Comparison of an artificial neural network and a conceptual rainfall–runoff model in the simulation of ephemeral streamflow

ABSTRACT

The rainfall–runoff process is governed by parameters that can seldom be measured directly for use with distributed models, but are rather inferred by expert judgment and calibrated against historical records. Here, a comparison is made between a conceptual model (CM) and an artificial neural network (ANN) for their ability to efficiently model complex hydrological processes. The Sacramento soil moisture accounting model (SAC-SMA) is calibrated using a scheme based on genetic algorithms and an input delay neural network (IDNN) is trained for variable delays and hidden layer neurons which are thoroughly discussed. The models are tested for 15 ephemeral catchments in Crete, Greece, using monthly rainfall, streamflow and potential evapotranspiration input. SAC-SMA performs well for most basins and acceptably for the entire sample with R² of 0.59–0.92, while scoring better for high than low flows. For the entire dataset, the IDNN improves simulation fit to R² of 0.70–0.96 and performs better for high flows while being outmatched in low flows. Results show that the ANN models can be superior to the conventional CMs, as parameter sensitivity is unclear, but CMs may be more robust in extrapolating beyond historical record limits and scenario building.

EDITOR M.C. Acreman; ASSOCIATE EDITOR not assigned     

A Bayesian method for missing rainfall estimation using a conceptual rainfall–runoff model

The estimation of missing rainfall data is an important problem for data analysis and modelling studies in hydrology. This paper develops a Bayesian method to address missing rainfall estimation from runoff measurements based on a pre-calibrated conceptual rainfall–runoff model. The Bayesian method assigns posterior probability of rainfall estimates proportional to the likelihood function of measured runoff flows and prior rainfall information, which is presented by uniform distributions in the absence of rainfall data. The likelihood function of measured runoff can be determined via the test of different residual error models in the calibration phase. The application of this method to a French urban catchment indicates that the proposed Bayesian method is able to assess missing rainfall and its uncertainty based only on runoff measurements, which provides an alternative to the reverse model for missing rainfall estimates.     

Use of spatially distributed water table observations to constrain uncertainty in a rainfall–runoff model

The Generalised Likelihood Uncertainty Estimation (GLUE) methodology is used to investigate how distributed water table observations modify simulation and parameter uncertainty for the hydrological model TOPMODEL, applied to the Sæternbekken Minifelt catchment in Norway. Errors in simulating observed flows, continuously-logged borehole water levels and more extensive, spatially distributed water table depths are combined using Bayes' equation within a `likelihood measure' L. It is shown how the distributions of L for the TOPMODEL parameters change as the different types of observed data are considered. These distributions are also used to construct corresponding simulation uncertainty bounds for flows, borehole water levels, and water table depths within the spatially-extensive piezometer network. Qualitatively wide uncertainty bounds for water table simulations are thought to be consistent with the simplified nature of the distributed model.     

Suitability of a lumped rainfall–runoff model for flashy tropical watersheds in New Caledonia

ABSTRACT

The GR4H lumped hourly rainfall–runoff model was assessed for its integration in a ridge-to-reef modelling framework. Particular attention was paid to rainfall representation, robustness of parameter estimates and ability to reproduce the main runoff features. The study was conducted in four tropical mountainous watersheds in New Caledonia, which are exposed to intense rainfall events, large annual climatic variations triggered by El Niño oscillation, and wildfires. The inverse distance and elevation weighting algorithm outperformed other classical rainfall interpolation methods under data-limited conditions. The time span of data needed for robust calibration was site specific and varied from 6–7 years to 10 years, which may be linked to El Niño events and to wildfires. With sufficient data, simulation quality was equivalent during the calibration and validation periods. The GR4H model was generally able to simulate both flash floods and large annual variations. The model was more reliable when simulating wet years and watersheds not subject to land-cover changes.     

