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Trapezoidal hyetographs are common in both real-world small watersheds and laboratory watersheds because (1) real-world hyetographs are often represented by line charts that can be divided into multiple trapezoidal rainfall pulses, and (2) laboratory rainfalls are usually generated by rainfall simulators uniformly in space and time, but when considering infiltration loss, the excess hyetographs may be approximated to be trapezoidal. Particularly, a trapezoidal hyetograph can be converted to a runoff hydrograph simply, accurately, and theoretically based on the general unit hydrograph model. The objective of this research is thus to test the theoretical trapezoidal hyetograph method with laboratory watershed rainfall-runoff data. The results showed that this theoretical method agrees very well with laboratory watershed data, with determination coefficients r2>0.93 for both constant and variable (incident) rainfall intensities. Therefore, the trapezoidal hyetograph method can be used to convert any line-chart hyetograph to a runoff hydrograph analytically, where rectangular and triangular hyetographs are special cases. Finally, the trapezoidal hyetograph method for a constant excess rainfall intensity (or the general rational method) is comparable to the classic kinematic wave theory for overland flow, but it is much simpler in applications. [ABSTRACT FROM AUTHOR]

In hydraulic and hydrologic modeling, the storage (S)-discharge (Q) relation is often represented by a straight line or a curve, although when plotted using field or experimental data it is found to be hysteretic or looped. The characteristics of this looped relation depend on geometric, hydrologic, and hydraulic conditions. Despite the widespread use of the storage-discharge relation, there does not appear to have been a mathematical treatment discussing what causes the relation to be looped or double-valued. The objective of this study, therefore, is to analyze the S-Q relation analytically for a catchment represented by a rectangular plane, considering rainfall excess (rainfall minus infiltration) and surface runoff or overland flow modeled by kinematic wave approximation. Depending on the duration of rainfall excess, two cases - equilibrium and partial equilibrium - are distinguished and for each case the looped relation is analyzed. It is shown that the loop is different for the two cases. [ABSTRACT FROM AUTHOR]

Time of concentration is an important parameter in rainfall–runoff models, such as the rational method and the unit hydrograph method, used for drainage design. There are several equations for computing the time of concentration. Many of these equations are empirical and are mostly based on length and slope, and some equations depend also on drainage area. Equations have also been derived using the kinematic wave theory, which accounts for length, slope, roughness coefficient, quality of flow (laminar, transient or turbulent) and shape (rectangular, converging, diverging, or diverging-converging), and rainfall or rainfall excess intensity and duration. In all of the equations, it is assumed that the rainstorm is stationary, but rainstorms are often dynamic and move in a particular direction and for a particular period of time, which significantly affect the time of concentration. There seems to have been no attempt to evaluate the impact of storm direction and duration as well as watershed shape on the time of concentration. The objective of this paper therefore is to revisit the concept of time of concentration and empirically derived equations, present the time of concentration equations for rectangular, converging, and diverging planes under stationary storms reported in the literature, examine the impact of moving storms for a rectangular plane, and compare these equations with empirically derived equations. The objective here is not to test or validate these equations for different watersheds. [ABSTRACT FROM AUTHOR]

Introduction and ObjectiveGiven the application of hydrological response in a watershed, various methods have been used to determine this response and the results have shown a high degree of accuracy and accuracy variability depending on the data used. By reviewing and summarizing the results of research carried out in the modeling of rainfall-runoff, particularly the time-area method, it was found that in most of these studies, the concept of watershed time concentration was used, which in most of the formulas used, the physical properties of the watershed were used and the dependence of time concentration on rainfall conditions was not studied. Therefore, this study was conducted to evaluate these methods using the kinematic wave method in the GIS environment, the HEC-1 method, and optimization methods using genetic algorithms in a V-shaped experimental watershed.Materials and Methods Observational data available in the V-shaped experimental watershed of the University of Illinois was used for rainfall-runoff modeling. The studied watershed had an impermeable aluminum surface and two uniform side sheets with a one-sided slope towards the channel with a constant value of 1%. In addition, a central channel with a one-sided slope towards the outlet of the watershed with a constant value of 1% was present. The roughness coefficient in this watershed was determined based on trial and error at 0.014.Results and DiscussionAfter preparing the time-area histogram of the watershed using each of the mentioned methods, the corresponding outflow hydrographs of the watershed were determined. Then, the results were compared with observational data, and various components of the computational hydrographs were also examined. The results showed that the performance of the genetic algorithm in determining the peak time of the hydrograph with a 15% relative error was better than the performance of the kinematic wave and HEC-1 models. Additionally, the genetic algorithm model had the highest correlation coefficient with observational hydrographs with an average Nash-Sutcliffe Index of 0.968 and an average correlation coefficient of 0.983. Furthermore, by fitting the curve to the modeling results, an equation was obtained to determine the equilibrium time of the watershed relative to rainfall intensity, with a determination coefficient of 0.999. This equation expresses the inverse relationship between equilibrium time and rainfall intensity (with a power of 0.33), i.e., doubling the rainfall intensity reduces the equilibrium time by 20%. Finally, the coefficient of the equation determining the equilibrium time for this watershed was found to be 495.2, and for each rainfall intensity, its corresponding equilibrium time can be calculated with high accuracy.Conclusion and Suggestions In this study, under experimental watershed conditions, rainfall-runoff modeling was performed with three categories of events and three categories of different rainfall durations, each event category having four different rainfall intensity sizes. Corresponding hydrographs were obtained for each event by examining the computational hydrographs and comparing them with observational hydrographs, and it was found that the three models had one to two percent relative error in determining the maximum runoff, but in determining the time to reach the hydrograph peak, the kinematic wave and HEC-1 models had an average error of 44%. Finally, using the correlation and Nash-Sutcliffe coefficients, it was determined that the computational hydrographs produced by the genetic algorithm method were closer to the observational hydrographs and had a higher degree of correlation. It is worth mentioning that in this experimental watershed, the dependence of equilibrium time on rainfall intensity in impermeable conditions was confirmed. It is recommended that the effect of infiltration or changes in surface roughness and the determination of the dependence size be investigated.

