Soil Science Society of America Journal 67:52-61 (2003)
© 2003 Soil Science Society of America
DIVISION S-1—SOIL PHYSICS
Time Domain Reflectometry Field Calibration in the Little Washita River Experimental Watershed
Gary C. Heathman*,
Patrick J. Starks and
Michael A. Brown
USDA-ARS Grazinglands Research Laboratory, 7207 W. Cheyenne, El Reno, OK 73036
* Corresponding author (heathman{at}grl.ars.usda.gov)
 |
ABSTRACT
|
|---|
Accurate measurement of profile soil water content is essential to many areas of environmental and agricultural research. In this study five methods were evaluated for determining volumetric profile soil water content from time domain reflectometry (TDR) data at nine locations within the Little Washita River Experimental Watershed (LWREW) in south central Oklahoma. Soil compositions for the sites ranged between 24.6 to 86.4% for sand and 5.2 to 29.2% for clay. Comparisons were made between gravimetric soil sample data and soil water content as determined by the TDR factory instrument calibration, two methods of site-specific calibration, a regional calibration technique, and an empirically derived universal approach. Method 1 is the factory calibration, which uses average values for model coefficients that were derived from extensive laboratory work and theoretical analysis. Method 2 fits a site-specific linear regression of TDR time delay on measured soil-core water content. Method 3 uses the factory calibration equation and site-specific values for the ratio of TDR time delay in dry soil, to that in air (Ts/Ta). In Method 4, a regional linear regression equation was developed from an analysis combining data from all study sites. Method 5 applies a universal equation based on the linear relationship between soil water content and the apparent dielectric constant of soil (Ka) measured by TDR. Statistical analysis of the data showed that of the five methods, only the mean root mean square error (RMSE) value for Method 2 was significantly different from all other methods (
= 0.05). Method 2 also had the smallest standard deviation and standard error, and the narrowest range of RMSE values. All field calibration methods show that it is necessary to include very low water content data in determining absolute water content. When compared with the factory calibration, all other methods improved the measurement of soil water content, with Method 2 providing the most accurate results at the site-specific level of analysis.
Abbreviations: LWREW, Little Washita River Experimental Watershed • ME, mean error • RMSE, root mean square error • TDR, time domain reflectometry • UO, instrument-specific calibration factor
|
INTRODUCTION
|
|---|
THE STATUS of soil water content in the root zone is a key parameter to many aspects of agricultural, hydrological, and meteorological research. In agriculture, accurate knowledge of soil moisture is essential for efficient water resource management, irrigation scheduling, crop production, and chemical monitoring (Ma et al., 1998; Hanson et al., 1999). In hydrology and meteorology, soil moisture plays a significant role in the partitioning of available energy at the earth's surface into sensible and latent heat exchange with the atmosphere as well as in the partitioning of rainfall into infiltration and runoff (Chaubey et al., 1999; Silberstein et al., 1999). Thus, accurate measurement of soil water content is essential to better understanding the impacts of agricultural management systems on the soil–plant–air continuum, as well as the components of mass and energy transfer at the earth's surface.
During the past two decades, considerable advancements have been made in the technique of TDR to measure in situ, profile soil water content, ionic solutes, and air in the mass and energy balances of the soil profile (Young et al., 1997; Topp and Reynolds, 1998). Because of these advancements, TDR is now widely used to measure volumetric water content in soils (Dirksen and Dasberg, 1993; Jacobsen and Schjønning, 1993; Hilhorst, 1998; Chan and Knight, 1999; Heathman, 2001). The technique is based on the relationship between the apparent dielectric constant of soil (Ka) measured by TDR, and the soil volumetric water content (
v). Hilhorst (1998) mentioned that according to a historical review by Grant et al. (1978), the technique has been in use since 1951. However, the relationship between the dielectric properties of a soil and its water content were the subject of much earlier work by Smith-Rose (1933).
Based on a comprehensive laboratory study, Topp et al. (1980) developed an empirical expression relating the apparent dielectric constant to soil water content. From this general relationship they derived an equation, usually referred to as the Topp equation, to find v from measured values of Ka:
 | [1] |
Equation [1] has proven to be a good general description of the measured calibration curves for a wide range of soil types (Roth et al., 1992; Yu et al., 1999). However, additional research suggests that for finer-textured soils or electrically conductive soils, individual calibration curves should be developed (White et al., 1994; Yu et al., 1999).
