The sensors calibrated during this study were the EC-20, ML2x, and SM200 (Table 1). The calibration equation of the EC-20 is a linear function that relates EC-20 readings (V) to the actual soil water content. There is a linear correlation between soil water content measured with the ML2x and the square root of the dielectric constant (√ɛ) [18,19]. The SM200 probe has a similar calibration equation as that of the ML2x.

Field calibrations of the selected sensors were performed at two depths of six monitoring locations across the upper Mākaha Valley sub-watershed (Figure 1). These locations, referred to as locations 1 through 6 from here onward, were initially selected to represent the spatial variations of the topography, soil, and vegetation covers across the study area (Table 2). Soils in the lower valley are less permeable than those along the valley ridges. The soils over the valley floor and along the southeastern ridge of the upper valley are mainly clay loam, silty loam, and silty clay [20].

Disturbed and undisturbed soil core samples were collected in three replicates from each depth of the six locations. The undisturbed soil core samples (radius = 2.5 cm; height = 7.5 cm) were collected with a sludge hammer soil sampler (Soilmoisture Equipment Crop. Santa Barbara, CA, USA). The trimmed soil cores were sealed with plastic caps, placed in labeled zip-lock plastic bags, and taken to the laboratory to measure their ρ_b and θ_t following the standard procedures described by Grossman and Reinsch [21] and Flint and Flint [22], respectively.

Replicates of the disturbed bulk soil samples were thoroughly mixed to produce a representative sample for each depth and location. These samples were air dried and sieved (<2 mm); a sub-sample was used to determine particle size distribution using the hydrometer method [23]. The textural triangle of the United States Department of Agriculture (USDA) classification scheme was used to determine the soil particle size distributions. Color schemes were used to determine the NRCS (Natural Resources Conservation Services) soil series information. EC and pH of these samples were measured from their 1:2 soil:water solutions with a multi-functional sympHony^® meter (Model SB90M5; Batavia, IL, USA) and the respective electrodes.

Two units of each EC-20, ML2x, and SM200 sensor were installed at 20 and 80 cm depths at locations 1 through 6 following standard procedures [8]. Various soil water content levels ranging between field capacity (∼0.23 cm³ cm⁻³) and saturation (∼0.59 cm³ cm⁻³) were generated by intermittently applying water at and surrounding the sensor installation points. Watermark soil matric potential sensors were used to monitor the soil water potential at various soil water content levels. The soil water sensors and matric potential sensors were logged with their corresponding data loggers at 1-min intervals. At least 3 uniform sensor readings were averaged and used with the corresponding actual water content determined in the laboratory from intact soil core samples collected in three replicates from the close proximity of the sensors’ zone of influence such that the center of the soil cores aligned with the center of the individual sensor. These samples were used to determine actual soil water content following the thermo-gravimetric method. These samples were also used to determine ρ_b and θ_t. Total porosity was also estimated from the following equation: (1) θ t = 1 − ρ b ρ swhere ρ_s is the particle density (2.65 g cm⁻³).

Values of actual soil water content were plotted versus the respective readings (V) of the EC-20, ML2x, and SM200 to establish field calibration equations separately for the two depths (20 and 80 cm) at each location. A factorial analysis of variance (ANOVA) was conducted to evaluate the effect of soil depths and locations on ρ_b, θ_t, CC, EC, and pH using Statistix software package [24]. The coefficient of correlation (r), which represents the degree of association between the calculated and the actual water content; the root mean square error (RMSE), which represents the accuracy of calibration equation to predict actual water content; and the mean bias error (MBE), which is an indicator of sensor’s accuracy in form of the difference between means of the calculated and actual water contents, were used to evaluate the field and default calibration equations. The RMSE (cm³ cm⁻³) and MBE (cm³ cm⁻³) were calculated as follows: (2) RMSE = ∑ i = 1 n ( θ c i − θ a i ) 2 / n (3) MBE = ∑ i = 1 n ( θ c i − θ a i ) / nwhere θ_ci and θ_ai are the calculated and actual water content in cm³ cm⁻³, respectively, and n is the number of observations. Positive and negative values of MBE indicate over-estimation and under-estimation of the actual water content by the sensor, respectively. Larger r and smaller RMSE and MBE represent high sensor accuracy and vice versa.

