Journal of Hydrologic Engineering

An engineering methodology is developed to build hazard curves to evaluate the probability of flood-induced overtopping of barriers in watershed-reservoir-dam systems. The probable maximum precipitation in the watershed under consideration and its distribution in time during the acting storm is estimated. Considering the effects of the local geology, soil, topography, and land use, a random representation of the storm hourly rain is translated into effective runoff, including losses due to evaporation, interception, and surface retention. The uncertainty in the hydrological characteristics of the drainage basin is captured by a random time to concentration. Random hourly unit graphs are constructed analytically for a convex watershed and convoluted with the storm time-history to result in the random hydrograph for the inflow flood into the reservoir of the dam system. Flood routing through the reservoir is then computed with or without noise in the model. The deterministic path leads to a hydrograph for the water level at the barrier upstream face. The stochastic path evaluates through simulation the probability density function of variates (at discrete times) of the nonstationary random process of this pool level. The characterization of the reservoir-pool maxima allows the estimation of the probability of barrier overtopping.

The effects of roughness on the flow structure in a gravel-bed channel were investigated by using particle image velocimetry. The bed was composed of gravel particles, of which the median diameter, $d_{50}$, (i.e., the diameter at which 50% are smaller) ranged from 2.5 to 35.0 mm. The flow covered a wide range of Reynolds numbers ($\mathsf{R}=3,048–69,982$). The experimental results showed that the logarithmic-law region of the velocity profile changed with the size of the roughness elements. Under the large-scale roughness condition, that is, $h/d_{50}=1.78$ (the ratio of flow depth to median diameter), the mean velocity distribution deviated from the logarithmic law in the near-wall region. In addition, a new formula was established to calculate the Darcy-Weisbach friction factor for the gravel bed, expressed for the Reynolds number and the surface geometric parameters. On the basis of the boundary layer theory, the displacement thickness was introduced to estimate the limit of the roughness effect, and it was found to be greatly affected in the range of $35,000<\mathsf{R}<50,000$.

A continued important area of research in hydrologic modeling is the issue of spatial and temporal scaling of biogeochemical properties and processes. Hurst analysis, which is a fractal-based scale invariant approach for analyzing long-term time series data, can provide insight into this issue as a quantitative approach for evaluating temporal scale in time series. The objectives of this paper were to compute the Hurst coefficient ($H$) for hydrologic and water quality variables, to study the effects of seasonality on $H$, and to determine how the $H$ for the water quality indicators are related to that of the hydrologic parameters (e.g., discharge and rainfall). Two sites were investigated, Little River and Walker Branch, both located in east Tennessee. The water quality indicators include total coliform for Little River data and nitrate, chloride, sulfate, and calcium concentrations for Walker Branch data. $H$ was estimated using spectral analysis. It was found that $H$ for water quality indicators were significantly different from hydrologic parameters in an untransformed series, whereas it is not different in deseasonalized series (except total coliform). The comparison of untransformed and deseasonalized data series showed that there is no statistically significant value to deseasonalize the data, although the data series appears to shift toward random scaling after deseasonalization.

Assuming time-averaged velocity as a random variable, this study develops an entropy theory for deriving the one-dimensional distribution of velocity in open channels. The theory includes five parts: (1) Tsallis entropy; (2) the principle of maximum entropy (POME); (3) the specification of information on velocity for constraints; (4) the maximization of entropy; and (5) the probability distribution of velocity and its entropy. An application of the entropy theory is illustrated by deriving a one-dimensional velocity distribution in open channels in which the dimension is vertical or the flow depth. The derived distribution is tested with field and laboratory observations and is compared to Chiu’s velocity distribution derived from Shannon entropy. The agreement between velocity values are computed with the entropy-based distribution.

An analytical solution of the nonlinear kinematic wave model of overland flow with time-varying rainfall on a sloping plane is presented by the characteristic equation. To obtain it in the closed form, we approximate discharge of Manning’s formula per unit width by a parabolic curve. It is compared with experimental data of rainfall and runoff process, and their agreement is satisfactory. It is also compared with the numerical result of the finite difference method, and their agreement is found to be good. When the rainfall is time-varying, the method of this study can derive the analytical solution. The analytical solution of the kinematic wave model with time-varying rainfalls is found to be suitable for estimating design flood from rainfall in a simple watershed. Floods in urban areas can be predicted by the kinematic wave model with given time-varying rainfalls when the urban areas consist of several simple watersheds.

Simulating irrigation systems by accounting for various water loss rates is necessary while modeling the hydrology of cultivated canal-irrigated watersheds. The existing approaches to modeling canal irrigation use situation-specific optimization procedures. In addition, they are focused on a water management perspective rather than a hydrologic perspective. In this study, an approach is developed to model canal irrigation systems and irrigation best management practices (BMPs) to adequately simulate the water balance of irrigated watersheds. The approach is based on the water requirement of crops, number and frequency of irrigation, and critical crop water requirement stages. Two irrigation BMPs are modeled as water savers rather than physical changes in irrigation appurtenances. Land leveling is modeled by changing model parameters and water management by changes in frequency, timing, and magnitude of irrigation with respect to cumulative precipitation. The developed approach was tested with a $1,692{\mathrm{km}}^2$ intensively cultivated, canal-irrigated watershed using the Soil and Water Assessment Tool (SWAT). Test results suggest that the approach captures water balance and observed runoff hydrograph of the study area adequately.