IntroductionSustainable irrigation management practice can be achieved by using decision support systems and improved monitoring tools (Adeyemi et al. 2017), such as dielectric sensors to measure soil water content. Such management is increasingly being used in agriculture (Sharma et al. 2017; Millan et al. 2019; Cvejić et al. 2020).Electromagnetic methods are the most commonly used indirect methods for determining soil water content and these are based on apparent permittivity (ε) measurement. The relative permittivity (εr) of water at 20°C and a frequency range of 0.1 to 1 GHz (Stuchly and Stuchly 1980) is about 80, which is much higher than the εr of other components of the soil, i.e., soil solids (εr=2−7) and air (εr=1). Therefore, the measured apparent permittivity of the soil depends mainly on the presence of liquid water (Topp and Ferré 2002).Due to the complex interactions among electromagnetic waves and soil components, it is not possible to apply a unique calibration relationship to determine soil water content. Factors influencing dielectric sensor measurement include differences in texture and mineralogy (Vaz et al. 2013; Datta et al. 2018; Singh et al. 2019), type and relative content of organic matter (Fares et al. 2016; Kassaye et al. 2019), soil bulk density (Matula et al. 2016; Parvin and Degre 2016), electrical conductivity (Dettmann and Bechtold 2018), and temperature (Bogena et al. 2007, 2017).Polar water molecules adsorbed on the surface of charged clay particles result in a bound water phase. Bound water molecules are less polarized when an electric field is applied, resulting in a lower dielectric permittivity (Hilhorst et al. 2001; Li et al. 2019). On the other hand, increasing clay content with a large surface area and cation exchange capacity leads to increased ionic conductivity and dielectric dispersion, resulting in a higher permittivity (Evett and Parkin 2005; Singh et al. 2019). Clay minerals with surface charge show a dispersion in real permittivity that increases at frequencies below 100 MHz (González-Teruel et al. 2020), which is a common operating range for many soil moisture sensors based on capacitance (Vaz et al. 2013; Kassaye et al. 2019; Singh et al. 2020) and impedance (Vaz et al. 2013; Kim et al. 2020). Humus particles are also negatively charged and have a high cation exchange capacity. Therefore, the same principles of action could apply to humus-rich organic soils. In addition, variations can also be attributed to a lower bulk density and higher porosity of organic materials compared to mineral soils. When soil bulk density is higher, the volume ratio of the solid particles is higher compared to the volume ratio of the air, and consequently dry soil permittivity is higher (Vaz et al. 2013; Bircher et al. 2016).Despite the fact that sensors are equipped with manufacturer calibration equations to cover a wide range of mineral and/or organic soils, many studies highlight the importance of soil-specific dielectric sensor calibration (Visconti et al. 2014; Parvin and Degre 2016; Roberti et al. 2018; Kassaye et al. 2019). Alternatively, some empirical correction functions based on easily measured soil properties have been proposed to improve sensor accuracy, e.g., considering the texture and clay content of a soil (Rüdiger et al. 2010; Singh et al. 2019). It is important to address the issue of sensor accuracy as it significantly affects irrigation efficiency when using soil-moisture–based irrigation scheduling systems (Soulis et al. 2015).The aims of our study were, firstly, to evaluate measurement error when using manufacturer’s calibration functions for different soil types for two commercially available but not yet widely studied sensor types, one capacitance-based, the other TDR-technology–based. Secondly, we aimed to (1) obtain coefficients of the two-point soil-specific calibration procedure, (2) to develop a general correction function, based on easy-to-measure soil parameters, and (3) to develop soil-specific calibration functions. Finally, our aim was to evaluate improvements after applying the two-point, the clay content correction, and the soil-specific calibration functions to the data set. We used nine