In this study, the feasibility of using inverse vadose zone modeling for
estimating field-scale actual evapotranspiration (ET

Evapotranspiration (ET) is an important component in terrestrial water and
surface energy balance. In the United States, ET comprises about 75 % of
annual precipitation, while in arid and semiarid regions, ET comprises more
than 90 % of annual precipitation (Zhang et al., 2001; Glenn et al.,
2007; Wang et al., 2009a). As such, an accurate estimation of ET is critical
in order to predict changes in hydrological cycles and improve water resource
management (Suyker and Verma, 2008; Anayah and Kaluarachchi, 2014). Given the
importance of ET, an array of measurement techniques at different temporal
and spatial scales have been developed (see Maidment,
1992; Zhang et al., 2014), including lysimeter, Bowen ratio, eddy covariance
(EC), and satellite-based surface energy balance approaches. However, simple,
low-cost, and accurate field-scale measurements of actual ET
(ET

As a complement to the above-mentioned techniques, recent studies have used
process-based vadose zone models (VZMs) for estimating field-scale
ET

In order to address the challenge of field-scale estimation of soil hydraulic
properties, here we utilize inverse modeling for estimating soil hydraulic
parameters based on field measurements of soil water content (SWC) (see
Hopmans and Šimunek, 1999; Ritter et al., 2003). While VZM-based inverse
approaches have already been examined for estimating groundwater recharge
(e.g., Jiménez-Martínez et al., 2009; Andreasen et al., 2013; Min et
al., 2015; Ries et al., 2015; Turkeltaub et al., 2015; Wang et al., 2016),
their application for ET

The aim of this study is to examine the feasibility of using inverse VZMs for
estimating field-scale ET

The study site is located in eastern Nebraska, USA, at the University of
Nebraska Agricultural and Development Center near Mead. The field site
(US-Ne3, 41.1797

Study site (Mead rain-fed/US-Ne3) location in Nebraska

Variability of soil texture in the study field based on Web Soil
Survey data (

An EC tower was constructed at the center of the field (Figs. 1 and
2a) and continuously measures water, energy, and CO

Eddy covariance tower

In addition, a CRNP (model CRS 2000/B, HydroInnova LLC, Albuquerque, NM, USA;
41.1798

The Hydrus-1D model (Šimunek et al., 2013), which is based on the
Richards equation, was used to calculate ET

Daily precipitation (

Based on the ASCE Penman–Monteith equation, ET

Since the study site has annual cultivation rotations between soybean and
maize, the root growth model from the Hybrid-Maize model (Yang et al., 2004)
was used to model the root growth during the growing season:

Inverse modeling was used to estimate soil hydraulic parameters for the van
Genuchten–Mualem model (Mualem, 1976; van Genuchten, 1980):

Daily SWC data from the four TP locations and CRNP location were used for the
inverse modeling. Based on the measurement depths of the TPs, the simulated
soil columns were divided into four layers for TP locations (i.e., 0–15,
15–35, 35–75, and 75–175 cm), which led to a total of 24 hydraulic
parameters (

In addition to the TP profile observations, we used the CRNP area-average SWC in the inverse procedure to develop an independent set of soil parameters. The CRNP was assumed to provide SWC data with an average effective measurement depth of 20 cm at this study site. The observation point was therefore set at 10 cm. As a first guess and in the absence of other information, soil properties were assumed to be homogeneous throughout the simulated soil column with a length of 175 cm. Because the CRNP was installed in 2011 at the study site, the periods of 2011, 2012–2013, and 2014 were used as spin-up, calibration, and validation periods, respectively, for the optimization procedure.

The lower and upper bounds of each van Genuchten parameter are provided in
Table 2. With respect to the goodness-of-fit assessment, root mean square
error (RMSE) between simulated and observed SWC was chosen as the objective
function to minimize in order to estimate the soil hydraulic parameters. The
built-in optimization procedure in Hydrus-1D was used to perform parameter
estimation. A sensitivity analysis of the six soil model parameters was
performed. In addition, three additional performance criteria, including
coefficient of determination (

Bounds of the van Genuchten parameters used for inverse modeling.

