Rainfall‐runoff modelling using artificial neural networks technique: a Blue Nile catchment case study

A rainfall‐runoff model based on an artificial neural network (ANN) is presented for the Blue Nile catchment. The best geometry of the ANN rainfall‐runoff model in terms of number of hidden layers and nodes is identified through a sensitivity analysis. The Blue Nile catchment (about 300 000 km²) in the Nile basin is selected here as a case study. The catchment is classified into seven subcatchments, and the mean areal precipitation over those subcatchments is computed as a main input to the ANN model. The available daily data (1992–99) are divided into two sets for model calibration (1992–96) and for validation (1997–99). The results of the ANN model are compared with one of physical distributed rainfall‐runoff models that apply hydraulic and hydrologic fundamental equations in a grid base. The results over the case study area and the comparative analysis with the physically based distributed model show that the ANN technique has great potential in simulating the rainfall‐runoff process adequately. Because the available record used in the calibration of the ANN model is too short, the ANN model is biased compared with the distributed model, especially for high flows. Copyright © 2005 John Wiley & Sons, Ltd.     

Hydrological behaviour of a drained agricultural peat catchment in the tropics. 2: Time series transfer function modelling approach

Abstract

Transfer function models of the rainfall–runoff relationship with various complexities are developed to investigate the hydrological behaviour of a tropical peat catchment that has undergone continuous drainage for a long time. The study reveals that a linear transfer function model of order one and noise term of ARIMA (1,0,0) best represents the monthly rainfall–runoff relationship of a drained peat catchment. The best-fitted transfer function model is capable of illustrating the cumulative hydrological effects of the catchment when subjected to drainage. Transfer function models of daily rainfall–runoff relationships for each year of the period 1983–1993 are also developed to decipher the changes in hydrological behaviour of the catchment due to drainage. The results show that the amount of rain water temporarily stored in the peat soil decreased and the catchment has become more responsive to rainfall over the study period.

Editor Z.W. Kundzewicz; Associate editor D. Hughes

Citation Katimon, A., Shahid, S., Abd Wahab, A.K., and Shabri, A., 2013. Hydrological behaviour of a drained agricultural peat catchment in the tropics. 2: Time series transfer function modelling approach. Hydrological Sciences Journal, 58 (6), 1310–1325.     

A Bayesian hierarchical spatio-temporal model for extreme rainfall in Extremadura (Spain)

A statistical study was made of the temporal trend in extreme rainfall in the region of Extremadura (Spain) during the period 1961–2009. A hierarchical spatio-temporal Bayesian model with a GEV parameterization of the extreme data was employed. The Bayesian model was implemented in a Markov chain Monte Carlo framework that allows the posterior distribution of the parameters that intervene in the model to be estimated. The results show a decrease of extreme rainfall in winter and spring and a slight increase in autumn. The uncertainty in the trend parameters obtained with the hierarchical approach is much smaller than the uncertainties obtained from the GEV model applied locally. Also found was a negative relationship between the NAO index and the extreme rainfall in Extremadura during winter. An increase was observed in the intensity of the NAO index in winter and spring, and a slight decrease in autumn.     

The effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment

Several rainfall measurement techniques are available for hydrological applications, each with its own spatial and temporal resolution and errors. When using these rainfall datasets as input for hydrological models, their errors and uncertainties propagate through the hydrological system. The aim of this study is to investigate the effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment, the 6.5‐km² Hupsel Brook experimental catchment. We used five distinct rainfall data sources: two automatic raingauges (one in the catchment and another one 30 km away), operational (real‐time and unadjusted) and gauge‐adjusted ground‐based C‐band weather radar datasets and finally a novel source of rainfall information for hydrological purposes, namely, microwave link data from a cellular telecommunication network. We used these data as input for the, a recently developed rainfall‐runoff model for lowland catchments, and intercompared the five simulated discharges time series and groundwater time series for a heavy rainfall event and a full year. Three types of rainfall errors were found to play an important role in the hydrological simulations, namely: (1) Biases, found in the unadjusted radar dataset, are amplified when propagated through the hydrological system; (2) Timing errors, found in the nearest automatic raingauge outside the catchment, are attenuated when propagated through the hydrological system; (3) Seasonally varying errors, found in the microwave link data, affect the dynamics of the simulated catchment water balance. We conclude that the hydrological potential of novel rainfall observation techniques should be assessed over a long period, preferably a full year or longer, rather than on an event basis, as is often done. Copyright © 2016 The Authors. Hydrological Processes. Published by John Wiley & Sons Ltd.     

