lakes is degrading the quality and usability of water globally. Accurate predictions of lake P dynamics are needed to understand whole-ecosystem P budgets, as well as the consequences of changing lake P concentrations for water quality. However, complex biophysical processes within lakes, along with limited observational data, challenge our capacity to reproduce short-term lake dynamics needed for water quality predictions, as well as long-term dynamics needed to understand broad scale controls over lake P. Here we use an emerging paradigm in modeling, process-guided machine learning (PGML), to produce a phosphorus budget for Lake Mendota (Wisconsin, USA) and to accurately predict epilimnetic phosphorus over a time range of days to decades. In our implementation of PGML, which we term a Process-Guided Recurrent Neural Network (PGRNN), we combine a process-based model for lake P with a recurrent neural network, and then constrain the predictions with ecological principles. We test independently the process-based model, the recurrent neural network, and the PGRNN to evaluate the overall approach. The process-based model accounted for most of the observed pattern in lake P; however it missed the long-term trend in lake P and had the worst performance in predicting winter and summer P in surface waters. The root mean square error (RMSE) for the process-based model, the recurrent neural network, and the PGRNN was 33.0 mu g P L-1, 22.7 mu g P L-1, and 20.7 mu g P L-1, respectively. All models performed better during summer, with RMSE values for the three models (same order) equal to 14.3 mu g P L-1, 10.9 mu g P L-1, and 10.7 mu g P L-1. Although the PGRNN had only marginally better RMSE during summer, it had lower bias and reproduced long-term decreases in lake P missed by the other two models. For all seasons and all years, the recurrent neural network had better predictions than process alone, with root mean square error (RMSE) of 23.8 mu g P L

Phosphorus (P) loading to lakes is degrading the quality and usability of water globally. Accurate predictions of lake P dynamics are needed to understand whole-ecosystem P budgets, as well as the consequences of changing lake P concentrations for water quality. However, complex biophysical processes within lakes, along with limited observational data, challenge our capacity to reproduce short-term lake dynamics needed for water quality predictions, as well as long-term dynamics needed to understand broad scale controls over lake P. Here we use an emerging paradigm in modeling, process-guided machine learning (PGML), to produce a phosphorus budget for Lake Mendota (Wisconsin, USA) and to accurately predict epilimnetic phosphorus over a time range of days to decades. In our implementation of PGML, which we term a Process-Guided Recurrent Neural Network (PGRNN), we combine a process-based model for lake P with a recurrent neural network, and then constrain the predictions with ecological principles. We test independently the process-based model, the recurrent neural network, and the PGRNN to evaluate the overall approach. The process-based model accounted for most of the observed pattern in lake P; however it missed the long-term trend in lake P and had the worst performance in predicting winter and summer P in surface waters. The root mean square error (RMSE) for the process-based model, the recurrent neural network, and the PGRNN was 33.0 mu g P L-1, 22.7 mu g P L-1, and 20.7 mu g P L-1, respectively. All models performed better during summer, with RMSE values for the three models (same order) equal to 14.3 mu g P L-1, 10.9 mu g P L-1, and 10.7 mu g P L-1. Although the PGRNN had only marginally better RMSE during summer, it had lower bias and reproduced long-term decreases in lake P missed by the other two models. For all seasons and all years, the recurrent neural network had better predictions than process alone, with root mean square error (RMSE) of 23.8 mu g P L

The General Lake Model (GLM) is a one-dimensional open-source code designed to simulate the hydrodynamics of lakes, reservoirs, and wetlands. GLM was developed to support the science needs of the Global Lake Ecological Observatory Network (GLEON), a network of researchers using sensors to understand lake functioning and address questions about how lakes around the world respond to climate and land use change. The scale and diversity of lake types, locations, and sizes, and the expanding observational datasets created the need for a robust community model of lake dynamics with sufficient flexibility to accommodate a range of scientific and management questions relevant to the GLEON community. This paper summarizes the scientific basis and numerical implementation of the model algorithms, including details of sub-models that simulate surface heat exchange and ice cover dynamics, vertical mixing, and inflow-outflow dynamics. We demonstrate the suitability of the model for different lake types that vary substantially in their morphology, hydrology, and climatic conditions. GLM supports a dynamic coupling with biogeochemical and ecological modelling libraries for integrated simulations of water quality and ecosystem health, and options for integration with other environmental models are outlined. Finally, we discuss utilities for the analysis of model outputs and uncertainty assessments, model operation within a distributed cloud-computing environment, and as a tool to support the learning of network participants. © 2019 Author(s).

