# 4.2 Methods to Estimate Depletion

Measuring or estimating the change in the volume of groundwater in storage over a time period is not straightforward as it cannot be measured directly. Estimations can rely on several alternative approaches, but all require the use of some unmeasured and uncertain properties and/or fluxes.

Perhaps the most direct approach to estimating depletion is to map the changes in head over the affected area of the aquifer and integrate those with estimates of the storage coefficient (or storativity; specific yield for unconfined aquifers). An example of this approach is presented for the High Plains aquifer as provided in Box 1. The storativity can vary horizontally and vertically, and in some cases, one may need to account for that variation to estimate reliable regional average values.

# Models

This approach is inherent to the way that a numerical groundwater flow model simulates the hydrodynamic responses in an aquifer. As part of its numerical solution of the governing groundwater flow equation, a model that is calibrated to observed changes in head (and/or fluxes) in the aquifer will provide calculations of changes in groundwater storage during each model time step, as well as cumulatively for the time period from the start of the model simulation, in its water budget output. Examples of simulation models applied to aquifers having substantial depletion include Faunt et al. (2009) for the Central Valley of California and Clark and Hart (2009) for the Mississippi Embayment aquifer.

# Water Budgets

One can also use a water budget approach for estimating depletion. For example, Kjelstrom (1995) used pumpage data in conjunction with other water budget estimates for the Snake River Plain aquifer in Idaho and eastern Oregon to estimate the changes in groundwater storage. But this approach has limited applicability because of the large uncertainties in estimates for all of the water budget elements. The difficulty arises because the change in storage may be small relative to the fluxes in and out of the aquifer so that errors in the estimated fluxes may exceed the magnitude of the rate of storage change. Nevertheless, a fair number of studies have been published using large scale (or even global) models of atmospheric and land-surface processes to estimate groundwater depletion, which is calculated as a residual in the budget equation (e.g., Wada et al., 2010). In its simplest form, depletion equals the difference between recharge and pumpage. Recharge is assumed to equal precipitation minus runoff and evapotranspiration, and pumpage estimates are typically based on land-use characterization and expected water use rather than on direct measurements of withdrawals. A primary difficulty here is that these approaches generally cannot simulate or predict the very effects and processes discussed in this book – namely that pumpage will be balanced by a combination of increased recharge and decreased discharge – because the water budget approaches do not simulate the hydrodynamic changes within a groundwater flow system nor its relation to surface water. Therefore, these global water-balance approaches tend to substantially overestimate the magnitude of groundwater storage depletion because they erroneously ignore capture and/or its hydrodynamic processes.

# Gravity Measurements

Another alternative approach to estimating groundwater depletion is through geophysical methods. Where groundwater depletion occurs, the mass of material in the Earth’s subsurface is reduced, and this affects the Earth’s gravity field. Very sensitive gravity measurements repeated over time can detect relatively small changes in the gravity field. If these gravity changes are derived solely or primarily from changes in total water storage (TWS), then the observed gravity changes can be used to estimate groundwater depletion if other possible contributors to changes in TWS are negligible or can be reliably estimated (such as changes in surface-water storage, snow and ice, and vadose zone/soil moisture). Land-based surface gravity measurements were repeated annually over several years in Arizona to estimate changes in groundwater storage in alluvial aquifers (Pool and Anderson, 2008). However, they reported that correlations between gravity-based estimates of storage change and water-level changes in observation wells were sometimes only poor to moderate.

# GRACE Remote Sensing

A much larger scale of gravity measurement is provided by the GRACE satellites (Gravity Recovery and Climate Experiment, a mission jointly sponsored by the United States and Germany), which are a pair of coupled satellites to measure spatial and temporal changes in the Earth’s gravity field (e.g., Tapley et al., 2004; Famiglietti and Rodell, 2013; and Famiglietti et al., 2015). GRACE has provided useful information about global changes in TWS, as well as global groundwater depletion for many large aquifer systems (e.g., Famiglietti et al., 2011; Tiwari et al., 2009; and Rodell et al., 2009). However, GRACE data provide estimates of total change in water storage over a relatively large footprint – a resolution on the order of 100,000 km2 as discussed by Scanlon et al. (2016). This scale is much larger than many aquifers. Although the accuracy is on the order of 1.5 cm of equivalent water height, the low spatial resolution of GRACE limits its ability to provide groundwater depletion data at a scale amenable for water managers to use effectively as discussed by Alley and Konikow (2015). Furthermore, the analysis of GRACE data still faces the challenge of separating all the components contributing to total water storage change as explained by Scanlon et al. (2015). Hence, using this approach to estimate groundwater depletion is most applicable to large aquifers in arid to semi-arid climatic areas and requires some caution in interpretation.

# Subsidence

An estimate of the minimum value for groundwater storage depletion in an area undergoing land subsidence due to groundwater withdrawals can be made by calculating the volume of subsidence. The groundwater storage depletion volume must equal or exceed the subsidence volume because the removal of pore water and the subsequent compaction of the sediments are the drivers for the subsidence. For example, in the Gulf Coastal Plain near Houston, Texas, the volume of land subsidence was estimated by Konikow (2013) using maps of historical subsidence (1906–2000). The calculated cumulative subsidence volume was 10.5 km3. For comparison, the cumulative water budget from a numerical model calibrated to field observations made from 1891 to 2000 indicates that 10.8 km3 of groundwater was removed from storage in the unconsolidated clay units as the clays compacted and subsidence progressed – essentially all of it during the 20th century according to Kasmarek and Robinson (2004). The small difference of less than 3 percent provides good support for the use of the subsidence approach, as well as for the quality of the model calibration and resulting reliability of the model calculations. For comparison, the volume of groundwater depletion derived from storage losses in interbedded clays (and associated with land subsidence) represents about 36 percent of the total groundwater storage depletion of 28.9 km3, with the remaining depletion derived from storage losses in the sand layers (Kasmarek and Robinson, 2004).

# Confining Layers

It is well established that confining layer storage is a significant source of water when confined aquifers are developed (e.g., Theis, 1940; Jacob, 1946; Hantush, 1960; Bredehoeft et al., 1983). In a regionally extensive confined aquifer, direct recharge may be limited to outcrop areas at the margins of the aquifer’s extent. So a stress on the aquifer in the form of groundwater withdrawal from wells distant from the outcrop area cannot be readily balanced by an increase in recharge. Thus, drawdown propagates large distances laterally and changes in vertical hydraulic gradients induce leakage from adjacent confining beds. Because the hydraulic conductivity of confining beds is low relative to that of the aquifer, precluding timely propagation of the head change to the other side of confining bed, that leakage will be derived primarily from storage depletion in the confining beds over timeframes of decades to centuries. In fact, the magnitude of storage depletion in the confining units can be much greater than the storage depletion in the confined aquifer itself. An example of this occurred in the Dakota Aquifer system as explained in Box 2. Konikow and Neuzil (2007) summarize a number of approaches for estimating the volume of depletion from confining units. Most methods require measurements or estimates of the hydraulic conductivity and specific storage properties of the confining layer, as well as observations of head changes within the confining layer. However, such data are rarely available because water supply wells rarely have open intervals in confining units. Konikow and Neuzil (2007) offer a simplified method that is based on head changes in the confined aquifer at the boundary with low-permeability confining units.