Agronomy Journal 95:365-379 (2003)
© 2003 American Society of Agronomy
SOIL MANAGEMENT
Using the Dual-Pathway Parallel Conductance Model to Determine How Different Soil Properties Influence Conductivity Survey Data
S. M. Lesch* and
D. L. Corwin
USDA-ARS George E. Brown, Jr., Salinity Lab., 450 West Big Springs Rd., Riverside, CA 92507-4617
* Corresponding author (slesch{at}ussl.ars.usda.gov)
Received for publication March 29, 2002.
 |
ABSTRACT
|
|---|
The correlation structure between apparent soil electrical conductivity (ECa) and various soil properties can often appear radically dissimilar in different field surveys. Ideally, some type of methodology for survey data validation should be developed that can predict the expected correlation structure between ECa survey data and various soil properties, given information about the soil properties themselves. In this paper, we review an existing model for ECa and hypothesize that this model can be used to accurately predict the expected correlation structure between ECa data and multiple soil properties of interest (such as soil salinity, saturation-paste percentage, and soil water content). Our objective is twofold: (i) to demonstrate how this model can be employed to produce the expected correlation structure and (ii) to extend this ECa model to handle survey data collected under low water content situations by dynamically adjusting the model's assumed water content function. This adjustment can be estimated using acquired ECa signal and soil sample data, and its statistical significance can be determined for each specific survey situation. We demonstrate both of these techniques using acquired electromagnetic induction signal data and measured soil properties of interest from 12 different field salinity surveys performed in California and Colorado and in Alberta, Canada. Results from these 12 surveys suggest that the ordinary model is able to accurately predict the expected correlation structure between conductivity and soil property when the water content is near field capacity and that the dynamically adjusted model is able to substantially improve the accuracy of the predicted correlation structure when the water content is significantly below field capacity.
Abbreviations: CalcECa, calculated soil electrical conductivity • DPPC, dual-pathway parallel conductance (model) • Dy-DPPC, dynamic water content partitioning (model) • ECa, apparent soil electrical conductivity • ECe, electrical conductivity of the saturated soil extract • ECwc, specific electrical conductivity of the continuous soil water phase • ECws, specific electrical conductivity of the series-coupled soil water phase • EM, electromagnetic induction • EMavg, average electromagnetic induction • SP, saturation percentage • 
g, gravimetric soil water content • w, volumetric soil water content • wc, volumetric soil water content in the continuous liquid pathway • ws, volumetric soil water content in the series-coupled pathway • 
b, bulk density • 
wc, adjusted volumetric soil water content of continuous liquid pathway • ws, adjusted volumetric soil water content of series-coupled pathway
|
INTRODUCTION
|
|---|
WITHIN THE LAST DECADE, the collection of spatial soil electrical conductivity data has played an increasingly important role in precision-farming research. The collection of such data typically focuses on the assessment of spatial variation in one or more soil properties, as inferred by the observed spatial variation in the ECa survey data. Depending on the specific survey application, the target variable of interest is usually soil salinity, soil texture, and/or soil water content although sometimes information about additional soil properties may also be ascertained (i.e., organic matter, clay content, sodium adsorption ratio, B, etc.).
There are numerous technical articles that document the relationships between ECa and various soil physicochemical properties, including soil salinity (Williams and Baker, 1982; Rhoades et al., 1989; Slavich and Petterson, 1990; Hendrickx et al., 1992; Rhoades, 1992, 1996a, 1996b; Lesch et al., 1995a);, clay content (Williams and Hoey, 1987; Cook et al., 1992), depth to clay layers (Doolittle et al., 1994), nutrient status (Suddeth et al., 1995), sand deposition (Kitchen et al., 1996), and moisture content (Kachanoski et al., 1988; Sheets and Hendrickx, 1995). Additionally, there are articles documenting the use of conductivity survey information for yield mapping (Jaynes et al., 1995), determining salt loading and field irrigation efficiency (Rhoades et al., 1997), estimating leaching and salt loading (Corwin et al., 1996, 1999; Rhoades et al., 1999a), estimating deep drainage (Triantafilis et al., 1998), and designing optimal salinity sampling and monitoring strategies (Lesch et al., 1995b, 1998). A comprehensive review of the various methods of soil salinity assessment via electrical conductivity measurements is given in Rhoades et al. (1999b) and Hendrickx and Kachanoski (2002), and the use of conductivity survey information for precision-farming applications is discussed in Rhoades et al. (1999b) and Corwin and Lesch (2003).
Particular interest in any given ECa survey is often focused toward ensuring that the acquired ECa data correlate well with the prespecified target soil variable. For example, in a soil salinity survey, one generally attempts to maximize the correlation between salinity and ECa by minimizing the corresponding variation in soil texture and water content using different area substratification schemes (for minimizing texture variation) or timing strategies (for minimizing water content variation). In spite of these efforts, considerable variation is sometimes observed in the observed correlation between salinity and ECa. Indeed, as indicated by the above-mentioned references, ECa often correlates to some degree with several different soil properties. Furthermore, the strength of these observed correlation estimates can vary widely from one survey to the next. To a certain extent, these apparent inconsistencies have resulted in some unfortunate confusion in the general soils literature with respect to how well different soil properties are expected to correlate with ECa data.