Many attempts have been made to improve measurements of water content obtained from dielectric data (Roth et al., 1992; Jacobsen and Schjønning, 1993; Dirksen and Dasberg, 1993; Chan and Knight, 1999; Ponizovsky et al., 1999; Yu et al., 1999). In some cases these studies involve the use of various mixing models to describe the functional relationship between v and the dielectric behavior of soils. The types of models range from complex physically based multi-phase dielectric mixing models (Roth et al., 1992) to empirical relationships derived from experimental data (Topp et al., 1980; Herkelrath et al., 1991; Heathman, 2001). Yu et al. (1999) gave a systematic framework for evaluating the TDR response of soil using several different modeling approaches and recommended that it would be more practical to use site-specific information for TDR calibrations. In general, they found that the soil solid fraction, porosity, and temperature have little effect on the measurement of Ka while particle surface area was an important factor affecting water content determination. These results are consistent with several studies in the literature (Wang and Schmugge, 1980; Roth et al., 1992; Ponizovsky et al., 1999), but inconsistent with others that have included the effects of such properties as bulk density and texture in their analyses (Dirksen and Dasberg, 1993; Jacobsen and Schjønning, 1993; Hilhorst, 1998). Thus, the influence of soil physical properties on the dielectric properties of a soil continues to be an active area of study. There does, however, seem to be general agreement that when using a dielectric sensor, the measured dielectric data should be calibrated to the water content of the actual soil involved for improved accuracy (White et al., 1994; Yu et al., 1999). Therefore, the work presented in this paper addresses the use of simple linear methods for in situ TDR calibration and discusses the physical significance of model coefficients derived by such means.
The work of Topp et al. (1980), with further analyses and related experimental work (Ledieu et al., 1986; Whalley, 1993; White et al., 1994; Timlin and Pachepsky, 1996) has demonstrated that a strong relationship exists between Ka and v. Furthermore, the relationship between K0.5a and v is linear over what can be considered a practical range of water content (Topp and Reynolds, 1998). Time domain reflectometry measures the time it takes for an electromagnetic pulse to travel along metal rods placed in the soil, with the travel time being a function of the Ka for the three-phase soil system (theory discussed below). Because the travel time of the TDR signal depends on the Ka of the soil, it is possible to obtain a linear calibrated relationship between travel time and soil-water content (Herkelrath et al., 1991; Hook and Livingston, 1996; Timlin and Pachepsky, 1996; Topp and Reynolds, 1998).
A relatively new, segmented TDR probe was used in this study to obtain profile soil water content from TDR travel time data as discussed above. The probe design is based on the work of Hook et al. (1992), where remotely switched shorting diodes in combination with differential detection techniques were used to improve measurement of soil water content in saline or layered soils. Although research using this type of probe has been reported in the literature (Hook and Livingston, 1995; Sun et al., 2000) the number of investigations seems small and restricted to closely controlled laboratory conditions. Based on the amount of literature suggesting that dielectric sensors should be calibrated to the water content of the field soils involved (Topp and Reynolds, 1998; Yu et al., 1999; Sun et al., 2000), and that this type probe design is relatively new, the objectives of this paper were to: (i) evaluate the accuracy of v measurement using the factory calibration, (ii) determine whether site-specific calibration improves measurements of v based on the linear relationship between v and K0.5a, (iii) determine if the site-specific linear regression coefficients have any physical significance in terms of soil matrix or soil water dielectric properties, and (iv) test the applicability of a universal calibration approach.
|
Time Domain Reflectometry Theory and Soil Water Measurement
|
|---|
Detailed descriptions of TDR theory and operation have been previously given by Topp et al. (1980), Topp and Davis (1985), and Cassel et al., (1994). We briefly review the theory in relation to the calibration methods presented in this paper. Volumetric soil water content determined by TDR involves measurement of the propagation velocity (or time delay) and attenuation of an electric step or pulse function applied along a transmission line in the soil. A time domain reflectometer generates an electric pulse, which propagates as an electromagnetic wave through the soil via a transmission line (waveguide). The propagation velocity (v) corresponds to the time it takes for a step pulse to travel a distance to the end of the transmission line and back. Velocity can be expressed as,
 | [2] |
where L is the linear distance traveled, and t is the measured travel time. The time interval is the variable quantity measured by the TDR technique and used to determine soil water content (Hook and Livingston, 1995). As soil water content increases, the time required to traverse the length of the transmission line also increases.
The propagation velocity is usually normalized to the speed of light and expressed in terms of the apparent dielectric constant (Ka) (Topp et al., 1980),
 | [3] |
where c is the speed of light (3 x 108 m s-1). Based on the model of Herkelrath et al. (1991), and using the transmission line theory of Eq. [2] and [3], Hook and Livingston (1996) derived a general formula to obtain soil water content from measured travel time (or time delay) given as,
 | [4] |
where they express v in terms of time intervals with T being the travel time of an electric pulse in soil and normalized with respect to the theoretical travel time of the transmission line in air (Ta). Travel time in oven-dried soil is Ts, and Kw is the dielectric constant for water equal to 80.37 at 20°C. Although Kw is considered a constant in this work, it is temperature dependent. A value of 0.002°C-1 may be used to calculate values of Kw between 15 and 30°C without introducing significant error (Weast, 1982). Pepin et al. (1995) investigated measurement errors in the apparent soil dielectric constant associated with soil temperature variations and suggested that a temperature correction of 0.00175°C-1 could be employed if there are large temperature gradients or changes in temperature within a soil profile during TDR measurements, otherwise the error is negligible. We use a constant value of Kw since the range in profile soil temperature was well within 15 to 30°C. Using a value of 80.37 for the dielectric constant of water, Eq. [4] has a theoretical slope of 0.1256 (Hook and Livingston, 1995). Hook and Livingston (1996) found an average value for Ts/Ta of 1.55 ns for their experimental data. With these values, Eq. [4] can be written as,
 | [5] |
The TDR instrument used in this study was the Moisture Point MP-9171 (E.S.I., Environmental Sensors, Inc., Victoria, BC, Canada).
