A Comprehensive Review of Specific Yield in Land Surface and Groundwater Studies

Abstract

Specific yield is a key parameter for estimating water table depth in land surface models, which can strongly modulate the interaction between soil moisture and groundwater and further affect the water budget between the land surface and the atmosphere. The error in water table simulation comes mainly from the uncertainty in determining the specific yield. The determination of specific yield in land surface models is simplified, and a uniform empirical constant value of specific yield is generally used in global simulations, especially for deep aquifers, for its convenience. However, a uniform fixed value is insufficient for worldwide aquifers with diverse environments. Before estimating specific yields for global aquifers in Earth system simulations, a comprehensive understanding of the specific yield and comparison of current determination methods are required. This study provides a comprehensive review of the literature focusing on different concepts of the specific yield, complex variabilities, and various determination methods. Specifically, we detail the distinction and interconversion of different subconcepts that are used to reflect the influence of different factors on the specific yield and are likely to confuse scholars; present the representative comparisons of previous estimated specific yields using different methods, and summarize the applicabilities and limitations of these methods, indicating directions for their future improvement.

Introduction

Specific yield (S_y) is the space available for the gain or loss of groundwater associated with the rise or fall of a water table, respectively. In land surface models (LSMs), the specific yield is a crucial parameter to convert the groundwater storage change to the water table change through the water table fluctuation (WTF) equation, in which the water table change is equal to the water storage change divided by the specific yield (e.g., Letts et al., 2000; Niu et al., 2007; Oleson et al., 2013; Pokhrel et al., 2015; Yang et al., 2011; Yeh & Eltahir, 2005). As summarized by Clark et al. (2015), a number of modern LSMs apply the specific yield, including the Community Land Model (CLM, Oleson et al., 2007, 2013), the Land Ecosystem–Atmosphere Feedback (LEAF, Miguez‐Macho et al., 2007), the Variable Infiltration Capacity model (VIC, Liang et al., 2003), and the Minimal Advanced Treatments of Surface Integration and Runoff with representation of water table dynamics (MATSIRO‐GW, Koirala et al., 2014, 2019; Pokhrel et al., 2015). In addition, two groundwater options in the Community Noah Land Surface Model with MultiParameterization Options (Noah‐MP, Niu et al., 2011; Yang et al., 2011) that were not listed in Clark et al. (2015) also adopt the specific yield.

Specifically, LEAF, using the improved groundwater scheme (Miguez‐Macho et al., 2007), uses the difference between the saturated water content and the water content in the unsaturated portion within the water table‐located layer to represent the specific yield for both shallow and deep water table conditions. Moreover, Noah‐MP, again with the groundwater scheme of Miguez‐Macho et al. (2007), applies the same method to determine the specific yield. In VIC, the specific yield is expressed as the effective porosity which here is referred to as the absolute difference between soil moisture content in the soil column constricted by the water tables between two time steps (Liang et al., 2003). In MATSIRO‐GW, which follows the groundwater scheme of Yeh and Eltahir (2005), the global simulation uses an empirical specific yield value of 0.08 (Koirala et al., 2014) or 0.15 (Pokhrel et al., 2015). Noah‐MP, this time with the simple groundwater module (SIMGM, Niu et al., 2007), employs an empirical value fixed at 0.2 in deep water table situations (where the water level is below the soil column), and uses the effective porosity, which is the volume of air pore space within the soil (Niu et al., 2007), to represent the specific yield in cases with a shallow water table (when the water level is within the soil column) (Yang et al., 2011). The CLM3.5 (Oleson et al., 2007) also uses a constant value of 0.2 when the water level is below the soil column, and adopts an empirical equation based on the effective porosity, introduced by Niu et al. (2007), to estimate the specific yield when the water level is within the soil column. In CLM4.5 (Oleson et al., 2013), the apparent specific yield, which considers the water table depth effect but is time‐independent and will be introduced below, is adopted for both shallow and deep aquifers. However, the main error in water table simulation is from the uncertainty in determining the specific yield value (Crosbie et al., 2005, 2019; Cuthbert, 2010; Fan et al., 2014; Healy & Cook, 2002; Logsdon et al., 2010; Machiwal & Jha, 2015; Maréchal et al., 2006; Scanlon et al., 2002; Yin et al., 2011).

The specific yield in LSMs such as CLM and Noah‐MP is usually referred to as the water drained by gravity divided by the aquifer area and the water table depth change (Freeze & Cherry, 1979). The specific yield is also commonly expressed as the ratio of the volume of water that saturated rock or soil yields by gravity to the total volume of the rock or soil (Meinzer, 1923). The specific yield can vary with a number of factors, such as soil texture, water table depth, and time (e.g., X. Chen et al., 2010; Shamsudduha et al., 2012; Wang & Pozdniakov, 2014); thus it has a high spatiotemporal variability, especially for shallow water tables (e.g., X. Chen et al., 2010; N. Shah & Ross, 2009; Sullivan et al., 2014). Therefore, as stated by Machiwal and Jha (2015), the specific yield obviously changes with the geology and land types due to aquifer heterogeneity. When taking a region (or a grid cell in an LSM) as a whole, a spatially averaged specific yield can be used (Carlson Mazur et al., 2014; J. Chen et al., 2016; Dettmann & Bechtold, 2016; Singh, 2011). In terms of the water table depth and time, the specific yield can be classified into the ultimate specific yield, the apparent (or depth‐dependent) specific yield, and the transient (or time‐dependent) specific yield. In addition, with a dropping or rising water table, the specific yield value is different. X. Chen et al. (2010) argued that using a single fixed specific yield value in an unconfined aquifer is an overly simplified approach. A constant specific yield value could greatly overestimate the groundwater recharge (Childs, 1960; Crosbie et al., 2005; Sophocleous, 1985). A study in Bangladesh (Shamsudduha et al., 2012) showed that the groundwater storage anomaly derived from distributed specific yields matches the Gravity Recovery and Climate Experiment satellite estimates better than that based on a fixed specific yield value of 0.1. This suggests that the specific yield determination in global LSMs is relatively simplified as mentioned above, and especially indicates that a single fixed value of specific yield is insufficient for a global simulation with diverse aquifers.

The study aims to (i) interpret the variation of specific yield versus water table depth, time, and other factors; and (ii) present representative comparisons of previous estimated specific yields using different specific yield determination methods and summarize the applicabilities and limitations of these methods. The comprehensive review is expected to potentially advance Earth system model development in terms of the simulation of groundwater.

Specific Yield Definition

A commonly cited definition of specific yield of Freeze and Cherry (1979) and Todd (1959) is a measure of the volume of water that an aquifer releases from or takes into storage per unit aquifer area per unit change in the water table depth, $S_y=V_w/(A\cdot \mathrm{\Delta }H)$ where V_w is the volume of the water drained from groundwater, A is the aquifer area, and $\mathrm{\Delta }H$ is the water table change. Dos Santos Jr. and Youngs (1969) gave a more specific expression, stating that the specific yield is the ratio of the water flux per unit area through the water table resulting from the water released or taken up by the unsaturated soil to the rate of the rise or fall of the water table. Neuman (1987) and Hillel (1998) defined a similar specific yield as the volume of water extracted from the groundwater per unit area when the water table is lowered by a unit distance.

