Hubert J. Morel-Seytoux

Soil water retention and maximum capillary drive from saturation to oven dryness

This paper provides an alternative method to describe the water retention curve over a range of water contents from saturation to oven dryness. It makes two modifications to the standard Brooks and Corey [1964] (B-C) description, one at each end of the suction range. One expression proposed by Rossi and Nimmo [1994] is used in the high-suction range to a zero residual water content. (This Rossi-Nimmo modification to the Brooks-Corey model provides a more realistic description of the retention curve at low water contents.) Near zero suction the second modification eliminates the region where there is a change in suction with no change in water content. Tests on seven soil data sets, using three distinct analytical expressions for the high-, medium-, and low-suction ranges, show that the experimental water retention curves are well fitted by this composite procedure. The high-suction range of saturation contributes little to the maximum capillary drive, defined with a good approximation for a soil water and air system as HcM = ∫0∞krw dhc, where krw is relative permeability (or conductivity) to water and hc is capillary suction, a positive quantity in unsaturated soils. As a result, the modification suggested to describe the high-suction range does not significantly affect the equivalence between Brooks-Corey (B-C) and van Genuchten [1980] parameters presented earlier. However, the shape of the retention curve near “natural saturation” has a significant impact on the value of the capillary drive. The estimate using the Brooks-Corey power law, extended to zero suction, will exceed that obtained with the new procedure by 25 to 30%. It is not possible to tell which procedure is appropriate. Tests on another data set, for which relative conductivity data are available, support the view of the authors that measurements of a retention curve coupled with a speculative curve of relative permeability as from a capillary model are not sufficient to accurately determine the (maximum) capillary drive. The capillary drive is a dynamic scalar, whereas the retention curve is of a static character. Only measurements of infiltration rates with time can determine the capillary drive with precision for a given soil.

Analytical results for prediction of variable rainfall infiltration

Abstract The basic equations that govern water movement in unsaturated soils are presented for a boundary condition of variable rainfall rate at the soil surface. In particular, a differential equation for the water content at the soil surface is derived. Solutions are then obtained for the time evolution of water content at the soil surface assuming a power law form for the relative permeability to water as a function of normalized water content. Ponding time formulae are obtained and compared with other previously published relations. Water content profiles are also obtained and their shapes are displayed graphically for the case of an exponent of 2 in the power law form of the relative permeability to water for a constant rainfall rate. Formulae are also derived for the situation of a variable rainfall pattern. A methodology for the coupling of the analytical procedures with an implicit numerical solution of the water content at the soil surface is suggested as a cost-effective alternative to the strict numerical solution of the partial differential equation that governs the water content profile evolution. Postponding infiltration formulae and water content profile equations are also provided.

GROUNDWATER RECHARGE ESTIMATION FROM EPHEMERAL STREAMS. CASE STUDY: WADI TABALAH, SAUDI ARABIA

Estimation of groundwater recharge to an unconfined aquifer is studied using analytical and numerical techniques and results are compared with field observations. There is an acute need for such estimation in water balance studies in arid climates, and the case study in this paper is for such a region. The wetting front movement in the unsaturated zone depends on antecedent soil moisture, the ponded water depth and its duration, and on the position of the water table and the hydraulic properties of the unsaturated zone. A hydraulic connection between the recharge basin and the aquifer is not immediately established because the wetting front is unsaturated. A numerical model is applied to estimate recharge in an arid-zone wadi, and its validity is tested by comparing it with an analytical solution of the equations. The calculated recharge values matched the piezometric levels observed at a well site at the edge of the wadi channel. The total recharge depths found by integration in the time domain provided a good estimate of the transmitted volume of water per unit length of wadi channel. The findings were confirmed by runoff volume measurements at gauging stations located in the basin.

Derivation of equations for rainfall infiltration

Abstract Formulae were derived for prediction of ponding time and cumulative infiltration following ponding under the influence of rainfall. The derivations do not assume immediate saturation at the surface nor a piston displacement of air by water; they include the viscous flow of air. The results were compared with experimental data of Rubin and Steinhardt and a formula proposed by Mein and Larson.

