TECHNICAL NOTE Time of concentration formulae for planes with upstream inflow

Abstract

Due to changes in physical characteristics, the valley side of a drainage basin may be represented by a series of overland planes. In such a situation, the downstream outflow from one plane becomes the upstream inflow for the subsequent plane. Based on the kinematic wave equations, two time of concentration (time to equilibrium) formulae are derived for planes subject to uniform rainfall excess and with a constant upstream inflow. For practical applications, the formulae are further developed in terms of the Manning resistance coefficient. The derived formulae are all consistent with those published for the case of zero upstream inflow.     

How nature uses overland flow regime to maximize equilibrium detention storage and flood attenuation

Equilibrium detention storage is an important parameter as it has a proportional effect on flood attenuation. In this paper, based on the kinematic wave theory, a working formula for the equilibrium detention storage of an overland plane with upstream inflow has been derived. Since the flow regime over a concrete plane can vary throughout the entire range laminar to turbulent, this case has been selected to examine the effect of flow regime on the equilibrium detention storage. In the examination, the derived formula has been applied to four flow regimes: (a) laminar, (b) transitional, (c) near turbulent, and (d) turbulent. The examination shows that for planes with a small discharge, laminar flow gives the maximum detention storage. For planes with a medium discharge, transitional flow gives the maximum detention storage, and for planes with a large discharge, near turbulent flow gives the maximum detention storage. The flow regime can cause more than two‐fold increase in detention storage. All these results can be attributed to the respective flow resistance, and have been endorsed with analyses of the water surface profile and the rising limb of the hydrograph. Finally, relating the results to real‐life situations, it shows that the flow regime that gives the maximum detention storage is also the dominating flow regime in nature. Hence, extraordinarily, the flow regimes that exist in nature in fact provide maximum flood attenuation. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of upstream inflow on wave celerity and time to equilibrium on an overland plane

Abstract

Based on the kinematic wave equations, formulae for the wave celerity along an overland plane subject to uniform rainfall excess and with a constant upstream inflow together with the corresponding average wave celerity and time to equilibrium for the entire plane are derived. The formulae are further developed in terms of both the Darcy-Weisbach resistance coefficient and the Manning resistance coefficient. By comparing the wave celerities, the average wave celerities and the time to equilibrium for planes with and without upstream inflow show that the upstream inflow causes the wave celerity and the average wave celerity to be faster and the times to equilibrium to be shorter. The effect of upstream inflow is greater with increasing inflow, but the marginal effect decreases with increasing inflow. The effect is greatest for laminar flow and least for turbulent flow. For the wave celerity, the effect is also greatest at the upstream end of the plane and least at the downstream end of the plane.     

Diverging overland flow

This study investigates divering overland flow utilizing kinematic wave theory, which does not appear to have been dealt with previously. Explicit analytical solutions are derived in dimensionless form for space-time invariant rainfall. Analytical solutions do not seem to be tractable for time-varying rainfall. Depending upon the duration of rainfall, equilibrium and partial equilibrium cases are distinguished explicitly. The effect of divergence parameter on the hydrograph shape is shown. The adequacy of kinematic approximation for characterization of diverging overland flow is tested against laboratory watershed results. The diverging overland flow model is found to yield results which compare well with observations and with those of a plane model.     

Mapping detention basins and deriving their spatial attributes from airborne LiDAR data for hydrological applications

This paper presents a new technique for mapping detention basins and measuring their spatial attributes using high‐resolution airborne LiDAR (Light Detection and Ranging) data. An efficient least‐cost search algorithm is employed to identify surface depressions from a bare‐earth LiDAR digital elevation model (DEM). Surface depressions are automatically delineated into hydrological objects using the connected component identification and indexing algorithm. Various spatial attributes are derived for these hydrologic objects, including location, perimeter, surface area, depth, storage volume and shape properties. Based on spatial attributes, a rule‐based classifier is established to separate detention basins from other types of surface depressions. We have successfully applied our technique to an urban watershed in the Houston Metropolitan area, Texas. Detention basins at regional and residential subdivision levels are mapped out for the watershed, and measurements on the spatial attributes are derived for each detention basin. The quantitative information derived from LiDAR data provides a scientific basis for formulating an appropriate management plan for detention basins and for assessing their effects on flood control and storm water quality treatment. Copyright © 2007 John Wiley & Sons, Ltd.     

