Journal of Hydrologic Engineering

A new ensemble-averaged kinematic wave equation is derived for the flow routing problem in channel networks. This derivation is performed by ensemble averaging the second-order Taylor series expansion of the point scale kinematic wave equation around the mean value of the equation’s parameters. Utilizing this ensemble-averaged kinematic wave equation, the ensemble-averaged solution for the same ordered channels (according to the Strahler–Horton ordering) are obtained. Instead of solving the flow at each channel one by one, the ensemble-averaged solution is computed for the ensemble of channels that are of the same order within the channel network. Ensemble averaging is only applied to the channel orders that include a sufficient number of channels to form an ensemble of adequate size. Using this methodology, the computational load, parameter data requirements, and time/effort required to set up the model are reduced substantially. Besides the obtained economy in computations, data requirements and effort to set up the model, this methodology also provides satisfactory results when compared to the numerical solutions of the flows within the actual, detailed channel network.

A multilinear stage-hydrograph routing method based on time distribution scheme is analyzed. The framework of the multilinear method is based on the Muskingum-type routing method, which is used as the linear submodel. The proposed method can implicitly model the nonlinear dynamics of the flood wave propagation by varying the model parameters at each routing time step. The suitability of this flood routing method is verified using a set of laboratory experimental data and the field data of the Tiber River in central Italy.

The aim of this study is to evaluate prediction accuracy and sensitivity of a distributed hydrologic model. Accurate predictions of runoff are needed where reservoir operations are used to control flooding and to manage water resources. The study area consists of watershed areas that are influent to reservoirs in the $967{\mathrm{km}}^2$ Yongdam basin, and the $\mathrm{2,293}{\mathrm{km}}^2$ Namgang basin located on the Korean Peninsula. For these basins with complex terrain, a physics-based distributed hydrologic model is set up with geospatial data, calibrated, and used to test sensitivity to accuracy of radar and rain gauge input and initial conditions. The events studied range in magnitude from 86 to over $249\mathrm{mm}$ and include two typhoons and two heavy rainfall events. Radar reflectivity is converted to rainfall rates using $Z\text{-}R$ relationships, and then corrected for bias using a spatially variable correction derived from the rain gauge networks that cover both basins. Adjustment of assumed model parameters for the Namgang and Yongdam watersheds improves hydrograph peak and volume. The prediction accuracy of the model is also evaluated using rainfall estimated with uncorrected radar and with rain gauge data as model input. Use of gauge-corrected radar results in better prediction accuracy than was achieved with raw radar or gauge-only input. The sensitivity of the watershed response to the initial degree of saturation is dependent on event magnitude but becomes increasingly sensitive at higher degrees of initial saturation. In both watersheds, the initial saturation of the soil affects prediction accuracy more than the uncertainty caused by model parameters or gauge-only input.

On a hillslope, overland flow first generates sheet erosion and then, with increasing flux, it causes rill erosion. Sheet erosion (interrill erosion) and rill erosion are commonly observed to coexist on hillslopes. Great differences exist between both the intensities and incidences of rill and interrill erosion. In this paper, a two-dimensional rill and interrill erosion model is developed to simulate the details of the soil erosion process on hillslopes. The hillslope is treated as a combination of a two-dimensional interrill area and a one-dimensional rill. The rill process, the interrill process, and the joint occurrence of rill and interrill areas are modeled, respectively. Thus, the process of sheet flow replenishing rill flow with water and sediment can be simulated in detail, which may possibly render more truthful results for rill erosion. The model was verified with two sets of data and the results seem good. Using this model, the characteristics of soil erosion on hillslopes are investigated. Study results indicate that (1) the proposed model is capable of describing the complex process of interrill and rill erosion on hillslopes; (2) the spatial distribution of erosion is simulated on a simplified two-dimensional hillslope, which shows that the distribution of interrill erosion may contribute to rill development; and (3) the quantity of soil eroded increases rapidly with the slope gradient, then declines, and a critical slope gradient exists, which is about 15–20° for the accumulated erosion amount.

Effective discharge $\left(Q_e\right)$ is an important design variable used in stream restoration design. $Q_e$ of a stream reach is affected by both the hydrological characteristics of the upstream watershed and the sediment-transport characteristics of the stream reach. This study identified the most critical hydrological and sediment-transport characteristics affecting $Q_e$ of small urban streams in southern Ontario. Continuous simulation of hypothetical watersheds was conducted to generate hourly streamflow data. $Q_e$ and other related variables of interest were determined based on simulated streamflow series and randomly generated sediment-transport rating curve parameters. Global sensitivity analysis using samples of input and output data indicated that $Q_e$ is highly sensitive to, first, the exponent of the sediment rating curve $\left(\beta \right)$ ; second, the watershed storage coefficient reflecting the storage characteristics of a watershed; and third, the time of concentration of a watershed. Further, this study showed that only when $\beta$ values are within a specific range, $Q_e$ and the discharge corresponding to a particular return period are close to each other.

This study investigated the impact of temporal and spatial sampling of rainfall on runoff predictions using a physically based [System Hydrologique European (MIKE SHE)] and conceptual [hydrologic modeling system (HMS)] hydrologic models. The numerical models were applied to Goodwin Creek watershed in northern Mississippi. The drainage area of Goodwin Creek is approximately $21.4{\mathrm{km}}^2$ . This study showed that MIKE SHE was more sensitive to both the spatial and the temporal samplings of rainfall than the HMS. The study also showed that errors introduced by coarse sampling scenarios can be significant. Overall, for this particular watershed size, increasing the rain gauge density from 1 to 2 resulted in the most significant improvement for both models. Similarly, a temporal sampling frequency beyond $1\mathrm{h}$ showed significant deterioration in the quality of the runoff prediction. The combined spatial–temporal sampling experiment showed that increasing the temporal sampling compensates, at least partially, for the loss of rainfall spatial information. It also showed that under poor temporal sampling frequency, the gain in model performance by increasing the spatial sampling density is negligible.

