Enhancing the Evaporation Method for Accurately Determining Unsaturated Soil Properties in the Wet Range

Fig. 3(a) shows the plexiglass sample box (left) and a saturation–calibration assembly kit (right) that we used to conduct all our EV experiments. The internal dimensions of the sample box were $12.0\times 9.0\times 6.0\mathrm{cm}$. In addition to the sample box, we also used the saturation–calibration assembly kit, which allowed us to properly saturate the soil and collect data for calibrating the tensiometers that were placed directly within the sample (the details of which are discussed subsequently). The dimensions of the saturation–calibration assembly kit were $12.0\times 9.0\times 10.0\mathrm{cm}$; it was composed of four sides without a bottom). The bottom of the sample box was equipped with 10 4.5-mm holes. A fine mesh was placed at the bottom of the box to prevent soil from washing out. The bottom holes were used for saturating the soil, but they could be sealed at any time using small rubber caps to prevent leakage. Two miniature tensiometers [TEROS 31, METER Group (Pullman, Washington)] were installed in the sample box via predrilled tensiometer holes in the front face of the sample box [Fig. 3(b)]. Two rubber O-rings were installed at each hole to ensure a proper seal to prevent water leakage and to guide the horizontal installation of the tensiometers (which measure pressure at their ceramic tips). The top and bottom tensiometers were placed at 1.5 and 4.5 cm below the top of the sample box (and the surface of the soil sample), respectively, which corresponded to about 25% and 75% of the sample’s height. The measurement range of the tensiometers used in the experiment was $-150$ to 50 kPa, which enabled precise measurement of both positive and negative pressures (the positive pressure data were utilized subsequently for tensiometer calibration). Our design is similar to the setup used by Schindler and Müller (2006). For data acquisition, we used a ZL6 system (METER Group) to record the tensiometer data. Both tensiometer and sample weight data were collected every 30 min. In addition, we independently measured the value of saturated hydraulic conductivity after conducting multiple experiments (seven times) using the falling head method.

The quality of data collected during the initial times (in the wet range) is highly dependent on the initial condition of the saturated soil sample. Achieving uniform and complete saturation across the entire sample can be a challenging task. This is because the degree of saturation can vary based on the sample packing condition and the techniques used for saturating the sample. In this study, we employed the following protocol to ensure uniformity in packing and consistency in the initial saturation level.

The soil material selected for this study was Tuscaloosa silt loam soil purchased from a local sand quarry in Tuscaloosa, Alabama. The soil was dried for 24 h in an oven at 105°C to remove all moisture. The dry soil sample was layered into the sample box in three equal layers with vibratory compaction (manually vibrating the sample by tapping it on a flat surface). When the sample box was filled, the mass of the sample (dry weight of the soil sample) was measured. After the packing step, a careful saturation procedure was employed to fully saturate the soil sample. In the published literature, others have used a bottom-up saturation procedure by placing samples in a water pan and letting the water slowly rise from approximately 0.5 cm above the sample bottom to about 0.2 mm below the sample surface, to minimize air entrapment (Schindler et al. 2010a). However, we found that achieving complete saturation can be a challenging task using this method, particularly for low-hydraulic-conductivity soils.

To achieve full saturation, we first increased the height of the sample box walls by placing the saturation–calibration assembly kit [Fig. 3(b)]. To prevent leakage, both the saturation–calibration assembly kit and the sample box were secured together using duct tape. The entire setup including the sample box attached to the saturation–calibration assembly kit then was placed in a bucket of water [Fig. 3(b)]. Using a peristaltic pump, we gradually raised the water level in the bucket. As the external free surface began to rise, the water level inside the sample box also started to rise, allowing the water to enter through the holes at the bottom of the sample box. The exterior free surface was raised gradually over 24 h until the free surface of the ponded water inside the sample box (ponded free surface) was approximately 2 cm below the external free surface [Fig. 3(b)]. This procedure was used to force the water to seep from the bottom of the sample box, slowly replacing the air. In this step, it was crucial to continuously maintain a low head difference between the internal and external free surfaces to prevent soil boiling, sample expansion, or air-trapping problems. When the soil was fully saturated, the sample box was removed from the bucket. Rubber seals were used to plug the bottom holes to prevent water drainage. After the sample was removed from the bucket, the soil continued to remain submerged under ponded water (the free surface was about 3.5 cm above soil the soil surface) in the assembly [Fig. 3(d)]. This ponding initial condition was required for the tensiometer calibration procedure used in this study.

