Sensitivity of hydrological models to uncertainty in rainfall input

Abstract

Different approaches used in hydrological modelling are compared in terms of the way each one takes the rainfall data into account. We examine the errors associated with accounting for rainfall variability, whether in hydrological modelling (distributed vs lumped models) or in computing catchment rainfall, as well as the impact of each approach on the representativeness of the parameters it uses. The database consists of 1859 rainfall events, distributed on 500 basins, located in the southeast of France with areas ranging from 6.2 to 2851 km². The study uses as reference the hydrographs computed by a distributed hydrological model from radar rainfall. This allows us to compare and to test the effects of various simplifications to the process when taking rainfall information (complete rain field vs sampled rainfall) and rainfall–runoff modelling (lumped vs distributed) into account. The results appear to show that, in general, the sampling effect can lead to errors in discharge at the outlet that are as great as, or even greater than, those one would get with a fully lumped approach. We found that small catchments are more sensitive to the uncertainties in catchment rainfall input generated by sampling rainfall data as seen through a raingauge network. Conversely, the larger catchments are more sensitive to uncertainties generated when the spatial variability of rainfall events is not taken into account. These uncertainties can be compensated for relatively easily by recalibrating the parameters of the hydrological model, although such recalibrations cause the parameter in question to completely lose physical meaning.

Citation Arnaud, P., Lavabre, J., Fouchier, C., Diss, S. & Javelle, P. (2011) Sensitivity of hydrological models to uncertainty of rainfall input. Hydrol. Sci. J. 56(3), 397–410.     

Combination of sensitivity and uncertainty analyses for sediment transport modeling in sewer pipes

Mitigation of sediment deposition in lined open channels is an essential issue in hydraulic engineering practice.Hence,the limiting velocity should be determined to keep the channel bottom clean from sediment deposits.Recently,sediment transport modeling using various artificial intelligence(AI) techniques has attracted the interest of many researchers.The current integrated study highlights unique insight for modeling of sediment transport in sewer and urban drainage systems.A novel methodology...     

Modeling cave cross-section evolution including sediment transport and paragenesis

Deposits within caves are often used to interpret past landscape evolution and climate conditions. However, cave passage shapes also preserve information about past conditions. Despite the usefulness of passage shape, no previous models simulate cave cross-section evolution in a realistic manner. Here we develop a model for evolving cave passage cross-sections using a shear stress estimation algorithm and a shear stress erosion rule. Our model qualitatively duplicates observed cave passage shapes so long as erosion rates vary with shear stress, as in the case of transport limited dissolution or mechanical erosion. This result provides further evidence that erosion rates within caves are not typically limited by surface reaction rates, even though current speleogenesis models predict surface-rate limitation under most turbulent flow conditions. By adding sediment transport and alluviation to the model we successfully simulate paragenetic channels. Simulations duplicate the hypothesized dynamics of paragenesis, whereby: 1) the cross-section of a phreatic passage grows until shear stress is sufficiently reduced that alluviation occurs, 2) the floor of the passage becomes armored and erosion continues on the ceiling and walls, 3) negative feedback produces an equilibrium cross-sectional area such that shear stress is sufficient to transport incoming sediment. We derive an approximate scaling relationship that indicates that equilibrium paragenetic channel width scales with the square root of discharge, and weakly with the inverse of sediment supply. Simulations confirm this relationship and show that erosion mechanism, sediment size, and roughness are secondary controls. The inverse scaling of width with sediment supply in paragenetic channels contrasts with surface bedrock channels, which respond to larger sediment supplies by widening. Our model provides a first step in simulating cave cross-section evolution and points to the need for a better understanding of the dominant erosion mechanisms in soluble bedrock channels. © 2020 John Wiley & Sons, Ltd.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Assessing titanium dioxide nanoparticles transport models by Bayesian uncertainty analysis

