Numeric Modeling Variably Saturated Flow Models

3.6.6 Numeric Modeling Variably Saturated Flow Models

Numerous equations and analytical mathematical models have been developed for esti- mating soil water movement and infiltration rates for various purposes such as irrigation and drainage, groundwater development, soil and groundwater contamination studies, managed aquifer recharge, and wastewater management, to name just a few. Ravi and Williams (1998) and Williams et al. (1998) have prepared a two-volume publication for the U.S. Environmental Protection Agency, in which they present a number of widely applied analytical methods, divided into three types: (1) empirical models, (2) Green- Ampt models, and (3) Richards equation models. These methods (except the empirical models) are based on widely accepted concepts of soil physics, and soil hydraulic and climatic parameters representative of the prevailing site conditions. The two volumes (1) categorize infiltration models presented based on their intended use, (2) provide

a conceptualized scenario for each infiltration model that includes assumptions, limi- tations, mathematical boundary conditions, and application, (3) provide guidance for model selection for site-specific scenarios, (4) provide a discussion of input parameter estimation, (5) present example application scenarios for each model, and (6) provide a demonstration of sensitivity analysis for selected input parameters (Ravi and Williams, 1998).

Common to all analytical methods is that they describe only one-dimensional wa- ter movement through the vadose zone and make various simplifying assumptions, of which those of a homogeneous soil profile and uniform initial soil water content are the most limiting. Because of the limitations of analytical equations, numeric models of water movement through the vadose zone and direct recharge of the water table are starting to prevail in practice. In addition, they are easily linked with, or are part of, numeric models of the saturated zone, which makes their development and utilization even more attractive. There are several versatile public domain unsaturated-saturated (variably sat- urated) flow, and fate and transport numeric models that can be used to estimate aquifer recharge rates. Examples of models with friendly graphical user interface (GUI) include VS2DT (developed by the USGS) and HYDRUS-2D/3D (available in public domain). The latter one, although not in public domain, is a successor of HYDRUS-1D initially developed at the U.S. Salinity Laboratory of the U.S. Department of Agriculture.

The use of VS2DT is illustrated with a study of recharge through a desert wash. In semiarid and arid groundwater basins, aquifer recharge is dependent on ephemeral

GroundwaterRecharge

Moisture content 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13

300 Depth below ground surface (ft) 400

F IGURE 3.30 Moisture content versus depth for model simulation of recharge through a desert

wash.

streams draining snowmelt or direct precipitation from surrounding highlands. Minimal recharge occurs through thick deposits on the basin floor due to low localized precipita- tion and high PET (Izbicki, 2002). As a result, it is very important to protect intermittent washes at the basin margins and to further understand how they drive groundwater recharge. This point is especially salient, given the increasing demand put on groundwa- ter basins in semiarid and arid settings. Physical and hydrologic parameters and wash dimensions are largely based on work by Izbicki (2002). As flow through the wash occurs during snowmelt periods or flash flood events, it is assumed that all infiltration occurs during the month of March. The total quantity of infiltration is approximately 10 percent of the total annual flow through the wash.

To illustrate flow patterns through deep vadose zones, the model is first run with homogenous fill deposits consisting of coarse sand, from the land surface down to the 415-ft-deep water table. The model is then run for 25 years to depict the resulting steady- state moisture profile through the vadose zone. Note that all recharge enters the model through the wash throughout the month of March. The moisture profiles for select months in the final year are shown in Fig. 3.30. The long-term deep drainage rate can be estimated from the model-simulated equilibrium moisture content of approximately 8 percent using the Darcy-Buckingham equation (3.9). It is important to reinforce that flow through the vadose zone does not occur as a uniform wetting front, but rather as a diffusing pulse of moisture that is dampened with depth. This diffusion causes the uniform gravity drainage below certain depth, as each recharge event is dampened to a relatively constant moisture content and pressure head.

