Published online 23 January 2008
Published in Vadose Zone J 7:22-30 (2008)
DOI: 10.2136/vzj2007.0015
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Correcting Dual-Probe Heat-Pulse Readings for Changes in Ambient Temperature
M. H. Younga,*,
G. S. Campbellb and
J. Yina
a Desert Research Institute, Nevada System of Higher Education, Las Vegas, NV 89119
b Decagon Devices, Inc., Pullman, WA 99163; J. Yin, Dep. of Geoscience, Univ. of Nevada Las Vegas, Las Vegas, NV 89154
* Corresponding author (michael.young{at}dri.edu).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 16 January 2007.
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ABSTRACT
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We examined three methods of analyzing dual-probe heat-pulse (DPHP) data for estimating volumetric water content of near-surface materials where diurnal temperature variations can approach ± 20°C. The three methods of analyzing thermal responses include: (i) the single-point method (SPM); (ii) a method that uses a Levenburg–Marquardt optimization of thermal conductivity, volumetric heat capacity, and drift in ambient temperature with subsequent calculation of water content (LM-Uncorrected); and (iii) an expansion of the LM-Uncorrected method that incorporates temperature dependencies of soil thermal conductivity and optimizes on volumetric water content, apparent needle spacing, and drift in ambient temperature during the measurement (LM-Corrected). Ambient temperature measurements were made with either a soil thermistor installed away from the DPHP sensor (SPM) or from the temperature response of the DPHP sensor itself (LM-Uncorrected and LM-Corrected). Methods were tested based on measurements made in April and August 2006 from sensors installed at ground surface in the Mojave Desert. The SPM results showed that large (summertime) diurnal temperature variations led to significant oscillations of water content, recorded as high as ± 0.10 m3 m–3. The LM-Uncorrected method showed a significant reduction in water content oscillations, but variations were still large. The LM-Corrected method showed that the time series of water content was significantly smoother than uncorrected water contents (i.e., ± 0.005 m3 m–3 in August). The DPHP-derived water contents compared favorably to data from water content reflectometers installed nearby. The results show that soil water content estimates from the LM-Corrected method were substantially less affected by large ambient temperature variations.
Abbreviations: DPHP, dual-probe heat-pulse • LM, Levenburg–Marquardt • SPM, single-point method
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INTRODUCTION
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Soil water content in near-surface soils (<5-cm depth) influences a variety of hydrological and ecological processes. Especially in water-limited systems like arid environments, near-surface water content provides resources that are critical for plants and other biological entities including biological soil crusts. A challenging task, however, is nondestructive and repeated measurement of soil water content in surface soils. Although numerous methods for determining water content are available (e.g., destructive sampling, neutron probe, time domain reflectometry), each has limitations in very near-surface applications when repeated measurements are needed. The dual-probe, heat-pulse (DPHP) method represents a sensible alternative choice in technologies. The sensor consists of two needles, typically 30 mm long with 6-mm spacing, and thus interrogates a small volume of soil (complete descriptions of sensor construction and operation can be found in earlier works: Campbell et al. [1991], Bristow et al. [1994], and Heitman et al. [2003], among others). Once installed, the sensor reading is nondestructive and has a relatively small range of influence.
The theoretical basis for analyzing DPHP sensor readings also has been described. Analytical approaches tend to differ by treating boundary conditions either as an instantaneous pulse (Campbell et al., 1991; Heitman et al., 2003) or as a thermal pulse of a known fixed width (Kluitenberg et al., 1993, 1995). Recently, fixed-pulse-width analysis has been shown to be more accurate than the instantaneous pulse (Knight and Kluitenberg, 2004). Since the original development of this type of sensor, several studies have described advancements for understanding the theoretical bases of the technique (e.g., Kluitenberg et al., 1995; Knight and Kluitenberg, 2004) for laboratory testing (Bristow et al., 1993; Song et al., 1998, 1999; Basinger et al., 2003) and field deployments (e.g., Campbell et al., 2002; Bremer, 2003; Heitman et al., 2003). Most studies have been conducted either under highly controlled laboratory conditions or in environments where the sensors are installed in soils at >10-cm depth, where diurnal fluctuations of ambient temperature are substantially dampened.
