Dual-probe Heat-pulse Sensors Research Articles

High‐Resolution Field Measurement of Soil Heat Capacity and Changes in Soil Moisture Using a Dual‐Probe Heat‐Pulse Distributed Temperature Sensing Approach

AbstractIncreasing interest in studying the variability of soil water content and its spatial scale dependency necessitates the development of new techniques to accurately monitor soil water over a wide range of spatial scales. Distributed Temperature Sensing (DTS) techniques offer unprecedented opportunities to measure temperature with a spatial resolution of a few centimeters over several kilometers, which can be used to measure soil moisture. This study is the first of its kind that investigates under field conditions the feasibility of combining the Dual‐Probe Heat‐Pulse (DPHP) technique with the DTS technology to measure soil thermal properties and variation in soil moisture. A field experiment was conducted over a 30 m transect in the Lake Wheeler Field laboratory in Raleigh, NC. Three different DPHP sensors were constructed from combinations of different fiber optic cables and heating elements and were tested to assess their performance and the effect of their construction characteristics on their accuracy. Measurements were taken over different soil moisture conditions and the system performance was compared against independent soil water content sensors. The system was able to track changes in soil water content with a mean RMSE of 0.02 m3 m−3 using the optimal DPHP sensor. The key advantage of the tested system is that it does not need any site‐specific calibrations typically required for other DTS‐based systems. The findings of this study provide some practical information and measures that need to be taken for successful DTS‐DPHP construction and application under field conditions.

Field test of two background temperature correction methods of dual probe heat pulse method

Dual probe heat pulse (DPHP) method is a useful method to measure many soil physical properties in-situ, which play important roles in soil science, meteorology, hydrology and so on. It is essential to remove the effect of background temperature fluctuations for DPHP estimations. We compared two background temperature correction methods of DPHP method, linear trend method (LTM) and reference temperature method (RTM) in field experiments. We found that misused LTM lead to large errors in DPHP estimations with shallow burial depth. When the burial depth of temperature probe (d) of DPHP sensor is <14 mm, background temperature changes are related to environmental factors such as solar radiation and wind, and RTM can decrease the relative error (RE) in thermal conductivity (λ) from 667% to 68%. Besides, our results also showed during the period from 9:00 to 16:00, the RTM method is valuable for getting accurate DPHP estimations with the 2 mm burial depth. After replacing LTM by RTM, REs were decreased to (6 ± 28)% from (17 ± 87) % in λ, and were decreased to (9 ± 17)% from (10 ± 18)% in volumetric heat capacity (Cv). But RTM is also affected by other factors such as the spatially heterogeneous temperature distribution of tested sample and should be taken into account in the further studies.

Analysis of heat paths in dual-probe-heat-pulse soil-moisture sensors for improved performance

We analyse heat paths of a packaged Dual-Probe-Heat-Pulse (DPHP) soil-moisture sensor to improve the sensor’s performance at higher levels of volumetric water content. A DPHP sensor consists of heater and temperature probes protruding out into the soil from a casing. The two probes help estimate the soil moisture content by assessing the heat conduction through the soil in the intervening space between them. At lower soil-moisture conditions, the heat conduction through soil dominates whereas at higher soil-moisture contents heat flow through soil decreases due to the increase in volumetric heat capacity and specific heat. Inappropriate placement of the heater element could lead to erroneous measurement due to the heat conduction to the temperature probe through the casing material and the epoxy adhesive inside the casing. To study the heat flow in DPHP sensors, and to develop an improved design, thermal paths in the DPHP sensors having different heater element positions were first analysed through Finite Element Analysis. A Lumped Element Model was also developed to further examine the heat paths in the DPHP sensor and suggest design modifications. The trend exhibited by the lumped model corroborates the results of Finite Element Analysis. Laboratory experiments were performed with DPHP sensors having different heater element positions, results of which validated the modeling outcomes. The insights gained in this study would serve as the design guidelines for manufacturing DPHP soil-moisture sensors with improved accuracy at minimal power consumption.

