Non-invasive estimation of root zone soil moisture

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Using GPR to estimate root zone soil moisture has been improved in the last decade, ... GPR wave velocity in the soil to retrieve soil moisture has ... ferent subsurface objects, such as interfaces between soil layers (Lu ... Second, accurate estimation of the ... are named as average velocity and interval velocity, re- spectively.
Plant Soil https://doi.org/10.1007/s11104-018-03919-5

METHODS PAPER

Non-invasive estimation of root zone soil moisture from coarse root reflections in ground-penetrating radar images Xinbo Liu & Xihong Cui & Li Guo & Jin Chen & Wentao Li & Dedi Yang & Xin Cao & Xuehong Chen & Qixin Liu & Henry Lin

Received: 26 February 2018 / Accepted: 16 December 2018 # Springer Nature Switzerland AG 2019

Abstract Background and aims Root zone soil moisture is an important component in water cycling through the soil-plant-atmosphere continuum. However, its measurement in the field remains a challenge, especially non-invasively and repeatedly. Here, we developed a new method that uses ground-penetrating radar (GPR) to quantify root zone soil moisture. Methods Coarse roots were chosen as reflectors to collect GPR radargrams. An automatic hyperbola detection algorithm identified coarse root reflections in GPR radargrams and determined the velocity of GPR wave, which then was used to calculate the average soil water content of a soil profile (ASWC) and soil water content in a depth interval (ISWC). In total, GPR reflection data of 55 root samples from three computer simulation scenarios and two field

experiments in sandy shrubland, one burying roots at known depths and the other under the undisturbed condition, were used to evaluate the proposed method. Results Both the simulated and the field collected data demonstrated the effectiveness of the proposed method for measuring root zone soil moisture with high accuracy. Even in the two field experiments, the root-meansquare errors of the estimated ASWC and ISWC relative to measurements from soil cores were as low as 0.003 and 0.012 m3·m−3, respectively. Conclusion The proposed method offers a new way of quantifying root zone soil moisture noninvasively that allows repeated measurements. This study expands the application of GPR in root and soil study and enhances our ability to monitor plantsoil-water interactions.

Responsible Editor: Peter J. Gregory. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11104-018-03919-5) contains supplementary material, which is available to authorized users. X. Liu : X. Cui : J. Chen : W. Li : X. Cao : X. Chen : Q. Liu State Key Laboratory of Earth Surface Processes and Resource Ecology, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China X. Liu : X. Cui (*) : J. Chen : W. Li : X. Cao : X. Chen : Q. Liu Beijing Engineering Research Center for Global Land Remote Sensing Products, Institute of Remote Sensing Science and Engineering, Faculty of Geographical Science, Beijing Normal

University, Beijing 100875, China e-mail: [email protected] L. Guo : H. Lin Department of Ecosystem Science and Management, The Pennsylvania State University, State College, PA 16802, USA D. Yang Department of Ecology and Evolution, Stony Brook University, Stony Brook, NY 11794, USA

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Keywords Ecohydrology . Near-surface geophysics . Plant-soil-water interactions . Sandy soil . Soil water content . Subsurface imaging Abbreviations GPR ground-penetrating radar ASWC average soil water content of a soil profile ISWC soil water content of a depth interval ROI region of interest RMSE root-mean-square error

Introduction Root zone soil moisture constitutes an essential component in water cycling through the soil-plant-atmosphere continuum (Norman and Anderson 2005). It is the primary water source to sustain plant growth in terrestrial environments, thereby influencing biodiversity (Vereecken et al. 2008) and the Critical Zone processes (Guo and Lin 2016). Root zone soil moisture is also a key factor in agriculture irrigation and water resource management (Polak and Wallach 2001) as well as weather forecast and climate modeling (Teuling et al. 2006). However, plant-soil-water interactions in the root zone are complex. On the one hand, plant roots absorb water from the soil that concentrates soil moisture to the root zone. On the other hand, soil macropores around roots are common preferential pathways, directing fast water transport that bypasses the bulk of the root zone soil (Guo and Lin 2018). Therefore, the accurate measurement of root zone soil moisture and its dynamics is vital for better understanding the plant-soil-water interaction and water flux in the subsurface (Collins and Bras 2007). Different methods have been established to quantify root zone soil moisture. At the large scale, satellite remote sensing (e.g., active and passive microwave radars) is used for mapping regional root zone soil moisture (Kumar et al. 2018). However, remote sensing data has a limited investigation depth (usually 5 mm) generate clear hyperbolic reflections in GPR radargrams that can be used to estimate wave velocity (Guo et al. 2013a). The efficiency of GPRbased root detection and quantification has been demonstrated, such as automatic root locating (Li et al. 2016), mapping root zone (Hruška et al. 1999), reconstructing root system architecture (Wu et al. 2014), and quantifying the diameter and biomass of

