Improving our ability to estimate the parameters that control water and heat fluxes in the shallow subsurface is particularly important due to their strong control on recharge, evaporation and biogeochemical processes. The objectives of this study are to develop and test a new inversion scheme to simultaneously estimate subsurface hydrological, thermal and petrophysical parameters using hydrological, thermal and electrical resistivity tomography (ERT) data. The inversion scheme – which is based on a nonisothermal, multiphase hydrological model – provides the desired subsurface property estimates in high spatiotemporal resolution. A particularly novel aspect of the inversion scheme is the explicit incorporation of the dependence of the subsurface electrical resistivity on both moisture and temperature. The scheme was applied to synthetic case studies, as well as to real datasets that were autonomously collected at a biogeochemical field study site in Rifle, Colorado. At the Rifle site, the coupled hydrological-thermal-geophysical inversion approach well predicted the matric potential, temperature and apparent resistivity with the Nash–Sutcliffe efficiency criterion greater than 0.92. Synthetic studies found that neglecting the subsurface temperature variability, and its effect on the electrical resistivity in the hydrogeophysical inversion, may lead to an incorrect estimation of the hydrological parameters. The approach is expected to be especially useful for the increasing number of studies that are taking advantage of autonomously collected ERT and soil measurements to explore complex terrestrial system dynamics.

Shallow subsurface moisture and temperature are two primary variables that play key roles in hydrological and biogeochemical processes in terrestrial environments. For example, watershed moisture content and temperature are the main factors that control the partitioning of precipitation into evapotranspiration, infiltration and runoff (Merz and Bardossy, 1998; Brocca et al., 2010). For ecosystems, moisture content and temperature conditions are closely linked to form, functioning and organization of vegetation, which in turn influence ecological diversity (Rodriguez-Iturbe, 2000). Subsurface moisture and temperature largely influence microbial activity in the subsurface, including respiration of greenhouse gases (Boone et al., 1998; Luo et al., 2013). However, monitoring the variability of subsurface moisture and temperature over spatiotemporal scales that are relevant to the local processes yet informative for predicting watershed or ecosystem functioning is challenging. Conventional point-sensing approaches can provide subsurface moisture and temperature. However, due to labor and costs involved in installing point-sensing systems and the invasive nature of the sensors, the spatial support scale of point-sensing systems is typically quite small compared to the scale of systems of interest.

Over the last 2 decades, many hydrogeophysical approaches have been developed to combine point and geophysical measurements for improved subsurface property estimation or process monitoring (see reviews provided by Rubin and Hubbard, 2005; Hubbard and Linde, 2011; Binley et al., 2015). Statistical approaches have been extensively used to integrate point measurements with commonly geophysical models/tomograms, such as ground-penetrating radar (GPR) and electrical resistance tomography (ERT). For example, Hubbard et al. (2001) applied a Bayesian algorithm to integrate surface and cross-hole GPR, seismic cross-hole tomography, cone penetrometer, borehole electromagnetic flowmeter and pumping tests to estimate the spatial distribution of subsurface hydraulic conductivity. Binley et al. (2002) estimated shallow subsurface hydraulic conductivity using both cross-well ERT and GPR. Doetsch et al. (2010) showed that merging seismic, GPR and ERT data could significantly improve the accuracy of aquifer zonation and associated zonal parameter estimation. Dafflon and Barrash (2012) used a stochastic approach to estimate the distribution of porosity from well data and GPR data. Tran et al. (2015) combined surface GPR and frequency domain reflectometry data to better quantify the spatiotemporal dynamics of moisture along a hillslope.