Simulating temporal variability in catchment response using a monthly rainfall–runoff model

Abstract

Temporal variability can result from shifts in climate, or from changes in the runoff response due to land- or water-use changes, and represents a potential source of uncertainty in calibrating hydrological models. Parameter values were determined using Monte Carlo parameter sampling methods for a monthly rainfall–runoff model (Pitman model) for different sub-periods on four catchments, with different types and degrees of temporal variability, in Australia and Africa. For some catchments, parameters were not dependent upon the sub-period used and fell within expected ranges given the relatively high degree of model equifinality. In other catchments, dependencies can be identified that are associated with signals contained within the sub-periods. While the Pitman model is relatively robust in the face of temporal variability, it is concluded that better simulations will always be obtained from calibration data that include signals representing the total variability in climate, land-use change and catchment responses.     

Data time-step dependency of conceptual rainfall—streamflow model parameters: an empirical study with implications for regionalisation

Abstract

Employing 1-, 2-, 4-, 6-, 12- and 24-hourly data sets for two catchments (10.6 and 298 km²) in Wales, the calibrated parameters of a unit hydrograph-based model are shown to change substantially over that range of data time steps. For the smaller basin, each model parameter reaches, or approaches, a stable value as the data time step decreases, providing a straightforward method of estimating time-step independent model parameter values. For the larger basin, the model parameters also reach, or approach, stable values using hourly data, but, for reasons given in the paper, interpretation of the results is more difficult. Model parameter sensitivity analyses are presented that give insights into the relative precision on the parameters for both catchments. The paper discusses the importance of accounting for model parameter data time-step dependency in pursuit of a reduction in the uncertainty associated with estimates of flow in ungauged basins, and suggests that further work along these lines be undertaken using different catchments and models.     

Are modern metaheuristics successful in calibrating simple conceptual rainfall–runoff models?

In recent years sampling approaches have been used more widely than optimization algorithms to find parameters of conceptual rainfall–runoff models, but the difficulty of calibration of such models remains in dispute. The problem of finding a set of optimal parameters for conceptual rainfall–runoff models is interpreted differently in various studies, ranging from simple to relatively complex and difficult. In many papers, it is claimed that novel calibration approaches, so-called metaheuristics, outperform the older ones when applied to this task, but contradictory opinions are also plentiful. The present study aims at calibration of two simple lumped conceptual hydrological models, HBV and GR4J, by means of a large number of metaheuristic algorithms. The tests are performed on four catchments located in regions with relatively similar climatic conditions, but on different continents. The comparison shows that, although parameters found may somehow differ, the performance criteria achieved with simple lumped models calibrated by various metaheuristics are very similar and differences are insignificant from the hydrological point of view. However, occasionally some algorithms find slightly better solutions than those found by the vast majority of methods. This means that the problem of calibration of simple lumped HBV or GR4J models may be deceptive from the optimization perspective, as the vast majority of algorithms that follow a common evolutionary principle of survival of the fittest lead to sub-optimal solutions.     

Hybrid denoising-jittering data pre-processing approach to enhance multi-step-ahead rainfall–runoff modeling

Successful modeling of stochastic hydro-environmental processes widely relies on quantity and quality of accessible data and noisy data might effect on the functioning of the modeling. On the other hand in training phase of any Artificial Intelligence based model, each training data set is usually a limited sample of possible patterns of the process and hence, might not show the behavior of whole population. Accordingly in the present article first, wavelet-based denoising method was used in order to smooth hydrological time series and then small normally distributed noises with the mean of zero and various standard deviations were generated and added to the smoothed time series to form different denoised-jittered training data sets, for Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) modeling of daily and multi-step-ahead rainfall–runoff process of the Milledgeville station of the Oconee River and the Pole Saheb station of the Jighatu River watersheds, respectively located in USA and Iran. The proposed hybrid data pre-processing approach in the present study is used for the first time in modeling of time series and especially in modeling of hydrological processes. Furthermore, the impacts of denoising (smoothing) and noise injection (jittering) have been simultaneously investigated neither in hydrology nor in any other engineering fields. To evaluate the modeling performance, the outcomes were compared with the results of multi linear regression and Auto Regressive Integrated Moving Average models. Comparing the achieved results via the trained ANN and ANFIS models using denoised-jittered data showed that the proposed data pre-processing approach which serves both denoising and jittering techniques could improve performance of the ANN and ANFIS based single-step-ahead rainfall–runoff modeling of the Milledgeville station up to 14 and 12% and of the Pole Saheb station up to 22 and 16% in the verification phase. Also the results of multi-step-ahead modeling using the proposed data pre-processing approach showed improvement of modeling for both watersheds.     