One issue surrounding the use of thermally based sensors for measuring water content is the temperature dependence of thermal properties, especially when sensors are placed in areas where temperature fluctuations are higher. These dependencies have been known for decades (cf., Philip and de Vries, 1957; de Vries, 1963). In laboratory or field environments where temperature fluctuations are small, corrections may not be needed. If study goals require thermal properties or water contents close to ground surface when temperature fluctuations are significant, however, then temperature corrections could significantly reduce measurement errors. For example, Heitman et al. (2003) showed data from sensors buried at 10-cm depth that revealed a significant positive (in-phase) relationship between water content and ambient temperature (i.e., high ambient temperature corresponded to high water content). Although physical processes could be used to describe this relationship, they suggested that the temperature dependency of variables found in the governing heat flow equation (described below) explained the variation in water content. Flint et al. (2005) showed evidence of temperature dependency of soil thermal properties when obtained from heat dissipation sensors, another class of thermal probes. These researchers corrected soil water potential estimates by normalizing thermal properties to 20°C and using previously obtained thermal conductivity–water content relationships to estimate soil water potential. Olmanson and Ochsner (2006) examined the temperature sensitivity of a specially designed heat pulse probe across a temperature range from 5 to 45°C and concluded that specific heat values of the solid, liquid, and gas phases were responsible for their temperature fluctuations.
The field environments where DPHP sensor use has been reported differ significantly from the rocky and coarse-textured surface soils of the Mojave Desert, where this study was conducted. Moreover, we know of no studies where DPHP sensors have been deployed in surface soils (i.e., <5-cm depth) and monitored for water content during summer periods when daily temperatures fluctuate on the order of ± 20°C (e.g., 
20°C during the nighttime and >60°C during the daytime). To account for this field scenario and the diurnal response of water content estimates, we developed a correction method for DPHP sensors installed in near-surface soils. Our goals were to: (i) develop an analytical method that accounts for temperature dependency; and (ii) compare the new method with other methods of data analysis using data collected from DPHP sensors during the months of April and August 2006.
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Materials and Methods
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Probe Description and Field Setup
Our research was conducted at the Mojave Global Change Facility (MGCF), located at the Nevada Test Site, approximately 150 km northwest of Las Vegas, NV (36°49' N, 115°55' W). The soil at MGCF is an Aridisol derived from calcareous alluvium on a north-facing alluvial fan. Soil textures are relatively uniform across the MGCF, with sandy loams (gravel, sand, and clay are 16.4, 54.5, and 8.7%, respectively) found in the shallow A1 horizon (0–0.16 m) (Meadows et al., 2006) and coarse sands found in the subsoil horizons (Phillips et al., 2000). Average and standard deviation of the bulk density in the A1 horizon is 1.23 ± 0.17 g cm–3. Vegetation has been characterized as a Larrea tridentate–Ambrosia dumosa desert scrub plant community (Titus et al., 2002).
Sensors used in this research were manufactured by East 30 Sensors, Inc. (Pullman, WA) and consisted of two needles each 30 mm long, 0.9 mm in diameter, with a spacing of 6 mm. One needle contained a 40-
heating wire (Evanohm, Wilbur B. Driver Co., Newark, NJ) and the other needle contained a thermistor as the measuring device. The needles were mounted to a circuit board to provide the correct spacing and rigidity. The Cu cladding on the circuit board was etched away between the needles, so the thermal connection between the needles was just through the circuit board material and the epoxy making up the probe head overmold.
A total of 14 DPHP sensors were installed at ground surface on 21 Mar. 2006 on each of two research plots (CW1 and CW4). The plots were separated by up to 25 m. Figure 1
shows the general location of sensors on Plots CW1 and CW4. All sensor leads were encased in small-diameter slit loom (i.e., plastic insulating tubing) from the sensor body for about 3 m and then fed into larger diameter slit loom to a multiplexer (Model AM16/32, Campbell Scientific, Logan, UT) located on each plot. Data were collected by a datalogger (Model 23X, Campbell Scientific) powered by a deep-cycle marine battery and solar panels. Immediately before initiating the heat pulse, the initial temperature at each sensor location was measured using the thermistor on the DPHP. The heat pulse was then generated by applying voltage for 8 s. The change in temperature was measured at the thermistor every 2 s for 80 s after turning the power off to the heating wire. Heating power was typically in the range of 600 J m–1 at Plot CW1 and 450 J m–1 at Plot CW4. The measurement method is similar to that described by Bristow et al. (1994) and Ochsner et al. (2003). All loggers and components were housed in either environmental enclosures or insulated ice chests at the plot location. Data were collected at 4-h intervals.
