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.     

Sensitivity and uncertainty analysis of a sediment transport model: a global approach

Computerized sediment transport models are frequently employed to quantitatively simulate the movement of sediment materials in rivers. In spite of the deterministic nature of the models, the outputs are subject to uncertainty due to the inherent variability of many input parameters in time and in space, along with the lack of complete understanding of the involved processes. The commonly used first-order method for sensitivity and uncertainty analyses is to approximate a model by linear expansion at a selected point. Conclusions from the first-order method could be of limited use if the model responses drastically vary at different points in parameter space. To obtain the global sensitivity and uncertainty features of a sediment transport model over a larger input parameter space, the Latin hypercubic sampling technique along with regression procedures were employed. For the purpose of illustrating the methodologies, the computer model HEC2-SR was selected in this study. Through an example application, the results about the parameters sensitivity and uncertainty of water surface, bed elevation and sediment discharge were discussed.     

Predictability performance enhancement for suspended sediment in rivers:Inspection of newly developed hybrid adaptive neuro-fuzzy system model

Reliable modeling of river sediments transport is important as it is a defining factor of the economic viability of dams, the durability of hydroelectric-equipment, river susceptibility to pollution, suitability for navigation, and potential for aesthetics and fish habitat. The capability of a new machine learning model, fuzzy c-means based neuro-fuzzy system calibrated using the hybrid particle swarm optimization-gravitational search algorithm（ANFIS-FCM-PSOGSA） in improving the estimation accur...     

The influence of parameter distribution uncertainty on hydrological and sediment modeling: a case study of SWAT model applied to the Daning watershed of the Three Gorges Reservoir Region, China

Parameter uncertainty involved in hydrological and sediment modeling often refers to the parameter dispersion and the sensitivity of the parameter. However, a limitation of the previous studies lies in that the assignment of range and specification of probability distribution for each parameter is usually difficult and subjective. Therefore, there is great uncertainty in the process of parameter calibration and model prediction. In this study, the impact of probability parameter distribution on hydrological and sediment modeling was evaluated using a semi-distributed model—the Soil and Water Assessment Tool (SWAT) and Monte Carlo method (MC)—in the Daning River watershed of the Three Gorges Reservoir Region (TGRA), China. The classic types of parameter distribution such as uniform, normal and logarithmic normal distribution were involved in this study. Based on results, parameter probability distribution showed a diverse degree of influence on the hydrological and sediment prediction, such as the sampling size, the width of 95% confidence interval (CI), the ranking of the parameter related to uncertainty, as well as the sensitivity of the parameter on model output. It can be further inferred that model parameters presented greater uncertainty in certain regions of the primitive parameter range and parameter samples densely obtained from these regions would lead to a wider 95 CI, resulting in a more doubtful prediction. This study suggested the value of the optimized value obtained by the parameter calibration process could may also be of vital importance in selecting the probability distribution function (PDF). Such cases, where parameter value corresponds to the watershed characteristic, can be used to provide a more credible distribution for both hydrological and sediment modeling.     

UNCERTAINTY AND SENSITIVITY ANALYSES OF SEDIMENT TRANSPORT FORMULAS

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Predictive uncertainty of a nearshore bed evolution model

Predictions of nearshore depth evolution using process-based numerical simulation models contain inherent uncertainties owing to model structural deficiencies, measurement errors, and parameter uncertainty. This paper quantifies the parameter-induced predictive uncertainty of the cross-shore depth evolution model Unibest-TC by applying the Bayesian Generalised Likelihood Uncertainty Estimation methodology to modelling depth evolution at Egmond aan Zee (Netherlands). This methodology works with multiple sets of parameter values sampled uniformly in feasible parameter space and assigns a likelihood value to each parameter set. Acceptable simulations (i.e., based on parameter sets with a nonzero likelihood) were found for a wide range of parameter values owing to parameter interdependence and insensitivity. The 95% uncertainty prediction interval of bed levels after the 33 days prediction period was largest (0.5–1 m) near the sandbar crests that characterize the Egmond depth profile, reducing to near-zero values in the sandbar troughs and the offshore area. The prediction interval built up during storms (when sediment transport rates are largest) and remained the same or even reduced slightly during less-energetic conditions. The prediction uncertainty ranges bracket the observations near the inner-bar crest, its seaward flank, and at the seaward flank of the outer bar, suggesting that elsewhere model structural errors (and, potentially, measurement errors) dominate over parameter errors. The interdependence and the non-Gaussian marginal posterior distribution functions of the free model parameters cast doubt on the ability of commonly applied multivariate normal distribution functions to estimate parameter uncertainty.     