Another commonly used definition of specific yield is the ratio of the volume of water that saturated rock or soil yields by gravity to the total volume of the rock or soil (Fetter, 1994; Lohman, 1972; Meinzer, 1923; Schwartz & Zhang, 2003). The formula $S_y={\theta }_s-S_r$ is generally used, namely, the specific yield is the difference between the porosity (θ_s) and the specific retention (S_r). The specific retention is the volume of water retained by the soil or rock per unit volume of soil or rock (Healy & Cook, 2002). Previous studies (Duke, 1972; Gribovszki, 2018; Neuman, 1987) have shown that the specific retention could be represented by the field capacity (Gillham, 1984; Meinzer, 1923; Nachabe, 2002; Nachabe et al., 2003) or the residual moisture content (Crosbie et al., 2005; Loheide II et al., 2005). Both the field capacity and the residual moisture content attempt to describe the lower limit of water content at which the water is significantly mobile (Duke, 1972).

Variable Specific Yield

To understand the specific yield more clearly, first it is necessary to introduce the capillary and subsurface water distribution, as shown in Figure 1. The variables of ΔH, θ_s, θ_r, and S_r have the same meanings as above (the same hereafter).

A small zone that is fully saturated under negative pressure exists above the water table. Moreover, in this zone, the closer to the water table, the closer the soil matric potential (pressure head) is to zero, as the matric potential (pressure head) at the water table is zero. This saturated zone occurs because the surface tension of water and the attractive forces of sediments can wick water up from the water table and hold it in the pore spaces. It is therefore known as the tension‐saturated zone. Regarding the concept of the capillary fringe, there are two different definitions: it is usually recognized as the tension‐saturated zone (e.g., Abdul & Gillham, 1984; Healy & Cook, 2002; N. Shah & Ross, 2009; Sophocleous, 1985); it is also defined as the space from the water table to the maximum capillary rise height (Figure 1a) in some studies (e.g., McCarthy & Johnson, 1993). The important role of the capillary fringe in water table and storage change calculations has been documented in previous literature (e.g., Cartwright et al., 2005; Gillham, 1984; Lehmann et al., 1998; Li et al., 1997; Nielsen & Perrochet, 2000; Sophocleous, 1985).

An increasing number of studies have pointed out that the specific yield varies with water table depth and time (Bear, 1972; Butler Jr. et al., 2007; Childs, 1960; Cloke et al., 2006; Crosbie et al., 2005; Dos Santos Jr. & Youngs, 1969; Duke, 1972; Fan et al., 2014; Gillham, 1984; Jayatilaka & Gillham, 1996; Loheide II, 2008; Mould et al., 2010; Nachabe, 2002; Said et al., 2005; N. Shah & Ross, 2009; Wang & Pozdniakov, 2014; Youngs & Smiles, 1963). The ultimate specific yield, a constant value, is valid only when the water table is sufficiently deep, and the time duration is sufficient to achieve the complete drainage by gravity or to reach the static equilibrium condition (e.g., Childs, 1960; Duke, 1972; Loheide II et al., 2005; Mould et al., 2010). In addition to water table depth and time, the specific yield is affected by other factors. As Fahle and Dietrich (2014) stated, the specific yield should be restricted to a specified time window under specified conditions. Most studies on specific yield variability were conducted under a situation of water releasing from an aquifer, and few studies have been carried out to identify its variation in response to different natural processes such as evapotranspiration and precipitation (N. Shah & Ross, 2009). This section details the factors that cause a variable specific yield, and compares the different concepts of specific yield in terms of water table depth, time, and rising or falling water table conditions.

Specific Yield as a Function of Water Table Depth

With sufficient time to reach equilibrium, the specific yield is equal to the difference in water content between the initial and final equilibrium soil moisture profiles integrated vertically from land surface to the final water table (FWT) depth divided by the change in water table depth, assuming there are no water sources or sinks in the vadose zone (Bear, 1972; Gribovszki, 2018; Loheide II et al., 2005; Nachabe, 2002). The water content between two equilibrium moisture profiles changes with the depth of the water table. Childs (1960) used a hypothetical moisture profile (Figure 2) to illustrate the specific yield variation with water table depth. For a falling deep water table (Figure 2a), the dashed line is the static equilibrium soil moisture profile above the initial water table (IWT), while the dash‐dot line is the reattained equilibrium profile after IWT declined by ΔH to the FWT. The static equilibrium profile can be represented by a water‐retention curve, such as the van Genuchten curve model (van Genuchten, 1980) or the Brooks‐Corey curve model (Brooks & Corey, 1964). The shadowed area is the volume of water released per unit area, which is equal to $({\theta }_s-S_r)\cdot \mathrm{\Delta }H$ by mathematical deduction, and then the specific yield value is θ_s−S_r. In the case of a shallow water table (Figure 2b), the released water can also be expressed by the shaded area, but it is much smaller than (θ_s−S_r)⋅ΔH. The closer the water table is to the ground surface, the smaller the specific yield will be. Specifically, because the capillary fringe zone has little or no storage capacity, the specific yield is almost equal to zero once the water table is close enough to the ground surface. In other words, a very small amount of rainwater can result in a rapid and large water table change (e.g., Abdul & Gillham, 1984; Cloke et al., 2006; Duke, 1972; Gillham, 1984).

In view of the water table depth dependence, the specific yield presented in Figure 2a can be called the ultimate specific yield, which is a constant, whereas that obtained from Figure 2b can be referred to either as the apparent specific yield (e.g., Childs, 1969; Crosbie et al., 2005; Duke, 1972; Sophocleous, 1985) or the depth‐dependent (or depth‐compensated) specific yield (e.g., Fan et al., 2014; Loheide II et al., 2005). We will hereafter refer to it in this study as the apparent specific yield. Note that some studies have used the ultimate specific yield concept for both deep and shallow water table situations (e.g., Cheng et al., 2015; Nachabe, 2002). When the water table depth is sufficiently deep, the capillary fringe effect can be ignored, and the apparent specific yield equals the ultimate specific yield. The depth needed to reach the ultimate specific yield is related to the soil texture. The ultimate specific yield can be reached when the water level is deeper than 1 m for coarse‐textured soil, such as sand (Fan et al., 2014; Yin et al., 2013), loam sediment (Loheide II et al., 2005), peat soil (Mould et al., 2010), and a mixture of sand, silt, clay, and laterite (Crosbie et al., 2019), whereas a depth exceeding 10 m is needed for fine‐textured soil (Duke, 1972). What follows are the existing numerical formulas for calculating the apparent specific yield.

Duke (1972) proposed a function of water table depth for the apparent specific yield as shown in Equation 1, with assumptions that the porous medium is uniform, there is a static equilibrium soil moisture profile above the IWT, and the static equilibrium profile can be reattained instantaneously after a change in the water table (Crosbie et al., 2005). [Image Omitted. See PDF]where H is the water table depth, h_a is the air‐entry (bubbling) pressure head, and λ is the pore‐size distribution index.

Nachabe (2002) introduced an improved formula to calculate the apparent specific yield, aiming to address the limitation that Duke's (1972) expression is only valid when the WTF is small compared with the IWT depth. Nachabe's (2002) formula is valid regardless of the water table's fluctuation magnitude. [Image Omitted. See PDF]where H_i and H_f are the initial and FWT depths, respectively (the same hereafter).

