Errors Of Hydrological Models Research Articles

Sensitivity of bias correction step on generating hydrological scenarios

ABSTRACT Significant shifts in hydro-climatic regimes are expected in many parts of the world during the 21st century, affecting the water cycle. Vulnerability, impact, and adaptation studies often use tailored modeling chains to assess the expected effects of climate change, but the robustness of these chains is rarely investigated. This highlights the need for more rigorous evaluation of modeling chains to ensure that they are reliable for informed decision-making processes. To address this gap, we propose a framework for evaluating the sensitivity of hydrological scenario production to the bias correction step. We apply the framework to the Senegal River Basin, using three bias correction methods (linear scale, empirical quantile mapping, and nested bias correction) and three procedures (climate-correction, hydrological-correction, and climate-hydrological-correction). Our results show that the choice of modeling chain has a significant impact on future hydro-climatic trajectories. In particular, the combination of climate-and-hydrological-correction procedures may be optimal when both climate biases and hydrological model errors are significant. Moreover, using multiple bias correction methods can strengthen the ensemble of future hydro-climatic conditions. These findings have implications for vulnerability–impact–adaptation studies and underscore the importance of rigorous modeling chain design and sensitivity analysis.

Towards a hybrid algorithm for the robust calibration of rainfall–runoff models

Abstract In this study, the hybrid particle swarm optimization (HPSO) algorithm was proposed and practised for the calibration of two conceptual rainfall–runoff models (dynamic water balance model and abcde). The performance of the developed method was compared with those of several metaheuristics. The models were calibrated for three sub-basins, and multiple performance criteria were taken into consideration in comparison. The results indicated that HPSO was derived significantly better and more consistent results than other algorithms with respect to hydrological model errors and convergence speed. A variance decomposition-based method – analysis of variance (ANOVA) – was also used to quantify the dynamic sensitivity of HPSO parameters. Accordingly, the individual and interactive uncertainties of the parameters defined in the HPSO are relatively low.

Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: Methodology development and investigation using toy models

We introduce an ensemble learning post-processing methodology for probabilistic hydrological modelling. This methodology generates numerous point predictions by applying a single hydrological model, yet with different parameter values drawn from the respective simulated posterior distribution. We call these predictions “sister predictions”. Each sister prediction extending in the period of interest is converted into a probabilistic prediction using information about the hydrological model's errors. This information is obtained from a preceding period for which observations are available, and is exploited using a flexible quantile regression model. All probabilistic predictions are finally combined via simple quantile averaging to produce the output probabilistic prediction. The idea is inspired by the ensemble learning methods originating from the machine learning literature. The proposed methodology offers larger robustness in performance than basic post-processing methodologies using a single hydrological point prediction. It is also empirically proven to “harness the wisdom of the crowd” in terms of average interval score, i.e., the obtained quantile predictions score no worse –usually better− than the average score of the combined individual predictions. This proof is provided within toy examples, which can be used for gaining insight on how the methodology works and under which conditions it can optimally convert point hydrological predictions to probabilistic ones. A large-scale hydrological application is made in a companion paper.

Probabilistic Hydrological Post-Processing at Scale: Why and How to Apply Machine-Learning Quantile Regression Algorithms

We conduct a large-scale benchmark experiment aiming to advance the use of machine-learning quantile regression algorithms for probabilistic hydrological post-processing “at scale” within operational contexts. The experiment is set up using 34-year-long daily time series of precipitation, temperature, evapotranspiration and streamflow for 511 catchments over the contiguous United States. Point hydrological predictions are obtained using the Génie Rural à 4 paramètres Journalier (GR4J) hydrological model and exploited as predictor variables within quantile regression settings. Six machine-learning quantile regression algorithms and their equal-weight combiner are applied to predict conditional quantiles of the hydrological model errors. The individual algorithms are quantile regression, generalized random forests for quantile regression, generalized random forests for quantile regression emulating quantile regression forests, gradient boosting machine, model-based boosting with linear models as base learners and quantile regression neural networks. The conditional quantiles of the hydrological model errors are transformed to conditional quantiles of daily streamflow, which are finally assessed using proper performance scores and benchmarking. The assessment concerns various levels of predictive quantiles and central prediction intervals, while it is made both independently of the flow magnitude and conditional upon this magnitude. Key aspects of the developed methodological framework are highlighted, and practical recommendations are formulated. In technical hydro-meteorological applications, the algorithms should be applied preferably in a way that maximizes the benefits and reduces the risks from their use. This can be achieved by (i) combining algorithms (e.g., by averaging their predictions) and (ii) integrating algorithms within systematic frameworks (i.e., by using the algorithms according to their identified skills), as our large-scale results point out.