Abstract This paper proposes a kinematic wave‐based adaptive transit signal priority control (KATC) aiming to minimize average passenger delay at intersection level. The passenger delay minimization problem is formulated as a mixed‐integer non‐linear program (MINLP) with two decision variables of green time and phase sequence. The adoption of the phase sequence in the optimization and not involving the common simplifying assumptions in the delay models are the main contributions of the current study. General traffic and public transportation (PT) vehicle delay are estimated using kinematic wave theory. Genetic algorithm is utilized to solve the MINLP problem at 1‐cycle intervals and for a decision horizon of 3 consecutive cycles. The performance of KATC is evaluated against SYNCHRO and the KATC model without phase sequence optimization, using VISSIM. The results of the experiments indicate superior performance of KATC over the two other models in terms of both average passenger delay and PT passenger delay, especially at low congestion levels. Furthermore, increasing PT passenger occupancy can effectively contribute to higher passenger delay improvements. The adverse impacts on passenger vehicles are restricted to a 3.4% and 2.7% increase in general traffic delay compared to SYNCHRO and the KATC model without phase sequence optimization, respectively.

This paper proposes a kinematic wave‐based adaptive transit signal priority control (KATC) aiming to minimize average passenger delay at intersection level. The passenger delay minimization problem is formulated as a mixed‐integer non‐linear program (MINLP) with two decision variables of green time and phase sequence. The adoption of the phase sequence in the optimization and not involving the common simplifying assumptions in the delay models are the main contributions of the current study. General traffic and public transportation (PT) vehicle delay are estimated using kinematic wave theory. Genetic algorithm is utilized to solve the MINLP problem at 1‐cycle intervals and for a decision horizon of 3 consecutive cycles. The performance of KATC is evaluated against SYNCHRO and the KATC model without phase sequence optimization, using VISSIM. The results of the experiments indicate superior performance of KATC over the two other models in terms of both average passenger delay and PT passenger delay, especially at low congestion levels. Furthermore, increasing PT passenger occupancy can effectively contribute to higher passenger delay improvements. The adverse impacts on passenger vehicles are restricted to a 3.4% and 2.7% increase in general traffic delay compared to SYNCHRO and the KATC model without phase sequence optimization, respectively. [ABSTRACT FROM AUTHOR]