The proposed method first estimates the average soil water content of a soil profile (ASWC) and then the soil water content in a depth interval (ISWC). ASWC refers to the average soil water content from the surface to the depth of a coarse root that is used for wave velocity estimation and soil water content calculation. ISWC refers to the average soil water content within a depth interval between two coarse roots (Fig. 1). Accordingly, the reflected wave velocities that are used to calculate ASWC and ISWC are named as average velocity and interval velocity, respectively. The estimation of ASWC and ISWC has three steps (Fig. 2), including (1) collecting GPR radargrams, (2) obtaining the average velocity and computing interval velocity, and (3) converting the average and interval velocities into ASWC and ISWC, respectively. GPR radargram collection During the collection of GPR data, the transmitter generates a beam of the electromagnetic wave into the subsurface with an elliptical footprint, and the receiver collects the reflected signals as a function of time. Because of the elliptically radiating pattern of the GPR wave, radar energy will be reflected before and after the antenna is dragged directly above a coarse root (Fig. 3a; Guo et al. 2013a). As the antenna moves closer to the root, the

Plant Soil Fig. 1 The definition of average soil water content from the surface to the depth of a coarse root (ASWC) and average soil water content within a depth interval between two coarse roots (ISWC). ASWC1 and ASWC2 refer to the average soil water content from the surface to the depth of Root 1 and Root 2, respectively, and ISWC12 refers to the average soil water content between Root 1 and Root 2

travel time decreases until the antenna is directly over it. When the antenna moves away from the root, the same phenomenon is repeated in reverse, which generates a hyperbolic reflection with its apex representing the actual location of a coarse root (Fig. 3b). The geometry relationship of the hyperbolic reflection can be described as (Fig. 3b) (Huisman et al. 2003; Li et al. 2016): tw 2 ðx−x0 Þ2 − ¼ 1;  2 d2 2d

ð3Þ

vsoil

where vsoil is the average velocity of the reflected wave, x is the horizontal position of the GPR antenna along the radargram, x0 is the horizontal

Fig. 2 Flowchart of the proposed method. ROI indicates the region of interest, i.e., the zone in which a hyperbola exists, and RHT stands for the Randomized Hough Transform method. The average velocity and interval velocity will be converted into the soil permittivity by Eq. (1), and then ASWC and ISWC by Topp’s equation (Eq. (2))

position of the hyperbola apex, tw is the two-way travel time at position x, and d is the depth of the coarse root. Average velocity An automatic hyperbola detection algorithm is adopted to obtain the average velocity in Eq. (3). This method includes generating the region of interest (ROI) of a hyperbola in the radargram, identifying the hyperbola by the Randomized Hough Transform method in each ROI, and determining the average velocity, which are detailed below.

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Fig. 3 a Measuring coarse roots by dragging a GPR system with shielded antenna (including a transmitter and a receiver) along the parallel survey lines (dotted line arrows). Here, the parallel survey lines don’t imply a specific survey design in this study but just illustrate the GPR measurement for coarse roots. b A reflection of a coarse root is displayed as a hyperbolic shape in the radargram

(also called a B-scan profile). The apex of the hyperbola represents the actual position of the coarse root; vsoil is the average velocity of the reflected wave; x is the horizontal distance of dragging the GPR system; x0 is the horizontal position of the coarse root; tw is the two-way travel time at position x; and d is the depth of the coarse root

ROI generation

identify hyperbola reflections in each ROI and solve the hyperbola function (Eq. (3)). The identification of hyperbola reflections is based on the transformation from a variable space to a parameter space by three steps (Fig. 5):

Generating the ROI aims to facilitate the automatic identification of hyperbolas by reducing the areas in radargrams to apply the Randomized Hough Transform method. Before ROI generation, raw GPR radargrams require several preprocessing procedures, such as zerotime correction, background removal, and amplitude compensation (Fig. 3; Guo et al. 2014). Zero-time correction adjusts the radar signal to start from the surface, which ensures accurate estimation of wave velocity and soil water content. Background removal eliminates noises, and amplitude compensation recovers GPR energy attenuation with penetrating depth and highlights the reflection pattern of root radar signals. Examples of radargrams before and after the preprocessing are shown in Fig. 4a and b, respectively. All preprocessing procedures are performed with the MATGPR package (Tzanis 2010). After preprocessing, an image edge extraction operator (Sobel filter) is applied to the gray-scale radargram (Li et al. 2016). Each connected edge in the processed radargram is considered an ROI (Fig. 4c). Hyperbola identification The Randomized Hough Transform method (Xu et al. 1990; Xu and Oja 1993) is employed to automatically

