Materials used for making thermo-TDR sensors.
Advanced sensors provide new opportunities to improve the understanding of soil properties and processes. One such sensor is the thermo-TDR sensor, which combines the functions of heat pulse probes and time domain reflectometry probes. Recent advancements in fine-scale measurements of soil thermal, hydraulic, and electrical properties with the thermo-TDR sensor enable measuring soil state variables (temperature, water content, and ice content), thermal and electrical properties (thermal diffusivity, heat capacity, thermal conductivity, and bulk electrical conductivity), structural parameters (bulk density and air-filled porosity) and fluxes (heat, water, and vapor) simultaneously. This chapter describes the theory, methodology, and potential applications of the thermo-TDR technique.
- thermo-TDR sensor
- heat pulse
- time domain reflectometry
- soil thermal properties
- soil physical measurements
Dynamic, in situ measurements of soil temperature (
In this chapter, the theories, methodologies and applications of the thermo-TDR technique are presented.
2. Theory and methodology of the thermo-TDR technique
2.1 Basic principles
The heat pulse technique can measure soil volumetric heat capacity (
2.2 Theories and calculations
2.2.1 Determination of soil thermal properties using the ILS theories
Thermo-TDR technique estimates soil thermal properties from the temperature change-by-time data at the sensing probes (heat pulse signals) based on line-source heat transfer models. The most widely known model is based on the infinite line source (ILS) theory considering an instantaneous or pulsed heating scheme, which assumes the heating probe as a line heat source with zero diameter and infinite length [9, 14, 15, 16]. For an isothermal and homogeneous soil with a uniform initial temperature distribution, the solution of the Fourier radial equation for heat conduction of a short-duration heat-pulse away from an infinite line source was developed by  further analyzed by [15, 16]. The temperature distributions in a cylindrical system are as follows:
2.2.2 Determination of soil thermal properties using the CPC solution
Ignoring the finite heat pulse probe properties (finite radius and finite heat capacity) can be a significant source of error when estimating soil thermal properties with the ILS theory, especially when there is a large contrast between the physical properties of probes and soil [18, 19]. Peng et al.  showed that finite probe effects on temperature rise with time curves were most significant in dry soils, and faded with increasing θ; the ILS theory can cause about 6% relative error in dry soil thermal property estimates . Knight et al. proposed a semi-analytical solution of the cylindrical perfect conductors (CPC) theory, accounting for the finite probe radius and finite probe heat capacity . The CPC theory was successfully applied in various studies [19, 21, 22]. This is especially true for the large sensor designs, in which the CPC theory reduces the error due to the finite probe effects. The theories and applications of CPC theory can be found in .
Figure 1 shows typical heat pulse signals (temperature change-by-time data) in two sensing probes of a thermo-TDR measurement on a loamy sand soil with water content of 0.15 m3 m−3. Generally, soil temperature starts to increase when the heat pulse is initiated and then decreases with time after the heat pulse ceases. The heating rate
2.2.3 Determination of soil water content and electrical conductivity
Soil θ and σ measurements are determined from the TDR waveforms obtained with the reflectometer device. Figure 2 presents a typical TDR waveform generated with the TDR200 device (Campbell Scientific Inc., Logan, UT). The TDR technique determines
Following Heimovaara et al.
2.3 Sensor configuration and construction
The design of the thermo-TDR sensor must meet several criteria to achieve the requirements of line-source heat-pulse theory to measure soil thermal properties and TDR principles to derive soil water content and electrical conductivity [1, 22]. The key parameters are probe diameter (
Various configurations have been proposed for the thermo-TDR sensor. The original sensor design consisted of three parallel probes with 40-mm length, 1.3-mm diameter, and 6-mm probe-to-probe spacing  (Figure 3). The middle probe acted as a heater that introduced a heat pulse into soil, while the two outer needles acted as the sensing probes that measured the soil temperature at a known distance (e.g., ∼6 mm) from the heating probe.