Abstract In many developing countries, due to economic constraints, a single station on a river reach is often equipped to record flow variables. On the other hand, hydrographs at the upstream sections may also be needed for especially assessing flooded areas. The upstream flow hydrograph prediction is called the reverse flood routing. There are some reverse flood routing pocedures requiring sophisticated methods together with substantial data requirements. This study proposes a new reverse flood routing procedure, based upon the simple kinematic wave (KW) equation, requiring only easily measurable downstream stage data. The KW equation is first averaged along a channel length at a fixed time, t, assuming that channel width is spatially constant, and then the spatially averaged equation is averaged in time, Δt. The temporally averaged terms are approximated as the arithmetical mean of the corresponding terms evaluated at time t and t + Δt. The Chezy roughness equation is employed for flow velocity, and the upstream flow stage hydrograph is assumed be described by a two parameter gamma distribution (Pearson Type III). The spatially averaged mean flow depth and lateral flow are related to the downstream flow stage. The resulting routing equation is thus obtained as a function of only downstream flow stage, meaning that the method mainly requires measurements of downstream flow stage data besides the mean values of channel length, channel width, roughness coefficient and bed slope. The optimal values of the parameters of reverse flood routing are obtained using the genetic algorithm. The calibration of the model is accomplished by using the measured downstream hydrographs. The validation is performed by comparing the model-generated upstream hydrographs against the measured upstream hydrographs. The proposed model is applied to generate upstream hydrographs at four different river reaches of Tiber River, located in central Italy. The length of river reaches varied from 20 to 65 km. Several upstream hydrographs at different stations on this river are generated using the developed method and compared with the observed hydrographs. The method predicts the time to peak with less than 5% error and peak rates with less than 10% error in the short river reaches of 20 km and 31 km. It also predicts the time to peak and peak rate in other two brances of 45 km and 65 km with less than 15% error. The method satisfactorily generates upstream hydrographs, with an overall mean absolute error (MAE) of 42 m3/s.

The storage–discharge (S-Q) relation, widely employed in hydrology and hydraulics, is often derived from empirical data and is found to be hysteretic or looped, although approximated by a straight line or a curve in hydrologic modeling. The nature of hysteresis depends on geometric and hydraulic conditions. Despite its ubiquitous use, an analytical treatment discussing what causes the storage–discharge relationship to exhibit a looped behavior does not seem to have been reported. This study analyzes the S-Q relation analytically using kinematic wave approximation for a watershed represented by a plane, considering simultaneously rainfall, infiltration, and surface runoff or overland flow. For purposes of simplicity and tractability of analytical solutions, both rainfall intensity and infiltration rate are assumed to be constant. Depending on the duration of rainfall, two cases—equilibrium and partial equilibrium—are distinguished. The hysteretic S-Q relationship is different for these two cases and requires close scrutiny, which is pursued in this study. It is emphasized that the assumptions of constant rainfall intensity and infiltration rate, rectangular geometry, and kinematic wave approximation undermine the dynamics of hysteresis. [ABSTRACT FROM AUTHOR]

Iran has geographically located in an arid and semi-arid climate in most regions. Precipitation and its distribution in such regions cause irreparable damage by creating seasonal floods. This study presents a suitable model for optimizing watershed management and flood control in order to reduce flood risks. To reach to this purpose, the concept of time-area diagram in HEC-HMS hydrological model as well Single Successive Sub-watershed Elimination (SSSE) is employed to simulate the flood hydrograph corresponding to the design precipitation for each sub-watershed. According to SCS model for estimating flood discharge and kinematic wave for flood routing, the curve number and Manning's roughness coefficient were calibrated and identified as the most effective parameters. After evaluating the different search methods and objective functions, the univariate gradient as best search method and the Nash-Sutcliffe as the best objective function was selected due to the highest consistency of the simulated discharge in the three events. Finally, the model was validated for 2 storms and the Nash-Sutcliffe values ​​were calculated as 0.948 and 0.892, respectively. After calculating the peak discharge of each sub-watershed, the effect of each on the output flood production was determined using F and f flood indices. Then, isochronic surfaces of the watershed were extracted using three methods and the spatial distribution of the sub-watersheds in the area was investigated. The results revealed that the level of 0.75-1 located in the middle part of the watershed is posed as the first priority. Also, it is colcluded that the surfaces near the outlet have played a much smaller role in peak discharge. In general, from the outlet to the upstream and middle parts of the watershed, as travel time level increases, the effect of sub-watersheds on peak flow discharge increases.

To estimate the damage caused by flooding rivers, it is critical to analyze unsteady flow and determine downstream water depth. Hydraulic methods for examining unsteady river flow require cross-sectional specifications of the river at a close distance with optimal accuracy. Obtaining these specifications is often time-consuming and expensive. In contrast, hydrologic routing methods, such as the linear Muskingum method, are more beneficial for the analysis of unsteady flow. In flood routing, the linear Muskingum method has only been utilized to calculate the outflow hydrograph (downstream). However, in practical problems regarding flood analysis, such as economic analysis, damage assessment, and flood management and engineering, downstream water depth is needed. By employing kinematic wave relations, the linear Muskingum method, and the Particle Swarm Optimization (PSO) algorithm, the present study estimates water depth, with respect to time, of a downstream section of the Karun River, between the Mollasani (upstream) and Ahwaz (downstream) hydrometric stations. The proposed approach is simpler and less expensive and more accurate than hydraulic methods. The current work estimated the values of the Mean Relative Error (MRE) to the total flood and the Mean Relative Error (MRE) to the peak section of input depth along with the absolute value of the peak deviations of the observed and routed depth (DPO) as 1.29, 0.24, and 1.16 percent, respectively. [ABSTRACT FROM AUTHOR]