Brixenbach research catchment: Quantification of runoff process proportions in a small Alpine catchment depending on soil moisture states and precipitation characteristics

The Brixenbach valley is a small Alpine torrent catchment (9.2 km², 820–1950 m a.s.l., 47.45°, 12.26°) in Tyrol, Austria. Intensive hydrological research in the catchment since more than 12 years, including a hydrogeological survey, pedological and land use mapping, measurements of precipitation, runoff, soil moisture and infiltration as well as the conduction of rainfall simulations, has contributed to understand the hydrological response of the catchment, its subcatchments and specific sites. The paper presents a synthesis of the research in form of runoff process maps for different soil moisture states and precipitation characteristics, derived with the aid of a newly developed Soil-hydrological model. These maps clearly visualize the differing runoff reaction of different subcatchments. The pasture dominated areas produce high surface flow rates during short precipitation events (1 h, 86 mm) with high rainfall intensity, whilst the forested areas often develop shallow subsurface flow. Dry preconditions lead to a slight reduction of surface flow, long rainfall events (24 h, 170 mm) to a dominance of deep subsurface flow and percolation.     

Emergence of non-extensive seismic magnitude-frequency distribution from a Bayesian framework

Non-extensive statistical mechanics has been used in recent years as a framework in order to build some seismic frequency-magnitude models. Following a Bayesian procedure through a process of marginalization, it is shown that some of these models can arise from the result shown here, which reinforces the relevance of the non-extensive distributions to explain the data (earthquake’s magnitude) observed during the seismic manifestation. In addition, it makes possible to extend the non-extensive family of distributions, which could explain cases that, eventually, could not be covered by the currently known distributions within this framework. The model obtained was applied to six data samples, corresponding to the frequency-magnitude distributions observed before and after the three strongest earthquakes registered in Chile during the late millennium. In all cases, fit parameters show a strong trend to a particular non-extensive model widely known in literature.     

Bayesian stochastic modelling for avalanche predetermination: from a general system framework to return period computations

Stochastic models are recent but unavoidable tools for snow avalanche hazard mapping that can be described in a general system framework. For the computation of design return periods, magnitude and frequency have to be evaluated. The magnitude model consists of a set of physical equations for avalanche propagation associated with a statistical formalism adapted to the input–output data structure. The friction law includes at least one latent friction coefficient. The Bayesian paradigm and the associated simulation techniques assist considerably in performing the inference and taking estimation errors into account for prediction. Starting from the general case, simplifying hypotheses allows computing the predictive distribution of high return periods on a case-study. Only release and runout altitudes are considered so that the model can use the French database. An inversible propagation model makes it possible to work with the latent friction coefficient as if it is observed. Prior knowledge is borrowed from an avalanche path with similar topographical characteristics. Justifications for the working hypotheses and further developments are discussed. In particular, the whole approach is positioned with respect to both deterministic and stochastic hydrology.     