Rhoades et al. (1989) developed a model for ECa based on data collected across the arid southwestern United States. This model was developed to predict the effects that soil salinity, soil texture, bulk density (b), and soil water content have on soil conductivity signal data. This model was originally intended to be used primarily for the prediction of soil salinity [expressed as electrical conductivity of the saturated soil extract (ECe)], given measurements of both the soil conductivity and remaining primary soil properties (texture, b, and water content). However, because this model is capable of simultaneously describing multiple soil property effects, we hypothesized that it might be successfully used to explain the diverse variation in observed ECa–soil property correlation estimates.
The purpose of this paper is twofold. First, we describe how the ECa model developed by Rhoades et al. (1989) can be used to accurately predict the expected correlation structure between ECa data and multiple soil properties of interest for an arbitrary survey process. The methodology that is developed to predict this correlation structure serves both as a useful procedure for survey data validation and, in a broader sense, a quantitative technique for understanding how different soil properties influence (and hence correlate with) the acquired ECa data. Furthermore, this technique is shown to be generally reliable, provided the relative soil water content (across the survey area) is not significantly below field capacity.
Second, we show how this ECa model can be extended to handle survey data collected under low water content situations by dynamically adjusting the assumed water content partitioning function specified in the model. This partitioning function can be estimated using acquired ECa survey and soil sample data, and its statistical significance can be determined for each specific survey situation. Under especially low water content situations, this adjustment can result in a substantial improvement in the accuracy of the predicted correlation structure. We demonstrate these results using data from 12 different salinity surveys performed over the last 10 yr in California and Colorado and in Alberta, Canada.
|
THEORY
|
|---|
In the following section, a model for ECa, originally developed by Rhoades et al. (1989), is reviewed. This model is then incorporated into a data validation procedure designed to be performed on measured ECa and soil sample survey data. This procedure produces the expected correlation levels between the acquired conductivity data and measured soil properties of interest and hence simultaneously addresses the expected ECa–soil variable question raised in the introduction. Finally, the original model introduced by Rhoades and his colleagues is extended to handle data collected under low water content survey conditions.
A Review of the Dual-Pathway Parallel Conductance Model
Rhoades et al. (1989) introduced a model describing the expected electrical conductivity of a mixed soil–water system, based on the partitioning of the system into three separate current-flow pathways acting in parallel. These pathways are illustrated in Fig. 1
and are as follows: (i) a conductance pathway traveling through alternating layers of soil particles and soil solution, (ii) a conductance pathway traveling through the continuous soil solution, and (iii) a conductance pathway traveling through or along the surface of soil particles in direct and continuous contact. Conceptually, the first pathway can be thought of as a solid-liquid, series-coupled element. Likewise, the second and third pathways represent continuous liquid and solid elements, respectively.
View larger version (95K):
[in this window]
[in a new window]
|
Fig. 1. The three theoretical current-flow pathways within a mixed soil–water system, as originally described by Rhoades et al. (1989): (1) the series-coupled pathway, (2) the continuous liquid pathway, and (3) indurated solid phase pathway.
|
|
Mathematically, this model can be written as:
 | [1] |
where
As reported by Rhoades et al. (1989), experimental work demonstrated that the conductance contributed by the indurated solid phase was negligible, i.e.,
Additionally, because volumetric soil water content (w) = ws + wc, Eq. [1] can be reduced to:
 | [2] |
which essentially represents a dual-pathway parallel conductance (DPPC) current flow system. Hence, Eq. [2] will be hereafter referred to as the DPPC model.
An important relationship inherent in the DPPC model is that the combined soil electrical conductivity (ECw) of both the continuous solution (ECwc) and soil–water interface (ECws) may be expressed as:
 | [3] |
Additionally, the expected relationship between ECw and soil salinity (ECe) is assumed to be
 | [4] |
where SP represents the saturation percentage of the soil. This latter relationship is only strictly valid for chloride-salt systems. However, this approximation has been found to work reasonably well for most mixed chemistry systems, as shown by Rhoades et al. (1989)( 1999b). Solving Eq. [3] for ECw yields
 | [5] |
where 
= ws/w. However, in Rhoades et al. (1989), an additional assumption of solution conductivity equilibrium was made, i.e., ECw = ECws = ECwc. Rhoades and colleagues argued that this assumption should be reasonable, provided the field water content was at or near field capacity.
Given the additional assumption of equilibrium, the DPPC model further simplifies to:
 | [6] |
where the parameters ss and ECss are abbreviated as s and ECs, respectively. This is the nonlinear form of the DPPC equation commonly presented in many of the technical salinity articles by Rhoades (1992)(1996b).