With the rapid growth of nanotechnology industry, nanomaterials as an emerging pollutant are gradually released into subsurface environments and become great concerns. Simulating the transport of nanomaterials in groundwater is an important approach to investigate and predict the impact of nanomaterials on subsurface environments. Currently, a number of transport models are used to simulate this process, and the outputs of these models could be inconsistent with each other due to conceptual model uncertainty. However, the performances of different models on simulating nanoparticles transport in groundwater are rarely assessed in Bayesian framework in previous researches, and these will be the primary objective of this study. A porous media column experiment is conducted to observe the transport of Titanium Dioxide Nanoparticles (nano-TiO₂). Ten typical transport models which consider different chemical reaction processes are used to simulate the transport of nano-TiO₂, and the observed nano-TiO₂ breakthrough curves data are used to calibrate these models. For each transport model, the parameter uncertainty is evaluated using Markov Chain Monte Carlo, and the DREAM_(ZS) algorithm is used to sample parameter probability space. Moreover, the Bayesian model averaging (BMA) method is used to incorporate the conceptual model uncertainty arising from different chemical reaction based transport models. The results indicate that both two-sites and nonequilibrium sorption models can well reproduce the retention of nano-TiO₂ transport in porous media. The linear equilibrium sorption isotherm, first-order degradation, and mobile-immobile models fail to describe the nano-TiO₂ retention and transport. The BMA method could instead provide more reliable estimations of the predictive uncertainty compared to that using a single model.     

Variable and conflicting shear stress estimates inside a boundary layer with sediment transport

This paper presents a comparison between two methods for estimating shear stress in an atmospheric internal boundary layer over a beach surface under optimum conditions, using wind velocities measured synchronously at 13 heights over a 1.7 m vertical array using ultrasonic anemometry. The Reynolds decomposition technique determines at‐a‐point shear stresses at each measurement height, while the Law‐of‐the‐Wall yields a single boundary layer estimate based on fitting a logarithmic velocity profile through the array data. Analysis reveals significant inconsistencies between estimates derived from the two methods, on both a whole‐event basis and as time‐series. Despite a near‐perfect fit of the Law‐of‐the‐Wall, the point estimates of Reynolds shear stress vary greatly between heights, calling into question the assumed presence of a constant stress layer. A comparison with simultaneously measured sediment transport finds no relationship between transport activity and the discrepancies in shear stress estimates. Results do show, however, that Reynolds shear stress measured nearer the bed exhibits slightly better correlation with sand transport rate. The findings serve as a major cautionary message to the interpretation and application of single‐height measurements of Reynolds shear stress and their equivalence to Law‐of‐the‐Wall derived estimates, and these concerns apply widely to boundary layer flows in general. © 2015 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

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.     

Nonlocal transport models for capturing solute transport in one-dimensional sand columns: Model review,applicability, limitations and improvement

Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scale-dependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.     

Uncertainty estimates for surface runoff models

A lower bound for variance in surface runoff modelling estimates is advanced. The bound is derived using a linear unit hydrograph approach which utilizes a discretization of the catchment into an arbitrary number of subareas, a linear routing technique for channel flow effects, a variable effective rainfall distribution over the catchment, and calibration parameter distributions developed in correlating rainfall-runoff data by the model. The uncertainty bound reflects the dominating influence of the unknown rainfall distribution over the catchment and is expressed as a distribution function that can be reduced only by supplying additional rainfall-runoff data. It is recommended that this uncertainty distribution in modelling results be included in flood control design studies in order to incorporate a prescribed level of confidence in flood protection facilities.     

Natural tracers for sediment transport studies

The use of natural differences in composition between marine and fluvial sediments makes it possible to determine their mixing ratio in estuarine deposits. Differences in chemical, mineralogical and isotope geochemical composition can be used as tracers, provided that three criteria are met: conservative behaviour during transport, with time, and after deposition. Examples of the utility of natural tracers are presented, including their use for the interpretation of pollutant patterns in estuaries. The application of natural tracers has shown that marine sediments may be transported past the freshwater boundary in estuaries, and thus contribute to the sedimentation in freshwater tidal areas.     