Distributed rainfall‐runoff modelling for flood frequency estimation and flood forecasting

Nowadays, in the scientific literature many rainfall‐runoff (RR) models are available ranging from simpler ones, with a limited number of parameters, to highly complex ones, with many parameters. Therefore, the selection of the best structure and parameterisation for a model is not straightforward as it is dependent on a number of factors: climatic conditions, catchment characteristics, temporal and spatial resolution, model objectives, etc. In this study, the structure of a continuous semi‐distributed RR model, named MISDc (‘Modello Idrologico Semi‐Distribuito in continuo’) developed for flood simulation in the Upper Tiber River (central Italy) is presented. Most notably, the methodology employed to detect the more relevant processes involved in the modelling of high floods, and hence, to build the model structure and its parameters, is developed. For this purpose, an intense activity of monitoring soil moisture and runoff in experimental catchments was carried out allowing to derive a parsimonious and reliable continuous RR model operating at an hourly (or smaller) time scale. Specifically, in order to determine the catchment hydrological response, the important role of the antecedent wetness conditions is emphasized. The application of MISDc both for design flood estimation and for flood forecasting is reported here demonstrating its reliability and also its computational efficiency, another important factor in hydrological practice. As far as the flood forecasting applications are concerned, only the accuracy of the model in reproducing discharge hydrographs by assuming rainfall correctly known throughout the event is investigated indepth. In particular, the MISDc has been implemented in the framework of Civil Protection activities for the Upper Tiber River basin. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessment of rainfall spatial variability and its influence on runoff modelling: A case study in the Brue catchment,UK

This study explores rainfall spatial variability and its influence on runoff modelling. A novel assessment scheme integrated with coefficient of variance and Moran's I is introduced to describe effective rainfall spatial variability. Coefficient of variance is widely accepted to identify rainfall variability through rainfall intensity, whereas Moran's I reflects rainfall spatial autocorrelation. This new assessment framework combines these two indicators to assess the spatial variability derived from both rainfall intensity and distribution, which are crucial in determining the time and magnitude of runoff generation. Four model structures embedded in the Variable Infiltration Capacity model are adopted for hydrological modelling in the Brue catchment of England. The models are assigned with 1, 3, 8, and 27 hydrological response units, respectively, and diverse rainfall spatial information for 236 events are extracted from 1995. This study investigates the model performance of different partitioning based on rainfall spatial variability through peak volume (Q_p) and time to peak (T_p), along with the rainfall event process. The results show that models associated with dense spatial partitioning are broadly capable of capturing more spatial information with better performance. It is unnecessary to utilize models with high spatial density for simple rainfall events, though they show distinct advantages on complex events. With additional spatial information, Q_p experiences a notable improvement over T_p. Moreover, seasonal patterns signified by the assessment scheme imply the feasibility of seasonal models.     

Testing a spatially distributed tracer‐aided runoff model in a snow‐influenced catchment: Effects of multicriteria calibration on streamwater ages

Integrating stable isotope tracers into rainfall‐runoff models allows investigation of water partitioning and direct estimation of travel times and water ages. Tracer data have valuable information content that can be used to constrain models and, in integration with hydrometric observations, test the conceptualization of catchment processes in model structure and parameterization. There is great potential in using tracer‐aided modelling in snow‐influenced catchments to improve understanding of these catchments' dynamics and sensitivity to environmental change. We used the spatially distributed tracer‐aided rainfall‐runoff (STARR) model to simulate the interactions between water storage, flux, and isotope dynamics in a snow‐influenced, long‐term monitored catchment in Ontario, Canada. Multiple realizations of the model were achieved using a combination of single and multiple objectives as calibration targets. Although good simulations of hydrometric targets such as discharge and snow water equivalent could be achieved by local calibration alone, adequate capture of the stream isotope dynamics was predicated on the inclusion of isotope data in the calibration. Parameter sensitivity was highest, and most local, for single calibration targets. With multiple calibration targets, key sensitive parameters were still identifiable in snow and runoff generation routines. Water ages derived from flux tracking subroutines in the model indicated a catchment where runoff is dominated by younger waters, particularly during spring snowmelt. However, resulting water ages were most sensitive to the partitioning of runoff sources from soil and groundwater sources, which was most realistically achieved when isotopes were included in the calibration. Given the paucity of studies where hydrological models explicitly incorporate tracers in snow‐influenced regions, this study using STARR is an important contribution to satisfactorily simulating snowpack dynamics and runoff generation processes, while simultaneously capturing stable isotope variability in snow‐influenced catchments.     