The original purpose of Eq. [6] was to provide a practical means of estimating soil salinity levels, given measurements of both ECa data and secondary soil properties that influence ECa (i.e., soil properties other than salinity). According to Eq. [6], the five parameters that combine together to determine ECa are w, s, ws, ECs, and ECw. According to Rhoades et al. (1989), these five theoretical parameters could be suitably related to the following four measurable soil properties: ECe (soil salinity), SP, gravimetric soil water content (g), and b, using the following assumed relationships and/or empirical, approximating equations:
Assumed relationships:
 | [7a] |
 | [7b] |
 | [7c] |
Empirical, approximating equations:
 | [7d] |
 | [7e] |
for w > 0.0305 and SP > 25. (In practical applications, when w < 0.0305 and/or SP < 25, then ws is defined to be equal to w and/or ECs is set equal to 0.041, respectively.) Rhoades et al. (1989) also suggested that the b could be reasonably estimated from the SP in most field survey conditions using the following linear relationship:
 | [8] |
Hence, in a practical survey application, Eq. [6] can be solved provided one obtains either accurate field estimates or, preferably, laboratory measurements of ECe, SP, and g. For the remainder of this paper, we will refer to such a solution as the calculated ECa (CalcECa).
It should be noted that Eq. [6] is designed to produce an estimate of the CalcECa referenced to 25°C for the specific depth zone that the soil properties are sampled from. This estimate should correspond on a one-to-one basis to a direct ECa measurement acquired from the same depth zone (after applying an appropriate temperature compensation). For example, there should be a one-to-one correspondence between this estimate and a conductivity measurement acquired using an insertion four-electrode probe (Rhoades et al., 1989). However, this estimate will not generally exhibit a one-to-one correspondence with an indirect measurement of ECa, such as conductivity signal data acquired using a noninvasive electromagnetic induction (EM) meter (like the Geonics EM-38 m).1 There are numerous reasons for this: (i) EM signal data meters obtain a nonlinear, depth-weighted ECa signal response that is not isolated to a particular depth zone; (ii) the Geonics meter in particular begins to exhibit a partial breakdown in the low induction number approximation (between apparent and true conductivity) when the true terrain conductivity exceeds 100 mS/m; and (iii) variations in the macro surface geometry of the soil environment (such as those induced by a typical bed-furrow structure) tend to exhibit a pronounced effect on the magnitude of the near surface–weighted ECa signal readings (McNeill, 1980; Lesch et al., 1995a; Rhoades et al., 1999b). (The measurement scales are also different: The EM-38 signal is expressed in mS/m, and the CalcECa is typically expressed in dS/m.) Nonetheless, the correlation between the CalcECa and measured EM signal response should be quite high, provided a large enough depth zone is sampled (
about 1 m) and the position of the instrument relative to the bed-furrow environment is kept constant throughout the survey process (Lesch et al., 1995a).
Definition and Application of a DPPC Correlation Analysis
The original DPPC equation was designed to be used as an ECe prediction model, given measurements of ECa and either measurements or estimates of the remaining primary soil properties (SP, w, and b). However, this equation can also be used in a different, yet equally important manner. Assuming that the underlying model is valid, Eq. [6] can be used in a general-purpose validation procedure for survey data, as described below.
Consider a typical field-scale salinity survey conducted using some type of soil conductivity instrument (such as a Geonics EM-38 meter). Suppose that this process is performed similar to the methodology described in Lesch et al. (1995a)(1995b); i.e., a large number of EM survey sites are acquired across the field, and then a few select sites are identified for calibration soil sampling. Additionally, assume that the soil sample data from these calibration sites are then analyzed for ECe, SP, and g. Based on this sample data, what can we infer about the expected correlation between these measured soil properties and the EM-38 signal data?
Obviously, the correlation between the EM signal data and any measured soil property can be directly calculated. However, as alluded to in the introduction, these correlation estimates can change quite radically from one field to the next and therefore often appear inconsistent and/or inconclusive. Clearly, a more desirable approach would be to examine the soil property data directly and then try to derive a general relationship relating these data observations to the acquired signal data.
In essence, this is exactly what the DPPC equation is designed to do. It takes as input a set of primary (i.e., defining) soil properties and produces as output a calculated conductivity (CalcECa). If this equation can be used produce an accurate estimate of the true (unknown) ECa, then it should also be highly correlated with the measured ECa (i.e., the EM sensor readings, acquired at the same calibration locations). Therefore, if this is indeed the case, then the expected correlation between the EM data and any particular primary soil property should be quite similar to the observed correlation between the CalcECa and that same soil property.
This correlation concept is shown graphically by the path diagram displayed in Fig. 2
. In this diagram, ECa,[d] represents the true ECa of the soil within a specific depth zone [d]. There are two ways to ascertain this value: (i) measure it directly or indirectly using some type of survey instrument (EM) or (ii) calculate it from the associated primary soil property measurements using an appropriate model (CalcECa). Both of these approaches are subject to some degree of error (
1 and 2). For example, errors can occur with respect to the survey data due to instrument miscalibration, signal attenuation, or signal penetration below the depth zone [d] of interest. Likewise, errors may enter into the modeling process due to unrealistic or improper modeling assumptions or less-than-adequate modeling approximations, etc. However, in an ideal situation, we expect these errors to be small and hence the EM and CalcECa data to be highly correlated. Mathematically, this can be written as:
 |
View larger version (7K):
[in this window]
[in a new window]
|
Fig. 2. Path diagram showing the correlation relationships between measured primary [electrical conductivity of the saturated soil extract (ECe), saturation percentage (SP), and gravimetric soil water content (g)] and secondary (Q) soil properties, calculated soil electrical conductivity (CalcECa), measured electromagnetic induction survey data, and true soil electrical conductivity (ECa,[d]) for depth zone [d].