Effect of spatial variations and desiccation cracks on the DPHP and MPHP sensors

In sensing soil-moisture, there are inherent field related issues such as uncertainty and unpredictable distribution of minute amounts of trapped water and morphological changes of soil such as lumps and cracks due to desiccation. This poses problems for measurements done using a dual-probe heat-pulse (DPHP) technique that uses a narrow cylindrical sampling zone between heater and temperature probes. Thus, DPHP sensors are susceptible to errors. Hence, we studied and compared single-point and multi-point soil-moisture measurements using the heat-pulse technique. For this, we designed and developed a multi-point heat-pulse (MPHP) sensor with three temperature probes that enhanced the sampling zone to a volume of 840 mm3, which is three times that of the DPHP sensor. Sequentially deployed DPHP and MPHP sensors with spatial variations revealed that the maximum difference between the measured percentage of moisture from the DPHP sensor and standard oven-dried instrument was more than 10%, whereas for the MPHP sensor the discrepancy was only around 3%. Furthermore, when cracks appeared in the soil mass, it was observed that the discrepancy of DPHP sensor is around 16% while that for the MPHP sensor was still only 3%.

Sensitivity analysis of temperature changes for determining thermal properties of partially frozen soil with a dual probe heat pulse sensor

Determining thermal conductivity (λ) and volumetric heat capacity (C) of partially frozen soils with a dual probe heat pulse (DPHP) sensor is challenging because an applied heat pulse melts ice surrounding the heater probe. Examining DPHP temperature changes with a commonly-used analytical solution that only accounts for heat conduction leads to inaccurate λ and C estimates for partially frozen soils at temperatures between −5 °C and 0 °C. In order to determine λ and C accurately and simultaneously, it is necessary to understand how various properties of partially frozen soil influence the temperature changes produced by DPHP sensors. The objective of this study is to determine the sensitivity of DPHP temperature changes to soil conditions and soil thermal properties. A numerical solution for radial heat conduction with soil freezing and thawing is developed. A series of simulations are performed, in which various errors are imposed onto a selected model parameter while other model parameters are held constant, and sensitivity coefficient values (φ) of the time of maximum probe temperature (tm) and of the maximum probe temperature rise (Tm) for each parameter are calculated. Temperature changes at the measurement probe are quite sensitive to initial soil temperature (φ values for tm and for Tm are −0.99 and 0.99, respectively), λ (φ value for tm is −0.93), and parameters determining the shape of the soil freezing characteristic (FC) curve, i.e., saturated water content θs (φ values for tm and for Tm are 0.59 and −0.73, respectively) and n (φ values for tm and for Tm are −2.7 and 2.4, respectively). Temperature changes are not very sensitive to C (φ values for tm and for Tm are 0.034 and −0.15, respectively). Although previous investigations tried to determine C by inverse analysis, this sensitivity analysis shows that the influence of C on temperature response to a heat pulse is masked by that of the FC. Thus, λ and FC parameters are the best candidate parameters to be determined by inverse analysis of DPHP data. This new result will guide further testing of DPHP sensors in partially frozen soils.

Compensation of temperature effects for in-situ soil moisture measurement by DPHP sensors

Dual probe heat pulse (DPHP) sensors are economical solutions for soil moisture measurements. However, in agriculture fields the temperature significantly changes from time to time during 24h, which affects response of the soil moisture sensor. This paper, analyzes and models the error produced in the response of the DPHP sensors due to variation of the soil temperature. For this purpose, first effect of the soil temperature on the response of the sensor is studied using eight different soil samples. Accordingly, the existing soil moisture model, used for DPHP devices, is modified and used for the temperature compensation. A low power DPHP sensor comprising one heater probe and one temperature sensor probe, placed 0.003m apart, is fabricated. A low power, automated system, dissipating average power of 30mW, is also developed for the field measurements to validate the proposed model. The developed system is deployed in the field and soil moisture is measured for 38h at every 1h interval. Field measurements indicates that volumetric moisture content measured without temperature compensation leads to error of about 3% and with temperature compensation the error is reduced to 0.5%.

