Application of a regionalized Clark IUH model with limited hydrologic data availability

To aid prediction of the flow hydrograph in a basin with limited data, a practical approach to determining a regionalized Clark instantaneous unit hydrograph (IUH) model is presented. The proposed model is described in terms of the synthetic time–area concentration curve, the concentration time, and a special regional similarity value that is valid in the whole basin. The latter was estimated from a Monte Carlo testing procedure based on the normal probability distribution of transformed regional similarity values composed of the time of concentration and the storage coefficient in gauged basins. The time–area concentration curve and the concentration time were calculated from a rational equation as in conventional methods. The method of transformation adopted was the Box–Cox power transformation, which is known to make non‐normal values resemble normal data. By introducing the regional similarity value into a Clark IUH, a statistically best estimate of IUH for given data conditions and its quantified degree of uncertainty were realized. The Wi River basin in Korea was used to test the applicability of the regionalized Clark IUH. The performance of the suggested methodology was evaluated by assuming an ungauged sub‐basin at the site. The results showed that the IUH model developed in this work was an effective tool, predicting a reliable hydrograph within the study area even though only limited data were available. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Models for recession flows in the upper Blue Nile River

Stream‐flow recessions are commonly characterized by the exponential equation or in the alternative power form equation of a single linear reservoir. The most common measure of recession is the recession constant K, which relates to the power function form of the recession equation for a linear reservoir. However, in reality it can be seen that the groundwater dynamics of even the simplest of aquifers may behave in a non‐linear fashion. In this study three different storage–outflow algorithms; single linear, non‐linear and multiple linear reservoir were considered to model the stream‐flow recession of the upper Blue Nile. The recession parameters for the linear and non‐linear models were derived by the use of least‐squares regression procedures. Whereas, for the multiple linear reservoir model, a second‐order autoregressive AR (2) model was applied first in order to determine the parameters by the least‐squares method. The modelling of the upper Blue Nile recession flow performed shortly after the wet season, when interflow and bank storage may be contributing considerably to the river flow, showed that the non‐linear reservoir model simulates well with the observed counterparts. The variation related to preceding flow on a recession parameter of the non‐linear reservoir remains significant, which was obtained by stratification of the recession curves. Although a similar stratification did not show any systematic variation on the recession parameters for the linear and multiple linear reservoir models. Copyright © 2004 John Wiley & Sons, Ltd.     

Application of the Kalman filter to the Nash model

The Nash model was used for application of the Kalman filter. The state vector of the rainfall–runoff system was constituted by the IUH (instantaneous unit hydrograph) estimated by the Nash model and the runoff estimated by the Nash model using the Kalman filter. The initial values of the state vector were assumed as the average of 10% of the IUH peak values and the initial runoff estimated from the average IUH. The Nash model using the Kalman filter with a recursive algorithm accurately predicted runoff from a basin in Korea. The filter allowed the IUH to vary in time, increased the accuracy of the Nash model and reduced physical uncertainty of the rainfall–runoff process in the river basin. © 1998 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.     

A novel predictor–corrector algorithm for sub‐structure pseudo‐dynamic testing

A new predictor–corrector (P–C) method for multi‐site sub‐structure pseudo‐dynamic (PSD) test is proposed. This method is a mixed time integration method in which computational components separable from experimental components are solved by implicit time integration method (Newmark β method). The experiments are performed quasi‐statically based on explicit prediction of displacement. The proposed P–C method has an important advantage as it does not require the determination of the initial stiffness values of experimental components and is thus suitable for representing elastic and inelastic systems. A parameter relating to quality of displacement prediction at boundaries nodes is introduced. This parameter is determined such that P–C method can be applicable to many practical problems. Error‐propagation characteristics of P–C method are also presented. A series of examples including linear and non‐linear soil–foundation–structure interaction problem demonstrate the performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.     

Book Review

Abstract

The instantaneous unit hydrograph (IUH) of a watershed is the result of one instantaneous unit of rainfall excess distributed uniformly over the watershed. Although the geomorphological characteristics of the basin remain relatively constant, the variable characteristics of storms cause variations in the shape of the resulting hydrographs. It is, therefore, inadequate to use one typical IUH to represent the hydrological response generated from any specific storm. In this study, a variable IUH was derived that directly reflects the time-varying rainfall intensity during storms. The rainfall intensity used to generate the variable IUH at time t is the mean rainfall intensity occurring from the time t—T _c to t in which T _c is the watershed time of concentration. Hydrological records from three watersheds in Taiwan were used to demonstrate the applicability of the proposed model. The results show that better simulations can be obtained by using the proposed model than by using the conventional unit hydrograph method, especially for concentrated rainstorm cases.     

