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The improvement of process representations in hydrological models is often only driven by the modelers' knowledge and data availability. We present a comprehensive comparison between two hydrological models of different complexity that is developed to support (1) the understanding of the differences between model structures and (2) the identification of the observations needed for model assessment and improvement. The comparison is conducted on both space and time and by aggregating the outputs at different spatiotemporal scales. In the present study, mHM, a process‐based hydrological model, and ParFlow‐CLM, an integrated subsurface‐surface hydrological model, are used. The models are applied in a mesoscale catchment in Germany. Both models agree in the simulated river discharge at the outlet and the surface soil moisture dynamics, lending their supports for some model applications (drought monitoring). Different model sensitivities are, however, found when comparing evapotranspiration and soil moisture at different soil depths. The analysis supports the need of observations within the catchment for model assessment, but it indicates that different strategies should be considered for the different variables. Evapotranspiration measurements are needed at daily resolution across several locations, while highly resolved spatially distributed observations with lower temporal frequency are required for soil moisture. Finally, the results show the impact of the shallow groundwater system simulated by ParFlow‐CLM and the need to account for the related soil moisture redistribution. Our comparison strategy can be applied to other models types and environmental conditions to strengthen the dialog between modelers and experimentalists for improving process representations in Earth system models.
Machine learning (ML) algorithms are being increasingly used in Earth and Environmental modeling studies owing to the ever-increasing availability of diverse data sets and computational resources as well as advancement in ML algorithms. Despite advances in their predictive accuracy, the usefulness of ML algorithms for inference remains elusive. In this study, we employ two popular ML algorithms, artificial neural networks and random forest, to analyze a large data set of flood events across Germany with the goals to analyze their predictive accuracy and their usability to provide insights to hydrologic system functioning. The results of the ML algorithms are contrasted against a parametric approach based on multiple linear regression. For analysis, we employ a model-agnostic framework named Permuted Feature Importance to derive the influence of models' predictors. This allows us to compare the results of different algorithms for the first time in the context of hydrology. Our main findings are that (1) the ML models achieve higher prediction accuracy than linear regression, (2) the results reflect basic hydrological principles, but (3) further inference is hindered by the heterogeneity of results across algorithms. Thus, we conclude that the problem of equifinality as known from classical hydrological modeling also exists for ML and severely hampers its potential for inference. To account for the observed problems, we propose that when employing ML for inference, this should be made by using multiple algorithms and multiple methods, of which the latter should be embedded in a cross-validation routine.
Machine learning (ML) algorithms are being increasingly used in Earth and Environmental modeling studies owing to the ever-increasing availability of diverse data sets and computational resources as well as advancement in ML algorithms. Despite advances in their predictive accuracy, the usefulness of ML algorithms for inference remains elusive. In this study, we employ two popular ML algorithms, artificial neural networks and random forest, to analyze a large data set of flood events across Germany with the goals to analyze their predictive accuracy and their usability to provide insights to hydrologic system functioning. The results of the ML algorithms are contrasted against a parametric approach based on multiple linear regression. For analysis, we employ a model-agnostic framework named Permuted Feature Importance to derive the influence of models' predictors. This allows us to compare the results of different algorithms for the first time in the context of hydrology. Our main findings are that (1) the ML models achieve higher prediction accuracy than linear regression, (2) the results reflect basic hydrological principles, but (3) further inference is hindered by the heterogeneity of results across algorithms. Thus, we conclude that the problem of equifinality as known from classical hydrological modeling also exists for ML and severely hampers its potential for inference. To account for the observed problems, we propose that when employing ML for inference, this should be made by using multiple algorithms and multiple methods, of which the latter should be embedded in a cross-validation routine.
Groundwater travel time distributions (TTDs) provide a robust description of the subsurface mixing behavior and hydrological response of a subsurface system. Lagrangian particle tracking is often used to derive the groundwater TTDs. The reliability of this approach is subjected to the uncertainty of external forcings, internal hydraulic properties, and the interplay between them. Here, we evaluate the uncertainty of catchment groundwater TTDs in an agricultural catchment using a 3-D groundwater model with an overall focus on revealing the relationship between external forcing, internal hydraulic properties, and TTD predictions. Eight recharge realizations are sampled from a high-resolution dataset of land surface fluxes and states. Calibration-constrained hydraulic conductivity fields (Ks fields) are stochastically generated using the null-space Monte Carlo (NSMC) method for each recharge realization. The random walk particle tracking (RWPT) method is used to track the pathways of particles and compute travel times. Moreover, an analytical model under the random sampling (RS) assumption is fit against the numerical solutions, serving as a reference for the mixing behavior of the model domain. The StorAge Selection (SAS) function is used to interpret the results in terms of quantifying the systematic preference for discharging young/old water. The simulation results reveal the primary effect of recharge on the predicted mean travel time (MTT). The different realizations of calibration-constrained Ks fields moderately magnify or attenuate the predicted MTTs. The analytical model does not properly replicate the numerical solution, and it underestimates the mean travel time. Simulated SAS functions indicate an overall preference for young water for all realizations. The spatial pattern of recharge controls the shape and breadth of simulated TTDs and SAS functions by changing the spatial distribution of particles' pathways. In conclusion, overlooking the spatial nonuniformity and uncertainty of input (forcing) will result in biased travel time predictions. We also highlight the worth of reliable observations in reducing predictive uncertainty and the good interpretability of SAS functions in terms of understanding catchment transport processes.
