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Keywords:

  • soil moisture;
  • electromagnetic method;
  • capacitance sensor;
  • α-mixing model;
  • sensor calibration;
  • vadose zone

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[1] Recently improved ECH2O soil moisture sensors have received significant attention in many field and laboratory applications. Focusing on the EC-5 sensor, a simple and robust calibration method is proposed. The sensor-to-sensor variability in the readings (analog-to-digital converter (ADC) counts) among 30 EC-5 sensors was relatively small but not negligible. A large number of ADC counts were taken under various volumetric water contents (θ) using four test sands. The proposed two-point α-mixing model, as well as linear and quadratic models, was fitted to the ADC – θ data. Unlike for conventional TDR measurements, the effect of sensor characteristics is lumped into the empirical parameter α in the two-point α-mixing model. The value of α was fitted to be 2.5, yielding a nearly identical calibration curve to the quadratic model. Errors in θ associated with the sensor-to-sensor variability for the two-point α-mixing model were ±0.005 cm3 cm−3 for dry sand and ±0.028 cm3 cm−3 for saturated sand. In the validation experiments, the highest accuracy in water content estimation was achieved when sensor-specific ADCdry and ADCsat were used in the two-point α-mixing model. Assuming that α = 2.5 is valid for most mineral soils, the two-point α-mixing model only requires the measurement of two extreme ADC counts in dry and saturated soils. Sensor-specific ADCdry and ADCsat counts are readily measured in most cases. Therefore, the two-point α-mixing model (with α = 2.5) can be considered as a quick, easy, and robust method for calibrating the ECH2O EC-5 sensor. Although further investigation is needed, the two-point α-mixing model may also be applied to calibrating other sensors.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[2] Measurement of soil moisture in the vadose zone is essential in many hydrologic, environmental, and agricultural applications. Considerable progress has been made in recent years, in the development of new technologies for sensors based on electromagnetic methods to automatically measure soil moisture in situ. Various types of soil moisture sensors are readily available for dielectric measurement [e.g., Blonquist et al., 2005]. The principle of electromagnetic method for measuring apparent dielectric constant (Ka) and estimating volumetric water content (θ) of soil can be found elsewhere [e.g., Topp and Ferré, 2002; Robinson et al., 2003]. Several relationships between Ka and θ have been developed and found to have broad applicability [e.g., Topp and Ferré, 2002] and typical Ka – θ relationships are summarized in the literature [e.g., Jacobsen and Schjønning, 1995; Topp and Ferré, 2002; Robinson et al., 2003]. On the basis of the three-phase α-mixing model, which is often used to determine soil moisture, Sakaki and Rajaram [2006] derived a general form of the two-point α-mixing model (equation (1)) for interpreting Ka values measured using time domain reflectometry (TDR);

  • equation image

where α is the geometry factor (typically α = 0.5 is assumed which leads to the two-point mixing model proposed by Robinson et al. [2005]), ϕ is the porosity of the porous medium, Ksat is the water-solid mixture dielectric constant of water-saturated soil, Kdry is the air-solid mixture dielectric constant of air-dry soil, and equation image is the volumetric water content. Throughout this paper, “dry” and “saturated” refer to air-dry and water-saturated conditions. The advantage of this model (with a typical value of α = 0.5) is that no fitting parameter is involved and two extreme values Ksat and Kdry can be easily measured [Robinson et al., 2005] or derived from a two-phase grain-scale mixing model [e.g., Sihvola and Kong, 1988]. Equation (1) represents the relationship between Ka and θ that is a sole property of the soil of interest when typical TDR probes are used.

[3] Recent developments and improvements of ECH2O soil moisture sensors [Decagon Devices, Inc., 2006a] allow for detailed monitoring of soil water content at relatively low cost. Whereas TDR measures travel time of an electromagnetic pulse along a waveguide embedded in soil, the ECH2O soil moisture sensor uses capacitance to measure the apparent dielectric constant of the surrounding medium. The ECH2O sensor reads mV and the Decagon data logger (e.g., Em50 data logger or ECH2O Check handheld reader, 12 bit, excitation voltage = 3 V, Decagon Devices, Inc., Pullman, Washington) converts the mV reading into an analog-to-digital converter number (hereinafter referred to as ADC count; the manufacturer also uses Raw in the user's manuals). Using a non-Decagon data logger will result in an output reading in mV. There are two methods to calibrate these sensors. The first method relates the ADC counts directly to volumetric water content values (θ) [e.g., Czarnomski et al., 2005, Kizito et al., 2008] (hereinafter referred to as the “direct calibration method”). In the second method, a two-step procedure as employed by Bogena et al. [2007] is used (hereinafter referred to as the “two-step calibration method”). In this method, the ADC counts are first related to apparent dielectric constant Ka (e.g., based on the standardized sensor characterization method using standard solutions with known dielectric constants [Jones et al., 2005]), and Ka is then related to volumetric water content θ. The Ka – θ relationship in the second step is relatively well understood [Jacobsen and Schjønning, 1995; Topp and Ferré, 2002; Robinson et al., 2003]. An advantage of the two-step calibration method is that, assuming that the Ka – θ relationship in the second step is valid for the soils of interest, recalibration of all sensors is not required when the sensors are installed in a different soil. On the other hand, in the direct approach, all sensors need to be recalibrated for each soil.

