Comparison of hydrological model structures based on recession and low flow simulations

A downward structural sensitivity analysis of hydrological models to improve low-flow simulation

Added value of distribution in rainfall-runoff models for the Meuse basin

The problems of identifying the most appropriate model structure for a given problem and quantifying the uncertainty in model structure remain outstanding research challenges for the discipline of hydrology. Progress on these problems requires understanding of the nature of differences between models. This paper presents a methodology to diagnose differences in hydrological model structures: the Framework for Understanding Structural Errors (FUSE). FUSE was used to construct 79 unique model structures by combining components of 4 existing hydrological models. These new models were used to simulate streamflow in two of the basins used in the Model Parameter Estimation Experiment (MOPEX): the Guadalupe River (Texas) and the French Broad River (North Carolina). Results show that the new models produced simulations of streamflow that were at least as good as the simulations produced by the models that participated in the MOPEX experiment. Our initial application of the FUSE method for the Guadalupe River exposed relationships between model structure and model performance, suggesting that the choice of model structure is just as important as the choice of model parameters. However, further work is needed to evaluate model simulations using multiple criteria to diagnose the relative importance of model structural differences in various climate regimes and to assess the amount of independent information in each of the models. This work will be crucial to both identifying the most appropriate model structure for a given problem and quantifying the uncertainty in model structure. To facilitate research on these problems, the FORTRAN‐90 source code for FUSE is available upon request from the lead author.

<p>Recent investigations have shown it is possible to simultaneously calibrate model structures and model parameters to identify appropriate models for a given task (Spieler et al., 2020). However, this is computationally challenging, as different model structures may use a different number of parameters. While some parameters may be shared between model structures, others might be relevant for only a few structures, which theoretically requires the calibration of conditionally active parameters. Additionally, shared model parameters might cause different effects in different model structures, causing their optimal values to differ across structures. In this study, we tested how two current “of the shelf” mixed-integer optimization algorithms perform when having to handle these peculiarities during the automatic model structure identification (AMSI) process recently introduced by Spieler et al. (2020).</p><p>To validate the current performance of the AMSI approach, we conduct a benchmark experiment with a model space consisting of 6912 different model structures.  First, all model structures are independently calibrated and validated for three hydro-climatically differing catchments using the CMA-ES algorithm and KGE as the objective function. This is referred to as standard calibration procedure. We identify the best performing model structure(s) based on validation performance and analyze the range of performance as well as the number of structures performing in a similar range. Secondly, we run AMSI on all three catchments to automatically identify the most feasible model structure based on the KGE performance. Two different mixed-integer optimization algorithms are used – namely DDS and CMA-ES. Afterwards, we compare the results to the best performing models of the standard calibration of all 6912 model structures.</p><p>Within this experimental setup, we analyze if the best performing model structure(s) AMSI identifies are identical to the best performing structures of the standard calibration and if there are differences in performance when using different optimization algorithms for AMSI. We also validate if AMSI can identify the best performing model structures for a catchment at a fraction of the computational cost than the standard calibration procedure requires by using “off the shelf” mixed-integer optimization algorithms.</p><p> </p><p> </p><p> </p><p>Spieler, D., Mai, J., Craig, J. R., Tolson, B. A., & Schütze, N. (2020). Automatic Model Structure Identification for Conceptual Hydrologic Models. Water Resources Research, 56(9). https://doi.org/10.1029/2019WR027009</p>

<p>Hydrological models are conventionally evaluated in terms of their response surface or likelihood surface constructed with the model parameter space. To evaluate models as hypotheses, we developed the method of <em>Flux Mapping</em> to construct a hypothesis space based on model process representation. Here we defined the hypothesis space based on dominant runoff generating mechanisms, and acceptable model runs are defined as total simulated flow with similar (and minimal) model error simulated by distinct combinations of runoff components. We demonstrate that the hypothesis space in each modeling case is the result of interplay between the factors of model structure, parameter sampling, choice of error metric, and data information content. The aim of this study is to disentangle the role of each factor in this interplay. We used two model structures (SACRAMENTO and SIMHYD), two parameter sampling approaches (small samples based on guided-search and large samples based on Latin Hypercube Sampling), three widely used error metrics (NSE, KGE, and WIA — Willmott’s Index of Agreement), and hydrological data from a range of Australian catchments. First, we characterized how the three error metrics behave under different error regimes independent of any modeling. We then conducted a series of controlled experiments, i.e. a type of one-factor-at-a-time sensitivity analysis, to unpack the role of each factor in runoff simulation. We show that KGE is a more reliable error metric compared to NSE and WIA for model evaluation. We also argue that robust error metrics and sufficient parameter sampling are necessary conditions for evaluating models as hypotheses under uncertainty. We particularly argue that sampling sufficiency, regardless of the sampling strategy, should be further evaluated based on its interaction with other modeling factors determining the model response. We conclude that the interplay of these modeling factors is complex and unique to each modeling case, and hence generalizing model-based inferences should be done with caution particularly in characterizing hydrological processes in large-sample hydrology.</p>

