Journal of Hydrologic Engineering

This paper presents a global sensitivity and uncertainty analysis of a dual drainage model applied to a $0.049{\mathrm{km}}^2$ (4.9-ha) urban catchment based on generalized likelihood uncertainty estimation (GLUE). The model solves the nonlinear bidimensional (2D) and one-dimensional (1D) Saint-Venant equations to compute respectively the surface runoff and the flow in the sewer network. The sensitivity of the outlet hydrograph to the input parameters of the model was determined by using variance-based Sobol sensitivity indices. These indices highlight the great effect of the overland flow parameters on the model output, in contrast with the limited effect of the sewer-network parameters. The Manning coefficient of the impervious terrains was identified as the most influential model parameter. The effect on model calibration of two subjective factors of the GLUE methodology (the acceptability threshold and the shaping factor of the likelihood function) was analyzed. From this analysis, a NSE acceptability threshold of 0.6 and a shaping factor of 1 were adopted for model calibration. Greater values of these parameters resulted in very narrow uncertainty bounds and therefore in low coverage ratios. The results obtained after calibration and validation show a satisfactory performance of the model, with NSE values within 0.78 and 0.98 and coverage ratios of the 95% confidence intervals in the range 66–91%. The worst performances are obtained in the events with lowest rainfall depths, since in those cases the overland flow in the whole catchment is extremely shallow and the runoff propagation is not well captured by the model.

The concepts and methods for planning and design of hydraulic structures subject to hydrologic extreme events that arise from nonstationary conditions have emerged in the last few years. The traditional approaches such as return period, risk, and reliability assume that extreme events are stationary and they are being reformulated for applications under nonstationary conditions. For this purpose, some of the previous developments have been based on the nonhomogeneous geometric distribution. The particular importance of this paper relates to the frequency of extreme events as time evolves, say for a given time period $n$. For stationary extreme events, the number of events exceeding the design quantity (e.g., design flood) over the design life of the project, say $n$, can be determined from the binomial distribution. The main objective of the research reported in this paper is to develop a conceptual framework so that the frequency of extreme events when the extremes are nonstationary can be determined from the Poisson binomial distribution. In addition, the use of the number of extreme events in the future as an alternative metric for hydrologic design is proposed with potential applications in flooding associated with both riverine and sea level extremes in coastal regions. The application of analytical concepts is demonstrated by using the annual flood maxima of the Assunpink Creek in New Jersey. Results suggest that the frequency of extreme events as an alternative metric for hydrologic design has a significant potential for applications in risk-based economic analysis of projects.

One of the basic assumptions usually made by researchers for obtaining optimal designs of flood mitigation measures that take into account the associated uncertainties is consideration of flood damage probability directly correlated with flood event probability. The present work demonstrates that this assumption leads to 42% underestimation of expected damages for the case study of the Kan River basin near the capital city of Iran, Tehran. To eliminate this limitation, in this paper, inherent rainfall uncertainties are included through random sampling techniques and simulation-based optimization approaches. A Monte Carlo simulation method is employed to generate multivariate synthetic rainfalls, which are then imported in a rainfall-runoff model. This model gives the flood hydrographs of subbasins for hydraulic routing in waterways of the watershed by a hydraulic model, considering different flood mitigation measures. These models are then coupled with the NSGA-II optimization algorithm to provide optimal Pareto solutions considering two competitive objectives of minimizing investment costs and expected physical and nonphysical damages in the flood-prone areas. The results obtained by applying the proposed hybrid model to a watershed show that some designs that seem inappropriate in terms of benefit-to-cost ratios may still be valuable for decision makers when nonphysical vulnerabilities are considered. Experimental results also showed that neglecting the spatial dependence of rainfalls throughout the watershed may lead to up to 26% underestimation of the calculated expected annual flood damages (EADs).

A distributed physically based model, soil and water assessment tool (SWAT), and a distributed conceptual model, distributed large basin runoff model (DLBRM), were selected to compare their applicability and performance in simulating daily runoff in the Heihe River watershed, the second-largest inland river (terminal lake) with a peak elevation of 5,584 m above sea level (asl) in arid northwest China. Both models have been calibrated against the observed daily runoff at the watershed outlet (Yingluoxia Hydrological Station) for the period of 1995–2004 and validated for the period of 2005–2009. Results show that both SWAT and DLBRM produced reasonable results in this study, and DLBRM performed better than SWAT. The difference in performance is mainly due to data constraints, different interpolation schemes, and spatial representations of landscape variations in the models. The tank storage-output principle used in DLBRM seems more suitable than the Soil Conservation Service curve number (SCS-CN) method used in SWAT to simulate daily flow in an arid area. Both models performed worse in simulating low flows mostly occurring in spring and winter, because of a lack of detailed representation of the impacts of snow-melting processes and frozen soils. The authors’ analysis indicates that consideration of the impacts of snow melting and frozen soils on the hydrological process is key to improving performance of hydrological models in mountainous areas. Because of their simpler operations, lower data requirements, fewer input parameters, and better performances, distributed conceptual models such as DLBRM seem more suitable for hydrological modeling in data-deficient, high elevation, and topographically complex mountainous watersheds in arid regions.