Coupled hydrogeophysical inversion approaches have also been developed to estimate soil hydrological parameters, which assimilate all geophysical and other key datasets into a model that consider physical hydrodynamics (i.e., Darcy's law) and electromagnetic laws (i.e., Maxwell's equations). Because coupled inversion approaches permit direct use of geophysical data for inversion, they avoid the errors typically associated with geophysical inversion process (e.g., Binley et al., 2002; Singha and Gorelick, 2005) and associated resolution issues (Day-Lewis and Lane, 2004). Kowalsky et al. (2005) and Lambot et al. (2009) developed coupled inversion schemes and used time-lapse GPR data to estimate hydraulic conductivity and matric potential functions. Johnson et al. (2009) jointly inverted time-lapse hydrogeologic and ERT data without a priori assumptions about petrophysical parameters. Using ERT data, Huisman et al. (2010) developed a coupled Bayesian hydrogeophysical inversion approach to determine the hydraulic properties and their uncertainties of flood-protection dikes. Kowalsky et al. (2011) employed time-lapse ERT, groundwater level and nitrate concentration data to estimate hydrogeochemical parameters and behavior of a contaminated subsurface system. Tran et al. (2014) developed a data assimilation scheme that is based on the maximum-likelihood ensemble filter technique to sequentially estimate the vertical soil moisture profile and parameters of water retention and hydraulic conductivity functions using full-wave GPR data.

To date, ERT is the geophysical technique that is most commonly collected in an autonomous manner for near-surface applications. ERT provides information about the distribution of subsurface electrical resistance; a review of ERT theory and inversion procedures is given by Binley and Kemna (2005). Due to the typically high sensitivity of electrical resistivity to pore fluid conductivity and saturation, ERT has been used widely for monitoring the vadose zone soil moisture and other terrestrial system processes (e.g., Binley et al., 2002; Kemna et al., 2002; McClymont et al., 2013; Hubbard et al., 2013). However, because the electrical resistivity is also sensitive to other subsurface properties (such as porosity, tortuosity, pore-grain electrochemistry, mineralogy and temperature), other measurements must be used with ERT to avoid large estimation errors (Binley et al., 2002). For example, dependence of subsurface electrical resistivity on temperature is well known but often not adequately accounted for in hydrogeophysical approaches. The subsurface temperature directly influences the subsurface electrical resistivity. It also controls the phase change of subsurface moisture, which ultimately affects the subsurface resistivity. In some cases, subsurface temperature variations affect subsurface resistivity more than moisture variations (Rein et al., 2004; Musgrave and Binley, 2011). The conventional approach for correcting for temperature effects on ERT data includes inverting data and then performing correction on the obtained resistivity/conductivity images (Hayley et al., 2007; Ma et al., 2014). This approach is not suitable for the coupled hydrogeophysical inversion, because the objective of the hydrogeophysical inversion is to estimate hydrological parameters (not electrical resistivity/conductivity image). Hayley et al. (2010) proposed a temperature-compensation approach that removes the temperature effect on the data before inversion, which appeared to better resolve the temperature dependence of the electrical resistivity. This approach can be used for the hydrogeophysical inversion. However, this approach first requires the inversion of electrical resistance data to obtain the correction factors. Secondly, the correction usually relies on temperature measurements at several specific points in time, which may not suffice due to high variability of moisture and temperature in space and time. To date, few studies have incorporated and evaluated the effect of the relationship between subsurface resistivity and temperature within a coupled hydrogeophysical inversion scheme.

The opportunities and challenges identified above motivate the three key objectives of this study: to (1) develop a coupled hydrological-thermal-geophysical inversion scheme that is capable of incorporating nonisothermal behavior of the shallow subsurface as well as multiphase moisture into hydrogeophysical inversion and that jointly uses different thermal, hydrological and geophysical data for inversion including ERT; (2) apply the developed inversion scheme to estimate hydrological (permeability and van Genuchten curve parameters), thermal (thermal conductivity) and petrophysical parameters to assess the evaporation/infiltration processes at a Department of Energy (DOE) experimental field site in Rifle, Colorado; and (3) perform synthetic studies to explore the importance of consideration of subsurface temperature variability and its direct and indirect influence on the electrical resistivity in the hydrogeophysical inversion. To our knowledge, this is the first study that explicitly integrates both direct and indirect dependence of electrical resistivity on temperature in the coupled hydrogeophysical inversion. While it has been tested at the Rifle, CO site, we envision the new inversion approach being widely useful at other study sites, particularly those that can take advantage of autonomous ERT and other datasets.