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.     

Geophysical flows under location uncertainty,Part I Random transport and general models

A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction, an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.     

Coupled and splitting bedload sediment transport models based on a modified flux-wave approach

Numerical modeling of free-surface flow over a mobile bed with predominantly bedload sediment transport can be done by solving the shallow water and Exner equations using coupled and splitting approaches.The coupled method uses a coupling of the governing equations at the same time step leading to a non-conservative solution.The splitting method solves the Exner and the shallow water equations in a separate manner,and is only capable of modeling weak free-surface and bedload interactions.In the current study,an extended version of a Godunov-type wave propagation algorithm is presented for modeling of morphodynamic systems using both coupled and splitting approaches.In the introduced coupled method the entire morphodynamic system is solved in the form of a conservation law.For the splitting technique,a new wave Riemann decomposition is defined which enables the scheme to be utilized for mild and strong interactions.To consider the bedload sediment discharge within the Exner equation,the Smart and Meyer-Peter&Müller formulae are used.It was found that the coupled solution gives accurate predictions for all investigated flow regimes including propagation over a dry-state using a Courant-Friedrichs-Lewy(CFL)number equal to 0.6.Furthermore,the splitting method was able to model all flow regimes with a lower CFL number of 0.3.     

Artificial neural networks for sheet sediment transport

Abstract

Sheet sediment transport was modelled by artificial neural networks (ANNs). A three-layer feed-forward artificial neural network structure was constructed and a back-propagation algorithm was used for the training of ANNs. Event-based, runoff-driven experimental sediment data were used for the training and testing of the ANNs. In training, data on slope and rainfall intensity were fed into the network as inputs and data on sediment discharge were used as target outputs. The performance of the ANNs was tested against that of the most commonly used physically-based models, whose transport capacity was based on one of the dominant variables—flow velocity (V), shear stress (SS), stream power (SP), and unit stream power (USP). The comparison results revealed that the ANNs performed as well as the physically-based models for simulating nonsteady-state sediment loads from different slopes. The performances of the ANNs and the physically-based models were also quantitatively investigated to estimate mean sediment discharges from experimental runs. The investigation results indicated that better estimations were obtained for V over mild and steep slopes, under low rainfall intensity; for USP over mild and steep slopes, under high rainfall intensity; for SP and SS over very steep slopes, under high rainfall intensity; and for ANNs over steep and very steep slopes, under very high rainfall intensities.     

MET-IRSL used to track pre-depositional sediment transport history

This paper explores a series of single grain MET-IRSL (multiple elevated temperature infra-red stimulated luminescence) determinations undertaken in order to assess the potential of this approach, developed over the last decade and previously applied to a range of applications, in determining how eroded material moves through environments. Three different approaches are explored here, namely: i) an assessment of the potential to use the technique for improving the robustness of IRSL or P-IR-IRSL age estimates by identifying only well-bleached grains, ii) a means to characterise patterns of grain transport within a catchment using a newly established parameter, the “burial-bleach ratio”, and iii) a novel proxy that responds to changes in light availability through time, here referred to as palaeophotochronometry. For the second approach that we explore, a direct comparison of the MET-IRSL results from several sites with particle size analysis (PSA) data for the same sediment is included. This comparison highlights striking similarities between dispersal of single grain (SG) MET-IRSL burial-bleach ratio data and PSA distributions for some samples, suggesting that we may be able to place a timescale on the acquisition of this fundamental sedimentary characteristic. Common to these three SG MET-IRSL approaches is the importance of characterising and interpreting the previous bleaching records for individual grains.     