Across the six soil water content monitoring locations, the soils at 20 cm depth had larger CC than those at 80 cm depth (Table 3). Clay content at 20 cm depth ranged from 157 at location 6 to 610 g kg⁻¹ at location 2; whereas, at 80 cm depth, the CC values ranged from 288 at locations 4 and 5 to 690 g kg⁻¹ at location 2. Soil from both depths at locations 1 and 4 were clay loam. Locations 2 and 3 had clay soils at both depths; whereas, at location 5, loam and sandy loam soils existed at 20 and 80 cm soil depths, respectively. Soil from the 80 cm depth at location 6 was silty clay. Soils at location 6 had the smallest CC among the other sampling locations. Different NRCS soil series were found across the watershed. Location 1 had Molisol, location 2 had Inceptisol, and locations 3 through 5 had Ultisol. Andisols, formed by weathering of volcanic ash under well-drained conditions, dominated location 6; they are characterized by low bulk density (Table 3) and are favorable for keeping aerobic conditions [25].

Larger ρ_b was observed at 80 cm depth than at 20 cm depth across the six locations except at location 4 (Table 3). The opposite was expected for θ_t, given the inverse relationship between θ_t and ρ_b. Smaller ρ_b had resulted in larger θ_t given their inverse relationship (Equation (1)). At the 20 cm depth, ρ_b ranged from 0.49 at locations 6 to 0.95 g cm⁻³ at location 4; however, at 80 cm depth, it ranged from 0.72 at location 6 to 1.27 g cm⁻³ at location 1. At the 20 cm depth, θ_t ranged from 0.66 at location 4 to 0.72 cm³ cm⁻³ at location 5; whereas, at 80 cm depth, it varied between 0.56 at location 1 and 0.67 cm³ cm⁻³ at locations 4.

The values of EC at 20 cm soil depth were almost double of those at 80 cm soil depth at locations 1 through 3; whereas, at locations 4 and 5, the EC values at 20 cm soil depth were 1.5 and 1.2 times those at 80 cm soil depth, respectively (Table 3). At 20 cm soil depth, the EC ranged from 426 at location 3 to 2,016 μS cm⁻¹ at location 1; whereas, at 80 cm soil depth, it ranged from 222 at location 3 to 1,270 μS cm⁻¹ at location 4. Decomposition of the organic matter from the tree litter might have resulted in the larger EC values of the soil samples of the 20 cm soil layer. Reduction in pH of the top soil layers at locations 1 through 3 might have also resulted from the decomposition of organic matter. The soils from the two depths of the six locations were acidic to neutral as their pH varied from 4.24 at 20 cm depth at location 2 to 5.81 at 20 cm depth at location 5.

ANOVA results showed a significant (P < 0.05) increase in ρ_b and EC values and a significant (P < 0.05) decrease in θ_t with increase in soil depth (Table 4). This may be due to compaction as a result of the overburden from the above soil load. Soil compaction enhanced ρ_b and thus reduced θ_t as shown by Equation (1). There was no significant effect of soil depth on CC and soil pH. Location had a significant (P < 0.05) effect on ρ_b, θ_t, and EC and a highly significant (P < 0.01) effect on CC.

In general, major soil properties including ρ_b and θ_t are consistent for a given soil type, series or order. Variations in ρ_b and θ_t are due to many factors such as high organic matter, CC or both. Most of the shrink-swell clays exhibited variability in ρ_b and θ_t. The shrink-swell behavior of the soils at locations 1 through 5 was confirmed from the good agreement between the actual θ_t and those calculated from Equation 1 (Figure 2). Small CC at location 6 suppressed soil shrinking and swelling at this location resulting in a weak correlation (r < 0.4) between the actual and calculated θ_t.

Pearson’s correlation test was conducted to correlate ρ_b and θ_t at 20 and 80 cm depths. Overall, there was a non-significant inverse relationship between ρ_b and θ_t except at 20 cm depth where a stronger (r = −0.93) inverse significant (P < 0.05) relationship existed. The strongest (r = 0.95) significant (P < 0.05) relationship between ρ_b at 20 and 80 cm depths reflected the increasing trend of ρ_b with soil depth at all experimental locations.