We organize this article as follows. Section 2 describes the development of the hydrological-thermal-geophysical inversion scheme. The application of the inversion scheme to the Rifle site study is described in Sect. 3. Section 4 compares two synthetic cases that perform geophysical inversion, with and without considering the subsurface temperature's influence. Section 5 offers a summary and concluding remarks.

In this study, we simulated the nonisothermal two-phase (gas and liquid),
three-component (air, water and heat) flow in the vadose zone using the
integral finite-difference simulator TOUGH2 (Transport of Unsaturated Groundwater and Heat; Pruess et al., 1999). TOUGH2
solves the mass and energy balance equations for each component over an
arbitrary volume

The mass flux term

Flowchart showing the steps involved in the coupled hydrological-thermal-geophysical inversion scheme. The objective function is represented by Eq. (15). Estimated parameters consist of hydrological-thermal and petrophysical parameters (blue rectangles). The navy blue rectangles denote the model inputs, including prior information about estimated parameters, and the top and bottom boundary conditions. The purple rectangles denote the forward TOUGH2, geophysical and petrophysical models. The teal and indigo rectangles, respectively, denote the simulation and measurement. Data for inversion in this study include matric potential, subsurface temperature and apparent resistivity.

The ERT forward model solves Poisson's equation, which describes the relationship between the potential field due to a given input current and the electrical conductivity distribution. In this study, we used the forward model of the Boundless Electrical Resistivity Tomography (BERT) package, developed by Rücker et al. (2006). BERT numerically solves Poisson's equation using the finite-element method in a three-dimensional, arbitrary topography. By incorporating unstructured, tetrahedral meshes, the model enables efficient refinement of the local mesh, and flexibly describes any geometry of the computational domain. The use of quadratic shape functions also helps to improve the accuracy of the simulation.

The bulk electrical conductivity (

The relationship between temperature and electrical conductivity can be
formulated using linear (Sen and Goode, 1992) or exponential (Llera et al.,
1990) equations. In this study, we chose the linear form:

We developed the coupled hydrological-thermal-geophysical inversion scheme
within iTOUGH2 (see Finsterle, 1999; Finsterle et al., 2012).
Figure 1 presents the flowchart of the scheme,
which includes seven steps: (1) simulate subsurface moisture content and
temperature using the TOUGH2 model; (2) transform the simulated moisture
content to an electrical conductivity image using petrophysical
relationships; (3) apply the temperature correction for the electrical
conductivity using the simulated temperature, and convert the corrected
conductivity to a resistivity image; (4) interpolate the electrical
resistivity image from the TOUGH2 computational mesh to the BERT mesh;
(5) execute the forward BERT model to simulate the electrical resistance from
the resistivity image; (6) convert the electrical resistance to the apparent
resistivity using geometric factors; and (7) minimize the misfit between
simulation and measurement of the apparent resistivity and other
hydrological-thermal (matric potential and temperature) data to estimate
hydrological-thermal and petrophysical parameters. The misfit is formulated by
the objective function as below:

The agreement between measured and modeled data was evaluated using the
Nash–Sutcliffe efficiency coefficient:

The uncertainties of estimated parameters are characterized by their
standard deviation values, which are the square root of the diagonal
elements of the covariance matrix of the estimated parameters:

Invert the matric potential data to obtain the subsurface hydrological parameters. In this step, we consider only the one-dimensional isothermal hydrological model.

Use the subsurface temperature data to estimate the thermal parameters of the one-dimensional nonisothermal hydrological model. The subsurface hydrological parameters obtained in step 1 are fixed and are used to simulate the hydrological processes.

Jointly invert the matric potential, temperature and apparent-resistivity data to obtain the subsurface hydrological-thermal and petrophysical parameters. The hydrological-thermal parameters from steps 1 and 2 are used as the initial guesses for this step. In this step, the inversion is performed for the two-dimensional nonisothermal hydrological model.