Duke's (1972) and Nachabe's (2002) functions are both based on the Brooks‐Corey water retention curve. The van Genuchten water retention curve has also been used in the analytic expression for the apparent specific yield. Crosbie et al. (2005) showed that Duke's (1972) function cannot be applied in a layered soil. Thus, they proposed a more general solution, shown in Equation 3, based on a static equilibrium profile characterized by the van Genuchten curve. Moreover, Loheide II et al. (2005) and Cheng et al. (2015) obtained a similar expression to Equation 3 using the van Genuchten water retention curve. [Image Omitted. See PDF]where α is reversely related to the air‐entry value in the van Genuchten curve, and n is a dimensionless parameter in the van Genuchten curve that is generally restricted to values greater than 1, $m=1-1/n$.

Specific Yield as a Function of Time

The water in the soil medium does not move instantaneously (e.g., Meinzer, 1923), and thus the shorter the accumulated time, the smaller the specific yield value. After the water table change commences, the soil medium near the water table will first reach the static equilibrium state (Nachabe, 2002) because the capillary fringe makes the medium near the water table have sufficient water supply. However, it would take a long time, potentially several months or years, to drain the entire vadose zone completely (X. Chen et al., 2010; Healy & Cook, 2002; Nwankwor et al., 1984). For example, Prill et al. (1965) found that it would take more than one year for a 1.71‐m‐long column of medium sand to reach static equilibrium, while the static equilibrium state in the bottom 0.6 m of the column was attained only 5 h after drainage commenced. This indicates that the specific yield is time‐dependent, particularly when the water table is shallow and the soil is fine‐textured with high air‐entry pressure (Nachabe, 2002; Pozdniakov et al., 2019). If the time step in a model is longer than the time needed to reach static equilibrium, the apparent specific yield can justifiably be adopted (Nachabe, 2002). However, the time step in LSMs is usually short (less than an hour), and the static equilibrium condition rarely occurs in such a short time step. In contrast to the apparent specific yield, the transient specific yield (Nachabe, 2002) is time‐dependent.

The transient specific yield should be obtained from the initial and time‐varying soil moisture profiles. Dos Santos Jr. and Youngs (1969) proposed the following theoretical formula for the transient specific yield: [Image Omitted. See PDF]where dW'/dt accounts for the changing shape of the moisture profile above the water table over time, dH/dt is the water table change rate, and α(H,t) is the air content at the surface at any time, which can be obtained from the measured moisture profile curves. For the static equilibrium condition (dW'/dt = 0), this equation is very similar to Duke's (1972) formula.

Based on the Brooks–Corey curve, the transient specific yield in Nachabe (2002) was calculated by: [Image Omitted. See PDF]where K_s is the saturated hydraulic conductivity; n is an exponent that can be set to (2+3λ)/λ; a normalized water content Θ is defined as $(\theta ‐S_r)/({\theta }_s‐S_r)$, accordingly Θ_b is the temporal evolution of water content profile, and Θ_sura is the water content at the surface and equal to $(2h_a/(H_i+H_f))\lambda$. Note that this equation describes the case of an instantaneous drop in the water table (Loheide II et al., 2005; Nachabe, 2002). In addition, this expression has several limitations: the initial moisture profile is assumed to be in the static equilibrium condition (Nachabe, 2002), the water table change should be known, and there is no downward or upward flux in the unsaturated zone. As noted above, the static equilibrium condition is uncommon, especially in those models with a short time step.

Pozdniakov et al. (2019) proposed a formula to predict the dynamic specific yield under periodic (seasonal or diurnal) water table oscillations. For a vertical column of porous medium with length L₀, assuming that the lower boundary of the column is fully saturated and its upper boundary is impenetrable, the water head H at time t can be written as: [Image Omitted. See PDF]where m₀ is the height of the column with full water saturation above the column bottom, ΔH_max is the oscillation amplitude (2⋅ΔH_max < m₀), and T is the oscillation period.

The average for half of the period value of specific yield can be calculated by: [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF]where Z_gw is the water table level, t_min is the time marker at which this point is in the lower position, and K is the hydraulic conductivity, which can be determined based on the van Genuchten curve. Note that this formula requires that the initial soil moisture profile is in hydrostatic distribution, and that the values of the oscillation period and the amplitude are known.

Effect of a Rising and Falling Water Table

The specific yield value is different for the falling and rising water table conditions, which can be represented by the drainable porosity and the fillable porosity, respectively (e.g., Fahle & Dietrich, 2014; Maréchal et al., 2006). Strictly speaking, the drainable porosity represents the drainability of an unconfined aquifer by a water table decline, whereas the fillable porosity reflects the water storage capacity under a water table rise. The fillable porosity can be smaller than the drainable porosity. Possible reasons for this difference may be the hysteresis (entrapped air) in the soil water and the air encapsulation below the water table, which are likely to reduce the water storage capacity for the table rising case compared with the falling situation (e.g., Acharya et al., 2012; Dunn & Silliman, 2003; Fan et al., 2014; Fayer & Hillel, 1986; Kayane, 1983; Logsdon et al., 2010; Loheide II et al., 2005; Nachabe, 2002; Nachabe et al., 2004).

Many studies distinguished the terms of specific yield and fillable porosity (Acharya et al., 2012; Fahle & Dietrich, 2014; Kayane, 1983; Maréchal et al., 2006; Sokolov & Chapman, 1974; Sophocleous, 1991), and the specific yield is considered equal to the drainable porosity (e.g., Fetter, 1994; Hillel, 1998; Lohman, 1972; Meinzer, 1923; Neuman, 1987; Schwartz & Zhang, 2003; Sophocleous, 1985). The term specific yield is also used for both the falling and rising water table conditions (e.g., Dos Santos Jr. & Youngs, 1969; Logsdon et al., 2010; Todd, 1959; Wang & Pozdniakov, 2014). In this study, the specific yield is regarded as a collective term for the drainable porosity and the fillable porosity.

Other Influencing Factors

The equations in Sections 3.1–3.2 imply that soil texture is an important factor in the specific yield determination. Coarser sediments generally take a shorter time to complete the drainage than finer sediments. In other words, the fine‐textured materials not only yield less water than the coarse‐textured ones, but also yield it more slowly (Meinzer, 1923). Specifically, fine‐textured materials such as clay have a large porosity and can hold large quantities of water, but release only a small part of it under gravity drainage, even after a long period of time (Johnson, 1967). The antecedent soil moisture condition is another influencing factor in estimating the specific yield (Childs, 1960; Loheide II et al., 2005; N. Shah & Ross, 2009; Zhang et al., 2011). In the equations in Sections 3.1–3.2, the initial soil content profile is assumed to be in static equilibrium. However, in practice, the initial soil content profile is rarely in the static equilibrium state, especially when considering the effects of rainfall and evapotranspiration. Additionally, the temperature and chemical composition of water can change the surface tension, viscosity, and specific gravity, and then affect the specific yield (Johnson, 1967; Meinzer, 1923; Moench, 1994). However, as Meinzer (1923) noted, the specific yield estimation does not generally take into account the effects of temperature and chemical composition. In addition, the specific yield is also related to plant water demand (Logsdon et al., 2010).