In Schindler’s EV method, the spatially averaged value (averaged over the entire sample) of volumetric water content, ${\theta }_{\mathrm{avg}}$, and the average of matric potential values measured at two different depths, $h_{\mathrm{avg}}$, are used to obtain the data needed for developing the SWR function (Schindler and Müller 2006). The average volumetric water content, ${\theta }_{\mathrm{avg}}$, is computed by determining the soil water volume, based on the mass of the soil sample (assuming 1 g of $\mathrm{water}=1{\mathrm{cm}}^3$). This calculated water volume is divided by the volume of the soil sample to determine the volumetric water content. The average matric potential, $h_{\mathrm{avg}}$, is calculated as the arithmetic mean of the two matric potential values, $h_u$ and $h_l$, measured at two different depths, $z_u$ and $z_l$ (where $z_u=0.25L$, and $z_l=0.75L$, where $L$ is the total height of the soil sample). Continuous monitoring of weight changes and matric potential allows one to track the temporal changes of ${\theta }_{\mathrm{avg}}$ and $h_{\mathrm{avg}}$ values as the system loses water over time due to evaporation.

The EV method is based on the assumption that the flux varies linearly with a maximum value at the top and zero at the bottom. Therefore, the flux at the midpoint of the sample should be half the maximum flux. After invoking this assumption, UHC values can be calculated by applying the Darcy–Buckingham law at each measurement time interval (Schindler 1980)where $\mathrm{\Delta }t$ = measurement time interval between two consecutive times, $t1$ and $t2$; $h_{\mathrm{avg}\mathrm{\Delta }t}$ = mean matric potential measured by the upper tensiometer at position $z_u$ and the lower tensiometer at position $z_l$, averaged over the time interval $\mathrm{\Delta }t$ ($h_{\mathrm{avg}\mathrm{\Delta }t}$ is the average of four individual $h$ measurements); $\mathrm{\Delta }{V}_w$ = evaporated water volume, which is obtained by dividing the mass, $\mathrm{\Delta }m$, lost over time interval $\mathrm{\Delta }t$ by the density of water, ${\rho }_w$; and $A$ = cross-sectional area of the sample. The average hydraulic gradient, $i_{\mathrm{avg}\mathrm{\Delta }t}$, experienced by the system over the time interval $\mathrm{\Delta }t$ is estimated using the matric potential measured by the upper and lower tensiometers ($h_u$ and $h_l$, respectively) at two consecutive times, $t1$ and $t2$, aswhere $z$ is the vertical coordinate, which is assumed to be positive in the downward direction. Furthermore, in Eqs. (2)–(4), we used the negative matric potential values measured for the unsaturated soil system.

Errors in tensiometer readings inevitably are included in the calculation of hydraulic gradients [i.e., Eqs. (2) and (3)]. We calibrated the tensiometer readings directly on the sample under hydrostatic conditions by establishing ponded water above the soil surface, ensuring hydrostatic conditions that are supposed to yield zero hydraulic gradient [Eqs. (2) and (3)]. We placed the saturated sample with ponded water on the balance and installed the tensiometer and the peristaltic pump tube as shown in Fig. 3(d). We ensured that the tube was in direct contact with the soil surface so that all the ponded water would be pumped out. We first let the system reach the initial ponded-equilibrium condition and recorded the tensiometer value. We then started the peristaltic pump to remove the ponded water. The pumping rate was set to a low value to decrease the ponded free surface at the rate of about $1\mathrm{cm}/\mathrm{h}$. Throughout this process, we recorded the tensiometer readings (pressure data) and actual values (estimates for hydrostatic conditions), which subsequently were used for tensiometer calibration. This method, which was applied directly to the sample, allowed us to avoid any separate calibration procedures. Furthermore, by using this method we were able to collect continuous pressure data as the system seamlessly transitioned from measuring positive to negative pressures. After pumping out all the ponded water, we quickly removed the tube and turned on the fan to start the evaporation experiment.