Step 1: Three points are randomly selected from the edge in an ROI and then used to solve a set of unknown parameters in Eq. (3), including vsoil, x0, and d. To solve three unknown parameters, three points on the hyperbola are required. Step 2: The solved set of the unknown parameters is recorded in an accumulator, and Step 1 is repeated until the number of iterations reaches to 10,000 because additional iterations do not significantly improve the accuracy (Li et al. 2016). The accumulator records the occurrence frequency of the solved set of parameters for all iterations. Step 3: The parameter set with the highest occurrence frequency in the accumulator is selected. The hyperbola curve is then determined using this set of parameters, which is the identified hyperbola in an ROI. Further details on hyperbola identification by Randomized Hough Transform method can be found in Li et al. (2016), Simi et al. (2008), Windsor et al. (2005) and Xu (2005).

Plant Soil

Fig. 4 Obtaining the average velocity of the GPR wave. a A raw GPR radargram collected by 900 MHz antenna, including two blurry hyperbolic reflections due to a low signal-to-noise ratio. b After preprocessing, the hyperbolic reflections become clearly displayed. c The GPR radargram is converted into a binary image after the edge extraction. Each connected edge is then considered as a region of interest (ROI). (d) Three hyperbolas (indicated by the red curves) are identified for each coarse root reflection after

Determining the average velocity Several hyperbolas can be identified for the same coarse root reflection in the radargram after applying the Randomized Hough Transform method (Fig. 4d), which results in different average velocity values. To select the most representative hyperbola for each coarse root reflection, we develop a selection criterion that the apex of the representative hyperbola is located above and closest to maximum amplitude (Fig. 4f). As shown in

Fig. 5 Hyperbola identification in each region of interest (ROI) by the Randomized Hough Transform. Step 1 and Step 2 will be repeated until the number of iterations reached 10,000 and one set

applying the Randomized Hough Transform to the ROIs. e Only one representative hyperbola is selected for each coarse root reflection. White numbers are the average velocities determined for the selected hyperbolas. (f) The A-scan profile corresponds to the GPR signal collected at the position indicated by the vertical dashed line in (e) that is right above the apex of a hyperbolic signal. The red part of the A-scan indicates the optimal range to determine the average velocity

the red curve in Fig. 4f, this part is between the largest (positive or negative) amplitude and the zero-cross above it, which is considered the actual interface between the reflector and the medium (i.e., a coarse root and soil in this case). The selected hyperbola is used to determine the average velocity of the GPR wave (Fig. 4e), which will be used to compute ASWC and ISWC. Interval velocity Two adjacent roots at different depths are necessary for computing the interval velocity. In Fig. 6, v1 and v2 are

of vsoil, x0 and d is recorded in the accumulator after each iteration. The parameter set with the highest occurrence frequency in the accumulator is selected as the final result in Step 3

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and interval velocities by using Eq. (1). Then, the ASWC and ISWC are calculated by the empirical petrophysical relationship of εsoil-θsoil, such as the Topp’s equation (Eq. (2)).

Experiment design Simulation experiments

Fig. 6 Schematic of computing the interval velocity. Root 1 and Root 2 are distributed in a two-layer soil, e.g., Soil layer 1 and Soil layer 2. The dielectric permittivity of Soil layer 1 is different from that of Soil layer 2. To enable computations of the theoretical average velocity from the ground surface to Root 1 and the theoretical interval velocity between Root 1 and Root 2 in the simulation, the depth of Root1 is set to be consistent with the thickness of Soil layer 1 (see Scenario (III) in Supplementary)

average velocities above Root 1 and Root 2, respectively. t1 and t2 are the two-way travel time of the GPR wave propagating from the surface to Root 1 and Root 2, respectively. v1 , t1, v2 , and t2 can be determined using the automatic hyperbola detection algorithm. The interval velocity between two roots is labeled as v12 , and the two-way travel time is t12, then the relationship of the geometric position of the two roots can be expressed as: v1 t 1 þ v12 t 12 ¼ v2 t 2 ;

ð4Þ

Soil and coarse roots with five water content (or permittivity) levels were designed to represent various soil and root conditions (Fig. 7). Five root depths, from 0.1 m to 0.9 m with an increment of 0.2 m, were set to establish a depth gradient. Parameter values for roots and soil were based on field measurements in Inner Mongolia, China (see Table S1 in Supplementary), a typical arid and semi-arid area in northern China (Guo et al. 2013b, c). According to the information of shrub roots in Inner Mongolia reported in Guo et al. (2013b), the diameter of coarse roots was set to 0.015 m in all simulations. The center frequency of GPR was set to 900 MHz, the same with the GPR system used in field experiments in this study. The simulation experiments included three scenarios: (I) different soil and root conditions (Fig. 7); (II) different root depths (Fig. 7); and (III) a two-layer horizontal homogeneous soil medium with different values of soil water content (Fig. 6). A total of 36 simulation experiments were completed in three scenarios. Detail description of simulation experiments is presented in Supplementary (see Text S1).