Spatial and temporal variability of the hydrological response in a small Mediterranean research catchment (Vallcebre,Eastern Pyrenees)

This paper analyses the spatial and temporal variability of the hydrological response in a small Mediterranean catchment (Cal Rodó). The first part of the analysis focuses on the rainfall–runoff relationship at seasonal and monthly scale, using an 8‐year data set. Then, using storm‐flow volume and coefficient, the temporal variability of the rainfall–runoff relationship and its relationship with several hydrological variables are analysed at the event scale from hydrographs observed over a 3‐year period. Finally, the spatial non‐linearity of the hydrological response is examined by comparing the Cal Rodó hydrological response with the Can Vila sub‐catchment response at the event scale. Results show that, on a seasonal and monthly scale, there is no simple relationship between rainfall and runoff depths, and that evapotranspiration is a factor that introduced some non‐linearity in the rainfall–runoff relationship. The analysis of monthly values also reveals the existence of a threshold in the relationship between rainfall and runoff depths, denoting a more contrasted hydrological response than the one usually observed in humid catchments. At the event scale, the storm‐flow coefficient has a clear seasonal pattern with an alternance between a wet period, when the catchment is hydrologically responsive, and a dry summer period, when the catchment is much less reactive to any rainfall. The relationship between the storm‐flow coefficient and rainfall depth, rainfall maximum intensity and base‐flow shows that observed correlations are the same as those observed for humid conditions, even if correlation coefficients are notably lower. Comparison with the Can Vila sub‐catchment highlights the spatial heterogeneity of the rainfall‐runoff relationship at the small catchment scale. Although interpretation in terms of runoff processes remains delicate, heterogeneities between the two catchments seem to be related to changes in the ratio between infiltration excess and saturation processes in runoff formation. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of the catchment runoff coefficient on the performance of TOPMODEL in rainfall–runoff modelling

Effects of the catchment runoff coefficient on the performance of TOPMODEL in simulating catchment rainfall–runoff relationships are investigated in this paper, with an aim to improve TOPMODEL's simulation efficiency in catchments with a low runoff coefficient. Application of TOPMODEL in the semi‐arid Yihe catchment, with an area of 2623 km² in the Yellow River basin of China, produced a Nash–Sutcliffe model efficiency of about 80%. To investigate how the catchment runoff coefficient affects the performance of TOPMODEL, the whole observed discharge series of the Yihe catchment is multiplied with a larger‐than‐unity scale factor to obtain an amplified discharge series. Then TOPMODEL is used to simulate the amplified discharge series given the original rainfall and evaporation data. For a set of different scale factors, TOPMODEL efficiency is plotted against the corresponding catchment runoff coefficient and it is found that the efficiency of TOPMODEL increases with the increasing catchment runoff coefficient before reaching a peak (e.g. about 90%); after the peak, however, the efficiency of TOPMODEL decreases with the increasing catchment runoff coefficient. Based on this finding, an approach called the discharge amplification method is proposed to enhance the simulation efficiency of TOPMODEL in rainfall–runoff modelling in catchments with a low runoff coefficient. Copyright © 2004 John Wiley & Sons, Ltd.     

