Table of Contents

Introduction

Part I

Appendix A

Appendix B

Appendix C

Part II A and B

Part II C and D

Part III

Part IV

References

Summary

Appendix A. Physical Methods for Recharge Estimation

Physical methods rely on direct measurements of hydrological parameters or on estimates of soil and/or aquifer physical parameters. Physical methods are frequently used to estimate precipitation recharge because they are quick, inexpensive, or straightforward. However, these methods are often problematic in arid and semi-arid regions. There are several reasons for this (Hendrickx and Walker, 1997): 1) The low recharge fluxes depend to a large extent on the vadose zone physical parameters, and significant variations in fluxes may occur with small changes in these physical parameters. Unfortunately, it is almost impossible to detect such small changes in physical parameters; 2) The extreme temporal variability of arid climates means that long-time series are needed to assess mean annual recharge rate; and 3) Spatial variability caused by changes in local topography, soil type, and vegetation requires a large number of measurement sites to assess the spatially averaged recharge rate. Nevertheless, with prudent appreciation for their limitations, physical methods can be a helpful tool for evaluating precipitation recharge.

A1 Indirect Physical Methods

Indirect physical methods for estimating ground-water recharge consist of (1) empirical methods, (2) water-balance methods based on estimates of soil physical properties, and (3) numerical modeling methods. In principle, one of the simplest methods used for estimating diffuse recharge, R, is empirical expressions of the type

R = k₁(P – k₂), . . . . . . . . . (A–1)

where P is precipitation, and k₁ and k₂ are constants for a particular area. Such expressions have been used with varying degrees of success and are probably most useful for making first-guess estimates of recharge where annual recharge is fairly high, >2 inches/yr, and thus should seldom be used in arid or semiarid regions (Allison et al., 1994).

Methods relying on estimates of soil physical parameters generally fall into the following classes: (1) soil-water balance, (2) zero-flux plane method, (3) estimation of water fluxes beneath the root zone using unsaturated hydraulic conductivity and the gradient in soil-water potential, and (4) estimation of water fluxes in the saturated zone based on Darcy’s Law and flow-net analysis. Additional methods also exist that may not fit well into one of these classes, such as gravity surveys for measuring changes in aquifer storage resulting from recharge events. Increased accuracy in measuring temporal variations in the Earth’s gravity field has recently allowed the use of gravity observations to deduce subsurface water-mass changes resulting from precipitation and consequent recharge events.

A1.1 Water Balances

This group of methods estimates recharge as the residual of all other fluxes. The principle is that other fluxes can be measured or estimated more easily than recharge. Examples of water-balance methods include (1) soil-moisture budgets, in which rainfall and potential evapotranspiration are inputs to a soil-moisture accounting procedure, with actual evapotranspiration and recharge as the outputs; (2) river-channel water balances, when upstream and downstream flows are differenced to calculate recharge or—more accurately—transmission losses (a related stream-hydrograph analysis technique based on baseflow-separation techniques is founded on steady-state water-balance calculations, whereby the estimate of discharge based on baseflow-separation or baseflow-recession analysis of the stream hydrograph, must equal recharge. This technique is considered too empirical and approximate to give reliable quantitative estimates); and (3) water-table rises, when the volume stored beneath a rising water table is equated to recharge, after allowing for other inflows and outflows such as pumping wells and aquifer throughflow. The simplicity of the latter method made it a popular one. However, calculating the volume of water stored between lowest and highest water-table positions over a study period interval involves reliable estimates of the aquifer’s specific yield values, which may be difficult to obtain.

The advantages of water-balance methods (Lerner et al., 1990) are that they use readily available data (rainfall, runoff, water levels), are easy to apply, and they account for all water entering the system. The major disadvantage is that recharge is the residual or remainder of all other hydrologic components in the water-balance equation, and constitutes only a small difference between large-number components, such as precipitation and evapotranspiration. Errors can be high, with the errors in all the other fluxes accumulating in the recharge estimate. For example, high river flow can often only be estimated to ±25%. If recharge is 25% of flow, the error in estimating it is ±100%. Other disadvantages include the difficulty of estimating other fluxes in the water-balance equation. For example, evapotranspiration cannot be measured easily, yet it is often the largest outward flux. Physical properties like specific yield are central to some water-balance methods, such as the ones based on water-table rises, but are not easily defined or measured.

The natural time scale for water-balance methods is the duration of a recharge event. Recharge processes are often nonlinear, so that estimates based on longer time intervals should be summed over the individual events rather than calculated for the whole interval at once. Long records are available for much of the data used for balances (rainfall, runoff), so that long time series of recharge can often be calculated.

A methodology consisting of a combination of soil-moisture budget and water-table rise analyses is known as hybrid water fluctuation method (Sophocleous, 1991). This combination methodology, designed to minimize water-balance errors, was successfully applied in the central Kansas plains, which are characterized by semiarid to subhumid climate, relatively flat terrain, and relatively shallow water table.