The instrument measures T (referred to as measured time delay) from which v is calculated according to Eq. [5]. Based on recommendations in the literature regarding the development of soil or site-specific TDR calibrations, the work presented in this paper evaluates the accuracy of v estimated by Eq. [5] and compares the results to v obtained using TDR site-specific calibrations.
|
MATERIALS AND METHODS
|
|---|
In this section a description of the watershed and field site locations is presented, as well as a brief history of past and recent work on the watershed that relates to TDR installation and calibration. A discussion of TDR site selection is given and the procedure for soil sample collection and methods of statistical analyses are described. Finally, we present two methods for determining volumetric soil water content based on site-specific information and measured TDR time delay, a regional calibration, and a universal method based on the approach of Topp and Reynolds (1998).
Study Area and Field Sites
The TDR field study sites are located within the LWREW, which occupies approximately 610 km2 in south central Oklahoma (Fig. 1) . Average annual rainfall is 74.7 cm, with most precipitation occurring in spring and autumn (Allen and Naney, 1991). Soils in the watershed have been categorized into one of four hydrologic groups on the basis of the soil properties that are known to influence infiltration and runoff. In general, soils with moderate infiltration rates cover approximately 70% of the watershed. Certain areas of shallow soils in the western portion, as well as a few soils in the eastern region of the watershed have high runoff potential. The central portion of the watershed contains areas with very low runoff potential and higher infiltration because of predominately sandy soils.
View larger version (36K):
[in this window]
[in a new window]
|
Fig. 1. Map of Little Washita River Experimental Watershed nine time domain reflectometry sites and Micronet locations.
|
|
Research and demonstration projects in the LWREW date back to 1936, when a portion of the watershed was selected to study erosion control practices. The USDA–ARS began hydrologic monitoring in 1961 to assess the effectiveness of flood-control practices. Since that time an extensive network of 42 meteorological sites (Micronets) has been established along with additional measurement systems to support climate research and studies involving surface-water hydrology and surface energy exchange.
In the spring of 1997, 13 of the 42 Micronet locations were chosen as TDR soil moisture measurement sites to support the objectives of the Southern Great Plains 1997 Hydrology Experiment (Jackson et al., 1999). The sites were selected based on preexisting instrumentation, soil physical and hydraulic properties, and location within the watershed. Because of the variability of soil textures across the watershed, it was necessary to determine the effects of using a generalized factory-supplied calibration on the determination of soil water content from TDR time delay readings. Nine of the 13 TDR probe sites (Fig. 1) were chosen for calibration studies.
Soil Sample Collection and Analysis
Most devices commonly used to measure soil water content are calibrated against gravimetric determinations of soil water content (g) (Gardner, 1965). Calibration procedures presented in this work are based on this standard technique. Soil-core samples (54.3 cm3 per sample) were collected from three locations at each site approximately 1 m from the TDR probe on a given date. Measurements of g, bulk density, and texture were made at depth intervals coincident with TDR measurement intervals (TDR readings were taken just prior to soil sampling). Sample holes were carefully refilled with soil from the same area. Average soil core volumetric water content (sc) for each depth interval was determined from the three g samples based on soil-core bulk density. Samples were collected at various times to obtain a range of water contents (Fig. 2)
. Table 1 gives bulk density values and percentage of sand, silt, and clay for each site and depth interval based on soil-core laboratory analyses. Because sample size, area, and variation are important issues concerning field calibrations based on g sampling, Table 2 provides an example set of soil-core statistical data at each site for one of four sampling dates used in this study. Additionally, a set of soil-core samples were collected at five of the nine sites to serve as an independent test of TDR-measured soil water content using the five methods of converting time delay data to profile soil water content. The samples were collected in the same manner as described above and at various times to obtain a range of water content values. The sites used for the independent analysis were 133, 136, 151, 154, and LW02 (Table 1).
View larger version (32K):
[in this window]
[in a new window]
|
Fig. 2. Linear relationships between soil-core water content and time domain reflectrometry time delay for (a) Site 136, (b) Site LW02, (c) Site 134, (d) Site 154, (e) nine sites, and (f) the regional linear model.
|
|
View this table:
[in this window]
[in a new window]
|
Table 1. Soil physical properties at nine time domain reflectometry (TDR) study sites in the Little Washita River Experimental Watershed (LWREW).
|
|
View this table:
[in this window]
[in a new window]
|
Table 2. Mean, standard deviation, and standard error for the 0 to 60–cm gravimetric soil sampling at nine sties on 29 April 1997 with three replicates and a total of 12 samples per site.
|
|
Instrument Features and Methods for Soil Water Calculations
The MP-917 TDR system includes a hand-held data measurement, processing, and logging unit, a connecting cable, and TDR probe (transmission line). Once the unit is connected to the probe and activated, the instrument interrogates the probe, processes the electronic signals, and displays (and stores) the results as numerical data. The numerical data are stored in the data logger as instrument counts and as volumetric water content (m3 m-3). Stored data can be exported to a computer for archive and further processing using the MP-917 software.