Use of the recession characteristics of snowmelt hydrographs in the assessment of snow water storage in a basin

For a better management of water resources, the information on water stored in a basin in the form of snow is of immense use. Changes in the snow water storage with time influence the recession characteristics of the hydrographs. Recession is found to be slower in a basin when it contains higher snow water storage and becomes faster as the volume of stored water reduces. In other words, the recession coefficient is not constant throughout the melt season, it changes with time. In the present study, the possibility of assessing snow water storage at any time during the melt season using recession coefficients is examined. The hydrograph analyses have been made for the Glatzbach watershed in the Hohe Tauern region of the Austrian Alps. For this purpose, a relationship between snow water storage and the recession coefficients is developed. This study suggests a simple and useful approach to assess the snow water storage in a basin at any time during the snowmelt season. The information on the snow water storage of a basin can be obtained using a readily derived single parameter, the recession coefficient. The results are based on limited data, but they are sufficient to illustrate how the changes in snow water storage control the recession characteristics of the hydrographs. These investigations set the pace for further research in this area. Copyright © 2000 John Wiley & Sons, Ltd.     

Grid size effects analysis and hydrological similarity of surface runoff in flatland basins

The effects of grid-size modification on the derived topographic attributes are analysed and a procedure for scaling model parameters and similarity assessment between flow variables is proposed. Hydrological simulations are performed with a physically-based and spatially-distributed quasi-2D mathematical model. The scaled model parameters are the effective roughness coefficient associated with overland flow (n_ov) and the transverse slope in the cell (TSC). To scale the selected parameters, the criterion of equilibrium storage conservation between the different grid sizes is applied. Three basins of the central-east region of Argentina are modelled. The spatial variability of basin geomorphology is quantified using the entropy concept. The simulation results show that when grid size is increased, to obtain similar hydrological responses it is necessary to increase the n_ov or to reduce the TSC. In terms of similarity, the best results are achieved when TSC is scaled, particularly when water depths are considered.     

Parametric study of a physically-based,plot-scale hillslope hydrological model through virtual experiments

Abstract

A physically-based hillslope hydrological model with shallow overland flow and rapid subsurface stormflow components was developed and calibrated using field experiments conducted on a preferential path nested hillslope in northeast India. Virtual experiments were carried out to perform sensitivity analysis of the model using the automated parameter estimation (PEST) algorithm. Different physical parameters of the model were varied to study the resulting effects on overland flow and subsurface stormflow responses from the theoretical hillslopes. It was observed that topographical shapes had significant effects on overland flow hydrographs. The slope profiles, surface storage, relief, rainfall intensity and infiltration rates primarily controlled the overland flow response of the hillslopes. Prompt subsurface stormflow responses were mainly dominated by lateral preferential flow, as soil matrix flow rates were very slow. Rainfall intensity and soil macropore structures were the most influential parameters on subsurface stormflow. The number of connected soil macropores was a more sensitive parameter than the size of macropores. In hillslopes with highly active vertical and lateral preferential pathways, saturation excess overland flow was not evident. However, saturation excess overland flow was generated if the lateral macropores were disconnected. Under such conditions, rainfall intensity, duration and preferential flow rate governed the process of saturation excess overland flow generation from hillslopes.

Editor D. Koutsoyiannis; Associate editor C. Perrin     

Theoretical assessment of changes in design flood peak of an overland plane for two opposing urbanization sequences

By considering urbanization on an overland plane as a process whereby a relatively rough, permeable surface is gradually replaced by a relatively smooth, less permeable surface, the effect of urbanization sequence on the flood peak is theoretically assessed by the kinematic wave method. In the assessment, two opposing urbanization sequences are considered: one from downstream to upstream, and the other from upstream to downstream. The assessment is carried out in terms of the individual effect as well as the combined effect of the Manning resistance coefficient and the runoff coefficient. For both urbanization sequences and for all degrees of urbanization, the assessment shows that surface conversion from rough to smooth, or from permeable to less permeable causes the flood peak to increase. A comparison of the individual effects shows that for equal reductions in surface roughness and permeability, the reduction in permeability causes greater increases in the flood peak compared with the reduction in surface roughness. For a partially urbanized plane and for the same degree of urbanization, due to the partial area effect, urbanization at the downstream end generally causes greater increases in the flood peak. In terms of urbanization sequence, the downstream to upstream urbanization sequence generally causes greater increases in the flood peak. The effect of urbanization sequence on the flood peak, however, is only significant for the larger reductions in surface roughness and permeability. Finally, a comparison of the results of this study with those obtained from drainage basins shows that for most of the results from the basins, they correspond to those for the small reductions in surface roughness and permeability on an overland plane. For these cases, the effect of urbanization sequence on the flood peak is small. Copyright © 1999 John Wiley & Sons, Ltd.     

