ERRORS OF KINEMATIC-WAVE AND DIFFUSION-WAVE APPROXIMATIONS FOR SPACE-INDEPENDENT FLOWS ON INFILTRATING SURFACES

Error equations for the kinematic-wave and diffusion-wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic-wave, diffusion wave and dynamic-wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; and it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation.     

Modification and discussion of the Green-Ampt model for an evolving wetting profile

ABSTRACT

The Green-Ampt (GA) model has been widely used to evaluate soil water infiltration. While a simple piston profile is commonly used, the wetting profile of a soil changes during infiltration and a quarter-ellipse has been found to better describe its evolution. This study aims to improve the GA model and discuss the model parameters when the quarter-ellipse profile is utilized. The soil column is divided into three zones: saturated, transient and dry. The variable γ is introduced to express the ratio of the saturated zone depth to the wetting front depth. A modified GA model is derived via mathematical methods, but an exact solution is difficult to obtain. Therefore, a simplified (SGA) model is developed via a segmented method. Compared with the measured results, the SGA model is more accurate than the traditional model. Finally, the model parameters are discussed and a value of γ = 0.5 is recommended.     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces

Error equations for the kinematic wave and diffusion wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation.     

REPORT ON THE ACTIVITIES OF THE INTERNATIONAL COMMISSION ON SNOW AND ICE FOR THE PERIOD 1971–1975

ABSTRACT

An infiltration model based on the Green-Ampt assumptions is developed for a class of non-uniform soils in which saturated hydraulic conductivity decreases as an exponential function of depth, and the storage-suction factor C = ΔθΔΨ is a constant. An analysis of measured hydraulic conductivity and porosity data suggests that the model may be useful in some soils where the changes of hydraulic characteristics with depth are of this form. A method for using the model with time variable rainfall rates is given. The model is applied to simulate the experimental results of Childs &; Bybordi (1969) who measured infiltration into layered sand profiles. Agreement was satisfactory even for this case.     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces with lateral inflow neglected in the momentum equation

Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow, infiltration and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included.     

Analytical solution of transient flow in a sloping soil layer with recharge

Abstract

An analytical solution of planar flow in a sloping soil layer described by the linearized extended Boussinesq equation is presented. The solution consists of the sum of steady-state and transient-series solutions, the latter in a separation-of-variables form, and can satisfy an arbitrary initial condition via collocation; this feature reduces the number of series terms, making the solution efficient. Key parameter is the dimensionless linearization depth η _o (R), R being the dimensionless recharge. The variable η _o (R), not the slope, characterizes the flow as kinematic or diffusive, and R ≈ 0.2 demarcates the two regimes. The transient series converges rapidly for large η _o (large R, near-diffusive flow) and slowly as η _o → 0 (kinematic flow). The quasi-steady (QS) state method of Verhoest & Troch is also analysed and it is shown that the QS depth profiles approximate the transient ones well, only if Δt exceeds a system-dependent transition time between flow states (possibly >>1 day). In an application example for a 30-day recharge series, the QS solution differs from the transient one by as much as 20% (RMSE = 15%), does not track recharge changes as well and fails to conserve mass.     

Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited

Abstract

A tension-saturated water slug descends through a homogenous soil after a rainfall (irrigation) event and shrinks due to transpiration by a distributed root-sink and evaporation. The upper (drainage) and lower (imbibition) sharp fronts of the slug separate it from the superjacent and subjacent vadose zones, where water is immobile. In the slug, the hydraulic conductivity is constant according to the Green-Ampt model. The capillary pressures as well as effective porosities on the fronts are given (generally, different) constants that can be viewed as a kind of hysteresis. A volumetric sink models mild (no desaturation of the slug) soil water withdrawal by the plant roots. The sink intensity varies with the depth from the soil surface and with time. Mathematically, the hydraulic head is immediately expressed by double integration of a governing 1-D flow equation. The pressure and kinematic conditions on the fronts result in a Cauchy problem for a system of two ODEs, which is solved by computer algebra routines.

