Journal of Hydrologic Engineering

Assuming time-averaged velocity as a random variable, this study develops an entropy theory for deriving two-dimensional (2D) distribution of velocity in open channels. The theory comprises five parts: (1) Tsallis entropy; (2) principle of maximum entropy (POME); (3) specification of information on velocity in terms of constraints; (4) maximization of entropy; and (5) derivation of the probability distribution of velocity. The entropy theory is then combined with a hypothesis on the cumulative distribution function of velocity in terms of flow depth to derive a 2D velocity distribution. The derived distribution is tested using field as well as laboratory observations reported in the literature and is compared with known velocity distributions. Agreement between velocity values computed using the entropy-based distribution and observed values is found satisfactory. Also, the derived distribution compares favorably with known distributions.

Temporal distributions as well as spatial variability of rainfall have been investigated within the Densu River basin in Ghana to determine the duration pattern of rainfall events and their intensities and how these affect the partitioning of rainfall into overland flow and infiltration. Also, the use of daily rainfall data ($\mathrm{mm}/\mathrm{day}$) as inputs in physically based hydrological models for water balance computation and description of hydrological processes in the basin was assessed in relation to the actual duration of rainfall events in the basin. The threshold intensities for groundwater recharge in the Birimian, Granite, and Togo formation soils are below $70\mathrm{mm}/\mathrm{h}$, $85\mathrm{mm}/\mathrm{h}$, and $95\mathrm{mm}/\mathrm{h}$, respectively, and above $10\mathrm{mm}/\mathrm{h}$ in the entire basin. The amount of rainfall infiltrating into the groundwater system will diminish in the future because of the imminent effects of climate change on the intensity of rainfall events.

This paper presents the development of a novel acoustic sensor that enhances Doppler approaches to monitor groundwater vector flow. The technique is based on a high-resolution acoustic phase measurement: flowing water introduces a shift in the acoustic velocity component between the transmitter and receiver. By switching the transmitter and receiver modes at periodic intervals, the resulting magnitude of the acoustic phase shift yields the speed of water flow. The high-resolution of the measurement comes from the feedback loop architecture that forces an output toneburst to the transmitter to remain in quadrature with the signal recorded at the receiver. Flow velocity measurements in a column filled with saturated sand (subjected to salt tracer injections), were validated in an ASTM standard constant-head hydraulic test column. Several analytical solution solute transport models and a finite-element numerical model were applied to the test column and compared with measured data. Model predictions obtained before the actual experiments were conducted were very useful to determine expected salt breakthrough curves. The models were subsequently calibrated after the laboratory data were recorded. Results presented clearly indicate the importance of selecting models that incorporate appropriate boundary conditions.

The performance of storm water best management practices (BMPs) contains many uncertainties that make predicting BMP performance difficult. The objective of this study is to build a BMP performance model that incorporates uncertainty analysis and to evaluate this model using observed total suspended solids (TSS) from detention basin data sets in the International Stormwater BMP Database. The representative storage-treatment performance model, the $k\mathrm{\text{-}}{C}^{*}$ model, was chosen to represent BMP performance. Its input parameters, influent event mean concentration (EMC) ($C_{\mathrm{in}}$), and the areal removal rate constant ($k$) are considered with the uncertainty analysis. To estimate the variance associated with $k$, the prediction interval method is applied to the linear regression equation relating hydraulic loading rate ($q$) to $k$. To estimate the variance of $C_{\mathrm{in}}$, observed $C_{\mathrm{in}}$ data in the BMP database are used. This study assumes that both $C_{\mathrm{in}}$ and $k$ can be represented by lognormal distributions. The probability density function of effluent EMC ($C_{\mathrm{out}}$) is estimated and compared with observed effluent data $C_{\mathrm{out}}$ for three cases: uncertainty in $C_{\mathrm{in}}$, uncertainty in $k$, and uncertainty in both $C_{\mathrm{in}}$ and $k$. This study applies three different uncertainty methods: the derived-distribution method (DDM), Latin hypercube sampling (LHS), and the first-order second-moment (FOSM) method. Results show that LHS is the most efficient method among the three to characterize the uncertainty of $C_{\mathrm{out}}$ in univariate or bivariate cases in the $k\mathrm{\text{-}}{C}^{*}$ model. Moreover, the uncertainty of $C_{\mathrm{out}}$, considering uncertainty in both $C_{\mathrm{in}}$ and $k$, contains all observed data within a 95% confidence interval.

As a watershed is urbanized, characteristics of runoff from new upslope impervious surfaces may differ from runoff generated on the predevelopment soil surface in quantity, time of concentration, and sediment load. This may cause changes to the erosion regime on downslope soil surfaces. We simulated rainfall at three rates (20, 30, $40\mathrm{mm}/\mathrm{h}$) to generate runoff from $0.6{\mathrm{m}}^2$ boxes. Boxes were either treated with an impervious surface or filled with soil 0.2 m deep and were connected together in series of four boxes along the 4-m slope to produce different arrangements of impervious and pervious soil surfaces (0, 25, 50% impervious) and under different antecedent soil moisture conditions. Results indicate that previously established numerical models predicting runoff characteristics as a function of run-on characteristics generate good correlations at 0% imperviousness, but these correlations become insignificant as imperviousness increases. Imperviousness significantly influenced sediment regime, suggesting that some previously established equations relating soil erosion to run-on characteristics cannot be simply applied to areas where runoff production occurs on surfaces having an impervious component.