and the relationship of the two-way travel time can be expressed as: t 1 þ t 12 ¼ t 2 :

ð5Þ

Then, the interval velocity v12 is derived from Eqs. (4) and (5) as: v12 ¼

v2 t 2 −v1 t 1 : t 2 −t 1

ð6Þ

ASWC and ISWC For low conductive, nonmagnetic, and nonsaline soil, the soil permittivities can be computed from the average

Fig. 7 The design of simulation scenarios (I) and (II). Five types of soil (with different dielectric permittivities) and five types of root (with different dielectric permittivities) are simulated in the scenario (I). Five root depths are set in the scenario (II)

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All simulation experiments were completed in GprMax V2.0 software (Giannopoulos 2005). The theoretical velocity was computed using Eq. (1) because soil permittivity was known in each experiment. All theoretical velocities were compared with the estimated average and interval velocities to evaluate our proposed method.

in the controlled experiment. First, the GPR antenna clinging to the ground was dragged over the coarse roots along the survey line. Second, in the vicinity of every coarse root, soil cores were sampled with soil augers and used for measuring gravimetric soil water content by drying to a constant weight, which was then converted to volumetric soil water content to compare with GPRderived soil water content.

Field experiment under the controlled condition Field experiment under the undisturbed condition A controlled experiment was conducted in Abag Qi (43°55′55″ N, 114°41′32″ E), Inner Mongolia, China, in July 2016. The study area is located in a desert steppe region of northern China, with the soil at the site mainly being sand (~80% sand and ~20% silt and clay). A soil trench was dug with a length, width, and depth of 8.0, 1.5, and 1.2 m (Fig. 8). Eight roots of Caragana microphylla, a dominant shrub species in this area, were selected as experimental reflectors and labeled from No. 1 to No. 8, which were perpendicularly inserted into the trench wall at depths of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 m (Fig. 8). This experiment setup ensured a minimal disturbance to the soil structure. The horizontal interval between any two coarse roots was 1.0 m. All selected coarse roots were relatively straight and showed the same diameter and length of 0.015 and 0.5 m, respectively. To enhance GPR coarse root reflections in radargrams, these coarse roots were soaked in water for three days before the experiment. The GPR survey line perpendicular to the long axis of roots and right above coarse roots was previously marked on the ground surface. Finally, the trench was refilled, and the surface was flattened. A field-portable GPR system MF HI-MOD (Ingegneria Dei Sistemi Inc., Pisa, Italy) with a center frequency of 900 MHz shielded antenna was employed

Another measurement was conducted in May 2016 at Huailai county (40°15′33′′ N, 115°36′51′′ E) in Hebei Province, China. The GPR radargrams were collected by using the MF HI-MOD GPR system with the center frequency of 900 MHz. The field experiment was conducted on shrubland. The local soil was primarily sandy with some detritus or small stones. Compared with the GPR measurement under the controlled condition, GPR radargrams presented stronger background noises and clutters. Several shrub plants were located around a clear field with roots spreading beneath the flat area (Fig. 9). These shrub coarse roots provided natural reflectors to estimate the ASWC and ISWC. The detailed procedures of the field measurement were as follows. (1) GPR was used to explore the coarse root distribution in the flat area. Then, five coarse roots were selected as reflectors and labeled as No. ①, ②, ③, ④, and ⑤ (Fig. 9) considering their uniform distribution in the flat area and the minimal clutter interferences. In particular, roots No. ② and No. ③ were at different depths and were relatively close to each other at a horizontal distance of approximately 1.2 m. Thus, the two roots were used to estimate the ISWC between them. (2) The coarse roots were measured by using the GPR along the determined survey line, and soil cores were sampled by augers near

Fig. 8 Field experiment under the controlled condition. a The relative positions of root samples and the GPR survey line. Eight roots are perpendicularly inserted into one side of the sand trench

wall. The GPR survey line is set on the ground surface and perpendicular to the long axis of roots and right above roots. b A field photo of the sand trench and the root samples

Plant Soil Fig. 9 Locations of the five measured roots in the field experiment under the undisturbed condition. Inset is the zoom in the image of the root No. ①

the roots to measure gravimetric soil water content and soil bulk density.