In summary, the specific yield has high spatiotemporal variability that is particularly pronounced for shallow water tables. For a deep water table aquifer, Nachabe (2002) stated that a linear relationship holds between the WTF and the released water volume. Similarly, N. Shah and Ross (2009) indicated that the variation of specific yield is not that pronounced for deep water tables. Therefore, a constant specific yield is usually assumed to be acceptable to simulate the fluctuation of a deep water table (e.g., Fahle & Dietrich, 2014; Nachabe, 2002; N. Shah & Ross, 2009).

Applicability of Specific Yield Determination Methods

The key difficulty in determining the specific yield is to quantify how much water is gained or lost (Logsdon et al., 2010). A number of methods for determining the specific yield have been proposed. Traditional methods include the numerical method mentioned in Sections 3.1–3.2, the laboratory drainage experiment, the aquifer pumping test, the slug test, the texture‐based method, and the WTF method. Some new methods were later proposed, such as the rainfall‐water table response method, the geoelectrical method, and the magnetic resonance sounding method.

However, specific yield estimation is subject to uncertainty (Fan et al., 2014; Gehman et al., 2009; Healy & Cook, 2002; Yin et al., 2011). Thus, how to determine an appropriate specific yield value in practice is still a big challenge (Gehman et al., 2009), since, as Zhang et al. (2011) and Dietrich et al. (2018) argued, no widely accepted method for its estimation is available. Specifically, the various methods often produce inconsistent values for similar soil materials (Crosbie et al., 2005; Dos Santos Jr. & Youngs, 1969; Fan et al., 2014; Healy & Cook, 2002; Moench, 1994; Neuman, 1987; Nwankwor et al., 1984; Wang et al., 2014), even for a given test site (Kollet & Zlotnik, 2005), because each of them has its related applicability (Johnson, 1967; Todd, 1959; Yin et al., 2011). Table 1 lists the range of general values of specific yield for different soil texture types determined by different methods, while Table 2 presents the representative comparisons of specific yields using different methods at given study sites with specific soil types. The applicabilities and limitations of these methods are summarized in Table 3 which, in conjunction with Tables 1 and 2, provides a comprehensive understanding of the current determination methods.

1 TableGeneral Specific Yield Values for Different Soil Textures Determined by Different Studies

Soil texture	θs−θr (Carsel & Parrish, 1988; Loheide II et al., 2005; van Genuchten, 1980)	Apparent Sy equation of Loheide II et al. (2005)	From 17 studies compiled by Johnson (1967)	Trilinear graph of Johnson (1967) (Loheide II et al., 2005)	Reverse educing method based on evapotranspiration from groundwater (Loheide II et al., 2005)	Todd (1959)	Brooks and Corey (1964)	Corey et al. (1965)	Buckman and Brady (1960)	Type‐curve method (Prickett, 1965)	Boelter (1968)
Sand	0.385	0.38	–	0.34	0.32	–	–	–	–	–	–
Loamy sand	0.353	0.34	–	0.26	0.26	–	–	–	–	–	–
Sandy loam	0.345	0.29	–	0.19	0.17	–	–	–	0.361	–	–
Loam	0.352	0.19	–	0.095	0.075	–	–	–	–	–	–
Silt	0.426	0.11	0.08	0.06	0.026	–	–	–	–	–	–
Silty loam	0.383	0.12	–	0.07	0.037	–	–	–	0.172	–	–
Sandy clay loam	0.29	0.17	–	0.05	0.072	–	–	–	–	–	–
Clay loam	0.315	0.078	–	0.038	0.021	–	–	–	–	–	–
Silty clay loam	0.341	0.041	–	0.029	0.012	–	–	–	–	–	–
Sandy clay	0.28	0.068	0.07	0.025	0.015	0.08	–	–	–	–	–
Coarse sand	0.385	0.38	0.27	–	0.38	0.32	–	–	–	–	–
Medium sand	0.385	0.38	0.26	–	0.36	–	–	–	–	0.161–0.181	–
Fine sand	0.385	0.38	0.21	–	0.33	0.21	0.314	–	–	0.09–0.113	–
Very fine sand	0.385	0.38	–	–	0.31	–	–	–	–	–	–
Clay	–	–	0.02	–	–	–	–	–	–	–	–
Gravelly sand	–	–	0.25	–	–	–	–	–	–	–	–
Fine gravel	–	–	0.25	–	–	0.27	–	–	–	–	–
Medium gravel	–	–	0.23	–	–	–	–	–	–	–	–
Coarse gravel	–	–	0.22	–	–	–	–	–	–	–	–
Berea Sandstone	–	–	–	–	–	–	0.144	–	–	–	–
Hygiene sandstone	–	–	–	–	–	–	0.106	–	–	–	–
Touchet silt loam	–	–	–	–	–	–	0.349	–	–	–	–
Volcanic sand	–	–	–	–	–	–	0.296	–	–	–	–
Poudre sand	–	–	–	–	–	–	–	0.347	–	–	–
Dickinson fine sand	–	–	–	–	–	–	–	–	0.324	–	–
Wabash silty clay	–	–	–	–	–	–	–	–	0.146	–	–
Sand, medium to coarse	–	–	–	–	–	–	–	–	–	0.20–0.25	–
Sand, fine to medium	–	–	–	–	–	–	–	–	–	0.005–0.192	–
Sand, medium, silty	–	–	–	–	–	–	–	–	–	0.051	–
Sand, silty to medium	–	–	–	–	–	–	–	–	–	0.014	–
Sand, fine to coarse	–	–	–	–	–	–	–	–	–	0.014	–
Sand, fine with clay	–	–	–	–	–	–	–	–	–	0.021–0.206	–
Sand, fine with silt	–	–	–	–	–	–	–	–	–	0.018	–
Clay, silt, fine sand	–	–	–	–	–	–	–	–	–	0.039	–
Fibric peat	–	–	–	–	–	–	–	–	–	–	0.66
Hemic peat	–	–	–	–	–	–	–	–	–	–	0.26
Sapric peat	–	–	–	–	–	–	–	–	–	–	0.13

Notes. Note that the values obtained by the apparent S_y equation (in column 3) and the reverse educing method based on evapotranspiration from groundwater (in column 6) from Loheide II et al. (2005) are for a water table depth of 1 m.