Machine learning (ML) algorithms are being increasingly used in Earth and Environmental modeling studies owing to the ever-increasing availability of diverse data sets and computational resources as well as advancement in ML algorithms. Despite advances in their predictive accuracy, the usefulness of ML algorithms for inference remains elusive. In this study, we employ two popular ML algorithms, artificial neural networks and random forest, to analyze a large data set of flood events across Germany with the goals to analyze their predictive accuracy and their usability to provide insights to hydrologic system functioning. The results of the ML algorithms are contrasted against a parametric approach based on multiple linear regression. For analysis, we employ a model-agnostic framework named Permuted Feature Importance to derive the influence of models' predictors. This allows us to compare the results of different algorithms for the first time in the context of hydrology. Our main findings are that (1) the ML models achieve higher prediction accuracy than linear regression, (2) the results reflect basic hydrological principles, but (3) further inference is hindered by the heterogeneity of results across algorithms. Thus, we conclude that the problem of equifinality as known from classical hydrological modeling also exists for ML and severely hampers its potential for inference. To account for the observed problems, we propose that when employing ML for inference, this should be made by using multiple algorithms and multiple methods, of which the latter should be embedded in a cross-validation routine.
Most large-scale hydrologic models fall short in reproducing groundwater head dynamics and simulating transport process due to their oversimplified representation of groundwater flow. In this study, we aim to extend the applicability of the mesoscale Hydrologic Model (mHM v5.7) to subsurface hydrology by coupling it with the porous media simulator OpenGeoSys (OGS). The two models are one-way coupled through model interfaces GIS2FEM and RIV2FEM, by which the grid-based fluxes of groundwater recharge and the river-groundwater exchange generated by mHM are converted to fixed-flux boundary conditions of the groundwater model OGS. Specifically, the grid-based vertical reservoirs in mHM are completely preserved for the estimation of land-surface fluxes, while OGS acts as a plug-in to the original mHM modeling framework for groundwater flow and transport modeling. The applicability of the coupled model (mHM-OGS v1.0) is evaluated by a case study in the central European mesoscale river basin - Nagelstedt. Different time steps, i.e., daily in mHM and monthly in OGS, are used to account for fast surface flow and slow groundwater flow. Model calibration is conducted following a two-step procedure using discharge for mHM and long-term mean of groundwater head measurements for OGS. Based on the model summary statistics, namely the Nash-Sutcliffe model efficiency (NSE), the mean absolute error (MAE), and the interquartile range error (QRE), the coupled model is able to satisfactorily represent the dynamics of discharge and groundwater heads at several locations across the study basin. Our exemplary calculations show that the one-way coupled model can take advantage of the spatially explicit modeling capabilities of surface and groundwater hydrologic models and provide an adequate representation of the spatiotemporal behaviors of groundwater storage and heads, thus making it a valuable tool for addressing water resources and management problems.
Distributed environmental models such as land surface models (LSMs) require model parameters in each spatial modeling unit (e.g., grid cell), thereby leading to a high-dimensional parameter space. One approach to decrease the dimensionality of the parameter space in these models is to use regularization techniques. One such highly efficient technique is the multiscale parameter regionalization (MPR) framework that translates high-resolution predictor variables (e.g., soil textural properties) into model parameters (e.g., porosity) via transfer functions (TFs) and upscaling operators that are suitable for every modeled process. This framework yields seamless model parameters at multiple scales and locations in an effective manner. However, integration of MPR into existing modeling workflows has been hindered thus far by hard-coded configurations and non-modular software designs. For these reasons, we redesigned MPR as a model-agnostic, stand-alone tool. It is a useful software for creating graphs of NetCDF variables, wherein each node is a variable and the links consist of TFs and/or upscaling operators. In this study, we present and verify our tool against a previous version, which was implemented in the mesoscale hydrologic model (mHM; https://www.ufz.de/mhm, last access: 16 January 2022). By using this tool for the generation of continental-scale soil hydraulic parameters applicable to different models (Noah-MP and HTESSEL), we showcase its general functionality and flexibility. Further, using model parameters estimated by the MPR tool leads to significant changes in long-term estimates of evapotranspiration, as compared to their default parameterizations. For example, a change of up to 25 % in long-term evapotranspiration flux is observed in Noah-MP and HTESSEL in the Mississippi River basin. We postulate that use of the stand-alone MPR tool will considerably increase the transparency and reproducibility of the parameter estimation process in distributed (environmental) models. It will also allow a rigorous uncertainty estimation related to the errors of the predictors (e.g., soil texture fields), transfer function and its parameters, and remapping (or upscaling) algorithms.