We corrected the upper and lower tensiometer readings ($h_u$ and $h_l$) after accounting for the offset errors in the upper and lower tensiometers (i.e., ${\epsilon }_u$ and ${\epsilon }_l$). The offset errors can be defined by fitting the tensiometer readings (ℎ) to the actual values ($h^{\mathrm{actual}}$) using the following equations:where $u$ and $l$ denote upper and lower tensiometers, respectively [Fig. 3(d)]. Although the measured offset errors were relatively small, they had a substantial influence on the quality of the initial data, near the wet range. We adapted Eqs. (2) and (3) to compute the true gradient values after making appropriate correction as follows:where (${\epsilon }_l-{\epsilon }_u$) = net offset error, which can be either positive or negative, leading to classification as either a net-positive offset or a net-negative offset. The implications of these classifications and their respective impacts on the experimental results are discussed in the “Results and Discussion” section.

We first completed the proposed tensiometer calibration step to quantify the tensiometer offset error. This procedure estimated the magnitude of the offset error in both tensiometers, and also determined whether the net offset error was positive or negative. We then conducted the EV experiment to generate a baseline experimental data set after implementing proper tensiometer corrections (referred to here as Experiment 1 or Corrected data set). Subsequently, this baseline data set also was used to develop two derived data sets, details of which are discussed subsequently. We replicated the EV experiment two more times (referred to here as Experiments 2 and 3) using the same soil, and thus collected a total of three distinct data sets to test the reproducibility of the experimental results.

Fig. 4 presents the tensiometer calibration data obtained using the calibration procedure directly on the sample. The data in Fig. 4 employed ponded conditions with the initial free surface set at 3.5 cm above the soil surface. Because the upper and lower tensiometers were installed at 1.5 and 4.5 cm below the soil surface, the initial actual values (estimates based on hydrostatic conditions) of the tensiometers should have been 5.0 and 8.0 cm, respectively [Fig. 3(d)]. As the peristaltic pump slowly lowered the ponded free surface, the pressure at both measurement locations should have decreased linearly. The tensiometer readings did decrease linearly, as expected. However, they had offset errors of ${\epsilon }_u=0.27\mathrm{cm}$ and ${\epsilon }_l=-0.70\mathrm{cm}$ for the upper and lower tensiometers, respectively. These values were evaluated by fitting a linear trendline to the observed data points, estimating the deviation from the ideal line (which is the intercept value, because the ideal intercept is zero) [Fig. 3(d)].

The net offset error (i.e., ${\epsilon }_l-{\epsilon }_u$) can be either negative or positive depending on the values and signs of ${\epsilon }_u$ and ${\epsilon }_l$. For the results in Fig. 4, we obtained a net-negative offset error of $-0.97\mathrm{cm}$ for our system. In this study, we discuss issues related to both net-positive and net-negative offsets because they lead to different outcomes, yielding either under- or overestimation of UHC data, as discussed in the following section.

To illustrate all possible implications of tensiometer offset errors, we processed the Experiment 1 data set to generate two additional data sets to account for net-negative and net-positive offset errors. Because our system had a net-negative offset error of $-0.97\mathrm{cm}$, we simply used our observed data points without the tensiometer correction to assemble the net-negative offset error data set. To illustrate the effects of a net-positive offset error, we created an additional data set by reversing the direction of both offset errors (i.e., ${\epsilon }_u=-0.27\mathrm{cm}$ and ${\epsilon }_l=0.70\mathrm{cm}$). This resulted in a net-positive offset error of 0.97 cm, allowing us to assemble a net-positive offset error data set.

Fig. 5 compares the UHC functions (i.e., estimated UHC values plotted as a function of matric potential) evaluated using net-positive and net-negative offset error data sets against the function for the fully corrected baseline experimental data. The corrected data set yielded more-realistic values in the wet range. The UHC function obtained from the corrected data approached the independently measured saturated hydraulic conductivity value of $\sim 15\pm 8\mathrm{cm}/\mathrm{day}$ (a mean value of $15\mathrm{cm}/\mathrm{day}$ with a standard deviation of $8\mathrm{cm}/\mathrm{day}$ was measured using the falling head method, and these estimates are shown in the figure using an error bar). Conversely, the net-negative offset error data set resulted in an overestimating trend [similar to that in Fig. 1(a)], whereas the net-positive offset error data set caused an underestimating trend [similar to that in Fig. 1(b)]. We discuss these trends in the following section.