The hybrid water-fluctuation methodology can be summarized as follows (Sophocleous, 1991). Neutron-moisture profile readings are collected onsite at least once a week during the recharge season (usually spring and fall). The soil-water balance methodology for each recharge-producing storm period is applied, and the resulting water-table rise is noted, provided it is confirmed that the water-table rise is due to incoming soil water from above, as checked with tensiometer readings and/or deeper water-content measurements. The recharge estimate resulting from the soil-water balance is then divided by the corresponding water-table rise to obtain an estimate of effective storativity or fillable porosity of the region near the water table. Several such estimates are obtained and averaged. This average is, in effect, the site-calibrated effective storativity value, which can be used to translate each water-table rise, tied to a specific storm period, into a corresponding amount of ground-water recharge. In the central Kansas prairies, which are characterized by mostly permeable sandy soils and shallow water table, the time lags between the occurrence of a recharge-causing rainstorm and the corresponding water-table rise usually range from less than a day to just a few days.

Recharge-estimation errors in the hybrid water-fluctuation method are reduced by running a storm period-based soil-water balance throughout the year, in combination with the associated water-level rise, thus avoiding masking short periods of recharge by the averaging effect of monthly or larger time-interval data. Furthermore, during the recharge-producing rainstorm periods under consideration, the evapotranspiration (ET) estimates are usually significantly smaller than the precipitation amounts. Therefore, even a large ET error on a relatively small quantity may not significantly affect the recharge estimate. Also, by employing the Complementary Relation Areal Evapotranspiration (CRAE) methodology, which permits areal ET to be estimated from its effects on the routinely measured temperatures and humidities, the soil-plant system complexities can be avoided, as well as the need for locally calibrated coefficients. (The CRAE concept takes into account interactions between the evaporating surfaces and the overpassing air, whereby a decrease in the availability of water for areal ET causes the overpassing air to become hotter and drier, which in turn causes the potential ET to increase.) In addition, the errors inherent in the soil-water balance approach can be appreciably reduced by corroborating the estimation of recharge with increases in soil-water content at depth, and with unequivocal fluctuations of the water table, provided it is relatively shallow. Furthermore, close monitoring of shallow and deeper hydraulic gradients from multi-level piezometers makes it possible to ascertain whether water-table rises are due to lateral inflow at the site or to vertical accretion from rainfall percolation. This combined methodology results in better and more reliable recharge estimates than either the soil-water-budgeting procedure or the water-table-rise analysis used singly and does not require additional difficult-to-measure variables (Sophocleous, 1991).

A1.2 Zero-flux Plane Method

The zero-flux plane (ZFP) method relies on locating a plane of zero hydraulic gradient in the soil profile. Recharge during a time interval is obtained by summation of the changes in water content below this plane. Unfortunately, the method breaks down in periods of high infiltration when the hydraulic gradient becomes positive downward throughout the profile. This is when recharge fluxes are likely to be highest. Use of this technique can give good estimates of recharge for periods during the year when the ZPF exists.

A1.3 Estimation of Unsaturated Water Fluxes

Several studies have reported use of unsaturated-zone hydraulic conductivity, K(), or, K(), and water-retention data, (), to solve either Darcy’s Law or Richards’ equation in the unsaturated zone and to estimate soil-water flux for periods of months to years (Allison et al., 1994). If the water flux is calculated at such a depth in the profile that no further extraction by roots occurs, then the flux will be equal to ground-water recharge:

R =K()H_T, . . . . . . . . . (A–2)

where H_T is the total head gradient. For most soil systems, H_T = H_g + H_m, where H_g is the gravity head and H_m is the matric suction head.

Both K() and K() relationships are difficult and time-consuming to determine, both in the field and in the laboratory, with difficulty and uncertainty increasing with soil dryness. Slight differences in measured water content translate into large differences in unsaturated hydraulic conductivity. As a result, the annual recharge flux could vary significantly, depending on how the mean hydraulic conductivity is computed.

A1.4 Estimation of Saturated Water Fluxes

An equivalent method for recharge estimation based on saturated flow governed by Darcy’s Law is simpler, especially when assuming steady-state conditions and employing flow-net analysis. The only measurements needed are values of hydraulic head and hydraulic conductivity to construct a quantitative flow net. A flow net consists of a set of intersecting lines of equal hydraulic head values (known as equipotential lines) and flow lines representing two-dimensional steady flow through a porous medium (see figs. I–1 and I–2). Two-dimensional vertical-flow nets constructed along the general ground-water flow direction from water-table and hydraulic-head field measurements provide an approximate but straightforward way of identifying areas of recharge and discharge and estimating recharge.

A1.5 Numerical Models for Estimating Recharge

Different types of models are available for estimating ground-water recharge: (1) numerical models that solve one-, two-, or three-dimensional forms of the water flow or Richards equation; (2) parametric hydrologic models that use a numerical or analytical relationship between infiltration or precipitation and recharge; (3) ground-water flow models; and (4) combined or integrated watershed and ground-water models.

