Journal of Hydrologic Engineering

Temperature index snowmelt models often require representation of a snowpack’s melt rate. Defining the melt rate as a function of an accumulated number of warming degree-days is achieved in some temperature index models through the antecedent temperature index–melt rate (ATIMR) function, and provides a reasonable method for adjusting the melt rate during the season. Modelers have typically relied on a default ATIMR function developed two decades ago. However, literature concerning the nature of this default function and how it was developed is largely nonexistent. This paper presents results of a comparison between the default ATIMR function and ATIMR functions computed from field data from two headwater stations within the American River watershed upstream of Folsom Lake, California. An error analysis was also performed using the site-specific data. Using the Hydrologic Engineering Center’s hydrologic modeling system (HEC-HMS), it was found that modeled results often varied dramatically between the default curve and the computed curves. In one case, modeled results showed significant improvement between the default method and that of the data-derived approach. This finding suggests that conventional use of the default 1991 curve, often employed in practice irrespective of season and/or location, should at the very least be reconsidered.

This study compares time series models for stream flow that use lagged rainfall as an exogenous variable with models that use a small subset of discrete wavelet coefficients of lagged rainfall with cross product and quadratic terms of the wavelet coefficients. The models require the calculation of a moving discrete wavelet transform (MDWT) that is implemented as a multiscale transform. A comparison is made using data from three catchments in the Murray Darling Basin in Australia. For finite impulse response models, the adjusted coefficient of determination, ($R_{\mathrm{adj}}^2$), increased with the MDWT from 0.36 to 0.46 for the Tooma River Basin (TRB), from 0.43 to 0.52 for the Jingellic Catchment (JC), and from 0.56 to 0.59 for the Ovens Catchment (OC). The autoregressive models with exogenous input (ARX) with the wavelet transform further improved these results. The MDWT is based on a Haar wavelet so the wavelet coefficients have a physical interpretation. Predictions are further improved by a two-stage prediction procedure, in which an improved prediction is found as a quadratic function of the original prediction.

Soil erosion can lead to an increase in the concentration of sediment in the runoff and the surplus floodwater during flood season, which increases the likelihood of a flood disaster. To analyze the relationship between the risk of soil erosion and the surplus floodwater during flood season, a case study of the Jinghe River Basin located in the middle Loess Plateau of China was performed. A measure of the soil erosion risk $R_e$ was presented, which combined the five factors in universal soil loss equation (USLE) with information entropy theory. The results show that the northern watershed features both high and severe levels of soil erosion risk, especially the watershed controlled by the Qingyang (QY) station, whereas the risk level is low or slight in the southern Jinghe basin, the Ziwuling Mountains in the east, and the Liupanshan Mountains in the west. Compared with the USLE, the $R_e$ measure can better reflect the spatial distribution of soil erosion risk and identify the areas corresponding to different soil erosion levels. Data for the sediment yield rate from 37 subbasins also prove the correctness of the $R_e$ measure. The results from a sensitivity analysis indicate that the same amount of factor variability led to a larger soil erosion risk increment in 1986, followed by those of 2000 and 1995. The magnitude of the influences of the $R$, $C$, $P$, and $LS$ factors on the soil erosion risk features a descending order of $R>C>P>LS$. The regression analysis reveals a statistically significant linear relationship between the coefficient of surplus floodwater and the level of soil erosion risk. The higher level of soil erosion risk can cause more surplus floodwater downstream when the sediment concentration is smaller than the limit of the sediment concentration for river water use. The limit also has important influences on the amount of surplus floodwater during flood season.

The purpose of this paper is to propose an effective optimization technique that can overcome the local minimum problem resulting from the nonlinear construction of the rainfall-runoff model. First, this technique attempts to approximate the nonlinear function by using a finite number of terms of linear functions, referred to as the linearization process. Then, these linear functions would be optimized by the sum of squared errors (MSSE). Finally, the optimized parameters of a nonlinear function using the step-iterative algorithm were obtained. Its features and capabilities are demonstrated by means of a binary function and a conceptual rainfall-runoff model (Xinanjiang model). To optimize the model parameters, 10 years of historical data in the Changzhao basin are applied, whereas the most recent three years are utilized to verify these parameters. With reference to the binary function, the proposed linearlized search technique (LST) converge quickly from any starting point. With regard to the hydrological conceptual model, the simulation results are as the same as those obtained by shuffled complex evolution (SCE-UA).

