Journal of Hydrologic Engineering

The momentum equation in the kinematic wave model is a power law equation and involves two kinematic wave parameters. It is a common practice to use Manning’s equation to calculate the kinematic wave parameters. One can obtain a kinematic wave equation by inserting the momentum equation into the continuity equation. The kinematic wave equation becomes a partial differential equation with kinematic wave parameters that depend on the flow depth. However, working with the kinematic wave equation comprised of kinematic wave parameters that are independent of the flow depth, is a lot more convenient. Here, regression methods were used to calculate the kinematic wave parameters that are independent of the flow depth for a trapezoidal channel cross-section, which is a common cross-section shape. The developed expressions for the kinematic wave parameters provided very good approximation for the momentum equation of the kinematic wave model. The relationships among the geometry parameters of natural channel cross-sections were also investigated.

Selecting an appropriate digital elevation model (DEM) resolution is an essential part of distributed rainfall-runoff modeling since the resolution affects parameter values and, in turn, leads to predictive uncertainty. Moreover, the DEM resolution directly determines the computational workload required for model simulation. This study conducted several experiments to clarify the interaction between topographic and process parameters due to the spatial resolution of DEMs in distributed rainfall-runoff modeling. First, five different spatial resolutions (from 50 m to 1 km) were used to analyze the effects of DEM resolution on the topographic and process parameters of a distributed rainfall-runoff model [kinematic wave method for subsurface and surface runoff (KWMSS)]. Second, parameter compatibility was tested with regard to the sensitivity of model performance to optimal parameter values for each DEM, by applying the best-performing parameter combinations for each resolution to the models based on differing resolutions. Finally, the sensitivity of model performances to artificially generated parameters (deviating ±10% from optimal parameter sets) was analyzed to determine whether fine spatial discretization yielded equally good model performance measures or indistinguishable hydrographs (i.e., equifinality). The results indicate that differing topographic parameters due to distinct DEM sizes require differing process parameters to produce identically good runoff simulations. In addition, the parameter compatibility assessment suggests that increased spatial complexity due to fine DEM resolution results in decreased identifiability in process parameters. Consequently, nonoptimal parameter values can yield acceptable model performance measures when modeling is based on DEM resolutions of 250 m and smaller. The results of the sensitivity analysis also indicate that fine spatial discretization can be a dominant factor causing equifinality as well as overparameterization in distributed rainfall-runoff modeling. These findings may provide a new perspective on the equifinality problem, which many consider to be caused by huge model parameter requirements when operating distributed models.

Nash and Clark based geomorphological instanteneous unit hydrograph (GIUH) approach proved its usefulness to compute the synthetic unit hydrograph (SUH) and in turn the direct surface runoff component for ungauged catchments. In recent development, two-parameter Weibull’s distribution, coupled with Horton’s ratio, was used to derive the SUH. In continuation with these innovations, present study was conducted to test the adequacy of two-parameter Nakagami- $m$ distribution to derive the GIUH along with two-parameter logistic, two-parameter Weibull, and two-parameter gamma distributions (Nash model). Nakagami- $m$ distribution approach was first tested on the published data and then used to develop the GIUH for Bhagirathi-Bhilangana River catchment. Based on the results of comparison with other approaches, it seems that Nakagami- $m$ distribution-based GIUH can be a good substitute to other existing approaches.

Thermal infrared (TIR) surveys are effective methods to map surface spatial temperature patterns along a river. We used two data sets of TIR-derived longitudinal temperature profiles to analyze reach-scale spatial patterns of thermal heterogeneity of the Wenatchee River, in the Pacific Northwest region of the United States as part of a temperature total daily maximum load investigation. The TIR data indicate that the river has a general downstream heating trend; the magnitudes, reach variability, and longitudinal gradients are influenced by the headwater conditions, channel morphology, tributary locations, flow rates, and weather. Detailed TIR images facilitate identifying regions with high local thermal heterogeneity where we recommend a weighted average approach to estimate local spatial average temperature using temperatures from pixels of the thermally distinctive areas rather than using the temperature extracted from pixels sampled along the central part of the channel. TIR-derived daily maximum temperatures complement monitoring and modeling of spatial stream temperatures.