soils differing in texture, bulk density, organic matter content, and other soil properties, eight mineral soils, and one organic.Materials and MethodsDielectric SensorsWe used the SM150T (Delta-T Devices, Cambridge, UK) and TRIME-Pico 32 (IMKO micromodultechnik GmbH, Ettlingen, Germany) sensors that had been used in field experiments for at least two years. General information about both sensors is summarized in Table 1.SM150TSM150T sensors (Delta-T Devices) operate on the capacitance principle with an operating frequency of 100 MHz according to the manufacturer (Delta-T Devices 2016) and support soil water content and soil temperature measurement, with a soil water content measurement error of ±0.03 m3 m−3 in a range from 0 to 0.7 m3 m−3 and soil temperature measurement error of ±0.5°C. The sensors consist of a 4-cm diameter cylindrical head and two 5.1-cm-long metal rods at a distance of 2.2 cm. The volume of influence is cylindrically shaped with a diameter of 7 cm and length of 5.5 cm (volume 0.21 L). The relationship between the refractive index (ε) and the sensor output (V) is a fifth-order polynomial [Eq. (1)] (1) ε=1.0+14.4396U−31.2587U2+49.0575U3−36.5575U4+10.7117U5According to the manufacturer, the relationship between soil water content and ε is linear, where a0 (ε of dry soil) is the intercept parameter and a1 (approximately εwater when θ=1) is the slope [Eq. (2)]. Based on this information, the soil-specific calibration can be conveniently performed using the two-point calibration procedure, which is described in more detail in Appendix 1 of the manual (Delta-T Devices 2016) (2) Considering default values of a0 and a1 for mineral (1.6 and 8.4) and organic (1.3 and 7.7) soils, raw values expressed as voltages (U), in volts (V), are converted to soil water content values using the following equations (Delta-T Devices 2016) (3) θmineral=−0.0714+1.7190U−3.7213U2+5.84U3−4.3521U4+1.2752U5(4) θorganic=−0.0390+1.8753U−4.0596U2+6.371U3−4.7477U4+1.3911U5TRIME-Pico 32The commercially available Time Domain Reflectometry with Intelligent Micromodule Element (TRIME) TDR system (IMKO micromodultechnik) is an adaptation of the conventional TDR system, which similarly generates precisely-timed electrical pulses. But unlike in conventional TDR, transit time is not determined over the entire waveform. TRIME systems determine transit times (tTRIME) from reflection times at given voltage levels, which requires high-amplitude maintenance after reflection (IMKO 1996) as cited in Dettmann and Bechtold (2018). Because of differences in the thickness of rod coating, variations in initial amplitude and bias in timing control circuits, TRIME sensors convert tTRIME to “pseudo transit time” (tp) (Dettmann and Bechtold 2018). tp is converted to ε by Eq. (5) and tp to θ by Eq. (6), both equations were provided by the manufacturer (5) ε=5.56+0.05tp−4.00×10−4tp2+1.82×10−6tp3−3.45×10−9tp4+2.40×10−12tp5(6) θuniversal=(−20.2+0.36tp−2.33×10−3tp2+8.28×10−6tp3−1.32×10−8tp4+7.86×10−12tp5)/100These sensors operate at the frequency of 1 GHz and consist of a 3.2-cm diameter cylindrical head and two 11-cm-long PVC-coated rods at a distance of 2 cm. The volume of influence is cylindrical with a diameter of 5 cm and a height of 11 cm. Measurement accuracy depends on the water content of the soil and the range of electrical conductivity (EC). For θ between 0 and 0.4 m3 m−3 is ±0.01 m3 m−3 and for θ between 0.4 and 0.7 m3 m−3 it is ±0.02 m3 m−3 when the EC is between 0 and 6 dS m−1 (IMKO 2017).Volume of InfluenceBecause the gravimetric determination of θ was based on the temporal weighting of the entire soil sample, it was necessary to determine the correct volume of influence for both sensor types.The experiment was performed in a laboratory at a mean ambient temperature of 23.6°C with a standard deviation of ±0.4°C. We placed sensors of each type (n=3) in the middle of the shorter wall of a container (57 cm×37 cm×31 cm) filled with deionized water and immersed the rods (Fig. 1). We then moved them from the wall of the container toward the center at 2 mm micromovements, obtaining raw sensor output reading data at each point (Vaz et al. 2013). Sensor rods were immersed vertically in the