Editor D. Koutsoyiannis

Citation Kacimov, A. and Obnosov, U., 2013. Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited. Hydrological Sciences Journal, 58 (1), 1–12.     

Inundation extent as a key parameter for assessing the magnitude and return period of flooding events in southern Iceland

Abstract

River flow conditions in many watersheds of Iceland are particularly disturbed during winter by the formation, drifting and accumulation of river ice, whose impact on water encroachment and extent of inundations is not reflected in the discharge records. It is therefore necessary to use river discharge with great caution when assessing the magnitude of past inundations in Iceland, and to give attention to other flood magnitude parameters. A GIS-based methodology is presented that focuses on inundation extent as an alternative parameter for the assessment and ranking of the magnitude of past flooding events in the Ölfusá-Hvítá basin, known as one of the most dangerous flood-prone river complexes in Iceland. Relying ultimately on a macro-scale grid, the method enabled the reconstruction of the extent of inundations, the delineation of the flood plain, and, finally, some estimation of the likelihood of flooding of exposed areas that include marine submergences and river floods for both open water and ice conditions.

Citation Pagneux, E., Gísladóttir, G. & Snorrason, Á. (2010) Inundation extent as a key parameter for assessing the magnitude and return period of flooding events in southern Iceland. Hydrol. Sci. J. 55(5), 704–716.     

Seasonal climate patterns and their influence on calibration of the Hargreaves-Samani equation

Abstract

Annual patterns in climate parameters were studied to evaluate how these influence the quality of reference evapotranspiration (ETo) estimates obtained from the Hargreaves-Samani (HS) equation, since the method only uses the measured temperature directly. The work evaluates how these patterns can be used to improve the HS ETo estimates. Ten-year moving averages from a set of California Irrigation Management Information System (CIMIS) stations were used to evaluate the relationships between solar radiation (R_s), temperature (T) and ETo. The results indicate that T treads behind solar radiation and its value peaks some 25 days later. Thus, the main irrigation season in the Mediterranean climate (1 May–30 September) can be divided into three phases: increasing R_s and T; decreasing R_s with increasing T; and decreasing R_s and T. Non-univocal annual cycles were observed between R_s and T, ETo and R_s, and ETo and T. These annual patterns result in important seasonal changes in the ratio between the HS and Penman-Monteith (FAO PM) ETo estimates. The changes are particularly important during the irrigation season, where the FAO PM initially calculates greater ETo values than the HS methodology, and from the end of May to early September, where the HS equation overestimates the ETo values (by 17 mm, or 3%). These patterns obtained from 2000–2009 data were used to calibrate and improve HS ETo estimates at new sites for the 2010–2011 period. Calibration based on the proposed seasonal region-wide FAO PM/HS ETo ratios improved both the bias (decreased from 0.40 to 0.36 mm d^-1) and r² (increased from 0.67 to 0.87) of the ETo estimates for the irrigation season. The proposed methodology can be easily applied to other regions, even when the existing weather stations are sparse.

Editor Z.W. Kundzewicz     

LE CINQUANTIÈME ANNIVERSAIRE DE L'AISH / THE FIFTHIETH ANNIVERSARY OF THE IAHS

Abstract

One of the scale problems in hydrology is to relate nonlinearity in basin response to size and other factors. On the Sputka basin (103.4 km²), three groups of unit hydrographs were identified, each group having a common shape parameter, N, of the Nash model and each, therefore, representing one dimensionless response. The existence of the three dimensionless responses can be explained in the first place by there being different spatial rainfall patterns for the events from which they were derived. The time parameter, K, within the individual groups depends primarily on the initial flow and on the skewness of the rainfall time pattern. However, when the conditions of rainfall uniformity and of a minimum depth are strictly met, and the initial flow is in a certain range, the basin behaves in a linear fashion.     