|
|
In turn, the CalcECa data will exhibit some specific degree of correlation with each of the defining primary soil properties that determine it. These correlation values can be expressed as:
Additionally, this CalcECa may well correlate with some other soil property (Q) that does not directly determine it. This can occur if the secondary soil property happens to correlate with one or more of the primary soil properties; thus, an induced correlation is said to be present. This secondary correlation can be expressed as:
However, given these correlation estimates, the expected values of the correlation estimates between the EM signal data and each soil property can be shown to be
 | [9a] |
 | [9b] |
 | [9c] |
 | [9d] |
(a proof of this result is given in Appendix A.1). In other words, the expected correlation between the EM signal data and a specific soil property is simply the product of the CalcECa–soil variable correlation multiplied by the EM–CalcECa correlation.
Two important conclusions can be immediately deduced from the above results. First, the partitioning of the correlation structure lends itself naturally to an ideal data validation strategy, herein referred to as a DPPC correlation analysis. In a DPPC correlation analysis, each of the correlation estimates described above are calculated, in addition to each observed EM–soil property correlation estimate. If an accurate ECa model is employed and the errors associated with the EM signal data are minimal, then two results should occur. First, 
should be reasonably close to 1. Second, each observed EM–soil property correlation estimate should be reasonably close to its expected estimate (as defined above). When these two results do indeed occur, the overall survey process is said to exhibit a high degree of internal data validity and consistency.
Second, as the correlation between CalcECa and EM approaches unity, the expected EM–soil property correlation estimates reduce to the observed CalcECa–soil property correlation estimates. This implies that when an accurate soil conductivity model is used, the expected EM–soil property correlation estimates can be approximated by multiplying the observed CalcECa–soil property estimates by some reasonable value (i.e., 0.9, 0.95, etc.). This is an important point; i.e., this methodology can be used to estimate an expected correlation between EM and soil property in any given field (provided some soil sample data has been collected) before an EM survey is undertaken.
Modification of the DPPC Equation for Low Water Content Situations
Water contents substantially in excess of field capacity are not typically of concern in most practical field survey applications because EM or four-electrode surveys are not easily conducted across wet fields. However, survey data sometimes do get collected across fields with water contents significantly below field capacity. In practice, this can occur due to unavoidable timing or scheduling conflicts and/or misinformation about recent irrigation events. Additionally, unforeseen excessive variation in field water content levels can be encountered in some fields due to poor irrigation uniformity.
In general, we have found the DPPC correlation analysis procedure just described to provide a reliable data validation methodology in most salinity survey studies. However, we have also found that this methodology can perform poorly under unusually dry survey conditions. We believe that this poor performance normally occurs due to the attenuating effect (i.e., the drop-off) in ECa induced by the depletion of the water within the series-coupled soil water pathway. Hence, a need to extend the previously derived DPPC model to handle low water content situations clearly exists. Furthermore, a more robust model should prove useful for determining the specific degree of water content influence on conductivity signal data collected under low water content situations.
The ordinary DPPC model can be made more robust for low water content situations by redefining the ws, wc, and w water content–partitioning relationship as follows:
 | [10] |
where
 | [11] |
 | [12] |
and ws and wc are the adjusted volumetric soil water contents of series-coupled pathway and continuous liquid pathway, respectively, and 
is defined to be a function of the apparent water content. We have found that good results are obtained if is referenced to the water content relative to an estimate of the approximate field capacity (Rhoades et al., 1989). More specifically, assuming that the water content at field capacity (fc) can be approximated as:
 | [13] |
then the scaled water content relative to field capacity (
w) can be defined as:
 | [14] |
In turn, can be defined to be a suitable function of w. One simple, appealing equation that can be used to define is the logistic function:
 | [15] |
where ß0 and ß1 represent hyperparameters that control the shape of the logistic curve. Note that the use of this function restricts to lie in the (0,1) interval, with the hyperparameters essentially controlling the degree of apparent water content partitioning.
Based on the approach described above, a new version of the DPPC model can be derived (by replacing ws and wc with ws and wc in Eq. [6]), herein referred to as a dynamic water content partitioning model (Dy-DPPC). This Dy-DPPC model can be expressed as:
 | [16a] |
or equivalently as
 | [16b] |
where the ws and wc parameters have been replaced with the relationships shown in Eq. [11] and [12]. The effect of incorporating this parameter into the ordinary DPPC model is made clear by Eq. [16b]. First, as 
0, the slope term of Dy-DPPC model reduces to 0 (implying that the apparent conductivity signal strength will be significantly reduced as the soil dries out). Second, as 1, this Dy-DPPC model reduces exactly to the ordinary DPPC model (implying that can be conditioned to have no effect when the soil is at or near field capacity).
