Journal of Hydrologic Engineering

Although the importance of subgrid variability in the snow model has been recognized, only a few modeling studies on the parameterization of subgrid effects have been performed. This study proposes a new upscaling approach from a single-layered point-scale snow model toward a finite-scale model, using the probability density functions (PDF). The Fokker-Planck equation (FPE) for the snowmelt process is formulated in a two-dimensional probability domain for snow temperature versus snow depth. This Fokker-Planck equation, governing the evolution of the probability density of the snow temperature–snow depth bivariate state variable, can describe the subgrid effects of the snow process. The numerical solutions of the FPE are validated with Monte Carlo simulations. It is demonstrated that the derived FPE can express the spatial variability of the snow process sufficiently well once the necessary information on the spatial variation in shortwave radiation and snowfall are given. The validation results are encouraging and point toward potential use of this PDF model as an engine for large-scale grid-based modeling to capture the subgrid variability of snow processes.

The phenomenon of stream-aquifer interaction was investigated using a reduced scale sand tank model coupled with mathematical modeling using the Boussinesq equation. The effect of highly fluctuating transient stream level on the subsequent propagation of hydraulic transients in the adjacent aquifer was quantified using solutions to the linearized and the nonlinear Boussinesq equation. The semigroup solution of the linearized equation and the temporal-partial decomposition solution of the nonlinear equation were investigated subject to a transient, large-amplitude, periodic boundary condition. The models were verified with a limited numerical solution to the nonlinear Boussinesq equation and compared and assessed as to their ability to reproduce measured water table hydrographs at different locations in the laboratory model. Results indicated that the linearized solution and the nonlinear model coincided well with the numerical solution and with the observed hydrograph. Using decomposition the derivation of a solution to the nonlinear equation is simpler than that of a linear one.

A two-sample nonlinear heteroscedastic regression model is described and proposed for the purpose of evaluating a sewer basin rehabilitation by quantifying the reduction in rain-derived inflow and infiltration (RDII). The proposed methodology is used at the second stage of RDII studies after RDII volumes of individual rain events are estimated. The proposed methodology utilizes boundary conditions of system capacity and extrapolates the RDII behavior under usually unobserved heavy design storms in short-term flow data series—a common problem in RDII studies. As compared to the commonly used linear models, the proposed methodology offers flexibility in modeling, reasonable extrapolation, and simplicity in interpretation.

Undercutting, primarily considered due to fluvial mechanisms, has been reported to have a major impact on slope failure. Predicting bank collapse specifically due to seepage erosion undercutting by particle mobilization on layered streambanks has not been fully studied or modeled, even though its role in streambank erosion may be important. The limitation originates from the limited field measurements or laboratory experiments as well as the unavailability of discrete element models that can effectively simulate seepage particle mobilization, undercutting, and the corresponding mass wasting. The objective of this research was to demonstrate a procedure for incorporating seepage undercutting into bank stability models and to investigate the role of seepage undercutting on bank instability. The question to be addressed is whether seepage particle mobilization can lead to distances of undercutting that are a significant cause of bank instability. A numerical finite-element model, SEEP/W, was used to model soil-water pressure variations during seepage observed in laboratory experiments with two-dimensional soil lysimeters. Flow parameters were calibrated using measured soil-water pressure and cumulative discharge. A general limit equilibrium bank stability model (SLOPE/W) was used to simulate bank stability with and without seepage erosion undercutting by comparing the computed factor of safety, $\mathit{Fs}$ , at different stages of the seepage erosion process with regard to input parameter uncertainty using Monte Carlo analysis. The percentage decrease in the mean $\mathit{Fs}$ ranged between 42 and 91% as the depth of undercutting increased, dependent upon the initial stability of the bank. A stable bank (i.e., $\mathit{Fs}>1$ ) can quickly become unstable (i.e., $\mathit{Fs}<1$ ) when seepage undercutting is considered. For stable banks, the probability of failure reached 100% when the depth of the undercutting reached approximately $30\text{to}50\mathrm{mm}$ under these experimental conditions. The results derived are specific to the streambank simulated but are expected to be comparable for similar layered streambank lithologies reported to occur in numerous geographical locations. This research also highlights the need to incorporate the dynamic process of seepage erosion undercutting into integrated subsurface flow and streambank stability models.

A permeable pavement parking lot in eastern North Carolina consisting of four types of permeable pavement and standard asphalt was monitored from June 2006 to July 2007 for hydrologic differences in pavement surface runoff volumes, total outflow volumes, peak flow rates, and time to peak. The four permeable sections were pervious concrete (PC), two types of permeable interlocking concrete pavement (PICP) with small-sized aggregate in the joints and having 12.9% (PICP1) and 8.5% (PICP2) open surface area, and concrete grid pavers (CGP) filled with sand. The site was located in poorly drained soils, and all permeable sections were underlain by a crushed stone base layer with a perforated underdrain. All permeable pavements significantly reduced surface runoff volumes and peak flow rates from those of asphalt $(p<0.01)$ . Of the permeable pavements, CGP generated the greatest surface runoff volumes $(p<0.01)$ . The PICP1 and CGP cells generated significantly lower total outflow volumes than all other sections evaluated $(p<0.01)$ , and had the lowest peak flows and the longest time to peak. The response of the PICP1 cell was likely due to an increased base storage volume resulting from an elevated pipe underdrain whereas the CGP cell response was attributed to water retention in the sand fill layer. Overall, different permeable pavement sections performed similarly, but were substantially different from asphalt. Subtle differences in the performance of CGP were primarily due to the characteristics of the sand filled media compared to small aggregate typically used in PC and PICP joints and bedding.