Calibração conjunta de um modelo hidrológico com parâmetros de curva-chave para simulações de inundações bruscas em áreas urbanas

ABSTRACT Calibration process is usually time demanding and as much streamflow information as possible in rainfall-runoff models. Nevertheless, from a practical point of view, the available information is measurement of water level, which is essential to design rating curves. This manuscript proposes a set of joint calibration of hydrological model parameters with a range of rating curves, developed for the main channel of the catchment in a crowded urban area. As an alternative of free calibration, the simulations were carried out based on a list of proficient parameters. Four streamflow gauging stations were analysed and used to subdivide the basin. The hourly lumped rainfall-runoff model GR4H was applied to four critical flash flood events to create a rank of Nash-Sutcliffe efficiency criteria (NSE) applying the best set of parameters. The results indicated that the hydrological model errors were compensated by hydraulics errors and they presented an equifinality in the process.

Seasonal streamflow forecasts in the Ahlergaarde catchment, Denmark: the effect of preprocessing and post-processing on skill and statistical consistency

Abstract. In the present study we analyze the effect of bias adjustments in both meteorological and streamflow forecasts on the skill and statistical consistency of monthly streamflow and yearly minimum daily flow forecasts. Both raw and preprocessed meteorological seasonal forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) are used as inputs to a spatially distributed, coupled surface–subsurface hydrological model based on the MIKE SHE code. Streamflow predictions are then generated up to 7 months in advance. In addition to this, we post-process streamflow predictions using an empirical quantile mapping technique. Bias, skill and statistical consistency are the qualities evaluated throughout the forecast-generating strategies and we analyze where the different strategies fall short to improve them. ECMWF System 4-based streamflow forecasts tend to show a lower accuracy level than those generated with an ensemble of historical observations, a method commonly known as ensemble streamflow prediction (ESP). This is particularly true at longer lead times, for the dry season and for streamflow stations that exhibit low hydrological model errors. Biases in the mean are better removed by post-processing that in turn is reflected in the higher level of statistical consistency. However, in general, the reduction of these biases is not sufficient to ensure a higher level of accuracy than the ESP forecasts. This is true for both monthly mean and minimum yearly streamflow forecasts. We discuss the importance of including a better estimation of the initial state of the catchment, which may increase the capability of the system to forecast streamflow at longer leads.

ERM model analysis for adaptation to hydrological model errors

Hydrological conditions are changed continuously and these phenomenons generate errors on flood forecasting models and will lead to get unrealistic results. Therefore, to overcome these difficulties, a concept called model updating is proposed in hydrological studies. Real-time model updating is one of the challenging processes in hydrological sciences and has not been entirely solved due to lack of knowledge about the future state of the catchment under study. Basically, in terms of flood forecasting process, errors propagated from the rainfall-runoff model are enumerated as the main source of uncertainty in the forecasting model. Hence, to dominate the exciting errors, several methods have been proposed by researchers to update the rainfall-runoff models such as parameter updating, model state updating, and correction on input data. The current study focuses on investigations about the ability of rainfall-runoff model parameters to cope with three types of existing errors, timing, shape and volume as the common errors in hydrological modelling. The new lumped model, the ERM model, has been selected for this study to evaluate its parameters for its use in model updating to cope with the stated errors. Investigation about ten events proves that the ERM model parameters can be updated to cope with the errors without the need to recalibrate the model.

Improving probabilistic prediction of daily streamflow by identifyingPareto optimal approaches for modeling heteroscedastic residual errors

AbstractReliable and precise probabilistic prediction of daily catchment‐scale streamflow requires statistical characterization of residual errors of hydrological models. This study focuses on approaches for representing error heteroscedasticity with respect to simulated streamflow, i.e., the pattern of larger errors in higher streamflow predictions. We evaluate eight common residual error schemes, including standard and weighted least squares, the Box‐Cox transformation (with fixed and calibrated power parameterλ) and the log‐sinh transformation. Case studies include 17 perennial and 6 ephemeral catchments in Australia and the United States, and two lumped hydrological models. Performance is quantified using predictive reliability, precision, and volumetric bias metrics. We find the choice of heteroscedastic error modeling approach significantly impacts on predictive performance, though no single scheme simultaneously optimizes all performance metrics. The set of Pareto optimal schemes, reflecting performance trade‐offs, comprises Box‐Cox schemes withλof 0.2 and 0.5, and the log scheme (λ = 0, perennial catchments only). These schemes significantly outperform even the average‐performing remaining schemes (e.g., across ephemeral catchments, median precision tightens from 105% to 40% of observed streamflow, and median biases decrease from 25% to 4%). Theoretical interpretations of empirical results highlight the importance of capturing the skew/kurtosis of raw residuals and reproducing zero flows. Paradoxically, calibration ofλis often counterproductive: in perennial catchments, it tends to overfit low flows at the expense of abysmal precision in high flows. The log‐sinh transformation is dominated by the simpler Pareto optimal schemes listed above. Recommendations for researchers and practitioners seeking robust residual error schemes for practical work are provided.