The General Lake Model (GLM) is a one-dimensional open-source code designed to simulate the hydrodynamics of lakes, reservoirs, and wetlands. GLM was developed to support the science needs of the Global Lake Ecological Observatory Network (GLEON), a network of researchers using sensors to understand lake functioning and address questions about how lakes around the world respond to climate and land use change. The scale and diversity of lake types, locations, and sizes, and the expanding observational datasets created the need for a robust community model of lake dynamics with sufficient flexibility to accommodate a range of scientific and management questions relevant to the GLEON community. This paper summarizes the scientific basis and numerical implementation of the model algorithms, including details of sub-models that simulate surface heat exchange and ice cover dynamics, vertical mixing, and inflow-outflow dynamics. We demonstrate the suitability of the model for different lake types that vary substantially in their morphology, hydrology, and climatic conditions. GLM supports a dynamic coupling with biogeochemical and ecological modelling libraries for integrated simulations of water quality and ecosystem health, and options for integration with other environmental models are outlined. Finally, we discuss utilities for the analysis of model outputs and uncertainty assessments, model operation within a distributed cloud-computing environment, and as a tool to support the learning of network participants. © 2019 Author(s).

The rapid growth of data in water resources has created new opportunities to accelerate knowledge discovery with the use of advanced deep learning tools. Hybrid models that integrate theory with state-of-the art empirical techniques have the potential to improve predictions while remaining true to physical laws. This paper evaluates the Process-Guided Deep Learning (PGDL) hybrid modeling framework with a use-case of predicting depth-specific lake water temperatures. The PGDL model has three primary components: a deep learning model with temporal awareness (long short-term memory recurrence), theory-based feedback (model penalties for violating conversation of energy), and model pretraining to initialize the network with synthetic data (water temperature predictions from a process-based model). In situ water temperatures were used to train the PGDL model, a deep learning (DL) model, and a process-based (PB) model. Model performance was evaluated in various conditions, including when training data were sparse and when predictions were made outside of the range in the training data set. The PGDL model performance (as measured by root-mean-square error (RMSE)) was superior to DL and PB for two detailed study lakes, but only when pretraining data included greater variability than the training period. The PGDL model also performed well when extended to 68 lakes, with a median RMSE of 1.65 degrees C during the test period (DL: 1.78 degrees C, PB: 2.03 degrees C; in a small number of lakes PB or DL models were more accurate). This case-study demonstrates that integrating scientific knowledge into deep learning tools shows promise for improving predictions of many important environmental variables.

The modelling community has identified challenges for the integration and assessment of lake models due to the diversity of modelling approaches and lakes. In this study, we develop and assess a one-dimensional lake model and apply it to 32 lakes from a global observatory network. The data set included lakes over broad ranges in latitude, climatic zones, size, residence time, mixing regime and trophic level. Model performance was evaluated using several error assessment metrics, and a sensitivity analysis was conducted for nine parameters that governed the surface heat exchange and mixing efficiency. There was low correlation between input data uncertainty and model performance and predictions of temperature were less sensitive to model parameters than prediction of thermocline depth and Schmidt stability. The study provides guidance to where the general model approach and associated assumptions work, and cases where adjustments to model parameterisations and/or structure are required.

A national-scale quantification of metabolic energy flow in streams and rivers can improve understanding of the temporal dynamics of in-stream activity, links between energy cycling and ecosystem services, and the effects of human activities on aquatic metabolism. The two dominant terms in aquatic metabolism, gross primary production (GPP) and aerobic respiration (ER), have recently become practical to estimate for many sites due to improved modeling approaches and the availability of requisite model inputs in public datasets. We assembled inputs from the U.S. Geological Survey and National Aeronautics and Space Administration for October 2007 to January 2017. We then ran models to estimate daily GPP, ER, and the gas exchange rate coefficient for 356 streams and rivers across the continental United States. We also gathered potential explanatory variables and spatial information for cross-referencing this dataset with other datasets of watershed characteristics. This dataset offers a first national assessment of many-day time series of metabolic rates for up to 9 years per site, with a total of 490,907 site-days of estimates.

The modelling community has identified challenges for the integration and assessment of lake models due to the diversity of modelling approaches and lakes. In this study, we develop and assess a one-dimensional lake model and apply it to 32 lakes from a global observatory network. The data set included lakes over broad ranges in latitude, climatic zones, size, residence time, mixing regime and trophic level. Model performance was evaluated using several error assessment metrics, and a sensitivity analysis was conducted for nine parameters that governed the surface heat exchange and mixing efficiency. There was low correlation between input data uncertainty and model performance and predictions of temperature were less sensitive to model parameters than prediction of thermocline depth and Schmidt stability. The study provides guidance to where the general model approach and associated assumptions work, and cases where adjustments to model parameterisations and/or structure are required.

The modelling community has identified challenges for the integration and assessment of lake models due to the diversity of modelling approaches and lakes. In this study, we develop and assess a one-dimensional lake model and apply it to 32 lakes from a global observatory network. The data set included lakes over broad ranges in latitude, climatic zones, size, residence time, mixing regime and trophic level. Model performance was evaluated using several error assessment metrics, and a sensitivity analysis was conducted for nine parameters that governed the surface heat exchange and mixing efficiency. There was low correlation between input data uncertainty and model performance and predictions of temperature were less sensitive to model parameters than prediction of thermocline depth and Schmidt stability. The study provides guidance to where the general model approach and associated assumptions work, and cases where adjustments to model parameterisations and/or structure are required. (c) 2017 Published by Elsevier Ltd.