While the above scenario is useful as a proof of concept, it is more pertinent to examine flow through a heterogeneous vadose zone with layering of finer sedimentary deposits. The same recharge conditions are simulated for a period of 20 years, at which point all recharge in the month of March is cutoff due to a hypothetical “paving” of the wash. The

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Moisture content

April August December

300 Depth below ground surface (ft)

F IGURE 3.31 Model-simulated moisture content versus depth for wash recharge through a heterogeneous vadose zone with layering of finer sedimentary deposits, excluding clay and silt.

steady-state moisture profile for the 20-year duration is shown in Fig. 3.31, together with the layering of finer sedimentary deposits. As is evident from the figure, there is little variation in moisture content in time throughout the deeper vadose zone. This results in

a constant drainage flux, as in the homogenous model. A measurement of unsaturated hydraulic conductivity within any layer allows approximation of the long-term drainage rate throughout the entire system (Nimmo et al., 2002). However, the sedimentary het- erogeneity causes significant variation in moisture content with depth because of the increased water retention capacities of fine-grained soils. The flux reaching the water table will be less than that for the homogenous coarse-grained model because of signifi- cant moisture storage in and above fine-grained layers. Furthermore, lateral spreading of moisture will occur when a wetting front reaches deposits of lower permeability. It is in- tuitive that this spreading will further reduce the magnitude of downward flux through the vadose zone.

Once the recharge source is removed in year 20, moisture will continue to enter the saturated zone at the same rate for approximately 3 years, at which point the moisture content immediately above the capillary fringe will begin to decline. Figure 3.32 shows the moisture content profile in time at a point just above the capillary fringe directly below the wash. It is interesting to note that it takes approximately 20 years for any moisture to reach the water table. This number could be greater by an order of magnitude if clays or silts were present in the vadose zone. Vadose zone modeling is critical in establishing travel times of moisture through heterogeneous sediments. Another important point is that the moisture content (and thus the recharge flux) does not decrease at a rapid, uniform rate once the recharge source is cut off. Twenty-five years after the wash is paved over, recharge is still entering the water table, albeit at a decreasing rate every year. It

GroundwaterRecharge

Moisture content 0.060 0.055

Time (yr) F IGURE 3.32 Model-simulated moisture content versus time immediately above capillary fringe.

will take many more years for the unsaturated sediments to drain all stored moisture and return to residual moisture conditions. From a management perspective, the “time lag” between infiltration reduction and recharge reduction results in long-term, abstract consequences of land use changes. Paving washes to accommodate urbanization may not result in immediate water level declines. However, long-term effects are undeniable, and the danger is that, once disrupted, the natural recharge equilibrium will take many more years to be reestablished.

Distributed-Parameter Areal Recharge Models USGS has developed two versatile public-domain computer programs for estimating areally distributed deep percolation, or actual groundwater recharge, based on surficial processes that control various water budget elements: INFILv3 and Deep Percolation Model (DPM). A very detail report presenting the development and application of the distributed-parameter watershed model, INFILv3, for estimating the temporal and spa- tial distribution of net infiltration and potential recharge in the Death Valley region, Nevada and California, is given by Hevesi et al. (2003). To estimate the magnitude and distribution of potential recharge in response to variable climate and spatially varying drainage basin characteristics, the INFILv3 model uses a daily water balance model of the root zone, with a primarily deterministic representation of the processes controlling net infiltration and potential recharge (Fig. 3.33). The daily water balance includes pre- cipitation, as either rain or snow accumulation, sublimation, snowmelt, infiltration into the root zone, ET, drainage, water content change throughout the root-zone profile (rep- resented as a six-layered system in the Death Valley model), runoff and surface water run-on (defined as runoff that is routed downstream), and net infiltration simulated as drainage from the bottom root-zone layer. PET is simulated using an hourly solar radi- ation model to simulate daily net radiation, and daily ET is simulated as an empirical function of root-zone water content and PET.