[4] Using the direct calibration method that generally follows the standard procedure for calibrating capacitance sensors outlined by Starr and Paltineanu [2002], the manufacturer obtained ADC counts under various θ (hereinafter, referred to as ADC – θ data) for sand, sandy loam, silt loam, and clay. The ADC – θ data obtained using four mineral soils led to a linear relationship (θ = b ADC + c, where, b = 8.5 × 10−4, c = −0.48) [Decagon Devices, Inc., 2006b]. However, in the very low and high water content ranges, the manufacturer refers to the changes in sensor sensitivity [Decagon Devices, Inc., 2006c], as a result of which the ADC – θ relationship becomes somewhat nonlinear and is sometimes best fitted with a quadratic equation, especially in soils with high organic matter content [Decagon Devices, Inc., 2006a].

[5] The characteristics and performance of the ECH2O sensors have been examined by other researchers [e.g., Czarnomski et al., 2005; Blonquist et al., 2005; Bogena et al., 2007; Kizito et al., 2008]. Czarnomski et al. [2005] compared the accuracy of the ECH2O sensor (EC-20, measurement frequency = 10 MHz, sensor length = 20 cm), TDR (Tektronix 1502C), and water content reflectometer (CS615, Campbell Scientific, Inc., Logan, Utah) for measuring water content in natural and repacked soils. The calibration developed for each of the tested sensors adequately predicted water content regardless of soil type. Although temperature was found to affect the ECH2O sensor readings, they concluded that soil-specific calibration of the ECH2O sensors achieves performance results similar to those of TDR at a fraction of the cost. Blonquist et al. [2005] tested seven different electromagnetic sensing systems including the ECH2O EC-20 on the basis of the standardized method using liquids with known dielectric constants [Jones et al., 2005]. They found that the ECH2O EC-20 readings were impacted more by electric conductivity than by temperature. Bogena et al. [2007] performed detailed tests using the ECH2O EC-5 and EC-20 under various supply voltage, temperature, and electrical conductivity conditions. They employed the two-step calibration method and developed models for estimating dielectric constant as a function of supply voltage, temperature, and electrical conductivity. For the estimation of volumetric water content θ from the dielectric constant Ka, the empirical relation derived by Topp et al. [1980] was used. These calibration models were validated in the field and found to be accurate when the sensor signals were corrected for temperature and electrical conductivity. Kizito et al. [2008] investigated the EC-5 sensor using four different mineral soils (sand, sandy loam, silt loam, and clay) under various operating frequencies (up to 132 MHz), electrical conductivity conditions (up to 8 dS m−1), and volumetric water content (up to 0.30 cm3 cm−3). With a measurement frequency of 70 MHz, no significant sensor-to-sensor variation was observed and a single linear calibration that they developed appeared to be fairly robust over different soil types for the range of volumetric water contents that were considered. They also tested TE sensor (whose soil moisture sensing circuitry is the same as that of EC-5 [Kizito et al., 2008]) under different electrical conductivity and temperature conditions. The effect of temperature on the sensor reading was small and correctable. This led to the conclusion that no soil-specific or sensor-specific calibration was necessary.