This paper presents the application of an improved particle swarm optimization (PSO) technique for training an artificial neural network (ANN) to predict water levels for the Heshui Watershed, China. Daily values of rainfall and water levels from 1988 to 2000 were first analyzed using ANNs trained with the conjugate gradient, gradient descent, and Levenberg-Marquardt neural network (LM-NN) algorithms. The best results were obtained from the LM-NN, and these results were then compared with those from PSO-based ANNs, including the conventional PSO neural network (CPSONN) and the improved PSO neural network (IPSONN) with passive congregation. The IPSONN algorithm improves PSO convergence by using the selfish herd concept in swarm behavior. The results show that the PSO-based ANNs performed better than the LM-NN. For models run using a single parameter (rainfall) as input, the root mean square error (RMSE) of the testing data set for IPSONN was the lowest (0.152 m) compared to those for CPSONN (0.161 m) and LM-NN (0.205 m). For multiparameter (rainfall and water level) inputs, the RMSE of the testing data set for IPSONN was also the lowest (0.089 m) compared to those for CPSONN (0.105 m) and LM-NN (0.145 m). The results also indicate that the LM-NN model performed poorly in predicting the low and peak water levels in comparison to the PSO-based ANNs. Moreover, the IPSONN model was superior to CPSONN in predicting extreme water levels. Lastly, IPSONN had a quicker convergence rate compared to CPSONN.

Objective selection and tradeoffs have always been key central issues in rainfall-runoff models. In general, precision for high and low flows cannot be achieved or considered concurrently. Combination forecasts are potentially capable of producing more suitable or superior results through appropriate methods. In this study, we propose an automatic method, a runoff-scale weighting method (RSWM), to solve issues regarding flow precision trade-offs. Objective functions that emphasize precision at various flows were used to conduct combination forecasts and validate the effectiveness of this method. The results indicated that combination forecasting is capable of improving precision during all flow stages to further enhance model effectiveness. In addition, we used the fuzzy multiobjective function simple-average (FMOF-SA) and fuzzy multiobjective function-low (FMOF-low) as reference flows to test the robustness of parameters to determine whether the RSWM is affected by reference flows. The results indicated that the FMOF-low is relatively more robust than the FMOF-SA, although both had only a slight influence on the final results. According to the final results, the mean absolute relative residual of most flow stages is approximately 0.2, which shows that the RSWM can be applied to various runoff conditions.

Using the entropy theory, this study derives a function for modeling the flow duration curve (FDC) based on two equations that form simple constraints: (1) the total probability of all flow discharges, and (2) the mean discharge. Parameters of the derived curve are determined from the entropy theory with the use of these two constraints. For deriving the flow duration curve by the entropy theory, a nonlinear cumulative distribution function is assumed, which is tested using observed flow data. The derived flow duration curves are tested using field data and are found to be in agreement with observed curves. With the entropy parameter determined for each station, the flow duration curve can also be forecasted for different recurrence intervals. The main advantage of the use of the entropy theory–based FDCs is that the parameters are based on observations, and hence no fitting is needed. Second, the theory permits a probabilistic characterization of the flow duration curve and hence the probability density function underlying the curve. It also permits a quantitative assessment of the uncertainty of the flow duration curve. Additional work is needed to regionalize the FDC parameters.

Flood hazard and arising risks due to associated vulnerabilities still appear to be among the common problems in today’s hydrology in spite of highly motivated assessments and increasing knowledge and awareness as well as targeted measures for mitigation, preparedness, and emergency management. Beside the role of overall inaction, deficiencies in precautionary actions and presence of natural barriers and inaccurate or incomplete approaches in flood studies towards estimating flood magnitudes and frequencies are also assumed to have considerable impacts on limited control against the flood phenomenon. Prevalent claims about the invalidity of the stationarity assumption in hydrologic studies indicate any ignorance of nonstationarity as potential sources of ineffective flood assessments and the associated improper actions. The presented study investigates potential impacts and relative significance of observed trends on the magnitude and frequency of floods through comparisons performed over stationary and nonstationary flood frequency analyses. Results indicate slightly significant discrepancies between the estimates from both the stationary and nonstationary analyses by potentially pointing out to the arising needs for considering the nonstationarity in flood studies.

The effect of length of streamflow records on truncation level (TL) and consequent drought characterization using streamflow data for a 50 year period at Banda (Ken river) and Nandghat (Seonath river) sites in India are studied. The study demonstrates the divergence in estimates of TL from different sets of data of various assessment lengths of duration and severity of independent streamflow drought events. TL for each 10-day (sum of 10 days streamflow volume) period during the year have been estimated as 75% of dependable flow value from corresponding flow duration curves prepared for datasets of various lengths and periods. A pooling procedure has been used to identify independent streamflow drought events. The study revealed that the estimation of TL using data covering fewer than 30 years shows considerable variations and may lead to biased estimates in TL values in the study basins. However, the estimates of TL derived from datasets covering 30 years or more are reasonably close to that of TL derived from 50 years of data, and the assessment for duration and severity of drought events are comparable. Therefore, data spanning 30 years or more should be used for realistic stream flow drought characterization.