Cluster analysis, the generally used technique in delineation of hydrologic homogeneous regions for regional flood frequency analysis, requires standardization of flood governing attributes, and hence makes use of large subjective consideration. A new technique is developed for the delineation with no need of standardizing the attributes. The technique uses Natural Resources Conservation Services runoff curve number as a starting point in proposing the hydrologic regions. Five numbers of hydrologic regions were proposed inside the Nepalese territory by superimposing monsoon rainfall map over the runoff curve number map. The $L$ -moment based regional hydrologic homogeneity test led finalization of hydrologic regions with minor adjustments. Heterogeneity measure value, which is a regional homogeneity test parameter representing dispersion in sample moment coefficients among the basins, was found within or near acceptable limit in each of the region. The use of the regionalization for estimating extreme flood of different return periods is demonstrated for six example sites.

The Clark synthetic unit hydrograph and the Soil Conservation Service (SCS) curve number method has been used to simulate the rainfall and runoff behavior of a watershed for many years. Methodologies like Clark generally rely on the use of lumped or average rainfall and runoff parameters defined for the watershed, even though such parameters are spatially variable. In an attempt to leverage spatial parameters derived from geographic information, a modified Clark (ModClark) method or quasi-distributed model was developed for HEC-HMS. The ModClark method was initially developed to use the national network of WSR-88D radar (NEXRAD) rainfall data but few has been published on its application which is likely because of the difficulties in obtaining usable and reliable radar rainfall data and because of a lack of despisal preprocessing tools required to parameterize a ModClark simulation. While the original implementation and testing of the ModClark method required the use of NEXRAD data in specific formats, this study shows that it is possible to use any real or synthetic rainfall data whether it is spatially distributed or not. By not restricting the use of the distributed ModClark method to the use of spatially varying rainfall, distributed loss methods such as the commonly used SCS curve number can vary spatially over a grid and the effects of distributed watershed loss parameters can be analyzed with or without distributed rainfall. The implementation of the ModClark method in HEC-HMS is validated by comparing results to the Clark method using identical CN values. Further tests and examination of the SCS equation demonstrate that the runoff computed from distributed CN is always greater than the runoff computed from the traditional composite or area-averaged CN for ordinary ranges of rainfall depths. Moreover, by allowing a relatively fine grid resolution, the ModClark method determines the overall runoff from the watershed using a discharge weighted approach as opposed to weighted CN, which as reported in the National Engineering Handbook Part 630 is more accurate.

In this study, an experimental 12-h lead-time flood forecasting methodology that combines the fifth generation mesoscale model (MM5) of the U.S. National Center of Atmospheric Research with the physically based, spatially distributed watershed environmental hydrology (WEHY) model is described and applied to the Shiobara Dam watershed in Japan in order to explore its utility. The Shiobara-Dam watershed is a mountainous steep-sloped watershed that has an area of $123{\text{km}}^2$ . Meanwhile, the routine atmospheric assimilation data that are provided by the Japan Meteorological Agency (JMA) over Japan, have spatial resolution of 20 km and are at 12-h time intervals. In order to utilize the JMA’s atmospheric data at 12-h intervals as initial and boundary conditions for 12-h lead-time hourly precipitation forecast inputs to the WEHY model of Shiobara-Dam watershed for runoff forecasts, the MM5 nonhydrostatic atmospheric forecast model was chosen and nested inside the JMA’s data domain. The JMA’s atmospheric data were used as initial and boundary conditions for MM5 which then produced detailed forecasted precipitation fields for the WEHY model of Shiobara-Dam watershed for its hourly runoff forecasts for a 12-h lead time. The results of an application of this forecasting scheme to a 48-h rainfall-runoff event over Shiobara-Dam watershed are presented and discussed.