[6] Acquisition of a number of ADC – θ data points to which a reasonable functional relationship is fitted requires a significant amount of time and effort. From a practical stand point, a calibration method that requires less ADC – θ data points while maintaining accuracy would be ideal to the users. Because the ECH2O sensors utilize soil, water, and air as part of the dielectric of the sensor capacitor, the sensor reading (ADC count) is a function of the apparent dielectric constant Ka of the soil. As mentioned earlier, the two-point α-mixing model (equation (1) with α = 0.5, equivalent to the two-point mixing model proposed by Robinson et al. [2005]) for calibrating TDR is advantageous because only two easy-to-measure extreme Ka values are required. We now extend the idea of using two extreme sensor readings to the development of a calibration function for the ECH2O sensor. Rewriting equation (1) in terms of ADC counts yields

  • equation image

where ADCsat is the water-solid mixture ADC count of saturated soil, and ADCdry is the air-solid mixture ADC count of dry soil, both of which are mostly easy to measure. Although the dielectric constants are simply replaced by corresponding ADCs in equation (2), the physical meaning of α is quite different from that of α in equation (1). As mentioned earlier, equation (1) represents the Ka – θ relationship that is a sole property of the soil of interest. On the other hand, the ECH2O sensor measures the dielectric constant of the material surrounding thin fiberglass-enclosed prongs [e.g., Bogena et al., 2007]. Because of the nonparallel prong configuration, the printed circuit board (made of fiberglass) that encloses the electrodes, and the sensitivity of the sensor head that contains the circuitry, the relationship between ADC counts and Ka is expected to be somewhat complex. The manufacturer found a nonlinear relationship between ADC counts and Ka values [Decagon Devices, Inc., 2007a]. Because of the nonlinearity in the ADC – Ka relationship, α = 0.5 in equation (2) can no longer be used to yield the correct volumetric water content. Rather, α is an empirical fitting parameter into which the aforementioned characteristics of the sensor are lumped. If a value of α in equation (2) exists such that the ADC – θ relationship is well described with reasonable accuracy, the two-point α-mixing model would be a quick, easy, and robust method for calibrating ECH2O soil moisture sensors.

[7] In this study, among several types of ECH2O sensors (EC-5, EC-10, EC-20, TE, and TM) that differ in length, operation frequency, and capability, we focused on the EC-5 that has the shortest length, measures volumetric water content only and operates at a measurement frequency of 70 MHz. We first performed a series of preliminary experiments to quantify bulk sampling volume and variability among sensors of the same type. Then, a large quantity of ADC count data at various volumetric water content levels was collected using four silica sands that differ in mean grain size. The ADC – θ data were taken using a long-column apparatus under well-controlled boundary conditions. The main objectives of this study are (1) to fit the two-point α-mixing model that we propose as well as linear and quadratic models to the ADC – θ data and (2) to validate three calibration models for estimating soil water content in a series of long-column drainage experiments. Note that we employed the direct calibration method where the ADC counts are directly related to volumetric water contents. As the effects of temperature and electrical conductivity on the performance of the ECH2O soil moisture sensors have been investigated [Blonquist et al., 2005; Bogena et al., 2007; Kizito et al., 2008], we focused on the ADC – θ relationship under a relatively small ambient temperature fluctuation and low electrical conductivity. All the experiments were conducted in the laboratory where the ambient temperature was 23 ± 2°C using clean silica sands and degassed filtered tap water with an electrical conductivity of 0.4 dS m−1. A supply voltage of 3V for sensor excitation was used throughout the experiments. It should be noted that the ADC counts that we present in this study can be converted to mV values by multiplying by 0.732 [Decagon Devices, Inc., 2007b]. Therefore, our tests were analogous to those by Bogena et al. [2007] and Kizito et al. [2008].

[8] This paper is organized as follows; in section 2, test sands and sensor characteristics are described, then the experimental procedures for acquiring ADC – θ data and validating the calibration models using the long-column apparatus are presented. In section 3, experimental and curve fitting results are presented and discussed. Summary and conclusions are presented in section 4.

2. Material and Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

2.1. Sand Materials

[9] Four relatively uniform industrial silica sands that differ in mean grain size were used in this study. The silica sands are identified by the effective sieve numbers; #20, #30, #50, and #70 (Unimin Corporation, Emmett, Idaho, 1997, sold as Granusil 4095, 4060, 4010, and 7030, respectively). The mean grain diameter d50 of the four sands ranges from 0.2 mm (#70 sand) to 0.7 mm (#20 sand). All sands have similar porosity values of 0.42–0.43. On the basis of the technical sheet provided by the manufacturer, the grain shape is classified as subangular.