Results Simulation experiments Average velocity estimation Table 1 summarizes the results of the average velocity estimation in scenario (I) (for different soil and root

conditions) and the theoretical average velocities computed by Eq. (1). Overall, the average velocities determined by the automatic hyperbola detection algorithm in all 25 simulation experiments are close to the theoretical values, and their relative errors are all less than 5.00%. Thus, the automatic hyperbola detection algorithm provides an accurate and stable average velocity estimation for each type of soil conditions and root conditions for the simulated data. Three cases with greater relative errors than other results are presented in Table 1 (marked by a grey background). The reason for them is probably that the minimal contrast in the

Table 1 Results for average velocity (normal texts and in m·ns−1) estimations through the proposed method in the simulation scenarios (I), and relative errors (italic texts) compared with theoretical velocities (bold texts) Gravimetric root water content = 70% (εroot = 7.59)

Gravimetric root water content = 80% (εroot = 9.21)

Gravimetric root water content = 100% (εroot = 13.06)

Gravimetric root water content = 120% (εroot = 17.81)

Gravimetric root water content = 140% (εroot = 23.53)

Theoretical velocity (m·ns-1)

Volumetric soil water content =4.33% (εsoil = 3.70)

0.155 (0.64%)

0.155 (0.64%)

0.154(1.28%)

0.153 (1.92%)

0.155 (0.64%)

0.156

Volumetric soil water content =12.56% (εsoil = 6.35)

0.119 (0.00%)

0.119 (0.00%)

0.119 (0.00%)

0.119 (0.00%)

0.119 (0.00%)

0.119

Volumetric soil water content =16.67% (εsoil = 8.28)

0.101 (2.89%)

0.100 (3.85%)

0.106 (1.92%)

0.105 (0.96%)

0.105 (0.96%)

0.104

Volumetric soil water content =19.76% (εsoil = 9.98)

0.097 (2.11%)

0.092 (3.16%)

0.096 (1.05%)

0.097 (2.11%)

0.096 (1.05%)

0.095

Volumetric soil water content =25.56% (εsoil = 13.67)

0.083 (2.47%)

0.083 (2.47%)

0.083 (2.47%)

0.083 (2.47%)

0.083 (2.47%)

0.081

Each column shows the results for five types of soil. Each row shows average velocity results for five types of roots. Three cases marked by a grey background in this table indicated greater errors than other cases because a minimal contrast in the permittivity of soil and roots lead to a poor performance of the automatic hyperbola detection algorithm. Detailed description for soil and roots are presented in Supplementary (see Table S1)

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permittivity (or water content) of soil and root leads to weak reflection signals, thereby influencing the identification of hyperbolic reflections and then the estimation of average velocity. Figure 10 shows the results of the average velocity estimation in scenario (II) (for different root depths). The estimated average velocities are also very close to the theoretical velocities, with all relative errors less than 1.00%.

In summary, simulation results demonstrated that the proposed method achieves a satisfactory performance in determining the average and interval velocities. Given the strong correspondence between the GPR wave velocity and soil moisture content (Eq. (2)), simulation results also suggest the proposed method is effective to measure soil moisture.

Field experiment under the controlled condition Interval velocity estimation The simulation results of scenario (III) (for the two-layer horizontal homogeneous soil medium) are demonstrated in Fig. 11 and Table 2. The theoretical average velocity above Root 1 and the theoretical interval velocity between Root 1 and Root 2 were computed using Eq. (1) (Table 2). In Table 2, the relative errors of the estimated average velocity (v1 ) above Root 1 are less than 3.00% in all simulations except for the sixth experiment with 4.21%, which is attributed to poor performance of the automatic hyperbola detection algorithm. The relative errors of the estimated interval velocities (v12 ) range from 0.84% to 4.21% for the first five simulations whereas that of the sixth simulation is up to 9.62%. This is likely due to the larger error (4.21%) of the estimated average velocity above Root 1. If v1 and t1 for Root 1 are respectively replaced with the theoretical velocity (0.095 m·ns−1) and travel time derived from simulation parameters, the interval velocity computed using Eq. (6) would be 0.158 m·ns−1, and its relative error would be just 1.28% in the sixth experiment.

All root samples form clear hyperbolic reflections in the preprocessed GPR radargram (Fig. 12a). The estimated average velocities (indicated by the white numbers in Fig. 12a) show a decreasing trend with the increase in depth but in a small variation range, reflecting the varied soil moisture values along the depth. The value of the estimated ASWC varies in a limited range, from 0.075 m3·m−3 to 0.106 m3·m−3. The estimated ASWC matches well with the results from soil cores (with a correlation coefficient of 0.939) and a small RMSE of 0.005 m3·m−3. Furthermore, the estimated values of ISWC between roots No. 2 and No. 4, No. 4 and No. 6, and No. 6 and No. 8 are compared with soil core measurements. Here only three ISWC results were estimated for two major reasons. First, the 900 MHz GPR antenna is limited to a vertical resolution of about 0.1 m; but practically, the resolution would be coarser (i.e., > 0.1 m) when the depth increases, because of the dispersion effect (Rial et al. 2009). Second, there is little variation in the ISWC based on the measurement of the soil vertical profile;