Suspended sediment yield modeling in Mahanadi River,India by multi-objective optimization hybridizing artificial intelligence algorithms

River sediment produced through weathering is one of the principal landscape modification processes on earth.Rivers are an integral part of the hydrologic cycle and are the major geologic agents that erode the continents and transport water and sediments to the oceans.Estimation of suspended sediment yield is always a key parameter for planning and management of any river system.It is always challenging to model sediment yield using traditional mathematical models because they are incapable of handling the complex non-linearity and non-stationarity.The suspended sediment modeling of the river depends on the number of factors such as rock type,relief,rainfall,temperature,water discharge and catchment area.In this study,we proposed a hybrid genetic algorithm-based multi-objective optimization with artificial neural network(GA-MOO-ANN)with automated parameter tuning model using these factors to estimate the suspended sediment yield in the entire Mahanadi River basin.The model was validated by comparing statistically with other models,and it appeared that the GA-MOO-ANN model has the lowest root mean squared error(0.009)and highest coefficient of correlation(0.885)values among all comparative models(traditional neural network,multiple linear regression,and sediment rating curve)for all stations.It was also observed that the proposed model is the least biased(0.001)model.Thus,the proposed GA-MOOANN is the most capable model,compared to other studied models,for estimating the suspended sediment yield in the entire Mahanadi river basin,India.The results also suggested that the proposed GA-MOO-ANN model is unable to estimate suspended sediment yield satisfactorily at gauge stations having very small catchment areas whereas performing satisfactorily on locations having moderate to the large catchment area.The models provide the best result at Tikarapara,the gauge station location in the extreme downstream,having the largest catchment area.     

Inverse modeling of a radial multistep outflow experiment for determining unsaturated hydraulic properties

Modeling flow and solute transport in the unsaturated zone on the basis of the Richards equation requires specifying values for unsaturated hydraulic conductivity and water potential as a function of saturation. The objectives of the paper are to evaluate the design of a transient, radial, multi-step outflow experiment, and to determine unsaturated hydraulic parameters using inverse modeling. We conducted numerical simulations, sensitivity analyses, and synthetic data inversions to assess the suitability of the proposed experiment for concurrently estimating the parameters of interest. We calibrated different conceptual models against transient flow and pressure data from a multi-step, radial desaturation experiment to obtain estimates of absolute permeability, as well as the parameters of the relative permeability and capillary pressure functions. We discuss the differences in the estimated parameter values and illustrate the impact of the underlying model on the estimates. We demonstrate that a small error in absolute permeability, if determined in an independent experiment, leads to biased estimates of unsaturated hydraulic properties. Therefore, we perform a joint inversion of pressure and flow rate data for the simultaneous determination of permeability and retention parameters, and analyze the correlations between these parameters. We conclude that the proposed combination of a radial desaturation experiment and inverse modeling is suitable for simultaneously determining the unsaturated hydraulic properties of a single soil sample, and that the inverse modeling technique provides the opportunity to analyze data from nonstandard experimental designs.     

Estimation of the Amount of Suspended Sediment in the Tigris River using Artificial Neural Networks

The amount of sediment should be taken into consideration in the planning of water structures for efficient use of limited water resources. It is important to estimate the amount of sediment for the successful operation of these structures in their future performances. Such estimations can be achieved by Artificial Neural Network (ANNs) with low error percentages as seen in many other disciplines. These networks also enable the modeling of nonlinear relationships between the parameters affecting the event. The purpose of this research is to establish models for sediment amounts in the Tigris River at the Diyarbakir measurement station in Turkey. Rainfall, temperature and discharge are taken as independent variables in the models, whereas sediment is taken as the dependent variable. Fourteen different models are generated using ANNs and Regression Analysis (RA). The results are compared with each other and with the observed data. The relative error and determination coefficient are used as comparison criteria. It is concluded that due to their nonlinear modeling capability, ANNs give better results than RA.     