2.2. Basic Characteristics of EC-5 Soil Moisture Sensor

2.2.1. Sampling Volume

[10] Sampling volume may be defined as the volume of soil around the sensor, within which a change in water content affects the sensor readings. The sampling volume has to be known for collecting an appropriate amount of soil samples to determine accurate volumetric water content values. Detailed quantification of the sampling volume including the effect of electromagnetic energy density distribution that decreases with distance from the prong surface can be numerically performed (e.g., as summarized by Robinson et al. [2003]). One of the prongs of the EC-5 sensor is the plus prong and the other is the ground. Our preliminary experiments showed that the sensitivity of the plus prong to be different from that of the ground prong, and that the sensor head (that includes the circuitry) also has a slight sensitivity. Therefore, we employed an experimental procedure for a “bulk” quantification of the sampling volume (hereinafter referred to as the bulk sampling volume). The quantification was performed for two extreme cases where the EC-5 sensor was immersed in water with an approaching air boundary and vice versa. It is known that in a layered system, the sampling volume is somewhat different than that in a homogeneous medium. After a series of experiments, it was found that the effect of higher sensitivity of the plus prong was more significant than that for conditions whether the sensor was in water or air. The bulk sampling volume of the EC-5 sensor was thus determined to be approximately 2 cm (parallel to prongs) × 1 cm (perpendicular to prongs) × 9 cm (longitudinal including sensor head) = 18 cm3.

2.2.2. Sensor-to-Sensor Variability in ADC Counts

[11] In order to investigate the variability in ADC counts among different EC-5 sensors, we have taken ADC counts in dry and saturated sands using 30 EC-5 sensors. To eliminate uncertainty resulting from using different data loggers, a handheld reader (ECH2O Check, excitation voltage = 3V, 12 bit, Decagon Devices, Inc., Pullman, Washington) was used. Two PVC containers (diameter = 15.2 cm, height = 35 cm, significantly larger than the sensor's sampling volume) were filled with dry and saturated #70 sand. The sand in each container was compacted thoroughly to a mean porosity of 0.427. The first sensor was connected to the handheld reader, the entire sensor (including the sensor head) was placed in the dry sand, the sand was recompacted to the same porosity, and an ADC count was taken. The sensor was then installed completely in the water-saturated sand, the sand was recompacted to the same porosity, and another measurement was taken. These steps were repeated for 30 sensors. The obtained mean ADC counts and standard deviations (SD) were ADCdry = 509 and SD = 5.9 (thus, 95% confidence interval = 497–521) for dry sand, and ADCsat = 1072 and SD = 11.8 (thus, 95% confidence interval = 1048–1095) for water-saturated sand, respectively. For comparison, ADC counts in dry and water-saturated sands were taken 30 times using a single sensor (this sensor was installed and removed for each of the 30 measurements). The results showed that the mean ADC counts and standard deviations were ADCdry = 508 and SD = 2.4 (thus, 95% confidence interval = 503–513) for dry sand, and ADCsat = 1070 and SD = 3.1 (thus, 95% confidence interval = 1064–1077) for water-saturated sand. Multiple sensors yielded roughly 3 to 4 times larger SD values in ADC counts than those measured by a single sensor suggesting that sensor-specific calibration can lead to a further reduction of estimation error.

2.3. Acquisition of ADC – θ Data Using a Long Column

[12] The long-column apparatus used in this study was constructed using a PVC pipe (length = 60 cm, inner diameter I.D. = 15.2 cm, outer diameter O.D. = 16.8 cm, wall = 0.8 cm) with a total of four EC-5 sensors installed at two different elevations (50 and 55 cm from the bottom of the column, Figure 1a). The sensors were completely embedded in the sand in such a way that the long axis of the sensors was horizontal and the flat plane was vertical (the plus prong to the top). Each EC-5 sensor was tied to a 7-cm-long brass pipe that was fixed horizontally to the PVC pipe. The adjacent EC-5 sensors were approximately 3 cm apart and did not interfere on the basis of the sampling volume described in section 2.2.1. An Em50 data logger [Decagon Devices, Inc., 2007b] was used.

image

Figure 1. Long-column apparatuses for (a) ADC – θ data acquisition and (b) validation experiment with alternating EC-5 sensors and TDR probes.

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[13] After the sensors were fixed in place, the column was filled with degassed filtered tap water (electrical conductivity = 0.4 dS m−1) roughly up to 15 cm and dry sand was poured from the top. When approximately 10 cm of sand was added, the sand was compacted by thoroughly tapping the column with a rubber mallet. This was repeated, with the water level kept always higher than that of sand until the column was filled with sand. The weight of the sand was recorded and the mean porosity was calculated assuming a grain density of 2.65 g cm−3 [Unimin Corporation, 1997]. The top boundary was covered with a plastic sheet to avoid evaporation but allow for air to enter the column freely as it drained. The bottom boundary was connected to a constant-head water reservoir to induce suction in the sand sample.