Monitoring water content dynamics of biological soil crusts

Biological soil crusts (hereafter, “biocrusts”) dominate soil surfaces in nearly all dryland environments. To better understand the influence of water content on carbon (C) exchange, we assessed the ability of dual-probe heat-pulse (DPHP) sensors, installed vertically and angled, to measure changes in near-surface water content. Four DPHP sensors were installed in each of two research plots (eight sensors total) that differed by temperature treatment (control and heated). Responses were compared to horizontally installed water content measurements made with three frequency-domain reflectometry (FDR) sensors in each plot at 5-cm depth. The study was conducted near Moab, Utah, from April through September 2009. Results showed significant differences between sensor technologies: peak water content differences from the DPHP sensors were approximately three times higher than those from the FDR sensors; some of the differences can be explained by the targeted monitoring of biocrust material in the shorter DPHP sensor and by potential signal loss from horizontally installed FDR sensors, or by an oversampling of deeper soil. C-exchange estimates using the DPHP sensors showed a net C loss of 69 and 76 g C m−2 in control and heated plots, respectively. The study illustrates the potential for using the more sensitive data from shallow installations for estimating C exchange in biocrusts.

A general in situ probe spacing correction method for dual probe heat pulse sensor

The dual probe heat pulse (DPHP) method is gaining popularity for measuring soil thermal properties. However, because of the fact that the DPHP measured heat capacity (c) of soil is hyper-sensitive to probe spacing variation, probe deflection causes large error in the measured c. To deal with probe deflection, recently, Liu et al. (2013) has proposed an in situ probe spacing correction method, but, their method was based on the inline deflection assumption. Wen et al. (2015) found that for non-inline deflected DPHP sensors, the method of Liu et al. (2013) provided poor reduction of the error in c. To cope with the non-inline deflection, in this study, we introduce a new DPHP sensor design by using three thermistors within the same temperature probe. A related probe spacing correction method for non-inline deflected probes was also presented. Both numerical simulation and experiment were conducted to test the new model. We define θ as the inclination angle of the probe deviation from the vertical direction. For experiment of the outward deflection (5.8°<θ<6.8°), the error in c is in the range from −23% to −76%; after inline in situ correction, the error decreases to the range of 12% to 44%; after using our non-inline in situ correction, the error is between 1% and 8%. Our three-dimensional finite element numerical simulation also demonstrates that, compared with the method of Liu et al. (2013), the new sensor and correcting method can significantly eliminate errors in c caused by probe deflections. The new DPHP sensor design and the non-inline deflection model have the potential to replace the method of Liu et al. (2013), and become the standard method for correcting probe spacing in situ.

A Dual‐Probe Heat‐Pulse Sensor with Rigid Probes for Improved Soil Water Content Measurement

The dual-probe heat-pulse (DPHP) method is attractive for measuring soil thermal properties and volumetric water content. The purpose of this study was to develop and test a DPHP sensor having rigid probes made from thick-walled stainless steel tubing (2.38-mm outside diameter). The probes of this sensor are much more resistant to deflection than those of conventional DPHP sensors, decreasing measurement error caused by probe deflection during insertion into the soil. Laboratory experiments were conducted across a wide range of saturation levels with glass beads and three soils of different textures. For inferring soil properties from the proposed sensor, we applied the recently developed identical cylindrical perfect conductors (ICPC) model instead of the infinite line source (ILS) model that is typically used. The ICPC model improves solution for heat transport through the probe–soil system by accounting for the heat capacity and radius of the probes. Our results show a root mean square error of 1.4% volumetric water content and elimination of the measurement bias typically encountered with DPHP measurements. We conclude that the improved sensor, in combination with the ICPC model, provides a general, soil-independent water content estimate that is especially suitable for field soil water content monitoring because of its robust design with rigid probes. Because of its simplicity and measurements independent of soil type, we propose the presented DPHP method as an excellent alternative to other available measurement techniques for soil water content.

