Bayesian model averaging assessment on groundwater management under model structure uncertainty

This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the “1,500-foot” sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used.     

Use of caesium‐137 data to evaluate SHETRAN simulated long‐term erosion patterns in arable lands

The caesium‐137 method of quantifying soil erosion is used to provide field data for validating the capability of the SHETRAN modelling system for predicting long‐term (30‐year) erosion rates and their spatial variability. Simulations were carried out for two arable farm sites (area 3–5 ha) in central England for which average annual erosion rates of 6·5 and 10·4 t ha^?1 year^?1 had already been determined using caesium‐137 measurements. These rates were compared with a range of simulated values representing the uncertainty in model output derived from uncertainty in the evaluation of model parameters. A successful validation was achieved in that the simulation range contained the measured rate at both sites, whereas the spatial variability was reproduced excellently at one site and partially at the other. The results indicate that, as the caesium‐137 technique measures the erosion caused by all the processes acting at a site, it is relevant to hydrologically based models such as SHETRAN only if erosion by wind, agricultural activities and other processes not represented in the model are insignificant. The results also indicate a need to reduce the uncertainty in model parameter evaluation. More generally, the caesium‐137 technique is shown to provide field data that improve the severity of the validation procedure (accounting for internal as well as outlet conditions) and that add spatial variability to magnitude as a condition for identifying unrealistic parameter sets when seeking to reduce simulation uncertainty. Copyright © 2004 John Wiley & Sons, Ltd.     

Uncertainty assessment of a process-based integrated catchment model of phosphorus

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km²), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R ²) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of "pilot points" as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.     

Uncertainty and sensitivity analysis of runoff and sediment yield in a small agricultural watershed with KINEROS2 / Analyse d'incertitude et de sensibilité des simulations d'écoulement et de transport solide de KINEROS2 dans un petit bassin versant agricole

Abstract

Using the Monte Carlo (MC) method, this paper derives arithmetic and geometric means and associated variances of the net capillary drive parameter, G, that appears in the Parlange infiltration model, as a function of soil texture and antecedent soil moisture content. Approximate expressions for the arithmetic and geometric statistics of G are also obtained, which compare favourably with MC generated ones. This paper also applies the MC method to evaluate parameter sensitivity and predictive uncertainty of the distributed runoff and erosion model KINEROS2 in a small experimental watershed. The MC simulations of flow and sediment related variables show that those parameters which impart the greatest uncertainty to KINEROS2 model outputs are not necessarily the most sensitive ones. Soil hydraulic conductivity and wetting front net capillary drive, followed by initial effective relative saturation, dominated uncertainties of flow and sediment discharge model outputs at the watershed outlet. Model predictive uncertainty measured by the coefficient of variation decreased with rainfall intensity, thus implying improved model reliability for larger rainfall events. The antecedent relative saturation was the most sensitive parameter in all but the peak arrival times, followed by the overland plane roughness coefficient. Among the sediment related parameters, the median particle size and hydraulic erosion parameters dominated sediment model output uncertainty and sensitivity. Effect of rain splash erosion coefficient was negligible. Comparison of medians from MC simulations and simulations by direct substitution of average parameters with observed flow rates and sediment discharges indicates that KINEROS2 can be applied to ungauged watersheds and still produce runoff and sediment yield predictions within order of magnitude of accuracy.     

Remote Sensing-Derived Water Extent and Level to Constrain Hydraulic Flood Forecasting Models: Opportunities and Challenges

Accurate, precise and timely forecasts of flood wave arrival time, depth and velocity at each point of the floodplain are essential to reduce damage and save lives. Current computational capabilities support hydraulic models of increasing complexity over extended catchments. Yet a number of sources of uncertainty (e.g., input and boundary conditions, implementation data) may hinder the delivery of accurate predictions. Field gauging data of water levels and discharge have traditionally been used for hydraulic model calibration, validation and real-time constraint. However, the discrete spatial distribution of field data impedes the testing of the model skill at the two-dimensional scale. The increasing availability of spatially distributed remote sensing (RS) observations of flood extent and water level offers the opportunity for a comprehensive analysis of the predictive capability of hydraulic models. The adequate use of the large amount of information offered by RS observations triggers a series of challenging questions on the resolution, accuracy and frequency of acquisition of RS observations; on RS data processing algorithms; and on calibration, validation and data assimilation protocols. This paper presents a review of the availability of RS observations of flood extent and levels, and their use for calibration, validation and real-time constraint of hydraulic flood forecasting models. A number of conclusions and recommendations for future research are drawn with the aim of harmonising the pace of technological developments and their applications.     

Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling

In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes.     