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FIG. 1. Image showing dual-probe heat-pulse (DPHP) sensor locations at Plots (A) CW1 and (B) CW4. Solid circles are DPHP sensors; white boxes are 107 thermistor probes installed at 0-cm depth; triangles are water content reflectometers; hatched boxes are locations of multiplexers and enclosures. Insets show an example of a DPHP sensor installed at the ground surface and a schematic of sensor orientation.
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Plots CW1 and CW4 differ by surface treatment. Plot CW1 is a control and Plot CW4 is irrigated and disturbed (surface disturbance refers to destruction of the biological crust by scuffing and trampling). Eight sensors per plot were installed below canopies of L. tridentada and six more sensors were installed between shrubs, known as intercanopies. Under-canopy sensors were split, with four installed at the ground surface on each of the north and south sides of the shrub, with the DPHP sensor needles oriented vertically downward. Intercanopy sensors were installed at the ground surface (six per plot), with sensor needles oriented vertically downward, exposing the sensor head (see inset in Fig. 1).
In addition to the DPHP sensors, three soil thermistors (Model 107, Campbell Scientific) were installed horizontally at ground surface on each of the three plots and used to measure ambient temperature. Figure 1 shows the locations of the soil thermistors, which were positioned a sufficient distance from the DPHP sensors to not be affected by the measurement. Temperatures were recorded from the soil thermistors immediately before initiating heating of the DPHP sensor, and then every 2 s thereafter while the DPHP readings were taking place. Temperatures from the three soil thermistors were then arithmetically averaged. The first measurement was taken as the ambient temperature. Subsequent measurements during the next 80 s were used to calculate ambient temperature changes during the DPHP measurement. The change in ambient temperature was used to correct the DPHP measurements from Method 1 (as described below).
Examples of Diurnal Response of Water Content
Figures 2A and 2B
show example 10-d time series of water content and ambient temperature for one sensor installed in Plots CW1 and CW4, respectively. The figures show substantial diurnal responses of water content (obtained using the single-point method of Bristow et al. [1994]) as a function of time and a close relationship between water content and ambient temperature, as measured by the soil thermistors immediately before initiating the heating. In the case of Probe 2179 (Plot CW1, Fig. 2A), water content values varied from 0.025 to 0.135 m3 m–3 during a time interval of 8 h even though no water input occurred at the site for >8 d. Also, the data show a significant positive (in-phase) relationship with temperature, with the highest daily water content occurring close to the temperature peak and the lowest water content occurring in the early morning, similar to that reported by Heitman et al. (2003). The same behavior also can be seen in Fig. 2B for Probe 2215 in Plot CW4, although the diurnal response for this probe was less than shown in Fig. 2A. No plausible physical explanation is readily available to explain the large variation in near-surface water content—including formation of dew, which would not increase water content by the 0.10 m3 m–3 observed, or resaturation from deeper soils, although this has been observed for several days after rainfall events. The oscillation of water content clearly increases the difficulty in identifying precipitation and evaporative demand. Both of these manifestations illustrate the need for a more robust approach for analyzing sensor output.
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FIG. 2. Examples of diurnal fluctuations of water contents using (A) Probe 2179 on Plot CW1 and (B) Probe 2215 on Plot CW4 for data collected from 11 to 21 Aug. 2006.
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Data Analysis and Temperature Correction
The rates of temperature increase and decrease in soils are functions of thermal capacity and thermal conductivity, both of which are affected by soil water content. A number of analytical expressions have been proposed for obtaining water content from thermal properties. We focused our efforts on the analytical solution to the heat flow equation for a short-duration heat pulse through an infinite line source. For radial coordinates, the temperature, T, at a known distance, r, from the line source is (de Vries, 1952; Kluitenberg et al., 1993)
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where
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and
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where t is time from beginning of heating, t0 is time after heating ceases, Q' is the source strength per unit time (m2 °C s–1), calculated from q', the quantity of heat liberated per unit length of heater per unit time (J m–1) divided by C, the volumetric heat capacity (J m–3 °C), 
is the thermal diffusivity (m2 s–1), and Ei is the exponential integral.
Based on this analytic solution, we used three methods to calculate and C. The following equations are derived from Eq. [3], which is appropriate for the measurements after heating ceases.