The TDR probes used in this study were constructed of rectangular stainless steel bars (1.3 cm in width) separated by 1.5 cm of epoxy that vary in length according to probe type. The probes are segmented devices having known distances between segment endpoints. Probe design is based on TDR remote diode shorting technology (Hook et al., 1992) that enables profile measurements of v in layered soils. The probes were permanently installed at each site using a probe insertion/extraction tool kit. The probes used in this experiment consisted of one 5-segmented probe with 0- to 15-, 15- to 30-, 30- to 60-, 60- to 90-, and 90- to 120-cm segments, and eight 4-segment probes with 0- to 15-, 15- to 30-, 30- to 45-, and 45- to 60-cm segments.
Specific information about the operation of the MP-917 instrument was necessary at the time of this study to properly calculate v from measured time delay. These points are mentioned here for the benefit of other MP-917 users that may consider using site-specific calibrations. Measured time delay displayed by the unit is in nanoseconds (ns) and uncorrected. However, the unit stored measured time delay as instrument counts, which must be converted to nanoseconds and then corrected. This distinction is important to note when downloading data files and converting time delay to water content by site-specific calibration. Conversion of instrument counts to uncorrected time delay (Tm) in nanoseconds is obtained by multiplying counts by the instrument-specific calibration factor (UO). Corrected time delay (Tmc) in nanoseconds is obtained via Tmc = Tm/B - A, where A and B are segment-specific factory calibration coefficients. Values for A and B are related to segment length and geometry and are the same for a given segment depth interval and probe type, but differ segment to segment along the length of the probe. According to the manufacture, A and B coefficients vary by only 2% and, thus, average values are used for a specific probe type (ESI, personal communication, 1998). A 2% error in the coefficients A or B would result in a change in TDR-measured v ranging from 0.002 to 0.011 m3 m-3. The UO calibration factor and A and B coefficients can be obtained using the MP-917 Viewpoint software while connected to a probe.
Five calibration methods were evaluated in this study to determine which provided the most accurate measurement of v from TDR time delay measurements. The universal equation of Topp and Reynolds (1998) was chosen as a standard for comparison (Method 5) against other methods used in this work. Each method for determining v from measured time delay is described below.
Method 1. Volumetric soil water content stored by the MP-917 data logger at the time of measurement is calculated as in Eq. [4] using the factory calibration,
 | [6] |
Method 2. Volumetric soil water content is calculated based on the site-specific linear regression of sc, and the corresponding Tmc. This approach is analogous to the standard method of field calibration for the neutron probe (van Bavel et al., 1956), where neutron count ratio would be used rather than Tmc. The equation is written as,
 | [7] |
where the slope (m) and intercept (b) are site-specific regression coefficients that apply to all segments of a particular probe type. The work of Whalley (1993) and White et al. (1994) show that the intercept in such equations as Eq. [7] is related to the soil matrix properties (bulk density, dielectric of the solids, etc.) whereas the slope is primarily determined by the dielectric properties of soil water.
Method 3. This method uses the factory calibration equation, but rather than assuming the factory value of 1.55 for Ts/Ta in all soils, an average site-specific Ts/Ta is determined from the measured Tmc and corresponding sc over a range of moisture values. More precisely, since it has been shown in earlier work that the apparent dielectric of soil, Ka, is a function of travel time and that v
is linear, we ultimately determine values of Ka in situ for the soil at each site. The approach uses this linear relationship to solve for the x-intercept (Ts/Ta) where y(Tmc) equals zero and therefore Tmc/Ta is equal to Ts/Ta. It must be noted however, that the value of Ka for each site is determined based on the theoretical value of slope, which is assumed constant. The equation used in Method 3 is,
 | [8] |
thus,
 | [9] |
The average value for Ts/Ta is applied to all probe segments at a specific site.
Method 4. A linear regression was performed on all sc and Tmc data pairs collected at each of the nine sites to give one equation for estimating v from time delay measurements. This approach would serve as a regional calibration for a cross-section of soil types typical of the watershed. For our set of data the expression is,
 | [10] |
Method 5. This method is based on an empirical relationship between the apparent dielectric constant of a soil, Ka, and volumetric water content, v, developed by Topp et al. (1980). Using calibration data from numerous sources Topp and Reynolds (1998) have fitted a linear relationship as an alternative to the earlier polynomial curve (Eq. [1]) by performing a linear regression of K0.5a on v that gives rise to,
 | [11] |
In the paper by Topp and Reynolds (1998), K0.5a is expressed as apparent relative permittivity, 
0.5ra, or simply as T/Ta (as in Eq. 4), with the three terms being interchangeable and equivalent to Tmc in Eq. [7].