NUMERICAL SIMULATION OF TURBIDITY CURRENT IN RESERVOIR

I. INTRODUCTIONWhen a sediment--laden flow reaches the backwater zone of a reservoir, the suddenreduction of flow velocity causes sediment particles to settle toward the river bed. Undercertain circumstsnces, it will plunge and form a layer of sediment--water mixture flowingbeneath the water surface. This flowing layer is called the turbidity current. A turbiditycurrent is relatively stable and has important impacts on reservoir sedimentation.In the case of deep reservoirs, due to temper…     

Distributed dynamic modelling of interrill overland flow

A distributed, dynamic, process-based model for interrill overland flow that has previously been shown to predict accurately both total runoff and runoff hydraulics for a site on semi-arid shrubland is assessed in terms of (i) its portability, (ii) its sensitivity to the quality of data inputs, and (iii) its sensitivity to the size of cell used in the model. It is found that the model can be used at another site, but only after modifications to take account of the local controls of runoff routing. The model is portable, but not readily so. The model is sensitive to both the quality of data input and the size of cell. Data input cannot be reduced by use of stochastic distribution of model parameters without significant loss of accuracy in model predictions, particularly of runoff hydraulics. Larger cells produce poorer predictions of the runoff hydrograph. It is concluded that process-based modelling of interrill runoff may not be a realistic tool for predicting soil erosion, but is one that may be useful for identification of our present poor understanding of erosion processes. Such models help to define the research agenda for soil erosion studies. © 1997 John Wiley & Sons, Ltd.     

Simulation of long‐term soil redistribution by tillage using a cellular automata model

The process of tillage translocation is well studied and can be described adequately by different existing models. Nevertheless, in complex environments with numerous obstacles, such as olive orchards, the application of conventional tillage erosion models is not straightforward. However, such obstacles have important effects on the spatial pattern of soil redistribution and on resulting soil properties. Cellular automata could provide a valuable alternative here. This study aims at developing a cellular automata model for tillage translocation (CATT) that can take into account such obstacles, exploring its possibilities and limitations. Firstly, model outcome was tested on a traditional field with rolling topography, for which caesium‐137 (¹³⁷Cs) inventories are available. The observed spatial soil redistribution patterns could be adequately represented by the CATT model. Secondly, a global sensitivity analysis was performed to explore the effect of input parameter uncertainty on several selected model outputs. The variance‐based extended Fourier Amplitude Sensitivity Test (FAST) method was used to determine first‐ and total‐order sensitivity indices. Tillage depth was identified as the input parameter that determined most of the output variance, followed respectively by tillage direction and speed. The high difference between the total‐ and first‐order sensitivity indices indicated that, in spite of the simple model structure, the model behaves non‐linearly with respect to some of the model output variables. Higher order interactions were especially important for determining the proportion of eroding and deposition cells. Finally, simulations were performed to analyse the model behaviour in complex landscapes, applying it to a field with protruding obstacles (representing olive trees). The model adequately represented some morphological features observed in actual olive orchards, such as mounds around the olive trees. The results show that cellular automata are an appropriate tool to describe long‐term tillage soil redistribution. Copyright © 2010 John Wiley & Sons, Ltd.     

When does spatial resolution become spurious in probabilistic flood inundation predictions?

Advances in remote sensing have enabled hydraulic models to run at fine scale resolutions, producing precise flood inundation predictions. However, running models at finer resolutions increase their computational expense, reducing the feasibility of running the multiple model realizations required to undertake uncertainty analysis. Furthermore, it is possible that precision gained by running fine scale models is smoothed out when treating models probabilistically. The aim of this paper is to determine the level of spatial complexity that is required when making probabilistic flood inundation predictions. The Imera basin, Sicily is used as a case study to assess how changing the spatial resolution of the hydraulic model LISFLOOD‐FP impacts on the skill of conditional probabilistic flood inundation maps given model parameter and boundary condition uncertainties. We find that model performance deteriorates at resolutions coarser than 50 m. This is predominantly caused by changes in flow pathways at coarser resolutions which lead to non‐stationarity in the optimum model parameters at different spatial resolutions. However, although it is still possible to produce probabilistic flood maps that contain a coherent outline of the flood extent at coarser resolutions, the reliability of these maps deteriorates at resolutions coarser than 100 m. Additionally, although the rejection of non‐behavioural models reduces the uncertainty in probabilistic flood maps the reliability of these maps is also reduced. Models with resolutions finer than 50 m offer little gain in performance yet are more than an order of magnitude computationally expensive which can become infeasible when undertaking probabilistic analysis. Furthermore, we show that using deterministic, high‐resolution flood maps can lead to a spurious precision that would be misleading and not representative of the overall uncertainties that are inherent in making inundation predictions. Copyright © 2015 The Authors Hydrological Processes Published by John Wiley & Sons Ltd.     