[14] The water level in the reservoir was initially set to the top surface of the column (Figure 1a) and initial ADC counts under full saturation at two elevations were measured. The constant-head water reservoir was lowered to a certain elevation so that the ADC counts from the sensors roughly reached the desired values (such that ADC counts were reasonably distributed between ADCdry and ADCsat). Then, the outflow valve was shut off and roughly 25–30 cm3 of sand sample (a little more than the sensor's bulk sampling volume of 18 cm3) was collected in the immediate vicinity of each sensor. The volumetric water content values of the collected samples were determined using the gravimetric method [e.g., Topp and Ferré, 2002], the column was repacked, and a different magnitude of suction was applied. This was repeated, for the four test sands, until a sufficient amount of ADC – θ data was obtained for the entire volumetric water content range. Approximately 60 ADC – θ data points were obtained for each test sand.

[15] The following three calibration models were fitted to the ADC – θ data and the coefficients were determined. Linear model

  • equation image

Quadratic model

  • equation image

Two-point α-mixing model

  • equation image

where a, b, c, and α are the coefficients to be determined. In equation (5), for dry sand, ADC = ADCdry, thus θ = 0, and for saturated sand, ADC = ADCsat, thus, θ = ϕ.

2.4. Validation Experiments Using a Long Column

[16] The long-column apparatus used in the validation experiments was similar to that used for ADC – θ data acquisition. The column was equipped with three EC-5 sensors and eight TDR probes horizontally installed in alternating configuration at 5 cm vertical increments as shown in Figure 1b. An Em50 data logger [Decagon Devices, Inc., 2007b] was used for the EC-5 sensors. Each TDR probe consisted of a pair of brass pipes that were fixed to the PVC pipe in such a way that two pipes were in a horizontal plane. The pipe length = 12.5 cm, O.D. = 0.4 cm, and separation = 1.5 cm. The TDR measurements were performed using a Campbell Scientific TDR100 system [Campbell Scientific, Inc., 2007]. The conditions at the top and bottom boundaries were identical to the ADC – θ data acquisition experiments described in section 2.3. The underlying assumption in the measurements was that the water pressure distribution along the column was hydrostatic at equilibrium and air pressure was atmospheric everywhere. Thus, when water and air in the column were at equilibrium, the relative height from the water level in the constant-head water reservoir to any point in the column was equal to the capillary pressure head (hc) at the point.

[17] After performing a preliminary experiment it was found that the TDR probes with the dimensions described above measure volumetric water content in a layer with a thickness of ∼2 cm. The EC-5 sensor also measures volumetric water content in a 2-cm-thick slice of the column because of the way it is installed. Within the sampling height of 2 cm, the effect of hydrostatic pressure distribution can be neglected for the sands tested here [Sakaki and Illangasekare, 2007]. Therefore, for practical purposes, the volumetric water content in the 2-cm-thick layers being measured is uniform and the estimated volumetric water content represents the point value at the sensor location.

[18] The same packing procedure described in section 2.3 was used. The water level in the reservoir was initially set to the top surface of the column (Figure 1b) and ADC counts at three EC-5 sensors as well as the Ka values at eight TDR probes were measured. The constant-head water reservoir was lowered by vertical increments of 0.5–2.5 cm (depending on the grade of the sands, in general, small increments were used for coarse sands and large increments for fine sands), equilibrium was assumed when outflow ceased, and the next measurement was taken. This was repeated until the lowermost TDR probe (5 cm above the bottom) started to show a decrease in volumetric water content. By using small increments of lowering of head, a sufficient number of EC-5- and TDR-measured hc – θ data points were obtained. Because each EC-5 sensor and TDR probe measures volumetric water content in a 2-cm-thick layer as mentioned above, it is appropriate to assume that EC-5- and TDR-measured hc – θ data can be directly compared. Upon completion, sand samples (about 30 cm3 each) near the top three EC-5 sensors and three TDR probes were collected and the volumetric water content was determined using the gravimetric method [e.g., Topp and Ferré, 2002]. This was done to double check the residual water content values estimated by the EC-5 and TDR.

3. Results and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

3.1. ADC – θ Data and Calibration Model Fitting

[19] Figure 2 shows the ADC – θ data obtained using the long-column apparatus shown in Figure 1a. It can be observed that (1) the ADC – θ data for the four sands that differ in mean grain size present a similar relationship, (2) the ADC – θ relationship is nonlinear, and (3) the ADC – θ data are more scattered with increasing volumetric water content (as inferred from the variation discussed in section 2.2.2).

image

Figure 2. ADC – θ data measured for the four test sands using the long-column apparatus. Two extreme points were determined as the mean of ADCdry (=517) and ADCsat (=1084) counts for the four test sands. The value of α was fitted to be 2.5.