The newly developed approach was tested at a floodplain adjoining the Colorado River, near Rifle, Colorado (USA) (Fig. 2). The perched aquifer at the site overlies low-permeability mud and siltstones of the Eocene Wasatch Formation. Above the Wasatch Formation is a Quaternary alluvial layer consisting of sandy, gravelly unconsolidated sediments. The uppermost layer is a silty clay fill with a thickness of around 1.5–2 m, which replaced contaminated soils and sediments removed from the site following uranium reclamation activities. Groundwater elevations fluctuate seasonally with snowmelt infiltration and Colorado River stage, and vary from around 3.5 to 2.4 m below ground surface.

The Berkeley Lab and others in the scientific community have performed many
studies at the Rifle site to explore complex subsurface hydro-biogeochemical
behavior and to test the development of new characterization and modeling
approaches. For example, Li et al. (2010) used reactive transport modeling
to investigate the influence of physical and geochemical heterogeneities on
the spatiotemporal distribution of mineral precipitates and biomass that
formed during a biostimulation experiment. Yabusaki et al. (2011) developed
a three-dimensional hydro-biogeochemical reactive transport model of Rifle
to improve understanding of the uranium variability, hydrological
conditions and soil properties under the pulsed acetate amendment. Chen et
al. (2013) developed a data-driven biogeophysical approach to quantify
redox-driven biogeochemical transformations using geochemical measurements
and induced polarization data. Wainwright et al. (2015) used induced
polarization data and stochastic methods to estimate the spatial
distribution of naturally reduced zones in the subsurface, which served as
biogeochemical hot spots; the geophysical information was used to
constrain simulations of biogeochemical cycles across the Rifle floodplain.
Arora et al. (2016) used reactive transport modeling approaches to explore
seasonal variations in biogeochemical fluxes occurring from bedrock to
canopy as well as laterally to the Colorado River. They found that CO

In this study, we tested our new approach using data collected along a Rifle, CO ERT transect, which includes 112 electrodes with a distance between any two adjacent electrodes of 1 m (Fig. 2). The ERT data were autonomously collected every day from April through June 2013 using the Wenner electrode array. These data were used for two purposes: (1) determining subsurface stratigraphy to support construction of the hydrological model and (2) estimating hydrological-thermal and petrophysical parameters through the coupled inversion approach.

Plan view of the Rifle floodplain of the Colorado River, Colorado, and the location of the TT02 and TT03 wells and ERT line.

For characterizing subsurface stratigraphy and specifying the depths of the
fill, alluvium and Wasatch layers, we used the BERT inversion package
(Günther et al., 2006) to invert the ERT data that were
collected on 20 May 2013. The electrical resistivity image obtained by
inversion is shown in Fig. 3a. As expected, the
clay-rich fill and Wasatch layers exhibit less resistivity than the alluvium
layer. To specify the locations of the fill–alluvium and alluvium–Wasatch
interfaces from ERT geophysical inversion, we used the depths of these
interfaces observed at the TTO2 and TTO3 wells as the references to determine
resistivity thresholds. Accordingly, a grid cell with a resistivity greater
than 1.52

We developed a computational domain that is a rectangle centered at the TT02
well, with a width of 30 m, as shown in Fig. 3b.
Previous work at this site has suggested that the spatial variability over
the extent of the simulation transect is not likely to be significant (Li et
al., 2010). Consequently, we assumed the computational domain includes two
homogeneous layers: namely, fill and alluvium. The porosity is 0.4 for the
fill and 0.2 for the alluvium layer (Tetsu K. Tokunaga, personal
communication, 2015). The top boundary of the domain is the atmospheric layer, and
the bottom is the impermeable Wasatch layer. We set the depth of the bottom
boundary at the average depth of the Wasatch layer,

We performed the hydrological-thermal simulation during the snow-free period from 4 May 2013 to 25 November 2013 (194 days). All meteorological data (atmospheric pressure, temperature, humidity and rainfall) were measured at a nearby meteorological station. The surface boundary conditions include land surface temperature, atmospheric pressure, air mass fraction and rainfall. The land surface temperature was adjusted from the atmospheric temperature, based on a regression approach proposed by Zheng et al. (1993), while the air mass fraction was calculated from the atmospheric pressure and relative humidity data. The bottom boundary condition of pressure was calculated from the groundwater table data, and the bottom temperature was approximated from the land surface temperature. The initial conditions were derived from the measured data at the beginning of the simulation period. For more detailed information about initial and boundary conditions, we refer to Tran et al. (2016).