2 TableComparison of the Specific Yield Values at Given Study Sites With Specific Soil Obtained by Different Methods

Texture	Study site and specific soil	Reference	Method	Sy	Supplementary information
Sand and gravel	A valley location in the Hidegviz Valley experimental catchment in Hungary, with sand and loamy sand.	Gribovszki (2018)	Trilinear graph of Johnson (1967)	0.348
Reverse educing method based on evapotranspiration from groundwater from Loheide II et al. (2005)	0.285
Slug test	0.052	Based on van Beers (ILRI, 1972).
0.047	Based on USBR (1984).
Two field sites within the Tomago Sandbeds near Newcastle, Australia, with fine sand.	Crosbie et al. (2005)	θs−θr	0.230–0.363	The ultimate specific yield is 0.363 for site 40a and 0.23 for site SK5498.
Type‐curve method	0.065–0.136	The obtained specific yield is 0.136 for site 40a and 0.065 for site SK5498.
A field site in an unconfined medium‐grained sand aquifer at the Canadian Forces Base Borden, Ontario.	Nwankwor et al. (1984)	Type‐curve method	0.07–0.08
Volume‐balance method	0.02–0.25	Time is from15 min to 3,870 min.
Laboratory drainage experiment	0.3	Ultimate specific yield.
An unconfined surficial aquifer on Bribie Island in Australia, with sandy soil.	Fan et al. (2014)	Laboratory drainage experiment	0–0.25	The values are for different depths to water table; results calculated from the rainfall–water table response method are smaller than those obtained from the laboratory drainage experiments, especially at the middle range of depths to water table.
Rainfall–water table response method	0–0.25
A study area in Ejina Oasis, northwestern China, with sand.	Wang and Pozdniakov (2014)	The numerical equation of Crosbie et al. (2005)	0.35–0.36	Apparent specific yield.
θs−θr	0.391	Ultimate specific yield.
Two field sites within a sandy aquifer in Ejina Oasis, located in the lower reaches of the Heihe River Basin, China.	Wang et al. (2014)	The numerical equation of Crosbie et al. (2005)	0.34–0.35	Apparent specific yield.
Reverse educing method based on evapotranspiration from groundwater from Loheide II et al. (2005)	0.32
The Upper Danube catchment of southern Germany and northern Italy, with unconsolidated alluvial sand and gravel deposits.	Zhang et al. (2011)	WTF method based on water budget equation	0.01–0.25	Values at 30 wells.
The Larned Research Site in the coarse‐sand and gravel aquifer located adjacent to a U.S. Geological Survey stream‐gauging station on the Arkansas River near Larned, Kansas, USA.	Butler Jr. et al. (2007)	WTF method based on neutron meter	0.19–0.21	Cited from McKay et al. (2004).
The Ordos Plateau in China, with sand and sandstone.	Yin et al. (2011)	Type‐curve method	0.08–0.18	Values at 47 wells.
The Biose Hydrogeophysical Research Site in Boise, Idaho (USA), with unconsolidated cobble and sand fluvial deposits.	Malama (2011)	Type‐curve method	0.052–0.090	Values at four wells based on the type‐curve method of Neuman (1972).
0.052–0.083	Values at four wells based on the type‐curve method of Moench (1997).
0.185–0.283	Values at four wells based on the type‐curve method of Malama (2011).
The Udaipur district study area within a hard rock aquifer located in the southern part of Rajasthan, western India.	Machiwal and Jha (2015)	WTF method based on water budget equation	0.002–0.038	Zone‐wise regional values for 25 zones in the study area.
Loam	A study site in the central portion of the Walnut Creek watershed in Jasper County, Iowa, USA, with silty clay loam.	Schilling and Kiniry (2007)	Rainfall–water table response method	0.027–0.157	The obtained specific yield value is different in different months.
A study area in Ejina Oasis, northwestern China, with silt loam.	Wang and Pozdniakov (2014)	The numerical equation of Crosbie et al, 2005	0.18–0.19	Apparent specific yield.
θs−θr	0.383	Ultimate specific yield.
The Tonzi Ranch site in California, with fractured rock with thin (0.6–1 m) surface soil (silt loam to rocky silt loam).	Miller et al. (2010)	WTF method based on water budget equation	0.056
A central Iowa field with a Webster soil (fine‐loamy, mixed，superactive, mesic Typic Endoaquolls).	Logsdon et al. (2010)	WTF method based on neutron meter	0.19
Rainfall–water table response method	0.02–0.08	Remove the wetting of the vadose zone from the rain.
0.06–0.50	If the wetting of the vadose zone is not subtracted from the rain, the specific yield will be overestimated.
The numerical equation of Loheide II et al. (2005)	0.19	The apparent specific yield for loamy soil.
A study area within the state of Haryana in India, with soils of sandy loam to fine loam.	Singh (2011)	Type‐curve method	0.09–0.23	Cited from Groundwater Cell (2007).
A study area in Ejina Oasis, northwestern China, with loam.	Wang and Pozdniakov (2014)	The numerical equation of Crosbie et al. (2005)	0.24–0.25	Apparent specific yield.
θs−θr	0.352	Ultimate specific yield.
A study area in Ejina Oasis, northwestern China, with sandy loam.	Wang and Pozdniakov (2014)	The numerical equation of Crosbie et al. (2005)	0.31–0.32	Apparent specific yield.
θs−θr	0.345	Ultimate specific yield.
Clay	A study site located within the Del Azul Creek basin in the Pampean plain region in Argentina, with thin clay layers (0–1.4 m) intermixed within loessic sediments.	Dietrich et al. (2018)	WTF method based on geoelectrical resistivity measurement	0.019–0.115	Values at different times based on Shah and Singh's (2005) function to convert resistivities to water content.
0.034–0.13	Values at different times using the function of Frohlich and Parke (1989) to convert resistivities to water content.
The Otmoor wetland site in England with high clay content.	Mould et al. (2010)	Laboratory drainage experiment	0.03	Cited from Acreman et al. (2008).
Silt	A field site in the Last Chance Watershed located on the eastern slope of the Sierra Nevada Mountains in California, USA, with silty sediment.	Butler Jr. et al. (2007)	Reverse educing method based on evapotranspiration from groundwater from Loheide II et al. (2005)	0.02–0.03
A study area in Ejina Oasis, northwestern China, with silt.	Wang and Pozdniakov (2014)	The numerical equation of Crosbie et al. (2005)	0.16–0.18	Apparent specific yield.
θs−θr	0.426	Ultimate specific yield.
Peat	A grassland site located in the Spreewald wetland in the southeast of Berlin, Germany, with a shallow peat layer over sand.	Fahle and Dietrich (2014)	WTF method based on lysimeter	0.044–0.079

Abbreviation: WTF, water table fluctuation.