Projections of future deterioration in UK river quality are hampered by climatic uncertainty under extreme conditions

ABSTRACTA modelling study was undertaken to quantify effects that the climate likely to prevail in the 2050s might have on water quality in two contrasting UK rivers. In so doing, it pinpointed the extent to which time series of climate model output, for some variables derived following bias correction, are fit for purpose when used as a basis for projecting future water quality. Working at daily time step, the method involved linking regional climate model (HadRM3-PPE) projections, Future Flows Hydrology (rainfall–runoff modelling) and the QUESTOR river network water quality model. In the River Thames, the number of days when temperature, dissolved oxygen, biochemical oxygen demand and phytoplankton exceeded undesirable values (>25°C, <6 mg L−1, >4 mg L−1 and >0.03 mg L−1, respectively) was estimated to increase by 4.1–26.7 days per year. The changes do not reflect impacts of any possible change in land use or land management. In the River Ure, smaller increases in occurrence of undesirable water quality are likely to occur in the future (by 1.0–11.5 days per year) and some scenarios suggested no change. Results from 11 scenarios of the hydroclimatic inputs revealed considerable uncertainty around the levels of change, which prompted analysis of the sensitivity of the QUESTOR model to simulations of current climate and hydrology. Hydrological model errors were deemed of less significance than those associated with the derivation and downscaling of driving climatic variables (rainfall, air temperature and solar radiation). Errors associated with incomplete understanding of river water quality interactions with the aquatic ecosystem were found likely to be more substantial than those associated with hydrology, but less than those related to climate model inputs. These errors are largely a manifestation of uncertainty concerning the extent to which phytoplankton biomass is controlled by invertebrate grazers, particularly in mid-summer; and the degree to which this varies from year to year. The quality of data from climate models for generating flows and defining driving variables at the extremes of their distributions has been highlighted as the major source of uncertainty in water quality model outputs.EDITOR A. Castellarin; ASSOCIATE EDITOR X. Fang

Estimating the Uncertainty of Hydrological Predictions through Data-Driven Resampling Techniques

AbstractEstimating the uncertainty of hydrological models remains a relevant challenge in applied hydrology, mostly because it is not easy to parameterize the complex structure of hydrological model errors. A nonparametric technique is proposed as an alternative to parametric error models to estimate the uncertainty of hydrological predictions. Within this approach, the above uncertainty is assumed to depend on input data uncertainty, parameter uncertainty and model error, where the latter aggregates all sources of uncertainty that are not considered explicitly. Errors of hydrological models are simulated by resampling from their past realizations using a nearest neighbor approach, therefore avoiding a formal description of their statistical properties. The approach is tested using synthetic data which refer to the case study located in Italy. The results are compared with those obtained using a formal statistical technique (meta-Gaussian approach) from the same case study. Our findings prove that the nea...

Comparison of joint versus postprocessor approaches for hydrological uncertainty estimation accounting for error autocorrelation and heteroscedasticity

AbstractThe paper appraises two approaches for the treatment of heteroscedasticity and autocorrelation in residual errors of hydrological models. Both approaches use weighted least squares (WLS), with heteroscedasticity modeled as a linear function of predicted flows and autocorrelation represented using an AR(1) process. In the first approach, heteroscedasticity and autocorrelation parameters are inferred jointly with hydrological model parameters. The second approach is a two‐stage “postprocessor” scheme, where Stage 1 infers the hydrological parameters ignoring autocorrelation and Stage 2 conditionally infers the heteroscedasticity and autocorrelation parameters. These approaches are compared to a WLS scheme that ignores autocorrelation. Empirical analysis is carried out using daily data from 12 US catchments from the MOPEX set using two conceptual rainfall‐runoff models, GR4J, and HBV. Under synthetic conditions, the postprocessor and joint approaches provide similar predictive performance, though the postprocessor approach tends to underestimate parameter uncertainty. However, the MOPEX results indicate that the joint approach can be nonrobust. In particular, when applied to GR4J, it often produces poor predictions due to strong multiway interactions between a hydrological water balance parameter and the error model parameters. The postprocessor approach is more robust precisely because it ignores these interactions. Practical benefits of accounting for error autocorrelation are demonstrated by analyzing streamflow predictions aggregated to a monthly scale (where ignoring daily‐scale error autocorrelation leads to significantly underestimated predictive uncertainty), and by analyzing one‐day‐ahead predictions (where accounting for the error autocorrelation produces clearly higher precision and better tracking of observed data). Including autocorrelation into the residual error model also significantly affects calibrated parameter values and uncertainty estimates. The paper concludes with a summary of outstanding challenges in residual error modeling, particularly in ephemeral catchments.