container to determine the radius of influence and horizontally to determine the length of influence. Sensor head touched the wall of the container at zero point for determining the radius as shown in Fig. 1. The same procedure was repeated in air, moving the sensors 2 mm away from the water-filled container. Normalized sensor output Ynor was calculated for both media using Eq. (7) proposed by Vaz et al. (2013) (7) where Yi = response of the sensor at any location; Yref = response of the sensor in air when measured in water and vice versa; and Yc = response of the sensor at a distance of 150 mm from the edge of the container toward the center.Sensor-to-Sensor VariabilityWe evaluated sensor-to-sensor variability by measurements in 2-isopropoxyethanol (i-C3E1) and its mixtures with deionized water. Liquids were selected due to their nonrelaxing properties over a wide frequency range, described by Jones et al. (2005). We used pure i-C3E1 and its ratios of 92∶8 and 80∶20 as suggested by Bogena et al. (2007). A fraction of i-C3E1 was selected based on permittivity values that can be equated with θ and are relevant for irrigation management. A cylindrically shaped plastic container with a diameter of 14 cm and a height of 18 cm was filled with reference liquid, which was thoroughly mixed before each series of measurements. The measurements were performed at an ambient temperature of 25.1°C (±0.3°C) and were performed with nine sensors of each type in 10 replicates.Soil PropertiesWe obtained disturbed soil samples with different soil properties (as shown in Table 2) from different locations across Slovenia. Sand, silt, and clay content was determined using the sieve and sedimentation method [ISO 11277 (ISO 2009)]. Organic matter content (OM) was determined using the difference between organic and total carbon after dry combustion [ISO 10694 (ISO 1996)] and the volumetric carbonate content method [ISO 10693 (ISO 2014a)] multiplied by 1.724. EC was determined using the standardized method [ISO 11265 (ISO 2014b)]. Dry soil bulk density (ρb) was determined using undisturbed soil cores, ρb, being calculated using Eq. (8) with mineral soil samples dried at 105°C and organic soil samples at 55°C. Soil samples were subjected to a matric pressure of −33 and −1,500 kPa [ISO 11274 (ISO 1998)] to determine soil water retention characteristics in the pressure plate extractor.Laboratory Calibration ProcedureWe modified a sampling protocol developed for the calibration of an undisturbed soil sample as proposed by Holzman et al. (2017). Due to microlocal variability of soil properties, we used homogeneous soil samples to compare the two sensor types. We selected an appropriate size of PVC cylinders (as shown in Table 1) based on the influence volume of each sensor type, adding additional length and radius due to the possible shrinkage of some soil samples. A mesh with filter paper was attached to one end of each cylinder to prevent sample loss. Soil samples were air-dried, sieved through a 5-mm mesh, and packed in PVC cylinders to their original soil bulk density. Cylinders packed with the same soil type were placed in containers, into which tap water was added so soil could passively absorb it from the bottom to the top. When the samples were completely saturated, we removed them and let the excess water drain off. A sensor was then inserted in the middle of each soil sample (Fig. 2). After each sensor reading, we weighed the whole sample together with the inserted sensor and an unconnected cable for the gravimetric determination of θ. During the experiment, the mean ambient temperature was 21.6°C (±1.0°C) and the mean relative humidity was 58.2% (±2.44%). We repeated this procedure at approximately one-day intervals until θgrav was below the permanent wilting point (with the exception of TRIME-Pico 32 soil SaL), which meant at least 12 measurement points per replicate. Mineral soil samples were oven dried at 105°C and organic soil at 55°C for at least 48 h and then reweighed to determine the dry mass of each sample at the end of the measurement series. Gravimetrically determined reference water content (θgrav) was calculated using the following equations (8) (9) θgrav=mws−msms×ρbρwwhere