Enhanced identification of a hydrologic model using streamflow and satellite water storage data: A multicriteria sensitivity analysis and optimization approach

Hydrologic model development and calibration have continued in most cases to focus only on accurately reproducing streamflows. However, complex models, for example, the so‐called physically based models, possess large degrees of freedom that, if not constrained properly, may lead to poor model performance when used for prediction. We argue that constraining a model to represent streamflow, which is an integrated resultant of many factors across the watershed, is necessary but by no means sufficient to develop a high‐fidelity model. To address this problem, we develop a framework to utilize the Gravity Recovery and Climate Experiment's (GRACE) total water storage anomaly data as a supplement to streamflows for model calibration, in a multiobjective setting. The VARS method (Variogram Analysis of Response Surfaces) for global sensitivity analysis is used to understand the model behaviour with respect to streamflow and GRACE data, and the BORG multiobjective optimization method is applied for model calibration. Two subbasins of the Saskatchewan River Basin in Western Canada are used as a case study. Results show that the developed framework is superior to the conventional approach of calibration only to streamflows, even when multiple streamflow‐based error functions are simultaneously minimized. It is shown that a range of (possibly false) system trajectories in state variable space can lead to similar (acceptable) model responses. This observation has significant implications for land‐surface and hydrologic model development and, if not addressed properly, may undermine the credibility of the model in prediction. The framework effectively constrains the model behaviour (by constraining posterior parameter space) and results in more credible representation of hydrology across the watershed.     

Regional calibration of a watershed model

Abstract

As watershed models become increasingly sophisticated and useful, there is a need to extend their applicability to locations where they cannot be calibrated or validated. A new methodology for the regionalization of a watershed model is introduced and evaluated. The approach involves calibration of a watershed model to many sites in a region, concurrently. Previous research that has sought to relate the parameters of monthly water balance models to physical drainage basin characteristics in a region has met with limited success. Previous studies have taken the two-step approach: (a) estimation of watershed model parameters at each site, followed by (b) attempts to relate model parameters to drainage basin characteristics. Instead of treating these two steps as independent, both steps are implemented concurrently. All watershed models in a region are calibrated simultaneously, with the dual objective of reproducing the behaviour of observed monthly streamflows and, additionally, to obtain good relationships between watershed model parameters and basin characteristics. The approach is evaluated using 33 basins in the southeastern region of the United States by comparing simulations using the regional models for three catchments which were not used to develop the regional regression equations. Although the regional calibration approach led to nearly perfect regional relationships between watershed model parameters and basin characteristics, these “improved” regional relationships did not result in improvements in the ability to model streamflow at ungauged sites. This experiment reveals that improvements in regional relationships between watershed model parameters and basin characteristics will not necessarily lead to improvements in the ability to calibrate a watershed model at an ungauged site.     

Uncertainty based modeling of rainfall-runoff: Combined differential evolution adaptive Metropolis (DREAM) and K-means clustering

Simulation of rainfall-runoff process in urban areas is of great importance considering the consequences and damages of extreme runoff events and floods. The first issue in flood hazard analysis is rainfall simulation. Large scale climate signals have been proved to be effective in rainfall simulation and prediction. In this study, an integrated scheme is developed for rainfall-runoff modeling considering different sources of uncertainty. This scheme includes three main steps of rainfall forecasting, rainfall-runoff simulation and future runoff prediction. In the first step, data driven models are developed and used to forecast rainfall using large scale climate signals as rainfall predictors. Due to high effect of different sources of uncertainty on the output of hydrologic models, in the second step uncertainty associated with input data, model parameters and model structure is incorporated in rainfall-runoff modeling and simulation. Three rainfall-runoff simulation models are developed for consideration of model conceptual (structural) uncertainty in real time runoff forecasting. To analyze the uncertainty of the model structure, streamflows generated by alternative rainfall-runoff models are combined, through developing a weighting method based on K-means clustering. Model parameters and input uncertainty are investigated using an adaptive Markov Chain Monte Carlo method. Finally, calibrated rainfall-runoff models are driven using the forecasted rainfall to predict future runoff for the watershed. The proposed scheme is employed in the case study of the Bronx River watershed, New York City. Results of uncertainty analysis of rainfall-runoff modeling reveal that simultaneous estimation of model parameters and input uncertainty significantly changes the probability distribution of the model parameters. It is also observed that by combining the outputs of the hydrological models using the proposed clustering scheme, the accuracy of runoff simulation in the watershed is remarkably improved up to 50% in comparison to the simulations by the individual models. Results indicate that the developed methodology not only provides reliable tools for rainfall and runoff modeling, but also adequate time for incorporating required mitigation measures in dealing with potentially extreme runoff events and flood hazard. Results of this study can be used in identification of the main factors affecting flood hazard analysis.     