Rainfall–runoff response and event-based runoff coefficients in a humid area (northwest Spain)

Abstract

The hydrological response of a small agroforestry catchment in northwest Spain (Corbeira catchment, 16 km²) is analysed, with particular focus on rainfall events. Fifty-four rainfall–runoff events, from December 2004 to September 2007, were used to analyse the principal hydrological patterns and show which factors best explain the hydrological response. The nonlinearity between rainfall and runoff showed that the variability in the hydrological response of the catchment was linked to the seasonal dynamics of the rainfall and, to a lesser extent, to evapotranspiration. The runoff coefficient, estimated as the ratio between direct runoff and rainfall volume, on an event basis, was analysed as a function of rainfall characteristics (amount and intensity) and the initial catchment state conditions prior to an event, such as pre-event baseflow and antecedent rainfall index. The results revealed that the hydrological response depends both on the soil humidity conditions at the start of the event and on rainfall amount, whereas rainfall intensity presented only a significant correlation with discharge increment. The antecedent conditions seem to be a key point in runoff production, and they explain much of the response. The hydrographs are characterized by a steep rising limb, a relatively narrow peak discharge and slow recession limb. These data and the observations suggest that the subsurface flow is the dominant runoff process.

Editor Z.W. Kundzewicz; Associate editor T. Wagener

Citation Rodríguez-Blanco, M.L., Taboada-Castro, M.M. and Taboada-Castro, M.T., 2012. Rainfall–runoff response and event-based runoff coefficients in a humid area (northwest Spain). Hydrological Sciences Journal, 57 (3), 445–459.     

Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model

Abstract

One of the main challenges faced by hydrologists and water engineers is the estimation of variables needed for water resources planning and management in ungauged river basins. To this end, techniques for transposing information, such as hydrological regional analyses, are widely employed. A method is presented for regionalizing flow-duration curves (FDCs) in perennial, intermittent and ephemeral rivers, based on the extended Burr XII probability distribution. This distribution shows great flexibility to fit data, with accurate reproduction of flow extremes. The performance analysis showed that, in general, the regional models are able to synthesize FDCs in ungauged basins, with a few possible drawbacks in the application of the method to intermittent and ephemeral rivers. In addition to the regional models, we summarize the experience of using synthetic FDCs for the indirect calibration of the Rio Grande rainfall–runoff model parameters in ungauged basins.

Editor D. Koutsoyiannis

Citation Costa, V., Fernandes, W., and Naghettini, M., 2013. Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model. Hydrological Sciences Journal, 59 (2), 262–277.     

Sensitivity and fuzzy uncertainty analyses in the determination of SCS-CN parameters from rainfall–runoff data

Spatial and seasonal variations of curve number (CN) and initial abstraction ratio (λ) in a watershed can result in inaccurate runoff volume estimations when using the US Natural Resources Conservation Service (SCS-CN) method with constant values for these parameters. In this paper, parameters of CN and λ are considered as calibration parameters and the sensitivity of estimated runoff to these parameters using the SCS-CN method is scrutinized. To incorporate the uncertainty associated with CN and λ, fuzzy linear regression (FLR) is applied to derive the relationships of CN and λ with rainfall depth (P) by employing a large dataset of storm events from four watersheds in Iran. Results indicate that the proposed approach provides more accuracy in estimation of runoff volume compared to the SCS method with constant values of CN and λ, and gives a straightforward technique for evaluating the hydrological effects of CN, λ, and P on runoff volume.     