Fig. 10 Average velocities (indicated by the white numbers) obtained by the proposed method in simulation scenario (II). vtheory is the theoretical velocity computed by Eq. (1). The red curves refer to the hyperbolas identified by the Randomized Hough Transform method

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Fig. 11 Average velocities (indicated by the white numbers) obtained by the proposed method in simulation scenario (III). The red curves refer to the hyperbolas identified by the

Randomized Hough Transform method. εAbove is the dielectric permittivity of the above soil layer, and εBelow is the dielectric permittivity of the below soil layer

specifically, the range of variation is only around 0.03 m 3 ·m −3 according to the data of soil cores (Fig. 12c). Therefore, to ensure a certain level of changes in the vertical ISWC gradient so as to verify the proposed method effectively, three pairs of root objects with a vertical distance of 0.2 m were used to estimate ISWCs. Figure 12c shows that ISWC estimation agrees well with the results from soil cores (with a correlation coefficient of 0.975). The RMSE of the estimation is 0.012 m3·m−3. Above results indicate that the proposed method performs well in estimating the ASWC and ISWC and captures the minimal vertical variations of soil moisture in the controlled experiment. Figure 13 shows the absolute errors in ASWC and ISWC between the proposed method and soil core

measurements. The accuracy of the ISWC estimation is lower than that of the ASWC. This also implies that the error of the average velocity estimation could impair accurate estimation of the ISWC.

Field experiment under the undisturbed condition Figure 14 compares the average velocities determined for five selected root samples in the field measurement. Table 3 shows that the estimation of ASWC is very close to the soil moisture measurements of soil cores, with the RMSE less than 0.003 m3·m−3. Furthermore, the estimated ISWC between roots No. ② and ③ is 0.142 m 3 ·m −3 , which has the absolute error of

Table 2 Results for average velocity (v1 ) and interval velocity (v12 ) estimations through the proposed method in the simulation scenario (III), and relative errors (italic texts) compared with theoretical values (bold texts) Combination of soil layers

εAbove = 3.70; εBelow = 9.98 εAbove = 3.70; εBelow = 6.35 εAbove = 6.35; εBelow = 9.98 εAbove = 6.35; εBelow = 3.70 εAbove = 9.98; εBelow = 6.35 εAbove = 9.98; εBelow = 3.70

Estimated velocity

Theoretical velocity

v12 (m·ns−1)

v1 (m·ns−1)

v12 (m·ns−1)

v1 (m·ns−1)

0.099 (4.21%)

0.155 (0.64%)

0.095

0.156

0.120 (0.84%)

0.152 (2.56%)

0.119

0.156

0.099 (4.21%)

0.119 (0.00%)

0.095

0.119

0.161 (3.21%)

0.119 (0.00%)

0.156

0.119

0.122 (2.52%)

0.097 (2.11%)

0.119

0.095

0.171 (9.62%)

0.099 (4.21%)

0.156

0.095

εAbove is the permittivity of the above soil layer. εBelow is the permittivity of the below soil layer

Plant Soil Fig. 12 Results of root zone soil moisture estimation for the field experiment under the controlled condition. a Average velocities (indicated by the white numbers) obtained by the proposed method. The red curves are the hyperbolas identified by Randomized Hough Transform method. b ASWCs estimated by the proposed method (the red triangles) are compared with those obtained by soil core measurements (the blue dots). c ISWCs estimated by the proposed method (the red triangles) are compared with those obtained by soil core measurements (the blue points)

0.030 m3·m−3 relative to the measurement from the soil cores (0.112 m3·m−3). In summary, the proposed method has achieved a satisfactory level of performance in estimating ASWC and ISWC, for both the controlled and the field experiments. The accuracy of the

Fig. 13 Absolute errors of ASWC and ISWC estimations through the proposed method in the field experiment under the controlled condition

estimation of ASWC and ISWC is affected by the error of the average velocity. Moreover, the accuracy of ISWC estimation is lower than that of ASWC estimation in the field experiments under both controlled (Fig. 13) and undisturbed conditions.