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[20] The three calibration models (equations (3)(5)) that were fitted to the ADC – θ data using the least squares method are also shown in Figure 2. The fitted coefficients and r2 values are summarized in Table 1. The linear model (equation (3)) represented the ADC – θ data relatively well but would underestimate volumetric water content for ADC < 650 and ADC > 950, and overestimate for 650 < ADC < 950, leading to the lowest r2 value. The quadratic model (equation (4)) showed a better agreement with the ADC – θ data. For an evaluation of α in equation (5), ADCdry = 517, ADCsat = 1084, and porosity ϕ = 0.425 were used; these were the mean values for the four test sands. As a result, the value of α was fitted to be 2.5. This fitted value is an empirical parameter into which the effect of sensor characteristics such as the prong geometry, printed circuit board (made of fiberglass) that encloses the electrodes, and sensor head sensitivity are lumped. The resulting two-point α-mixing model was nearly identical to the quadratic model, showing the same r2 value as in the quadratic model. To fit the quadratic model with reasonable accuracy, a sufficient number of ADC – equation image data points are required. On the other hand, it is reasonable to assume that the α value determined in this study is applicable to most mineral soils because Kizito et al. [2008] observed a similarity of calibrations for a wide range of soil types including sand, sandy loam, silt loam, and clay. If this is the case, only two extreme values (ADCsat and ADCdry, typically easy to measure) are needed to establish the two-point α-mixing model that is as accurate as the quadratic model. To establish this, sensitivity of α was investigated by calculating r2 values for 1.5 < α < 3.5. It was observed that α = 2.5 was the optimal value for the ADC – θ data and that the values of α between 2 and 3 led to high r2 values (>0.96), suggesting that the calibration equation was fairly robust for 2 < α < 3.

Table 1. Fitted Coefficients of the Calibration Models and r2 Values
ModelabcADCdryaADCsataϕaαr2
  • a

    Mean of four test sands.

Linear-7.65E-4−4.37E-1----0.958
Quadratic6.11E-7−2.29E-4−5.00E-2----0.973
Two-point α mixing---51710840.4252.50.973

[21] Using a total of 243 ADC – θ data points obtained for the four test sands, the fitted value of α in equation (5) was found to be 2.5. In section 2.2.2, it was shown that 30 sensors installed in #70 sand led to some sensor-to-sensor variability. On the basis of the standard deviations presented in section 2.2.2, the 95% confidence intervals for ADCdry and ADCsat were 497–521 and 1048–1095, respectively. When the mean ADCdry and ADCsat counts are used in the two-point α-mixing model, errors in estimated θ that are associated with the sensor-to-sensor variability are ±0.005 cm3 cm−3 for dry sand and ±0.028 cm3 cm−3 for saturated sand. This level of variability is comparable to other commercially available water content sensors (for example, the probe-to-probe variability of CS616 water content reflectometer is ±0.005 cm3 cm−3 for dry soil and ±0.015 cm3 cm−3 for typical saturated soil [Campbell Scientific, Inc., 2006]). Although the above mentioned variability may be acceptable in many applications, the accuracy can further be improved by using sensor-specific ADCdry and ADCsat values.

[22] The sensor-specific calibration for the conventional linear and quadratic models requires a considerable amount of time and effort as a sufficient quantity of sensor-specific ADC – θ data is needed. On the other hand, the sensor-specific ADCdry and ADCsat values are easily measurable because dry and saturated soil samples are easy to prepare for each sensor in the laboratory before field deployment. Using the sensor-specific ADCdry and ADCsat values, every sensor would estimate θ in dry sand as 0, and for saturated sand equal to the porosity, eliminating the above mentioned errors resulting from not using the sensor-specific ADCdry and ADCsat values. Intermediate θ values are estimated on the basis of α = 2.5 that is expected to describe the nonlinear ADC – θ relationship between ADCdry and ADCsat values for each sensor. It is thus recommended to use sensor-specific ADCdry and ADCsat values when available.