Method 1: Single-Point Method
In this method, we corrected for changes in ambient temperature that occurred while the measurement was being taken, and we used the expressions of and C (Bristow et al., 1994) as
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and
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where rn is the apparent needle spacing of the DPHP, tm is the time of the maximum temperature change, and 
Tm is the maximum temperature increase (°C) as recorded from the DPHP thermistor. Measurements made by the 107 thermistor probes were used to correct Tm. Thus, if the 107 thermistor probes recorded an ambient temperature increase during the DPHP measurement at the time corresponding to tm, then Tm is reduced by that amount, and vice versa. In this way, energy gained or lost at the soil surface due to environmental conditions is subtracted or added, respectively, to the energy added to the soil by the DPHP heating wire. After C was estimated, volumetric water content 
w (m3 m–3) was determined (de Vries, 1963) by
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where m is the volume fraction of soil, Cm is the volumetric heat of soil (J m–3 °C–1), and Cw is the volumetric heat of water (J m–3 °C–1). (Note: The use of for volumetric water content is for consistency with de Vries and others, but 
is a more commonly used symbol for volumetric water content.) The bulk density of water was assumed to be 1000 kg m–3.
Method 2: Levenburg–Marquardt Uncorrected Method
In this method, the term uncorrected indicates that temperature dependency of the soil thermal conductivity is not incorporated into the analytical approach. The solution of the temperature change (T) at distance r (de Vries, 1952; Mori et al., 2003) is
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A temperature drift, s (°C), was added to the right-hand side of Eq. [7] to account for potential ambient temperature change occurring as a function of time, t, during the measurement period. The temperature drift was used in lieu of readings from the 107 thermistors, as described in Method 1. The resulting equation is
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The routine uses a Levenburg–Marquardt (Marquardt, 1963) optimization algorithm that is particularly common in hydrologic applications. More specifically, because T is a function of , C, and s, the LM-Uncorrected method optimizes these three parameters simultaneously by searching for the minimum objective function, OF:
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where n is the number of observed temperature measurements in each data set, T(m)i is the ith measured change in temperature, and T(c)i is the ith predicted change in temperature. Water content is then obtained using Eq. [6] and the optimized volumetric heat capacity (C).
Method 3: Levenburg–Marquardt Corrected Method
In this method, we explicitly corrected for temperature dependency of soil thermal conductivity, and optimized w, rn, and s; thus, w and rn are now treated as fitting parameters in this method. Thermal dependencies are found in the equations of de Vries (1963) and Hopmans and Dane (1986). Campbell et al. (1994) gave the following equation to explicitly derive the thermal conductivity of soil, 
(W m–1 °C–1):
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where is the volume fraction, 
is a weighting factor, and subscripts w, g, and m denote water, gas, and mineral, respectively. The weighting factors i are calculated (Campbell and Norman, 1997) by
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where gc and ga are shape factors. Campbell and Norman (1997) suggested that ga has a value around 0.1 for mineral soils and gc = 1 – 2ga. In Eq. [11], f is the conductivity of the soil water, calculated as
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where fw is calculated as
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where 0 is the critical water content at which return flow of water within the soil pores is disrupted and q is a fitting parameter. Here, 0 was chosen as 0.15 and q was chosen as 4.0, both being consistent for a soil with sandy loam texture (Campbell and Norman, 1997). Table 8.2 in Campbell and Norman (1997) provides the values of w, m, and g, which is calculated by
 | [14] |
where a is the thermal conductivity of air (Campbell and Norman, 1997, Table 8.2), 
is the latent heat of vaporization of water (Campbell and Norman, 1997, Appendix A.2), is the slope of the saturation vapor pressure function, hr is the relative humidity in the soil, 
is the molar density of the air (mol cm–3), v is the vapor diffusivity for soil, pa is the atmospheric pressure (Pa), and pe is the saturation vapor pressure:
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where a, b, and c are fitting parameters (Campbell and Norman, 1997). Rearranging Eq. [6] becomes the expression of the volumetric heat capacity:
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During optimization, values of w and rn were constrained such that w was allowed to float between 0 and 0.5 m3 m–3 and rn was allowed to float between 5 and 7 mm.