How much complexity is needed to simulate watershed streamflow and water quality? A test combining time series and hydrological models

Modelled hydrologic processes are represented in a set of numerical equations; the complexity of which can be measured by the total number of variables needed. A single dominant hydrologic process could control the hydrologic response of a watershed, and so the identification of the corresponding dominant variable(s) would aid in identifying a parsimonious model and in collecting more reliable data. By accounting for both model complexity and serial correlation in the variables, a model is used to identify the dominant variables for representing watershed scale streamflow, sediment transport and phosphorus yields. Long‐term water quantity and quality data were used to show that rainfall and non‐linear soil water storage were the dominant variables for weekly streamflow, suspended sediment and particulate phosphorus. Model accuracy did not consistently improve when other statistically significant variables were included. The results suggest that improved model performance may not justify the added model complexity. As such, identification of dominant variables would be the priority for developing parsimonious hydrologic models, especially at watershed scales. Copyright © 2013 John Wiley & Sons, Ltd.     

Improving a regional model using reduced complexity and parameter estimation

The availability of powerful desktop computers and graphical user interfaces for ground water flow models makes possible the construction of ever more complex models. A proposed copper-zinc sulfide mine in northern Wisconsin offers a unique case in which the same hydrologic system has been modeled using a variety of techniques covering a wide range of sophistication and complexity. Early in the permitting process, simple numerical models were used to evaluate the necessary amount of water to be pumped from the mine, reductions in streamflow, and the drawdowns in the regional aquifer. More complex models have subsequently been used in an attempt to refine the predictions. Even after so much modeling effort, questions regarding the accuracy and reliability of the predictions remain. We have performed a new analysis of the proposed mine using the two-dimensional analytic element code GFLOW coupled with the nonlinear parameter estimation code UCODE. The new model is parsimonious, containing fewer than 10 parameters, and covers a region several times larger in areal extent than any of the previous models. The model demonstrates the suitability of analytic element codes for use with parameter estimation codes. The simplified model results are similar to the more complex models; predicted mine inflows and UCODE-derived 95% confidence intervals are consistent with the previous predictions. More important, the large areal extent of the model allowed us to examine hydrological features not included in the previous models, resulting in new insights about the effects that far-field boundary conditions can have on near-field model calibration and parameterization. In this case, the addition of surface water runoff into a lake in the headwaters of a stream while holding recharge constant moved a regional ground watershed divide and resulted in some of the added water being captured by the adjoining basin. Finally, a simple analytical solution was used to clarify the GFLOW model's prediction that, for a model that is properly calibrated for heads, regional drawdowns are relatively unaffected by the choice of aquifer properties, but that mine inflows are strongly affected. Paradoxically, by reducing model complexity, we have increased the understanding gained from the modeling effort.     