A low-power, low-cost soil-moisture sensor using dual-probe heat-pulse technique

This paper presents the development and testing of an integrated low-power and low-cost dual-probe heat-pulse (DPHP) soil-moisture sensor in view of the electrical power consumed and affordability in developing countries. A DPHP sensor has two probes: a heater and a temperature sensor probe spaced 3mm apart from the heater probe. Supply voltage of 3.3V is given to the heater-coil having resistance of 33Ω power consumption of 330mW, which is among the lowest in this category of sensors. The heater probe is 40mm long with 2mm diameter and hence is stiff enough to be inserted into the soil. The parametric finite element simulation study was performed to ensure that the maximum temperature rise is between 1°C and 5°C for wet and dry soils, respectively. The discrepancy between the simulation and experiment is less than 3.2%. The sensor was validated with white clay and tested with red soil samples to detect volumetric water-content ranging from 0% to 30%. The sensor element is integrated with low-power electronics for amplifying the output from thermocouple sensor and TelosB mote for wireless communication. A 3.7V lithium ion battery with capacity of 1150mAh is used to power the system. The battery is charged by a 6V and 300mA solar cell array. Readings were taken in 30min intervals. The life-time of DPHP sensor node is around 3.6 days. The sensor, encased in 30mm×20mm×10mm sized box, and integrated with electronics was tested independently in two separate laboratories for validating as well as investigating the dependence of the measurement of soil-moisture on the density of the soil. The difference in the readings while repeating the experiments was found out to be less than 0.01%. Furthermore, the effect of ambient temperature on the measurement of soil-moisture is studied experimentally and computationally.

Evaluation of a self-correcting dual probe heat pulse sensor

The dual probe heat pulse method (DPHP) can be used to measure soil thermal properties. However, in situ probe spacing is prone to change resulting in large errors of measured soil heat capacity c. A newly designed DPHP sensor has two thermistors in the temperature probe which can be used to calculate in situ changes in probe spacing. This new sensor has been tested under the limited condition of linear coplanar probe deflection. i.e., probes were deflected in-line but were not bent in different directions. However, actual probe deflections may not always be coplanar linear. In this study the applicability of the new DPHP sensor is evaluated in fine sand and in silica sand for a variety of probe deflections. Probes are deflected at the bottom end (bottom) or top end (top) of probes. Results indicate that the new sensor can significantly eliminate errors in c caused by coplanar and non-coplanar probe deflections. Compared with bottom deflections, top deflections have larger errors in c. Thus, theory used to correct for deflections is more applicable to bottom deflections than to top deflections. The errors in c for saturated soil materials are larger than the errors in c for dry soil materials, because of the finite response times of the thermistors used in the probes. Clearly, the newly designed DPHP sensors have the potential for reducing errors caused by various kinds of probe deflections that may be encountered in the field.

A Self-Calibrated Dual Probe Heat Pulse Sensor for In Situ Calibrating the Probe Spacing

Dual probe heat pulse method (DPHP) is a popular method for measuring soil thermal properties. However when this method is applied in the field, the distance between the temperature probe and the heating probe (probe spacing) may change due to probe deflection, and thus cause error in measured heat capacity (c) of soil. We developed a self-calibrated DPHP for in situ calibration of probe spacing, using a temperature probe with two imbedded thermistors (10 mm apart in the longitudinal direction). Experimental results for sand and fine sand samples indicate that this method can significantly reduce error caused by the probe deflection. If we define σ as the inclination angle of probe deviation from the vertical direction, for inward deflection with 0.8° < θ < 0.9°, the error in c is between –8.1 and –14.3%; after in situ calibration, it is between –0.1 and –4.3%. For outward deflection with 3.2° < θ < 3.5°, the error in c is in the range from 22.9 to 38.8%; after in situ calibration, the error reduces to from –3.8 to –7.8%. This new DPHP design may be applied in the field for reducing error caused by probe deflection.