Abstract. Benchmarking model performance across large samples of catchments is useful to guide model selection and future model development. Given uncertainties in the observational data we use to drive and evaluate hydrological models, and uncertainties in the structure and parameterisation of models we use to produce hydrological simulations and predictions, it is essential that model evaluation is undertaken within an uncertainty analysis framework. Here, we benchmark the capability of several lumped hydrological models across Great Britain by focusing on daily flow and peak flow simulation. Four hydrological model structures from the Framework for Understanding Structural Errors (FUSE) were applied to over 1000 catchments in England, Wales and Scotland. Model performance was then evaluated using standard performance metrics for daily flows and novel performance metrics for peak flows considering parameter uncertainty. Our results show that lumped hydrological models were able to produce adequate simulations across most of Great Britain, with each model producing simulations exceeding a 0.5 Nash–Sutcliffe efficiency for at least 80 % of catchments. All four models showed a similar spatial pattern of performance, producing better simulations in the wetter catchments to the west and poor model performance in central Scotland and south-eastern England. Poor model performance was often linked to the catchment water balance, with models unable to capture the catchment hydrology where the water balance did not close. Overall, performance was similar between model structures, but different models performed better for different catchment characteristics and metrics, as well as for assessing daily or peak flows, leading to the ensemble of model structures outperforming any single structure, thus demonstrating the value of using multi-model structures across a large sample of different catchment behaviours. This research evaluates what conceptual lumped models can achieve as a performance benchmark and provides interesting insights into where and why these simple models may fail. The large number of river catchments included in this study makes it an appropriate benchmark for any future developments of a national model of Great Britain.

The impacts of climate change on the seasonality of extremes i.e. both high and low flows in the Columbia River basin were analyzed using three seasonality indices, namely the seasonality ratio (SR), weighted mean occurrence day (WMOD) and weighted persistence (WP). These indices reflect the streamflow regime, timing and variability in timing of extreme events respectively. The three indices were estimated from: (1) observed streamflow; (2) simulated streamflow using simulated inputs from ten combinations of CMIP5 inputs for the future climate (2040–2070) including the pathway RCP4.5 (3) simulated streamflow using simulated inputs from ten combinations of CMIP5 inputs for the future climate (2040–2070) including the pathway RCP8.5. The hydrological model was calibrated at 1/16 latitude-longitude resolution and the simulated streamflow was routed to the subbasin outlets of interest. These three cases are compared to assess the effects of forcing by different climate models and different pathways on the three indices. The results showed significant differences between three cases indicating a shift in streamflow regime and timing of extreme events such as high and low flows in the Columbia River Basin. The persistence of high flows are similar in all cases. The results will help to understand the effects of climate change on three important seasonality properties: regime, timing and persistence and associated errors. Conclusion Multi-model Averaging of 10 Climate Forcing Data Results: Climate change impacts on high flows (Q90) Acknowledgment  High flows occur between mid-April and June: ~day 100th and 180 respectively in Fig 2  Winter low flows are observed in snow dominated northern and southeastern CRB where precipitation is kept as snow or ice in winter (Fig 2).  High flow persistence is increasing in all six locations by 2040s (Table 1)  No significant difference was found between RCP45 and 85 for WP  SR is increasing in all locations except for Revelstoke  Weighted mean high flow occurrence day (WMOD) is about ten day late as compared to observed WMOD of high flows. The delay is 20 days in Orofino by 2040s based on RCP85 scenario The Seasonality Ratio (SR): This index reveals the streamflow characteristics in summer and winter periods. The definitions of extremes (high or low flow) and the seasons (months for winter and summer) are crucial for the SR results as the underlying hydrological processes for summer and winter streamflows are different. In this study we focus on high flows and use the 90% exceedence probability (Q90) as a threshold for defining summer high flow (Q90s) and winter high flow (Q90w). The SR index is calculated as the ratio of Q90s and Q90w (Eq 4) A value of SR greater than one indicates the presence of a winter high flow regime and a value smaller than one indicates the presence of a summer high flow regime. Weighted Mean Occurrence Day (WMOD) The days at which the discharge is above the Q90 threshold are transformed into Julian dates Di, i.e. the day of the year ranging from 1 to 365 in regular years and 1 to 366 in leap years. The day number of each high flow event (Di) is weighted by the inverse high flow value (1/Qi) on the same day to address the severity of a high flow event as well as its occurrence day. The weighted mean day of occurrence is estimated first in radians to represent the annual cycle correctly. Otherwise, a simple averaging of high flow occurrences in winter months, e.g. January and December, can lead to a large error in the results. The weighted mean of Cartesian coordinates xθ and yθ of a total of high flow days i is defined as The values of θ can vary from 0 to 2π, where a zero value indicates the 1st of January, π/2 represents the 1st of April, pi represents the 1st of July and 3π /2 represents the 1st of October. The main advantage of using circular statistics is that it allows us to correctly average high flow occurrences in the winter half-year period. The WMOD is then obtained by back-transforming the weighted mean angle to a Julian date: (4)