Bootstrap based artificial neural network (BANN) analysis for hierarchical prediction of monthly runoff in Upper Damodar Valley Catchment

Estimation of runoff is a prerequisite for many applications involving conservation and management of water resources. This study is undertaken in the Upper Damodar Valley Catchment (UDVC) having a drainage area of 17513.08 km² for prediction of monthly runoff. Thirty one microwatersheds and 15 sub-watersheds were selected from a total of 716 microwatersheds in the catchment area for this study. The feasibility of using different soil attributes (particle size distribution, organic matter content and apparent density), topographic attributes (primary, secondary and compound), geomorphologic attributes (basin, relief and network indices) and vegetation attribute as Normalized Difference Vegetation Index (NDVI), on prediction of monthly runoff were explored in this study. Principal Component Analysis (PCA) was applied to minimize the data redundancy of the input variables. Ten significant input variables namely; watershed length (km), elongation ratio, bifurcation ratio, area ratio, coarse sand (%), fine sand (%), elevation (m), slope (°), profile curvature (rad/m) and NDVI were selected. The selected input variables were added in hierarchy with monthly rainfall (mm) as inputs for prediction of monthly runoff (mm) using Bootstrap based artificial neural networks (BANN). The performance of the models was tested using Spearman’s correlation coefficient (r), coefficient of efficiency (COE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). Best performance was observed for model with monthly rainfall, slope, coarse sand, bifurcation ratio and Normalized Difference Vegetation Index (NDVI) as inputs (r = 0.925 and COE = 0.839). Increase in number of input variables did not necessarily yield better performances of the BANN models. Selection of relevant inputs and their combinations were found to be key elements in determining the performance of BANN models. Annual runoff map was generated for all the microwatersheds utilizing the weights of the best performing BANN model. This study reveals that the specific combinations of soil, topography, geomorphology and vegetation inputs can be utilized for better prediction of monthly runoff.     

A nonlinear time series analysis using two‐stage genetic algorithms for streamflow forecasting

Streamflow forecasting is very important for the management of water resources: high accuracy in flow prediction can lead to more effective use of water resources. Hydrological data can be classified as non‐steady and nonlinear, thus this study applied nonlinear time series models to model the changing characteristics of streamflows. Two‐stage genetic algorithms were used to construct nonlinear time series models of 10‐day streamflows of the Wu‐Shi River in Taiwan. Analysis verified that nonlinear time series are superior to traditional linear time series. It is hoped that these results will be useful for further applications. Copyright © 2008 John Wiley & Sons, Ltd.     

Semi-empirical prediction method for monthly precipitation prediction based on environmental factors and comparison with stochastic and machine learning models

ABSTRACT

Precipitation prediction is central in hydrology and water resources planning and management. This paper introduces a semi-empirical predictive model to predict monthly precipitation and compares its predictive skill with those of machine learning (ML) methods. The stochastic method presented herein estimates monthly precipitation with one-step-ahead prediction properties. The ML predictive skill of the algorithms is evaluated by predicting monthly precipitation relying on the statistical association between precipitation and environmental and topographic factors. The semi-empirical predictive model features non-negative matrix factorization (NMF) for investigating the influence of multiple predictor variables on precipitation. The semi-empirical predictive model’s parameters are optimized with the hybrid genetic algorithm (GA) and Levenberg-Marquardt algorithm (LM), or GALMA, yielding a validated model with high predictive skill. The methodologies are illustrated with data from Hubei Province, China, which comprise 27 meteorological station datasets from 1988–2017. The empirical results provide valuable insights for developing semi-empirical rainfall prediction models.     