In many developing countries, due to economic constraints, a single station on a river reach is often equipped to record flow variables. On the other hand, hydrographs at the upstream sections may also be needed for especially assessing flooded areas. The upstream flow hydrograph prediction is called the reverse flood routing. There are some reverse flood routing pocedures requiring sophisticated methods together with substantial data requirements. This study proposes a new reverse flood routing procedure, based upon the simple kinematic wave (KW) equation, requiring only easily measurable downstream stage data. The KW equation is first averaged along a channel length at a fixed time, t, assuming that channel width is spatially constant, and then the spatially averaged equation is averaged in time, Δt. The temporally averaged terms are approximated as the arithmetical mean of the corresponding terms evaluated at time t and t + Δt. The Chezy roughness equation is employed for flow velocity, and the upstream flow stage hydrograph is assumed be described by a two parameter gamma distribution (Pearson Type III). The spatially averaged mean flow depth and lateral flow are related to the downstream flow stage. The resulting routing equation is thus obtained as a function of only downstream flow stage, meaning that the method mainly requires measurements of downstream flow stage data besides the mean values of channel length, channel width, roughness coefficient and bed slope. The optimal values of the parameters of reverse flood routing are obtained using the genetic algorithm. The calibration of the model is accomplished by using the measured downstream hydrographs. The validation is performed by comparing the model-generated upstream hydrographs against the measured upstream hydrographs. The proposed model is applied to generate upstream hydrographs at four different river reaches of Tiber River, located in central Italy. The length of river reaches varied from 20 to 65 km. Several upstream hydrographs at different stations on this river are generated using the developed method and compared with the observed hydrographs. The method predicts the time to peak with less than 5% error and peak rates with less than 10% error in the short river reaches of 20 km and 31 km. It also predicts the time to peak and peak rate in other two brances of 45 km and 65 km with less than 15% error. The method satisfactorily generates upstream hydrographs, with an overall mean absolute error (MAE) of 42 m3/s. [ABSTRACT FROM AUTHOR]

Every year, about ten glaciers in the Western Pamirs are in the active stage of movement. The time from the beginning of the movement of kinematic waves along the glacier to the full completion of the pulsation takes, as a rule, 1– 2 years, and in some cases lasts up to 5 years. Activity of the Pamir glaciers in 2020 is discussed in this paper, and we suppose that some pulsations are still in progress in the following years. Data from a number of automatic satellite instruments were used for the analysis, but mainly these were obtained from the International Space Station. In 2020, 10 glaciers in the basins of the Surkhob, Muksu, Seldara, Kyzylsu and Vanch rivers became more active, and in some cases surged. Similar dynamic instability of glaciers was also characteristic for the preceding four years. At present, several major surges are taking place in the Western Pamirs; the Byrs, Vali, Lenin, and Medvezhy glaciers started the active phase of their developments. Therefore, it is necessary to study them by field methods and continue permanent monitoring of them from automatic satellites and the International Space Station.

Various dispersion mechanisms are known to link the spatial heterogeneity of the basin morphology and flow dynamics to the hydrologic response. Recent studies have conducted spatial analysis of the kinematic and geomorphological dispersion coefficients that characterize these mechanisms, as well as identified the influence of hillslopes, channels, and runoff production on their values. Nevertheless, an explicit and distributed dynamic representation of the travel times has not been used for this purpose. This study quantifies dispersion mechanisms by calculating spatially distributed flood wave travel times and hillslope and channel velocities, with a spatially distributed kinematic‐wave based model that explicitly accounts for the path heterogeneity, the dynamics of upstream flow contributions, and the nonlinear dependence on runoff intensity. Hence, the role of these factors and their influence on the dispersion mechanisms across different scales is studied in detail. Using different runoff intensities, the scaling of the dispersion mechanism coefficients according to the contributing areas within the Quintero Creek basin and two of its sub‐basins (in central Chile) is obtained. These scaling relationships are compared against those previously reported in the literature, which were obtained with approaches that simplify the treatment of travel times. Both basin‐specific and more general factors manifesting in the behavior of the dispersion mechanisms are found. Dispersion coefficients increase with area, and the role of the hillslope‐channel transition is controlled by runoff intensity, affecting the relative contribution of the dispersion mechanisms to the total dispersion at different spatial scales. Key Points: A distributed travel time model was used to analyze dispersion mechanisms by the explicit calculation of travel timesChanges in roughness and runoff intensity have an effect on the behavior of dispersion mechanisms across spatial scalesResults obtained through an explicit calculation of travel times differ from those obtained through simplified cases or parameterizations [ABSTRACT FROM AUTHOR]