Limitations on linear elastic procedures in performance assessment of regular frames

Linear elastic analysis procedures are employed exclusively in the traditional seismic design of new structures and widely employed in the seismic assessment of existing structures. It is also a convenient tool for the initial checking of deformations in displacement‐based design. The limitations that should be imposed on linear elastic procedures have been evaluated in this study by comparing the deformation‐based response quantities obtained from response spectrum analysis with those from the nonlinear time history analysis. Both procedures were applied to different design variants of 5, 8, and 12 story moment frames, subjected to 20 strong motion components exhibiting a variety of intensities. Member plastic rotations and interstory drift ratios were employed as the basic response parameter in performance assessment. It has been found that average column demand to capacity ratio (DCR) (the ratio of flexural demand from linear elastic analysis to flexural capacity) and average beam DCR at the critical story are the most effective parameters in determining the validity range of linear elastic procedures in regular moment frames. Limiting values for these response parameters are proposed. Furthermore, amplification factors for member rotation demands predicted by the linear procedures are suggested for moment frames when these limiting values are exceeded. These factors ensure that the amplified linear elastic rotations are not smaller than 84 percentile (mean – 1sigma) of the rotations obtained from nonlinear time history analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

A Best-Estimate Approach for Determining Self-potential Parameters Related to Simple Geometric Shaped Structures

A new approach is proposed in order to interpret field self-potential (SP) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on solving a set of algebraic linear equations, and directed towards the best estimate of the three model parameters, e.g., electric dipole moment, depth, and polarization angle. Its utility and validity are demonstrated through studying and analyzing synthetic self-potential anomalies obtained by using simulated data generated from a known model and a statistical distribution with different random errors components. Being theoretically tested and proven, this approach has been consequently applied on two real field self-potential anomalies taken from Colorado and Turkey. A comparable and acceptable agreement is obtained between the results derived by the new proposed method and those deduced by other interpretation methods. Moreover, the depth obtained by such an approach is found to be very close to that obtained by drilling information.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

Use of Nash's IUH and DEMs to identify the parameters of an unequal‐reservoir cascade IUH model

Under the assumption that hydrograph generation was affected by n linear reservoirs with the same value of storage coefficient k, Nash proposed the formulation of the Instantaneous Unit Hydrograph (IUH), which has been widely used in rainfall–runoff simulation and flood forecasting. However, the assumption of the parameter k having the same value in all reservoirs is obviously unphysical as it results in the estimated value of n not being integral. In this study, for parameter n integral, the different k value for each reservoir was derived using the Laplace transform and developing a general rule for the equation of the IUH of any order. The relationship between parameter k and the slope of the river channel estimated using digital elevation model (DEM) data is established, the parameter estimation procedures are given. As in most unit hydrograph studies, only isolated storm events are considered here. Seventeen flood events in three catchments were selected for the case studies. Application results show that the proposed method is slightly better than Nash's IUH with higher model efficiency and smaller absolute relative errors. This work provides a new methodology for the formulation of the IUH. Copyright © 2008 John Wiley & Sons, Ltd.     

How to construct recursive digital filters for baseflow separation

Recursive digital filtering of hydrographs is a baseflow separation method that can easily be automated and has been recommended for providing reproducible results. In the past, different formulations of the most simple filter type, the so‐called one‐parameter filter, have been proposed. In this paper, a theoretical framework is developed for filter algorithms that were constructed under the assumption that the outflow from an aquifer is linearly proportional to its storage. It is shown that these one‐parameter filters describing an exponential baseflow recession are all special cases of a two‐parameter filter whose equation is specified. Its parameters are the recession constant—which can be objectively determined by a recession analysis—and BFI_max, the maximum value of the baseflow index that can be modelled by the algorithm. This introduces a subjective element into the baseflow calculation, since BFI_max is not measurable. A preliminary analysis based on the results of conventional separation techniques shows that it might be possible to find typical BFI_max values for classes of catchments that can be unequivocally distinguished by their hydrological and hydrogeological characteristics. Copyright © 2004 John Wiley & Sons, Ltd.     

Regional variation of recession flow power‐law exponent

Recession flows of a basin provide valuable information about its storage–discharge relationship as during recession periods discharge occurs due to depletion of storage. Storage–discharge analysis is generally performed by plotting ?dQ/dt against Q , where Q is discharge at time t . For most real world catchments, ?dQ/dt versus Q show a power‐law relationship of the type: ?dQ/dt = kQ^α . Because the coefficient k varies across recession events significantly, the exponent α needs to be computed separately for individual recession events. The median α can then be considered as the representative α for the basin. The question that arises here is what are the basin characteristics that influence the value of α ? Studies based on a small number of basins (up to 50 basins) reveal that α has good relationship with several basin characteristics. However, whether such a relationship is universal remains an important question, because a universal relationship would allow prediction of the value of α for any ungauged basin. To test this hypothesis, here, we study data collected from a relatively large number of basins (358 basins) in USA and examine the influence of 35 different physio‐climatic characteristics on α . We divide the basins into 2 groups based on their longitudes and test the relationship between α and basin characteristics separately for the two groups. The results indicate that α is not identically influenced by different basin characteristics for the two datasets. This may suggest that the power‐law exponent α of a region is determined by the way local physio‐climatic forces have shaped the landscape.     