ρb = soil bulk density; Vt = soil sample volume; ms = dry soil mass; θgrav = volumetric water content; mws = water and soil mass; and ρw = water density.Table 1. General information about the SM150T and TRIME-Pico 32 sensorsTable 1. General information about the SM150T and TRIME-Pico 32 sensorsSensorWorking principleWorking frequencyData loggerSoftwarer (cm)h (cm)V (cm3)SM150TCapacitance100 MHzDelta-T GP2DeltaLink 184.108.40.206666.6TRIME-Pico 32TRIME TDR1 GHzDataTaker DT80—2.512235.6Table 2. Soil properties analysed: texture, bulk density (ρb), organic matter content (OM), electrical conductivity (EC), and water content (θ) when samples were subjected to matric potentials of −33 and −1,500 kPaTable 2. Soil properties analysed: texture, bulk density (ρb), organic matter content (OM), electrical conductivity (EC), and water content (θ) when samples were subjected to matric potentials of −33 and −1,500 kPaSoilSand (%)Silt (%)Clay (%)Textureρb (g cm−3)OM (%)EC (dS m−1)θ at −33 kPa (m3 m−3)θ at −1,500 kPa (m3 m−3)C5.822.471.8Clay1.220.50.010.530.31SiC8.149.642.3Silty clay1.004.30.150.440.28SiCL15.551.433.1Silty clay loam1.540.70.080.490.20CL121.946.731.4Clay loam1.314.10.090.400.22CL229.340.230.5Clay loam1.3220.127.116.110.17LCL43.330.226.5Loam-clay loam1.518.104.22.1680.15L37.044.318.7Loam1.700.70.090.340.11SaL68.820.310.9Sandy loam1.421.90.070.310.11O———Organic0.4545.90.49——Data AnalysisWe obtained raw values of SM150T (V), which we converted to ε using Eq. (1), to θ for mineral soils using Eq. (3), and to θ for organic soil using Eq. (4). For TRIME-Pico 32, we initially obtained values of θ, which we had to inversely fit to Eq. (6) to obtain raw values (tp). We searched for zeros of the fifth-order polynomial for each value of θ. After calculating raw values, we were able to calculate ε using Eq. (5).We developed linear or polynomial calibration functions that relate θgrav to raw sensor output for each sensor and soil type, referred to as the soil-specific calibration function (SSCF). The polynomial order was based on sequential F-tests comparing models of different orders for each calibration curve. Parameters of two-point soil-specific calibration a0 and a1 were calculated based on θgrav and ε. The coefficients of the two-point calibration showed a statistically significant dependence on clay content. We developed a sensor specific empirical clay content correction function (CCF). Considering the clay content of the soil, we also analysed the influence of the bulk density of the soil and the organic matter content, but we did not find a statistically significant dependence.For each sensor and soil type we calculated measurement errors as EMi=θi−θgrav,i, i=1,⋯n, n being the number of measurements in the calibration procedure of each sensor. The EMi values were first graphically presented for the analysis of their dependence on θgrav,i. Then we calculated the root mean square error (RMSE) for each calibration procedure, shown in Eq. (10), as a measure of the sensor’s accuracy (10) RMSE=1n∑i=1n(θi−θgrav)2All data analyses were performed using the R program version 3.5.3 (R Core Team 2019).Results and DiscussionVolume of InfluenceFig. 3 shows the normalized sensor output when the sensor rods are moved away from the wall of the container in water and in air. When the SM150T was touching the wall horizontally, the normalized output was 0.972 in water and 0.997 in air. When touching the wall vertically, the normalized output was 0.986 in water and 0.997 in air. In both media, the full length and radius of influence of the SM150T was covered over a distance of approximately 26 mm. The normalized output of the TRIME-Pico 32 did not change when moved horizontally or vertically away from the edge of the container, either in water or in air.Sensor-to-Sensor VariabilityTable 3 shows the results of measurements of raw values, ε and θMCF, obtained in reference liquids of i-C3E1 and its water mixtures with different permittivity values corresponding to soil water content conditions of about 0.4 m3 m−3 (i80) to 0.2 m3 m−3 (i100) (Bogena et al. 2017), which often corresponds to θ at field capacity and permanent wilting point in medium- to heavy-textured soils. The ε