A wavelet based approach for combining the outputs of different rainfall–runoff models

The rainfall–runoff modelling being a stochastic process in nature is dependent on various climatological variables and catchment characteristics and therefore numerous hydrological models have been developed to simulate this complex process. One approach to modelling this complex non-linear rainfall–runoff process is to combine the outputs of various models to get more accurate and reliable results. This multi-model combination approach relies on the fact that various models capture different features of the data, and hence combination of these features would yield better result. This study for the first time presented a novel wavelet based combination approach for estimating combined runoff The simulated daily output (Runoff) of five selected conventional rainfall–runoff models from seven different catchments located in different parts of the world was used in current study for estimating combined runoff for each time period. Five selected rainfall–runoff models used in this study included four data driven models, namely, the simple linear model, the linear perturbation model, the linearly varying variable gain factor model, the constrained linear systems with a single threshold and one conceptual model, namely, the soil moisture accounting and routing model. The multilayer perceptron neural network method was used to develop combined wavelet coupled models to evaluate the effect of wavelet transformation (WT). The performance of the developed wavelet coupled combination models was compared with their counterpart simple combination models developed without WT. It was concluded that the presented wavelet coupled combination approach outperformed the existing approaches of combining different models without applying input WT. The study also recommended that different models in a combination approach should be selected on the basis of their individual performance.     

Crossing the rural–urban boundary in hydrological modelling: How do conceptual rainfall–runoff models handle the specificities of urbanized catchments?

Landscape differences induced by urbanization have prompted hydrologists to define a fuzzy boundary between rural- and urban-specific hydrological models. We addressed the validity of establishing this boundary, by testing two rural models on a large sample of 175 French and United States (US) urbanized catchments, and their 175 rural neighbours. The impact of urbanization on the hydrological behaviour was checked using four metrics. Using a split-sample test, we have compared the performances, parameter distributions, and internal fluxes of GR4H and IHACRES, two conceptual and continuous models running at the hourly time step. Both model structures are based on soil moisture accounting reservoirs (infiltration, runoff, and actual evapotranspiration) and quick flow/slow flow routing components, with no consideration of any specific feature related to urbanization. Results showed: (a) Except for the ratio of streamflow flashiness to precipitation flashiness, the range of hydrological signature metrics in rural catchments encompassed the specificities of urbanized ones. Overall, the urbanized catchments showed higher ratios of mean streamflow to mean precipitation (median values: 0.39 vs. 0.27) and streamflow flashiness to precipitation flashiness (0.13 vs. 0.03), besides lower baseflow index (0.42 vs. 0.62) and shorter characteristic response time (3 vs. 14 hr). (b) The performances of GR4H revealed no significant distinction between rural and urbanized catchments in terms of Kling–Gupta Efficiency (KGE), whereas IHACRES better simulated urbanized catchments, especially during summer. (c) With respect to differences in urbanization level, the GR4H and IHACRES parameters showed different distributions. The differences in parameters were consistent with the differences in hydrological behaviour, which is promising for a model-based assessment of the impact of urbanization. (d) The models agreed less in reproducing the internal fluxes over the urbanized catchments than over the rural ones. These results demonstrate the flexibility of conceptual models to handle the specificities of urbanized catchments.     

Contribution to hydrological modelling of small Amazonian catchments: application of rainfall–runoff models to simulate flow duration curves

Abstract

The objective of this study is to analyse three rainfall–runoff hydrological models applied in two small catchments in the Amazon region to simulate flow duration curves (FDCs). The simple linear model (SLM) considers the rainfall–runoff process as an input–output time-invariant system. However, the rainfall–runoff process is nonlinear; thus, a modification is applied to the SLM based on the residual relationship between the simulated and observed discharges, generating the modified linear model (MLM). In the third model (SVM), the nonlinearity due to infiltration and evapotranspiration is incorporated into the system through the sigmoid variable gain factor. The performance criteria adopted were a distance metric (δ) and the Nash-Sutcliffe coefficient (R²) determined between simulated and observed flows. The good results of the models, mainly the MLM and SVM, showed that they could be applied to simulate FDCs in small catchments in the Amazon region.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Blanco, C.J.C., Santos, S.S.M., Quintas, M.C., Vinagre, M.V.A., and Mesquita, A.L.A., 2013. Contribution to hydrological modelling of small Amazonian catchments: application of rainfall–runoff models to simulate flow duration curves. Hydrological Sciences Journal, 58 (7), 1–11.     

