Geoderma 401 (2021) 115349

Available online 15 July 20210016-7061/© 2021 Elsevier B.V. All rights reserved.

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

Yujie Sang a, Gang Liu a,*, Tusheng Ren b

a Department of Land Use Engineering, College of Land Science and Technology, China Agricultural University, Beijing 100193, China b Department of Soil and Water Sciences, College of Land Science and Technology, China Agricultural University, Beijing 100193, China

A R T I C L E I N F O

Handling Editor: Morgan Cristine L.S.

Keywords: Dual probe heat pulse (DPHP) method Linear trend method (LTM) Reference temperature method (RTM) Thermal properties

A B S T R A C T

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.

1. Introduction

Soil thermal properties generally refer to soil thermal conductivity (λ), volumetric heat capacity (Cv), and thermal diffusion coefficient (α). Understanding soil thermal properties is necessary for analyzing soil thermal conditions (Hu et al. 2016), which has extremely important effects on soil biological, chemical and physical processes. The heat pulse probe method includes both the single probe method and the DPHP method (Liu et al., 2020; Lu et al., 2020; Heitman et al., 2020; He et al., 2018); the single probe method can only be used to measured λ (Bristow et al., 1994a; Abu-Hamdeh, 2001; Liu et al., 2017), and the DPHP method is a reliable and accurate method for obtaining soil α, λ and Cv (α = λ/Cv) both in laboratory and field experiments (Bristow et al., 1994b; Liu et al., 2016; Sang et al., 2020). Campbell et al. (1991) used DPHP method to measure soil heat capacity (the quotient value of Cv and bulk density) in laboratory with the coefficient of variation within 2.1%. Bristow et al. (1994a), Bristow et al. (1994b) performed laboratory DPHP experiments on air-dry sand and clay materials, and their measured thermal properties agreed well with those measured by other independent methods. The field experiments of Zhang et al. (2014)

supported the finding of Bristow et al. (1994a), Bristow et al. (1994b) and showed DPHP measured Cv values had root mean square error (RMSE) of 0.34 MJ m− 3 K− 1. Because of the good performance of DPHP method on soil thermal property measurements, DPHP method has gain popularity in recent years. Researchers have used this method to mea-sure soil water content (Bristow et al., 1993; Kamai et al., 2015; Li et al., 2016), soil evaporation (Heitman et al., 2008a; Trautz et al., 2014), ground heat flux (Peng et al., 2017; Lu et al., 2018a; Heitman et al., 2010), soil bulk density (Lu et al. 2018b), snow density (Liu and Si 2008), water flux (Kluitenberg et al., 2007), frozen soil thermal prop-erties (Kurz et al., 2017; Kojima et al., 2018), and ice content (Kojima et al., 2016). Recently, the theory of DPHP method have also been applied to distributed temperature sensing method (He et al. 2018). So, improving the accuracy of DPHP measured soil thermal properties is attracting the interests of researchers from different branches of scien-tific research.

In laboratory DPHP experiments, background temperature can be specifically controlled. Liu et al., (2013a), Liu et al. (2013b), and Liu et al. (2016) and Wen et al., (2015) controlled background temperature fluctuation within 0.02 ℃ during each DPHP measurement. But in field,

* Corresponding author. E-mail address: liug@cau.edu.cn (G. Liu).

Contents lists available at ScienceDirect

Geoderma

journal homepage: www.elsevier.com/locate/geoderma

https://doi.org/10.1016/j.geoderma.2021.115349 Received 25 February 2021; Received in revised form 5 July 2021; Accepted 6 July 2021

Geoderma 401 (2021) 115349

2

the measured samples (soils, plants or snow) are usually warming or cooling by the diurnal temperature cycle, resulting in the temperature changes of measured samples that are not caused by the heating probe of DPHP sensor alone. Jury and Bellantuoni (1976) assumed that the background temperature change during a heat pulse measurement could be modeled by a linear trend. They conducted single probe heat pulse measurement in laboratory experiments and demonstrated that at 5 cm burial depth, LTM significantly reduced standard error in λ from 1.38 W m− 1 K− 1 to 0.04 W m− 1 K− 1. Following Jury and Bellantuoni (1976), some researchers applied LTM in field DPHP experiments. Heitman et al. (2008b) installed six DPHP sensors at 0–66 mm depth and used LTM to measure soil water evaporation dynamics. Zhang et al. (2014) used DPHP method with LTM to measure thermal properties at eight soil layers (0–6, 2–6, 6–12, 12–18, 18–24, 24–30, 30–36, and 36–42 mm). Lu et al. (2018a) used DPHP method with LTM to measure soil ground heat flux with the top probe installed at 1 mm depth. Although LTM is widely popular in filed experiments, there is no previous studies had tested whether LTM performed well or not. Besides, the background temper-ature change with shallow burial depth might be drastic and there are at least two problems with using LTM: (1) the temperature versus time data might deviate from a linear trend (Zhang et al. 2017); (2) the temper-ature evolution before and after turning on the heating power might follow different trend (Sang et al., 2020). So large errors also occurred in field DPHP estimated λ and Cv even when LTM was used (Zhang et al., 2014; Sang et al., 2020). In addition, when DPHP sensors were buried near the soil surface, analytical solutions of Kluitenberg and Philip, 1999 and Liu et al., 2013b should be chosen.