<p>Lumped karst hydrological models often suffer from the over-simplified structures. In recent days, hydrochemical has been used as an auxiliary information to define realistic karst model structures. For karst aquifers, the hydrochemical dynamics of karst springs contain important information about the internal behavior of the karst aquifer that can be conducive to model identification and calibration. In this presentation, electrical conductivity (EC), as a substitution for Ca<sup>2+</sup> concentration of the spring discharge, is evaluated for its potential for model structure identification and reduction of simulation uncertainty. A new framework to integrate EC in karst modeling is developed at a small, well-instrumented karst catchment near Guilin City, China. A set of different hydrologic models were enabled to consider the linear dissolution process of Ca<sup>2+</sup> and its transport to investigate the models’ abilities to reproduce the behavior of spring discharge and EC. We found that most hydrologic models obtain similar performances concerning spring discharge, however, their performances in simulating spring EC show obvious differences. The combination of observed spring discharge and EC could identify a more realistic model structure that was in accordance with the observed perception of this karst aquifer’s functioning. Using the identified “most realistic” model, we use sensitivity analysis to show that spring EC only improves the identifiability of one hydrologic parameter mostly due to too complex EC dynamics during recharge events and therefore has limited potential to reduce discharge simulation uncertainty. Consequently, our new framework to include EC in karst models opens new doors for more realistic simulation but an explicit treatment of uncertainties remains necessary due to EC’s limited potential to reduce simulation uncertainty. The next step of our work is to integrate appropriate nonlinear dissolution process of carbonate rock in the model to further improve the simulation of spring EC (Ca<sup>2+</sup>).</p>

The spatiotemporal heterogeneity in precipitation and underlying surfaces and hybrid runoff generation mechanism make hydrological modelling and forecasting in semi-arid regions becoming a challenging work. Therefore, to provide a reference for the development of hydrological models in such regions, two nested hydrological experimental watersheds in semi-arid regions were selected for attribution analysis. Based on the concept of large-sample hydrology, large-scale numerical simulation experiments were performed by constructing different spatial and temporal scale rainfall schemes and combining three hydrological models with different runoff generation mechanisms. Finally, the influences of the time step, station density, and model structure on the flood simulations in semi-arid regions were evaluated. The spatial interpolation technique was used simultaneously to describe the high-dimensional complicated nonlinear relationships between the influencing factors and simulation results. The results show the following: (1) the flood simulation accuracy was more sensitive to the time step than the spatial station density of the rainfall schemes and was highly dependent on the time step of the original observation data, and (2) compared with the accuracy of the rainfall schemes, the model structure plays a dominant role in flood simulation accuracy. Thus, the hybrid model has significant potential for flood forecasting in semi-arid regions by combining different runoff generation mechanisms. (3) The spatial interpolation technique based on the k-nearest neighbour algorithm can construct a high-dimensional distribution between the influencing factors and model simulation accuracy, and describe the complicated relationships among the time step, station density, model structure, and flood simulations.