Climate change impacts on bedload transport in alpine drainage basins with hydropower exploitation

Sediment transport is known to have a significant impact on hydropower infrastructures and changes in sediment transport rates are important for sediment management measures and hydroelectricity production. In this study, we present how climate change may affect bedload transport in 66 high alpine catchments used by hydropower companies in the Valais, Switzerland. Future sediment yield is estimated with a runoff‐based sediment transport model for the two future 30 year time periods 2021–2050 and 2070–2099. The analysis is integrated into a modelling chain in which error‐corrected and downscaled climate scenarios generated in the framework of the ENSEMBLES project are coupled to the hydrological model PREVAH, glacier retreat and bedload transport. To calibrate the sediment transport model, we used the observed sediment volumes in water intakes and reservoirs if such data were available. The results obtained show on average a decrease of sediment yield due to the reduced runoff generation during summer, especially for the scenario period 2070–2099. A shift of the seasonal sediment transport regime with a current maximum during July and August to earlier months in the year is predicted. Projections of future sediment yield rely on the accuracy of the individual modeling chain elements. The different sources of uncertainty are discussed qualitatively. Copyright © 2015 John Wiley & Sons, Ltd.     

Addressing snow model uncertainty for hydrologic prediction

Streamflow forecasting methods are moving towards probabilistic approaches that quantify the uncertainty associated with the various sources of error in the forecasting process. Multi-model averaging methods which try to address modeling deficiencies by considering multiple models are gaining much popularity. We have applied the Bayesian Model Averaging method to an ensemble of twelve snow models that vary in their heat and melt algorithms, parameterization, and/or albedo estimation method. Three of the models use the temperature-based heat and melt routines of the SNOW17 snow accumulation and ablation model. Nine models use heat and melt routines that are based on a simplified energy balance approach, and are varied by using three different albedo estimation schemes. Finally, different parameter sets were identified through automatic calibration with three objective functions. All models use the snow accumulation, liquid water transport, and ground surface heat exchange processes of the SNOW17. The resulting twelve snow models were combined using Bayesian Model Averaging (BMA). The individual models, BMA predictive mean, and BMA predictive variance were evaluated for six SNOTEL sites in the western U.S. The models performed best and the BMA variance was lowest at the colder sites with high winter precipitation and little mid-winter melting. An individual snow model would often outperform the BMA predictive mean. However, observed snow water equivalent (SWE) was captured within the 95% confidence intervals of the BMA variance on average 80% of the time at all sites. Results are promising that consideration of multiple snow structures would provide useful uncertainty information for probabilistic hydrologic prediction.     

Modeling uncertainties of reservoir flushing simulations

Every dam or barrage construction affects the watercourse and the retention of sediment that previously was carried by the river, which can lead to siltation of the reservoir and obstruction of water intakes over time, reducing their capacities. However, the information available regarding the effect of sediment and drawdown parameters, sediment management at reservoirs, as well as different equational approaches, is scarce. The current research aims to evaluate the effect of parameters associated with numerical modeling of sediment management in reservoirs considering scenarios with different drawdowns, transport equations, sediment size distributions, and thickness of the initial sediment layer. The case study of the Aimorés Hydropower Plant (HPP) is used, applying the Delft3D-FLOW model for two-dimensional modeling. All parameters influenced the volume of mobilized sediment, among which the initial layer thickness was the parameter that resulted in the greatest changes in simulated results. In general, the results show that the uncertainties in the input parameters outweigh the uncertainties between the techniques, which found large variations in results when evaluating the use of different transport equations. These results indicate the importance of proper estimation of model parameters for predicting effects with accuracy and the need for such studies before planning and management operations are evaluated to avoid environmental harm and energy waste.     

Estimation of bedload discharge in sewer pipes with different boundary conditions using an evolutionary algorithm

Sediment transport is a complex phenomenon due to the nonlinearity and uncertainties of the process.The present study applies Gene Expression Programming(GEP) to develop bedload transport models in sewer pipes. In this regard, two types of bedload were considered: loose bed(deposition state) and rigid bed(limit of deposition state). In order to develop the models, two scenarios with different input combinations were considered: Scenario 1 considers only hydraulic characteristics and Scenario 2 considers both hydraulic and sediment characteristics as inputs for modeling bedload discharge. The results proved the capability of GEP in prediction of sediment transport and it was found that for prediction of bedload transport in sewer pipes Scenario 2 performed more successfully than Scenario 1. According to the outcome of sensitivity analysis, F_(rm)(Modified Froude number) and d_(50/y)(relative particle size) for rigid boundary and F_(rm) for loose boundary had key roles in the modeling. The outcome of the GEP models also was compared with existing empirical equations and it was found the GEP models yielded better results. It was also found that pipe diameter affected the transport capacity of the sewer pipe. Increasing pipe diameter caused an increase in model efficiency. A pipe with a diameter of 305 mm yielded to the best results.     