Numerical modeling methods take transient flows and storage changes into account and can include spatial variability of physical properties, of which hydraulic conductivity is one of the most important. However, data requirements and computing load are high. Such models are used to estimate model parameters, in this case recharge, based on known values of hydraulic head. Such an approach is known as a solution of an inverse problem. This is in contrast to the forward or direct problem, where model parameters are considered known, and hydraulic head is computed.

Should one possess the analytical expressions for hydraulic head and transmissivity in the ground-water flow equation, determination of recharge would have been a trivial exercise of calculus in computing the derivatives of the ground-water flow equation. However, hydraulic heads are always measured with inaccuracies. Differentiating such noisy data leads to large errors in recharge estimation.

Integrated watershed and ground-water models allow a complete analysis of the land-based hydrologic cycle, thus providing the means for evaluating the impacts of land use, irrigation development, and climate change on both surface-water and ground-water resources (Sophocleous and Perkins, 2000). Such models allow predictions of the impact of management changes on total water supplies, including recharge. The seasonal variation of water-table levels and recharge can be more accurately predicted by the soil-moisture accounting system employed in the integrated model than by using only a ground-water model. This increased flexibility, however, comes at the expense of increased complexity and expertise needed to effectively use integrated watershed modeling. Although integrated models require extensive data, such integrated modeling constrains the adjustment of model parameters during calibration because overall water budgets must be observed. Whereas traditional methods used to calibrate ground-water models may include adjustments to recharge rates, in an integrated model, recharge is completely constrained by the overall water budget for the surface-water system. In addition, stream-aquifer interactions, including stream-derived recharge, are constrained by the generated amount of surface runoff to streams that in turn, impacts the stream stage and thus the driving forces for stream-aquifer interaction.

The principal advantages of the numerical methods are that they attempt to represent the actual physical processes of interest and that they allow predictions of future recharge regimes resulting from different land uses and climatic changes. These advantages are often countered by the need to make simplifying assumptions in order to reduce the computational effort. For example, numerical models of the soil zone usually assume a single porosity medium with no spatial variation in properties. In practice many soils may have dual porosity, with preferred pathways during high saturation—that is, at times of recharge.

The correct time scale for such models depends on the rate of fluctuation of heads, varying from seconds for rainfall into soil to seasonal or longer for seepage between aquifers. Effectively addressing the multiple temporal (as well as spatial) scales involved in recharge estimation constitutes a major problem in modeling recharge processes. In addition to such obstacles and uncertainties, large data requirements often make application of numerical models difficult.

A2. Direct Physical Methods

In contrast to the numerous indirect physical methods, only one method for estimating diffuse recharge is direct. This involves the construction of a lysimeter. Lysimeters comprise enclosed blocks of disturbed or undisturbed soil with or without vegetation that are hydrologically isolated from the surrounding soil in order to assess or control various terms of the water balance. There is also only one direct method for estimating indirect recharge associated with surface-water bodies in direct hydraulic connection with an underlying aquifer. This involves the use of seepage meters that are inserted in the streambed or lakebed that could provide direct-point measurements of localized recharge.

Lysimeters are expensive and permanent instruments (Allison et al., 1994). They are typically filled with disturbed soils, which generally have water-content profiles that differ in some degree from those found in surrounding soils. Drainage can occur only when a water table develops at the base of the lysimeter, unless solution samplers (e.g., ceramic-cup extractors) and a vacuum system are installed at the base of the lysimeter. This last factor, however, is unlikely to be a problem if the lysimeter is relatively deep and the vegetation is shallow rooted. While lysimeters have been useful in quantifying drainage at waste sites under arid conditions, they have limited ability to document the spatial variability produced by natural and human-induced changes in surface- and subsurface-flow pathways. Construction cost and logistics limit size and depth to generally no more than a few square feet and a 10-ft depth although lysimeters as deep as 60 ft have been constructed (Allen et al., 1991; Gee et al., 1992). Because lysimeters are effective for the study of recharge mechanisms and yield the high-quality data needed in computer-model calibration for simulating the water balance, some specialists recommend that more lysimeter-recharge studies be undertaken worldwide in a variety of climatic and soil conditions. However, the initial construction costs and the long-term monitoring requirements demand serious extended commitment.

Seepage meters were originally developed to measure canal seepage losses. They involve a seepage bell or cylinder that is pushed into the canal-bed sediment, and the infiltration rate is measured by constant- or falling- head techniques. Their advantages include being (1) lightweight and easily transportable, (2) relatively cheap, (3) simple to operate, (4) rapidly measurable, and (5) directly convertible into a seepage value. Difficulties are encountered in gravelly or stony sediments, or in sandy sediments, which may be washed from around the seepage cylinder by eddy currents, sediment disturbance, and ineffective seal of the inserted seepage cylinder. The number of measurements per unit of area needed to arrive at a reasonable average depends on the degree of heterogeneity in the seepage loss at the specific site. In conclusion, the seepage meter gives a rapid and direct measurement at low cost, but the figures obtained are only point measurements (Lerner et al., 1990).