Climate warming is rapidly modifying glacier and snowmelt processes, with impacts that propagate across spatial and temporal scales, from high-elevation cryospheric dynamics to basin-scale streamflow. Capturing these cross-scale interactions requires hydrological models that explicitly represent cryospheric processes, such as glacier dynamics and snow redistribution, while also accounting for uncertainty arising from data scarcity and model structure. To address these challenges, we present a one-way coupling that integrates the Global Glacier Evolution Model (GloGEM) with Raven, a flexible hydrological modeling framework designed to emulate multiple model structures for systematic uncertainty assessment. Glacier simulations are first improved by incorporating snowline observations as an additional calibration constraint to the geodetic mass balance, reducing parameter equifinality and enhancing glacier runoff estimates. The resulting glacier runoff is then provided to the hydrological model, leading to a more robust representation of snowmelt processes and their contribution to streamflow. By evaluating multiple hydrological model structures within Raven, we further quantify uncertainties in simulated melt contributions arising from structural model choices. The framework is applied to multiple data-scarce Indus headwaters as representative high-mountain catchments, simulating melt contributions and streamflow across scales. By explicitly coupling cryosphere and hydrological models, this framework aims to improve projections of future water availability in data-scarce regions and provides a transferable approach for integrated cryosphere-hydrology modeling in complex mountain regions.

Hydrological modelling of ungauged catchments, which lack observed streamflow data, is an important practical goal in hydrology. A major challenge is to identify a model structure that reflects the hydrological processes relevant to the catchment of interest. Paraphrasing a well-known adage, “all models are wrong, but some model-mechanisms (process representations) might be useful.”We extend a method previously introduced for mechanism identification in gauged basins, by formulating the Bayesian inference equations in the space of (regionalized) flow indices principal components and by accounting for posterior parameter uncertainty. We use a flexible hydrological model to generate candidate mechanisms and model structures. Then, we use statistical hypothesis testing to identify the "dominant" (more a posteriori probable) hydrological mechanism. We assume that the error in the regionalization of flow indices principal components dominates the error of the hydrological model structure.The method is illustrated in 92 catchments from northern Spain. We treat 16 out of the 92 catchments as ungauged. We use 624 model-structures from FUSE (flexible hydrological model framework). The case study includes real data and synthetic experiments.The findings show that routing is among the most identifiable processes, whereas percolation and unsaturated zone processes are the least identifiable. The probability of making an identification (correct or wrong), remains stable at ~25%, both in the real and in the synthetic experiments. In the synthetic experiments, where the “true” mechanism is known, we can evaluate the reliability, i.e., the probability of identifying the true mechanism when the method makes an identification. Reliability varies between 60%-95% depending on the magnitude of the combined regionalization and hydrological error. The study contributes perspectives on hydrological mechanism identification under data-scarce conditions.Prieto et al. (2022) An Exploration of Bayesian Identification of Dominant Hydrological Mechanisms in Ungauged Catchments, WRR, 58(3), doi:10.1029/2021WR030705.

Various hydrological models have been developed for estimating root zone soil moisture dynamics. These models, however, incorporated their own parameterization approaches indicating that the output from the different model inherent structures might include uncertainties because we do not know which model structure is correct for describing the real system. More recently, multimodel approaches using a Bayesian Model Averaging (BMA) scheme can improve the overall predictive skill while individual models retain their own uncertainties for simulated soil moisture based on a single set of weights in modeling under different land surface wetness conditions (e.g., wet, moderately wet, and dry conditions). In order to overcome their limitations, we developed a BMA‐based multimodel simulation approach based on various soil wetness conditions for estimating effective surface soil moisture dynamics (0–5 cm) and quantifying uncertainties efficiently based on the land surface wetness conditions. The newly developed approach adapts three different hydrological models (i.e., Noah Land Surface Model, Noah LSM; Soil‐Water‐Atmosphere‐Plant, SWAP; and Community Land Model, CLM) for simulating soil moisture. These models were integrated with a modified‐microGA (advanced version of original Genetic Algorithm (GA)) to search for optimized soil parameters for each model. Soil moisture was simulated from the estimated soil parameters using the hydrological models in a forward mode. It was found that SWAP performed better than others during wet condition, while Noah LSM and CLM showed a good agreement with measurements during dry condition. Thus, we inferred that performance of individual models with different model structures can be different with land surface wetness. Taking into account the effects of soil wetness on different model performances, we categorized soil moisture measurements and estimated different weights for each category using the BMA scheme. Effective surface soil moisture dynamics were obtained by aggregating multiple weighted soil moisture. Our findings demonstrated that the effective soil moisture estimates derived by this approach showed a better match with the measurements compared to the original models and single‐weighted outputs. Multimodel simulation approach based on land surface wetness enhances the ability to predict reliable soil moisture dynamics and reflects the strengths of different hydrological models under various soil wetness conditions.