Multisource hydrologic modeling uncertainty analysis using the IBUNE framework in a humid catchment

Hydrologic cycle is a complex system associated with both certain and uncertain constituents. The propagation of confidence bounds from different uncertainty sources to model output is of great significance for hydrologic modeling. In this paper, we applied the integrated bayesian uncertainty estimator to quantify the effects of parameter, input and model structure uncertainty on hydrologic modeling progressively. Two hydrologic models (Xinanjiang model and TOPMODEL) were applied to a humid catchment under three scenarios. Case I: the shuffled complex evolution metropolis (SCEM-UA) algorithm was conducted to determine the posterior parameter distribution of hydrologic models and analyze the corresponding forecast uncertainty. Case II: input uncertainty was also considered by assuming rain depth bias follows a normal distribution, and integrated with SCEM-UA. Case III: Simulations from two models were combined by the Bayesian model averaging to fully quantify multisource uncertainty effects. Results suggested that, from Case I to II, the containing ratio (percentage of observed streamflow enveloped by 95% confidence interval) obviously increased by an average magnitude of 10% for the study period 2000–2006. Besides, it also found that the width of 95% confidence interval became wider and narrower for Xinanjiang model and TOPMODEL, respectively, from Case I to II. This may indicate that the uncertainty of TOPMODEL results was more remarkable than Xinanjiang model in Case I. By combining results from two models, model structure uncertainty was also considered in Case III. The accuracy of uncertainty bounds further improved with the containing ratio of 95% confidence interval >95%. In addition, the optimized deterministic results from the uncertainty analysis showed that the average Nash–Sutcliffe coefficient increased continually from Case I to II and III (0.82, 0.84 and 0.90, respectively) for the study period. The analysis demonstrated the improvement of modeling accuracy when extra uncertainty sources were also quantified, and this finding also proved the applicability of IBUNE framework in hydrologic modeling.     

Rainstorm-generated sediment yield model based on soil moisture proxies (SMP)

This study develops improved Soil Moisture Proxies (SMP) based suspended sediment yield (SMPSY) models corresponding to three antecedent moisture conditions (AMCs) (i.e., AMC-I-AMC-III) by coupling the improved initial abstraction (I_a-λ) model, the SMA procedure and the SMP concept for modelling the rainfall generated suspended sediment yield. The SMPSY models specifically incorporate a watershed storage index (S) model to accentuate the transformation from storm to storm and to avoid the sudden jumps in sediment yield computation. The workability of the SMPSY models is tested using a large dataset of rainfall and sediment yield (98 storm events) from twelve small watersheds and a comparison has been made with the existing MSY model. The goodness-of-fit (GOF) statistics is evaluated in terms of the Nash Sutcliffe efficiency (NSE), and error indices, i.e., root mean square error (RMSE), normalized root mean square error (nRMSE), standard error (SE), mean absolute error (MAE), and RMSE-observations standard deviation ratio (RSR). The NSE values vary from 74.31% to 96.57% and from 75.21% to 91.78%, respectively for the SPMSY and MSY model. The NSE statistics indicate that the SMPSY model has lower uncertainty in simulating sediment yield as compared to the MSY model. The error indices are lower for the SMPSY model than the MSY model for most of the watersheds. These results show that the SMPSY model has less uncertainty and performs better than the MSY model. A sensitivity analysis of the SMPSY model shows that the parameter β is most sensitive followed by parameter S, α and A. Overall, the results show that the characterization of soil moisture variability in terms of SMPs and incorporation of improved delivery ratio and runoff coefficient relationship improves the simulation of the erosion and sediment yield generation process.     

Assessing effects of model complexity and structure on predictions of hydrological responses using serial and parallel model design

By utilizing functional relationships based on observations at plot or field scales, water quality models first compute surface runoff and then use it as the primary governing variable to estimate sediment and nutrient transport. When these models are applied at watershed scales, this serial model structure, coupling a surface runoff sub-model with a water quality sub-model, may be inappropriate because dominant hydrological processes differ among scales. A parallel modeling approach is proposed to evaluate how best to combine dominant hydrological processes for predicting water quality at watershed scales. In the parallel scheme, dominant variables of water quality models are identified based entirely on their statistical significance using time series analysis. Four surface runoff models of different model complexity were assessed using both the serial and parallel approaches to quantify the uncertainty on forcing variables used to predict water quality. The eight alternative model structures were tested against a 25-year high-resolution data set of streamflow, suspended sediment discharge, and phosphorous discharge at weekly time steps. Models using the parallel approach consistently performed better than serial-based models, by having less error in predictions of watershed scale streamflow, sediment and phosphorus, which suggests model structures of water quantity and quality models at watershed scales should be reformulated by incorporating the dominant variables. The implication is that hydrological models should be constructed in a way that avoids stacking one sub-model with one set of scale assumptions onto the front end of another sub-model with a different set of scale assumptions.     