An evaluation of conditioning data for solute transport prediction

The large and diverse body of subsurface characterization data generated at a field research site near Oyster, Virginia, provides a unique opportunity to test the impact of conditioning data of various types on predictions of flow and transport. Bromide breakthrough curves (BTCs) were measured during a forced-gradient local-scale injection experiment conducted in 1999. Observed BTCs are available at 140 sampling points in a three-dimensional array within the transport domain. A detailed three-dimensional numerical model is used to simulate breakthrough curves at the same locations as the observed BTCs under varying assumptions regarding the character of hydraulic conductivity spatial distributions, and variable amounts and types of conditioning data. We present comparative results of six cases ranging from simple (deterministic homogeneous models) to complex (stochastic indicator simulation conditioned to cross-borehole geophysical observations). Quantitative measures of model goodness-of-fit are presented. The results show that conditioning to a large number of small-scale measurements does not significantly improve model predictions, and may lead to biased or overly confident predictions. However, conditioning to geophysical interpretations with larger spatial support significantly improves the accuracy and precision of model predictions. In all cases, the effects of model error appear to be significant in relation to parameter uncertainty.     

A process‐based conversion model for caesium‐137 derived erosion rates on agricultural land: an integrated spatial approach

There is increasing recognition that ¹³⁷Cs data remain one of the few sources of spatially distributed information concerning soil erosion. However, many of the conversion models that have been used to convert ¹³⁷Cs data into soil redistribution rates failed to account for some of the key factors affecting the redistribution of ¹³⁷Cs in agricultural landscapes. The conversion model presented in this paper aims to overcome some of the limitations associated with existing models and therefore to provide more realistic estimates of soil erosion rates on agricultural land. The conversion model aims at coupling soil redistribution processes directly with ¹³⁷Cs redistribution. Emphasis is placed on the spatial representation of soil redistribution processes and the adequate simulation of tillage processes. The benefits of the presented model arise from the two‐dimensional spatial integration of mass balance models with soil erosion models. No a priori assumptions about the intensity of any soil redistribution process are necessary and the level of agreement between observed and simulated ¹³⁷Cs inventories enables us to evaluate the performance of the model. The spatial implementation and the use of fuzzy parameter sets also allow us to assess the uncertainties associated with soil erosion estimates. It was shown that an adequate simulation of tillage processes is necessary and that simplified tillage models may lead to erroneous estimates of soil redistribution. The model was successfully applied to a study site in the Belgian Loam Belt and the results indicated that tillage is the dominant process. Furthermore, the uncertainties associated with the estimation of water erosion rates were much higher than those associated with tillage, especially for depositional areas. Copyright © 2003 John Wiley & Sons, Ltd.     

Bioturbation and erosion rates along the soil-hillslope conveyor belt,part 2: Quantification using an analytical solution of the diffusion–advection equation

Particles on soil-mantled hillslopes are subject to downslope transport by erosion processes and vertical mixing by bioturbation. Both are key processes for understanding landscape evolution and soil formation, and affect the functioning of the critical zone. We show here how the depth–age information, derived from feldspar-based single grain post-infrared infrared stimulated luminescence (pIRIR), can be used to simultaneously quantify erosion and bioturbation processes along a hillslope. In this study, we propose, for the first time, an analytical solution for the diffusion–advection equation to calculate the diffusivity constant and erosion–deposition rates. We have fitted this model to age–depth data derived from 15 soil samples from four soil profiles along a catena located under natural grassland in the Santa Clotilde Critical Zone Observatory, in the south of Spain. A global sensitivity analysis was used to assess the relative importance of each model parameter in the output. Finally, the posterior probability density functions were calculated to evaluate the uncertainty in the model parameter estimates. The results show that the diffusivity constant at the surface varies from 11.4 to 81.9 mm² a^-1 for the hilltop and hill-base profile, respectively, and between 7.4 and 64.8 mm² a^-1 at 50 cm depth. The uncertainty in the estimation of the erosion–deposition rates was found to be too high to make a reliable estimate, probably because erosion–deposition processes are much slower than bioturbation processes in this environment. This is confirmed by a global sensitivity analysis that shows how the most important parameters controlling the age–depth structure in this environment are the diffusivity constant and regolith depth. Finally, we have found a good agreement between the soil reworking rates proposed by earlier studies, considering only particle age and depth, and the estimated diffusivity constants. The soil reworking rates are effective rates, corrected for the proportion of particles actually participating in the process. © 2019 John Wiley & Sons, Ltd.     