Data for inversion included time-lapse matric potential, temperature and
apparent-resistivity measurements. Assuming that the lateral variation in
subsurface temperature between TTO2 and TTO3 wells (see the TT03 location in
Fig. 2) was insignificant, we used temperature
data at the TTO3 well for inversion. Temperature was measured every 5 min at
six depths below the surface:

All of the hydrological-thermal and petrophysical parameters that were considered in this study are presented in Table 1. The first and second columns present the parameter names and ranges, respectively. From the third to the last column, we present the estimated parameters obtained from different inversion cases, namely hydrological inversion (HI), thermal inversion (TI), and coupled hydrological-thermal-geophysical inversion (HTGI).

The sensitivity coefficients

The sensitivity coefficient of the matric potential data with respect to the
subsurface hydrological parameters at all measured depths (0.5, 1, 1.5, 2,
2.5, 3 m) is shown in Fig. 4a. The figure
indicates that the matric potentials are more sensitive to the parameters of
van Genuchten's retention curve than to the absolute permeability. At the
fill layer, the influence of parameter

The sensitivity of the subsurface temperature data with respect to the
thermal conductivity of the fill and alluvium layers at depths from 0.75 to
6 m is depicted in Fig. 4b. The figure indicates
that the sensitivity coefficient

Constraints and estimated values of the hydrological-thermal and
petrophysical parameters for different inversion cases. Hydrological
inversion used matric potential data to estimate hydrological parameters
(

Based on the above sensitivity analysis with the matric potential and
temperature data, we selected the six most sensitive hydrological-thermal
parameters (

The estimated parameters and their associated uncertainties based on
hydrological, thermal and coupled hydrological-thermal-geophysical
inversions are presented in Table 1. For the
hydrological inversion, we used the matric potential data to estimate six
hydrological parameters:

The hydrological inversion reveals that, compared to the other hydrological
parameters, the uncertainty of the absolute permeability (

Results of the thermal inversion show that the uncertainties of the thermal
conductivity (

The coupled inversion results are shown in the last column of
Table 1. Compared to the hydrological inversion,
the coupled inversion causes the parameter

Comparison of the measured and modeled matric potential of all eight
datasets is presented in Fig. 5. The figure shows
that there is good agreement between measured and modeled data, with a
Nash–Sutcliffe efficiency criterion of 0.92. We also observe that the
temporal variations of the matric potential over the simulation period
mostly occur at the fill layer (

The modeled and measured temperatures at depths from 0.75 to 6 m are shown
in Fig. 6. The figure indicates the model is
capable of reproducing the spatial and temporal variations of the subsurface
temperature. The Nash–Sutcliffe efficiency criterion is equal to 0.98. The
figure also shows that at the upper depths (0.75 and 1 m) the model
slightly underestimates the measurement. This can be explained by the errors
of simplification at the land surface boundary. The heat and energy
exchanges at the land surface between the atmosphere and land surface were
not fully considered. Instead, the land surface temperature was approximated
based on the historical data of atmospheric and land surface temperature
(see the Supplement). The evaporation was represented by the upward
flux from the land surface to the atmosphere. The figure also shows that the
temporal variation of the measured and modeled temperature data decrease
with increasing depth. For example, while the temperature at depth

Comparison of the measured and modeled matric potential data for all measurement occasions. The red symbols represents the modeling results obtained from the coupled hydrological-thermal-geophysical inversion. The blue symbols denote the measurements.

Comparison of the measured and modeled temperatures at depths of 0.75, 1, 1.5, 2.5, 4.63 and 6 m during the simulation period. The black line denotes the modeling results obtained from the coupled hydrological-thermal-geophysical inversion. The red line represents the measurements.