As defined above, the Dy-DPPC model depends critically on the value of , which from Eq. [15], is defined to be:
 | [17] |
where ß0 and ß1 represent empirical fitting parameters. Figure 3
displays two hypothetical curves, and each curve is designed to produce a value of = 0.5 when the scaled water content also equals 0.5 (w = 0.5). The different shapes of these curves are controlled by the magnitude of the ß1 parameter, as indicated in Fig. 3. The 0.5 curve midpoint values are produced by the ß0 parameter, specifically by setting ß0 = -0.5ß1. Figure 4
shows the corresponding water content repartitioning effects on the ws/w and wc/w ratios induced by these assumed functions and contrasts these with ws/w and wc/w ratios assumed in the ordinary DPPC model.
It is impossible to determine in advance the exact values of ß0 and ß1 in any particular survey situation. However, reasonable bounds can be placed on these parameters, and then the acquired survey and soil sample data can be used to estimate these values via a suitable optimization approach. The approach used here is simply a detailed grid search over the assumed parameter space (as described in the Methods section). Such an optimization approach does not produce any standard error estimates for ß0 and ß1. However, when the correlation is found to increase (over the correlation estimate produced using the ordinary DPPC model calculations), an approximate F test can still be constructed to determine if the increase in the correlation estimate is statistically significant (details concerning this test are given in Appendix A.2).
|
METHODS
|
|---|
Field Survey Information
Survey data from 12 fields are discussed in this paper. These 12 fields have been chosen from a larger database (of 100+ fields) compiled by the Salinity Laboratory over the last decade and represent the range of conditions typically encountered when performing soil salinity surveys.
Table 1 lists the field ID codes, survey area size, and basic soil taxonomy of each survey area. Table 2 lists the types of conductivity and soil variable information collected across these 12 fields. Only Geonics EM-38 conductivity signal data is analyzed although the analysis methods presented here are applicable to any EM and/or insertion four-electrode ECa signal data. The primary soil properties considered are salinity (ECe, dS/m); SP (%); the estimated w (ratio: estimated from the SP and g); and in one field, the b (g/cm3). Some secondary soil properties were also measured in a few of the fields; these secondary properties include the sodium adsorption ratio, B (g/L), and percentage clay (%).
Basic EM-38 and soil sample summary statistics are given in Tables 3a and 3b for each field. These statistics include the calculated mean, standard deviation, minimum and maximum reading for each measured variable, along with the number of samples acquired. The number of EM-38 readings in all but one case ranges from 100 to >4000 while the number of soil sample sites ranges from 12 to 40. This oversampling of EM signal data is typical of soil salinity surveys; the goal is to use the abundant, rapidly acquired EM data to infer information about the much more difficult to acquire (i.e., expensive and time consuming to sample) soil data. In most cases, the sampling strategies for the selection of soil sampling sites were developed from model-based site selection techniques similar (or identical) to those described in Lesch et al. (1995b). Additionally, in all but one case, soil samples were collected to a depth of 1.2 m at 0.3-m increments. For the sake of brevity, only the 0- to 1.2-m bulk average data have been analyzed (as reported in Tables 3a and 3b).
Table 3c shows how the 12 fields were divided into two separate groups (A and B), based on each field's calculated soil water content relative to field capacity (100 x w). The six Group A fields shown in Table 3a represent surveys where the relative water content data appears to be at or near field capacity. In contrast, the six Group B fields all exhibited relative water content levels significantly below the calculated field capacity. We will show (in the Results section) that the soil water content relative to field capacity represents a critically important parameter when performing a DPPC correlation analysis.
View this table:
[in this window]
[in a new window]
|
Table 3c. Scaled water content summary statistics (% basis): Groups A and B (note: percentage water | field capacity calculated as 100 x w, where w = scaled water content relative to field capacity).
|
|
Some additional details concerning each field survey project are given in Table 4. As indicated, 10 of the survey projects were performed within California, but fields CO-4 and ACA-7 were located in Colorado and in Alberta, Canada, respectively. Unless indicated otherwise, EM-38 and soil sample data were collected by George E. Brown, Jr., Salinity Laboratory staff. Additionally, in all but one case, the EM-38 signal data consists of both horizontal and vertical readings, and soil variable information (as reported in Tables 3a, 3b, and 3c) represents the arithmetic average of four 30-cm samples acquired from a 0- to 1.2-m sampling depth.
Data Analysis
In 11 of the 12 survey projects, both horizontal and vertical conductivity readings were acquired at each sample site. Hence, these readings had to first be combined into a single, average EM value before the CalcECa–conductivity correlation estimate could be computed. Additionally, because both the EM signal conductivity readings and soil chemical data exhibited highly right-skewed (i.e., lognormal) data distributions, all of these data were log-transformed before the correlation analyses were performed. (This log transformation helped stabilize the correlation estimates and correct for the nonlinear EM signal response in fields with readings above 100 mS/m.)