Except for LTM, Jury and Bellantuoni (1976) proposed the RTM by placing a thermocouple horizontally 5 cm away from the probe to record background temperature trend in laboratory experiments. But their re-sults showed RTM was less accurate than LTM for the single probe heat pulse method. In order to use the RTM, Bristow et al. (1993) introduced a new DPHP design that contains a reference temperature probe to correct background temperature changes under laboratory condition. They found that RTM gave accurate estimations with most of the measured and the predicted soil water content values collapsed onto or near the 1:1 line. Unlike the horizontal placement of reference tem-perature probes, Young et al. (2008) installed DPHP sensors vertically to measure soil water content in the field, at the same time, they installed thermistors on the soil surface (other than at the same depth as the heating probe) to correct background temperature drift. They found unexplainable cyclical changes in measured soil water content, espe-cially when the single point method (Bristow et al., 1994) was used. Besides, their results indicated that the measured soil water content fluctuations sometimes exceeded 0.10 m3 m− 3 during a day with no precipitation. Compared to LTM, few researchs about the RTM in the field is conducted, but this method might improve the accuracy of DPHP measurements when background temperature change is significant. However, RTM consumes more thermocouples or thermistors and re-sults in occupying more sampling channels of datalogger, which in-creases the cost.

Researchers prefer to use LTM to correct the background tempera-ture (Heitman et al., 2008b; Zhang et al., 2014; Lu et al., 2018a), this might be because the mathematical calculation of LTM is simple and convenient, and using LTM does not require additional hardware component. However, the linear assumption of Jury and Bellantuoni (1976) is violated frequently in daytime and LTM had shown limitations in the field (Zhang et al., 2017; Sang et al., 2020). In this study, we compared the performance of LTM and RTM in field experiments with different burial depth, aim at telling researchers under which conditions should we use which method (LTM or RTM) to obtain accurate DPHP estimations.

2. Materials and method

2.1. Device and installation

The DPHP sensor used in this study is illustrated schematically in Fig. 1(a). It consists of one heating probe and four temperature probes, which were constructed from stainless-steel tubing (Small Parts Inc., Miami Lakes, FL) with 1.27-mm-o.d. and 0.84-mm-i.d. The heating probe has a length of 40 mm and each temperature probe has a length of 20 mm. A heating wire (Nichrome A, 79-μm diam, 205 Ω m− 1, Pelican Wire Co., Naples, FL) was installed in the heating probe, and a therm-istor (0.46-mm diam., 10 kΩ at 25 ◦C, Model 10K3MCD1, Betatherm Corp., Shrewsbury, MA), 20 mm away from the sensor base, was installed in each temperature probe. Five probes are secured to a 30.0 mm thick Delrin plug using epoxy. Previous studies have shown that if probe spacing is calibrated in an agar solution, the DPHP method tends to overestimate heat capacity of dry soil (Tarara and Ham, 1997; Ham and Benson, 2004). Thermal contact resistance between the probes and the surrounding soil is a possible reason for the overestimations (Basinger et al., 2003; Liu et al., 2012). Therefore, we used the method of Mori et al. (2003) and Sang et al. (2020) to calibrate the probe spacing in dry sand with known heat capacity of 751 J kg –1 K –1 (measured by differential scanning calorimeter, DSC, Q2000, TA, Instruments, New Castle, DE).

We fixed a DPHP sensor in a 10 cm by 15 cm by 15 cm cubic acrylic container (Fig. 1(b)). The burial depth of the heating probe was 8 mm, which caused the burial depths of the temperature probes to be 2 mm, 8 mm, 14 mm, respectively. A second DPHP sensor was fixed as the reference temperature sensor, with horizontal spacing between the reference temperature probe and the temperature probe (h) of 4 or 2 cm. And only the temperature probes of the reference temperature sensor were connected to the datalogger (Fig. 1(d)), similar to the laboratory experiment setting of (Bristow et al., 1993). To exclude the effect caused by soil evaporation and uneven distribution of soil moisture, we used dry samples as our tested samples just as Jury and Bellantuoni (1976) and Bristow et al. (1994) did. We oven-dried the sand (98.24% sand, 1.65% clay and 0.11% silt) at 105 ◦C for 24 h and passed it through a 2 mm sieve, then we packed it into the container by 10 mm thick layers with bulk density of 1690 kg m− 3 after fixing the DPHP device on the wall of the container by epoxy. According to the finding of Sang et al. (2020), rapid net solar radiation variation cause huge errors in DPHP measured soil thermal properties. Therefore, a net solar radiometer was installed 10 cm above the soil surface. A 12-V battery powered CR3000 data logger (Campbell Scientific, Logan, UT) collected the temperature and the net solar radiation signals simultaneously. Wind velocity also be obtained from the meteorological station installed next to the experi-mental site and 2 m above the soil surface. To monitor the background temperature evolution, 60 s temperature signals were recorded before turned on the heating power (Ren et al. 2020).