Wave flood is the one kind of gradually varied flow. Flood prediction and flood control are very significant; therefore, one of the essential factors in design and evaluation of hydraulic structures and water resources planning is the prediction of flow discharge in rivers which is done by flood routing operation. Muskingum cunge is classified under hydraulic routing categories. This method has been used for modeling unsteady flows. Since this technique has sufficient accuracy, it does not need recorded data. In this study, in addition to the description of constant and variable parameters Muskingum-cunge method, the results were compared by numerical solution included kinematic wave using HEC-RAS software and dynamic model using Mike 11. Results represent that Muskingum-cunge method surely can be used for flood flow routing in rivers. [ABSTRACT FROM AUTHOR]

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the "simple" wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement. [ABSTRACT FROM AUTHOR]

[Display omitted] • Exponent in the kinematic wave equation α derived from column drainage experiments. • Variations in α related to the architecture of macropore networks imaged by X-ray. • Small α and thus fast macropore flow in cores from plough pan and subsoil horizons. • These pore networks were poorly connected, yet with vertically continuous biopores. • Results suggest pedotransfer approaches based on land use and horizon type. The rapid flow of water through soil macropores significantly affects the partitioning of precipitation between surface runoff and infiltration and also the rate of solute transport in soil, both of which have an impact on the risk of contamination of surface water and groundwater. The kinematic wave equation is often employed as a model of gravity-driven water flow through soil macropores. The exponent in this simple model influences the pore water velocity attained in the macropores at any given input rate and is usually estimated by inverse modelling against measured flow rates or water contents. In theory, the exponent in the kinematic wave equation should depend on the geometry and topology of the conducting macropore networks, although these relationships have not so far been investigated. In this study, we related metrics of soil structure derived from X-ray images to values of the kinematic exponent estimated from drainage experiments on twenty-two columns sampled at three different field sites under two contrasting land uses and at three different depths. We found that smaller values of the exponent in the kinematic wave equation, which would equate to more rapid flow of water through soil macropores, were found in plough pan and subsoil columns of smaller macroporosity, for which biopores comprised a significant fraction. The macroporosity in these columns was more vertically oriented and poorly inter-connected, though still continuous across the sample. In contrast, topsoil columns from both arable land and grassland had better connected, denser and more isotropically-distributed macropore networks and larger values of the kinematic exponent. Our results suggest that for predictive modelling at large scales, it may be feasible to estimate the kinematic exponent using class pedotransfer functions based on pedological information such as land use and horizon type. [ABSTRACT FROM AUTHOR]

Prediction of surface and subsurface runoff as elements of direct runoff of catchment is very important for designing hydraulic structures. In many of the catchments with high permeability and suitable vegetation, subsurface flow is also highly important. In this research, Hortonian mechanism has been used for predicting surface runoff of catchment overland using Kinematic wave method. For prediction of subsurface runoff of catchments hillslopes, Richard equation in an unsaturated zone by means of Hydrus software was used. Runoff hydrograph of subsurface runoff was calculated. For verification, experimental data from rainfall simulator with length of 2 meters, width of 1 meter and depth of 0.35 with loamy sand was used. The experiments were conducted under three angles of 0.1, 6.3 and 9 degrees and under rainfall intensity of 31.73, 47.6 and 63.46 millimeter per hour (mm / h), respectively. The subsurface and surface flow of the system were compared with the results of the kinematic wave in the surface flow and the results of the Hydrus model in the subsurface flow. The peak runoff mean error predicted by the kinematic wave method in the 12 events calculated is 3.5% and the mean prediction error of the subsurface runoff peak in 9 events is 10%, which is an acceptable value. The results of the Hydrus model for predicting the slope of zero tilt angle had 40% error in calculating the subsurface runoff peak that has not been acceptable.