There was a linear increase in ρ_b and a linear decrease in θ_t with increase in soil water content at all depths and locations (Figure 3). Slopes of the ρ_b—water content and θ_t—water content models for the two depths and six locations were non-uniform reflecting a great spatial variability in these properties. This was an indicator of great soil water content dynamics due to shrinking and swelling—induced changes in ρ_b and θ_t. Such behavior of water content dynamics emphasized the need for site-specific calibration equations for soil water content sensors. There were weak θ_t—water content relationships (r = 7E-04, 0.02) at location 6 [Figures 3(r,x)] partially due to high ash and organic matter contents and partially due to poor structure of highly weathered soil (personal observations). Volcanic ash soils are classified as an Andisol with low densities and assumption of ρ_s = 2.65 g cm⁻³ may not be valid for these soils [25]. Moreover, Andisol usually have peculiar permittivity relations due to high surface area and low densities [26–30]. Our results showed that variations in ρ_b can affect soil water content estimation of high CC soils due to their shrink-swell behavior. Fares et al. [31] and Polyakov et al. [32] reported similar results for a sandy clay loam soil and for a weathered clay loam soil, respectively. Yule [33] and Smith [34] have reported errors in volumetric water content calculation made from ρ_b information when the ρ_b was not determined at the right moisture content.

Since soil depths and locations had significant effect on ρ_b, θ_t, CC, and EC (Table 4) in addition to the significant effect of ρ_b and θ_t on soil water content dynamics (Figure 3), field calibration equations for each sensor were established for each depth and location (Table 5). These site-specific field calibration equations of the EC-20, ML2x, and SM200 accurately predicted the actual water content (r > 0.88; RMSE 0.011 to 0.054 cm³ cm⁻³), compared with their respective default equations (r > 0.86; RMSE 0.026 to 0.247 cm³ cm⁻³). The values of RMSE and MBE of the actual water content and the calculated water content using default equations are inside the parentheses in Table 5. The values of MBE for the site-specific field calibration equations were smaller than those of their corresponding default equations indicating that the site-specific field calibration equations had significantly improved the accuracy of soil water content measurements of these sensors. On the other hand, the default calibration equations substantially under-estimated (larger absolute negative value of MBE) the actual water content compared with their corresponding site-specific field calibration equations (smaller MBE).

The watershed-scale field calibration equations (one equation of each sensor for all depths and locations) of the three sensors seem to substantially (P < 0.001) improve the accuracy of the tested sensors (Table 6). Estimation of actual water content using these new equations resulted in smaller RMSE and MBE as compared with their corresponding default equations. The ML2x exhibited the highest improvement in its accuracy with the use of the new calibration equation (r = 0.81; RMSE 0.038 cm³ cm⁻³) over its default equation (r = 0.79; RMSE 0.189 cm³ cm⁻³).

Similar improvement in the accuracy of the SM200 was achieved with the watershed-scale field calibration equations (RMSE 0.042 cm³ cm⁻³) compared with the default equation (RMSE 0.155 cm³ cm⁻³). There was a better agreement between actual water content and that measured by the SM200 watershed-scale field calibration equation (MBE −0.001 cm³ cm⁻³) than between actual water content and that determined by the default equation (MBE −0.126 cm³ cm⁻³). EC-20 showed the least improvement in its accuracy among the tested sensors with the use of watershed-scale field calibration equation (RMSE 0.054 cm³ cm⁻³; MBE −0.034 cm³ cm⁻³) compared to that of its default equation (RMSE 0.068 cm³ cm⁻³; MBE −0.014 cm³ cm⁻³).

The performance of the default and watershed site-specific calibration equations in tracking the actual water content is detailed in Figure 4. There was a minimal difference between the performance of the field and the default (MBE −0.034 cm³ cm⁻³ vs. −0.014 cm³ cm⁻³) equations of EC-20 (Figure 4(a); Table 6).