Two field experiments were conducted: Experiment I was conducted from DOY 247 to DOY 253 of 2019 with h of 4 cm. We buried the container and dry sand with the DPHP sensor into the field soil, details about the experimental set-up can be found in Sang et al. (2020). Experiment II was added to eliminate the effect of inhomogeneous temperature field on RTM and conducted from DOY 342 to DOY 347 of 2019 with h of 2 cm. During Experiment II, to minimize the inhomo-geneous effects in horizontal direction. We dug a round pit with a radius of 40 cm and a depth of 20 cm and covered the pit with a large plastic sheet to isolate the surrounding soil from the pit. After that, the pit was filled with dry sand. Then the acrylic container with the DPHP device and dry sand was buried in the center of the sandpit (Fig. 1(c)). During the two field experiments, the measurement interval was set as half an hour (Akuoko et al., 2018) and no rainfall has occurred.

Y. Sang et al.

Geoderma 401 (2021) 115349

3

2.2. Theory

For an infinite, homogeneous and isotropic medium with uniform initial temperature, when an infinite linear heat source releases a heat pulse of duration t0, the temperature rise (ΔT) at radial distance r (m) is (de Vries, 1952):

ΔT(r, t) =q′

4πλ

{

Ei[

− r2

4α(t − t0)

]

− Ei[− r2

4αt

]}

t⩾t0 (1)

where q’ is the energy input per unit length of heater per unit time (W m− 1), λ is the thermal conductivity (W m− 1 K− 1), -Ei(-x) is the expo-nential integral, α is the thermal diffusivity (m2 s− 1), t is the time (s) beginning from a heat pulse initiation.

To reduce the errors caused by the soil-atmosphere interface (Philip and Kluitenberg, 1999; Xiao et al., 2015), Liu et al. (2013), Liu et al., 2017 approximated the air–soil interface as an adiabatic boundary and derived Eq. (2) by using the image method (Carslaw and Jaeger, 1959) and introducing a virtual heating probe:

ΔT =q

′

4πλ

{

Ei[

− r2

4α(t − t0)

]

− Ei[− r2

4αt

]}

+q′

4πλ

{

Ei[

− l2

4α(t − t0)

]

− Ei[− l2

4αt

]} (2)

Where l is the distance between the temperature probe and the vir-tual heating probe (m). The first term of the Eq. (2) is the ΔT value caused by the heating probe. And the second term of the Eq. (2) is the ΔT value caused by the virtual heating probe which is equivalent to the temperature rise induced by the accumulation of heat near the soil- atmosphere interface (Philip and Kluitenberg 1999). Field experiment of Zhang et al. (2014) demonstrated that the Eq. (2) could improve the

accuracy of DPHP measurements in field remarkably. Meanwhile, their result also showed that when d > 6 mm, Eq. (1) performs rather well, so in this study, only when d = 2 mm we will use Eq. (2).

2.3. Data processing

The processing of LTM: we performed the following linear regression on the temperature versus time data collected before turning on the heating power (Jury and Bellantuoni 1976).

Tf = a⋅t+ b (3)

where a and b are two regression parameters. Then ΔT (t) can be calculated as:

ΔT(t) = Tt − Tf (4)

where Tt, Tf were the temperature signals measured by the temperature probe and the temperature values calculated through Eq. (3), respectively.

The processing of RTM: we obtained ΔT (t) by subtracting Tt from the temperature measured by the reference temperature probe (Tr):

ΔT(t) = Tt − Tr (5)

After obtained ΔT (t) versus time data, the built-in “Findfit” function of Wolfram Mathematica 11.3 (Wolfram Research, Inc., Champaign, IL) was used to obtain λ and Cv.

2.4. Statistical analysis

Relative error (RE) and RMSE were calculated to evaluate the per-formance of the two background temperature correction methods (LTM

Fig. 1. The structure diagrams of DPHP sensor (a); Schematic diagram of the container with DPHP sensors and dry sand (b); Top view of the device used in Experiment II (c, except that there was no sandpit, top view of in Experiment I was same as that in Experiment II); Vertical deployment of the temperature probe and the reference temperature probe (d).

Y. Sang et al.

Geoderma 401 (2021) 115349

4

and RTM), and the extent of temperature deviated from the linear trend (Eq. (3)) during each DPHP measurement, respectively. Mean and standard deviation of net solar radiation (Rni) during 180 s period (Rn and σRn) were also calculated to explicate the fluctuations in solar ra-diation during each DPHP measurement.

RE(\%) = 100) = 100 × (m − m0)/m0 (6)

RMSE =

∑n

i=1(Tri − Tfi)/n

√

(7)

Rn = (∑n

i=1Rni)/n (8)

σRn =

[∑n

i=1(Rni − Rn)2

]/

n

√√√√ (9)

where m represents the measured values of λ (or Cv), m0 represent the actual values measured in laboratory, n is 180 for each DPHP measurement.

3. Result and discussion

3.1. The influence of solar radiation and burial depth on temperature change

Fig. 2(a) shows a diurnal variation of the net solar radiation (Rn) and the temperature without DPHP heating (Tr) at depth of 2 mm on DOY 252. From Fig. 2(a), we know that the lowest Tr (12.15℃) occurred at 4:30 and the highest one (39.85℃) occurred at 14:00, and the trend of Tr followed the trend of Rn. The part marked with a hollow circle in Fig. 2 (a) is enlarged in Fig. 2(b-d), which shows the transient Rn and Tr evolution patterns were complex. As showed in Fig. 2(b), in the morning at 9:00, the change of Tr can be approximated with a linear trend during the first 60 s period. But then the Tr change deviated from the linear trend gradually. Solar radiation caused surface heating might be the reason, for Rn = 82.78 ± 3.27 W m− 2 at 9:00 of DOY 252. At 13:00, the zig-zag Tr pattern showed in Fig. 2(c) can no longer be approximated by a linear trend. The temperature rose during the first 22 s, then from 22 s to 139 s, the temperature dipped from 38.18℃ to 38.10℃, finally the temperature returned to initial linearly upward trend from 139 s.

