Regionalization of unit hydrograph Parameters: 2. Uncertainty analysis

Hydrologic model parameters obtained from regional regression equations are subject to uncertainty. Consequently, hydrologic model outputs based on the stochastic parameters are random. This paper presents a systematic analysis of uncertainty associated with the two parameters, N and K, in Nash's IUH model from different regional regression equations. The uncertainty features associated with N and K are further incorporated to assess the uncertainty of the resulting IUH. Numerical results indicate that uncertainty of N and K from the regional regression equations are too significant to be ignored.     

Regionalization of unit hydrograph parameters: 1. Comparison of regression analysis techniques

Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.     

Regionalization of unit hydrograph parameters: 1. Comparison of regression analysis techniques

Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.     

Determination of unit hydrographs by multiple storm analysis

This paper discusses the derivation of a unit hydrograph by multiple storm analysis using least squares methods. Variations of least squares method was generalized using the framework of weighted ridge analysis. The paper also shows two theorems to support using multi-storm analysis to derive UH. In addition, an issue was addressed on the scaling effect in the conventional multi-storm analysis which could create potential bias toward large storms in deriving a multi-storm UH. For that, a simple scaling procedure was proposed to reduce such potential bias problem. Numerical investigations were conducted to examine the performance of the scaling procedure by comparing with the conventional multi-storm analysis (without scaling) and the HEC-1 weighing procedures. Based on various performance criteria using a total of 39 storms from three watersheds, the proposed scaling procedure was found to produce a quite desirable UH.     

Reliability analysis of hydraulic structures considering unit hydrograph uncertainty

Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.     

Reliability analysis of hydraulic structures considering unit hydrograph uncertainty

Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.     

Meixner functions for derivation of the unit hydrograph

The Meixner functions are utilized to relate the effective rainfall, the direct runoff and the unit hydrograph through linkage equations. The linkage equations are then employed to derive the unit hydrograph for given rainfall-runoff data on a small agricultural watershed. These functions are tested with regard to their ability to reproduce and predict the direct runoff hydrograph. The Meixner functions are found to be an effective analytical tool for hydrograph synthesis. Further, they compare well with the least squares and linear programming methods of the unit hydrograph derivation.     

Runoff estimation for an ungauged catchment using geomorphological instantaneous unit hydrograph (GIUH) models

A geomorphological instantaneous unit hydrograph (GIUH) is derived from the geomorphological characteristics of a catchment and it is related to the parameters of the Clark instantaneous unit hydrograph (IUH) model as well as the Nash IUH model for deriving its complete shape. The developed GIUH based Clark and Nash models are applied for simulation of the direct surface run‐off (DSRO) hydrographs for ten rainfall‐runoff events of the Ajay catchment up to the Sarath gauging site of eastern India. The geomorphological characteristics of the Ajay catchment are evaluated using the GIS package, Integrated Land and Water Information System (ILWIS). The performances of the GIUH based Clark and Nash models in simulating the DSRO hydrographs are compared with the Clark IUH model option of HEC‐1 package and the Nash IUH model, using some commonly used objective functions. The DSRO hydrographs are computed with reasonable accuracy by the GIUH based Clark and Nash models, which simulate the DSRO hydrographs of the catchment considering it to be ungauged. Inter comparison of the performances of the GIUH based Clark and Nash models shows that the DSRO hydrographs are estimated with comparable accuracy by both the models. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparative analysis of a geomorphology‐based instantaneous unit hydrograph in small mountainous watersheds

A conceptual insytnataneous unit hydrograph (IUH) based on geomorphologival association of linear reservoirs (GR) previously developed by the authors has been compared with other IUH models: a distributed GR variation (GR(v)), the Nash IUH, the Chutha and Dooge IUH, and the Troutman and Karlinger IUH for the analysis of direct runoff hydrographs recorded in three experimental watershed of the north of Spain. The comparison was made through a calibration‐validation process in which a leave‐one‐out cross‐validation method was applied. The results indicate the satisfactory performance of all the models, with the advantage for the GR model of the dependence on only one parameter, which can be identified from the watershed and event characteristics. This property makes its use easier than that of other models. Copyright © 2011 John Wiley & Sons, Ltd.     

Incremental distributed modelling investigation in a small agricultural catchment: 1. Overland flow with comparison with the unit hydrograph model

A distributed overland flow model is presented and the test results compared with those of the unit hydrograph (UH) model. Infiltration excess in the overland model was calculated using both a modified Green and Ampt (G–A) method and a more complicated method that keeps track of the soil moisture content. The two‐dimensional partial differential flow equations with kinematic flow approximation were solved using both backward‐central explicit and implicit finite‐difference schemes. Moreover, a baseflow component was added to the flow model. Each part of the model was built by replacing a process by a parallel process or by adding a completely new component. When the model was developed and validated in small agricultural fields 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. Apart from the basic model, all the other distributed models outperformed the UH approach. The implicit scheme was clearly more accurate than the explicit scheme, and the baseflow component improved the results significantly. There was no major difference between the performances of the infiltration models, but the G–A method was more stable and much faster. The approaches that were best in the calibration were also the best in the verification. The full distributed model provides a potential method for running water‐quality models and testing their different processes. Copyright © 2006 John Wiley & Sons, Ltd.     