Integrated numerical modeling for basin-wide water management: The case of the Rattlesnake Creek basin in south-central Kansas

The objective of this article is to develop and implement a comprehensive computer model that is capable of simulating the surface-water, ground-water, and stream-aquifer interactions on a continuous basis for the Rattlesnake Creek basin in south-central Kansas. The model is to be used as a tool for evaluating long-term water-management strategies. The agriculturally-based watershed model SWAT and the ground-water model MODFLOW with stream-aquifer interaction routines, suitably modified, were linked into a comprehensive basin model known as SWATMOD. The hydrologic response unit concept was implemented to overcome the quasi-lumped nature of SWAT and represent the heterogeneity within each subbasin of the basin model. A graphical user-interface and a decision support system were also developed to evaluate scenarios involving manipulation of water rights and agricultural land uses on stream-aquifer system response. An extensive sensitivity analysis on model parameters was conducted, and model limitations and parameter uncertainties were emphasized. A combination of trial-and-error and inverse modeling techniques were employed to calibrate the model against multiple calibration targets of measured ground-water levels, streamflows, and reported irrigation amounts. The split-sample technique was employed for corroborating the calibrated model. The model was run for a 40 y historical simulation period, and a 40 y prediction period. A number of hypothetical management scenarios involving reductions and variations in withdrawal rates and patterns were simulated. The SWATMOD model was developed as a hydrologically rational low-flow model for analyzing, in a user-friendly manner, the conditions in the basin when there is a shortage of water.     

Implementation of an automatic calibration procedure for HYDROTEL based on prior OAT sensitivity and complementary identifiability analysis

Efficiency of hydrological models mostly depends on the quality of the calibration performed prior to use. In this paper, an automatic calibration framework for the distributed hydrological model HYDROTEL is proposed. The calibration procedure was performed for three watersheds characterized with different hydroclimatological conditions: the Sassandra located in Ivory Coast, Africa, and the Montmorency and Beaurivage watersheds located in Quebec (Canada). Results of one‐a‐time (OAT) sensitivity analysis showed that the order of the most sensitive parameters differs for each watershed. Thus, the sensitivity depends on the hydroclimatic and physiographic characteristics of the watersheds. Co‐linearity indices showed that all model parameters were identifiable, that is, none of the studied parameters could be explained by a combination of the other parameters. Following these findings, an automatic calibration was run. Results indicated there was good agreement between simulated and measured streamflows at the outlet of each watershed; Nash–Sutcliffe efficiency (NSE) ranging between 0.77 and 0.92 and R² ranging from 0.87 to 0.97. When comparing NSE and R² values obtained using a process‐oriented, multiple‐objective, manual calibration strategy, a slight increase in model efficiency was reached with the automatic calibration procedure (4.15% for NSE and 2.95% for R²) improving predictions of peak flows for the Montmorency and Beaurivage watersheds (temperate climate conditions) and flows beyond the rainfall season in the Sassandra watershed. The proposed automatic calibration procedure introduced in this paper may be applied to other distributed hydrological model. Copyright © 2013 John Wiley & Sons, Ltd.     

Input-output model for runoff-sediment yield processes

Runoff (log-transformed) and sediment yield (log-transformed) sequences on a monthly or daily basis can be regarded as input and output for the watershed fluvial system. These sequences are nonstationary in general in different hydrological environments. Frequency and time domain analyses have shown that a parsimonious model can be built directly in terms of these nonstationary input-output sequences on a monthly and daily basis. A first-order dynamic model was found adequate to model the monthly runoff-sediment yield process; a second-order model adequately modeled the daily runoff-sediment yield process. The noise component in both cases possessed the characteristics of a white-noise sequence.     

Prediction of algal blooms using genetic programming

In this study, an attempt was made to mathematically model and predict algal blooms in Tolo Harbor (Hong Kong) using genetic programming (GP). Chlorophyll plays a vital role in blooms and was used in this model as a measure of algal bloom biomass, and eight other variables were used as input for its prediction. It has been observed that GP evolves multiple models with almost the same values of errors-of-measure. Previous studies on GP modeling have primarily focused on comparing GP results with actual values. In contrast, in this study, the main aim was to propose a systematic procedure for identifying the most appropriate GP model from a list of feasible models (with similar error-of-measure) using a physical understanding of the process aided by data interpretation. Evaluation of the GP-evolved equations shows that they correctly identify the ecologically significant variables. Analysis of the final GP-evolved mathematical model indicates that, of the eight variables assumed to affect algal blooms, the most significant effects are due to chlorophyll, total inorganic nitrogen and dissolved oxygen for a 1-week prediction. For longer lead predictions (biweekly), secchi-disc depth and temperature appear to be significant variables, in addition to chlorophyll.     