The model uses daily climate records of precipitation and air temperature from a re- gionally distributed network of climate stations and a spatially distributed representation of drainage basin characteristics defined by topography, geology, soils, and vegetation. The model simulates daily net infiltration at all locations, including stream channels with intermittent streamflow in response to runoff from rain and snowmelt. The tempo- ral distribution of daily, monthly, and annual net infiltration can be used to evaluate the potential effect of future climatic conditions on potential recharge.

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GIS and preprocessing routines (digital map files) Soil

Climate and

Atribute

meteorological data

tables

preprocessing

Drainage Basin

routines

characteristics

Bedrock and deep alluvium

Daily climate

Climate station

properties

location parameters

Vegetation

INFILv3 properties

Monthly climate

Model-control options

Monthly atmospheric

Simulation period

properties

Time step (hours) Initial conditions Storm duration

Snowmelt parameters Sublimation parameters Input/output file names

Postprocessing

Time-series outputs

Spatially distributed results

Summary

Daily results

Daily water-balance maps

statistics

Monthly results

Annual water-balance maps

Water-year results

Average annual water-balance maps

F IGURE 3.33 Inputs and outputs in the program structure of the INFLv3 model of the Death Valley region, Nevada and California. (From Hevesi et al., 2003.)

The INFILv3 model inputs representing drainage basin characteristics were devel- oped using a geographic information system (GIS) to define a set of spatially distributed input parameters uniquely assigned to each grid cell of the INFILv3 model grid (Hevesi et al., 2003).

The USGS’ DPM calculates, on a daily basis, the potential quantity of recharge to an aquifer via the unsaturated zone. Recharge is defined as the amount of water leaving either the active root zone (deep percolation) or, in the case of bare soils such as sand dunes, the mapped depth of the soil column (called the soil zone to distinguish it from the root zone). Recharge is derived from precipitation and irrigation. The model is phys- ically based and, to the extent possible, was developed so that few parameters need to

be calibrated. It was developed to fill the need between rigorous unsaturated flow mod- els (or complex land surface process models) and overly simple methods for estimating groundwater recharge. The model can be applied to areas as large as regions or as small as a field plot. For a detailed description of DPM, see Bauer and Vaccaro (1987) and Bauer and Mastin (1997). DPM calculates daily PET, snow accumulation and ablation, plant in- terception, evaporation of intercepted moisture, soil evaporation, soil moisture changes (abstractions and accumulations), transference of unused energy, plant transpiration,

GroundwaterRecharge

and surface runoff. The residual, including any cumulative errors associated with cal- culations, is deep percolation (recharge). Transference is the amount of unused PET that is transferred to potential plant transpiration after abstractions from snow sublimation, evaporation of intercepted water, and soil evaporation (Vaccaro, 2007).

DPM spatially distributes input parameters to distinct areas within a modeled region, watershed, or area, or to a point that has a unit area. These distinct areas subdivide the modeled area, and they can be of any size or shape and are called hydrologic response units (HRUs). Generally, the physical properties for a HRU are such that the hydrologic response is assumed to be similar over the entire area of an HRU. The land use and land cover (LULC) can vary by HRU. For typical applications of DPM, the soil properties and LULC are the factors that define the HRU’s hydrologic response. For forested mountain- ous terrains with winter snowpacks, a watershed model would provide better estimates of deep percolation than those calculated by DPM (Vaccaro, 2007).

One of DPM’s convenient features is that the user can input observed surface runoff directly into the model. Direct surface runoff is defined as observed daily streamflow minus an estimate of daily baseflow made by a user, both in units of cubic feet per second. The use of observed streamflow allows the model to calculate improved estimates of recharge, which generally is one of the smaller components of the water budget, because at times the potential error in calculated surface runoff can be larger than the calculated recharge. Calculated runoff can be used when direct runoff data are unavailable.

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CHAPTER 4

Climate Change