Newer versions of thermo-TDR sensor designs, with various probe sizes and configurations (i.e.,
The small sensing volume of the Ren et al. sensor design made it suitable for fine-scale measurements, but the short probes somewhat restricted the accuracy of TDR measurements [1, 38]. Recently Peng et al. introduced a large-size thermo-TDR with a probe length of 70 mm, and a probe-to-probe spacing of 10-mm, a diameter of 2.38 mm for the heater probe, and a diameter of 2 mm for the sensing probe (Figure 4) . As a result, this sensing volume was three times larger than that of the Ren et al.  sensor, and greater accuracy was achieved with TDR θ measurement accuracy due to the reduction of the superimposed reflections. Peng et al. also integrated updated algorithms to determine soil thermal and dielectric properties in order to produce accurate θ, ρb and porosity values .
Thermo-TDR sensors are not readily commercially available. One may be able to make special order sensors from some companies, but in most cases the sensors are constructed in soil physics research laboratories. As shown in Figure 3, a thermo-TDR sensor usually consists of three probes that house the heating wire and temperature sensors (thermocouples or thermistors), an epoxy base that fixes the probes in place, extension wires for the heater and temperature sensors, and a coaxial cable for TDR measurement. The stainless-steel tubes that serve as housings for heating and sensing probes, can be custom made or produced from hypodermic needles with the specified diameter and length.
The heating probe is constructed by threading an enameled resistance heater wire (e.g., 38-gauge Nichrome 80 Alley), through the heating needle two or four times for a total resistance of about 888 Ω m−1. The sensing probes are typically constructed by positioning a thermocouple or a thermistor enclosed at the midpoint of each probe (Figure 3). More than one thermocouple (Type E, chromel-constantan, 40 American wire gauge [AWG]) can be also used to detect soil temperatures at several locations along the probe to enable in situ corrections of
For TDR measurements, a 75-Ω coaxial cable is connected to the sensor by soldering the inner conductor to the central probe and the shield to the outer probes. The thermocouple wires are extended by connecting them to longer extension wires of the same type (e.g., Type E, chromel-constantan, 36 American wire gauge [AWG]). The extension thermocouple and resistance wires are kept within 5 m to avoid signal losses in long wires. Finally, the three probes and wires are kept in place with a mold and casting resin.
|Thermocouple||Type E, chromel-constantan, 40 AWG, OMEGA Engineering, CT|
|Thermocouple extension wire||Type E, chromel-constantan, 36 AWG, OMEGA Engineering, CT|
|Thermistor||Model 10K3MCD1, 0.46-mm diam., 10 kΩ at 25°C; Betatherm Corp., Shrewsbury, MA|
|Resistance wire||79-μm diameter, 40 AWG, enameled, 205 Ω m−1, Nichrome 80 Alloy, Pelican Wire Co., Naples, FL|
|Stainless-steel tube||Ren et al. : 1.27-mm o.d. and 0.84-mm i.d for both heating and sensing probes .|
Peng et al. : 2.38-mm o.d., 0.71-mm wall thickness for heating probe, 2.00-mm o.d., 0.25-mm wall thickness for sensing probes .
|Coaxial cable||75 Ω coaxial cable, RG 187 A/U, Newark Electronics|
|Epoxy inside probes||High thermal conductivity, Omegabond 101, Omega Engineering, Stamford, CT|
|Casting resin for sensor body||Water proof, Cr600 Casting Resin, Micro-Mark, Berkeley Heights, NJ|
2.4 Equipment and sensor operation
The operation of a thermo-TDR sensor requires a setup to generate the heat pulses, a TDR device that generates a fast-rise-time electromagnetic pulse, samples and digitizes the resulting reflection waveform, and data acquisition and control systems (Figure 3). For the TDR part, a coaxial cable tester (e.g., model 1502B, Tektronix Inc., Beaverton, OR) or a TDR200 reflectometer system (Campbell Scientific Inc., Logan, UT) generates the reflection waveform for analysis or storage. Simultaneous and automatic collection of multiple TDR measurements can be achieved with compatible multiplexers connected to a datalogger (e.g., model CR1000x or CR3000, Campbell Scientific Inc., Logan, UT) that retrieves TDR waveforms or dielectric constants for further analysis of θ or σ.