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Fig. 14 Average velocities (indicated by the white numbers) are estimated by the proposed method in field experiment under the undisturbed condition. The red curves are the hyperbolas identified by Randomized Hough Transform method

Discussion Advantages of using coarse root reflections to estimate root zone soil moisture In this study, we propose a new non-invasive and automatic method to estimate the root zone soil moisture based on GPR reflections of coarse roots. The proposed method improves the ability of common GPR reflected wave method by using two characteristics of coarse roots, the wide spatial distribution of roots in the soil and the hyperbolic shape of root reflections in the radargram. First, coarse roots are natural reflectors in the subsurface and form clear reflections in radargrams, which make the non-invasive and repeated estimation for ASWC and ISWC by using GPR root reflections possible. Second, the hyperbolic shape of coarse root reflections opens an opportunity to automatically obtain the average velocities through the automatic hyperbola detection algorithm without prior knowledge of the

depth of roots (Li et al. 2016; Simi et al. 2008). Third, the spatial distribution of coarse roots in soil creates a favorable condition for computing the vertical soil moisture profile. It is also possible to map the horizontal soil moisture distribution by interpolating soil moisture values obtained from various roots distributed at the same depth. Both results from simulation and field measurements demonstrate the feasibility of the proposed method in sandy shrubland. Compared with ASWC estimations in previous studies, with the RMSE of 0.01 m3·m−3 under controlled conditions (Grote et al. 2002; Stoffregen et al. 2002) and 0.018 m3·m−3 in natural settings (Lunt et al. 2005), the proposed method obtained not only accurate ASWC estimation, with the RMSE of 0.005 m3·m−3 under the controlled condition and 0.003 m3·m−3 under the undistributed condition, but also the vertical soil moisture profile. The proposed method provides a new means of using the spatial distribution and signal shape of reflectors to improve the capability of GPR in measuring soil moisture.

Table 3 Results for the average velocity and ASWC estimations through the proposed method and soil cores, and the depth and diameter of root samples in the field experiment under the undisturbed condition Root sample

Depth of root Diameter of root Estimated average velocity (m) (m) (m·ns−1)

ASWC from proposed method (m3·m−3)

ASWC from soil cores (m3·m−3)

No. ①

0.55

0.092 (0.001)

0.093

0.017

0.128

No. ②

0.33

0.010

0.127

0.094 (0.003)

0.091

No. ③

0.39

0.008

0.122

0.104 (0.002)

0.102

No. ④

Nan

Nan

0.137

0.075 (0.005)

0.080

No. ⑤

0.31

0.009

0.131

0.086 (0.001)

0.087

The italic texts in parentheses are absolute errors between the proposed method and soil cores. Nan refers to the unavailable data

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Moreover, the ASWC and ISWC obtained by the proposed method represent soil moisture conditions above and between coarse roots, which can shed new insight on better understanding the interaction between roots and soil (Collins and Bras 2007). Uncertainties of the proposed method The proposed method demonstrates a considerable degree of advantages over the common GPR reflected wave method. However, some limitations still exist in its practical applications. First, the coarse root, as an object reflector, is the prerequisite for the ASWC and ISWC estimations; and its location of distribution will dictate the detectable area. Second, the proposed method largely depends on the effectiveness of the automatic hyperbola detection algorithm; therefore, future attention should be paid to the improvement of the hyperbolic automatic detection algorithm or the exploration of alternative methods in order to better estimate the average velocity. Third, the ASWC estimation by the proposed method only needs one coarse root; the ISWC estimation, however, requires two coarse roots at different depths. This additional requirement will restrict the ISWC estimation by the proposed method because of the limited root pairs in the field. In addition, the vertical and horizontal distances between two roots used in Eq. (6) need to be at a reasonable range. Theoretically, the vertical distance needs to be greater than the vertical resolution (Δh) of the GPR, which is usually defined as (Annan 2003) τ p ⋅c Δh≈ pffiffiffiffiffiffiffiffi ; 4 εsoil

ð7Þ

where τp is the duration of the radar pulse, c is the free-space electromagnetic propagation velocity (3 × 108 m·s−1), and εsoil is the soil permittivity. The horizontal distance depends on the user’s demands and the soil heterogeneity, since the Eq. (6) assumes that the soil condition between the two roots should be homogeneous horizontally and with similar soil moisture. In this respect, the Eq. (6) tends to obtain the vertical profile of the soil moisture. In cases where the soil is highly heterogeneous, and the soil moisture has spatial variation, vertically and/or horizontally, the proposed method should be adjusted for better estimating the horizontal ISWC distribution. Our recommendation to address this issue includes