Due to its simplicity, the kinematic wave is commonly applied to open-channel routing in watershed hydrologic modeling. However, these applications must fulfill certain conditions, such as relatively large riverbed slopes and long time of rise in the flow. This study attempts to determine the most appropriate kinematic wave scheme for open-channel routing in the highly regulated Peace River, Canada. Five schemes were used to simulate a 5-day hydrograph with sudden plunges and hikes. The outputs from these five schemes were compared visually and statistically with the observed hydrograph. It was found that all five schemes are applicable to open-channel routing for the highly regulated Peace River if the temporal and spatial increments are set properly. However, one scheme, which is a total variation diminishing (TVD) high-resolution scheme, is the most appropriate scheme for this purpose. This scheme allows large temporal and spatial increments while relatively high accuracy can be achieved. [ABSTRACT FROM AUTHOR]

Predicting the behavior of overland flow with analytical solutions to the kinematic wave equation is appealing due to its relative ease of implementation. Such simple solutions, however, have largely been constrained to applications on simple planar hillslopes. This study presents analytical solutions to the kinematic wave equation for hillslopes with modest topographic curvature that causes divergence or convergence of runoff flowpaths. The solution averages flow depths along changing hillslope contours whose lengths vary according hillslope width function, and results in a one‐dimensional approximation to the two‐dimensional flow field. The solutions are tested against both two‐dimensional numerical solutions to the kinematic wave equation (in ParFlow) and against experiments that use rainfall simulation on machined hillslopes with defined curvature properties. Excellent agreement between numerical, experimental and analytical solutions is found for hillslopes with mild to moderate curvature. The solutions show that curvature drives large changes in maximum flow rate qpeak and time of concentration tc, predictions frequently used in engineering hydrologic design and analysis. [ABSTRACT FROM AUTHOR]

A distributed hydrologic model based on a kinematic wave approximation with surface and subsurface flow components is applicable to basins that have temperate climatic conditions similar to those in Japan. However, it is difficult to present long-term river discharge using the existing model structure in basins with different climatic conditions. This study aims to improve the model structure for better estimates of long-term discharge in the Nam Ngum River, the main tributary of the Mekong River, by incorporating bedrock aquifers as part of the slope flow component of the original model structure. Three bedrock groundwater structures are configured to incorporate the original model structure. The results show that a combination of the original model component and one unconfined aquifer structure are the best representations of the river flow regime from the original model structure, in which the rate of infiltration from the layer into the bedrock aquifer was calculated using vertical hydraulic conductivity. The Nash--Sutcliffe efficiency coefficient of the original and improved models increased from 0.80 to 0.86 during the calibration period and from 0.56 to 0.62 during the validation period. The results of this study show that the improved model structure is applicable for long-term hydrologic predictions in Southeast Asian catchments with distinct dry and rainy seasons. [ABSTRACT FROM AUTHOR]

In our study, a system of seven natural terraces interspersed with six field belts situated at the Knínice locality (the Ore Mts., North-West Bohemia) was selected as the experimental catchment area. Overland flow was computed using two different methods: the kinematic wave method and the SCS dimensionless Unit hydrograph (UH). For the kinematic wave method calculations the KINFIL software was used; for SCS dimensionless hydrograph the HEC-HMS software was applied. The results compare hydrographs with N-year recurrence of rainfall-runoff time, where N = 10, 20, 50, and 100 years. The comparison provides hydraulic results with terraces and without terraces computed using both mentioned software products. Although two different methods of overland flow computation were performed, the input data obtained from geodetic and hydrological measurements were identical. Results of the comparison are presented and discussed.

This paper describes the continuation of simulated outcomes from the plots No. 4 and No. 5 with two different soils, using the KINFIL model to assess the runoff from extreme rainfall. The KINFIL model is a physically-based, parameter-distributed 3D model that has been applied to the Třebsín experimental station in the Czech Republic. This model was used for the first time in 2012 to simulate the impact of overland flow caused by natural or sprinkler-made intensive rains on four of the nine experimental plots. This measurement of a rain simulator producing a high-intensity rainfall involves also hydraulic conductivity, soil sorptivity, plot geometry and granulometric curves to be used for the present analysis. However, since 2012, the KINFIL model has been amended to provide a more effective comparison of the measured and computed results using the values of new parameters such as storage suction factor and field capacity on plot 4 and plot 5. The KINFIL model uses all input data mentioned above, and it produces the output data such as gross rainfall, effective rainfall, runoff discharge hydraulic depths, hydraulic velocities and shear velocities as well as shear stress values depending on the soil particle distribution. These processes are innovative, physically based, and both the measured and the computed results fit reliably.