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Results and Discussion
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Comparison of Analytical Methods
Figures 3A and 3B
show the results of the three analytical methods for two probes (Probe 2179 on Plot CW1 and Probe 2215 on Plot CW4) during April 2006. During the early portion of the month, temperature maxima centered on 30°C, but increased toward the end of the month when maximum temperatures exceeded 50°C. Water contents on the two plots trended downward, as expected, with the onset of warmer, drier conditions and increased soil evaporation rates. All three methods show two precipitation events (11.3 mm on 4–5 April and 2.2 mm on 14 April). Both events were clearly recorded by Probe 2179, which showed excellent sensor response. Only one event was observed by Probe 2215, but a slight inflection in water content traces detected by all three methods could be due to precipitation. Differences between these two probes can be explained by heterogeneity of surface conditions, especially the undulating condition of the biological crust into which Probe 2179 was inserted and the relatively smooth surface monitored by Probe 2215 (note that all other sensors on Plot CW4 showed both events).
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FIG. 3. Water contents obtained using the single-point method and the uncorrected and corrected Levenburg–Marquardt (LM) analytical methods for April 2006: (A) Probe 2179 on Plot CW1, (B) Probe 2215 on Plot CW4.
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Figures 3A and 3B show significant differences in diurnal fluctuations in water content, and thus illustrate differences in results from the analytical methods. The SPM shows relatively stable measurements when ambient temperatures in early April were moderate, but much higher fluctuations toward the end of April, sometimes exceeding 0.10 m3 m–3 during a 24-h period even though no precipitation occurred. Throughout the month, however, the water contents were higher during midday and lower during the evening and early morning. Some of these fluctuations could be due to the use of only two characteristics of the temperature response curve (Tm and tm) and the relatively coarse data collection interval of 2 s. The LM-Uncorrected measurements are significantly smoother with time, reflecting the benefits of using the entire response curve for the analysis; however, the results continue to show higher water content values at midday. Note especially the April 26 to 30 measurements when ambient temperatures were warmer and overall diurnal variations in water content were higher (e.g., ± 0.03 m3 m–3 for Probe 2179 and ± 0.02 m3 m–3 for Probe 2215). In contrast, the LM-Corrected method, accounting for temperature-dependent thermal properties, produced a time series of water content values that is significantly smoother (both probes show ± 0.005 m3 m–3 for the same time period).
Of the eight sensors analyzed using all three methods, results from six sensors showed water contents out of phase with temperature (i.e., lower water content values were recorded at midday when soil evaporation was highest and higher water content values were recorded during the evening when rehydration from deeper soils, or perhaps dew, could be supplying water to near-surface soils). We do not have a ready explanation for why a small number of sensors indicate in-phase responses with temperature, although perhaps air gaps around the needles or uneven coverage of the needles by the soil could affect the readings. The soil water contents obtained from the LM-Corrected method appear to settle on about 0.05 m3 m–3 for both probes after a couple of weeks without precipitation, whereas the SPM and LM-Uncorrected methods showed higher values. Given the relatively sandy texture of the soil, lower water content values were expected.
Benefits of the LM-Corrected method are seen more clearly for the two probes presented when ambient temperatures in August 2006 typically cycled ± 20°C at the ground surface (Fig. 4A
and 4B). Our results show that water content fluctuations decreased progressively from Method 1 (SPM) to Method 3 (LM-Corrected). Table 1
shows descriptive statistics for data collected toward the end of August, after several weeks had passed without water input. Results also show that water contents obtained using the SPM were too variable to accurately identify the timing of the 25-mm irrigation event that occurred on Plot CW4 on 8 August (Fig. 4B). Results from the other two methods allowed the irrigation event to be detected, however. The LM-Uncorrected method also shows water content fluctuations, but the magnitude of water content in the evening and early morning varied between 0.02 and 0.03 m3 m–3 for Probe 2179 and between 0.08 and 0.09 m3 m–3 for Probe 2215. Daytime water contents, however, were still higher than evening water contents, even though precipitation had not occurred on Plot CW1 for >30 d and irrigation had not occurred on Plot CW4 for >13 d. The range in water contents during this relatively quiescent period decreased when including optimization in the LM-Uncorrected method and when adding thermal dependencies in the LM-Corrected method. Using Probe 2179, for example, the ranges in water contents using the three analytical methods decreased from 0.106 to 0.063 to 0.015 m3 m–3 (Table 1). When accounting for the effects of temperature-dependent latent heat, thermal vapor diffusivity, and material specific heat in the LM-Corrected method, the water content fluctuations were significantly reduced.