However, the Tr signal showed in Fig. 2(d), can be approximated with a linear trend during the entire 180 s period.

In spite of the complicated background temperature evolution trends, most researchers have accepted the constant change rate assumption of the background temperature (Jury and Bellantuoni 1976) and used LTM to analyze DPHP data (Lu et al., 2018a; Zhang et al., 2014; Heitman et al., 2008b). When LTM was used, the difference between the background temperature and the linear trend (Eq. (3)) will affect DPHP estimations. Fig. 3 shows the value of RMSE between the in-situ measured Tr and the linear trend (Eq. (3)), and the values of Tr Rn, Rn, σRn and wind velocity. Long wave radiation from ground was the major component of atmosphere-soil energy exchange before 9:00 and after 18:00, during this period the Rn value varied from 1 W m− 2 to 77 W m− 2 with 1 < σRn < 8 W m− 2 (Fig. 3(c)). For d ≤ 14 mm, each day from sunset to sunrise (18:00–9:00), RMSE < 0.02 ℃ suggesting that without direct solar radiation there is no dramatic background tem-perature changes, and the background temperature changes were approximately linear. Each day with clear sky, from 9:00 to 18:00, the ground was heated by the incoming solar radiation, the value of RMSE was correlated with the value of net solar radiation and its fluctuations during each DPHP measurement. The mechanism for this correlation relating might be solar radiation with big values and big fluctuations could change the background temperature rapidly and vigorously like the one shown in Fig. 2(c) (RMSE = 0.12 ℃). We might conclude that the variation of solar radiation caused inhomogeneous heating bound-ary across the soil-atmosphere interface and thus affected the perfor-mance of LTM (Fig. 4). Additionally, wind is another important factor affecting the value of RMSE, similar to the finding of Sang et al (2020). During the period from DOY 345 to DOY 347, for d = 2 mm, RMSE ranged from 0.01℃ to 0.38℃ (Fig. 3(e)) with Rn, Rn and σRn within 157 W m− 2, 70 W m− 2 and 0.38 W m− 2, respectively, which showed little correlation between RMSE and net solar radiation. That because the wind velocity measured during this period was much higher than those during other durations of our experiments (Fig. 3(h)). This phenomenon was also observed and explained by Sang et al. (2020). Besides, the value of RMSE decreased as the measuring depth increased. For example, at 9:00 of DOY 247, the value of RMSEs were 0.21℃ (d = 2 mm), 0.09℃ (d = 8 mm) and 0.04℃ (d = 14 mm). That because the effect of solar ra-diation (Gao et al. 2008) and wind velocity (Sang et al., 2020) on the soil temperature decreases with increasing depth.

Fig. 2. The net solar radiation signals (Rn) and the temperature signals collected by the reference temperature probe (Tr) at 2 mm depth on DOY 252 (a); Typical Rn and Tr evolutions of (a), the vertical dashed line stands for the onset of heating pulse (b–d).

Y. Sang et al.

Geoderma 401 (2021) 115349

5

3.2. The performance of LMT in thermal property estimations

Fig. 4 shows time series of DPHP measured REs in λ and Cv at different burial depths with the LMT and RMT method, respectively. In general, the magnitude of RE in both λ and Cv, by using LTM, was large and was decreased with burial depth. For d = 2 mm, the largest REs in λ and Cv were 667% and 38%, respectively. The corresponding difference between Tr and linear trend (Eq. (3)) was RMSE = 0.42 ℃ (Fig. 3(a)) during this DPHP measurement. Fig. 5(a) shows the corresponding Tt and Tr signals, respectively. Both Tt and Tr increased with time linearly before turned on the heating power. But Tr depart from the linear trend since 85 s and decreased sharply, which was not reflected in the Tt signals. Because, in LTM, ΔT is calculated by using coefficients (a and b of Eq. (3)) obtained from fitting linear trend prior to the onset of heating the DPHP probes, the Tr change showed in Fig. 5(a) led to LTM per-formed poorly. But our results also shows that LTM could perform well in the deeper soil layer even though poor performance was occurred in the shallow soil layer. For example, at the same time, Tr change with time can be described by a linear relationship with RMSE = 0.026℃ for 8 mm depth and 0.005℃ for 14 mm depth, respectively. Consequent on that, RE was decreased to 3% in λ and 2% in Cv for 8 mm depth and was decreased to 4% in λ and 4% in Cv for 14 mm depth, respectively.