The 12 ordinary DPPC correlation analyses were calculated as follows. First, in all fields except BWD-T1, the b was estimated using Eq. [8]. Next, the CalcECa data vector was computed using the ordinary DPPC model (Eq. [6]), after calculating the values of the appropriate model parameters using Eq. [7a] through [7e]. The EM signal data, computed CalcECa data, and all soil chemical data were then log-transformed, and the average EM signal level was defined to be ln(EMavg) = 0.5[ln(EMv) + ln(EMh)], where EMv and EMh are EM-38 vertical and horizontal signal data, respectively. All of the relevant, individual DPPC correlation estimates were then calculated. Finally, the predicted EM–soil variable correlation estimates were computed using the correlation product relationship (Eq. [9a] through [9d]), and approximate 95% confidence intervals for each of these predictions were constructed (using the 95% confidence interval formula described in Appendix A.3).
As explained previously, the Dy-DPPC model (Eq. [16b]) depends on both the ordinary (prespecified) DPPC model parameters and an additional parameter, which itself is modeled as a function of the observed scaled water content. The assumed g() logistic function (Eq. [17]) describes this relationship and in turn depends on two new, unknown parameters (ß0 and ß1).
Optimized estimates for ß0 and ß1 were obtained for the Dy-DPPC model by maximizing the observed ln(CalcECa)–ln(EMavg) correlation estimate over a prespecified (ß0, ß1) parameter space. This was performed directly, i.e., by employing a detailed grid search over a range of suitable ß0 and ß1 values and then choosing the pair of (b0, b1) values that produced the maximum correlation estimate. Bounds for the search grid were specified by constraining the curve midpoint value to lie within an interval of 0.25 to 0.75 and restricting the slope parameter to lie within the interval of 2 to 25 [implying that ß1 
(2,25) and ß0 (-0.75ß1,-0.25ß1)]. The first range reflected the assumption that might potentially assume a value of 0.5 anywhere within a water content range of 25 to 75% field capacity. In a similar manner, the ß1 range endpoints were selected to reflect a potentially wide adjustment in the slope of the curve.
When optimized (b0, b1) values were determined, the statistical significance of the improved ln(CalcECa)–ln(EMavg) correlation estimate was judged using the F score test results. In these analyses, a significance level of = 0.1 was used to indicate significant vs. nonsignificant improvement. If the improvement in the primary correlation estimate was found to be statistically significant, a new DPPC correlation analysis was performed using the optimized Dy-DPPC model in place of the ordinary DPPC model.
All of the statistical quantities pertaining to the above analyses (DPPC correlation estimates, F tests, and 95% correlation confidence intervals) were calculated using the ESAP-Calibrate software program, Version 2.21, and verified using SAS Version 8.1 (SAS Inst., 1999).
|
RESULTS
|
|---|
Ordinary DPPC Correlation Analysis Results
Table 5a lists the DPPC results from the six Group A correlation analyses, corresponding to the six fields exhibiting high relative water content levels during the actual survey processes. Five of the six ln(CalcECa)–ln(EMavg) correlation estimates exceed 0.85, and three of these values appear to be around 0.95. Additionally, the vast majority of the predicted ln(EMavg)–soil property correlation estimates agree well with the observed estimates. The only notable exceptions are associated with the CV-K93 and WL-99 survey data. With respect to the CV-K93 data, the observed ln(EMavg)–ln(ECe) and ln(EMavg)–SP estimates of 0.891 and -0.200 appear to fall right on the edge of the corresponding 95% confidence intervals associated with the predicted estimates, which were 0.841 and 0.064, respectively. A similar pattern is evident in the WL-99 data.
View this table:
[in this window]
[in a new window]
|
Table 5a. Dual-pathway parallel conductance (DPPC) correlation analysis results: Group A surveys using ordinary DPPC model.
|
|
Table 5b lists the equivalent DPPC results from the six Group B correlation analyses, corresponding to the six fields exhibiting relative water content levels that are lower than normal. In general, these results do not appear to be as good as the results shown in Table 5a. Two of the six ln(CalcECa)–ln(EMavg) correlation estimates appear to be extremely poor (fields IID-113 and IID-34, with estimates of 0.480 and 0.524, respectively). These poor primary correlation estimates suggest that the ordinary DPPC model is incapable of reproducing the observed survey–soil property correlation structure in these two fields. Furthermore, many of the predicted ln(EMavg)–soil property correlation estimates associated with the remaining four fields appear to be rather different from the observed estimates. Statistically significant differences show up between the predicted vs. observed ln(EMavg)–w estimates in fields ACA-7 and CO-4. Nearly significant differences are apparent in about half of the remaining predicted vs. observed correlation estimates. Overall, the only survey where all of the results seem satisfactory appears to be field IID-14.
View this table:
[in this window]
[in a new window]
|
Table 5b. Dual-pathway parallel conductance (DPPC) correlation analysis results: Group B surveys using ordinary DPPC model.
|
|
Optimized Dy-DPPC Correlation Analysis Results
The preceding results suggest that a DPPC correlation analysis using the ordinary DPPC model generally yields very good results when the water content is near field capacity but can produce less-than-adequate results when applied to survey data collected under low water content conditions. In those instances, the more robust Dy-DPPC model (Eq. [16b]) should be employed.