3 TableApplicabilities and Limitations for Determination Methods

Method	Principle	Features
Numerical method	The specific yield can be obtained based on the soil content profile (van Genuchten or Brooks–Corey water‐retention curve), as shown in Equations 1 2 3 4 5 6 7 8 9.	The moisture profile, especially the initial one, is required to be in static equilibrium (Cheng et al., 2015; Duke, 1972; Loheide II et al., 2005; Nachabe, 2002; Pozdniakov et al., 2019). The upper boundary of the soil column is usually assumed to be impenetrable (Pozdniakov et al., 2019) or there is no downward or upward water flux in the vadose zone (Nachabe, 2002). The initial and final water table depths have to be given (Cheng et al., 2015; Dos Santos Jr. & Youngs, 1969; Loheide II et al., 2005; Nachabe, 2002).
Laboratory drainage experiment	It is carried out for a given resaturated soil sample under climate‐controlled conditions (Healy & Cook, 2002; Johnson, 1967; Meinzer, 1932).	It is often used to measure the ultimate specific yield under complete gravity drainage. It is time‐consuming (Johnson, 1967; Prill et al., 1965). An undisturbed sample of aquifer material is needed. However, the laboratory sample may be disturbed and thus may not be representative (Johnson, 1967; Todd, 1959).
Regression equations based on grain‐size analyses	The specific retention can be calculated by the regression equations (Equations 10 11 12 13 14) based on grain‐size analyses (Robson, 1993). Then, the specific yield is equal to the porosity minus the specific retention.	The specific yield can be determined with relatively low capital and time costs when the soil texture information is known. The samples can be disturbed in grain‐size analyses (Robson, 1993).
Trilinear graph	The specific yield can be obtained from a trilinear graph based on the soil texture classifications (Johnson, 1967).	It is low‐cost in capital and time.
Type‐curve method	The specific yield can be derived by analyzing the time‐drawdown pumping test data using the theoretical type‐curves (Boulton, 1963; Dagan, 1967; Malama, 2011; Moench, 1994, 1995, 1996, 1997; Neuman, 1972, 1974, 1975; Prickett, 1965; Tartakovsky & Neuman, 2007)	This method has high costs. The obtained specific yield is usually smaller than those from the volume‐balance method and the laboratory experiment (Malama, 2011; Moench, 1994; Nwankwor et al., 1984, 1992). When an experimental drawdown curve agrees with a theoretical curve, it does not necessarily imply that the aquifer necessarily follows the assumptions in the theoretical curve development (Healy & Cook, 2002).
Volume‐balance method	The specific yield is estimated by the ratio of the volume of pumped water to the volume of the water table drawdown cone (Nwankwor et al., 1984; Remson & Lang, 1955; Wenzel et al., 1946).	It needs more instrumentation and computations than the type‐curve method (Moench, 1994). It usually obtains a slightly smaller specific yield than that from the laboratory drainage experiment. The assumption that the discharge only comes from the observed cone of depression may result in an exaggerated specific yield value (Neuman, 1987).
Slug test method	Analysis of the slug test data is another option to determine the specific yield.	Slug tests can be performed quickly and need less equipment and labor than pumping tests (Bouwer & Rice, 1976; Gribovszki, 2018; Malama et al., 2011).
WTF method	The WTF method combined with aquifer storage change data can be used for estimating the specific yield.	The water table and storage changes should be known. The storage change can be obtained by the following methods: a. Gravity survey (Gehman et al., 2009; Howle et al., 2003; Montgomery, 1971; Pool & Eychaner, 1995; Pool & Schmidt, 1997). It is applicable in regions where the annual water table fluctuations are significant, such as greater than 0.14 m (Healy & Cook, 2002). b. Water budget equation (Gburek & Folmar, 1999; Gerhart, 1986; Hall & Risser, 1993; Logsdon et al., 2010; Machiwal & Jha, 2015; Maréchal et al., 2006; Walton, 1970). c. Neutron meter (Meyer, 1962; Sophocleous, 1991; Weeks & Sorey, 1973). d. Lysimeter (Fahle & Dietrich, 2014). e. Geoelectrical resistivity measurement (Dietrich et al., 2018).
Rainfall–water table response method	The ratio of infiltrated precipitation to subsequent water table rise can approximate the specific yield.	This method is valid in shallow groundwater areas such as wetlands (Gerla, 1992; Rosenberry & Winter, 1997; Schilling & Kiniry, 2007). It may be inappropriate when a thicker vadose zone is presented and the antecedent soil moisture is below the field capacity (Gribovszki et al., 2010; Loheide II et al., 2005). It tends to overestimate the specific yield if the portion of precipitation retained by the soil is included in the infiltrated precipitation (Carlson Mazur et al., 2014; Fan et al., 2014; Logsdon et al., 2010). The water table rise caused by other factors such as surface runoff should be removed (Hill & Durchholz, 2015).
Geoelectrical method	The geoelectrical resistivity data can be used to estimate the specific yield as shown in Equation 15 (Frohlich & Kelly, 1988; Tizro et al., 2012).	It has lower capital and labor costs than the pumping test (Onu, 2003; Tizro et al., 2012). It is nondestructive, and can supply continuous measurements (Samouëlian et al., 2005). The electrical contact may be poor under dry climatic conditions or on rocky ground (Hesse et al., 1986; Samouëlian et al., 2005). The vertical heterogeneity of the soil has impact on the electrical resistivity data (Samouëlian et al., 2005). It is not applicable in clayey environments (Vouillamoz et al., 2014).
Magnetic resonance sounding (MRS) method	The specific yield can be calculated based on the MRS water content and pore‐size parameters, shown in Equations 16 17 18 (Vouillamoz et al., 2014).	The equations in this method were proposed based on the hard rock aquifer (Vouillamoz et al., 2014). It is noninvasive, but has relatively high costs of capital and time.
Reverse educing method based on evapotranspiration from groundwater	The specific yield can be obtained from evapotranspiration from groundwater (Loheide II et al., 2005)	The specific yield estimation is under the diurnal water table fluctuation situation in Loheide II et al. (2005). It assumes that the water table depth is greater than 1 m and the specific yield is independent of the fluctuation magnitude and the antecedent moisture (Loheide II et al., 2005).

Abbreviation: WTF, water table fluctuation.

Numerical Method

As introduced in Sections 3.1–3.2, the apparent specific yield can be obtained based on the soil moisture profile characterized by the van Genuchten or Brooks–Corey soil moisture characteristic curves, under equilibrium conditions (Cheng et al., 2015; Duke, 1972; Loheide II et al., 2005; Nachabe, 2002). Moreover, the transient specific yield that changes with time can also be estimated from the soil moisture profile, which requires that the initial moisture profile is in equilibrium (Nachabe, 2002). As shown in Table 1 and from the Wang and Pozdniakov (2014) result in Table 2, the apparent specific yields calculated by the equations of Loheide II et al. (2005) and Crosbie et al. (2005) are all smaller than the ultimate specific yields determined by θ_s−θ_r. The limitations that prevent the numerical method from being applied in models are as follows: the moisture profile (especially the initial profile) is assumed to be in the equilibrium condition, which is uncommon in model calculations; there is no downward or upward water flux in the vadose zone (Nachabe, 2002) or the upper boundary of the soil column is usually assumed to be impenetrable (Pozdniakov et al., 2019); the initial and FWT depths have to be given (Cheng et al., 2015; Dos Santos Jr. & Youngs, 1969; Loheide II et al., 2005; Nachabe, 2002), but the specific yield itself is needed to calculate the FWT depth.

Laboratory Drainage Experiment

The laboratory drainage experiment involves draining a sample of resaturated aquifer material using gravity; the specific yield is equal to the volume of drained water divided by the volume of material sample. This method is carried out for a given soil column under climate‐controlled conditions (X. Chen et al., 2010; Johnson, 1967; Prill et al., 1965; Sophocleous, 1985). The soil column should be sufficiently long to avoid too much of it being occupied by the capillary fringe (Johnson, 1967). Moreover, the aquifer material samples must be undisturbed. However, the laboratory samples may be disturbed, and thus may not be representative of the aquifer of interest (Todd, 1959). Since this method is often used to measure the ultimate specific yield with complete gravity drainage, it is time‐consuming (Johnson, 1967; Prill et al., 1965). As an example, the laboratory drainage experiment obtained the ultimate specific yield of 0.3 at a site with medium‐grained sand in Nwankwor et al. (1984), shown in Table 2.

Texture‐based Method

The texture‐based method includes two approaches: the regression equations based on grain‐size analyses and the trilinear graph based on soil texture classifications. The texture‐based method requires relatively less time and financial cost.

Regression Equations Based on Grain‐Size Analyses

Robson (1993) proposed five regression equations for the specific retention (S_r) based on grain‐size analyses (Equations 10 11 12 13 14); the specific yield can then be obtained by subtracting the specific retention from the porosity (θ_s). Robson pointed out that the average S_r value of the five regression equations is comparable to that derived from laboratory analyses. Unlike the laboratory samples in drainage experiments, which must be undisturbed, the samples used in particle‐size analyses can be disturbed. [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF]where D₅₀ is the 50th‐percentile grain diameter at which 50% of the sample is finer, in mm; D₇₀ and D₉₀ are the 70th‐percentile and 90th‐percentile grain diameters, respectively, in mm; P.0625 and P.125 represent the percentage of the sample that is finer than 0.0625 and 0.125 mm, respectively.