An Adiabatic Boundary Condition Solution for Improved Accuracy of Heat-Pulse Measurement Analysis Near the Soil-Atmosphere Interface

The infinite line source model (ILS model) is widely used in the dual-probe heat pulse (DPHP) method for measuring the thermal conductivity (k), specific heat capacity (c), and thermal diffusivity (α) of soil. However, there exists errors when sensors are located very close to the soil–atmosphere interface. The purpose of this study is to develop a new method to accurately determine k and c near the soil–atmosphere interface. The method of images was used to obtain the ILS solution with an adiabatic boundary condition (ILS–ABC), when DPHP sensors are near the soil–atmosphere interface. Both finite element simulations and DPHP experiments verified that the soil–atmosphere could be approximated by the adiabatic boundary condition (ABC). The new solution performed well in predicting the thermal properties of the samples when compared with the ILS model, which ignored the existence of the soil–atmosphere interface. If the ILS model was used to compute k and c rather than the new ILS–ABC model, the magnitude of the error in k and c increased rapidly with decreases in burial depth (h) and could be larger than 30% at h ≤ 3 mm. The solution may be helpful for better extracting soil thermal properties near the soil–atmosphere interface.

Sensor and Numerical Simulator Evaluation for Porous Medium Desiccation and Rewetting at the Intermediate Laboratory Scale

Soil desiccation, in conjunction with surface infiltration control, is considered at the Hanford Site as a potential technology to limit the flux of technetium and other contaminants in the vadose zone to the groundwater. An intermediate‐scale experiment was conducted to test the response of a series of instruments to desiccation and subsequent rewetting of porous media. The instruments include thermistors, thermocouple psychrometers, dual‐probe heat pulse sensors, heat dissipation units, and humidity probes. The experiment was simulated with the multifluid flow simulator STOMP, using independently obtained hydraulic and thermal porous medium properties. All instrument types used for this experiment were able to indicate when the desiccation front passed a certain location. In most cases the changes were sharp, indicating rapid changes in moisture content, water potential, or humidity. However, a response to the changing conditions was recorded only when the drying front was very close to a sensor. Of the tested instruments, only the heat dissipation unit and humidity probes were able to detect rewetting. The numerical simulation results reasonably match the experimental data, indicating that the simulator captures the pertinent gas flow and transport processes related to desiccation and rewetting and may be useful in the design and analysis of field tests.

Effect of Probe Deflection on Dual‐Probe Heat‐Pulse Thermal Conductivity Measurements

The dual‐probe heat‐pulse (DPHP) method is useful for measuring soil thermal properties; however, the probes of a DPHP sensor can deflect when inserted into the soil. Theoretical analysis has shown that measurements of thermal conductivity (λ) should be unaffected by deflection‐induced changes in probe spacing. To verify this result, the conductivities of water, dry sand, and saturated sand were measured using DPHP sensors with probes subject to inward deflection, no deflection, and outward deflection. No error in λ was detected when probes were deflected inward by an amount that caused a 14% reduction in probe spacing. Outward deflection (15% increase in spacing) caused error in λ estimates, but the errors were small (≤0.04 W m−1 K−1) and likely to be of little consequence in most applications. We conclude that estimates of λ obtained with the DPHP method are largely unaffected by changes in probe spacing caused by deflection.

Correcting Dual‐Probe Heat‐Pulse Readings for Changes in Ambient Temperature

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.

In situ measurements of the thermal properties of a northern peatland: Implications for peatland temperature models

Carbon uptake/release in peat soils (the latter especially in the form of methane) is strongly dependent on soil temperature. However, previous peatland temperature models have not represented soil temperatures accurately due to either errors in their parameterization or errors in the representation of heat transfer processes. Dual probe heat pulse sensors (DPHPS) and triple‐probe heat pulse sensors (TPHPS) were used to provide detailed in situ measurements of the soil thermal properties of Sphagnum peat and the advective liquid heat flux resulting from percolating rainfall. The difficulties of applying the DPHPS approach within poorly decomposed Sphagnum peat are first considered. Our results suggest that measurement‐induced advective vapor and liquid heat fluxes occurred when using the DPHPS. The analytical equations normally used to calculate the thermal diffusivity and volumetric heat capacity (C) from DPHPS measurements, therefore, cannot be applied within unsaturated Sphagnum peat. However, a numerical approach enabled the soil thermal properties to be estimated when an instrument‐induced advective vapor flux was significant. When an instrument‐induced advective liquid heat flux was significant, the relevant DPHPS data were identified and rejected. The measurements of the soil thermal properties were used to (1) develop an empirical model of the vertical variations in C through the unsaturated zone of poorly decomposed Sphagnum peat and (2) to develop an empirical relationship between the thermal conductivity (k) and C. The TPHPS measurements showed that the advective heat flux due to percolating rainfall occurred for a maximum of 24 hours after rainfall events. Its influence on soil temperatures may therefore be negligible.