In this paper, we present a stochastic-analytical approach for uncertainty modeling in two-dimensional, statistically nonuniform groundwater flows. In particular, we develop simple closed-form expressions that can be used to predict the variance of Darcy velocities caused by random small-scale heterogeneity in hydraulic conductivity. The approach takes advantage of the scale disparity between the nonstationary mean and fluctuation processes and invokes an order-of-magnitude analysis, enabling major simplifications and closed-form solutions of the nonstationary perturbation equations. We demonstrate the accuracy and robustness of the derived closed-form solutions by comparing them with the corresponding numerical solutions for a number of nonstationary flow examples involving unconfined conditions, transient conditions, complex trends in mean conductivity, sources and sinks, and bounded domains.

Field experiments carried out on five reaches of the meandering cobble-bed Beheshtabad River in central Iran showed that the position of the maximum velocity was independent of the relative submergence ( $h/d_{50}$ less or more than 4) and relative curvature $\left(R/W\right)$ (where $h$ is the flow depth, $d_{50}$ is the median diameter of sediment, $R$ is the radius of curvature, and $W$ is the river width). A new method, called the boundary-layer characteristic method, was employed for the determination of shear velocity. The shear velocity values estimated with this method were in agreement with those obtained using the parabolic law. The law of the wall was valid for low and high relative curvatures in the inner, outer, and central zones of the meandering reaches. However, this law was not suitable for determining the shear velocity for the relative submergence range of $2.7<h/d_{50}<9.6$ due to its high sensitivity to near-bed velocities. Interestingly, it was possible to predict the flow velocity in meandering reaches using the Shields parameter.

This paper presents a hydrologic gray model integrated with a global search method to improve the accuracy of real-time flood forecasting for two watersheds. The model’s applicability is evaluated by comparing the runoff forecasts to the observed values. The model’s accuracy is compared with the accuracy of two base models that employ multiple regression equations and the model capability is verified in real situations. The model parameters are corrected by combining the gray system parameters. The fifth-order differential equation is adopted to represent the characteristics of the study watersheds. The statistical values between the observed values and the runoff forecasts in calibration and validation indicate that the simulations are in close agreement with the observations. The model provides more consistent and satisfactory runoff forecasts than the multiple regression models across all flow ranges; the accuracy of the runoff forecasts varies according to hydrograph stages and lead times. These results demonstrate that the proposed model is able to reasonably forecast runoff with 1–6 h of lead time for the two study watersheds.

Interest in thermal pollution due to storm-water runoff has risen significantly since it was recognized that fish habitat in coldwater streams may deteriorate or even disappear following urban development or logging. The need to project changes in both runoff temperature and volume in response to land use changes has been recognized. Surface runoff hydrographs can be predicted or simulated using a variety of existing models. Few tools exist to predict or simulate the thermograph of that runoff, i.e., the water flow rate and temperature as a function of time. To simulate runoff temperature for small parcels of land of uniform cover such as parking lots, a new hydrothermal runoff model was developed. The runoff portion of the model is semianalytical and spatially integrated. The runoff model is discrete in time, so that it may be used to analyze events with observed rainfall intensity variations at a resolution of 15 min or less. The runoff model closely approximates the simulation results of a one-dimensional kinematic wave model. For runoff temperature simulations, a heat transfer model was linked to the runoff model. The heat transfer model includes heat conduction to the ground and heat exchange with the atmosphere. Weather data at short time resolution (e.g., 15 min) are a model input requirement. To test and illustrate the usefulness of the hydrothermal runoff model, the response of a 24-acre parking lot to three midsummer rainfall events was simulated. The model was found to predict the average runoff temperatures within $0.3–0.5°\text{C}$ of observed values, and total runoff volumes within 1–15%. The root-mean-square error of simulated 2 min runoff temperatures was $1.1°\text{C}$ . The proposed model is to be included in a simulation tool to assess the hydrothermal impact of proposed land development on coldwater streams. Additional features are being added to the hydrothermal model for applications to pervious, vegetated land. Areas targeted for development are divided into small subwatersheds which are simulated individually. The change in total runoff temperature and volume due to development will be obtained by routing of subwatershed outputs.