Effects of subsurface drainage tiles on streamflow in Iowa agricultural watersheds: Exploratory hydrograph analysis

Flow from artificial subsurface (tile) drainage systems may be contributing to increasing baseflow in Midwestern rivers and increased losses of nitrate‐nitrogen. Standard hydrograph analysis techniques were applied to model simulation output and field monitoring from tile‐drained landscapes to explore how flow from drainage tiles affects stream baseflow and streamflow recession characteristics. DRAINMOD was used to simulate hydrologic response from drained (24 m tile spacing) and undrained agricultural systems. Hydrograph analysis was conducted using programs PART and RECESS. Field monitoring data were obtained from several monitoring sites in Iowa typical of heavily drained and less‐drained regions. Results indicate that flow from tile drainage primarily affects the baseflow portion of a hydrograph, increasing annual baseflow in streams with seasonal increases primarily occurring in the late spring and early summer months. Master recession curves from tile‐drained watersheds appear to be more linear than less‐tiled watersheds although comparative results of the recession index k were inconsistent. Considering the magnitude of non‐point source pollutant loads coming from tile‐drained landscapes, it is critical that more in‐depth research and analysis be done to assess the effects of tile drainage on watershed hydrology if water quality solutions are to be properly evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Determination of the unit hydrograph of a typical urban basin using genetic programming and artificial neural networks

An application of genetic programming (GP) and artificial neural networks (ANNs) in hydrology is proposed, showing how these two techniques can work together to solve the problem of modelling the effect of rain on the runoff flow in a typical urban basin. The ability of GP to include the physical basis of a problem and even to analyse the results is discussed, and a case study is included as an example. We propose a solution to this problem by using an ANN for the prediction of the daily flow due to human activity of the citizens and the use of GP for the prediction of the flow rate resulting from the rain. Finally, it is shown that the methodology can be used to solve similar problems by combining both techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimation of irrigation flow by hydrograph analysis in a complex agricultural catchment in subtropical China

Estimating the amount of irrigation water is challenging at the catchment scale because of the difficulties in direct measurement and interactions between the flow components. The objectives of the study were to characterize the catchment flows in an agricultural catchment with an irrigation system in subtropical China and to estimate catchment irrigation flow using hydrograph analysis methods. A weighting model and multiple regression models were established to estimate catchment irrigation outflow according to the hydrographs of the inflows and outflows of the catchment. The multiple regression models took into consideration the drainage time of base flow, resulting in better estimation on an event and annual basis. Using the MR‐6d method, the estimated irrigation outflows amounted to 3700 mm, 2600 mm and 2760 mm during 2001, 2002 and 2003 respectively, which covered 70%, 60% and 64% respectively of the total catchment outflows in the corresponding years. Copyright © 2007 John Wiley & Sons, Ltd.     

Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem

In this paper, we present the uncertainty analysis of the 2D electrical tomography inverse problem using model reduction and performing the sampling via an explorative member of the Particle Swarm Optimization family, called the Regressive‐Regressive Particle Swarm Optimization. The procedure begins with a local inversion to find a good resistivity model located in the nonlinear equivalence region of the set of plausible solutions. The dimension of this geophysical model is then reduced using spectral decomposition, and the uncertainty space is explored via Particle Swarm Optimization. Using this approach, we show that it is possible to sample the uncertainty space of the electrical tomography inverse problem. We illustrate this methodology with the application to a synthetic and a real dataset coming from a karstic geological set‐up. By computing the uncertainty of the inverse solution, it is possible to perform the segmentation of the resistivity images issued from inversion. This segmentation is based on the set of equivalent models that have been sampled, and makes it possible to answer geophysical questions in a probabilistic way, performing risk analysis.     

Reservoir rainfall‐runoff geomorphological model. II: analysis,calibration and validation

The model presented in the complementary document entitled, Reservoir rainfall‐runoff geomorphological model I: parameter application and analysis is analysed, calibrated and validated in this paper. The accuracy of simulated hydrographs is analysed by means of the efficiency defined by Nash and Sutcliffe. The sensitivity of the influence of five parameters on the behaviour of the model developed is analysed. Two different calibration and validation processes of Reservoir rainfall‐runoff geomorphological model are performed in Aixola watershed. Twelve events have been selected for calibrations and 25 for validations. With the first calibration and validation process, the model parameters are set by assigning the medians' values of the distributions obtained by means of the optimum results. The second process is performed by calibrating the most determinant parameter in the adjustment, which is the one that indicates the proportion of infiltrated water that is retained and does not flow; this is done with an empirical formulation depending on the event characteristics. Subsequently, the obtained results are validated. This last process has achieved very good adjustments in both calibrated and validated events. Copyright © 2012 John Wiley & Sons, Ltd.     