Roots Affect the Accuracy of Dual-probe Heat-pulse Method for Measuring Water Content in Plant Growth Media

Little attention has been paid to how the presence of roots influences water content measurements obtained with water content sensors. This issue is especially important if sensors are deployed in densely rooted soil or growth media. This work addresses the impact of roots on water content measurements obtained with dual-probe heat-pulse (DPHP) sensors. In the DPHP method, the maximum temperature rise in response to heating (Tmax) is used to calculate volumetric heat capacity, which in turn is used to calculate volumetric water content. The accuracy of DPHP sensors was evaluated in unrooted and rooted 0.25–1 mm baked ceramic aggregate. For both restricted and unrestricted volumes of aggregate the presence of roots caused DPHP sensors to consistently overestimate water content by 0.05–0.09 cm3·cm-3. Measured values of Tmax were lower in the presence of roots, which resulted in overestimation of volumetric heat capacity that was attributed to the high specific heat of water contained in roots in addition to that contained within the aggregate. Differences in water content and aggregate heating between unrooted and rooted aggregate equilibrated to the same matric potential were less distinct in unrestricted volumes, where the decrease in bulk density has the offsetting effect of lowering the heat capacity. Error in water content caused by the presence of roots and changes in bulk density was estimated by developing a theoretical mixing model for volumetric heat capacity that accounted for the heat capacity of all constituents, including aggregate, water, root water, and root tissue. Predicted errors in volumetric water content due to changes in bulk density or changes in heat capacity due to roots agreed well with direct measurement.

SIMPLIFIED COMPUTATIONAL APPROACH FOR DUAL‐PROBE HEAT‐PULSE METHOD

Two equations are currently available for estimating soil volumetric heat capacity (pc) with the dual-probe heat-pulse (DPHP) method. One is simple but gives only approximate results because it assumes that the DPHP sensor releases an impulse of heat instantaneously. The other explicitly accounts for the finite duration of heating and gives exact results. Unfortunately, the equation that gives exact results involves the exponential integral function, which is not available in most computer spreadsheet software packages or data logger function libraries. In this note we introduce an approximation of the exact equation that contains only simple algebraic functions. The approximation consists of the first five terms of a Taylor series, which are written as a telescoped polynomial for computational purposes. For most applications of the DPHP method, the polynomial approximation gives estimates of pc that are at least an order of magnitude more accurate than estimates obtained from the simple equation based on instantaneous heating.

SIMPLIFIED COMPUTATIONAL APPROACH FOR DUAL-PROBE HEAT-PULSE METHOD

Two equations are currently available for estimating soil volumetric heat capacity (ρc) with the dual-probe heat-pulse (DPHP) method. One is simple but gives only approximate results because it assumes that the DPHP sensor releases an impulse of heat instantaneously. The other explicitly accounts for the finite duration of heating and gives exact results. Unfortunately, the equation that gives exact results involves the exponential integral function, which is not available in most computer spreadsheet software packages or data logger function libraries. In this note we introduce an approximation of the exact equation that contains only simple algebraic functions. The approximation consists of the first five terms of a Taylor series, which are written as a telescoped polynomial for computational purposes. For most applications of the DPHP method, the polynomial approximation gives estimates of ρc that are at least an order of magnitude more accurate than estimates obtained from the simple equation based on instantaneous heating.