A method for error analysis of sediment yields derived from estimates of lacustrine sediment accumulation

The logistical demands of coring lake sediments tend to preclude the replicate coring necessary to establish error estimates for measured sedimentary parameters. However, if such parameters are to be used to reconstruct sediment yield, and particularly to identify temporal variability of sediment yield, reasonable error estimates are required. In this paper data from a series of alpine lakes in British Columbia are applied to develop a new method for deriving such estimates. Regression surfaces fitted to point values of sediment mass are used to model the physically controlled spatial variability of sedimentation. Deviations from these surfaces are assumed to represent remaining unstructured variance, which constitutes a conservative error estimate. Application of the technique to the alpine lake dataset gives sediment yield estimates with error ranges of ±7–21 per cent. The potential error is minimized where the spatial variability of sedimentation is strongly predictable. The best fits were achieved for elongate lakes of simple basin morphology. The range of the error estimates is sufficiently low to allow detection of variability in Holocene sediment yield to one of the lakes. By using this technique, absolute sediment yields with associated error estimates may be derived. The associated gains in precision justify multicore approaches to lake sediment‐based reconstructions of sediment yield. Copyright © 2000 John Wiley & Sons, Ltd.     

The comparison of sensitivity analysis of hydrological uncertainty estimates by GLUE and Bayesian method under the impact of precipitation errors

The input uncertainty is as significant as model error, which affects the parameter estimation, yields bias and misleading results. This study performed a comprehensive comparison and evaluation of uncertainty estimates according to the impact of precipitation errors by GLUE and Bayesian methods using the Metropolis Hasting algorithm in a validated conceptual hydrological model (WASMOD). It aims to explain the sensitivity and differences between the GLUE and Bayesian method applied to hydrological model under precipitation errors with constant multiplier parameter and random multiplier parameter. The 95 % confidence interval of monthly discharge in low flow, medium flow and high flow were selected for comparison. Four indices, i.e. the average relative interval length, the percentage of observations bracketed by the confidence interval, the percentage of observations bracketed by the unit confidence interval and the continuous rank probability score (CRPS) were used in this study for sensitivity analysis under model input error via GLUE and Bayesian methods. It was found that (1) the posterior distributions derived by the Bayesian method are narrower and sharper than those obtained by the GLUE under precipitation errors, but the differences are quite small; (2) Bayesian method performs more sensitive in uncertainty estimates of discharge than GLUE according to the impact of precipitation errors; (3) GLUE and Bayesian methods are more sensitive in uncertainty estimate of high flow than the other flows by the impact of precipitation errors; and (4) under the impact of precipitation, the results of CRPS for low and medium flows are quite stable from both GLUE and Bayesian method while it is sensitive for high flow by Bayesian method.     

A new approach for linking event‐based upland sediment sources to downstream suspended sediment transport

In this study, we proposed a new approach for linking event sediment sources to downstream sediment transport in a watershed in central New York. This approach is based on a new concept of spatial scale, sub‐watershed area (SWA), defined as a sub‐watershed within which all eroded soils are transported out without deposition during a hydrological event. Using (rainfall) event data collected between July and November, 2007 from several SWAs of the studied watershed, we developed an empirical equation that has one independent variable, mean SWA slope. This equation was then used to determine event‐averaged unit soil erosion rate, Q_S/A, (in kg/km²/hr) for all SWAs in the studied watershed and calculate event‐averaged gross erosion E_ea (in kg/hr). The event gross erosion E_t (in kilograms) was subsequently computed as the product of E_ea and the mean event duration, T (in hours) determined using event hydrographs at the outlet of the studied watershed. Next, we developed two linear sediment rating curves (SRCs) for small and big events based on the event data obtained at the watershed outlet. These SRCs, together with T, allowed us to determine event sediment yield SY_e (in kilograms) for all events during the study period. By comparing E_t with SY_e, developing empirical equations (i) between E_t and SY_e and (ii) for event sediment delivery ratio, respectively, we revealed the event dynamic processes connecting sediment sources and downstream sediment transport. During small events, sediment transport in streams was at capacity and dominated by the deposition process, whereas during big events, it was below capacity and controlled by the erosion process. The key of applying this approach to other watersheds is establishing their empirical equations for Q_S/A and appropriately determining their numbers of SWAs. Copyright © 2011 John Wiley & Sons, Ltd.