Soil water is continuously moving in response to pressure gradients. These pressure gradients are caused by capillary and hydraulic forces unique to each soil element according to its pore structure, water content, chemicals, and other minor effects. This water redistribution within the soil profile plays a significant role in the replenishment, deep percolation and plant water abstraction processes. It is a very necessary process to be computed for any ET-soil water model to provide realistic simulations, although one of the more difficult processes to represent because of the detailed mathematics and data requirements.
A simplified form of the Darcy equation for vertical water flow up or down between the specified soil layers has been included in SPAW. The Darcy equation in finite difference form is
|q = k(θ)||[h(θ) + Z]||(t)|
|q||=||estimated water flow per time step across layer boundaries, cm|
|k(θ)||=||mean hydraulic conductivity of the two layers being considered as a function of their respective water contents, cm/hr|
|h(θ)||=||matric potential head difference between the two layers being considered as a function of their respective water contents, cm|
|Z||=||distance between the layer midpoints, cm|
|θ||=||water content, cm3/cm3|
While many solutions are available for the equation Darcy (or similar Richards equation) which use sophisticated numerical analysis techniques, a simplified method of forward differencing by constant time steps was programmed for SPAW. The objective was to keep the computations to a minimum, and still provide reasonable redistribution estimates and computational stability.
The pressure and conductivity relationships as a function of moisture content are the most difficult to obtain and input into the model for the redistribution solutions. Measured values of these relationships are very seldom available for hydrologic study sites, yet it is important to use curves that approximate the water holding characteristics of the soil layers. There are numerous estimating methods in literature for various curve parameters, but many require at least some field or laboratory data.
To stay consistent with the SPAW model goals of developing applicable methods without undue burden of data requirements, we have sought to develop an estimating method for water holding characteristics based on commonly available soil profile descriptions. The developed technique is a set of generalized equations which describe soil pressure and conductivity relationships versus moisture content and based primarily on soil textures. The basis of the equations was a very large data set assembled by the USDA Hydrology Laboratory (Rawls, et al., 1982) and re-analyzed to provide continuous curve estimates from dry to saturation (Saxton et al. 1986),. The equations are valid within a range of soil textures approximately 5-60% clay content and 5-95% sand content (Figure 11). Recent additions to the method have included effects of organic matter, bulk density, gravel and salinity. This methodology is incorporated in the SPAW model and is also available as a stand-alone program. Access the method by the soil screen and clicking the icon before the sand percentage. The HELP from the texture triangle screen provides additional information and references.
First estimates of the water holding characteristics can be made from the texture descriptions of each soil layer. Adjustments for the other variables of organic matter and density can be made if these values are known. If there are any measured values from either laboratory or field such as field capacity or saturated conductivity, the texture values can be used as calibration values to find a representative texture which possesses approximately those characteristics. Either the sand or clay percentages can be estimated, although water characteristics are most sensitive to clay.
The solution for the Darcy equation programmed in SPAW is a simplified forward difference, non-iterative method with time steps to complete 24 hours. To limit computation costs, the time step intervals begin at some entered maximum (e.g. 4 hrs), evenly divisible into 24 hours. But if strong pressure gradients or high conductivity cases exist, this delta time may allow too much change within the time step to be computationally correct or stable. Therefore, a limit of pressure change (200 cm has been successful) is set at the default, and when exceeded, the delta time is halved and the entire computation restarted. Usually, this sets the necessary time step during the first time increment and it remains sufficient for the remainder of the day because the profile is tending to equilibrate after the previously computed additions and subtractions. A limit for the minimum time step size is also entered to avoid excessive daily incrementation. Cases of significant infiltration, sandy soils or thin soil layers (less than 4 inches or 10 cm) cause the smaller time steps and result in excessive computation time by this part of the model. Other more sophisticated computation methods, such as the tri-diagonal matrix solution, have been tested and provide and provide very similar hydrologic budgets.
The upper and lower boundary conditions for a one dimensional flow equation such as Darcy must be specified. An upper (evaporative) and lower (image) boundary layer have been added to the segmented soil profile to provide this information. Separate rules of operation are provided for each of these. While these rules are somewhat arbitrary, they provide useful values to the overall water budgeting processes.
The upper (evaporative) layer is considered to be a very thin layer (about 0.5-1.0 inch) which rapidly dries with no resistance, as in stage 1 soil water evaporation. It re-wets to near saturation by precipitation and dries to a percentage between field capacity (FC) and completely dry soil.
A lower soil layer is specified below the last real soil layer of interest and termed an "image" layer because it is similar to the last real layer. The image layer controls deep percolation or upward-flowing water back to the profile. It is assumed to have the same water characteristics (pressure and conductivity) as the last real layer, and a specified thickness. If the water content of the image layer exceeds its field capacity, that water is cascaded downward to become groundwater recharge and is lost from the control volume. If the last real layer becomes drier than the image layer, water will move up from the image layer according to the Darcy calculation; however, the image layer cannot pull water up from below itself if it gets dry. Thus, the image layer serves as a temporary water storage or water source, and this volume can be varied by the thickness assigned. It does not need to be the same thickness as the last real layer, usually, 6 inches to 2 feet will provide useful results.
The depth incrementation of the soil profile and the assigned water characteristic curves for each layer are entered data. Except for the two boundary layers, the layers should reflect the soil profile changes plus provide an incrementation to allow soil water profile definitions and changes. Usually, smaller increments (4 to 8 inches) are used in the first 2 or 3 feet below the surface, then 12 to 18 inch increments thereafter. Thinner layers are not warranted and cause excessive computations.