Traditionally, regional frequency analysis was developed for stable environmental conditions. Nevertheless, recent studies have identified significant changes in hydrological records under changing environments. Besides, uncertainty in hydrological frequency analysis is persistent. This study aims to investigate the impact of one of the most important uncertainty sources, parameter uncertainty, together with nonstationarity, on design rainfall depth in Qu River Basin, East China. A spatial bootstrap is first proposed to analyze the uncertainty of design rainfall depth estimated by at-site frequency analysis and by regional frequency analysis based on L-moments and the index variable method. Meanwhile, a method combining the generalized additive model with a 30-year moving window is employed to analyze nonstationarity existing in an extreme rainfall regime. The results show that the uncertainty of 100-year design rainfall depth due to parameter uncertainty reaches 15.42 and 12.45% with generalized extreme value (GEV) and Pearson type III (PE3) distributions, respectively, on the regional scale, while such uncertainty is up to 19.16% with GEV and 16.17% with PE3 on the at-site scale. Under the nonstationarity condition, the uncertainty of the design rainfall depth with 0.01 annual exceedance probability is 24.83% with GEV and 16.94% with PE3. The uncertainty of the design rainfall depth resulting from parameter uncertainty is less than that from nonstationarity frequency analysis with both GEV and PE3.

A general analytical model for one-dimensional (1D) contaminant transport in infinite domain with time-dependent transport parameters is presented in this paper. The model is based on the advection-dispersion equation with a time-dependent flow velocity, a time-dependent dispersion coefficient, and a time-dependent distribution coefficient due to sorption. It takes into account a first-order irreversible reaction (decay), an arbitrary initial distribution of the contaminant, and an arbitrary space- and time-dependent sink/source term. The model can handle any time-dependent transport parameter. Analytical solutions are provided for both the advection dominant and the advection-dispersion transport equations. The proposed analytical solutions are general and they can be used for problems where one or more parameters are time-dependent. It is shown that the presented solutions can be reduced to other existent solutions where one transport parameter is assumed to be time-dependent. The general analytical solutions are obtained by using the Fourier transform, and they are presented in integral forms. Several closed-form solutions can be derived from the general integral form. Such closed-form solutions are of great interest since they allow the dependence of the solutions on the underlying physical parameters to be studied in an analytical manner. In particular, the author presents some closed-form solutions for the case of an initial step function and discusses through the numerical examples some insights about the errors that can be made by assuming constant parameters instead of time-dependent ones. These assumptions may lead to overestimated or underestimated concentrations. The proposed analytical solutions are useful for benchmarking numerical solutions to problems in hydrogeology and chemical engineering. They are also of great importance to the investigation of quantitative accuracy assessment. One of the presented closed-form solutions is used to compare with numerical solutions.

The heavy sediment load of the Yellow River makes it difficult to simulate sediment concentration using classic numerical models. In this paper, on the basis of the classic one-dimensional numerical model of open channel flow, a variational-based data assimilation method is introduced to improve the simulation accuracy of sediment concentration and to estimate parameters in sediment carrying capacity. In this method, a cost function is introduced first to determine the difference between the sediment concentration distributions and available field observations. A one-dimensional suspended sediment transport equation, assumed as a constraint, is integrated into the cost function. An adjoint equation of the data assimilation system is used to solve the minimum problem of the cost function. Field data observed from the Yellow River in 2013 are used to test the proposed method. When running the numerical model with the data assimilation method, errors between the calculations and the observations are analyzed. Results show that (1) the data assimilation system can improve the prediction accuracy of suspended sediment concentration; (2) the variational inverse data assimilation is an effective way to estimate the model parameters, which are poorly known in previous research; and (3) although the available observations are limited to two cross sections located in the central portion of the study reach, the variational-based data assimilation system has a positive effect on the simulated results in the portion of the model domain in which no observations are available.

Nonpoint source pollution is a critical problem in Canadian prairie watersheds. However, sediment mobilization and export are poorly represented in existing models for these watersheds. The poor representation is partly because the hydrology of the region is highly influenced by the existence of numerous dynamically-connected landscape depressions that vary in storage capacity and because of the complex freeze-thaw cycles in the region. The objective of this research was to improve sediment export simulation modeling in these cold-climate prairie watersheds by incorporating a probability distribution function of depression storage capacity and a seasonally varying soil erodibility factor into the soil and water assessment tool (SWAT) model. The probability distribution function is used to represent the variation in storage capacity of the numerous depressions, whereas the seasonally varied soil erodibility factor is used to account for changes in erodibility as the soil freezes and thaws. Results from two case study watersheds confirm an improvement in sediment export predictions when varying storage capacity is represented and the sediment loss routine includes seasonally varying soil erodibility.

