INFILTRATION The downward flow of water from the land surface into the soil medium is called infiltration. The rate of this movement is called the infiltration rate ft. The process of infiltration of water and subsequent water movement is an extremely complex process. If water is ponded at the surface (an ample supply), then infiltration occurs at the potential infiltration rate. If the rate of supply is less than the potential rate, then the actual infiltration rate is somewhat less than the potential rate. Most infiltration equations describe the potential rate. The cumulative infiltration rate is the accumulated depth of water infiltrated and is the integral of the rate with time. Prof. Dr Taj Ali Khan

Infiltration Capacity Infiltration is the actual rate at which water is entering the soil at any given time(SCSA, 1976). Infiltration capacity: Maximum rate (LT-1). The area under the infiltration curve for any time interval represents the depth of water infiltrated during that interval. Ft = cumulative infiltration at time t, mm The downward movement of water and the resulting change in soil moisture is shown in Figure 1 and 2.

Figure 1: Moisture zones during infiltration. Moisture Content i s Saturation zone Transition zone Transmission zone Depth Wetting zone Wetting front Figure 1: Moisture zones during infiltration.

Figure 2: Moisture profile as a function of time during infiltration. Moisture Content i s Ground surface t1 t2 t3 t4 Depth t5 Figure 2: Moisture profile as a function of time during infiltration.

In general, the infiltration rate is dependent on Factors Affecting Infiltration In general, the infiltration rate is dependent on soil physical properties vegetative cover antecedent soil moisture conditions rainfall intensity the slope of the infiltrating surface.

Infiltration Potential Factors Affecting Infiltration Soil Physical Properties Soil Type, porosity, hydraulic conductivity Soil Type Sand Silt Clay Runoff Potential Infiltration Potential Taylor & Ashcroft, 1972

Vegetative cover Rainfall Intensity Bare soils tend to have lower infiltration rates than soil protected by a vegetative cover. The energy of the falling rain breaks down soil aggregates and small particles are carried into the soil pores. The net result is a lowering of the infiltration rate. Soil Cover Effects Effect of Rain Intensity Rainfall Intensity Rainfall intensity affects the infiltration rates in two ways. For high-intensity rains, the raindrops tend to be larger and have more energy when they strike the soil. Thus high-intensity rains are more effective in sealing the soil surface than are low-intensity rains.

Factors Affecting Infiltration Effect of Initial Water Content Antecedent soil moisture conditions The antecedent soil water content also alters the infiltration rate. Generally, a wet soil has a lower infiltration rate than a dry one. Slope of the infiltrating surface. The infiltration opportunity time is a function of the slope of the infiltration surface. On a steep slope, the water tends to run off rapidly and thus have less opportunity for infiltration than on a gentle slope.

Infiltration Models Richard’s Equation Richard's equation (1931) for one-dimensional flow of water in porous media is a combination of Darcy's law with the continuity equation as: where: θ = volumetric moisture content [vol/vol] K(θ) = unsaturated hydraulic conductivity [L/T] D(θ) = diffusivity coefficient [L2/T] ( = -K(θ)(ψ/θ) ) ψ = suction head [L] z = medium depth (positive downward) [L] Difficult to solve and are usually solved with numerical analyses procedures 2-space derivatives (two boundary conditions) 1-time derivative (initial condition)

One-Dimensional Versions There are two formulations for the Richard’s equation – h-based and theta-based. h-based theta-based

Richard’s Equation Richard's equation is a non-linear second order partial differential equation. Up to now, this equation has been the most common basic mathematical expression for unsaturated flow phenomena in porous media. This equation describes unsteady flow in a one-dimensional anisotropic and non-homogeneous soil matrix by means of a partial differential equation. For the modelling of water dynamics in the unsaturated zone, one has to solve this equation with the help of suitable algorithms. The models can be grouped into analytical and numerical approaches, with the latter being far more popular. Analytical solutions are often more difficult to obtain because the coefficients of Richard's equation are functions of the dependent variables.

Richard’s Equation Exact analytical solutions can be obtained by making simplifying assumptions regarding soil moisture characteristics and the flow domain. Richard’s equation can be solved using complex numerical techniques such as finite difference, finite element, boundary integral etc. Difficulties experienced in using the Richard's equation are the non-uniformity of soils, both spatially and with depth; the great number of measurements needed to define the required parameters; and the difficulty of solving the relationships when the required data are available. A further difficulty is that of specifying the applicable boundary conditions for the equation. Richard’s equation have found limited application in design hydrology.

Infiltration Models 1. Approximate Models 1.1 Empirical Models The approximate and analytical equations can be used to characterize the infiltration process with rather simple, straight-forward methods. 1.1 Empirical Models Kostiakov (1932) Horton (1939) Holtan (1961) 1.2 Simplified Models Models derived by application of the theory of soil water movement with certain simplifications and assumptions. Examples include: Green and Ampt (1911) Philip (1957) Smith (1972) 2. Numerical Models Numerical procedures (finite difference and finite element) for solving Richards equation have been developed by many researchers such as: Rubin (1968) Amerman (1969) Freeze (1971) Khan (1996)

Horton's Model Horton (1933) suggested: It assumes that the infiltration capacity of a given soil is govern by Horton’s Equation Horton (1933) suggested: ft = infiltration rate at any time t, mm hr-1 t = time from beginning of rain, hr f0 = initial infiltration rate (at t=0), mm hr-1 fc = final infiltration rate (infiltration capacity), mm hr-1 k = empirical constant, hr-1, (Decay constant ~ T-1 ) i = rainfall rate, mm hr-1 Note: i > ft at all times. The cumulative infiltration rate A difficulty with the Horton equation is that it makes infiltration rate a function of time and does not account for variations in rainfall intensity. The equation has no provision for a recovery of infiltration capacity during periods of low or no rainfall.

Holtan’s Model f = a Fpn + fc Holton (1961) has advanced an empirical infiltration equation based on the concept that the infiltration rate is proportional to the unfilled capacity of the soil to hold water. The Holton model for infiltration is f = a Fpn + fc Where f is the infiltration rate, fc is the final infiltration rate, Fp is the unfilled capacity of the soil to store water, and a and n are constants. The exponent n has been found to be about 1.4 for many soils. The value of Fp ranges from a maximum of the available water capacity (AWC) to zero. Values of AWC are given for many soils in the US Agricultural Research Service Publication (1968).

Green-Ampt Equation In 1911, Green and Ampt developed an approximate infiltration model based on Darcy’s law. Assumptions: They assumed vertical flow, a uniform water content, a sharp boundary between the dry and wetted soil zones, and the water movement occurs as piston or slug flow. Where moisture content (θ) and the soil suction potential (ψ), Given K, t, ψ, and Δθ, a value of F is calculated by successive substitution from Equation 2, which is then substituted into Equation 1 to determine the corresponding potential infiltration rate f.

Philip’s Equation Philip’s Equation – derived from 1-D solution of Richard’s equation Where S is a parameter called sorptivity, which is a function of moisture content (θ) and the soil suction potential (ψ), and A is called transmissivity. Both S and A depend on soil properties and initial moisture content. Differentiating the above equation with respect to t yields infiltration rate f(t) as:

SCS Curve Number Method (Indirect Method) Q = runoff (in) P = rainfall (in) S = potential maximum retention after runoff begins (in) CN = Curve number – reflects soil and cover conditions (0-100)

 index method A simpler method because it assumes no variation in f(t) with time. Hence, an infiltration index is used which assumes infiltration to be constant through time (at  mm hr-1).