Trilinear Graph

Johnson (1967) presented that when the soil texture is known the specific yield can be estimated from a trilinear graph where the lines of equal specific yield are showed based on the textural classifications. In the trilinear graph, the specific yields were obtained by both laboratory and field methods, and the textural classes were determined by particle‐size analysis of samples. For example, Richey et al. (2015) used the trilinear graph of Johnson (1967) to estimate the specific yield values for 37 aquifers across the globe.

Aquifer Pumping Test Method

The aquifer pumping test requires the installment of pumping and observation wells. Such a method is costly, and it includes two submethods: the type‐curve method and the volume‐balance method.

Type‐Curve Method

In the type‐curve method, the specific yield can be obtained by fitting the time‐drawdown pumping test data from observation wells to the theoretical type‐curves (Boulton, 1963; Dagan, 1967; Malama, 2011; Moench, 1994, 1995, 1996, 1997; Neuman, 1972, 1974, 1975; Prickett, 1965; Tartakovsky & Neuman, 2007). It should be noted that when an experimental drawdown curve agrees with a theoretical curve, it does not necessarily mean that the aquifer necessarily adheres to the assumptions in the theoretical curve development (Healy & Cook, 2002).

Volume‐Balance Method

The volume‐balance method is based on the pumping test data and a water budget applied to the observed cone of water table depression around a pumping well. First, the water table is lowered by pumping a measured quantity of water, then the volume of the water table drawdown cone is determined. The specific yield can be estimated from the ratio of the cumulative volume of pumped water to the volume of the water‐table drawdown cone (Healy & Cook, 2002; Neuman, 1987; Nwankwor et al., 1984; Remson & Lang, 1955; Wenzel et al., 1946).

Comparison Between the Type‐Curve Method and the Volume‐Balance Method

The type‐curve method needs less instrumentation and computation than the volume‐balance method (Moench, 1994). The specific yield estimated by the type‐curve method is usually significantly smaller than that obtained from the volume‐balance method and from a laboratory drainage experiment (Malama, 2011; Moench, 1994; Nwankwor et al., 1984, 1992). The volume‐balance method may, however, generate slightly smaller specific yields than the laboratory drainage experiment (Moench, 1994; Nwankwor et al., 1984). For example, Nwankwor et al. (1984) showed that the specific yields obtained by the type‐curve method varies from 0.07 to 0.08; the values from the volume‐balance method range from 0.02 to 0.25 when the measurement time varies from 15 min to 3,870 min; and the ultimate specific yield gained by the laboratory drainage experiment is 0.3 (Table 2).

For the volume‐balance method, Neuman (1987) showed that the assumption that the discharge is all drained from the observed cone of depression may cause an exaggerated specific yield value, because water is also released from the part outside the radius of the observed cone of depression even though the water table drawdown there may be imperceptible. For the type‐curve method, some studies indicated that the low specific yield is the result of the inadequate representation of the delayed drainage in the unsaturated zone (Akindunni & Gillham, 1992; Moench, 1994; Nwankwor et al., 1984, 1992). For example, the type‐curve theory of Neuman (1972, 1974) assumed that the drainage from the unsaturated zone above the water table occurs instantaneously in response to a water table decline. The pumping test duration is often only a few hours or days due to the high cost (Yin et al., 2011), hence the drained water derives from the limited thickness of the aquifer materials near the water table (or within the zone of groundwater fluctuation) since the water table response to the pumping is much faster than the drainage of the unsaturated zone above the water table (Bevan et al., 2005; X. Chen et al., 2010; Nwankwor et al., 1992). Therefore, the specific yield gained by the type‐curve method is smaller than the ultimate specific yield. Moench (1994) showed that the type‐curve method can obtain a value consistent with that from the volume‐balance method when partial penetration is taken into account and composite plots are used with a single match point for all measured drawdown data.

Slug Test Method

The slug test method is one of the most common techniques for determining the hydraulic conductivity or transmissivity of an aquifer. It also has the potential to estimate the specific yield (Malama et al., 2011; Sun, 2016). After an instantaneous water table change in a well, caused by suddenly injecting or removing a certain volume or slug of water, its recovery over time is observed in the same well for a single well test, or the response in another well is observed for a multiwell test (Bouwer & Rice, 1976; Malama et al., 2011; Papadopulos et al., 1973). The detailed solution for the specific yield can be found in the above‐mentioned literature. Compared with the pumping test, the slug test can be performed relatively quickly and requires less equipment and labor (Bouwer & Rice, 1976; Gribovszki, 2018; Malama et al., 2011). The results from Gribovszki (2018) in Table 2 showed that this method estimates a smaller specific yield than the texture‐based method.

WTF Method

The WTF method combined with the aquifer water storage change data is another way to estimate the specific yield, which requires both the water table and storage changes to be known. The main task is to determine the water storage change, which can be obtained using the following approaches. (i) Gravity measurement: The use of gravity measurement data in specific yield estimation was first demonstrated by Montgomery (1971), and many studies have shown that the gravity change measurement is very useful in estimating groundwater mass variations associated with a rising or falling water table (Gehman et al., 2009; Howle et al., 2003; Pool & Eychaner, 1995; Pool & Schmidt, 1997). Moreover, the gravity measurement approach is applicable in regions where the annual WTFs are significant, such as greater than 0.14 m (Healy & Cook, 2002). (ii) Water budget equation: The groundwater storage change can be obtained through the water budget equation when the other water budget components are known (e.g., Gburek & Folmar, 1999; Gerhart, 1986; Hall & Risser, 1993; Logsdon et al., 2010; Machiwal & Jha, 2015; Maréchal et al., 2006; Walton, 1970). The WTF method based on the water budget equation can be used to estimate the regionally averaged specific yield (e.g., Machiwal & Jha, 2015; Maréchal et al., 2006). For example, Machiwal and Jha (2015) obtained the zone‐wise regional specific yields (0.002–0.038) for 25 zones in the Udaipur district study area within a hard rock aquifer located in the southern part of Rajasthan, western India. (iii) Neutron meter: Meyer (1962) proposed that a neutron meter can be used to determine the water storage change, and later this approach was adopted by Weeks and Sorey (1973), Sophocleous (1991), and McKay et al. (2004). (iv) Lysimeter: Fahle and Dietrich (2014) gained the water storage change through lysimeter measurements. (v) Geoelectrical resistivity measurement: Dietrich et al. (2018) obtained the water content change based on the geoelectrical resistivity measurements and then calculated the specific yield through the WTF method.