Assessment of sediment transport approaches for sand-bed rivers by means of machine learning

Abstract

The quantification of the sediment carrying capacity of a river is a difficult task that has received much attention. For sand-bed rivers especially, several sediment transport functions have appeared in the literature based on various concepts and approaches; however, since they present a significant discrepancy in their results, none of them has become universally accepted. This paper employs three machine learning techniques, namely artificial neural networks, symbolic regression based on genetic programming and an adaptive-network-based fuzzy inference system, for the derivation of sediment transport formulae for sand-bed rivers from field and laboratory flume data. For the determination of the input parameters, some of the most prominent fundamental approaches that govern the phenomenon, such as shear stress, stream power and unit stream power, are utilized and a comparison of their efficacy is provided. The results obtained from the machine learning techniques are superior to those of the commonly-used sediment transport formulae and it is shown that each of the input combinations tested has its own merit, as they produce similarly good results with respect to the data-driven technique employed.

Editor Z.W. Kundzewicz     

A framework to estimate sediment loads using distributions with covariates: Beaurivage River watershed (Québec,Canada)

A framework to estimate sediment loads based on the statistical distribution of sediment concentrations and various functional forms relating distribution characteristics (e.g. mean and variance) to covariates is developed. The covariates are used as surrogates to represent the main processes involved in sediment generation and transport. Statistical models of increasing complexity are built and compared to assess their relative performance using available sediment concentration and covariate data. Application to the Beaurivage River watershed (Québec, Canada) is conducted using data for the 1989–2004 period. The covariates considered in this application are streamflow and calendar day. A comparison of different statistical models shows that, in this case, the log‐normal distribution with a mean value depending on streamflow (power law with an additive term) and calendar day (sinusoidal), a constant coefficient of variation for streamflow dependence and a constant standard deviation for calendar day dependence provide the best result. Model parameters are estimated using the maximum likelihood estimation technique. The selected model is then used to estimate the distribution of annual sediment loads for the Beaurivage River watershed for a selected period. A bootstrap parametric method is implemented to account for uncertainties in parameter values and to build the distributions of annual loads. Comparison of model results with estimates obtained using the empirical ratio estimator shows that the latter were rarely within the 0·1–0·9 quantile interval of the distributions obtained with the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Sediment fingerprinting in fluvial systems： review of tracers,sediment sources and mixing models

Suspended sediments in fluvial systems originate from a myriad of diffuse and point sources, with the relative contribution from each source varying over time and space. The process of sediment fingerprinting focuses on developing methods that enable discrete sediment sources to be identified from a composite sample of suspended material. This review identifies existing methodological steps for sediment fingerprinting including fluvial and source sampling, and critically compares biogeochemical and physical tracers used in fingerprinting studies. Implications of applying different mixing models to the same source data are explored using data from 41 catchments across Europe, Africa, Australia, Asia, and North and South America. The application of seven commonly used mixing models to two case studies from the US （North Fork Broad River watershed） and France （Bldone watershed） with local and global （genetic algorithm） optimization methods identified all outputs remained in the acceptable range of error defined by the original authors. We propose future sediment fingerprinting studies use models that combine the best explanatory parameters provided by the modified Collins （using correction factors） and Hughes （relying on iterations involving all data, and not only their mean values） models with optimization using genetic algorithms to best predict the relative contribution of sediment sources to fluvial systems.     

Machine Learning Approach to Predict Sediment Load – A Case Study

In this study, a novel machine learning technique called the support vector machine (SVM) method is proposed as a new predictive model to predict sediment loads in three Malaysian rivers. The SVM is employed without any restriction to an extensive database compiled from measurements in the Muda, Langat, and Kurau rivers. The SVM technique demonstrated a superior performance compared to other traditional sediment‐load methods. The coefficient of determination, 0.958, and the mean square error, 0.0698, of the SVM method are higher than those of the traditional method. The performance of the SVM method demonstrates its predictive capability and the possibility of the generalization of the model to nonlinear problems for river engineering applications.