Ten stochastic optimization methods—adaptive simulated annealing (ASA), covariance matrix adaptation evolution strategy (CMAES), cuckoo search (CS), dynamically dimensioned search (DDS), differential evolution (DE), genetic algorithm (GA), harmony search (HS), pattern search (PS), particle swarm optimization (PSO), and shuffled complex evolution–University of Arizona (SCE–UA)—were used to calibrate parameter sets for three hydrological models on 10 different basins. Optimization algorithm performance was compared for each of the available basin-model combinations. For each model-basin pair, 40 calibrations were run with the 10 algorithms. Results were tested for statistical significance using a multicomparison procedure based on Friedman and Kruskal-Wallis tests. A dispersion metric was used to evaluate the fitness landscape underlying the structure on each test case. The trials revealed that the dimensionality and general fitness landscape characteristics of the model calibration problem are important when considering the use of an automatic optimization method. The ASA, CMAES, and DDS algorithms were either as good as or better than the other methods for finding the lowest minimum, with ASA being consistently among the best. The SCE–UA method performs better when the model complexity is reduced, whereas the opposite is true for DDS. Convergence speed was also studied, and the same three methods (CMAES, DDS, and ASA) were shown to converge faster than the other methods. The SCE–UA method converged nearly as fast as the best methods when the model with the smallest parameter space was used but was not as worthy in the higher-dimension parameter space of the other models. Convergence speed has little impact on algorithm efficiency. The methods offering the worst performance were DE, CS, GA, HS, and PSO, although they did manage to find good local minima in some trials. However, the other available methods generally outperformed these algorithms.

The present study demonstrates the capability of two preprocessing techniques such as wavelets and moving average (MA) methods in combination with feed-forward neural networks—namely, back propagation (BP) and radial basis (RB) and multiple linear regression (MLR) models—in the prediction of the daily inflow values of the Malaprabha reservoir in Belgaum, India. Daily data on 11 years of rainfall, inflow, and streamflow at an upstream gauging station have been used. The observed inputs are decomposed into subseries using discrete wavelet transform with different mother wavelet functions, and then the appropriate subseries is used as input to the neural networks for forecasting reservoir inflow. Model parameters are calibrated using 7 years of data, and the remaining data are used for model validation. More statistical indices have been used to determine the optimal models. Optimum architectures of the wavelet neural network (WNN) models are selected according to the obtained evaluation criteria in terms of the Nash–Sutcliffe efficiency coefficient, root mean squared error, and correlation coefficient. The result of this study has been compared by developing two standard neural network models and a multiple linear regression (MLR) model and MA. The results of this study indicate that the WNN model performs better compared to artificial neural network (ANN) and MLR models in forecasting the inflow hydrograph effectively. The study only used reservoir inflow data from one area, and further studies using data from various areas may be required to strengthen these conclusions.

Basin discretization effects in HSPF simulations were investigated to provide useful insights for hydrologists to determine the proper catchment size for basin scale modeling. The next generation radar (NEXRAD) rainfall estimates were incorporated into the HSPF modeling environment to generate streamflows at various catchments sizes ranging from 37 to $\mathrm{2,484}{\mathrm{km}}^2$. This research aims to identify how HSPF model performance can be improved by a marginal level of spatial discretization in rainfall-runoff modeling. Parameter estimation software was used for model calibration using data periods from 1998 to 2000. All simulations at different discretization levels above approximately 23% of the basin size resulted in good statistical values, with correlation coefficients of 0.82–0.87 and Nash-Sutcliffe efficiency coefficients of 0.61–0.73. However, the modeling performances of HSPF are limited when the catchment size reaches below 8.18% of the basin size, regardless of automatic calibration efforts. The result indicates that basin discretization at finer scales does not necessarily improve HSPF simulation results with NEXRAD inputs.