Reservoir rainfall–runoff geomorphological model. I: application and parameter analysis

This article describes and formulates a model designed to simulate runoff in wet weather events, called reservoir rainfall–runoff geomorphological model (R³GeM). In these wetlands, soil saturation is the main mechanism for the generation of surface runoff. To determine the saturated areas, the model applies a relationship based on the topographic index, between watershed storage and saturated surface. Precipitation is separated into surface runoff by saturation, subsurface runoff and losses; then, the flow of surface and subsurface runoff is performed. This hydrological model has five parameters and has been implemented in 37 events in Aixola watershed and 15 in Oiartzun watershed, both located on the Cantabrian coast of Spain. We analysed the influence of these five parameters in their behaviour, and we have proven, noting the efficiency gains, that the proposed model is valid to simulate the rainfall–runoff process. Copyright © 2012 John Wiley & Sons, Ltd.     

A review of the synthetic unit hydrograph: from the empirical UH to advanced geomorphological methods

Abstract

This review paper critically examines one of the most popular flood hydrograph modelling techniques for ungauged basins, the synthetic unit hydrograph (SUH), and its recent developments and advances. For this purpose, the SUH models were first grouped into four main classes, as follows: (a) traditional or empirical models; (b) conceptual models; (c) probabilistic models; and (d) geomorphological models. It was found that the geomorphological class is the most useful and interesting, since it is able to employ topographic information, so limiting the role of the calibration parameters. This review is expected to be helpful to hydrologists, water managers and decision-makers searching for models to study the flood hydrograph, modelling techniques and related processes in ungauged basins. It was completed as the International Association of Hydrological Sciences (IAHS) Decade (2003–2012) on predictions in ungauged basins (PUB), drew to a close.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Singh, P.K., Mishra, S.K., and Jain, M.K., 2013. A review of the Synthetic Unit Hydrograph: from the empirical UH to advanced geomorphological methods. Hydrological Sciences Journal, 59 (2), 239–261.     

Uncertainty analysis: one-dimensional radioactive nuclide transport in a single fractured media

Uncertainty analysis of radioactive nuclide transport for one-dimensional single fracture has been studied. First order differential analysis is applied to introduce analytical form of output expectation and variance for contaminant transport equation, by regarding uncertainty of dispersion coefficient and retardation factor. Breakthrough curve of dimensionless concentration is demonstrated by taking I-129 as radioactive nuclide in fracture transport. It is possible to pick up critical ranges in spatial and temporal domain from the output variance. From the viewpoint of preliminary performance assessment for nuclear waste disposal the parameter importance in such system can be substantially measured in the site characterization in future.     

Improved understanding of spatio‐temporal controls on regional scale groundwater flooding using hydrograph analysis and impulse response functions

Controls on the spatio‐temporal extent of groundwater flooding are poorly understood, despite the long duration of groundwater flood events and distinct social and economic impacts. We developed a novel approach using statistical analysis of groundwater level hydrographs and impulse response functions (IRFs) and applied it to the 2013/2014 Chalk groundwater flooding in the English Lowlands. We proposed a standardized index of groundwater flooding which we calculated for monthly groundwater levels for 26 boreholes in the Chalk. We grouped these standardized series using k‐means cluster analysis and cross‐correlated the cluster centroids with the Standardized Precipitation Index accumulated over time intervals between 1 and 60 months. This analysis reveals 2 spatially coherent groups of standardized hydrographs that responded to precipitation over different timescales. We estimated IRF models of the groundwater level response to effective precipitation for 3 boreholes in each group. The IRF models corroborate the Standardized Precipitation Index analysis showing different response functions between the groups. We applied identical effective precipitation inputs to each of the IRF models and observed differences between the hydrographs from each group. It is suggested this is due to the hydrogeological properties of the Chalk and of overlying relatively low permeability superficial deposits (recent unconsolidated sediments overlying the bedrock, such as clays and tills), which are extensive over 1 of the groups. The overarching controls on groundwater flood response are concluded to be a complex combination of antecedent conditions, rainfall, and catchment hydrogeological properties. These controls should be taken into consideration when anticipating and managing future groundwater flood events. The approach presented is generic and parsimonious and can be easily applied where sufficient groundwater level and rainfall data are available.