Transferability of hydrological model parameters between basins in data-sparse areas, subarctic Canada

Hydrological models used for the simulation of runoff are often calibrated only on the basis of data obtained at the catchment outlet but the parameters thus derived are then applied to the simulations for the subbasins. Such a practice is common for the data-sparse areas such as the subarctic. However, it may yield erroneous results when the calibrated model parameters are applied to basins of various sizes, or with divergent physical characteristics. This study assesses the feasibility of transferring parameter estimates derived for one basin of a particular size to other basins of different dimensions, using the SLURP model for simulation and the Liard and two of its subbasins as an example. Results indicate that other than the snowmelt factor, the parameter values obtained from the subbasins are similar, but values of several parameters (e.g. maximum capacity of the soil water and groundwater storage, and snowmelt factor) are different from those derived for the large basin. Compared with applying the Liard basin parameters, the subbasins parameter sets generate higher evapotranspiration, earlier termination of the snowmelt period, more soil water storage, a shorter period with significant soil water storage and a better overall agreement between the observed and simulated runoff. It is recommended that adequate attention be given to the transferability of the parameter values to improve the simulation of subbasins hydrology.     

Implication of the flow resistance formulae on the prediction of flood wave propagation

ABSTRACT

This study examines the difference in the predictions of flood wave propagation in open channels depending on the flow resistance formulae, such as the Chézy and Manning’s equation. The celerity and diffusion coefficient are functions of the channel geometry, slope, roughness as well as the resistance formulae. The results suggest that substituting the Chézy equation with Manning’s equation results in different characteristics of flood propagation, which are consistent regardless of the cross-sectional geometry except for a circular cross-section: increasing celerity and decreasing diffusion coefficient. The celerity is more sensitive to the selection of resistance formulae than the diffusion coefficient. Geometry has a greater effect on the celerity and diffusion coefficient, and consequently on the resulting hydrographs. Manning’s equation results in a larger difference in celerity and diffusion coefficient compared to Chézy equation regardless of the water depth. Overall, this study shows that the selection of resistance formulae is important in terms of the resulting hydrographs and peak flow.

EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR not assigned     

Development of unbiased plotting position formula for General Extreme Value distributions

Expressions for the expected values of GEV order statistics have been derived in simple summation form and in terms of probability weighted moments. Using exact plotting positions from GEV order statistics a new unbiased plotting position formula has been developed for the General Extreme Value distribution. The formula can, explicitly, take into account the coefficient of skewness, (or the shape parameter, k), of the underlying distribution.The developed formula better approximates the exact plotting positions as compared to other existing formulae and is quite easy to use.     

Development of unbiased plotting position formula for General Extreme Value distributions

Expressions for the expected values of GEV order statistics have been derived in simple summation form and in terms of probability weighted moments. Using exact plotting positions from GEV order statistics a new unbiased plotting position formula has been developed for the General Extreme Value distribution. The formula can, explicitly, take into account the coefficient of skewness, (or the shape parameter, k), of the underlying distribution.The developed formula better approximates the exact plotting positions as compared to other existing formulae and is quite easy to use.     

Détermination des variations de la capacité d'absorption d'un sol en place sous averses simulées / Obtaining variations of field infiltration capacity from simulated rainstorm experiments

Abstract

By sprinkling an experimental plot with different intensities of simulated rainfall starting with different initial conditions of soil moisture, the variations of infiltration capacity and consequently the response of the soil surface to runoff are evaluated. The following values are successively determined from experimental data: the mean depth of surface storage; the mean depth of detention and the parameters of a chosen infiltration formula.     

2.5D modelling, inversion and angle migration in anisotropic elastic media

2.5D modelling approximates 3D wave propagation in the dip‐direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful. We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in‐plane and out‐of‐plane geometrical spreading. We also derive some new inversion/migration results. An AVA‐compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common‐image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy‐flux‐normalized plane‐wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation. Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in‐plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out‐of‐plane geometrical spreading, necessary for amplitude‐preserving computations, for the TI medium is dependent on the same parameters that govern in‐plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in‐plane kinematics and the scattering coefficients. Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude‐preserving migration followed by AVA analysis. SYMBOLS AND NOTATION A list of symbols and notation is given in Appendix D .     