Rainfall disaggregation in time can be useful for the simulation of hydrologic systems and the prediction of floods and flash floods. Disaggregation of rainfall to timescales less than $1\mathrm{h}$ can be especially useful for small urbanized watershed study, and for continuous hydrologic simulations and when Hortonian or saturation-excess runoff dominates. However, the majority of rain gauges in any region record rainfall in daily time steps or, very often, hourly records have extensive missing data. Also, the convective nature of the rainfall can result in significant differences in the measured rainfall at nearby gauges. This study evaluates several statistical approaches for rainfall disaggregation which may be applicable using data from West-Central Florida, specifically from $1\mathrm{h}$ observations to $15\min$ records, and proposes new methodologies that have the potential to outperform existing approaches. Four approaches are examined. The first approach is an existing direct scaling method that utilizes observed $15\min$ rainfall at secondary rain gauges, to disaggregate observed $1\mathrm{h}$ rainfall at more numerous primary rain gauges. The second approach is an extension of an existing method for continuous rainfall disaggregation through statistical distributional assumptions. The third approach relies on artificial neural networks for the disaggregation process without sorting and the fourth approach extends the neural network methods through statistical preprocessing via new sorting and desorting schemes. The applicability and performance of these methods were evaluated using information from a fairly dense rain gauge network in West-Central Florida. Of the four methods compared, the sorted neural networks and the direct scaling method predicted peak rainfall magnitudes significantly better than the remaining techniques. The study also suggests that desorting algorithms would also be useful to randomly replace the artificial hyetograph within a rainfall period.

The accuracy of soil moisture vertical profiles simulated by a conceptual model during erratic rainfall is investigated through laboratory and field experiments. Simulations were performed by a conceptual model earlier formulated for the estimate of local infiltration into vertically homogeneous soils. Laboratory and field experiments were set up. The results indicated that the conceptual model appropriately simulated the observed vertical profiles of soil water content during the stages of infiltration and reinfiltration produced by a wide variety of rainfall patterns. Thus, the conceptual model investigated may be considered a suitable component of watershed hydrological models as well as of models coupling soil and atmosphere.

This study focuses on the sensitivity of streamflow simulations to temporal variations in radar reflectivity–rainfall (i.e., $Z–R$ ) relationships. The physically based continuous-mode distributed hydrologic model—gridded surface subsurface hydrologic analysis—is used to predict runoff during three major rainfall-runoff periods observed in a $35{\mathrm{km}}^2$ experimental watershed in southern Louisiana. $Z–R$ relationships are derived at a series of temporal scales ranging from a climatological scale, where interstorm $Z–R$ variations are ignored, down to a subevent scale, where variations in rainfall type (convective versus stratiform) are taken into account. The analysis is first performed using $Z$ and $R$ data pairs derived directly from disdrometer drop size distribution measurements, and then repeated using WSR-88D radar reflectivity data. The degree of sensitivity in runoff simulations to temporal variations in $Z–R$ relationships depends largely on the method used to derive the parameters of these relationships. Using event-specific $Z–R$ relationships results in accurate hydrographs when the parameters are derived based on bias removal and minimization of random errors of rainfall estimates. Methods based on least-squares fitting require refining the derivation of $Z–R$ parameters down to a subevent scale, which is not practically feasible. A simple and practical method based on selection of a climatologically representative exponent of the $Z–R$ relationships and adjusting the multiplier coefficient through bias removal still results in reasonably accurate runoff simulations, but only when event-specific $Z–R$ relationships are used.

This paper describes laboratory experiments that provide evidence of infiltration of excess runoff water from upstream areas that moves downslope over unsaturated areas (run-on process). The experiments were carried out using a tilting tank that was packed with two different natural soils to a depth of $70\mathrm{cm}$ and subjected to artificial rainfalls from a rainfall simulator. Different rainfall patterns were generated over the surface at different slope settings. Measurements of overland flow, deep flow, and soil water content, together with photographs of soil surface, were used to quantify the main features of the run-on process. The results indicate that the interaction between Hortonian overland flow and local infiltration over the permeable areas can be appropriately described by representing the flow depth per unit time as an “additional” rainfall rate. Thus, these experimental results support the representation of the run-on process that was adopted in previous numerical studies that evaluated the effects of the run-on process.

We present an analytical solution of the one-dimensional contaminant transport undergoing advection, dispersion, sorption, and first-order decay, subject to a first-order decaying contaminant concentration at the source and a Type I, Dirichlet, boundary at infinity. This solution is unique because of the boundary conditions imposed, but similar to other published solutions. We briefly describe the governing equations, boundary and initial conditions, and the solution techniques used to develop the analytical solution. We provide and discuss the analytic solution using examples with source decay less than, equal to, and greater than contaminant decay during transport. Then we compare the results to several published solutions in the fields of radioactive waste disposal and recalcitrant nonaqueous phase liquid modeling. The other analytical solution results are similar to ours, but the RT3D solution shows more numerical dispersion than our solution.

The attenuation is considered to be a serious problem when rainfall is measured by $C$ or $X$ -band weather radar. In this study, a stability analysis has been presented which showed that: (1) a numerical attenuation correction algorithm should be unstable if the sum of measured reflectivity at a gate and path integrated attenuation up to the previous gate is greater than an upper limit, which in turn depends on the slope of the specific attenuation curve; (2) two true reflectivities exist for a particular measured reflectivity and both the true reflectivities may need to be retrieved. Besides these, it has also been shown that the attenuation correction scheme can be very sensitive to measurement error when the true reflectivities are greater than or equal to $60\mathrm{dBZ}$ .