Deep percolation from the root zone of water intensive crops reduces irrigation efficiency, minimizes water productivity and becomes an environmental threat by carrying chemical residues to groundwater systems. Quantification of the percolation process is often made indirectly without actual field observations. In the present case study, simple, locally constructed drainage type lysimeters were utilized to monitor daily deep percolation from the root zone of unpuddled sandy loam soil throughout the growth periods of rice and berseem fodder crops. Similarly, other water balance components were monitored on daily time steps during the crop growth periods (2013 and 2014). It was observed that a large volume of water is returned as deep percolation loss as physically demonstrated from lysimeter measurements. Overall, approximately 82% of the input water volume in rice season and 61.8% in berseem season accounted for deep percolation in unpuddled sandy loam soil of the experimental field. A simple water balance model was employed to compute deep percolation from the crop root zone. The deep percolation computed on a daily basis did not agree with the measured values; however, cumulative deep percolation computed on an extended time interval of seven days (weekly basis) for rice and between wetting intervals for berseem seasons agreed well with the model computed cumulative percolation. This could be attributable to the fact that some time is needed for drainage water to arrive lysimeter outlets located well below the crop root zone. Consequently, it can be concluded that in application of drainage type lysimeter water balance, estimation of deep percolation from a cropped area can be made fairly well in longer time steps than shorter time intervals. Specifically, heavy rainfall events resulted in large percolation losses. This study also proves that locally constructed lysimeters could effectively be utilized in water balance studies of a cropped area when used in combination with root zone soil moisture monitoring devices.

Studies examining potential evapotranspiration (PET) for a mature forest reference compared with standard grass are limited in the current literature. Data from three long-term weather stations located within 10 km of each other in the USDA Forest Service Santee Experimental Forest (SEF) in coastal South Carolina were used to (1) evaluate monthly and annual PET estimates from five different methods with varying complexities [Penman-Monteith (P-M), Turc, Thornthwaite (Thorn), Priestley-Taylor (P-T), and Hargreaves-Samani (H-S)] at two grass reference sites; and (2) compare results for the grass sites with PET estimated using the P-M method for a forest reference site using measured daily climatic data for the 2011–2014 period. The grass reference sites are located at the SEF headquarters (SHQ) and in the Turkey Creek watershed (TC). The forest reference station is on a 27-m-tall tower above the canopy of a pine/mixed hardwood forest in watershed WS80 in the SEF. At the WS80 forest site, the highest annual PET (1,351 mm) was observed in 2011 with the lowest rainfall (934 mm), and the lowest PET (1,017 mm) was observed in 2013 with the highest rainfall (1,433 mm), which is consistent with the two grass sites. The temperature-based H-S method yielded estimated monthly and annual PETs that were in better agreement than those of another temperature-based Thorn method at both grass sites when compared against the P-M PET for the forest site. The P-M–based PET values estimated for the SHQ grass site were significantly lower ($\alpha =0.05$) than those obtained at the TC grass site and the P-M PET values for the WS80 forest site. The solar radiation-based Turc and temperature-based Thorn PET estimates at both grass sites were significantly different ($\alpha =0.05$) from the P-M PET estimates for the forest. These results for the grass sites demonstrate that PET estimates are sensitive to the method used, resulting in significantly different estimates using a single method even for nearby sites because of differences in the complexity of describing the PET process, climatic factors, and interaction with site vegetation types. When compared with the P-M PET for the forest site, the P-T method was in the closest agreement, with the highest $R^2$ of 0.96 and the least bias of 9.7% in mean monthly estimates, followed by the temperature-based H-S with an $R^2$ of 0.95 and a bias of 12.6% at the SHQ grass site. It is concluded that the simpler P-T and H-S methods appear to be adequate to estimate forest P-M PET and that their estimates are within the error bounds of the data-intensive P-M PET method for coastal forests.

These days wavelet analysis is becoming popular for hydrological time series simulation and forecasting. There are, however, a set of key issues influencing the wavelet-aided data preprocessing and modeling practice that need further discussion. This article discusses four key issues related to wavelet analysis: discrepant use of continuous and discrete wavelet methods, choice of mother wavelet, choice of temporal scale, and uncertainty evaluation in wavelet-aided forecasting. The article concludes with a personal reflection on solving the four issues for improving and supplementing relevant wavelet studies, especially wavelet-based artificial intelligence modeling.