Application of newly developed ensemble machine learning models for daily suspended sediment load prediction and related uncertainty analysis

ABSTRACT

Ensemble machine learning models have been widely used in hydro-systems modeling as robust prediction tools that combine multiple decision trees. In this study, three newly developed ensemble machine learning models, namely gradient boost regression (GBR), AdaBoost regression (ABR) and random forest regression (RFR) are proposed for prediction of suspended sediment load (SSL), and their prediction performance and related uncertainty are assessed. The SSL of the Mississippi River, which is one of the major world rivers and is significantly affected by sedimentation, is predicted based on daily values of river discharge (Q) and suspended sediment concentration (SSC). Based on performance metrics and visualization, the RFR model shows a slight lead in prediction performance. The uncertainty analysis also indicates that the input variable combination has more impact on the obtained predictions than the model structure selection.     

Global sensitivity analysis of hydrologic processes in major snow‐dominated mountainous river basins in Colorado

The performance of watershed models in simulating stream discharge depends on the adequate representation of important watershed processes. In snow‐dominated systems, snow, surface and subsurface hydrologic processes comprise a complex network of nonlinear interactions that influence the magnitude and timing of discharge. This study aims to identify critical processes and interactions that control discharge hydrographs in five major mountainous snow‐dominated river basins in Colorado, USA. A comprehensive watershed model (Soil and Water Assessment Tool) and a variance‐based global sensitivity analysis technique (Fourier Amplitude Sensitivity Test) were used in conjunction to identify critical models parameters and processes that they represent. Average monthly streamflow and streamflow root mean square error over a period of 20 years were used as two separate objective functions in this analysis. Examination of the sensitivity of monthly streamflow revealed the influence of parameters on flow volume, whereas the sensitivity of streamflow root mean square error also exposed the influence of parameters on the timing of the hydrographs. A stability analysis was performed to investigate the computational requirements for a robust sensitivity analysis. Results show that streamflow volume is mostly influenced by shallow subsurface processes, whereas interactions between groundwater and snow processes were the key in the timing of streamflows. A large majority of important parameters were common among all study watersheds, which underlies the prospect for regionalization of process‐based hydrologic modelling in headwater river basins in Colorado. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of kernel density estimation methods for daily precipitation resampling

Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses (e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry spell resampling methodology presented in Lall et al. (1996).     

Evaluation of kernel density estimation methods for daily precipitation resampling

Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses (e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry spell resampling methodology presented in Lall et al. (1996).     

Maximum entropy-Gumbel-Hougaard copula method for simulation of monthly streamflow in Xiangxi river,China

A maximum entropy-Gumbel-Hougaard copula (MEGHC) method has been proposed for monthly streamflow simulation. The marginal distributions of monthly streamflows are estimated through the maximum entropy (ME) method with the first four non-central moments (i.e. mean, standard deviation, skewness and kurtosis) being the constraints. The Lagrange multipliers in ME-based marginal distributions are determined using the conjugate gradient (CG) method which is of superlinear convergence, simple recurrence formula and less calculation. Then the joint distributions of two adjacent monthly streamflows are constructed using the Gumbel-Hougaard copula (GHC) method. The developed MEGHC method has been applied for monthly streamflow simulation in Xiangxi river, China. The goodness-of-fit statistical tests, consisting of K–S test, A–D test, RMSE and Rosenblatt transformation with Cramér von Mises statistic, show that the MEGHC method can reflect dependence structure in adjacent monthly streamflows of Xiangxi river, China. Comparison between simulated streamflow generated by MEGHC and observations indicates the satisfactory performance of MEGHC with small relative errors.     

