Journal of Hydrologic Engineering

A rainfall-runoff model based on a digital elevation model was employed for investigation of spatial variability in hydrologic modeling in a small catchment (3 km²) in South Australia. The study improves an existing model, THALES, by further developing the time-variant, spatially distributed watershed moisture representation, and by also developing spatially distributed rainfall as input rainfall data. A time-variant threshold or boundary wetness index is developed as a function of antecedent baseflow of the storms. The boundary wetness index was used to distinguish and represent spatially and temporally variable saturation and nonsaturation areas of a watershed at the beginning of and during a storm. Spatially distributed rainfalls were developed to reduce the impact of single-gauge rainfall on runoff prediction results. The representation of moisture distribution was found to be the most important factor for runoff prediction in this study, while spatial rainfall was the second most important. The study suggests that runoff prediction errors are closely related to the lack of spatial resolution in input data, as well as the lack of effective tools to describe spatial variability, particularly under dry field conditions.

The Muskingum model is a two-parameter model that is applicable for single inflow flood routing. In real world problems, a number of tributaries join the main channel at different locations constituting a channel network. In order to simulate the flood flow in river networks using the Muskingum method, the multiple inflows are substituted by the equivalent single inflow. The present model structure is simple and gives a general form of the basic Muskingum equation. The numerical application of the model was performed using flood events of the upper Narmada Basin (India). The parameters k and x for the single equivalent network inflow were estimated using the finite-difference form of the model. The performance of this model is compared with other reported multiple inflows routing models. Application of the model to an example of single inflow routing problem shows that the present model is efficient in estimating the Muskingum model parameters. Results of the sensitivity analysis of the model parameters shows that a unique set of parameters exists that would result in the best performance for a given multiple inflows routing problem.

A method to convert a known unit hydrograph to unit hydrographs of different durations, as an alternative to the S-Hydrograph method, is introduced. The method—called the Complementary Hydrograph method—involves a process of decomposing a known unit hydrograph of duration $t_o$ into a pair of “complementary” hydrographs associated with two sequential rainfalls with the sum of their durations equal to $t_o\text{.}$ In converting the $t_o$-hour unit hydrograph into a $t_a$-hour unit hydrograph, the method produces a unit hydrograph of duration $t_b=(t_o-t_a)$ concurrently. In hydrograph conversion, the Complementary Hydrograph method produces an identical result to the well-established S-Hydrograph method and involves a comparable number of computational steps. In certain special cases, such as converting a unit hydrograph into one with half its duration, the new method requires fewer computational steps. While the two methods employ different approaches in their solutions of hydrograph conversion problems, the agreement in their results stems from the fact that both methods are founded on the same principles of superposition and linearity of the unit hydrograph method. The S-Hydrograph method can also be viewed as a special case of the Complementary Hydrograph method in which the known hydrograph is associated with a storm of infinite duration and uniform intensity. The Complementary Hydrograph method offers a more unified and versatile approach in dealing with various types of unit-hydrograph conversion problems. For example, the method can be extended to derive unit hydrographs from a hydrograph associated with a multiperiod, varied intensity rainfall. The use of S-Hydrograph method for hydrograph derivation can only be applied to hydrographs resulting from a single-period rainfall of uniform intensity.

The operational cycle of a stormwater quality control basin can be divided into the waiting period between events and the filling and draining period during an event. In this study, an inherent overflow risk is defined as the probability of having a large event exceed the basin storage capacity. Such a probability is prescribed by the basin storage capacity and the local distribution of rainfall event depths. An operational overflow risk is defined as the probability of having the basin overwhelmed by a subsequent storm event during the draining process. An operational risk is found to be dependent on watershed runoff coefficient, basin drain time, local average rainfall event depth, and average rainfall interevent time. In practice, the selection of a basin drain time is a tradeoff between the removal of suspended solids in stormwater and the overflow risk. The concept of “the longer, the better” applies to the sedimentation process, but concern for the overflow risk requires that the basin drain as fast as possible. This paper presents a design method by which the overflow risk associated with a basin storage volume can be evaluated for various drain times. The mathematical models developed to describe the distribution of rainfall interevent time and the runoff capture curve provide good agreement with the long-term continuous rainfall data recorded in seven metropolitan areas in the United States. The risk-based approach developed in this study provides a quantifiable basis for making the decision on the operation of a stormwater quality control basin.

Competing theories used to describe coupled transport of heat and water in soil are irreversible thermodynamics (IT) and the Philip–de Vries (PD) theory. In practice, PD has dominated the field and advanced understanding through models used to predict the thermal status of soil and soil-atmosphere interaction. However, the principle of Onsager reciprocity in IT has also found considerable acceptance in thermal physics. The applicability of IT reciprocity to soil physics has been extensively scrutinized without substantial agreement being reached. Examination of PD equations reveals that they do not satisfy Onsager reciprocity. One coefficient is missing from PD that would produce equations consistent with reciprocity. The coefficient is associated with the thermal water flux, but it fails to appear a second time in the heat flux equation as expected with reciprocity. This missing coefficient can be readily calculated for inclusion in models based on PD. The value of the coefficient varies with temperature and water potential from negligible to several times the PD coefficient to which it must be added. Heat of transport is also calculated and found to vary from 0.33 J/g in relatively wet soil to 9,071 J/g in drier soil, increasing slightly also with temperature.

The lognormal distribution is frequently used in hydrological studies. However, the distribution is in the form of an integral that cannot be expressed in the form of elementary functions. Thus, the lognormal distribution cannot be used for analytical purposes such as the application of the inverse transform method for generation of a sequence of lognormally distributed random numbers. In this study, a function that closely approximates the lognormal distribution is presented and its use demonstrated in hydrological studies.

Time of travel in channel is an important parameter in drainage design. By means of the kinematic wave theory, it is possible to obtain an analytical time of travel formula for certain idealized channel conditions. Hitherto, the kinematic wave theory has been applied to the rectangular channel of special cases only, such as the wide rectangular channel, the square channel, and the deep rectangular channel. In this paper, the discharge-flow area parameters are derived for a rectangular channel of any flow depth, namely, the general rectangular channel. If these parameters are incorporated into the existing computer programs, it will enable these programs to model the general rectangular channel. Further, based on the kinematic wave theory, a generalized time of travel formula for a rectangular channel is developed. It is applicable to the general rectangular channel subject to a uniform lateral inflow and a constant upstream inflow. For the case of zero upstream inflow, the general formula is compared with the formulas for the wide rectangular channel, the square channel, and the deep rectangular channel. The comparisons show that the general formula is consistent with the formulas of special cases.