On the importance of soil moisture in calibration of rainfall–runoff models: two case studies

Streamflow modelling results from the GR4H and PDM hydrological models were evaluated in two Australian sub-catchments, using (1) calibration to streamflow and (2) joint-calibration to streamflow and soil moisture. Soil moisture storage in the models was evaluated against soil moisture observations from field measurements. The PDM had the best performance in terms of both streamflow and soil moisture estimations during the calibration period, but was outperformed by GR4H during validation. It was also shown that the soil moisture estimation was improved significantly by joint-calibration for the case where streamflow and soil moisture estimations were poor. In other cases, addition of the soil moisture constraint did not degrade the results. Consequently, it is recommended that GR4H be used, in preference to the PDM, in the foothills of the Murrumbidgee catchment or other Australian catchments with semi-arid to sub-humid climate, and that soil moisture data be used in the calibration process.     

Prediction and modelling of rainfall–runoff during typhoon events using a physically-based and artificial neural network hybrid model

Abstract

The accurate prediction of hourly runoff discharge in a watershed during heavy rainfall events is of critical importance for flood control and management. This study predicts n-h-ahead runoff discharge in the Sandimen basin in southern Taiwan using a novel hybrid approach which combines a physically-based model (HEC-HMS) with an artificial neural network (ANN) model. Hourly runoff discharge data (1200 datasets) from seven heavy rainfall events were collected for the model calibration (training) and validation. Six statistical indicators (i.e. mean absolute error, root mean square error, coefficient of correlation, error of time to peak discharge, error of peak discharge and coefficient of efficiency) were employed to evaluate the performance. In comparison with the HEC-HMS model, the single ANN model, and the time series forecasting (ARMAX) model, the developed hybrid HEC-HMS–ANN model demonstrates improved accuracy in recursive n-h-ahead runoff discharge prediction, especially for peak flow discharge and time.     

From rainfall to spring discharge: Coupling conduit flow,subsurface matrix flow and surface flow in karst systems using a discrete–continuum model

Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples.     

Comparison of two rainfall–runoff models: effects of conceptualization on water budget components

Rainfall–runoff models with different conceptual structures for the hydrological processes can be calibrated to effectively reproduce the hydrographs of the total runoff, while resulting in water budget components that are essentially different. This finding poses an open question on the reliability of rainfall–runoff models in reproducing hydrological components other than those used for calibration. In an effort to address this question, we use data from the Glafkos catchment in western Greece to calibrate and compare the ENNS model, a research-oriented lumped model developed for the river Enns in Austria developed for the river Enns in Austria, with the operational MIKE SHE model. Model performance is assessed in the light of the conceptual/structural differences of the modelled hydrological processes, using indices calculated independently for each year, rather than for the whole calibration period, since the former are stricter. We show that even small differences in the representation of hydrological processes may impact considerably on the water budget components that are not measured (i.e. not used for model calibration). From all water budget components, direct runoff exhibits the highest sensitivity to structural differences and related model parameters.

EDITOR M.C. Acreman

ASSOCIATE EDITOR S. Huang     

Quantifying uncertainty in rainfall–runoff models due to design losses using Monte Carlo simulation: a case study in New South Wales,Australia

With the potentially devastating consequences of flooding, it is crucial that uncertainties in the modelling process are quantified in flood simulations. In this paper, the impact of uncertainties in design losses on peak flow estimates is investigated. Simulations were carried out using a conceptual rainfall–runoff model called RORB in four catchments along the east coast of New South Wales, Australia. Monte Carlo simulation was used to evaluate parameter uncertainty in design losses, associated with three loss models (initial loss–continuing loss, initial loss–proportional loss and soil water balance model). The results show that the uncertainty originating from each loss model differs and can be quite significant in some cases. The uncertainty in the initial loss–proportional loss model was found to be the highest, with estimates up to 2.2 times the peak flow, whilst the uncertainty in the soil water balance model was significantly less, with up to 60 % variability in peak flows for an annual exceedance probability of 0.02. Through applying Monte Carlo simulation a better understanding of the predicted flows is achieved, thus providing further support for planning and managing river systems.