A method to identify and track rainfall structures using $1\text{-}\mathrm{h}$ accumulated NEXt generation RADar (NEXRAD) rainfall data is presented and used to analyze the dynamics of storm features over an area in Texas. Storm features are identified from a Gaussian mixture model using the expectation maximization algorithm. The method assigns NEXRAD pixels to storm features, simultaneously producing a smooth fitted function to the rainfall intensity distribution. Once the storm features are identified, they are tracked using inverse cost functions and using the fact that continuous features overlap each other from frame to frame in the accumulated data. The inverse cost functions also account for storm feature merging, splitting, birth, and death. Application of this storm identification and tracking algorithm for Brazos County $\left(\mathrm{1,500}{\mathrm{km}}^2\right)$ in southeastern Texas distinguishes several characteristics of the storm feature dynamics. From September through April, storm features are predominantly of a frontal nature, with storm features following geostrophic flow along low pressure fronts moving in from the north. In summer (May–August), storm features are convective in nature following random track directions. Both types of storm features have durations of $1–3\mathrm{h}$ in Brazos County due to the county’s relatively small size compared to the measured average storm speed of $40\mathrm{km}∕\mathrm{h}$ and due to the fact that most storms only intersect the county over part of their area.

Generalized models for predicting the storage–yield–reliability functions of surface water reservoirs are developed using multiple linear regression and multilayer perceptron, artificial neural networks (ANNs). Linear regression was used to model the total capacity using the over-year capacity as one of the inputs. However, the ANNs were used to simultaneously model directly the intrinsically nonlinear over-year and total (i.e., within- $\text{year}+\text{over}$ -year) capacity-yield-reliability functions. The inputs used for the ANNs were basic runoff and systems variables such as the coefficient of variation of annual and monthly runoff, minimum monthly runoff, the demand ratio, and reliability. The results showed that all the models performed well during development and when tested with independent data sets. Both models offer avenues for predicting reservoir capacity at gauged sites without the expense of time-series based simulation alternatives.

Time of concentration of overland flow is an important parameter in many hydrologic design methods. This technical note traces the evolution of the kinematic wave time of concentration formulas for overland flow only. It commenced with Henderson and Wooding’s 1964 formula for a single plane. This formula, however, cannot be easily applied in practice because the parameters were not related to the physical characteristics of an overland plane. Nearly four decades later, in 2002, Wong developed a powerful formula, which can be applied to a series of planes which are of different lengths, different slopes, different roughnesses, different flow regimes, different soil types and infiltration rates resulting in different net rainfall intensities, and for planes subject to different net rainfall intensities, and a combination of all these variables. Finally, a comparison of Wong’s 1996 formula with Overton’s 1971 formula shows that Overton’s formula for a series of planes is incorrect.

A model for real-time flood forecasting in river systems with large drainage areas has been developed. Flow variations between upstream and downstream stations are interlinked and are typically governed by reach properties. Unique paired variations establish useful flow correspondence resulting in inflow and outflow forecasting models for a reach. The proposed model can generate forecasts with increased lead time without applying a separate inflow forecasting model and can also provide updated forecasts essential for real-time applications. The model was applied to flood forecasting in Tar River Basin, N.C., covering a drainage area of $\mathrm{13,921}{\mathrm{km}}^2$ . The model aggregates multiple upstream flows to provide long range forecasts for two downstream stations in the basin. Applicability of the model in estimating complete upstream and downstream hydrographs was demonstrated using a textbook example. Application results indicate that the new model can provide complete and updatable evolution of hydrographs using the current flow state.

The aim of this study was to develop an optimum flow prediction method, based on the adaptive neural-based fuzzy inference system (ANFIS) and artificial neural network (ANN). Each methodology was applied to river flow predicting in Manavgat Stream in the southern part of Turkey. In application, Manavgat Stream flows were predicted from Dalaman Stream, Alara Stream, and Göksu Stream flows. Each stream is located in different catchments. For monthly streamflow predictions, data were taken from the General Directorate of Electrical Power Resources Survey and Development Administration. Used data covered a $35-\text{year}$ period (1969–2003) for monthly streamflows. The ANFIS and ANN models had only one output with three input variables. Comparison of the ANFIS and ANN models showed a better agreement between the ANFIS model estimations and measurements of monthly flows than ANN. With the help of the ANFIS model for interbasin flow prediction, it was possible to estimate missing or unmeasured data.

This paper proposes a particle tracking technique for applying the Eulerian–Lagrangian localized adjoint method or the Eulerian–Lagrangian method to solve transport equations in a rapidly changing unsteady flow. The proposed particle tracking technique uses a linear temporal interpolation of velocity to avoid the error introduced when using a stepwise temporal approximation of the velocity, which has been adopted in many existing particle tracking techniques. Numerical experiments were carried out on several example problems to demonstrate the superior accuracy and efficiency of the proposed particle tracking technique over Cheng’s and Pollock’s methods. The numerical results show that the use of a linear temporal interpolation of velocity can allow an increase in time step size without causing a significant decrease in accuracy, particularly under a complicated transient flow or a rapidly changing velocity field with time.