3.2. Validation of Three Calibration Models

[23] In this section, the three calibration models (equations (3), (4), and (5)), using the coefficients from Table 1, were validated with capillary pressure head (hc) – volumetric water content data (hereinafter, referred to as hc − θ data) for the four test sands. The validation was done by comparing the hc − θ data measured using the EC-5 and TDR. Hereinafter, the EC-5- and TDR-measured volumetric water contents are referred to as θEC-5 and θTDR, respectively. The apparent dielectric constant values (Ka) measured with TDR were converted to volumetric water content (θTDR) using equation (1) with known porosity values, Kdry = 2.9 and Ksat ≈ 28, that were measured for each sand, and α = 0.5. The hc − θTDR data compared well with those obtained for the same type of sands used by Sakaki and Illangasekare [2007]. It was thus assumed that the hc − θTDR data best represented the hc − θ behavior of the test sands. The sand in the column was assumed to be homogeneous so that the sand at all sensor locations results in the same hc − θ behavior. The validation of the calibration models was performed by comparing the hc − θTDR and hc − θEC-5 estimated using equations (3)(5).

[24] Because the EC-5 sensors and TDR probes were installed in alternating elevations as shown in Figure 1b, the agreement between θEC-5 and θTDR values was evaluated in two steps. The Brooks-Corey model [Brooks and Corey, 1964] was first fitted to the hc − θTDR data, allowing us to estimate volumetric water content (hereinafter, referred to as θBC) for any given hc. Using a computer code RETC [van Genuchten et al., 1998], residual water content θr, displacement pressure head hd, and pore size distribution index λ were fitted. The ADC counts obtained by the EC-5 sensors were converted to θEC-5 using equations (3)(5), i.e., linear, quadratic, and two-point α-mixing models. For the two-point α-mixing model, both mean and sensor-specific ADCdry and ADCsat values were used for comparison. For each pair of hc − θEC-5 data, θBC was calculated using the Brooks-Corey model. Using the assumption mentioned earlier, the calculated θBC best represents the volumetric water content at a given hc. Then, errors between θEC-5 and θBC, and r2 values were evaluated. All calibration models resulted in high r2 values suggesting that the hc − θ relations measured using the EC-5 and TDR agreed closely. The linear model (equation (3)) yielded the lowest r2 value (=0.955) as expected from the lowest r2 value observed in Table 1. The quadratic model (r2 = 0.969) and two-point α-mixing model with the mean ADCdry and ADCsat values (r2 = 0.971) led to approximately the same r2 values. This was expected, because the quadratic and two-point α-mixing models yielded nearly identical curves in Figure 2 and the same r2 values in Table 1 (fitting equations (3)(5) to ADC − θ data). Further improvement in the r2 value (= 0.979) was achieved by using the sensor-specific ADCdry and ADCsat values in equation (5). The hc − θEC-5 and hc − θTDR data for the four test sands are shown in Figures 3a3d. The residual water content (θr) at the location of three EC-5 sensors and top three TDR probes, that were determined by the gravimetric method [e.g., Topp and Ferré, 2002] at the end of the experiments, fall on the hc − θ data measured using the EC-5 and TDR.

image

Figure 3. (a–d) The hc – θ data for the four test sands obtained using the EC-5 and TDR. Triangles are the residual water content that was determined at the end of each experiment by gravimetric (destructive sampling) method. Sensor-specific ADCdry and ADCsat values were used in equation (5) to calculate θEC-5.

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4. Summary and Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[25] A simple and practical two-point α-mixing model (equations (2) and (5)) for calibrating the ECH2O EC-5 soil moisture sensor was proposed and validated against a series of long-column drainage experiments. Equation (1) with a typical value of α = 0.5 or similar is widely used for TDR to represent the Ka − θ relationship that is a sole property of the soil of interest. In the proposed two-point α-mixing model, the characteristics of the sensor are lumped into α, thus, the physical meaning of α is quite different from that of α in equation (1). Preliminary experiments showed that the “bulk” sampling volume of the EC-5 sensor was found to be roughly 2 × 1 × 9 cm = 18 cm3 with a slight sensitivity around the sensor head. The sensor-to-sensor variability in ADC counts among 30 sensors of the same type was relatively small but not negligible.

[26] A total of 243 ADC − θ data was obtained for four test sands that differ in mean grain size using a long-column apparatus under well-controlled boundary conditions. The ADC − θ relationship was nonlinear. The scatter in the ADC − θ data was small in the low volumetric water content range and increased with volumetric water content. Three calibration models (linear, quadratic, and two-point α mixing) were fitted to the ADC − θ data. Although all three models yielded high r2 values, the linear model showed the lowest r2 value because of the nonlinearity in the ADC − θ data. For the two-point α-mixing model, the optimal value of the empirical parameter α was found to be 2.5. The sensitivity analysis showed that the value of α was relatively insensitive to the ADC − θ data between 2 and 3. The calibration curves for quadratic and two-point α-mixing models were nearly identical.