A methodology for maximum precipitation (MP) estimation that uses a physically based numerical atmospheric model is proposed in this paper. As a case study, the model-based 72-h MP was estimated for the American River watershed (ARW) in California for the December 1996–January 1997 flood event. First, a regional atmospheric model, MM5, was calibrated and validated for the December 1996–January 1997 historical major storm event for the ARW, on the basis of the U.S. National Center for Atmospheric Research (NCAR) reanalysis data to demonstrate the model capability during the historical period. Then, the model-simulated historical storm event was maximized by modifying its boundary conditions. The model-simulated precipitation field in the ARW was successfully validated at nine individual rain gauge stations in the watershed. The computed basin-averaged precipitation was somewhat higher than observations obtained by the spatial interpolation of the rain gauge observations. This result suggests a limitation of the spatial interpolation of ground rain gauge observations because they are mostly located in valleys, and the distribution of precipitation is highly heterogeneous over the mountainous terrain of the ARW. Next, to maximize precipitation over the watershed, the initial and boundary conditions in the outer nesting domain of the atmospheric model were modified. In this demonstrative study, the boundary conditions were modified by three methods: (1) maximizing the atmospheric moisture by setting the relative humidity at 100%; (2) maintaining the atmospheric boundary conditions corresponding to the state of the heaviest precipitation (maintaining equilibrium conditions); and (3) spatially shifting the atmospheric conditions to render the atmospheric moisture flux to hit the watershed. Because these modifications significantly increased the precipitation over the ARW, they clearly show the importance of wind and moisture conditions at the boundary of the atmospheric modeling domain. These different maximization methods produced similar 72-h precipitation depths, which were 549 mm by the combination of 100% relative humidity and equilibrium high precipitation conditions at the outer boundary of the model domain, and 541 mm from shifting the historical atmospheric conditions to the south by 5.0°. Accordingly, the 72-h maximum precipitation over the ARW was estimated to be approximately 550 mm. Although this study presents only a demonstrative maximization work, it shows that the presented modeling approach can be a potential alternative to standard probable maximum precipitation (PMP) estimation without depending on the linear relationships required in the standard PMP method. Also, because the proposed modeling approach is based on the initial and boundary atmospheric conditions from a synoptic scale that may be obtained from the NCAR/National Centers for Environmental Prediction reanalysis data for the historical period and from the general circulation model (GCM) climate projections, it can account for any nonstationarity that may be present in the hydro-climate system.

By using the double-decomposition (DD) method, this study simulates transient sediment waves caused by aggradation described by a diffusion-type partial differential equation (PDE). The DD method solves the PDE by decomposing the solution function for sediment rate into a summation of $M$ number of components, where $M$ stands for the order of approximation. The solution was approximated by considering only the first three terms. The model satisfactorily simulated laboratory-measured aggradation bed profiles with, on average, a mean absolute error (MAE) of 0.70 cm, a root-mean-square error (RMSE) of 0.84 cm, a mean relative error (MRE) of 1.11%, and $R^2=0.95$. The model performance was also tested by using numerical and error-function solutions. In addition, the results obtained from application of the DD solution to hypothetical field cases were found to be theoretically compatible with what may be observed in natural streams. However, sediment wave fronts in later periods of the simulation time reached equilibrium bed levels more quickly, around in the middle section of the channel.

A total of 21 gauges across the mountainous leeward portion of the island of Oʻahu, Hawaiʻi, were used to compare rainfall interpolation methods and assess rainfall spatial variability over a 34-month monitoring period from 2005 to 2008. Traditional and geostatistical interpolation methods, including Thiessen polygon, inverse distance weighting (IDW), linear regression, ordinary kriging (OK), and simple kriging with varying local means (SKlm), were used to estimate wet and dry season rainfall. The linear regression and SKlm methods were used to incorporate two types of exhaustive secondary information: (1) elevation extracted from a digital elevation model (DEM), and (2) distance to a regional rainfall maximum. The Thiessen method produced the highest error, whereas OK produced the lowest error in all but one period. The OK method produced more accurate predictions than linear regression of rainfall against elevation when the correlation between rainfall and elevation is moderate ($R<0.82$). The SKlm method produced lower error than linear regression and IDW methods in all periods. Comparison of the OK interpolation map with gridded isohyet data indicate that the areas of greatest rainfall deficit were confined to the mountainous region of west Oʻahu.

Monthly streamflow forecasting during spring-summer runoff season using snow telemetry (SNOTEL) precipitation and snow water equivalent (SWE) as predictors in the Rio Grande Headwaters Basin in Colorado was investigated. The transfer-function noise (TFN) models with SNOTEL precipitation input were built for monthly streamflow. Then, one-month-ahead forecasts of TFN models for the spring-summer runoff season were modified with SWE using an artificial neural networks (ANN) technique denoted in this study as hybrid $\mathrm{TFN}+\mathrm{ANN}$. The results indicated that the hybrid $\mathrm{TFN}+\mathrm{ANN}$ approach not only demonstrated better generalization capability but also improved one-month-ahead forecast accuracy significantly when compared with single TFN and ANN models. The normalized root mean squared errors (NRMSE) of one-month-ahead forecasts of TFN, ANN, and $\mathrm{TFN}+\mathrm{ANN}$ approaches for spring-summer runoff season were 0.38, 0.30, and 0.25. These findings accentuate that the presented stochastic hybrid modeling approach is an advantageous option to improve one-month-ahead forecast accuracy of monthly streamflow in spring-summer runoff season in the Rio Grande Headwaters Basin.