To explain these UHC data further and to fully understand their implications, we prepared two additional figures that summarize the results of the various intermediate calculations used to compute the UHC values. Fig. 6(a) presents the temporal changes in hydraulic gradient values, whereas Fig. 6(b) presents the corresponding temporal changes in UHC values. To understand the over- or underestimation trends in Fig. 5, we first review the hydraulic gradient values estimated for the corrected data set [Fig. 6(a), square symbols]. The corrected data points followed the expected trend, in which the gradient starts at zero and then increases as the sample dries. This should be expected because we initiated the system under hydrostatic conditions and then dried the soil by evaporating the water from the top surface. Furthermore, the smoothed trend of corrected data points also depicts a decrease in UHC values as the sample dried [Fig. 6(b)]. The UHC values estimated near the wet range (at early times) were close to the independently measured value for the saturated hydraulic conductivity, and indicate an overall decrease to lower values with time, despite the short-term noisy fluctuations in the data.

Unlike the corrected data set, the net-negative offset error data set (Fig. 5, triangle symbols) had an unrealistic overestimation trend that was almost identical to the spurious trend observed in some UHC functions in the literature data [Fig. 1(a), hollow circles]. This overestimation trend originated from the inaccuracies in the hydraulic gradient calculations, which can be inferred from the data in Fig. 6(a). The hydraulic gradient values for the net-negative offset error data set [Fig. 6(a), triangle symbols] yielded negative hydraulic gradient values during the initial drying period [for about 2 days (3,000 mins)]. These negative values are unrealistic because we initiated the system under hydrostatic conditions, and hence the starting gradient should have been zero, not a negative value. In turn, Fig. 6(b) (triangle symbols) illustrates how these incorrect negative hydraulic gradient values impacted UHC calculations. The UHC data [computed using Eq. (1)] also yielded unrealistic negative values until 3,000 mins. At about 3,000 min, the data had spurious oscillations in which the UHC values swung from extreme negative values to extreme positive values. This oscillation region corresponds to the period in which the estimated hydraulic gradient values gradually transition from negative to positive values [Fig. 6(a)]. During this period, the computed values of hydraulic gradient first become extremely small and negative (almost close to zero); and subsequently, after crossing the zero point, they become extremely small but positive; this leads to the undershoot and subsequent overshoot observed in UHC data. The value of the matric potential measured at the zero-crossing point (about 3,000 min) was about 160 cm, and the under- and overshoot effects are evident in Fig. 5 at about 160 cm of matric potential. Typically, in the published literature, researchers used a log-scale graph to present the UHC functions; because these graphs ignore negative data, they cannot display the oscillation in the negative direction. However, the oscillation in the positive direction (upward overshoot trend) is evident in some published data sets [e.g., Fig. 1(b)]. Of course, all these incorrect data points often are ignored, and are dealt with simply by invoking arbitrary rejection criteria (Peters and Durner 2008). In this study, for the first time, we clearly illustrate this spurious oscillation problem by carefully analyzing a measured data set with a net-negative offset error.

The circle symbols in Figs. 5 and 6(a and b) illustrate the implications of a net-positive offset error, which results in a systematic underestimation of the UHC values in the wet range. Interestingly, there were no oscillations in the net-positive offset error case, because the hydraulic gradient values were consistently positive from the beginning [Fig. 6(a), circle symbols]. However, these initial positive hydraulic gradient values are unrealistic because we started the experiment under hydrostatic conditions. Fig. 6(b) (circle symbols) illustrates how these incorrect positive hydraulic gradient values yield lower UHC values that are nearly an order of magnitude less than the expected corrected values.

The previous section demonstrated how various over- or underestimation problems in UHC data (Fig. 1) can be resolved by using the proposed experimental protocol. However, the literature data also show issues with the reproducibility of SWR data (Fig. 2). To illustrate the robustness of the proposed experimental protocol in yielding stable and reproducible UHC and SWR data sets, we compared the results of the three independent experiments (i.e., different samples prepared using the same soil) completed with the proposed experimental procedure. Figs. 7(a and b) compare the UHC and SWR data collected from Experiments 1, 2, and 3, all of which used the proposed tensiometer-correction and sample-saturation procedures. These data show that the proposed protocol greatly improves SWR reproducibility; all three data sets are almost identical. Unlike the literature case (Fig. 2), which had considerable variability near the wet range due to incomplete saturation, the variations in the SWR data sets in Fig. 7(b) are almost negligible. The UHC data did have some natural random variability, but these were of the same order of magnitude as that observed in the measured values of saturated hydraulic conductivity.