Rainfall–runoff modelling of railway embankment steep slopes

Abstract

A distributed 1D rainfall–runoff model is presented. It consists of the Saint Venant continuity and momentum equations for overland flow and a modified Green-Ampt model for the infiltration on railway embankment steep slopes. The model is applied to adjacent 10-m-wide erosion control experimental plots with different percentages of grass cover. A relationship between the 2-day antecedent rainfall and initial moisture content was established and used to predict the saturated hydraulic conductivity (Ks). Average values of Ks for 0, 50 and 100% grass cover were found to be 0.1, 1.19 and 2.56 mm/h, respectively. For the majority of cases, the model simulated runoff with acceptable accuracy, 68% having Nash-Sutcliffe efficiency (NSE) values above 0.50. The average NSE value varied between 0.60 and 0.80, with 0% grass-covered plots yielding the highest values. As expected, the runoff volume decreased with increasing percentage of grass cover.

Citation Sajjan, A.K., Gyasi-Agyei, Y., and Sharma, R.H., 2013. Rainfall–runoff modelling of railway embankment steep slopes. Hydrological Sciences Journal, 58 (5), 1162–1176.

Editor D. Koutsoyiannis     

Towards using pedotransfer functions for estimating infiltration parameters

ABSTRACT

Water infiltration into soils is an important component of hydrological processes. Direct measurement of infiltration is time consuming, expensive and often involves large spatial and temporal variability. The objective of this study was to develop and verify parametric pedotransfer functions (PTFs) to predict infiltration parameters. Consequently, 119 double-ring infiltration data were collected. The parameters of Philip, Kostiakov, Kostiakov-Lewis and Horton models were obtained, using the sum of squares error optimization method. Some parametric PTFs were then derived to predict the parameters of the infiltration models, using stepwise regression analysis. The results indicated a reasonable estimation of infiltration parameters by the derived PTFs. These results were more accurate when the land use of the studied area was considered. Overall results of this study suggest infiltration-based PTFs could be established as a reasonable indirect method for estimating infiltration parameters.

Editor M.C. Acreman; Associate editor N. Verhoest     

THEORETICAL APPROACH TO THE SOLUTION OF THE INFILTRATION PROBLEM

ABSTRACT

The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content.

Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data.

Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme.

Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate.     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows with lateral inflow neglected in the momentum equation

Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; and it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included.     

On a fractional derivative form of the Green-Ampt infiltration model

The Green-Ampt model for infiltration into homogeneous soils predicts a monotonically decreasing infiltration rate and a wetting front that initially advances as the square root of time. Infiltration in heterogeneous soils, however, can exhibit non-monotonic infiltration rates and wetting front advances that differ from the square root of time (“anomalous diffusion”).Here it is postulated, that if the length scales of the heterogeneities can be assumed to be power law distributed, it may be appropriate to model infiltration in heterogeneous soils in terms of fractional derivatives. Then, by expressing the hydraulic flux as a Caputo fractional derivative (order 0 < α ? 1) of the head, a fractional Green-Ampt infiltration model is obtained. It is shown that solutions of this model predict non-monotonic and anomalous diffusion behaviors consistent with observations in field infiltration trials; a finding that indicates that a non-local moisture flux model, based on fractional derivatives, is a plausible model for describing infiltration into heterogeneous soils.     

Magnetic equilibria resulting from a helically symmetric kink instability

Abstract

This paper explores magnetic equilibria which could result from the kink instability in a cylindrical magnetic flux tube. We examine a variety of cylindrical magnetic equilibria which are susceptible to the kink, and simulate its evolution in a frictional fluid. We assume that the evolution takes place under conditions of helical symmetry, so the problem becomes effectively two-dimensional. The initial cylindrical equilibrium field is specified in terms of its twist function k(r) = B _θ/(rB_z ) and for a variety of k(r) functions we calculate linear growth rates for the kink instability, assuming that it develops under helical symmetry with pitch τ. We find that the growth rate is sensitive to the value of τ.