Field investigation and modelling of coupled stream discharge and shallow water‐table dynamics in a small Mediterranean catchment (Sardinia)

In the semi‐arid Mediterranean environment, the rainfall–runoff relationships are complex because of the markedly irregular patterns in rainfall, the seasonal mismatch between evaporation and rainfall, and the spatial heterogeneity in landscape properties. Watersheds often display considerable non‐linear threshold behavior, which still make runoff generation an open research question. Our objectives in this context were: to identify the primary processes of runoff generation in a small natural catchment; to test whether a physically based model, which takes into consideration only the primary processes, is able to predict spatially distributed water‐table and stream discharge dynamics; and to use the hydrological model to increase our understanding of runoff generation mechanisms. The observed seasonal dynamics of soil moisture, water‐table depth, and stream discharge indicated that Hortonian overland‐flow was negligible and the main mechanism of runoff generation was saturated subsurface‐flow. This gives rise to base‐flow, controls the formation of the saturated areas, and contributes to storm‐flow together with saturation overland‐flow. The distributed model, with a 1D scheme for the kinematic surface‐flow, a 2D sub‐horizontal scheme for the saturated subsurface‐flow, and ignoring the unsaturated flow, performed efficiently in years when runoff volume was high and medium, although there was a smoothing effect on the observed water‐table. In dry years, small errors greatly reduced the efficiency of the model. The hydrological model has allowed to relate the runoff generation mechanisms with the land‐use. The forested hillslopes, where the calibrated soil conductivity was high, were never saturated, except at the foot of the slopes, where exfiltration of saturated subsurface‐flow contributed to storm‐flow. Saturation overland‐flow was only found near the streams, except when there were storm‐flow peaks, when it also occurred on hillslopes used for pasture, where soil conductivity was low. The bedrock–soil percolation, simulated by a threshold mechanism, further increased the non‐linearity of the rainfall–runoff processes. Copyright © 2013 John Wiley & Sons, Ltd.     

Incremental distributed modelling investigation in a small agricultural catchment: 2. Erosion and phosphorus transport

Distributed physically based erosion and phosphorus (P) transport models, run by the overland flow model described in Taskinen and Bruen (2006. Hydrological Processes 20 : this issue), are described. In the erosion model, the additional components to the basic model were the outflow of the particles by infiltration and a new model component, i.e. deposition when rainfall stops. Two ways of calculating the shielding factor due to the flow depth were compared. The P transport model had both dissolved P (DP) and particulate P (PP) components. The processes included in the DP model were desorption from the soil surface, advection, storage in the overland flow and infiltration. The PP model accounted for advection, storage in the flow, infiltration, detachment from the soil surface by flow and rainfall and deposition both when transport capacity of suspended solids (SS) is exceeded and when rainfall ceases. When the models were developed and validated in small agricultural fields of cohesive soil types in southern Finland, comparisons were made between corresponding processes and the significance of added components were estimated in order to find out whether increased model complexity improves the model performance. The sedigraphs were found to follow the dynamics of rainfall, emphasizing the importance of the rainfall splash component. The basic model was too slow to react to changes in rainfall and flow rates, but infiltration and deposition that acts during the cessation in rainfall improved the model significantly by enabling the modelled SS to fall sharply enough. The shielding effect of flow depth from the splash detachment was found to play a significant role. Transport capacity should also be included in erosion models when they are applied to cohesive soils. In this study, the Yalin method worked well. A strong correlation was obvious between the measured SS and total P concentrations, indicating that the main form of P in runoff is PP. This emphasizes the importance of a good sediment transport model in P transport modelling. The submodel used for DP desorption from the soil surface produced plausible results without any calibration. Copyright © 2006 John Wiley & Sons, Ltd.     

Rainfall‐runoff modelling using artificial neural networks: comparison of network types

Growing interest in the use of artificial neural networks (ANNs) in rainfall‐runoff modelling has suggested certain issues that are still not addressed properly. One such concern is the use of network type, as theoretical studies on a multi‐layer perceptron (MLP) with a sigmoid transfer function enlightens certain limitations for its use. Alternatively, there is a strong belief in the general ANN user community that a radial basis function (RBF) network performs better than an MLP, as the former bases its nonlinearities on the training data set. This argument is not yet substantiated by applications in hydrology. This paper presents a comprehensive evaluation of the performance of MLP‐ and RBF‐type neural network models developed for rainfall‐runoff modelling of two Indian river basins. The performance of both the MLP and RBF network models were comprehensively evaluated in terms of their generalization properties, predicted hydrograph characteristics, and predictive uncertainty. The results of the study indicate that the choice of the network type certainly has an impact on the model prediction accuracy. The study suggests that both the networks have merits and limitations. For instance, the MLP requires a long trial‐and‐error procedure to fix the optimal number of hidden nodes, whereas for an RBF the structure of the network can be fixed using an appropriate training algorithm. However, a judgment on which is superior is not clearly possible from this study. Copyright © 2004 John Wiley & Sons, Ltd.     