Statistical Analysis
Statistics for the mean, standard deviation and standard error of soil-core samples are given in Table 2. Regression was used to calculate the calibration equations in Methods 2 and 4. According to Webster (2001) the most important things to know regarding regression analyses are the slope (m), in defining the rate of change, and the correlation coefficient (R), an expression of the linear relationship between two variables. These data, as well as the intercepts (b) are given in Table 3 for all site-specific regression analyses. Statistics of the mean error or bias (ME), RMSE, and correlation coefficient (R) were used to determine which of the five methods best approximates measured values. Willmott and Wicks (1980) and Willmott (1981)(1982) raised concerns about the exclusive use of R in the context of measuring the correspondence between observed and predicted values. Therefore, we consider a combination of the statistical results (ME, RMSE, and R) in evaluating the five methods. The ME and RMSE statistics are defined as:
 | [12] |
 | [13] |
where P is water content predicted by one of the five methods, O is the corresponding observed soil core water content and n is the number of observations. Student's t-statistic ( = 0.05) was used where appropriate to compare mean values of soil water content between methods, RMSE values, and to test for differences among the slopes and intercepts from Method 2 at all study sites.
View this table:
[in this window]
[in a new window]
|
Table 3. Statistical analysis for linear regression coefficients (slope and intercept) and site-specific values of Ts/Ta at nine study sites.
|
|
|
RESULTS AND DISCUSSION
|
|---|
The results for each of the five methods for determining v from TDR time delay measurements are discussed in detail below. Linear regression analysis for the relationship between soil core water content (sc), and corrected time delay (Tmc) at four of the nine study sites are plotted in Fig. 2a through 2d. These sites were chosen from the nine to illustrate differences in regression analyses for different soil types. The regression lines for all nine sites are shown in Fig. 2e to illustrate the differences in slope and intercept. Figure 2f shows the regional (Method 4) regression analysis, which uses sc and Tmc data pairs from all nine sites. In Fig. 3a through 3e
we plot volumetric soil core water content vs. TDR-measured v for each of the five methods. Finally, we present the 1:1 relationships for the independent set of soil-core sample data in Fig. 4a through 4e
for each of the five methods.
View larger version (34K):
[in this window]
[in a new window]
|
Fig. 3. Comparisons between time domain reflectometry and soil-core water contents using the calibration data set for (a) Method 1, (b) Method 2, (c) Method 3, (d) Method 4, and (e) Method 5.
|
|
View larger version (30K):
[in this window]
[in a new window]
|
Fig. 4. Comparisons between time domain reflectometry and soil-core water contents using the independent data set for (a) Method 1, (b) Method 2, (c) Method 3, (d) Method 4, and (e) Method 5.
|
|
Method 1
Estimates of v obtained using the factory calibration (Eq. [6]) were compared with field observations resulting in RMSE values ranging from 0.032 to 0.078 m3 m-3 for the nine study sites (Table 4). In both the calibration data set and independent sample data, use of the factory calibration resulted in the highest and widest range of ME and RMSE. The data in Fig. 3a and 4a indicate that v tends to be overestimated at higher water contents using the factory calibration of Method 1. Of the five methods, the results from paired t tests indicated that there was a significant difference ( = 0.05) between the mean value of v from Method 1 compared with the mean value of measured soil-core water content for the available data sets.
Method 2
Once a linear regression was performed for each of the nine sites, the site-specific linear model was used to determine v from TDR time delay data at a given site. Plots for all regression analyses in Fig. 2e show that the slope and intercept varied among soil types. The slopes and intercepts for the regression equations were compared using the Student's t-statistic at a significance level of 0.05. There were significant differences among the slopes at all sites except Site 151. Only two of the nine sites, however, showed a significant difference among intercepts. The results from site-specific analyses at nine sites gave an average slope of 0.1082 ± 0.0272 (Table 3) and an average value of 1.33 ± 0.28 for Ts/Ta (x-intercept). Both the theoretical (0.1256) and experimental (0.1193) values for slope and the average value for Ts/Ta (1.55) reported by Hook and Livingston (1996) lie within the 95% confidence interval for the range of values that we obtained from the field.
In the work by Whalley (1993) and White et al. (1994), they showed that the intercept in such equations as Method 2 is related to the soil matrix dielectric and the slope is primarily determined by the dielectric properties of the water within the soil. Changes in slope would indicate that the water in the soil has changed electrical properties compared with bulk water and thus a different slope applies to water in the soil. The evidence presented in our work suggests that, for these soils, the electrical properties of soil water dominated the calibration. This may explain why the factory calibration, having a greater slope, tends to overestimate v. However, as the results in Method 3 show, solving for a site-specific value of Ts/Ta in the factory equation reduced this effect.
Of the five methods, Method 2 resulted in the highest correlation coefficient (R = 0.93) and the lowest RMSE value of 0.0314 m3 m-3 (Table 4) for the site-specific data at nine sites. Although Method 1 shows the highest correlation for the independent data set (R = 0.90), as in the calibration data it maintains the highest degree of error among the five methods (RMSE = 0.044 m3 m-3). Correlation coefficients for all site-specific analyses ranged from 0.86 to 0.93 (Table 3). The average RMSE in Method 2 was found to be significantly different from the other methods ( = 0.05) for the calibration data set.