Impacts of climate change on the seasonality of low flows in 134 catchments in the River Rhine basin using an ensemble of bias-corrected regional climate simulations

Abstract. The impacts of climate change on the seasonality of low flows were analysed for 134 sub-catchments covering the River Rhine basin upstream of the Dutch-German border. Three seasonality indices for low flows were estimated, namely the seasonality ratio (SR), weighted mean occurrence day (WMOD) and weighted persistence (WP). These indices are related to the discharge regime, timing and variability in timing of low flow events respectively. The three indices were estimated from: (1) observed low flows; (2) simulated low flows by the semi-distributed HBV model using observed climate as input; (3) simulated low flows using simulated inputs from seven combinations of General Circulation Models (GCMs) and Regional Climate Models (RCMs) for the current climate (1964–2007); (4) simulated low flows using simulated inputs from seven combinations of GCMs and RCMs for the future climate (2063–2098) including three different greenhouse gas emission scenarios. These four cases were compared to assess the effects of the hydrological model, forcing by different climate models and different emission scenarios on the three indices. Significant differences were found between cases 1 and 2. For instance, the HBV model is prone to overestimate SR and to underestimate WP and simulates very late WMODs compared to the estimated WMODs using observed discharges. Comparing the results of cases 2 and 3, the smallest difference was found for the SR index, whereas large differences were found for the WMOD and WP indices for the current climate. Finally, comparing the results of cases 3 and 4, we found that SR decreases substantially by 2063–2098 in all seven sub-basins of the River Rhine. The lower values of SR for the future climate indicate a shift from winter low flows (SR &gt; 1) to summer low flows (SR &lt; 1) in the two Alpine sub-basins. The WMODs of low flows tend to be earlier than for the current climate in all sub-basins except for the Middle Rhine and Lower Rhine sub-basins. The WP values are slightly larger, showing that the predictability of low flow events increases as the variability in timing decreases for the future climate. From comparison of the error sources evaluated in this study, it is obvious that different RCMs/GCMs have a larger influence on the timing of low flows than different emission scenarios. Finally, this study complements recent analyses of an international project (Rhineblick) by analysing the seasonality aspects of low flows and extends the scope further to understand the effects of hydrological model errors and climate change on three important low flow seasonality properties: regime, timing and persistence.

Accounting for seasonal dependence in hydrological model errors and prediction uncertainty

[1] Streamflows often vary strongly with season, and this leads to seasonal dependence in hydrological model errors and prediction uncertainty. In this study, we introduce three error models to describe errors from a monthly rainfall-runoff model: a seasonally invariant model, a seasonally variant model, and a hierarchical error model. The seasonally variant model and the hierarchical error model use month-specific parameters to explicitly account for seasonal dependence, while the seasonally invariant model does not. A Bayesian prior is used in the hierarchical error model to account for potential variation and connection among model parameters of different months. The three error models are applied to predicting streamflows for five Australian catchments and are compared by various performance scores and diagnostic plots. The seasonally variant model and the hierarchical model both perform substantially better than the seasonally invariant model. From a cross-validation analysis, the hierarchical error model provides both the most accurate prediction mean and the most reliable prediction uncertainty distribution in most situations. The use of the prior to constrain the model parameters in the hierarchical model produces more robust parameter estimation than the other two models.

Pitfalls and improvements in the joint inference of heteroscedasticity and autocorrelation in hydrological model calibration

Residual errors of hydrological models are usually both heteroscedastic and autocorrelated. However, only a few studies have attempted to explicitly include these two statistical properties into the residual error model and jointly infer them with the hydrological model parameters. This technical note shows that applying autoregressive error models to raw heteroscedastic residuals, as done in some recent studies, can lead to unstable error models with poor predictive performance. This instability can be avoided by applying the autoregressive process to standardized residuals. The theoretical analysis is supported by empirical findings in three hydrologically distinct catchments. The case studies also highlight strong interactions between the parameters of autoregressive residual error models and the water balance parameters of the hydrological model.