Multi-hydro hydrological modelling of a complex peri-urban catchment with storage basins comparing C-band and X-band radar rainfall data

ABSTRACT

The spread of impervious surfaces in urban areas combined with the rise in the intensity of rainfall events as a result of climate change has led to dangerous increases in storm water flows. This paper discusses a new implementation of the fully distributed hydrological model Multi-Hydro (developed at École des Ponts ParisTech), when operating storage basins, and its ability to deal with high-resolution radar rainfall data. The peri-urban area of Massy (south of Paris, France) was selected as a case study for having six of these drainage facilities, used extensively in flood control. Two radar rainfall datasets with different spatiotemporal resolutions were used: Météo-France’s PANTHER rainfall product (C-band) and ENPC’s X-band DPSRI. The rainfall spatiotemporal variability was analysed statistically using Universal Multifractals (UM). Finally, to validate the application, the water level simulations were compared with local measurements in the Cora storage basin located next to the catchment’s single outlet.     

Bayesian dynamic modelling for nonstationary hydroclimatic time series forecasting along with uncertainty quantification

Forecasting of hydrologic time series, with the quantification of uncertainty, is an important tool for adaptive water resources management. Nonstationarity, caused by climate forcing and other factors, such as change in physical properties of catchment (urbanization, vegetation change, etc.), makes the forecasting task too difficult to model by traditional Box–Jenkins approaches. In this paper, the potential of the Bayesian dynamic modelling approach is investigated through an application to forecast a nonstationary hydroclimatic time series using relevant climate index information. The target is the time series of the volume of Devil's Lake, located in North Dakota, USA, for which it was proved difficult to forecast and quantify the associated uncertainty by traditional methods. Two different Bayesian dynamic modelling approaches are discussed, namely, a constant model and a dynamic regression model (DRM). The constant model uses the information of past observed values of the same time series, whereas the DRM utilizes the information from a causal time series as an exogenous input. Noting that the North Atlantic Oscillation (NAO) index appears to co‐vary with the time series of Devil's Lake annual volume, its use as an exogenous predictor is explored in the case study. The results of both the Bayesian dynamic models are compared with those from the traditional Box–Jenkins time series modelling approach. Although, in this particular case study, it is observed that the DRM performs marginally better than traditional models, the major strength of Bayesian dynamic models lies in the quantification of prediction uncertainty, which is of great value in hydrology, particularly under the recent climate change scenario. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Rainfall estimation using raingages and radar — A Bayesian approach: 2. An application

In Seo and Smith (this issue), a set of estimators was built in a Bayesian framework to estimate rainfall depth at an ungaged location using raingage measurements and radar rainfall data. The estimators are equivalent to lognormal co-kriging (simple co-kriging in the Gaussian domain) with uncertain mean and variance of gage rainfall. In this paper, the estimators are evaluated via cross-validation using hourly radar rainfall data and simulated hourly raingage data. Generation of raingage data is based on sample statistics of actual raingage measurements and radar rainfall data. The estimators are compared with lognormal co-kriging and nonparametric estimators. The Bayesian estimators are shown to provide some improvement over lognormal co-kriging under the criteria of mean error, root mean square error, and standardized mean square error. It is shown that, if the prior could be assessed more accurately, the margin of improvement in predicting estimation variance could be larger. In updating the uncertain mean and variance of gage rainfall, inclusion of radar rainfall data is seen to provide little improvement over using raingage data only.