Spatially distributed travel time (SDTT) methods have been developed as an alternative to semidistributed and fully distributed methods for rainfall‐runoff modeling. In these methods, the travel times of grid cells are summed along flow paths and then convoluted to generate the hydrograph at the outlet. One central aspect of SDTT models that remains partially addressed is the effect of upstream flow contributions and their dynamics on the calculated flood wave travel times. Some methods neglect upstream contributions, but these are known to produce incorrect representations of the hydrological response. Other methods assume static upstream contributions, but the reliability of this approximation is poorly understood. In this study, we develop a new travel time method that accounts for dynamic upstream contributions. We test our method in three synthetic basins generated with a landscape evolution model that allows explicit control of primary watershed characteristics. We evaluate the method's performance for different storms by comparing its response to that produced by a fully distributed kinematic wave model. Furthermore, the method is tested in a real basin. We also analyze the dynamic behavior of the upstream contribution and travel times within the synthetic basins. Results show that existing static upstream contribution approaches in SDTT models do not adequately reproduce the hydrographs from the fully distributed kinematic wave model nor the observed hydrograph of the real basin. The proposed method improves the reproduction of hydrograph peak flows and temporal variability. Furthermore, the instantaneous unit hydrographs produced by the new method exhibit more positive skewness than the static approximations. Key Points: A particle tracking approach was used to account for dynamic upstream contributions in a travel time formulation applied to SDTT modelsConsidering dynamic upstream contributions significantly improves the performance of SDTT models as compared to assuming static onesThe asymmetry of the hydrographs produced by a fully distributed kinematic wave model is better reproduced with the proposed approach [ABSTRACT FROM AUTHOR]

Ecological theory emphasizes headwater streams and wetlands as hotspots for metabolism of terrestrially derived organic matter and biogeochemical transformations. Time of concentration Tc is defined as the wave travel time from the most hydraulically remote point to the point of study. Tc is an important element in hydrological studies, especially in drainage system designs and the estimations of flood arrival time. The common approach in the estimation of Tc is based on Kinematic Wave (KW) approximation for both overland flow and river routing. This approximation, however, may not be appropriate on a flood plain with inundations. The main objective of this study is to propose the estimation of Tc with Diffusive Wave (DW) approximation considering the effect of flood inundation. The proposed method is demonstrated in the Kelantan River basin, Malaysia, focusing on a severe flood event in December 2014. This study compares the estimated Tc with other estimations based a Rainfall-Runoff-Inundation simulation and with a simple correlation method between rainfall amount in different durations and peak river discharges. In consequence, the proposed method with DW approximation with flood inundation showed closer estimations of Tc by the other two methods. [ABSTRACT FROM AUTHOR]

Real and scenario prognosis in engineering hydrology often involves using simulation techniques of mathematical modelling the rainfall-runoff processes in small catchments. These catchments are often up to 50 km2 in area, their character is torrential, and the type of water flow is super-critical. Many of them are ungauged. The damage in the catchments is enormous, and the length of the torrents is about 23% of the total length of small rivers in the Czech Republic. The Smědá experimental mountainous catchment (with the Bílý potok downstream gauge) in the Jizerské hory Mts. was chosen as a model area for simulating extreme rainfall-runoff processes using two different models. For the purposes of evaluating and simulating significant rainfall-runoff episodes, we chose the KINFIL physically-based 2D hydrological model, and ANN, an artificial neural network mathematical "learning" model. A neural network is a model of the non-linear functional dependence between inputs and outputs with free parameters (weights), which are created by iterative gradient learning algorithms utilizing calibration data. The two models are entirely different. They are based on different principles, but both require the same time series (rainfall-runoff) data. However, the parameters of the models are fully different, without any physical comparison. The strength of KINFIL is that there are physically clear parameters corresponding to adequate hydrological process equations, while the strength of ANN lies in the "learning procedure". Their common property is the rule that the greater the number of measured rainfall-runoff events (pairs), the better fitted the simulation results can be expected.

A modified Green-and-Ampt model is formulated to quantify infiltration on sloping terrain underlain by homogeneous soil wetted by surficial water application. This paper’s theory for quantifying infiltration relies on the mathematical statement of the coupled partial differential equations (pdes) governing infiltration and runoff. These pdes are solved by employing an explicit finite-difference numerical method that yields the infiltration, the infiltration rate, the depth to the wetting front, the rate of runoff, and the depth of runoff everywhere on the slope during external wetting. Data inputs consist of a water application rate or the rainfall hyetograph of a storm of arbitrary duration, soil hydraulic characteristics and antecedent moisture, and the slope’s hydraulic and geometric characteristics. The presented theory predicts the effect an advancing wetting front has on slope stability with respect to translational sliding. This paper’s theory also develops the 1D pde governing suspended sediment transport and slope degradation caused by runoff influenced by infiltration. Three examples illustrate the application of the developed theory to calculate infiltration and runoff on a slope and their role on the stability of cohesive and cohesionless soils forming sloping terrain. [ABSTRACT FROM AUTHOR]