The experiment setup commonly used for a heat pulse measurement, which consists of a datalogger, a circuit, and a DC power (Figure 5). The circuit consists of a relay and a 1-Ω precision resistor, which is controlled by the datalogger. A DC power supply or a 12-volt battery applies a constant current for a fixed time to the heater wires to generate the heat pulse. The extension wires of thermocouples/thermistors are connected to a datalogger for temperature measurements. A switch to control the heat pulse is through a relay embedded in the circuit that can be activated by the datalogger. The resistance wire is heated for a controlled amount of time (typically 8–20 s for small sensors and 15–30 s for large sensors). During the heat pulse process, the current in the heater wire is determined automatically by measuring the voltage drop across a 1-Ω precision resistor which is in series with the heater wire.
Once the measurement is initiated, the current in the resistance wire and soil temperatures of the sensing probes are recorded at a 1-s interval for about 100–300 s with a datalogger (e.g., model CR1000x or CR3000, Campbell Scientific Inc., Logan, UT). The total measurement time can be set to be longer than 300 s, especially when the background soil temperature varies significantly with time under the field conditions. In this case, a linear temperature correction procedure is needed for the soil thermal property calculations [39, 40]. The heating intensity should be carefully controlled to achieve a clear heat pulse signals at the sensing probe and to avoid potential heat induced moisture redistributions at the same time. Normally, the heat pulse duration is set to make sure that the temperature changes at the sensing probes typically fall in the range of 0.5–1.0°C.
The thermo-TDR sensor can be placed horizontally or vertically in a soil profile, depending on the application objectives. Special care is required to avoid needle deflection and to keep good soil-probe contact during installation. It is recommended to install the sensor under moist conditions when probe deflection is less likely to occur .
2.5 Sensor calibrations
Accurate information about parameters
Wen et al. designed a probe-spacing-correction thermo-TDR sensor with 6-cm long sensing probe, each enclosed with three thermistors at different distances away from the sensor base . This enabled the calculation of probe deflection angles to estimate actual in situ
For TDR-σ measurements with the thermo-TDR sensor,
3. Applications of the thermo-TDR technique
3.1 Determination of soil thermal property and electrical conductivity curves
The thermo-TDR technique permits routine measurements of soil thermal properties, water content and electrical conductivity on repacked soil columns and in situ field measurements. Figure 6 presents the results of soil thermal properties on a repacked sand soil, showing typical trends of
Figure 7 shows measured apparent σ values for sand wetted by various salt solution concentrations to θ ranging from 0.08 to 0.25 m3 m−3. It is clear that the increases in salt concentrations lead to significant increases in σ, and σ also increases with θ. Soluble salt ions in soil solution can enhance the electric conductivity of bulk soil. For salt affected soils, the Peng et al.  thermo-TDR sensor can measure σ values as large as 22.5 dS m−1. Thus, important observations of solute, heat and water properties in soil are possible with thermo-TDR sensors.
3.2 Determination of soil bulk density, porosity and air-filled porosity
The thermo-TDR technique soil thermal property and water content data can be used to estimate soil structure changes [43, 48, 49]. The thermo-TDR technique can be applied to determine in situ ρb,
Thermo-TDR determinations of ρb depend on the de Vries
From Eq. (11), ρb is derived as,
where cs is the specific heat of soil solids (kJ kg−1 K−1), ρw is the density of water (1.0 g cm−3), and cw is the specific heat of water (4.18 kJ kg−1 K−1) . Once soil
Because λ measurements using the heat pulse technique are not influenced by needle deflection, Lu et al. proposed the λ-based thermo-TDR method to determine in situ ρb . An empirical equation that related λ to ρb, θ, and soil texture was used ,
An iterative approach is used to numerically solve for ρb because there is no explicit solution for ρb from Eqs. (13)–(15). The nonlinear equation solver (
The empirical Lu et al. λ model introduced uncertainty in ρb estimates, especially for coarse soils . Thus, Tian et al. proposed a simplified version of the physically-based de Vries λ model to inversely estimate ρb, and they found that their λ model performed better than the
It is commonly recognized that a tilled soil layer undergoes great structural changes due to agricultural management and rainfall effects. The in situ measurements of ρb in tilled soil layers using a thermo-TDR technique indicated that soil ρb increased following tillage because rainfalls caused soil particles to settle and consolidate [48, 49]. Figure 8 shows that soil ρb increased and then leveled off, and the thermo-TDR method determined ρb values mostly matched the core sample values.