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FIG. 4. Water contents obtained using the single-point method and the uncorrected and corrected Levenburg–Marquardt (LM) analytical methods for August 2006: (A) Probe 2179 on Plot CW1, (B) Probe 2215 on Plot CW4.
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TABLE 1. Descriptive statistics for data collected 21 to 31 Aug. 2006 and analyzed using three analytical methods: the single-point method and the uncorrected and corrected Levenburg–Marquardt (LM) methods.
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Recall that thermal conductivity in the LM-Corrected method is calculated after w has been obtained, rather than directly from the solution to the heat flow equation as in the SPM and LM-Uncorrected methods. We thus examined whether thermal conductivities obtained from the LM-Corrected method are physically realistic. Figures 5A and 5B
show estimated (w) thermal conductivity–water content relationships for three soils (quartz, loam, and organic) using Eq. [8.13] in Campbell and Norman (1997), and assuming that bulk density = 1.33 g cm–3, temperature = 25°C, ga = 0.1, m = 2.2 W m–1 °C–1, and 0 = 0.1. Paired values of and w for April and August 2006 are plotted onto the graphs for comparison. The magnitude of the field data is very similar to the estimated thermal conductivity values for the loam soil, and the general shape of the curve estimated by the field data is clearly similar to the theoretical curve using the function described by Campbell and Norman (1997). Thermal conductivity values ranged from 0.2 to 0.3 W m–1 °C–1 during dry periods without precipitation or irrigation and are similar to those reported by Hopmans and Dane (1986), Campbell et al. (1994), and Bristow et al. (1994)—although direct comparisons are difficult given differences in water contents, soil texture, and experimental conditions.
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FIG. 5. Comparison of thermal conductivity and volumetric water content functions for three soil types and for data collected in April and August 2006 in Plots (A) CW1 and (B) CW4.
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Perhaps one limitation of this study is the paucity of independently collected values of water content that could be used to compare with values estimated using the LM-Corrected method at the same scale of measurement as the DPHP (i.e., nondestructive estimates of volumetric water content in the upper 30 mm of soil). Measurements of water content were available, however, from sensors installed for an unrelated study in the same field plots as the DPHP. These additional measurements were taken with 300-mm-long water content reflectometers (WCR, Model CS-616, Campbell Scientific) at 4-h intervals, contemporaneously with the DPHP system. The WCR probes were located within meters of the DPHP sensors and were vertically installed. Figures 6A and 6B
show time series of water contents using the WCR and DPHP methods. Figure 6A (April 2006) shows water contents measured with the WCR at both research plots that are higher than the water contents measured with the DPHP. Higher water contents measured with the WCR are probably the result of using a longer probe that sampled deeper soil, which still contained soil moisture from winter precipitation events. The low water content values of surface soil (i.e., upper 30 mm) measured with the DPHP sensors reflects moisture loss due to soil evaporation. Figure 6B (August data using the same comparison) shows close similarity between the WCR and DPHP data, especially for Plot CW1, which experienced a prolonged period without water input. Data from Plot CW4 shows the 25-mm irrigation event on 8 August, with more responsiveness of the DPHP sensor that samples only the uppermost soil and a more subdued response (both wetting and drying) of the WCR. Water contents obtained using the WCR and DPHP methods converged toward the end of the month, illustrating overall drying of the deeper soil profile. Although we have obvious differences in measurement volumes using these two methods, comparison of the results indicates that the optimized water contents are physically realistic and similar to values measured independently. Success of the optimization was examined, in part, by plotting the RMSEs in terms of w and rn (Fig. 7A
–7D) (temperature drift, s, was found to be on the order of 0.2–0.7°C for 80 s and not correlated to w or rn). The OF plots show a global minimum (identified by the symbol) and no evidence of any presence of local minima or nonuniqueness. These results indicate a relatively well-behaved mathematical problem. We also tested for correlation between w, rn, and s, which would reduce the strength of the parameter set. Results showed weak covariance in most cases (r2 < 0.100) and a small number of cases with r2 > 0.500.
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FIG. 6. Comparison of water content data collected from dual-probe heat-pulse sensors (Probes 2179 and 2215) in (A) April and (B) August 2006 vs. data collected using water content reflectometers (616) at both field plots.
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FIG. 7. Root mean square errors for optimization of data from 18 Aug. 2006 for (A and B) Probe 2179 and (C and D) Probe 2215 from readings taken at 0400 h (left column) and 1600 h (right column). Red dot on graph indicates global minima.