The time series of the average SWC from the four TP locations along with 1
standard deviation at each depth are plotted in Fig. 4. Based on the large
spatial standard deviation values (Fig. 4), despite the relatively small
spatial scale (

Temporal evolution of daily SWC (

As an illustration, Fig. 7 shows the daily observed and simulated SWC
during the calibration (2008–2010) and validation (2011–2012) periods at
the TP 1 location (the simulation results of the other three sites can be
found in the Supplement Figs. S1, S2, and S3). The results of objective
function criterion (RMSE) and the other three performance criteria (e.g.,

Goodness-of-fit measures for simulated and observed SWC data at
different depths during the calibration period (2008–2010) and validation
period (2011–2012) at TP locations. Note that we assume a good fit as an RMSE
between 0 and 0.03 cm

In this research, we define RMSE values less than 0.03 cm

Time series of daily CRNP and spatial average TP SWC (

Annual precipitation (

Daily observed and simulated SWC (

The results of inverse modeling using the CRNP data also indicate the
feasibility of using these data to estimate effective soil hydraulic
parameters (Fig. 8 and Table 4). Based on the performance criteria (Table 4),
the simulated data are fairly well matched with the observed SWC data
during both the calibration and validation periods. Additional information
from deeper soil probes or more complex modeling approaches, such as data
assimilation techniques (Rosolem et al., 2012; Renzullo et al., 2014), may be
needed to fully utilize the CRNP data for the entire growing season. However,
this was beyond the scope of the current study and merits further
investigation given the global network of CRNP (Zreda et al., 2012) dating
back to

Goodness-of-fit measures for simulated and observed SWC data during the calibration period (2012–2013) and validation period (2014) at the CRNP location.

Table 5 summarizes the optimized van Genuchten parameters for the four
different depths of the four TP locations and the single layer for the CRNP
location. The optimized parameters were then used to estimate ET

Because a longer set of climatic data was available at the study site (as
compared to SWC data), we used 2004–2006 as a spin-up period. Using the best-fit
soil hydraulic parameters for the four TP locations and the single CRNP
location, the Hydrus-1D model was then run in a forward mode to calculate
ET

Daily observed and simulated SWC (

Simulated daily ET

Optimized van Genuchten parameters in different locations at the study site. Note that 95 % confidence intervals are in parentheses.

Goodness-of-fit measures for simulated and observed daily
ET

Given that CRNPs have a limited observational depth and that only a single
soil layer was optimized in the inverse model for the CRNP, one could expect
the simulated daily ET

On the annual scale, ET

In this research, we compared simulated ET

Summary of simulated yearly and average actual evapotranspiration
(ET

Following the sensitivity analysis, we repeated the optimization experiment
using only

A sensitivity analysis of ET

Sensitivity analysis of the effect of soil hydraulic parameters on
average annual ET

Sensitivity analysis of the effect of root depth on ET

Given their simplicity and the widespread availability of ground data, ET

Although sparsely distributed, widespread state, national, and global
meteorological observations paired with SWC profiles (Xia et al., 2015) and
the VZM framework provide an opportunity to better constrain ET

In this study, the feasibility of using inverse vadose zone modeling for field-scale
ET

The climatic and EC data used in this research can be found
at

The authors declare that they have no conflict of interest.

This research is supported financially by the Daugherty Water for Food Global Institute at the University of Nebraska, NSF EPSCoR FIRST Award, the Cold Regions Research Engineering Laboratory through the Great Plains CESU, and an USGS104b grant. We sincerely appreciate the support and the use of facilities and equipment provided by the Center for Advanced Land Management Information Technologies, School of Natural Resources and data from Carbon Sequestration Program, the University of Nebraska-Lincoln. T.E. Franz would like to thank Eric Wood for his inspiring research and teaching career. There is no doubt that the skills T.E. Franz learned while at Princeton in the formal course work, seminars, and discussions with Eric will serve him well in his own career. Edited by: M. McCabe Reviewed by: R. B. Jana and two anonymous referees