Left panels: an example of “quantitative” plots of the modeled and measured apparent-resistivity data on 8 May 2013. Right panel: comparison of all measured and modeled apparent-resistivity data in a 1 : 1 plot. The modeled data were obtained from the coupled hydrological-thermal-geophysical inversion.

The measured and modeled apparent-resistivity data on 8 May 2013 (when the modeled data were obtained through inversion) are depicted in Fig. 7a. The figure indicates that the coupled hydrological-thermal-geophysical simulation effectively reproduces the measured data. Particularly, the lateral variation of the apparent resistivity is simulated with high accuracy. Both measured and modeled data clearly indicate that the upper part of the subsurface section is more conductive (lower resistivity) than the deeper part. This is reasonable, as the deeper section contains more sand and cobbles, while the upper section contains more clayey and silty soils and therefore is more electrically conductive. Comparison of the measured and modeled resistivity data obtained from the whole simulation period is presented in Fig. 7b. The Nash–Sutcliffe efficiency criterion is equal to 0.94. Both Fig. 7a and b indicate that the estimation is less accurate for the high apparent-resistivity values. This can be explained by the fact that the high apparent-resistivity values are more sensitive to deeper locations and thus are harder to fit due to the influence of above soil. Another possible reason is that, with the same relative measurement error (5 %), the measurement error variances of the high resistivity values are larger than those of low resistivity values. As a result, their weights in the objective function (Eq. 15) are smaller, and they are less accurately estimated.

The water saturation and temperature versus time over the simulation period
at depths

The temporal variation of the water flux, which is the sum of the vapor and
liquid fluxes versus time over the simulation period at depths from 0.025 to
1.525 m, is shown in Fig. 9. Comparing Figs. 8 and 9, we
observe that the temporal variation of the water flux is highly correlated
with that of the water saturation and temperature. The greatest variation occurs
at

Temporal variation of the simulated water saturation and
temperature at depths

It is worth noting that our study assumed the Rifle subsurface was composed of two homogeneous layers, namely, fill and alluvium. For studies where the spatial heterogeneity is high, we suggest that users construct the model parameters as spatially correlated random fields characterized by variogram functions and then estimate the parameters (e.g., correlation length, anisotropy value, variance) of these variogram functions as proposed in Finsterle and Kowalsky (2007).

In this section, we consider the effects of the temperature dependence of
the electrical resistivity on the estimated subsurface hydrological
parameters, which are obtained by inverting apparent-resistivity data in
synthetic isothermal and nonisothermal scenarios. For the isothermal
scenario, the temperature was assumed to be constant in time and space at
the value averaged over the whole computational domain and over the
simulation period. For the nonisothermal scenario, the spatial and temporal
variability of the temperature under the influences of the atmospheric
temperature and hydrological-thermal parameters was fully considered. It is
worth noting that the influences of temperature variability on the
electrical resistivity include both direct
(temperature–electrical-resistivity relationship) and indirect (via changing the
hydrological-thermal processes, e.g., gas–liquid phase transition) effects.
The synthetic experiment was implemented as below:

Run nonisothermal hydrological-thermal-geophysical forward simulation to generate artificial apparent-resistivity data. Add Gaussian white noise (mean of 0 and standard deviation of 5 % of artificial apparent-resistivity data) to the artificial data to obtain the synthetic data.

Invert the synthetic apparent-resistivity data to estimate the subsurface hydrological parameters, assuming that the subsurface temperature is spatiotemporally constant (isothermal scenario).

Invert the synthetic apparent-resistivity data to estimate the subsurface hydrological parameters considering the nonisothermal process (nonisothermal scenario).

Compare inversion results of the two scenarios to evaluate the effect of the subsurface temperature variability on the hydrogeophysical inversion.

Temporal variation of the simulated water flux at depths

Comparison of the synthetic van Genuchten water retention curve and the ones obtained by the isothermal and nonisothermal hydrogeophysical inversion is exhibited in Fig. 10a. Although the nonisothermal hydrogeophysical inversion does not perfectly estimate the synthetic parameters (due to the nonuniqueness and the correlation between parameters), its estimation is close to the synthetic ones. Meanwhile there is a large difference between the synthetic and estimated curves obtained by the isothermal hydrogeophysical scenario.