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We also sought to identify possible correlation between ambient temperature, the minimum value of the objective function (OFmin), and rn. Figure 8
shows how OFmin changes throughout the month of August for both example probes. Probe 2179 shows a relatively consistent level of error throughout the time period (mean OFmin = 0.010°C, SD = 0.0009°C) and no relationship with temperature (r2 = 0.062). Probe 2215 shows a lower OFmin, a slightly higher level of variability (mean = 0.0089°C, SD = 0.0057°C), and a slightly higher apparent correlation to temperature (r2 = 0.266). Differences between these two sensors could be due to slight variations in the probe installation relative to the soil surface or to the potential for formation of air gaps with time (although each probe was periodically field checked during the experiment).
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FIG. 8. Root mean square errors as a function of time and ambient temperature for August 2006 data collected with Probes 2179 and 2215 on Plots CW1 and CW4, respectively.
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Figure 9
shows optimized values of apparent needle spacing (rn) for both sensors as a function of time and ambient temperature. Some fluctuations are apparent, as is a subtle cycling of rn with ambient temperature. Needle spacing is an important parameter in the DPHP method and has been shown to greatly affect uncertainty in thermal measurements and water content estimates. Kluitenberg et al. (1993) showed that 2% uncertainty in rn leads to 4% uncertainty in heat capacity and hence the water content. This strong dependence on apparent needle spacing is the motivator behind using agar-stabilized water for independently identifying DPHP needle spacing (i.e., Campbell et al., 1991; Ren et al., 2003; Ochsner et al., 2003; Gao et al., 2006; etc.). In this method, however, we treated rn as a fitting parameter that can vary within a set range (5–7 mm) in the optimization. Final values for rn did vary somewhat during the month. Values of rn for Probes 2179 and 2215 were 6.379 mm (SD = 0.0086 mm) and 6.587 mm (SD = 0.010 mm), with coefficients of variation equaling about 1.3 and 1.5%, respectively. Slight deflections of the needles as the soil heats and cools is possible but is not being considered as an explanation for the relatively small amount of variation in water content observed in this study.
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Conclusions and Implications
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Multineedle sensors used to measure thermal properties of soil, and in turn the soil water content, offer a unique capability to obtain measurement of very near-surface soil material. Effects from large temperature fluctuations (during the measurement itself and from some thermal dependencies), however, affect the accuracy of water content measurements. Under near-surface conditions where ambient temperature changes substantially, the SPM for analyzing DPHP data may not be a suitable choice (Bristow et al., 1993). Moreover, the use of the DPHP technology itself could be limited by the possible presence of thermal gradients in the domain of the DPHP sensor during the measurements, which could lead to errors in water content estimates. In our case, sensors were installed vertically to enhance the detection of small precipitation events that could wet only the uppermost soil material, so a tradeoff was necessary.
The temperature correction described herein was shown to significantly dampen diurnal cycling of water content in near-surface soil material. Our preferred method incorporates temperature dependency of numerous relationships, including the specific heat of solid, liquid, and gas phases; thermal vapor diffusivity; and the thermal distillation effects from latent heat absorption and release within soil pores. By optimizing soil water content and apparent needle spacing, and explicitly solving for thermal conductivity and volumetric heat capacity, the heat flow equation can be solved easily and compared with observed data without estimating other parameters. This method was found to be stable, repeatable over time, and sensitive enough to detect precipitation events of only 2 mm. We showed that a unique combination of soil water content and apparent needle spacing could be found in the objective function, and sensitivity analysis indicated that the solution is not prone to local minima. In short, we suggest that this correction method can lead to more accurate water content estimates in near-surface soils.
This new analytical method could widen the use of DPHP sensors to include harsher near-surface environments. We tested the DPHP sensors in rocky, desert soils that are subjected to daily temperature swings of ± 20°C and found this sensor technology to provide stable and physically realistic water contents; the paradox, of course, is our inability to directly confirm the magnitude of the water content without destroying the soil we seek to characterize.
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ACKNOWLEDGMENTS
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We greatly acknowledge support of the Andrew W. Mellon Foundation, the U.S. Department of Energy Program for Ecological Research (DE-FG03-00ER63049), and the National Science Foundation (DEB-0212812 and EPS-0447416). We acknowledge the help of John Goreham with the field work and important discussions with Gerard Kluitenberg at Kansas State University.
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INTRODUCTION