of TRIME-Pico 32 in reference liquids is lower than that of the SM150T. Regardless of the lower ε, the values of the converted θMCF of TRIME-Pico 32 are consistently higher than those of SM150T.Table 3. Sensor-to-sensor variability for each sensor type (n=9) in reference liquids, represented as raw sensor output, apparent permittivity (ε) and water content (θMCF), determined using the manufacturer’s calibration functionTable 3. Sensor-to-sensor variability for each sensor type (n=9) in reference liquids, represented as raw sensor output, apparent permittivity (ε) and water content (θMCF), determined using the manufacturer’s calibration functionLiquidSensorMeanCV (%)MeanCV (%)MeanCV (%)i100SM150T0.251.610.81.40.201.4TRIME-Pico 32448.51.810.72.30.252.5i92SM150T0.422.214.171.124.310.9TRIME-Pico 32541.31.3126.96.36.1991.9i80SM150T0.633.127.74.00.442.9TRIME-Pico 32634.61.8188.8.131.524.6Based on the mean values of the measured ε, water content (θTopp) was calculated using the empirical polynomial equation of Topp et al. (1980). θTopp in i100 was 0.20 m3 m−3 for both sensor types. θTopp in i92 was 0.31 m3 m−3 for SM150T and 0.27 m3 m−3 for TRIME-Pico 32. θTopp in i80 was 0.43 m3 m−3 for SM150T and 0.39 m3 m−3 for TRIME-Pico 32. The theoretical values of ε (denoted ε* at 25°C for i100, i92, and i80) are 10.8, 18.1, and 26.3 (Kaatze et al. 1996; Domínguez-Niño et al. 2019), with the calculated θTopp* of 0.20, 0.32, and 0.41 m3 m−3, respectively. There is a good agreement between θTopp and θMCF for SM150T, while θMCF of TRIME-Pico 32 overestimates the water content compared to the Topp’s equation, which means the Topp’s equation would not be appropriate to apply to the TRIME-Pico 32 data set.Sensor-to-sensor variability is shown as the coefficient of variation (CV) in Table 3. It is generally low for both sensor types; however, it is higher for TRIME-Pico 32 compared to SM150T. Because sensor-to-sensor variability is a combination of factors, such as variations in electrical components and microvariations in probe geometry (Bogena et al. 2017), a greater variability of the TRIME-Pico 32 sensors could be due to thinner PVC-coated rods, which are more flexible and more susceptible to changes in rod geometry.Manufacturer’s Calibration FunctionFig. 4 shows the relationship between θgrav and θMCF for each sensor and soil type. Individual soil and sensor type data series do not cover the entire water content range, the maximum value of θgrav depending on soil water retention properties and the minimum value of θgrav on soil drying degree. It also shows that measuring intervals differ according to sensor and soil type. In general, SM150T measurement series cover a wider range, especially in drier conditions. TRIME-Pico 32 data is more scattered as previously shown with the results of sensor-to-sensor variability.Two-Point CalibrationFor both sensors, we evaluated the two-point calibration procedure recommended by Delta-T Devices. First we evaluated dependence of ε on θgrav. Based on sequential F-tests, the SM150T sensor’s dependence of ε on θgrav was a third-order polynomial for soils C, SiC, SiCL, CL1, CL2, LCL, and O, a second-order polynomial for SaL, and linear only for L. For TRIME-Pico 32 it was a third-order polynomial for SiC and CL1 soil types, a second-order polynomial for C, SiCL, CL2, L, and SaL soil types, and linear for LCL and O soil types. Although the linear function for both sensors could be fitted to all the soils studied.Measurements with fitted functions are shown in Fig. 5: the gray line represents the default function provided by Delta-T with coefficients for mineral [Fig. 5(a)] and organic [Fig. 5(b)] soils, the line is only relevant for comparison with SM150T. The coefficients of intercept (a0) and slope (a1) are shown in Table 4. Delta-T Devices (2016) states that for SM150T, the a0 or ε of dry soil is typically between 1.3 and 2.3, which was true for all but C and O soils. a1, which is approximately εwater at θ=1, typically takes a value of 8.0, but bound water can cause higher values of a1, which again was true for soil types C (a1=11.0) and O (a1=9.9). The a0 values of TRIME-Pico 32 were somehow similar to those of SM150T, while a1 or the slope