[27] In the validation experiments, the volumetric water content values estimated from ADC counts using the linear, quadratic, and two-point α-mixing model with α = 2.5 were found to be accurate, showing a close agreement with those estimated with TDR. The highest accuracy was achieved when the sensor-specific ADCdry and ADCsat were used in the two-point α-mixing model. As mV − θ data (analogous to our ADC − θ data) for a wide range of mineral soils (sand, sandy loam, silt loam, and clay) obtained by Kizito et al. [2008] appeared to be independent of soil type, it is appropriate to assume that α = 2.5 is valid for most mineral soils. Equation (5) infers that the accuracy of θ is directly dependent on porosity ϕ. For cases where porosity is readily obtained (such as laboratory experiments or field with least heterogeneity), the two-point α-mixing model only requires the measurement of two extreme ADC counts in dry and saturated soils.

[28] The above mentioned sensor-to-sensor variability in ADC counts led to variability in volumetric water content estimation (when the mean ADCdry and ADCsat values that were averaged for 30 sensors were used). This variability was roughly the same magnitude as the probe-to-probe variability of CS616 water content reflectometer [Campbell Scientific, Inc., 2006], for example. Although this may be acceptable in many applications, the accuracy can further be improved by using sensor-specific ADCdry and ADCsat values. Sensor-specific ADCdry and ADCsat counts are readily measured in most cases whereas the coefficients in the conventional linear and quadratic relationship have to be determined using a large quantity of ADC − θ data. Acquisition of sensor-specific ADC − θ data for the linear and quadratic models would be extremely time consuming. Therefore, the two-point α-mixing model (with α = 2.5) can be considered as a quick, easy, and robust method for calibrating the ECH2O EC-5 sensor. For field measurements where porosity variation can be an issue, the sensor-specific calibration using site-specific soil samples is recommended. In other words, for each sensor, ADCdry, ADCsat, and ϕ values should be obtained using a soil sample that is collected from the location where the sensor is to be installed.

[29] The applicability of the two-point α-mixing calibration model has to be further examined for field soils with silt, clay, and organic matter. Furthermore, if the design of the sensor (circuitry, prong configuration, thickness of printed circuit board) were significantly changed, α = 2.5 may no longer be valid. All the experiments performed in this study were conducted in the laboratory where the ambient temperature was 23 ± 2°C and using degassed filtered tap water with electrical conductivity of 0.4 dS m−1. In a separate experiment, we observed that the ambient temperature variation mentioned above led to a temperature change of roughly ±2°C in the dry and saturated sands with a slight time lag. However, the ADCdry and ADCsat counts were relatively stable with a small fluctuation of ±2. Under different temperature and electrical conductivity conditions, the value of α may be different. Although α may not be 2.5, the two-point α-mixing model is expected to work well for ECH2O TE and TM sensors as the circuitry for volumetric water content measurement of these sensors is the same as that of EC-5 [Kizito et al., 2008]. For ECH2O EC-10 and EC-20 sensors with different lengths and measurement frequency, further investigation is necessary.

[30] Finally, the two-point α-mixing model may also be applicable to other sensors (e.g., CS616 water content reflectometer [Campbell Scientific, Inc., 2006]) that exhibit similar nonlinearity between the sensor output and volumetric water content. For example, the calibration data collected using a CS616 during laboratory measurements in a loam soil with a porosity of 0.47 (an example provided in the instruction manual, [Campbell Scientific, Inc., 2006]) shows a quadratic relation between the output period (Per, in μs) and volumetric water content. The extreme values may be estimated from the graph in the manual as; Perdry = 15.0 at θ = 0, Persat = 32.4 at θ = 0.47. Although not shown, substituting these values in place of ADCdry and ADCsat, respectively, and α = 2.2 (best fit for this sensor in the loam soil tested) into equation (5) yielded a curve that was nearly identical to the quadratic function provided by the manufacturer [Campbell Scientific, Inc., 2006]. Although further investigation is needed, this implies that the two-point α-mixing model may potentially be used for soil moisture sensors other than ECH2O EC-5.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[31] This research was funded by grants from the National Science Foundation (DMS-0222286 and CNS-0720875) and Army Research Office award W911NF-04-1-0169. The authors are grateful to Colin S. Campbell and Douglas R. Cobos of Decagon Devices, Inc., Pullman, Washington, for providing technical information regarding the ECH2O EC-5 soil moisture sensor used in this study.

References

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  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Material and Methods
  5. 3. Results and Discussion
  6. 4. Summary and Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information
FilenameFormatSizeDescription
wrcr11740-sup-0001-t01.txtplain text document0KTab-delimited Table 1.

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