The case for Method 2 was not quite as evident from the independent data analysis when compared with the calibration data set. Overall, the results for the independent data analyses for Methods 2, 3, and 4 were very similar and support the results of the calibration data analysis in that better estimates of v were achieved using site-specific information (Table 4). Interestingly, the pattern of data points for Methods 2 and 3, in both the calibration and independent data sets, are basically the same with the only difference being the location of the points relative to the 1:1 lines (Fig. 3b,c and 4b,c). This appears to be a consequence of using site-specific coefficients. The same similarity exist among the data patterns for Methods 1, 4, and 5 where general expressions where used to convert time delay to v (Fig. 3a,d,e and 4a,d,e). This is a rather surprising characteristic of the data considering that each of the general expressions were derived by very different means and from different soils.
Method 3
In Method 3 the average value for Ts/Ta in the factory equation was replaced with a site- specific value determined from soil-core moisture sample analysis. We considered this approach to determine whether legitimate values for Ts/Ta could be obtained in such a simple manner and if so, to what degree this might improve the measurement of soil water content. Analyses of the data show that the values we obtained for Ts/Ta (Table 3) are comparable with those reported in the literature for similar soils (Hook and Livingston, 1995; Timlin and Pachepsky, 1996; Yu et al., 1999). The regression lines for the data plotted in Fig. 3c and 4c show a close fit to the 1:1 relationship compared with other methods, although there is scatter in the data. This suggest that, although the factory calibration equation in Method 1 may be considered theoretically valid, determining site-specific values for Ts/Ta will improve the accuracy of measurement and reduce measurement bias. The results further support our view that knowledge of the x-intercept (Ts/Ta) among site-specific linear calibration methods is critical in determining absolute water content, which again emphasizes the need for very low soil water-content data to obtain an accurate x-intercept value. The RMSE for Method 3 ranged from 0.032 to 0.057 m3 m-3 and the mean error (bias) was equal to zero to two decimal places (Table 4).
Method 4
A considerable amount of research has been aimed at finding a general or universal equation for determining soil water content from TDR data, and thus, we considered this type approach for the nine study sites in this work. The regression equation in Fig. 2f was derived from sample data at all nine sites and used as the regional linear model in Method 4. An R of 0.88 was determined for calibration data. In the calibration data set, the smallest mean difference was obtained using Method 4 (ME = 3.25 x 10-5 m3 m-3). In the independent data analysis, the values for RMSE for each of the three field calibration methods were quite close and ranged from 0.0307 to 0.0348 m3 m-3, with Method 4 having the smallest RMSE equal to 0.0307 m3 m-3, but also the highest mean error (Table 4). Although Method 2 had the lowest and most narrow range of error on a site-specific basis, results from the independent data set indicate that the use of Method 4 would be sufficient for similar soil types within the watershed where site-specific information was yet to be obtained.
Method 5
The results from Topp and Reynolds linear model (Eq. 11) are plotted in Fig. 3e and 4e for the calibration and independent data sets, respectively. In both Fig. 3e and 4e, the TDR-measured v values determined by this method compare well with measured sc. The correlation is high between the data (R = 0.87 and 0.89) with relatively little mean error or bias (ME = 0.004 and -0.01 m3 m-3) for the calibration and independent data sets, respectively. As in Methods 3 and 4, however, there was a greater degree of scatter in the data as indicated by slightly higher RMSE values for Method 5 (0.0326 to 0.0581 m3 m-3) compared with Method 2 (0.0314 to 0.0422 m3 m-3) among the nine sites (Table 4). However, the use of Topp and Reynolds linear model (Method 5) would certainly be preferable to using the factory calibration if no site-specific analyses were available.
Findings from our field data analyses are consistent with those of Topp and Reynolds (1998) where a linear relationship between v and TDR time delay from their data sources gave an average slope of 0.115 and a value of 1.53 for Ts/Ta. For example, the linear equation we fitted to the data at Site LW02 showing v = 0.1096 (Tmc) - 0.1768 is very close to their equation (Method 5), where v = 0.115 (Tmc) - 0.176. Thus, we agree with their suggestion that fitting a linear relationship where possible should offer an improvement over fitting a polynomial calibration curve (Eq. [1]) since the linear function has only two parameters to fit and is somewhat easier to use. In addition, we found that because of the differences in slope and intercept among the regressions, the calibration data set requires very low water content values to determine absolute water content. The work of Topp and Ferre (2000) made an important note of this as well.
|
CONCLUSIONS
|
|---|
The primary objective of this study was to quantify any improvement that site-specific linear calibration may have over the factory calibration using several study sites (soil types) in the LWREW in south central Oklahoma. Three methods of field calibration were investigated and the results compared with the factory supplied calibration and results using the universal equation of Topp and Reynolds (1998). When compared with the factory calibration, all four methods improved the measurement of soil water content, with site-specific linear regression (Method 2) providing the best results. Overall, Method 2 was consistent in having the smallest measurement error when compared with other methods. Furthermore, because there were significant differences among the regression coefficients (slope) for all but one field site, we believe it is preferable to perform site-specific calibrations when using the linear relationship between v and K0.5a as measured by TDR for improved accuracy. However, use of the universal equation in Method 5 for converting TDR time delay measurements to v would certainly be a good alternative to the factory calibration if no site-specific calibrations were available.