The advection-dispersion equation (ADE) or aggregated dead zone (ADZ) models and their derivatives are frequently used to describe mixing processes within rivers, channels, pipes, and urban drainage structures. The residence time distribution (RTD) provides a nonparametric model that may describe mixing effects in complex mixing contexts more completely. Identifying an RTD from laboratory data requires deconvolution. Previous studies have successfully applied maximum entropy deconvolution to solute transport data, with RTD subsampling used for computational simplification. However, this requires a number of configuration settings which have to date not been rigorously investigated. Four settings are investigated here: the number and distribution of sample points, the constraint function, and the maximum number of iterations. Configuration options for each setting have been systematically assessed with reference to representative solute transport data by comparing the goodness-of-fit of recorded and predicted downstream profiles using the Nash-Sutcliffe efficiency index, evaluating RTD smoothness with a measure of entropy, and through consideration of the mass-balance of the RTD. New methods for defining sample point distribution are proposed. The results indicate that goodness-of-fit is most sensitive to constraint function and that smoothness is most sensitive to the number and distribution of sample points. A set of configuration options that includes a new sample point distribution is shown to perform robustly for a representative range of laboratory solute transport data.

Artificial neural networks (ANNs) are generally regarded to behave as black-box systems. Recent research explores various methods that can provide an insight into the internal connections and relationships existing within the network. Various methodologies that understand the input variable contribution are analyzed in detail, and rule extraction approaches for a trained artificial neural network are addressed. To understand the contribution of input variables to rainfall-runoff model combination systems, this paper for the first time investigates knowledge extraction from artificial neural network, which is used to combine the results obtained from different competing rainfall-runoff models, using three different approaches: (1) Garson’s algorithm; (2) neural interpretation diagram (NID); and (3) sensitivity analysis (SA). For the purpose of investigating knowledge extraction techniques, the trained multilayer perceptron neural network to combine the results from four different rainfall-runoff models for the Brosna Catchment located in Ireland has been chosen. The results of the three approaches obtained in this study indicate that they can be used to reduce the complexity of rainfall-runoff model combination systems by eliminating the least significant contributing input variables. Based on these approaches, the paper helps to provide guidance in the optimal number of rainfall-runoff models that best perform in a combination system.

Reservoir storage prediction is essential to the operation and management of reservoirs. In this paper, a genetic algorithm (GA)-based support vector machine (SVM) model was developed for the prediction of monthly reservoir storage of Miyun Reservoir (the only surface drinking water source for Beijing city) over the period of 1995 to 2011. At the same time, two other SVM-based models that combine grid search and particle swarm optimization methods respectively for the parameter optimization, were used for comparison. The results showed that the developed GA-SVM model had the best performance in calibration and prediction. Owing to its high accuracy, the GA-SVM model would be popularized to the prediction of reservoir storage in other regions.

Estimating design quantiles for extreme floods in river basins under nonstationary conditions is an emerging field. Nonstationarities could arise from a variety of human and natural factors such as urbanization and climate change. Concepts of return period, design quantile (return level), and risk have already been developed for situations in which increasing or decreasing trends and abrupt shifts in extreme events are present. Because of limited data records, sampling variability, model errors, and the errors in projections into the future, significant uncertainties in the estimates of design floods of future projects will arise. To address the issue of uncertainty resulting from limited sample size of the observations, three methods have been developed for computing confidence intervals for the design quantile corresponding to a desired return period under a nonstationary framework, including (a) delta, (b) bootstrap, and (c) profile likelihood methods. These methods have been developed assuming a generalized extreme value distribution with nonstationary parameters. The applicability and comparison of the proposed methods for determining the confidence interval of quantiles have been demonstrated by using the annual flood maxima of the Assunpink Creek in New Jersey. The delta method, with numerically derived local derivatives, and the approximate bootstrap can be computationally efficient. The profile likelihood method, which is known to be more accurate, is quite burdensome computationally but provides more realistic asymmetric confidence intervals.

This study presents the formulation and application of a linear programming model for the maximization of net annual farm income from an area located in the Rohtak district of Haryana, India. A groundwater balance constraint was imposed on the model, which mitigates the waterlogging problem of the area, while making an optimal allocation of land and water resources. The model results showed a reduction in rice, gram, barley, and mustard areas against an increase in wheat, cotton, and sugarcane under optimal conditions. Under the optimal land and water allocation, groundwater use is increased while canal allocation is decreased. The net annual farm income from the command area has increased by about 26% under optimal allocations. The sensitivity analysis of the model parameters showed that a better price of crops is the most sensitive parameter, followed by the crop area and cost of cultivation. State agencies and farmers involved in the actual agricultural production process are advised to practice conjunctive use of canal water and groundwater for maximizing their farm income. This strategy would also mitigate hydrological imbalances in the groundwater system without installing expensive drainage systems, which is not feasible because the groundwater quality is poor and drainage water may pose a serious disposal problem.