Table 6 lists the optimized Dy-DPPC modeling results for the 12 case studies previously discussed. One field failed to optimize (CV-W96), but the primary ln(CalcECa)–ln(EMavg) correlation estimates exhibited at least some degree of improvement in the remaining 11 fields. For fields IID-113 and IID-34, the improvement in the ln(CalcECa)–ln(EMavg) correlation was found to be substantial. Overall, the improvement in the primary correlation estimate in six of the fields was judged to be statistically significant, according to the F-test results. The final hyperparameter estimates for these six fields are also shown in Table 6.
View this table:
[in this window]
[in a new window]
|
Table 6. Ordinary dual-pathway parallel conductance (DPPC) vs. optimized dynamic water content partitioning (Dy-DPPC) modeling results.
|
|
Table 7 lists the new, optimized DPPC correlation results for the six fields where the Dy-DPPC model was found to produce a statistically significant improvement in the primary correlation estimate. Five of the six ln(CalcECa)–ln(EMavg) correlation estimates now exceed 0.9, and all but one of the predicted ln(EMavg)–soil variable correlation estimates now agree well with the observed estimates. These results suggest that the optimized repartitioning of the DPPC water content parameters substantially improves the model's ability to correctly reproduce the observed survey–soil variable data correlation estimates under low water content situations.
View this table:
[in this window]
[in a new window]
|
Table 7. Dual-pathway parallel conductance (DPPC) correlation analysis results for surveys WL-99, IID-113, ACA-7, IID-34, PV-01, and CO-4 using the optimized dynamic water content partitioning (Dy-DPPC) model.
|
|
An example of the intermediate calculation details associated with both models is shown in Table 8 for field IID-34. This table shows the raw EM-38 and soil sample data for each calibration sample site, along with the intermediate calculations used to estimate both the ordinary DPPC and the Dy-DPPC model. As shown in Table 8, the value of the water content–partitioning parameter () ranged from 0.006 to 0.797. In turn, this has a pronounced effect on the dynamic water content parameter estimates (wc and ws), which are quite different from the ordinary DPPC parameter estimates (wc and ws).
The overall effect of this adjusted water content partitioning is shown in Fig. 5a and 5b
. Figure 5a shows the apparent correlation structure between the log-calculated conductivity using the ordinary DPPC model and the average of the log EM signal measurements (r = 0.524). Figure 5b shows the new correlation structure between the log-calculated conductivity using the optimized Dy-DPPC model and the same log EM signal measurements (r = 0.903). This pronounced improvement in the correlation structure suggests that the relatively low water content levels significantly affected (i.e., dampened) the EM signal measurements in this field.
View larger version (16K):
[in this window]
[in a new window]
|
Fig. 5. Calculated soil electrical conductivity (CalcECa) vs. electromagnetic induction (EM) correlation results in field IID-34 from (a) ordinary DPPC model and (b) optimized, dynamic water content–partitioning DPPC model.
|
|
|
DISCUSSION
|
|---|
Most agricultural ECa surveys are done with the expressed goal of gaining information about the spatial distribution of one or more soil properties from the acquired conductivity data. Generally, this information is quantified by using some type of statistical modeling procedure (i.e., an empirical equation that can calibrate soil sample data with ECa signal data). While such an approach has obvious advantages, it lacks an objective technique for judging the validity of the instrument and soil sample data as a whole.
The results from a DPPC correlation analysis can prove to be extremely useful with respect to this issue. First, they provide the analyst with an objective way to judge the general validity of the data set, via the calculation of both the primary CalcECa–EM correlation estimate (this value should be close to 1) and the secondary predicted EM–soil variable correlation estimates (these values should closely match the corresponding observed estimates). Second, the results from such an analysis represent an excellent procedure for classifying the expected degree of correlation between specific soil properties and the acquired ECa data. They automatically yield the exact correlation levels between each soil property and the model-calculated conductivity (CalcECa); multiplying each of these values by the primary CalcECa–EM correlation level yields the corresponding predicted values. Hence, provided prior soil sample data is available and the employed DPPC model is realistic, this procedure can be used to project the expected EM–soil variable correlation levels. This technique is especially useful in precision-farming applications where the target variable of interest is often something other than salinity (Corwin and Lesch, 2003).
Of course, the final accuracy inherent in a DPPC correlation analysis depends on the validity of the model itself. When the relative soil water content level is at or near field capacity, the ordinary DPPC equation generally produces excellent results. In our surveying experiences, fields like WL-99 represent the exception and tend to occur infrequently. However, when the relative water content drops substantially below field capacity, the assumptions inherent in the ordinary equation can begin to break down. More specifically, these analyses suggest that the projected vs. observed correlation results can often be significantly improved by dynamically repartitioning the ws and wc water content components. The method proposed for achieving this (a logistic function conditioned on the scaled water content) does not represent the only conceivable partitioning strategy, but we have found this approach to produce both robust and accurate results in practice.
Based on the limited number of low water content data sets analyzed herein, the hyperparameter estimates (ß0 and ß1, shown in Table 6) appear to be quite variable from field to field. This suggests that these parameters are probably field specific and perhaps influenced by other secondary soil physicochemical properties. Additionally, a careful analysis of Eq. [3] shows that the primary DPPC water content parameters (ws and wc) are inherently confounded with the assumption of conductivity equilibrium (ECw = ECws = ECwc). Hence, the variation in the hyperparameter estimates might also reflect field-specific nonequilibrium effects because this latter assumption could also be expected to break down under low water content situations. Nonetheless, the minimum safe relative water content level appears to be fairly stable. Specifically, it appears that the repartitioning effect does not generally become a serious issue unless the relative water content drops below 65% (Table 3c). Hence, when conducting a salinity survey, we recommend that the minimum water content with respect to field capacity be kept above 65% whenever possible.