We simulate nonlinear evolution of the kink using a Lagrangian frictional code which constrains the field to have helical symmetry of a given pitch τ. Ideal MHD is assumed and the plasma pressure is taken to be small in order to mimic conditions in the solar corona. In some cases the flux tube evolves to a new smooth helically symmetric equilibrium which involves a relatively small change in the maximum electric current. In other cases there is evidence of current-sheet formation.     

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.     

Field investigation of a dry detention pond with underground detention storage

Abstract

A dry pond is an urban drainage component designed to temporarily store stormwater runoff and to encourage infiltration of surface water to the subsurface layer. This paper investigates field measurement of a dry pond at Taiping Health Clinic, Perak, Malaysia that has been functioning well for five years. The pond has a surface area of 195 m², maximum depth of 32 cm, and a storage capacity of 31.88 m³. The study focused on the infiltration functionality of the constructed dry pond and the results show that it has an average infiltration rate of 125 mm/h and dries up in 330 min after being filled to a depth of 31 mm. A public-domain hydrological model was then employed to simulate hydrographs of ponding and draining, the results of which matched observations with 86–98% accuracy. These results can lead to better understanding of the system and allow duplication of such a drainage design elsewhere.

Editor D. Koutsoyiannis

Citation Lai, S.H. and Mah, D.Y.S., 2012. Field investigation of a dry detention pond with underground detention storage. Hydrological Sciences Journal, 57 (6), 1249–1255.     

Identification of optimal soil hydraulic functions and parameters for predicting soil moisture

Abstract

The accuracy of six combined methods formed by three commonly-used soil hydraulic functions and two methods to determine soil hydraulic parameters based on a soil hydraulic parameter look-up table and soil pedotransfer functions was examined for simulating soil moisture. A novel data analysis and modelling approach was used that eliminated the effects of evapotranspiration so that specific sources of error among the six combined methods could be identified and quantified. By comparing simulated and observed soil moisture at six sites of the USDA Soil Climate Analysis Network, we identified the optimal soil hydraulic functions and parameters for predicting soil moisture. Through sensitivity tests, we also showed that adjusting only the soil saturated hydraulic conductivity, K_s , is insufficient for representing important effects of macropores on soil hydraulic conductivity. Our analysis illustrates that, in general, soil hydraulic conductivity is less sensitive to K_s than to the soil pore-size distribution parameter.

Editor D. Koutsoyiannis; Associate editor D. Hughes

Citation Pan, F., McKane, R.B. and Stieglitz, M., 2012. Identification of optimal soil hydraulic functions and parameters for predicting soil moisture. Hydrological Sciences Journal, 57 (4), 723–737.     

Flooding and drying mechanisms of the seasonal Sudd flood plains along the Bahr el Jebel in southern Sudan

Abstract

The flooding and drying mechanisms of the seasonal flood plains of the Sudd swamps in southern Sudan are, while dependent on the river levels, influenced by a complex interaction between soil, vegetation, topography and seasonal trends in rainfall and evapotranspiration. Based on field measurements, these components have been assessed in detail and evaluated regarding their function in the seasonal cycle of flooding and drying. A detailed analysis of soil and evapotranspiration conditions, as well as the interaction with vegetation and meteorological conditions, has been conducted using field and laboratory experiments. Sources, processes, flow directions and the fate of the floodwaters on both the river-fed seasonal flood plains and the rain-fed grasslands have been established. The results show that river spill is responsible for flooding these areas while no return flow occurs, and drying is caused by evapotranspiration. Rainfall can only cause temporary flooding in extreme events.

Citation Petersen, G. & Fohrer, N. (2010) Flooding and drying mechanisms of the seasonal Sudd flood plains along the Bahr el Jebel in southern Sudan. Hydrol. Sci. J. 55(1), 4–16.