With the thermo-TDR determined θ and ρb, soil
where θtotal is defined as the sum of volumetric θ values of root and soil. Fu et al. report that when the maize root density is greater than 0.037 g cm−3, Eqs. (21, 22) should be used to estimate ρb from thermo-TDR measured
3.3 Measuring soil ice contents during freezing and thawing
Although in-situ determination of soil ice content during freezing and thawing is challenging, a thermo-TDR technique has been developed to measure soil liquid water and ice contents in partially frozen soils. Tian et al. report that thermo-TDR determined heat capacity and liquid water content in partially frozen soil can be used to determine soil ice content . According to , the volumetric heat capacity of a partially frozen soil can be expressed as,
Tian et al. reported that the heating strength of heat pulse measurements should be carefully controlled for measurements in partially frozen soil to minimize ice melting during the process . Their results indicated that the heat pulse method failed to provide accurate thermal properties at soil temperatures between −5 and 0°C because of temperature field disturbances from latent heat of fusion. The optimized heating application strategy was found to be a 60-s heat duration (450 J m−1) or a 90-s heat duration (450–900 J m−1), and the
Tian et al. reported that the
For soils experiencing seasonal or diurnal freezing and thawing cycles, Kojima et al. proposed an approach with TDR-θ determinations made before and after an imposed ice melting process caused by heating the soil surrounding the sensor . The θi value was equivalent to the difference between the two TDR-θ values, which represented the liquid water content and total water content in the soil. Their method only relied on the two TDR-θ values but required long measurement intervals and a relatively large heat input to melt the ice.
3.4 Measuring heat, water, and water vapor fluxes in soil
The thermo-TDR method is a useful tool that can be used in laboratory and field experiments to study transient in-situ properties and processes related to coupled heat and water transfer in soil. Heitman et al. used thermo-TDR sensors in a closed soil cell with imposed transient boundary conditions to obtain non-uniform temperature, water and thermal property distributions . Thermo-TDR sensors were used to obtain soil thermal conductivity during wetting and drying processes on quartz sands for geothermal applications [59, 60, 61, 62].
Significant improvements in both sensor configurations and theories have been made in fine-scale measurements of coupled water and heat transfer process in soil under field conditions, especially in near surface soils . Based solely on the heat pulse function of the thermo-TDR sensor, the use of a series of such sensors aligned in a soil profile permitted the determination of soil heat fluxes, liquid water fluxes, and soil-water evaporation fluxes .
Based on Fourier’s law, the one-dimensional heat flux density (
A heat pulse technique based on the sensible heat balance of near-surface soil layers was able to determine in situ soil water evaporation (
An analytical solution that related soil water flux density (
Figure 11 presents a flowchart of the uses and outcomes for the thermo-TDR method. Generally, the thermo-TDR determined state variables and physical parameters can be estimated with proper models and methods. The most promising aspect of the thermo-TDR technique is the capability to determine in situ bulk density, porosity, heat flux, water flux and vapor flux. These provide opportunities to study transient heat and water processes in field soils, including water evaporation, sensible and latent heat, and liquid water fluxes [64, 68, 69, 82].
This chapter includes descriptions of thermo-TDR sensors, methods for collecting and analyzing data, and reviews of current and potential thermo-TDR applications. The thermo-TDR sensor, which combines a heat pulse probe with a time domain reflectometry probe for soil thermal and electrical properties determinations, provides new opportunities for improved soil measurements on thermal properties, water content, bulk electrical conductivity, ice content, bulk density, air-filled porosity, heat flux, water flux, and vapor flux. The thermo-TDR technique has the potential to monitor in situ soil physical properties and processes for vadose zone soils.
This work was funded by the National Natural Science Foundation of China (41977011 and 41671223), the U.S. National Science Foundation (2037504) and USDA-NIFA Multi-State Project 4188.