The effect of rainfall spatial distribution and duration on determining rainfall spatial resolution for runoff discharge prediction and equilibrium time estimation was studied. We simulated hydrographs and equilibrium times of storms which have the same spatial averaged rainfall intensity with wide range of spatial distributions and durations under stationary storm conditions on an idealized plane. The equilibrium times under various rainfall conditions were estimated with an approximate solution based on the kinematic wave assumption. The runoff hydrographs were simulated using a kinematic wave runoff model. The approximate and computed results were used to investigate the relationship between the spatial–temporal rainfall characteristics and rainfall spatial resolution. From the simulated results, it was found that (i) A required rainfall spatial resolution to achieve threshold accuracy depended on rainfall spatial distribution. For the simulated cases, the critical rainfall spatial resolution was higher as the slope of rainfall spatial distribution was steeper. (ii) The rainfall duration, as well as rainfall spatial distribution, was an important factor for determining a required rainfall spatial resolution for accurate flood prediction. The required rainfall spatial resolution to achieve threshold prediction accuracy was higher as the rainfall duration was shorter. (iii) The rainfall spatial distribution and duration which were traditionally neglected need to be considered in lumped runoff modelling or measurement as an important factor. Although limited to the ideal test cases, the maximum errors due to the low rainfall spatial resolution for the equilibrium time and peak discharge were about 25% and 35%, respectively. [ABSTRACT FROM AUTHOR]

Despite advancements in developing physics-based formulations to estimate the sheet-flow travel time ( t SHF ), the quantification of the relative impacts of influential parameters on t SHF has not previously been considered. In this study, a brief review of the physics-based formulations to estimate t SHF including kinematic wave (K-W) theory in combination with Manning’s roughness (K-M) and with Darcy-Weisbach friction formula (K-D) over single and multiple planes is provided. Then, the relative significance of input parameters to the developed approaches is quantified by a density-based global sensitivity analysis (GSA). The performance of K-M considering zero-upstream and uniform flow depth (so-called K-M1 and K-M2), and K-D formulae to estimate the t SHF over single plane surface were assessed using several sets of experimental data collected from the previous studies. The compatibility of the developed models to estimate t SHF over multiple planes considering temporal rainfall distributions of Natural Resources Conservation Service, NRCS (I, Ia, II, and III) are scrutinized by several real-world examples. The results obtained demonstrated that the main controlling parameters of t SHF through K-D and K-M formulae are the length of surface plane (mean sensitivity index T ̂ i  = 0.72) and flow resistance (mean T ̂ i  = 0.52), respectively. Conversely, the flow temperature and initial abstraction ratio of rainfall have the lowest influence on t SHF (mean T ̂ i is 0.11 and 0.12, respectively). The significant role of the flow regime on the estimation of t SHF over a single and a cascade of planes are also demonstrated. Results reveal that the K-D formulation provides more precise t SHF over the single plane surface with an average percentage of error, APE equal to 9.23% (the APE for K-M1 and K-M2 formulae were 13.8%, and 36.33%, respectively). The superiority of Manning-jointed formulae in estimation of t SHF is due to the incorporation of effects from different flow regimes as flow moves downgradient that is affected by one or more factors including high excess rainfall intensities, low flow resistance, high degrees of imperviousness, long surfaces, steep slope, and domination of rainfall distribution as NRCS Type I, II, or III. [ABSTRACT FROM AUTHOR]

Although process-based distributed hydrological models (PDHMs) are evolving rapidly over the last few decades, their extensive applications are still challenged by the computational expenses. This study attempted, for the first time, to apply the numerically efficient MacCormack algorithm to overland flow routing in a representative high-spatial resolution PDHM, i.e., the distributed hydrology-soil-vegetation model (DHSVM), in order to improve its computational efficiency. The analytical verification indicates that both the semi and full versions of the MacCormack schemes exhibit robust numerical stability and are more computationally efficient than the conventional explicit linear scheme. The full-version outperforms the semi-version in terms of simulation accuracy when a same time step is adopted. The semi-MacCormack scheme was implemented into DHSVM (version 3.1.2) to solve the kinematic wave equations for overland flow routing. The performance and practicality of the enhanced DHSVM-MacCormack model was assessed by performing two groups of modeling experiments in the Mercer Creek watershed, a small urban catchment near Bellevue, Washington. The experiments show that DHSVM-MacCormack can considerably improve the computational efficiency without compromising the simulation accuracy of the original DHSVM model. More specifically, with the same computational environment and model settings, the computational time required by DHSVM-MacCormack can be reduced to several dozen minutes for a simulation period of three months (in contrast with one day and a half by the original DHSVM model) without noticeable sacrifice of the accuracy. The MacCormack scheme proves to be applicable to overland flow routing in DHSVM, which implies that it can be coupled into other PHDMs for watershed routing to either significantly improve their computational efficiency or to make the kinematic wave routing for high resolution modeling computational feasible. [ABSTRACT FROM AUTHOR]