Rainfall‐Water Table Response Method

Gerla (1992) and Rosenberry and Winter (1997) showed that the ratio of infiltrated precipitation to subsequent water table rise can approximate the specific yield. This method has proved to be valid in shallow groundwater areas such as wetlands (Gerla, 1992; Rosenberry & Winter, 1997; Schilling & Kiniry, 2007). However, it may be inappropriate when a vadose zone is thicker and the antecedent soil moisture is below the field capacity (Gribovszki et al., 2010; Loheide II et al., 2005). In practice, some of the precipitation will first moisten the soil before any notable water table rise occurs. Therefore, if the infiltrated precipitation includes the portion retained by the soil, this method tends to overestimate the specific yield (Carlson Mazur et al., 2014; Fan et al., 2014; Logsdon et al., 2010). For example, as shown by the study of Logsdon et al. (2010) in Table 2, when the portion retained by the soil is removed from the infiltrated precipitation, the estimated specific yields range from 0.02 to 0.08; otherwise, they are overestimated as 0.06–0.5. When using this method, the water table rise caused by other factors (e.g., surface runoff) should be subtracted (Hill & Durchholz, 2015).

Geoelectrical Method

Geoelectrical technology (vertical electrical sounding) is an effective tool to ascertain the subsurface geological framework. Based on geoelectrical resistivity data, Tizro et al. (2012) adopted Frohlich and Kelly's (1988) formula to determine the specific yield, which is comparable with that obtained from pumping tests in the Tizro et al. (2012) study. The formula is as follows: [Image Omitted. See PDF]where ρ_sat is the aquifer resistivity; ρ_w is the water resistivity; ρ_unsat is the resistivity of the unsaturated zone; m is a coefficient characterizing the degree of cement grain forming porous media; and n is a parameter like m, and equal to two in most cases. This method is based on the assumptions that the rock matrix is an insulator, and that an electrical current passes through when water is present in the pores (Niwas et al., 2011). The electrical resistivity technology is nondestructive and can provide continuous measurements over a long time and at various spatial scales (from macroscopic to field scale) through the electrode spacing configuration (Samouëlian et al., 2005). Compared with the pumping test, this method has relatively low financial and labor costs (Onu, 2003; Tizro et al., 2012). The electrical resistivity can be affected by several factors. The soil's vertical heterogeneity has an effect on the electrical resistivity data (Samouëlian et al., 2005). Poor electrical contact in the soil may occur under dry climatic conditions or on rocky ground (Hesse et al., 1986; Samouëlian et al., 2005). In addition, the electrical resistivity technology is not applicable in clayey environments (Vouillamoz et al., 2014). As shown in Section 4.6, Dietrich et al. (2018) also estimated the specific yield from the changes in water content and water level based on the geoelectrical resistivity measurement.

Magnetic Resonance Sounding Method

The specific yield can be derived based on the magnetic resonance sounding (MRS) method. Vouillamoz et al. (2014) proposed two linear equations based on the MRS water content and the pore‐size parameter, respectively: [Image Omitted. See PDF] [Image Omitted. See PDF]where θ_MRS is the MRS water content; and T₂^∗ is the decay time of the MRS signal, which is assumed to be controlled mainly by the pore geometry. Considering that θ_MRS and $T_2^{\ast }$ reflect different information about an aquifer, they can be combined to estimate the specific yield, $S_y={\theta }_{\text{MRS}}-S{r}_{\text{MRS}}$, where Sr_MRS is the MRS specific retention, which is linked to the mean size of the saturated pores and can be calculated from $T_2^{\ast }$. With an assumption that the relationship between Sr_MRS and $T_2^{\ast }$ satisfies a sigmoid function, a nonlinear equation was proposed as follows: [Image Omitted. See PDF]where s is the sloping parameter of the sigmoid function, and C is its pseudo‐centroid. Detailed description of the MRS method can be found in Vouillamoz et al. (2014). Note that these equations were proposed based on a hard rock aquifer. This method is noninvasive, and the time and financial costs are relatively high.

Reverse Educing Method Based on Evapotranspiration from Groundwater

Loheide II et al. (2005) obtained the specific yield from evapotranspiration of groundwater under the diurnal WTFs for a water table depth of 1 m, with the assumptions that the specific yield is independent of the fluctuation magnitude and the antecedent moisture. Note that, since the specific yield values were obtained under the diurnal WTF situation, it is likely to provide a smaller value than the apparent specific yield; this is clearly demonstrated by the comparison of specific yields for different soil textures in columns 3 and 6 of Table 1 and by the study of Wang et al. (2014) in Table 2.

Discussion of Spatial Scale of Determination Methods

All the determination methods involve spatial scale issues. Due to the high spatial heterogeneity of specific yield and the scale mismatch (Koirala et al., 2014; Pokhrel et al., 2015), the specific yield obtained at a point scale is generally not representative of the specific yield value at a regional or grid scale in models. To estimate the specific yields for grids in LSMs, all the methods should be implemented at the grid scale. Generally, in the authors' view, when applied to a grid cell that is taken as a whole, the WTF method combined with the water budget equation, the numerical method, the rainfall‐water table response method, and the reverse educing method based on evapotranspiration from groundwater can generate the averaged specific yield of this grid, while the other methods (e.g., the pumping test, the laboratory drainage experiment, and the regression equations based on grain‐size analyses) could obtain the areal mean specific yield by averaging distributed specific yields obtained through the spatial arrangement of corresponding measurement equipment within the grid.

Conclusions

A reliable estimate of the specific yield is of great importance for the simulation of groundwater, which can affect land‐atmosphere water and energy exchanges in Earth system models. This study provides a comprehensive review of the literature to summarize different subconcepts of the specific yield, factors affecting specific yield, and its determination methods.

The specific yield has a high spatial and temporal variability, especially for shallow water tables, and it can be affected by many factors including water table depth, time since rise or fall of the water table, hysteresis, soil texture, antecedent soil moisture condition, temperature and chemical composition of water, as well as plant water demand. Involving the effects of water table depth, time, and hysteresis, the specific yield can be classified into five categories: the ultimate specific yield, apparent specific yield, transient specific yield, fillable porosity, and the drainable porosity. For a study site, the ultimate specific yield, which is a constant, is obtained only when the water table is sufficiently deep and sufficient time is allowed for the soil to reach the static equilibrium condition (or drain completely) under gravity. The transient specific yield varies with both the water table depth and time, while the apparent specific yield varies only with the water table depth and is time‐independent. Moreover, the apparent specific yield can be adopted if the time step in a model is longer than the time needed to reach static equilibrium, but the time step in LSMs is usually short. Generally, the temporal heterogeneity of specific yield should not be neglected for shallow water table conditions, while a constant value of specific yield can be assumed in deep water table conditions. This suggests that, in LSMs, a variable specific yield should be considered in a shallow aquifer, and a constant value of specific yield (the ultimate specific yield) is acceptable in a deep aquifer. However, it is not feasible for all of the worldwide deep aquifers to use a uniform fixed value, because each deep aquifer has its own corresponding constant value of specific yield. Moreover, this study summarized the methods available for determining the specific yield. The associated applicability and uncertainty should be considered when choosing the determination method—for example, Table 1 shows a wide range of specific yields obtained by different methods for the same soil texture type.

The applicabilities and limitations for the different methods summarized here also point out their areas for future improvement. On the other hand, developing a new physical‐based method, which could avoid the difficulty of determining the specific yield and the uncertainty it causes, is another way to improve water table depth simulation. Understanding these issues can potentially advance the development of Earth system models in terms of groundwater modeling.

Acknowledgments

The study was supported jointly by the National Key R&D Program of China (2018YFA0606004) and the National Natural Science Foundation of China (41805008, 91637103). The authors are grateful to the anonymous reviewers for the useful suggestions to improve the study.

Data Availability Statement

This review article does not involve any calculation data.