Infiltration in the Corgo River basin (northern Portugal): coupling water balances with rainfall—runoff regressions on a monthly basis

Abstract

A combination of water balances and rainfall—runoff regressions is used to calculate infiltration, overland flow, baseflow and change to the surface water reservoir, on a monthly basis; evapotranspiration from the underground reservoir, on an annual basis; and a lag phase of maximum infiltration and maximum baseflow within a hydrological year. The water balance equations are written for catchment areas formed on crystalline rocks and located in temperate climates. The regression lines are fitted to precipitations and river flows. In a first run, the model is tested with the Corgo River hydrographic basin, a small watershed in the Trás-os-Montes and Alto Douro province, northern Portugal. The results compare favourably with results of other groups, working under similar environmental conditions. The sensitivity of the model to changes in the basin characteristics and climate is tested by a second run using data from the Terva River basin, a nearby catchment that is much smaller than the Corgo basin and has a much lower effective precipitation, defined here as a difference between precipitation and potential evapotranspiration. As a consequence of having a lower effective precipitation, the river dry-out starts earlier in the Terva (May) than in the Corgo (June).     

Evaluating overland flow sediment transport capacity

An equation for evaluating the sediment transport capacity of overland flow is a necessary part of a physically based soil erosion model describing sediment detachment and transport as distributed processes. At first, for the hydraulic conditions of small-scale and large-scale roughness, the sediment transport capacity relationship used in the WEPP model is calibrated by Yalin and Govers' equation. The analysis shows that the transport coefficient K_t depends on the Shields parameter, Y, according to a semi-logarithmic (Yalin) or a linear (Govers) equation. The reliability of the semi-logarithmic equation is verified by Smart's, and Aziz and Scott's experimental data. Then the Low's formula, whose applicability is also proved by Smart's, and Aziz and Scott's data, is transformed as a stream power equation in which a stream power coefficient, K_SP, depending on Shields parameter, slope, sediment and water-specific weight, appears. A relationship between transport capacity and effective stream power is also proposed. Finally, the influence of rainfall on sediment transport capacity and the prediction of critical shear stress corresponding to overland flow are examined. © 1998 John Wiley & Sons, Ltd.     

A drought frequency formula

Abstract

The important elements of a drought phenomenon are the longest duration and the largest severity for a desired return period. These elements form a basis for designing water storage systems to cope with droughts. At times, a third element, drought intensity, is also used and is defined as the ratio of severity to duration. The commonly available statistics for the causative drought variables such as annual rainfall or runoff sequences are the mean, the coefficient of variation and the lag one serial correlation coefficient, and occasionally some indication of the probability distribution function (pdf) of the sequences. The extremal values of the duration and severity are modelled in the present paper using information on the aforesaid parameters at the truncation level equal to the mean of the drought sequence, which is generally taken as the truncation level in the analysis of droughts. The drought severity has been modelled as the product of the duration and intensity with the assumption of independence between them. An estimate of drought intensity has been realized from the concept of the truncated normal distribution of the standardized form of the drought sequences in the normalized domain. A formula in terms of the extremal severity and the T-year return period has been suggested similar to the flood frequency formulae, commonly cited in hydrological texts.     

THE UTILIZATION OF RIVER WATER RESOURCES IN ARID ZONES

ABSTRACT

Flood data were assembled for 168 Scottish basins containing 3071 station-years of record. Multiple regression techniques were used to produce equations for predicting mean annual flood from physiographic and climatological basin characteristics. Mean annual rainfall (SAAR) gave better results than measures of extreme rainfall (M52D and RSMD). Percentage area of lake storage (LOCH) was found to be a better predictor than fraction of the basin draining through a lake (LAKE). Apart from SAAR and LOCH, the recommended equation requires the basin area (AREA), stream frequency (STMFRQ) and an index of the soil type (SOIL). Measures of average basin slope (AVES) and main stream slope (S1085) were not statistically significant. The standard error of the estimate of the predicted mean annual flood is 0.147. The equation has a coefficient of determination, R², of 0.914 and appears robust over a wide range of basin types without requiring regionally derived multipliers or coefficients. No significant improvement in fit was acheived by ridge regression, Stein estimation or use of the influence function.     

Challenges of hydrological analysis for water resource development in semi-arid mountainous regions: case study in Iran

Abstract

This study modified the BTOPMC (Block-wise TOPMODEL with the Muskingum-Cunge routing method) distributed hydrological model to make it applicable to semi-arid regions by introducing an adjustment coefficient for infiltration capacity of the soil surface, and then applied it to two catchments above the dams in the Karun River basin, located in semi-arid mountain ranges in Iran. The application results indicated that the introduced modification improved the model performance for simulating flood peaks generated by infiltration excess overland runoff at a daily time scale. The modified BTOPMC was found to fulfil the need to reproduce important signatures of basin hydrology for water resource development, such as annual runoff, seasonal runoff, low flows and flood flows. However, it was also very clear that effective model use was significantly constrained by the scarcity of ground-gauged precipitation data. Considerable efforts to improve the precipitation data acquisition should precede water resource development planning.

Editor D. Koutsoyiannis