the following steps: (1) obtaining a sufficient amount of samples for the average velocity at different depths; (2) converting the average velocity values at each depth into the soil permittivity and then interpolating the soil permittivity distribution; (3) converting the soil permittivity distribution at each depth into the corresponding average velocity distribution; (4) using the average velocity distribution derived in the last step to compute the distributions of the interval average velocity by Eq. (6), eventually generating the ISWC distribution. Both the field soil conditions and the root growth patterns are complex. Such complexity influences the quality of coarse root reflections and thus the process of hyperbola identification. As shown in Fig. 15, in terms of the radar signal level, root hyperbolic reflections are possibly accompanied by the low signal-to-noise ratio, incompleteness, interference, noises and clutters due to unfavorable soil, root, and GPR conditions (Hirano et al. 2009; Li et al. 2016). We recommend Fig. 15 as a reference for the comprehensive evaluation of possible factors contributing to the measurement biases through the proposed method and under more complex field situations. In the field measurement, these possible difficulties for identifying influenced hyperbolic reflections can be alleviated by improved GPR hardware, data preprocessing, and data acquisition methods. For example, a multi-measurement is conducted to ensure a good data quality during the GPR data acquisition (Guo et al. 2015); only hyperbolic reflections with favorable quality (strong signal, complete hyperbola, and minimal interference) are picked from sufficient coarse root reflections during data preprocessing. In the proposed method, converting the average velocity and interval velocity into the ASWC and ISWC needs the use of εsoil-θsoil relationship. An inappropriate εsoil-θsoil relationship may cause errors in the ASWC and ISWC estimations. Here, the used Topp’s equation (Eq. (2)) achieved a good performance because the soil in the experimental fields were both sandy soil. However, these results in this paper do not mean that the proposed method based on the Topp’s equation is suitable to all soil environments. Generally, establishing a precise εsoil-θsoil relationship needs a time-consuming in-situ calibration (Huisman et al. 2002; Steelman and Endres 2011). To conveniently estimate the ASWC and ISWC in the field, we recommend building a lookup table associating each soil environment with the εsoil-θsoil relationship in advance.

Plant Soil

Fig. 15 Influencing factors and their possible effects on the proposed method (revised from Li et al. 2016). Influencing factors possibly lead to bad quality of coarse root reflection signals, thereby affecting the performance of the automatic hyperbola

detection algorithm. Furthermore, the bad performance of the automatic hyperbola detection algorithm and the inappropriate εsoil-θsoil relationship possibly affect the accuracy or stability of the proposed method

Potential of the proposed method

et al. 2014). This species has well developed lateral root systems (Schenk and Jackson 2002) and becomes a dominant shrub species encroaching the grassland in Inner Mongolia. A distinctive feature of the proposed method is to measure the ASWC and ISWC while detecting roots simultaneously. Thus, the proposed method will be used to explore the role of root-soil water interaction on shrub encroachment.

As a non-invasive, repeatable and automatic measurement method at the medium scale, the proposed method has the potential in monitoring the temporal and spatial dynamics of root zone soil moisture, characterizing ecohydrological processes, and addressing the uncertainty of upscaling the point-scale observation to area average soil moisture in the land surface hydrologic models. Moreover, given the increasing use of GPR for ecohydrological studies, we expect broader applications of our experimental protocol that can be extended to other reflectors, such as small stones, cables, pipes, and rebar, also present standard hyperbolic reflections in the radargrams to enhance the field measurement of soil moisture at the medium scale (Liu et al. 2017). Our future work will apply this method to enhance understanding the interactions between soil moisture and plants and its implication on ecological processes, for example, shrub encroachment in Inner Mongolia. Shrub encroachment has been a global ecological problem and is characterized by the increase of dominant shrub species (Van Auken 2009). Studies on the underground of shrubland are challenging because of lacking effective field measurement and data (Cao et al. 2018). Our previous work has successfully applied GPR to map and quantify the roots of Caragana microphylla (Cui et al. 2011, 2013; Guo et al. 2013b; Li et al. 2016; Wu

Conclusions Ground-penetrating radar (GPR) provides an alternative to measure soil moisture at the medium spatial scale, noninvasively and repeatedly. In this study, we established a new method to extend the application of GPR for the estimation of root zone soil moisture. The proposed method automatically identified coarse root reflections in the radargram and calculated the wave velocity from the ground surface to a root reflector or that between two roots distributed at different depths. Based on the close correspondence between the GPR wave velocity and soil water content, our method obtained the average soil moisture to a root (ASWC) and the soil moisture of a depth interval between two roots (ISWC). Results from comprehensive simulation experiments and field measurements (both under a controlled condition and an undisturbed condition) verified the

Plant Soil

effectiveness of the proposed method to measure root zone soil moisture. Even using data collected from the field experiments, high accuracy of ASWC and ISWC estimations was achieved by this method, with the RMSEs of ASWC and ISWC as low as 0.003 m3·m−3 and 0.012 m3·m−3, respectively. This study enhances the utility of GPR in measuring soil moisture and sheds new lights to clarifying the complex interactions between soil moisture and plant roots. We also advocate continued efforts to test and refine the GPR-based methods in the field measurement of soil moisture. Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 41571404) on project of State Key Laboratory of Earth Surface Processes and Resource Ecology. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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