Soil properties show high heterogeneity at different spatial scales and their correct characterization remains a crucial challenge over large areas. The aim of the study is to quantify the impact of different types of uncertainties that arise from the unresolved soil spatial variability on simulated hydrological states and fluxes. Three perturbation methods are presented for the characterization of uncertainties in soil properties. The methods are applied on the soil map of the upper Neckar catchment (Germany), as an example. The uncertainties are propagated through the distributed mesoscale hydrological model (mHM) to assess the impact on the simulated states and fluxes. The model outputs are analysed by aggregating the results at different spatial and temporal scales. These results show that the impact of the different uncertainties introduced in the original soil map is equivalent when the simulated model outputs are analysed at the model grid resolution (i.e. 500 m). However, several differences are identified by aggregating states and fluxes at different spatial scales (by subcatchments of different sizes or coarsening the grid resolution). Streamflow is only sensitive to the perturbation of long spatial structures while distributed states and fluxes (e.g. soil moisture and groundwater recharge) are only sensitive to the local noise introduced to the original soil properties. A clear identification of the temporal and spatial scale for which finer-resolution soil information is (or is not) relevant is unlikely to be universal. However, the comparison of the impacts on the different hydrological components can be used to prioritize the model improvements in specific applications, either by collecting new measurements or by calibration and data assimilation approaches. In conclusion, the study underlines the importance of a correct characterization of uncertainty in soil properties. With that, soil maps with additional information regarding the unresolved soil spatial variability would provide strong support to hydrological modelling applications.
Soil properties show high heterogeneity at different spatial scales and their correct characterization remains a crucial challenge over large areas. The aim of the study is to quantify the impact of different types of uncertainties that arise from the unresolved soil spatial variability on simulated hydrological states and fluxes. Three perturbation methods are presented for the characterization of uncertainties in soil properties. The methods are applied on the soil map of the upper Neckar catchment (Germany), as an example. The uncertainties are propagated through the distributed mesoscale hydrological model (mHM) to assess the impact on the simulated states and fluxes. The model outputs are analysed by aggregating the results at different spatial and temporal scales. These results show that the impact of the different uncertainties introduced in the original soil map is equivalent when the simulated model outputs are analysed at the model grid resolution (i.e. 500 m). However, several differences are identified by aggregating states and fluxes at different spatial scales (by subcatchments of different sizes or coarsening the grid resolution). Streamflow is only sensitive to the perturbation of long spatial structures while distributed states and fluxes (e.g. soil moisture and groundwater recharge) are only sensitive to the local noise introduced to the original soil properties. A clear identification of the temporal and spatial scale for which finer-resolution soil information is (or is not) relevant is unlikely to be universal. However, the comparison of the impacts on the different hydrological components can be used to prioritize the model improvements in specific applications, either by collecting new measurements or by calibration and data assimilation approaches. In conclusion, the study underlines the importance of a correct characterization of uncertainty in soil properties. With that, soil maps with additional information regarding the unresolved soil spatial variability would provide strong support to hydrological modelling applications.
Most large-scale hydrologic models fall short in reproducing groundwater head dynamics and simulating transport process due to their oversimplified representation of groundwater flow. In this study, we aim to extend the applicability of the mesoscale Hydrologic Model (mHM v5.7) to subsurface hydrology by coupling it with the porous media simulator OpenGeoSys (OGS). The two models are one-way coupled through model interfaces GIS2FEM and RIV2FEM, by which the grid-based fluxes of groundwater recharge and the river-groundwater exchange generated by mHM are converted to fixed-flux boundary conditions of the groundwater model OGS. Specifically, the grid-based vertical reservoirs in mHM are completely preserved for the estimation of land-surface fluxes, while OGS acts as a plug-in to the original mHM modeling framework for groundwater flow and transport modeling. The applicability of the coupled model (mHM-OGS v1.0) is evaluated by a case study in the central European mesoscale river basin - Nagelstedt. Different time steps, i.e., daily in mHM and monthly in OGS, are used to account for fast surface flow and slow groundwater flow. Model calibration is conducted following a two-step procedure using discharge for mHM and long-term mean of groundwater head measurements for OGS. Based on the model summary statistics, namely the Nash-Sutcliffe model efficiency (NSE), the mean absolute error (MAE), and the interquartile range error (QRE), the coupled model is able to satisfactorily represent the dynamics of discharge and groundwater heads at several locations across the study basin. Our exemplary calculations show that the one-way coupled model can take advantage of the spatially explicit modeling capabilities of surface and groundwater hydrologic models and provide an adequate representation of the spatiotemporal behaviors of groundwater storage and heads, thus making it a valuable tool for addressing water resources and management problems.