Besides, the magnitude of RE in λ and Cv showed differ and could be explained as: the Cv value was sensitive to the max value of ΔT (ΔTm) while the λ value was sensitive to the time (tm) when ΔTm occurred (Bristow et al. 1994). As Fig. 5(c) showed, difference of ΔT versus time curves obtained by LTM and theoretically (obtained by Eq. (2), details about obtaining theoretical ΔT versus time curve can be found in Sang et al (2020)) were − 0.21 ℃ in ΔTm (relative difference of − 24%) and − 19 s in tm (relative difference of − 29%), respectively. The laboratory ex-periments of Lu et al. (2014) showed using late-time data reduced the errors caused by the finite probe properties of the heat pulse probes and thermal contact resistance between the probes and soil samples. But according to Fig. 5, choosing the method of Lu et al. (2014) in the field instead leads to an increase in error and it is important to correctly remove the effects of background temperature fluctuation.

3.3. The performance of RTM in thermal property estimations

Fig. 4 shows that most of the time RTM could reduce DPHP mea-surement errors greatly. For example, when RTM replacing LTM was used, the RE was decreased from 667% to 68% in λ and from 38% to 32% in Cv, respectively (Fig. 4(a) and Fig. 4(b)). But Fig. 4 also shows that the performance of RTM is limited. Sometimes after using RTM, the

Fig. 3. Time series of the values of RMSE between the linear evolution trend obtained from Eq. (3) and the in-situ measured Tr change at d = 2 mm, 8 mm and 14 mm, and the in-situ measured Tr, Rn, Rn, σRn and wind velocity, respectively.

Y. Sang et al.

Geoderma 401 (2021) 115349

6

magnitude of REs was decreased but might still be large (such as 68% in λ) and using RTM can also lead to degraded DPHP method performance. For example, the measurement performed at 15:00 of DOY 249, the REs were larger by using RTM than those by using LTM at depth of 2 mm, 8 mm and 14 mm. The uniformity of thermal environment in soil samples (Jury and Bellantuoni, 1976; Zhang et al., 2017) can be the main reason.

As Fig. 5(b) showed, before turning on the heating power, the trends of Tt and Tr were different. The difference between Tt and Tr ranged from 1.6℃ to 2.0℃, further Tt decreased with time while Tr increased with time. That might because the 4 cm h value was too long to capture the temperature change where the temperature probe placed correctly. Therefore, compared to the difference between the ΔT versus time curve using LTM and the theoretical ΔT versus time curve, the difference be-tween the ΔT versus time curve using RTM and the theoretical ΔT versus time curve was much greater (Fig. 5(d)). So the REs in λ and Cv by using RTM was greater than those by using LTM (Fig. 4). Based on the results of Fig.5, we might conclude that horizontal soil heterogeneity, as well as temperature gradient, will cause error in thermal properties. Non- uniform temperature distribution can be avoided by using infrared thermal camera. In addition, when DPHP probes were buried shallow, because of low soil bulk density, it is difficult to ensure that the reference temperature probe lies in the same depth as the DPHP probe, which will also introduce error in thermal properties. This problem can be solved by fixing all probes in a pre-drilled plastic plate with deliberately designed probes. However, the loose soil of surface layer might result in poor thermal contact, thus cause the overestimation of c (Liu et al., 2017, 2020).

Fig. 6 showed that after adding the sandpit as the temperature buffer and decreasing the h value from 4 cm to 2 cm, RTM performed better than LTM, and compared to REs in λ and Cv measured from DOY 247 to DOY 253, REs measured from DOY 341 to DOY347 were considerably decreased, especially when d ≥ 8 mm. When RTM was used with d = 8 mm, from DOY 247 to DOY 253 period, RE in λ ranged from − 20% to 49% and RE in Cv ranged from − 13% to 38% (Fig. 4), from DOY 341 to DOY 347, RE in λ ranged from − 16% to 9% and RE in Cv ranged from − 10% to 12% (Fig. 6). When LTM was used, the similar reduction also

Fig. 4. Time series of REs in DPHP measured λ and Cv (DOY 247 to DOY 253) at depths of 2 mm, 8 mm and 14 mm, respectively. The horizontal distance be-tween the temperature probe and the reference temperature probe (h) was 4 cm. And the vertical axises in (a) and (b) were broken from 50% to 400%.

Fig. 5. Temperature measured by the temperature probe (Tt) and the reference temperature probe (Tr) with the horizontal distance between the temperature probe and the reference temperature probe of 4 cm, respectively ((a) and (b)); The ΔT versus time curves obtained by LTM, RTM and theoretically by Eq. (2) (TE), respectively ((c) and (d)). The vertical dashed line stands for the onset of heating pulse.

Fig. 6. Time series of REs in DPHP measured λ and Cv at depths of 2 mm, 8 mm and 14 mm from DOY 341 to DOY 347, respectively. The horizontal distance between the temperature probe and the reference temperature probe (h) was 2 cm. And the vertical axises in (a) and (b) were broken from 50% to 400%.

Y. Sang et al.

Geoderma 401 (2021) 115349

7

occurred. As for d = 2 mm, RE with RTM in λ ranged from − 31% to 25% and RE in Cv ranged from –22% to 15% but RE with LTM could still be large from DOY 341 to DOY 347, which was only a significant reduction for RTM from the DPHP measurements performed from DOY 247 to DOY 253. Further, unlike REs measured from DOY 247 to DOY 253 had periodicity, similar to the results of Young et al. (2008), REs measured from DOY 341 to DOY 347 had no apparent periodicity. One possible explanation is, the temperature gradient of surface soil in Experiment I affected by evaporation from the surrounding soil surface and was larger than that in Experiment II. Other factors such as the smaller h value could also has contributed to the better performance of DPHP method with RTM. Further research is needed to clarify the effects of these factors.