A discrete kernel simulation model for conjunctive management of a stream—Aquifer system

Abstract A stream—aquifer simulation model was developed to conduct a conjunctive use management study in the South Platte River in Colorado. This model simulates both the physical and operational behavior of the system. The physical system modeled is comprised of the river and the saturated and unsaturated zones of the aquifer. A technique referred to as the “discrete kernel approach” was used to model the saturated zone of the aquifer. This technique is based on the classical Greens function method of solution of partial differential equations. The physical simulator was coupled to an allocation model which simulates the operational behavior of the system. The management model was applied to conduct a conjunctive use study involving the evaluation of a stream flow augmentation scheme. A summary of the results of this case study is presented.

The Turning Factor in the Estimation of Stream-Aquifer Seepage

A combined analytical-numerical approach is presented to characterize properly the exchange flow between a stream and a hydraulically connected aquifer. It eliminates the need to use a three-dimensional fine grid under and in the vicinity of the river cross section in order to obtain accurate results. Basically the approach matches an analytical solution in a vertical two-dimensional (2D) plane with the numerical description of the aquifer behavior in a 2D horizontal plane. The approach is compared with a finite-difference formulation such as used in MODFLOW.

Soil-aquifer-stream interactions — A reductionist attempt toward physical-stochastic integration

Abstract The paper suggests an approach to describe the various interactions between soil, aquifer and stream in a simplified but essentially physical and integrated manner. For practical applications, the complex hydrological processes cannot be thoroughly described at the smallest scale in time and space, at which theoretical or empirical physical laws are known. The successful passage from a smaller to a larger scale requires: enlightened simplification, integration in many senses that is: (1) in time; (2) in space; (3) in an expectation sense; and (4) in a process sense, and finally enlightened coupling . The paper illustrates in a simple manner this processus of multiple integration for the processes of infiltration, moisture redistribution, aquifer recharge and aquifer return flow, with emphasis on the stream-aquifer interaction. The paper suggests that temporal patterns of rainfall, spacial variation in soil properties, temporal fluctuations in river stage, sharp turns in flow directions (e.g. from vertical to horizontal direction at the interface of two soil layers with contrasting hydraulic properties or in the vicinity of a water table) etc., can significantly affect the response of a watershed. The paper also suggests that simple techniques can be devised that account to a large extent for these influences and will provide satisfactory tools for watershed modeling. As a sort of parenthesis, the paper shows that the purely statistical ARMA approach to hydrologic modeling will lead to incorrect identification of a perfectly stationary linear system as a nonstationary one. The combined physical-stochastic approach eliminates this potential error.

A composite hydraulic and statistical flow‐routing method

A simple and efficient method for flow routing, combining the kinematic wave equation with a statistical procedure, is introduced. It accounts for the nonlinearity and the dispersion of the flood wave propagation phenomenon and for lateral flow. The method is flexible, because it can be used to simulate a variety of flow variables, for example, water stage or discharge. Its calibration is based on historical records at both ends of the reach, and does not require geometric cross-section or longitudinal data. An application to the White Nile in Sudan demonstrates the practicality and accuracy of the method.

Water and air movement in a bounded deep homogeneous soil

Abstract A methodology, based on the knowledge of the characteristic curves of the soil, is presented to predict the infiltration rate into a soil, the evolution of the water content in the soil and the evolution of the water table under natural hydrological boundary conditions. Comparison with experimental results shows the method to be accurate. Infiltration rate curves are obtained for a number of situations involving different boundary and/or initial conditions. The results confirm the known experimental facts and the field observations that soil-air behavior is an important factor in infiltration phenomena.

Description of water and air movement during infiltration

Abstract An approximate analytical solution for the problem of one-dimensional infiltration into a homogeneous porous medium is presented. The solution is made possible by assuming that capillary pressure can be partially neglected. Two equations involving two unknowns, water saturation and total velocity, are derived and then solved in a step-wise fashion to yield the saturation profile and the total velocity at any time. Infiltration quantities are obtained by integration of the area under the saturation profile. Analytical concepts and procedures relevant to the determination of the evolving saturation profile are discussed in some detail. Particular attention is given to the nature and behavior of the fractional flow function. The occurrence of air counterflow during infiltration is also discussed.