On the prediction of persistent processes using the output of deterministic models

A problem frequently met in engineering hydrology is the forecasting of hydrological variables conditional on their historical observations and the hindcasts and forecasts of a deterministic model. On the contrary, it is a common practice for climatologists to use the output of general circulation models (GCMs) for the prediction of climatic variables despite their inability to quantify the uncertainty of the predictions. Here we apply the well-established Bayesian processor of forecasts (BPF) for forecasting hydroclimatic variables using stochastic models through coupling them with GCMs. We extend the BPF to cases where long-term persistence appears, using the Hurst-Kolmogorov process (HKp, also known as fractional Gaussian noise) and we investigate its properties analytically. We apply the framework to calculate the distributions of the mean annual temperature and precipitation stochastic processes for the time period 2016–2100 in the United States of America conditional on historical observations and the respective output of GCMs.     

Seasonal flooding in Bangladesh – variability and predictability

At present, Bangladesh has a flood forecasting lead time of only 3 days or so. There is demand for a forecasting lead time of a month to a season. The primary objectives of this paper are to study the variability and predictability of seasonal flooding in Bangladesh, as revealed by large‐scale predictors of the climate across the watersheds. To explore the source of predictability, accessible Bangladesh hydrological indicators are related to large‐scale oceanic variability and to large‐scale atmospheric circulation patterns predicted by general circulation models (GCMs). Correlation analyses between the flood‐affected area (FAA) for July–September and tropical sea‐surface temperature (SST) indicate connections to tropical Pacific and Indian Ocean SSTs, at a short lead time of a month or so. These are related to El Niño–southern oscillation (ENSO). Correlations between the SSTs of the preceding October–December and the July–September FAA are weaker but notable. Forecasts of the FAA using the leading principal components (PCs) of SST were made, which provided good skill with a lead time of a month or so. The streamflows and rainfall observed in Bangladesh have been added to these prediction models. Finally, the SST PCs were replaced with PCs of GCM prediction fields (precipitation). The prediction models at short lead time that were constructed for FAA were of generally similar levels of skill to that for SST. This is encouraging, as it suggests that linkages with SST can be successfully recovered in a physical model of the climate system in Bangladesh. This study concludes that seasonal flood prediction in Bangladesh is possible from the unusually warm or cold SST in parts of the tropics. This predictability can be enhanced with the information achievable from monitoring the downstream streamflows (which are generated mainly from upstream rainfall conditions) in advance of the flooding season. Finally, this study recommends formalizing a regional cooperation among the countries in the principal co‐basin areas of the Ganges–Brahmaputra–Meghna to achieve this goal. Copyright © 2006 John Wiley & Sons, Ltd.     

Regionalization of constraints on expected watershed response behavior for improved predictions in ungauged basins

Approaches to modeling the continuous hydrologic response of ungauged basins use observable physical characteristics of watersheds to either directly infer values for the parameters of hydrologic models, or to establish regression relationships between watershed structure and model parameters. Both these approaches still have widely discussed limitations, including impacts of model structural uncertainty. In this paper we introduce an alternative, model independent, approach to streamflow prediction in ungauged basins based on empirical evidence of relationships between watershed structure, climate and watershed response behavior. Instead of directly estimating values for model parameters, different hydrologic response behaviors of the watershed, quantified through model independent streamflow indices, are estimated and subsequently regionalized in an uncertainty framework. This results in expected ranges of streamflow indices in ungauged watersheds. A pilot study using 30 UK watersheds shows how this regionalized information can be used to constrain ensemble predictions of any model at ungauged sites. Dominant controlling characteristics were found to be climate (wetness index), watershed topography (slope), and hydrogeology. Main streamflow indices were high pulse count, runoff ratio, and the slope of the flow duration curve. This new approach provided sharp and reliable predictions of continuous streamflow at the ungauged sites tested.