3.4. Comparison of LTM and RTM performance

According to Figs. 4 and 6, among most of DPHP estimations RTM performed better than LTM, but RTM sometimes performed poorly especially from DOY 247 to DOY 253. To clearly compare the perfor-mance of LTM and RTM. We divided the day time into three periods: (1) from 0:00 to 9:00; (2) from 9:00 to 16:00; (3) from 16:00 to 24:00, and calculated mean values and standard deviation values of REs in measured λ and Cv during each period (Fig. 7) and the cumulative dis-tribution of the absolute values of REs from DOY 247 to DOY 253 and from DOY 341 to DOY 347 (Fig. 8), respectively. When d = 2 mm, the performance of RTM was significantly better than that of LTM (Fig. 7 and Fig. 8). When LTM was used, the largest values of REs in λ were 667% (DOY 247 to DOY 253) and 429% (DOY 341 to DOY 347), and when RTM was used the values decreased to 206% and 31%, respec-tively. Besides, Fig. 7 shows when d = 2 mm, with low wind velocity (DOY 247 to DOY 253), both LTM and RTM can get accurate DPHP estimations with RE < (-1 ± 3)% in λ and RE < (3 ± 3)% in Cv during the periods from 0:00 to 9:00 and from 16:00 to 24:00. With the interference of wind (DOY 341 to DOY 347), LTM no longer performing well during the two periods mentioned above. For example, during the period from 0:00 to 9:00, RE = (7 ± 35) % in λ with LTM. Conversely, RTM per-formed as well as ever with RE < (-5 ± 7) % in λ and RE < (-1 ± 4) % in Cv. As for the period from 9:00 to 16:00, the performance of RTM was better than that of LTM, for example as showed in Fig. 7(b), RE = (17 ±87)% in λ and RE = (10 ± 18)% in Cv with LTM, and when RTM ws used errors was decreased to RE = (6 ± 28)% in λ and RE = (9 ± 17)% in Cv. When d ≥ 8 mm, the performance of RTM was similar to that of LTM, DPHP measurements can obtain accurate λ and Cv estimations, which

was similar to the results of Zhang et al (2014) and Xiao et al (2015). Based on the results and analysis presented above, under low wind speed condition, we recommend to use LTM as a cost-effective method to remove temperature drift caused by solar radiation. New theoretical theory and corresponding analytical solution, originated from heat conduction equation, should be developed to fine tune the LTM method to correct temperature fluctuation more effectively.

Fig. 8a and b show that when d = 2 mm, the value of cumulative distribution using RTM was larger than that using LTM, which caused the mean REs and standard deviation values both in λ and Cv decreased when RTM replacing LTM (Fig. 7). Meanwhile, Fig.8c, d, e and f clearly demonstrated that, by increasing burial depth from 2 mm to 14 mm, although the performance of RTM is reduced, RTM is still better than LTM for extracting soil thermal conductivity and heat capacity. In conclusion, the results of Fig.8 tell us that, the performances of RTM are consistently better than the performances of LTM, despite the cost of RTM, which is an avoidable shortcoming.

4. Conclusion

In this study, the performances of two background temperature correction methods of DPHP method were compared in field experi-ments. We carried out DPHP measurements, net solar radiation mea-surements and wind velocity measurements simultaneously and found that background temperature changed unpredictably and then led to errors in thermal property DPHP estimations if LTM was used. For example, with LTM, the RMSE value between Tr and linear trend of 0.42℃ can caused RE in λ reached up to 667% and in Cv reached up to 38%, respectively. Using RTM instead of LTM can decrease the errors in DPHP estimations, especially when the burial depth of the temperature probe of the DPHP sensor was 2 mm. Besides, in the two field experi-ments we carried out, RTM performed better than LTM did at burial depth of 2 mm for the absolute values of REs with RTM were smaller than that with LTM, and the mean values and standard deviation values of REs during each individual period were smaller than those with LTM. And when d ≥ 8 mm, the performance of RTM was similar to that of LTM. So it is essential to use RTM instead of LTM in the shallow soil layers to reduce errors caused by background temperature variations.

Fig. 7. The mean values (showed as the columns) and standard deviation values (showed as the error bars) of DPHP measured REs in measured λ and Cv during the periods from 0:00 to 9:00 ((a) and (d)), from 9:00 to 16:00 ((b) and (e)) and from 16: 00 to 24: 00 ((c) and (f)), respectively.

Fig. 8. Cumulative distribution of the absolute value of REs.

Y. Sang et al.

Geoderma 401 (2021) 115349

8

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the Natural Science Foundation of China Grant No. 42077008 and Grant No. 41771257.

References

Akuoko, O., Kool, D., Sauer, T.J., Horton, R., 2018. Surface energy balance partitioning in tilled bare soils. Agric. Environ. Lett. 3 (1), 180039. https://doi.org/10.2134/ ael2018.07.0039.

Abu-Hamdeh, N.H., 2001. Measurement of thermal conductivity of sandy loam and clay loam soils using single and dual probes. J. Agric. Eng. Res. 80, 209–216.

Basinger, J.M., Kluitenberg, G.J., Ham, J.M., Frank, J.M., Barnes, P.L., Kirkham, M.B., 2003. Laboratory evaluation of the dual-probe heat-pulse method for measuring soil water content. Vadose Zone J. 2 (3), 389–399.