The fact that the ordinary DPPC equation may break down under abnormally low water content situations is actually not surprising. On the contrary, this problem is discussed in detail in Rhoades et al. (1999b), along with a number of important reasons for not performing soil conductivity surveys under low water content situations. Additionally, the use of the modified Dy-DPPC model does not mitigate this concern in any practical sense. In other words, although the Dy-DPPC model was successfully used to verify that the observed high EM–water content and low EM–salinity correlations were correct (in a data validation sense), this does not imply that the low EM–salinity correlation problem can be corrected. To achieve such a correction, one would need fairly precise water content estimates at each and every survey site, e.g., either actual water content measurements across the entire survey grid or a second set of instrument signal data that could be used to accurately estimate the spatial variation in soil water content. Neither type of measurement data is available for any of the 12 survey projects examined here. Hence, even though all 12 survey projects exhibit high internal validity, some of the survey processes will still clearly fail to yield accurate salinity maps (e.g., fields IID-113 and IID-34).
From a more general data interpretation perspective, these DPPC correlation analysis results demonstrate why there is often such significant variation in the various EM signal data–soil variable correlation estimates between different fields. As discussed in Corwin and Lesch (2003), the final correlation estimates in any specific survey situation are strongly influenced by both the variability of each (primary) soil property and the degree of correlation between these properties. Additionally, the degree of dynamic water partitioning (under low water content situations) will also have a pronounced effect. For example, when ECe represents the dominant soil property and the soil is near field capacity, the ECa–ECe correlation level is nearly always quite high. High correlation levels between the ECa and other soil properties (SP, percentage clay, w, etc.) typically only occur when these other properties simultaneously correlate well with salinity. However, as these other primary soil properties become more variable and less correlated with salinity, the ECa–ECe correlation level tends to drop off. Additionally, as the spatial variation in soil salinity decreases and the spatial variation in the other primary properties increases, one or more of these other properties will eventually supercede the soil salinity as the dominant soil property. Furthermore, as shown herein, if the relative water content drops too far below field capacity, then the spatial variation in water content can become the dominant factor influencing the ECa data, even in the presence of large spatial variation in salinity.
In general, the preceding analyses demonstrate the degree of potential variation that often occurs in ECa–soil property correlation estimates. A multitude of results are possible, but the final correlation levels ultimately depend on the joint distribution and relative spatial variation inherent in the primary soil properties. The simultaneous interaction of all of these properties must first be quantified before an accurate projection of the ECa–soil property correlation structure can be made. However, given such information, the preceding results suggest that accurate projections are possible under a wide variety of typical surveying conditions.
|
CONCLUSION
|
|---|
The aforementioned analyses demonstrate the usefulness of the DPPC modeling approach, from both a specific data validation perspective and a more general data interpretation perspective. These results demonstrate how the DPPC model developed by Rhoades et al. (1989) can be used to accurately predict the expected correlation structure between ECa data and multiple soil properties of interest for an arbitrary survey process. This methodology (referred to as a DPPC correlation analysis) represents a useful survey data validation procedure as well as a quantitative technique for describing how different soil properties correlate with the acquired ECa data. These results indicate that this technique generally works well in practice, provided the relative soil water content across the survey area is reasonably close to field capacity.
The ordinary DPPC model can be extended to handle survey data collected under low water content situations through the use of an adjusted, field-specific water content–partitioning function. A simple partitioning strategy has been presented, along with a technique for estimating and testing the partitioning hyperparameters for statistical significance. Results from 12 different salinity surveys suggest that this adjustment can induce a substantial improvement in the accuracy of the predicted correlation structure under especially low water content situations. However, low soil water content situations should still be avoided during actual EM–salinity survey applications because there is no way to adjust for the heightened water content effect at any of the noncalibration survey sites.
In a broader sense, these results demonstrate that the correlation structure between survey conductivity data and different soil properties in any specific field can be quite variable. This structure ultimately depends on the joint distribution of the primary ECe, SP, and w soil properties (under normal water content conditions) and also the degree of assumed continuous vs. series-coupled water content partitioning (under low water content conditions).
|
APPENDIX
|
|---|
Part A.1
A proof of the correlation product relationship can be developed as follows. Let X, Y, and Z represent three stochastic random variables with finite mean and variance, with the variance of Y defined as 
2Y. Suppose that both X and Z are related to Y in a linear manner, i.e.,
and that the residual error components (1 and 2) are independent. Then, if Corr(X,Y) = XY and Corr(Z,Y) = YZ, the expected value of Corr(X,Z) is simply equal to the product of XY x YZ. To show this explicitly, note that XY is equal to
and that
and
Therefore, because Var
= 2Y, XY can be rewritten as
TOP
ABSTRACT
INTRODUCTION