Modelling mean annual sediment yield using a distributed approach

In this paper a spatially distributed model for the calculation of sediment delivery to river channels is presented (SEDEM: SEdiment DElivery Model). The model consists of two components: (1) the calculation of a spatial pattern of mean annual soil erosion rates in the catchment using a RUSLE (Revised Soil Erosion Equation) approach; and (2) the routing of the eroded sediment to the river channel network taking into account the transport capacity of each spatial unit. If the amount of routed sediment exceeds the local transport capacity, sediment deposition occurs. An existing dataset on sediment yield for 24 catchments in central Belgium was used to calibrate the transport capacity parameters of the model. A validation of the model results shows that the sediment yield for small and medium sized catchments (10–5000 ha) can be predicted with an average accuracy of 41 per cent. The predicted sediment yield values with SEDEM are significantly more accurate than the predictions using a lumped regression model. Moreover a spatially distributed approach allows simulation of the effect of different land use scenarios and soil conservation techniques. Copyright © 2001 John Wiley & Sons, Ltd.     

An event simulation approach to the assessment of flood level frequencies: risk maps for the Warsaw reach of the River Vistula

Flood risk assessment is customarily performed using a design flood. Observed past flows are used to derive a flood frequency curve which forms the basis for a construction of a design flood. The simulation of a distributed model with the 1‐in‐T year design flood as an input gives information on the possible inundation areas, which are used to derive flood risk maps. The procedure is usually performed in a deterministic fashion, and its extension to take into account the design flood‐and flow routing model uncertainties is computer time consuming. In this study we propose a different approach to flood risk assessment which consists of the direct simulation of a distributed flow routing model for an observed series of annual maximum flows and the derivation of maps of probability of inundation of the desired return period directly from the obtained simulations of water levels at the model cross sections through an application of the Flood Level Frequency Analysis. The hydraulic model and water level quantile uncertainties are jointly taken into account in the flood risk uncertainty evaluation using the Generalized Likelihood Uncertainty Estimation (GLUE) approach. An additional advantage of the proposed approach lies in smaller uncertainty of inundation predictions for long return periods compared to the standard approach. The approach is illustrated using a design flood level and a steady‐state solution of a hydraulic model to derive maps of inundation probabilities. Copyright © 2016 John Wiley & Sons, Ltd.     

Uncertainties in DRAINMOD predictions of subsurface drain flow for an Indiana silt loam using the GLUE methodology

Good modelling practice requires the incorporation of uncertainty analysis into hydrologic/water quality models. The generalized likelihood uncertainty estimation procedure was used to evaluate the uncertainty in DRAINMOD predictions of daily, monthly, and yearly subsurface drain flow. A variance‐based sensitivity analysis technique, the extended Fourier amplitude sensitivity test, was used to identify the main sources of prediction uncertainty. The analysis was conducted for the experimental drainage field at the Southeast Purdue Agricultural Center in Indiana. Six years of data were used and the uncertainties in eight model parameters were considered to analyse how uncertainties in input parameters propagate to model outputs. The width of 90% confidence interval bands of drain flow ranged from 0 to 0·6 cm day^?1 for daily predictions, from 0 to 3·1 cm month^?1 for the monthly predictions, and from 7·6 to 12·4 cm year^?1 for yearly predictions. Annual drain flow predicted by DRAINMOD fell well within the 90% confidence bounds. Model results were most sensitive to the vertical saturated hydraulic conductivity of the restrictive layer and the lateral hydraulic conductivity of the deepest soil layer, followed by the lateral hydraulic conductivity of the top soil layer and surface micro‐storage. Parameter interactions also contributed to the prediction uncertainty. Copyright © 2006 John Wiley & Sons, Ltd.     

Uncertainty assessment and optimization of hydrological model with the Shuffled Complex Evolution Metropolis algorithm: an application to artificial neural network rainfall-runoff model

Assessment of parameter and predictive uncertainty of hydrologic models is an essential part in the field of hydrology. However, during the past decades, research related to hydrologic model uncertainty is mostly done with conceptual models. As is accepted that uncertainty in model predictions arises from measurement errors associated with the system input and output, from model structural errors and from problems with parameter estimation. Unfortunately, non-conceptual models, such as black-box models, also suffer from these problems. In this paper, we take the artificial neural network (ANN) rainfall-runoff model as an example, and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) is employed to analysis the parameter and predictive uncertainty of this model. Furthermore, based on the results of uncertainty assessment, we finally arrive at a simpler incomplete-connection artificial neural network (ICANN) model as well as with better performance compared to original ANN rainfall-runoff model. These results not only indicate that SCEM-UA can be a useful tool for uncertainty analysis of ANN model, but also prove that uncertainty does exist in ANN rainfall-runoff model. Additionally, in some way, it presents that the ICANN model is with smaller uncertainty than the original ANN model.