This study presents an approximate solution of the nonlinear Boussinesq equation (NBE). The approximate solution of NBE is assumed to consist of space function and the Fourier cosine series which has time-varying coefficients. The space function is very thin and constant in time. The summation of the space function and the Fourier cosine series satisfies the initial and boundary conditions. When the bottom is horizontal or sloped, the coefficients in the Fourier cosine series are analytically determined by Galerkin’s method (one of the methods of weighted residuals) and the consequent nonlinear ordinary differential equations are numerically solved by the fourth order Runge-Kutta-Gill method. The resultant numerical results are found to be in satisfactory agreement with the experimental data. When the effect of the bottom slope in NBE is assumed to be linearly distributed in the computational space domain, an approximate solution is easily found to give the fluid surface profile on the sloped bottom as the fluid surface profile on the horizontal cases. The computational result by the finite difference method is also compared with the experimental data and the approximate solution.

This study has experimentally and theoretically derived the boundary condition of the unconfined groundwater flow at the drawdown end. It has been shown that the hydraulic gradient is theoretically 1 at the drawdown end, including the physical conditions of the pressure and bottom slope. The theoretical boundary condition at the drawdown end has been proved to be in good agreement with the experimental data for different slope and hydraulic conductivity. The downstream boundary condition is expressed by a linear relationship (equation) between discharge and thickness of fluid layer at the drawdown end. In the linear relationship, the effect of the bottom slope has not been found, as the experimental result indicates. This shows that the consequent fluid surface slope or hydraulic gradient at the drawdown end are constant. The resultant downstream boundary condition for measured discharges and water depths at the drawdown end predicts the hydraulic conductivity of the unconfined groundwater flow in the field. The effect of the capillary force on the linear relationship for the experimental data are found to be not negligible for the thin thickness of fluid layer.

In this paper, the probabilistic symmetry analysis approach proposed in the previous paper by Cayar and Kavvas in 2009 is adopted and applied to the analysis of nonlinear two-dimensional (2D) groundwater flow subject to random hydraulic conductivity field. The resulting model has the form of a two-dimensional Fokker-Planck equation (FPE). Following the methodology reported by Cayar and Kavvas in 2009, the 2D Boussinessq equation for unconfined groundwater flow in a heterogeneous aquifer is transformed to a system of ordinary differential equations (ODEs) through Lie group symmetry analysis in order to eliminate the spatial derivatives occurring in the governing equation. Next, these derived stochastic ODEs are ensemble averaged with second-order cumulant expansion and converted into a linear, deterministic partial differential equation. This new equation is called the FPE, and describes the evolution of the probability density function (PDF) of the hydraulic head, thereby, describing the ensemble behavior of unconfined aquifer flow in a heterogeneous medium. Once a solution of this FPE is obtained, one can then obtain the ensemble average and ensemble variance behavior of the hydraulic head through an expectation operation. The numerical solutions of the FPE are validated with the Monte Carlo simulations. The validation results indicate that the FPE technique combined with Lie symmetry analysis can provide encouraging results in estimating the time-space behavior of the mean and variance of the hydraulic head in heterogeneous aquifers.

Symmetry methods can be used to transform almost any kind of linear or nonlinear partial differential equation (PDE) that represents a hydrologic process in any dimension to an equivalent ordinary differential equation (ODE). Meanwhile, Kavvas recently shown in 2003 that the conservation equations of hydrologic processes under uncertainty, expressed as linear or nonlinear stochastic ODEs or PDEs, have a one-to-one correspondence to a mixed Eulerian-Lagrangian nonlocal form of the Fokker-Planck equation (FPE) when the underlying process has finite correlation lengths. Under such correspondence, it is possible to obtain a solution for the ensemble behavior of a particular hydrologic process in terms of the solution of its corresponding FPE for the probability distribution function (PDF) of its state variables under appropriate initial and boundary conditions. A major issue with the resulting FPE in the case of conservation equations in PDE form is that spatial gradients of the process state variables appear in the resulting FPE that prevent its solution. Therefore, a formal algorithm is needed to reduce the PDE of a hydrologic process into an ODE in order to eliminate the original spatial gradients of the process state variables in the corresponding FPE of the process. This is accomplished by the symmetry methods. After such transformation, the resulting FPE, which is a linear deterministic PDE, can be solved to obtain the evolutionary PDF, ensemble average, ensemble variance, and any other statistical function of the hydrologic process being investigated.