Figure 10b presents the synthetic and modeled apparent-resistivity data using a 1 : 1 plot. The figure shows that the nonisothermal scenario better reproduces the synthetic apparent resistivity than the isothermal does. Correlation, bias and root mean square error (RMSE) between the synthetic and simulated nonisothermal electrical resistivity data are 0.98, 1 and 2.29, respectively, while these criteria for the isothermal scenario are 0.96, 0.98 and 3.54. In brief, ignoring temperature variability and its influence on electrical resistivity in the hydrogeophysical inversion is very likely to cause a large error for the model parameter estimation and to reduce agreement between modeled and measured geophysical data.

We developed a coupled hydrological-thermal-geophysical inversion scheme that quantifies the dependence of the electrical resistivity on both subsurface moisture and temperature, instead of solely moisture, as has been typical for previous hydrogeophysical inversion schemes. This scheme permits simulation of nonisothermal, multiphase subsurface heat and water fluxes, as well as the relationship between temperature, moisture and electrical resistivity. It accounts for the spatiotemporal variability of moisture and temperature in the shallow subsurface and can include multiple geophysical and non-geophysical measurement constraints. At present, TOUGH2 cannot simulate the land surface processes and energy balance at the land surface. To mitigate this disadvantage, this study approximated the top land surface temperature boundary condition from the atmospheric temperature using a regression approach. The evaporation was considered via the gas phase of moisture. The evaporation rate was simulated as the water vapor fluxes moving upward from the top layer to the atmosphere.

The new approach was applied to data collected at a field site in Rifle, Colorado. The ERT data were used to characterize subsurface stratigraphy and to constrain the computational domain for the hydrological-thermal model. The time-lapse ERT data were used with other hydrological and thermal data to constrain the inversion. The inversion results show that our developed scheme well reproduces the matric potential, temperature and apparent-resistivity data. The obtained results indicate that the temporal variation of the moisture mostly occurs at the overlying fill layer, due to the relatively small amount of rainfall and the high water-holding capacity of this layer. The alluvium moisture exhibits a minimal change. Both fill and alluvium layers have high thermal diffusivities, permitting the variation of the air temperature to rapidly move down. The obtained results also indicate that the thermal-conductivity and van Genuchten parameters of both fill and alluvium layers are well estimated with low uncertainties. However, due to limited temporal variations of moisture content (and thus ERT data), it is difficult to obtain the absolute permeability of the fill layer and the petrophysical parameters.

To evaluate the influence of the temperature dependence of the electrical resistivity on the estimation of the hydrological parameters in the hydrogeophysical inversion, we performed a synthetic study. By comparing the results obtained from the isothermal and nonisothermal scenarios, we determined that ignoring the spatial and temporal variability of the subsurface temperature may cause errors in the estimation of hydrological parameters.

Our study documents the value of accounting for the dependence of both moisture content and temperature on electrical resistivity within a hydrological-thermal-geophysical inversion framework. The inversion scheme presented here can be widely applied to many studies striving to quantify hydrological and thermal dynamics in the subsurface. We believe that this and other approaches (e.g., Kalman ensemble filter, maximum likelihood ensemble filter, particle filter) that permit rapid assimilation of autonomous monitoring datasets will greatly improve our understanding of terrestrial system properties and their behavior, including their response to environmental perturbations such as floods and droughts.

Both the data and input files necessary to reproduce the studies are available from the authors upon request (aptran@lbl.gov).

This material is based upon work supported as part of the Sub-surface Science Scientific Focus Area funded by the US Department of Energy, Office of Science, Office of Biological and Environmental Research under award number DE-AC02-05CH11231. The authors would like to thank Stefan Finsterle for providing iTOUGH2 codes and support, and Thomas Günther for providing the BERT codes. Edited by: N. Romano Reviewed by: N. Linde and J. Boaga