Evapotranspiration Estimation from Diurnal Water Table Fluctuations: Implementing Drainable and Fillable Porosity in the White Method

Abstract

Diurnal water table fluctuations (DWTFs), normally observed in shallow unconfined aquifers, are commonly used to estimate groundwater evapotranspiration (ETg) by applying the soil water balance pioneered by W.N. White in 1932. A key element of White‐based methods is the drainable porosity (or specific yield), a soil water storage parameter that significantly depends on both the vadose‐zone soil moisture fluxes and water table (WT) elevation. However, it has traditionally been treated as either a constant or a function of the WT under hydrostatic soil moisture conditions. Recent research has shown that, at any given shallow WT position, vadose zone fluxes cause the drainable porosity to behave hysteretically, hence requiring estimation of two distinct parameters, drainable (λd) and fillable porosity (λf), during ETg estimation from DWTFs. We present a White‐based method to estimate ETg that implements separate λd and λf parameters and hence accounts for both WT elevation and unsaturated zone moisture fluxes. The modified method not only improves the ETg estimates but also extend the applicability of the White method to periods during rainfall, unlike most previous implementations, which have been limited to omitting such periods. The modified method is demonstrated here for estimation of ETg from two crop fields in Northeast Florida for two growing seasons, each approximately 50 d, in 2010 and 2011, and the ETg estimates are compared with the standard Penman–Monteith method. The modified method significantly improved ETg estimates compared with the hydrostatic λd based method, reducing the root mean square error by 94 and 96% at hourly and daily resolutions, respectively.

Analytical Expressions of Drainable and Fillable Porosity for Layered Soils Under Shallow Groundwater Environments

“…The parameters λ d and λ f were usually used in subsurface flow modeling to investigate the water table behavior (e.g., Acharya & Mylavarapu, 2015;Acharya et al, 2012;Bartlett & Porporato, 2018;Hilberts et al, 2005;Troch et al, 2003;Wang, 2009) and in the estimation of groundwater consumption by plants based on the observed diurnal water table fluctuations by (modified) White method (Acharya et al, 2014;Fahle & Dietrich, 2014;Gribovszki et al, 2008;Loheide et al, 2005). In this study, we conducted several hypothetical scenarios, which consider both homogeneous soil and layered soil conditions, to present the behavior of water table dynamics with different expressions of drainable (and fillable) porosity (in 1-D Boussinesq-type equation), that is, using our newly proposed equation (i.e., Equation 16), the equations proposed by Acharya et al (2012) and Crosbie et al (2005), and the constant value, respectively.…”

“…In addition, to identify the applicability of using the (modified) van Genuchten-Gardner functions (e.g., Acharya et al, 2012Acharya et al, , 2014Yeh & Harvey, 1990) in characterizing the expressions of λ d and λ f , four different soil types (i.e., in cases A, B, C and D) were tested to present the differences of λ d and λ f between using the MVG-Gardner functions and van Genuchten-Mualem functions (VG-Mualem). The use of the MVG-Gardner functions in expressions of λ d and λ f showed slight differences with the numerical results when compared to the use of VG-Mualem functions (Figure 6).…”

“…Besides, a parameter corresponding to the concept of λ d is the fillable porosity ( λ f ), which can be defined as the amount of water taken into a soil column extending from the ground surface to water table, per unit surface area of per unit rise in the water table (Acharya et al., 2012; Sophocleous, 1991), and can be estimated as (Acharya et al., 2012): $$${\lambda }_{f}=\frac{{\Delta}{d}_{s}}{A{\Delta}h}$$$ where λ f is the fillable porosity, and ∆ d s is the change in total storage deficit of the aquifer resulting from ∆ h water table rise. The parameters λ d and λ f play a vital role in approaches of investigating the water table dynamics, such as subsurface modeling (Acharya et al., 2012; Hilberts et al., 2005; Wang, 2009; Xiao, Xu, Ren, et al., 2021) and estimation of groundwater consumption by plants (Acharya et al., 2014; Jiang et al., 2017; Loheide et al., 2005; McLaughlin & Cohen, 2014). Under hydrostatic assumption, the λ d and λ f values are considered to be equal for a given water table depth (WTD) in previous research (e.g., Crosbie et al., 2005).…”

“…where λ f is the fillable porosity, and ∆d s is the change in total storage deficit of the aquifer resulting from ∆h water table rise. The parameters λ d and λ f play a vital role in approaches of investigating the water table dynamics, such as subsurface modeling (Acharya et al, 2012;Hilberts et al, 2005;Wang, 2009;Xiao, Xu, Ren, et al, 2021) and estimation of groundwater consumption by plants (Acharya et al, 2014;Jiang et al, 2017;Loheide et al, 2005;McLaughlin & Cohen, 2014). Under hydrostatic assumption, the λ d and λ f values are considered to be equal for a given water table depth (WTD) in previous research (e.g., Crosbie et al, 2005).…”