We have shown, at nine field sites with different soil characteristics, that use of a site-specific linear regression approach reduces measurement error, as well as the range of error, when compared with soil moisture values obtained using the factory calibration. We also found that in collecting soil moisture samples for the regression analysis, it is important that the data set include very low moisture samples to determine absolute water content. It should be emphasized that considerable care should be taken during the collection of soil-core calibration samples in an effort to minimize the gravimetric sample error. For example, a small error in the measurement of bulk density can have considerable effects on calculating the volumetric water content. Analysis of the gravimetric sample data showed that the standard error of measurement can range from 0.0015 to 0.0459 m3 m-3. Thus, with the smallest RMSE being 0.0314 m3 m-3 in TDR measurements using Method 2, this would suggest that once calibrated, the TDR may be less error prone than the gravimetric method for v measurements (G.C. Topp, personal communication, 2001).
It can be concluded from this work that measured dielectric data should be calibrated to the water content of the field soils involved for determining absolute water content and that the linear relationship between v and the TDR-measured travel time affords a simple and effective means for obtaining site-specific calibrations over a practical range of soil water content.
|
ACKNOWLEDGMENTS
|
|---|
The authors express their sincere thanks to Mr. Alan Verser and Mr. Mark Smith for their field, lab, and computer work. We greatly appreciate the recommendations of the reviewers for improvements to the manuscript. We are also thankful for the cooperation by numerous private landowners in allowing us access to their property to do the essential field work.
|
NOTES
|
|---|
1 Trade names and company names are included for the benefit of the reader and do not imply any endorsement or preferential treatment of the product by the authors or the USDA. 
Received for publication October 15, 2001.
|
REFERENCES
|
|---|
- Allen, P.B., and J.W. Naney. 1991. Hydrology of the Little Washita River Watershed, Oklahoma, Data and Analyses. ARS-90. USDA-ARS-NAWQL, Durant, OK.
- Cassel, D.K., R.G. Kachanoski, and G.C. Topp. 1994. Practical considerations for using A TDR cable tester. Soil Technol. 7:113–126.
- Chaubey, I., C.T. Haan, S. Grunwald, and J.M. Salisbury. 1999. Uncertainty in the model parameters due to spatial variability of rainfall. J. Hydrol. (Amsterdam) 220:48–61.
- Chan, C.Y., and R.J. Knight. 1999. Determining water content and saturation from dielectric measurements in layered materials. Water Resour. Res. 35(1):85–93.
- Dirksen, C., and S. Dasberg. 1993. Improved calibration of time domain reflectometry for soil water content measurements. Soil Sci. Soc. Am. J. 57:660–667.[Abstract/Free Full Text]
- Gardner, W.H. 1965. Water Content. p. 82–125. In C.A. Black et al. (ed.) Methods of Soil Analysis, Part I. 1st ed. Agron. Monogr 9. ASA, Madison, WI.
- Grant, E.H., R.J. Sheppard, and G.P. South. 1978. Dielectric behavior of biological molecules in solution. Oxford University Press, Oxford.
- Hanson, J.D., K.W. Rojas, and M.J. Shaffer. 1999. Calibrating the root zone water quality model. Agron. J. 91:171–177.[Abstract/Free Full Text]
- Heathman, G.C. 2001. Estimating root zone soil water content using limited soils information and surface soil moisture data assimilation. Ph.D. diss. Univ. of Oklahoma, Norman, OK.
- Herkelrath, W.N., S.P. Hamburg, and F. Murphy. 1991. Automatic, real-time monitoring of soil moisture in a remote field area with time domain reflectometry. Water Resour. Res. 27:857–864.
- Hilhorst, M.A. 1998. Dielectric characteristics of soil. Ph.D. diss. Wageningen Agricultural University, Wageningen, The Netherlands.
- Hook, W.R., N.J. Livingston, Z.J. Sun, and P.B. Hook. 1992. Remote Diode Shorting Improves Measurement of Soil Water by Time Domain Reflectometry. Soil Sci. Soc. Am. J. 56:1384–1391.[Abstract/Free Full Text]
- Hook, W.R., and N.J. Livingston. 1995. Reducing propagation velocity measurement errors in time domain reflectometry determinations of soil water. Soil Sci. Soc. Am. J. 59:92–96.[Abstract/Free Full Text]
- Hook, W.R., and N.J. Livingston. 1996. Errors in converting time domain reflectometry measurements of propagation velocity to estimates of soil water content. Soil Sci. Soc. Am. J. 60:35–41.[Abstract/Free Full Text]
- Jackson, T.J., D.M. Le Vine, A.Y. Hsu, A. Oldak, P.J. Starks, C.T. Swift, J.D. Isham, and M. Haken. 1999. Soil moisture mapping at regional scales using microwave radiometry: The Southern Great Plains Hydrology Experiment. IEEE Trans. Geosci. Remote Sens. 37:2136–2151.
- Jacobsen, O.H., and P. Schjønning. 1993. Field evaluation of time domain reflectometry for soil water measurements. J. Hydrol. (Amsterdam) 151:159–172.