Perennial rivers (i.e., the Indus, the Ganges, the Brahamputra) originating from the Himalayas are fed by temperature-induced snowmelt, rainfall, and base flow. Daily, weekly, or monthly streamflows of non-monsoon periods are critical for about a billion people living in these perennial river basins for water supply, irrigation, hydropower, and other water needs. The streamflow in snow and glacier dominated watersheds are affected mainly by solar energy and temperature. The existing models for streamflow and snow depth estimation are tedious and lack reliability. The impact of climate change has further enhanced the uncertainty. The springtime streamflow for the study area has increased by 2% yearly due to changes in climate during the last 25 years. The paper describes a nomogram, which combines the effect of climate change, temperature, and melting snow depth to estimate the daily average flow/discharge during spring time for a subbasin in the Himalayas. The concept is simple and uses location-specific regressed weekly main temperature, snow depth and discharge during ablating snowpack. The analysis focused on 3 typical years (1983, 2003, and 2008) and an average of 5–6 years during the spring period. The results of the study indicate a shift in temperature trend over the years and identify critical temperatures influencing the rate of snowmelt. The use of the temperature trendline has improved the streamflow simulation and further adaptation of average conditions under the changing climate and human influences in the region has enhanced the predictability of snowmelt/runoff. The glacier melts mostly occur in the summer-monsoon season so this trend cannot be addressed here with the springtime data set. However, a similar nomogram can be prepared for the summer-monsoon season if there is a snow cover area (SCA) of more than 50%.

Recent improvements in the Soil and Water Assessment Tool (SWAT) model take account of hydrological processes controlling a variable source area (VSA). This model, SWAT-VSA, accounts for changes in the nature and extent of the VSA over the course of a hydrological cycle by considering global catchment storage capacity, which varies with soil moisture between threshold values whose spatial distribution is determined by topography. The objective of this work is to evaluate the contribution of several aquifers with specific storage capacities to global catchment storage, its dynamics; and subsequent effects on VSA and non-point-source pollution. For this purpose, a method called SWAT-mVSA (SWAT-multi VSA) was used in a catchment representative of the agricultural conditions of large perialpine lakes to calculate soluble reactive phosphorus (SRP) fluxes because SRP has a major influence on receiving waters. SWAT-mVSA predicted components of the hydrological balance and SRP fluxes more accurately than SWAT-VSA. This underlines the importance of VSAs in mobilizing and transporting non-point-source pollutants such as nutrients, pesticides, or bacteria.

The use of partial duration series (PDS) in hydrological application includes the difficulty in determining the exceedance threshold or the number of average peaks per year ($\lambda$) used to define extreme events from observation. The difficulty is exacerbated when the PDS is used in the context of regional frequency analysis; however, there are only limited studies to address this difficulty. This study aims to investigate the determination of an optimum regional value of $\lambda$ for the North Island of New Zealand by examining the performance of the PDS when used in a regional frequency analysis (RFA). The suitability of a number of frequency distributions to be used in the regional frequency is examined. The results confirmed that the generalized Pareto (GP) best described the PDS in the study area. The results also show that the best PDS/GP performance is obtained when the value of $\lambda$ is equal to 5.

An assessment has been conducted of the potential effect of climate change on runoff in Spain in the 21st century. Runoff depths were calculated with a precipitation runoff model that used as input downscaled global climate model (GCM) outputs. The spatial and temporal resolution of the calculations was $1{\mathrm{km}}^2$ and 1 month, respectively. The assessment consisted of comparing runoff values of the baseline period, 1961–1990, with those of three 21st century periods, 2011–2040, 2041–2070, and 2071–2100, all estimated with simulated temperature and precipitation time series. Twelve climate simulations (i.e., combinations of a GCM, a greenhouse gas emissions scenario, and a downscaling algorithm), and whose variability reflects the uncertainty over the future climate, were considered. Based on the results, a decline in runoff is to be expected throughout the country. With respect to the baseline period, and depending on the climate simulation considered, runoff depths are expected to change in the range of $+1$ to $-22\%$ in 2011–2040, $-5$ to $-34\%$ in 2041–2070, and 0 to $-40\%$ in 2071–2100.

A fully developed turbulent regime is considered as a specific case of non-Darcy flow, and an analytical approach has been developed to determine normal depth, water surface profile, and seepage discharge of the flow through coarse porous medium in steady condition. The results of a laboratory rock drain with length, height, and width of 6.4, 0.8, and 0.8 m, respectively, and longitudinal slope of 0.04 were compared with the analytical solution developed in this study, and the results showed a good agreement between analytical and experimental data. To see the compatibility of the solution, a Darcy-based form of the solution (Pavlovsky’s method) and a flow analysis of buried streams (FABS) model are compared with the proposed solution and experimental data. Compared with Pavlovsky’s solution and FABS model, the results showed a satisfactory agreement with experimental records from water surface profiles through rock drain.