Bristow, K.L., White, R.D., Kluitenberg, G.J., 1994a. Comparison of single and dual probes for measuring soil thermal properties with transient heating. Soil Res. 32 (3), 447. https://doi.org/10.1071/SR9940447.

Bristow, K.L., Campbell, G.S., Calissendorff, K., 1993. Test of a heat-pulse probe for measuring changes in soil water content. Soil Sci. Soc. Am. J. 57 (4), 930–934.

Bristow, K.L., Kluitenberg, G.J., Horton, R., 1994b. Measurement of soil thermal properties with a dual-probe heat-pulse technique. Soil Sci. Soc. Am. J. 58 (5), 1288–1294.

Campbell, G.S., Calissendorff, C., Williams, J.H., 1991. Probe for measuring soil specific heat using a heat-pulse method. Soil Sci. Soc. Am. J. 55 (1), 291–293.

Carslaw, H.S., Jaeger. J.C. 1959. Conduction of heat in solid. Oxford: Clarendon Press. de Vries, D.A., 1952. A nonstationary method for determining thermal conductivity of

soil in situ. Soil Sci. 73, 83–89. Gao, Z., Lenschow, D.H., Horton, R., Zhou, M., Wang, L., Wen, J., 2008. Comparison of

two soil temperature algorithms for a bare ground site on the Loess Plateau in China. J. Geophys. Res. 113 (D18) https://doi.org/10.1029/2008JD010285.

Ham, J.M., Benson, E.J., 2004. On the construction and calibration of dual-probe heat capacity sensors. Soil Sci. Soc. Am. J. 68, 1185–1190.

He, H.L., Dyck, M.F., Horton, R., Li, M., Jin, H.J., Si, B.C., 2018. Distributed temperature sensing for soil physical measurements and its similarity to heat pulse method. Adv. Agron. 148, 173–230.

Heitman, J.L., Horton, R., Sauer, T.J., DeSutter, T.M., 2008a. Sensible heat observations reveal soil-water evaporation dynamics. J. Hydrometeorol. 9, 165–171.

Heitman, J.L., Xiao, X., Horton, R., Sauer, T.J., 2008b. Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation. Water Resour. Res. 44, W00D05.

Heitman, J.L., Horton, R., Sauer, T.J., Ren, T.S., Xiao, X., 2010. Latent heat in soil heat flux measurements. Agric. For. Meteorol. 150 (7-8), 1147–1153.

Heitman, J.L., Xiao, X., Ren, T.S., Horton, R. 2020. Advances in heat-pulse methods: Measuring soil water evaporation with sensible heat balance. Soil Sci. Soc. Am. J. 77, 417–421.

Hu, Guojie, Zhao, Lin, Wu, Xiaodong, Li, Ren, Wu, Tonghua, Xie, Changwei, Qiao, Yongping, Shi, Jianzong, Li, Wangping, Cheng, Guodong, 2016. New Fourier- series-based analytical solution to the conduction-convection equation to calculate soil temperature, determine soil thermal properties, or estimate water flux. Int. J. Heat Mass Transf. 95, 815–823.

Jury, W.A. Bellantuoni, B. 1976. A background temperature correction for thermal conductivity probes. Soil Sci. Soc. Am. J. 40, 608–610.

Kamai, Tamir, Kluitenberg, Gerard J., Hopmans, Jan W., 2015. A dual-probe heat-pulse sensor with rigid probes for improved soil water content measurement. Soil Sci. Soc. Am. J. 79 (4), 1059–1072.

Kluitenberg, G.J., Philip, J.R., 1999. Dual thermal probes near plan interfaces. Soil Sci. Soc. Am. J. 63, 1585–1591.

Kluitenberg, G.J., Ochsner, T.E., Horton, R. 2007. Improved analysis of heat pulse signals for soil water flux determination. Soil Sci. Soc. Am. J. 71, 53–55.

Kojima, Yuki, Heitman, Joshua L., Flerchinger, Gerald N., Ren, Tusheng, Horton, Robert, 2016. Sensible heat balance estimates of transient soil ice contents. Vadose Zone J. 15 (5), 1–11.

Kojima, Yuki, Heitman, Joshua L., Noborio, Kosuke, Ren, Tusheng, Horton, Robert, 2018. Sensitivity analysis of temperature changes for determining thermal properties of partially frozen soil with a dual probe heat pulse sensor. Cold Reg. Sci. Tech. 151, 188–195.

Kurz, David, Alfaro, Marolo, Graham, Jim, 2017. Thermal conductivities of frozen and unfrozen soils at three project sites in northern Manitoba. Cold Reg. Sci. Tech. 140, 30–38.

Li, M., Si, B.C., Hu, W., Dyck, M. 2016. Single-probe heat pulse method for soil water content determination: comparison of methods. Vadose Zone J. 15, 0004.

Liu, G., Si, B.C., 2008. Dual-probe heat pulse method for snow density and thermal properties measurement. Geophys. Res. Lett. 35, L16404.

Liu, Gang, Lu, Yili, Wen, Minmin, Ren, Tusheng, Horton, Robert, 2020. Advances in the heat-pulse technique: Improvements in measuring soil thermal properties. Soil Sci. Soc. Am. J. 84 (5), 1361–1370.