Application and evaluation of a snowmelt runoff model in the Tamor River basin,Eastern Himalaya using a Markov Chain Monte Carlo (MCMC) data assimilation approach

Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree‐day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash–Sutcliffe metric ~0.84, annual volume bias < 3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002–2006 period is estimated to be 29.7 ± 2.9% (which includes 4.2 ± 0.9% from snowfall that promptly melts), whereas 70.3 ± 2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000–5500 m range contributes the most to basin runoff, averaging 56.9 ± 3.6% of all snowmelt input and 28.9 ± 1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree‐day melting model. Lastly, we demonstrate that the data assimilation approach is useful for quantifying and reducing uncertainty related to model parameters and thus provides uncertainty bounds on snowmelt and rainfall contributions in such mountainous watersheds. Copyright © 2013 John Wiley & Sons, Ltd.     

Salinograph trends as indicators of the recession characteristics of stream components

Compared to hydrograph recession analysis, which is widely applied in engineering hydrology, the quantitative assessment of stream salinity with time (i.e. the salinograph) has received significantly less attention. In particular, while in many previous hydrological studies an inverse relationship between hydrograph and salinograph responses is apparent, the concept of salinity accession (the inversely related salinity counterpart to hydrograph recession) has not been introduced nor quantitatively evaluated in previous literature. In this study, we conduct a mathematical analysis of salinograph accession, and determine new quantitative relationships between salinity accession and hydrograph recession parameters. An equation is formulated that reproduces the general trend in salinity accession. A salinity accession parameter k_c is then introduced and is shown to be the ratio of direct runoff to total stream flow recession parameters: k_r/k. The groundwater recession parameter k_g was estimated using a simple and rapid method that uses both salinograph and hydrograph data. Salinity accession type‐curves illustrate that under certain conditions, the relative steepness of individual salinographs is dependent upon the ratio of groundwater salinity to direct runoff salinity: C_g/C_r. The salinity accession algorithms are applied to two contrasting field settings: Scott Creek, South Australia and Sandy Creek, northern Queensland, Australia. It was found that k_g > k during periods of obvious stream flow recession, for the events analysed. Salinograph accession behaviour was fairly similar for both sites, despite contrasting environments. Using assumed end‐member salinities for groundwater and direct runoff based upon field observations, the behaviour of k_c from the Scott Creek site was approximately reproduced by varying the initial groundwater to runoff flow ratio: Q_g0/Q_r0, within reasonable parameter ranges. The use of salinograph information when used in addition to standard hydrograph analyses provided useful information on recession characteristics of stream components. Copyright © 2008 John Wiley & Sons, Ltd.     

Study of dynamic behaviour of recession curves

Since Brutsaert and Neiber (1977), recession curves are widely used to analyse subsurface systems of river basins by expressing ? dQ/dt as a function of Q, which typically take a power law form: ? dQ/dt = kQ^α, where Q is the discharge at a basin outlet at time t. Traditionally recession flows are modelled by single reservoir models that assume a unique relationship between ? dQ/dt and Q for a basin. However, recent observations indicate that ? dQ/dt ‐ Q relationship of a basin varies greatly across recession events, indicating the limitation of such models. In this study, the dynamic relationship between ? dQ/dt and Q of a basin is investigated through the geomorphological recession flow model which models recession flows by considering the temporal evolution of its active drainage network (the part of the stream network of the basin draining water at time t). Two primary factors responsible for the dynamic relationship are identified: (i) degree of aquifer recharge (ii) spatial variation of rainfall. Degree of aquifer recharge, which is likely to be controlled by (effective) rainfall patterns, influences the power law coefficient, k. It is found that k has correlation with past average streamflow, which confirms the notion that dynamic ? dQ/dt ‐ Q relationship is caused by the degree of aquifer recharge. Spatial variation of rainfall is found to have control on both the exponent, α, and the power law coefficient, k. It is noticed that that even with same α and k, recession curves can be different, possibly due to their different (recession) peak values. This may also happen due to spatial variation of rainfall. Copyright © 2012 John Wiley & Sons, Ltd.     

Adsorption Kinetic Modeling of Safranin onto Rice Husk Biomatrix Using Pseudo‐first‐ and Pseudo‐second‐order Kinetic Models: Comparison of Linear and Non‐linear Methods

Batch kinetic studies were carried out for the removal of safranin from aqueous solution using a biomatrix prepared from rice husk. The adsorption kinetic data were modeled using the pseudo‐first‐order and pseudo‐second‐order kinetic equations. The linear and non‐linear forms of these two widely used kinetic models were compared in this study. In order to determine the best‐fitting equation, the coefficient of determination (r²), the sum of the squares of the errors (SSE), sum of the absolute errors (SAE), average relative error (ARE), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), and the Chi‐squared test (χ²) were used as error analysis methods. Results showed that the non‐linear forms of pseudo‐first‐order and pseudo‐second‐order models were more suitable than the linear forms for fitting the experimental data. Non‐linear method is thus more appropriate for estimating the kinetic parameters and should primarily be used to describe adsorption kinetics.     

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.