- Ledieu, J., P. De Ridder, and A. Dautrebande. 1986. A method for measuring soil moisture by time-domain reflectometry. J. Hydrol. (Amsterdam) 88:319–328.
- Ma, L., H.D. Scott, M.D. Shaffer, and L.R. Ahuja. 1998. RZWQM simulations of water and nitrate movement in a tall fescue field. Soil Sci. 163:259–270.
- Pepin, S., N.J. Livingston, and W.R. Hook. 1995. Temperature-dependent errors in time domain reflectometry determination of soil water. Soil Sci. Soc. Am. J. 59:38–43.[Abstract/Free Full Text]
- Ponizovsky, A.A., S.M. Chudinova, and Y.A. Pachepsky. 1999. Performance of TDR calibration models as affected by soil texture. J. Hydrol. (Amsterdam) 218:35–43.
- Roth, C.H., M.A. Malicki, and R. Plagge. 1992. Empirical evaluation of the relationship between soil dielectric constant and volumetric water content as the basis for calibrating soil moisture measurement. J. Soil Sci. 43:1–13.
- Silberstein, R.P., M. Sivapalan, and A. Wyllie. 1999. On the validation of a coupled water and energy balance model at small catchment scales. J. Hydrol. (Amsterdam) 220:149–168.
- Smith-Rose, R.L. 1933. The electrical properties of soil for alternating currents at radio frequencies. Proc. R. Soc. London, Ser. A 140:359–377.
- Sun, Z.L., G.D. Young, R.A. McFarlane, and B.M. Chambers. 2000. The effect of soil electrical conductivity on moisture determination using time-domain reflectometry in sandy soil. Can. J. Soil Sci. 80:13–22.
- Timlin, D.J., and Y.A. Pachepsky. 1996. Comparison of three methods to obtain the apparent dielectric constant from time domain reflectometry wave traces. Soil Sci. Soc. Am. J. 60:970–977.[Abstract/Free Full Text]
- Topp, G.C., and J.L. Davis. 1985. Measurements of soil water content using time domain reflectometry (TDR): A field evaluation. Soil Sci. Soc. Am. J. 49:19–24.[Abstract/Free Full Text]
- Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16(3):574–582.
- Topp, G.C., and P.A. Ferre. 2000. In situ devices for soil water content. GEWEX/BAHC International Workshop on Soil Moisture Monitoring, Analysis and Prediction for Hydrometeorological and Hydroclimatological Applications. 16–18 May 2000. International GEWEX Project Office Publication Ser. No. 35. International GEWEX, Norman, OK.
- Topp, G.C., and W.D. Reynolds. 1998. Time domain reflectometry: A seminal technique for measuring mass and energy in soil. Soil Tillage Res. 47:125–132.
- Van Bavel, C.H.M., N. Underwood, and R.W. Swanson. 1956. Soil moisture measurement by neutron moderation. Soil Sci. 82:29–41.
- Wang, J.R., and T.J. Schmugge. 1980. An empirical model for the complex dielectric permittivity of soils as a function of water content. IEEE Trans. Geosci. Remote Sens. GE-18(4):289–295.
- Weast, R.C. (ed.) 1982. CRC Handbook of Chemistry and Physics. 63rd ed. CRC Press, Inc., Boca Raton, FL.
- Webster, R. 2001. Statistics to support soil research and their presentation. Eur. J. Soil Sci. 52:331–340.
- Whalley, W.R. 1993. Considerations on the use of time-domain reflectometry (TDR) for measuring soil water content. J. Soil Sci. 44:1–9.
- White, I., J.H. Knight, S.J. Zegelin, and G.C. Topp. 1994. Comments on ‘Considerations on the use of time-domain reflectometry (TDR) for measuring soil water content’ by W.R. Whalley. Eur. J. Soil Sci. 45:503–508.
- Willmott, C.J. 1981. On the validation of models. Physical Geographer 2:184–194.
- Willmott, C.J. 1982. Some comments on the evaluation of model performance. Bull. Am. Meteorol. Soc. 63:1309–1313.
- Willmott, C.J., and D.E. Wicks. 1980. An empirical method for the spatial interpolation of monthly precipitation within California. Physical Geographer 1:59–73.
- Young, M.H., J.B. Fleming, P.J. Wierenga, and A.W. Warrick. 1997. Rapid laboratory calibration of time domain reflectometry using upward infiltration. Soil Sci. Soc. Am. J. 61:707–712.[Abstract/Free Full Text]
- Yu, C., Warrick, A.W., and Conklin, M.H. 1999. Derived functions of time domain reflectometry for soil moisture measurement. Water Resour. Res. 35:1789–1796.
This article has been cited by other articles:
|
|
|
|
 
M. S. Seyfried, L. E. Grant, E. Du, and K. Humes
Dielectric Loss and Calibration of the Hydra Probe Soil Water Sensor
Vadose Zone J.,
November 11, 2005;
4(4):
1070 - 1079.
[Abstract]
[Full Text]
[PDF]
|
|
|
TOP
ABSTRACT
INTRODUCTION