Liu, G., Lu, Y.L., Wen, M.M., Ren, T.S., Horton, R., 2017. Advances in the heat-pulse technique: Improvements in measuring soil thermal properties. Methods Soil Anal. 2 (msa2015), 0028.

Liu, G., Si, B.C., Jiang, A.X., Li, B.G., Ren, T.S., Hu, K.L., 2012. Probe body and thermal contact conductivity affect error of heat pulse method based on infinite line source approximation. Soil Sci. Soc. Am. J. 76, 370–374.

Liu, Gang, Wen, Minmin, Chang, Xupei, Ren, Tusheng, Horton, Robert, 2013a. A self- calibrated dual probe heat pulse sensor for in situ calibrating the probe spacing. Soil Sci. Soc. Am. J. 77 (2), 417–421.

Liu, Gang, Wen, Minmin, Ren, Ruiqi, Si, Bing, Horton, Robert, Hu, Kelin, 2016. A general in situ probe spacing correction method for dual probe heat pulse sensor. Agric. For. Meteorol. 226-227, 50–56.

Liu, Gang, Zhao, Lijuan, Wen, Minmin, Chang, Xupei, Hu, Kelin, 2013b. An adiabatic boundary condition solution for improved accuracy of heat-pulse measurement analysis near the soil-atmosphere interface. Soil Sci. Soc. Am. J. 77 (2), 422–426.

Lu, Sen, Wang, Hesong, Meng, Ping, Zhang, Jinsong, Zhang, Xiao, 2018a. Determination of soil ground heat flux through heat pulse and plate methods: Effects of subsurface latent heat on surface energy balance closure. Agric. For. Meteorol. 260–261, 176–182.

Lu, Yili, Liu, Xiaona, Zhang, Meng, Heitman, Joshua, Horton, Robert, Ren, Tusheng, 2020. Thermo–time domain reflectometry method: Advances in monitoring in situ soil bulk density. Soil Sci. Soc. Am. J. 84 (5), 1354–1360.

Lu, Y., Horton, R., Ren, T., 2018b. Simultaneous determination of soil bulk density and water content: A heat pulse-based method. Eur. J. Soil Sci. 69 (5), 947–952.

Lu, Y.L., Wang, Y.J., Ren, T.S. 2014. Using late time data improves the heat-pulse method for estimating soil thermal properties with the pulsed infinite line source theory. Vadose Zone J. 12, 0011.

Mori, Y.J., Hopmans W., Mortensen A.P., Kluitenberg, G.J. 2003. Multi-functional heat pulse probe for the simultaneous measurement of soil water content, solute concentration, and heat transport parameters. Vadose Zone J. 2, 561–71.

Peng, X., Wang, Y., Heitman, J., Ochsner, T., Horton, R., Ren, T., 2017. Measurement of soil-surface heat flux with a multi-needle heat-pulse probe. Eur. J. Soil Sci. 68 (3), 336–344.

Philip, J.R., Kluitenberg, G.J. 1999. Errors of dual thermal probes due to soil heterogeneity across a plane interface. Soil Sci. Soc. Am. J. 63, 1579–1585.

Ren, Ruiqi, von der Crone, Jonas, Horton, Robert, Liu, Gang, Steppe, Kathy, 2020. An improved single probe method for sap flow measurements using finite heating duration. Agric. For. Meteorol. 280, 107788. https://doi.org/10.1016/j. agrformet.2019.107788.

Tarara, Julie M., Ham, Jay M., 1997. Measuring soil water content in the laboratory and field with dual-probe heat-capacity sensors. Agron. J. 89 (4), 535–542.

Sang, Yujie, Liu, Gang, Horton, Robert, 2020. Wind effects on soil thermal properties measured by the dual-probe heat pulse method. Soil Sci. Soc. Am. J. 84 (2), 414–424.

Trautz, Andrew C., Smits, Kathleen M., Schulte, Paul, Illangasekare, Tissa H., 2014. Sensible heat balance and heat-pulse method applicability to in situ soil-water evaporation. Vadose Zone J. 13 (1), 1–11.

Wen, Minmin, Liu, Gang, Li, Baoguo, Si, Bing C., Horton, Robert, 2015. Evaluation of a self-correcting dual probe heat pulse sensor. Agric. For. Meteorol. 200, 203–208.

Xiao, X., Zhang, X., Ren, T., Horton, R., Heitman, J.L., 2015. Thermal property measurement errors with heat-pulse sensors positioned near a soil-air interface. Soil Sci. Soc. Am. J. 79 (3), 766–771.

Young, M.H., Campbell, G.S., Yin, J. 2008. Correcting dual-probe heat-pulse readings for changes in ambient temperature. Vadose Zone J. 7, 22–30.

Zhang, Xiao, Heitman, Joshua, Horton, Robert, Ren, Tusheng, 2014. Measuring near- surface soil thermal properties with the heat-pulse method: correction of ambient temperature and soil-air interface effects. Soil Sci. Soc. Am. J. 78 (5), 1575–1583.

Zhang, X., Ren, T.S., Heitman, J., Horton, R., 2017. Advances in heat-pulse methods: measuring near-surface soil water content. Methods Soil Anal. 2 (msa2015), 0032.

Y. Sang et al.