<p>Recent studies have introduced methods to simultaneously calibrate model structure choices and parameter values to identify an appropriate (conceptual) model structure for a given catchment. This can be done through mixed-integer optimization to identify the graph structure that links dominant flow processes (Spieler et al., 2020) or, likewise, by continuous optimization of weights when blending multiple flux equations to describe flow processes within a model (Chlumsky et al., 2021). Here, we use the combination of the mixed-integer optimization algorithm DDS and the modular modelling framework RAVEN and refer to it as Automatic Model Structure Identification (AMSI) framework.</p><p>This study validates the AMSI framework by comparing the performance of the identified AMSI model structures to two different benchmark ensembles. The first ensemble consists of the best model structures from the brute force calibration of all possible structures included in the AMSI model space (7488+). The second ensemble consists of 35+ MARRMoT structures representing a structurally more divers set of models than currently implemented in the AMSI framework. These structures stem from the MARRMoT Toolbox introduced by Knoben et al. (2019) providing established conceptual model structures based on hydrologic literature.</p><p>We analyze if the model structure(s) AMSI identifies are identical to the best performing structures of the brute force calibration and comparable in their performance to the MARRMoT ensemble. We can conclude that model structures identified with the AMSI framework can compete with the structurally more divers MARRMoT ensemble. In fact, we were surprised to see how well we do with a simple two storage structure over the 12 tested MOPEX catchments (Duan et al.,2006). We aim to discuss several emerging questions, such as the selection of a robust model structure, Equifinality in model structures, and the role of structural complexity.</p><p> </p><p>Spieler et al. (2020). https://doi.org/10.1029/2019WR027009</p><p>Chlumsky et al. (2021). https://doi.org/10.1029/2020WR029229</p><p>Knoben et al. (2019). https://doi.org/10.5194/gmd-12-2463-2019</p><p>Duan et al. (2006). https://doi.org/10.1016/j.jhydrol.2005.07.031</p>

The definition of the objective function for hydrological model calibration and goodness-of-fit metrics for validation are crucial in characterising model performance and driving model development. Ideally, model developers and users should identify the most suitable metric to characterize model performance based on their specific use cases and objectives. The benefits of this are evident; for example, the optimal objective function to calibrate a hydrological model only used for flood forecasting should be different from the optimal one to be used for a model focusing only on low flows. However, in practice, most hydrological models are used for multiple applications and a standard generalist function is adopted for their calibration. The two most widely used generalist functions are the Nash-Sutcliffe Efficiency (NSE) and the Kling-Gupta Efficiency (KGE), in its standard and modified versions. While the NSE is a simple normalization of the mean square error (MSE), the KGE overcomes some of the NSE limitations based on the decomposition of the MSE into three components, i.e., the error in the mean simulated streamflow, the relative variability, and the linear correlation between simulations and observations. Still, KGE presents some limitations, including a large sensitivity to outliers and an assumption of linearity and normality in the error distribution, which are impactful especially for the characterization of performances over low flows. Some alternative calibration functions have been proposed in the literature to overcome these limitations, but no calibration function overcomes the traditional two options (NSE and KGE) in improving the simulation along the whole range of the flow duration curve. Here we present the results of an extensive comparison of hydrological models calibrated and validated with multiple functions, including new variants and combinations of KGE and information-theory metrics, that can be suitable to characterize the performance over high, low, and regime flows. Two hydrological models (GR4J and Open Source LISFLOOD) were calibrated with several alternative calibration functions over more than 200 catchments in Europe with a varied range of hydroclimatic conditions. Both models were evaluated using multiple metrics, including use-case specific hydrological signatures focusing on flood characteristics, average regime and low flows. Based on our analysis, a new function is proposed which combines the three KGE components with an additional component based on the Jensen-Shannon Divergence. The performance of the two models calibrated with the new function is shown to outperform the standard KGE and NSE over low flows with minimal change in performance over regimes and high flows. This study shows that more effort should be devoted to the choice of the optimal calibration function for hydrological model applications when aiming to improve specific aspects of model performance.

Stepwise modeling and the importance of internal variables validation to test model realism in a data scarce glacier basin