parameter was smaller compared to SM150T. We used these newly-developed soil-specific calibration coefficients of two-point calibration, applied them to our data set, and validated them with the calculation of the RMSE.Table 4. Soil-type-specific two-point calibration coefficients for mineral and organic soilsTable 4. Soil-type-specific two-point calibration coefficients for mineral and organic soilsSoila0a1r2a0a1r2C1.011.00.98184.108.40.206SiC1.78.00.99220.127.116.11SiCL2.07.60.992.06.50.97CL18.104.22.1681.96.00.94CL22.214.171.1242.05.80.94LCL1.78.00.992.25.00.97L2.08.10.99126.96.36.199SaL1.88.00.99188.8.131.52O0.69.90.991.07.70.94Clay Content Correction FunctionThe clay content correction function (CCF) was developed based on a linear relationship between clay content and each of the parameters a0 and a1 for both sensor types, shown in Fig. 6. SM150T’s linear relationship between clay content and coefficients a0 (r2=0.65) and a1 (r2=0.68) is shown in Eq. (11). TRIME-Pico 32’s is shown in Eq. (12) with a0 (r2=0.92) and a1 (r2=0.79)(11) SM150T θCCF=ε−a0a1=ε−(2.131−0.014 Clay)6.803+0.049 Clay(12) TRIME−Pico32 θCCF=ε−(2.516−0.016 Clay)4.463+0.040 ClayIn contrast to the linear relation we obtained, Singh et al. (2019), who similarly explored a relation between 1/a1 and a0/a1, the coefficients from the square root mixing model, and the clay content for the two reflectometers (TDR315 and CS655), observed a second-order polynomial relation.We used these newly-developed clay correction functions, calculated θCCF, and validated them by calculating values of the RMSE. The dependence of the coefficients on the clay content was stronger for TRIME-Pico 32 than for SM150T. The best-explained variation of coefficient and clay content was observed for the a0 (r2=0.92) of TRIME-Pico 32, followed by a1 (r2=0.79). Consequently, the application of the CCF to the TRIME-Pico 32 data set is expected to provide a better improvement in the RMSE compared to SM150T.Estimated Measurement ErrorsTable 5 shows the RMSE of applying the MCF, the two-point, the CCF, and the SSCF to the current data set. The RMSE of the MCF is higher for TRIME-Pico 32 compared to SM150T. However, the application of the CCF considering the clay content reduces the RMSE for TRIME-Pico 32 in all soils, which is due to a good model fit of the clay content and the coefficients a0 and a1. In contrast, applying the CCF to the SM150T data set results in higher RMSE values for soil types with already low RMSE using the MCF (CL1, CL2, LCL, and SiC), while some improvement is observed for soil types C, SiCL, and L. The coefficient a1 of SM150T exhibits a threshold behaviour for soils with clay content less than 40%, as shown in Fig. 6.Table 5. RMSE of each soil and sensor type using the manufacturer’s calibration function (MCF), the two-point, the clay corrected function (CCF), and the soil-specific calibration function (SSCF)Table 5. RMSE of each soil and sensor type using the manufacturer’s calibration function (MCF), the two-point, the clay corrected function (CCF), and the soil-specific calibration function (SSCF)SoilSM150TTRIME-Pico 32SM150TTRIME-Pico 32SM150TTRIME-Pico 32SM150TTRIME-Pico 32C0.0510.0390.0160.0320.0210.0340.0130.021SiC0.0160.0440.0120.0130.0280.0250.0090.008SiCL0.0230.0450.0080.0160.0160.0440.0070.013CL10.0120.0300.0140.0230.0150.0250.0070.018CL20.0110.0300.0110.0220.0160.0230.0080.015LCL0.0110.0350.0100.0150.0180.0180.0080.013L0.0420.0600.0090.0260.0340.0300.0080.015SaL0.0130.0400.0090.0190.0130.0270.0070.017O0.0510.0470.0090.022——0.0070.017External validation of the CCF was performed using data from Vaz et al. (2013), who tested several sensors in soils with different soil properties, including clay content, all collected in Arizona, US. The correction was evaluated only for the SM300 sensor (Delta-T Devices), which is similar to the SM150T. The changes in the RMSE after applying the CCF (SM150T) to their independent data varied depending on clay content. For soils with clay content between 3 and 21%, application of the CCF increased the RMSE. The RMSE increased from 0.017 to 0.051 for soils with 3% clay, from 0.039 to 0.053 for soils with 20.9% clay, and from 0.036 to 0.042 for soils with 21.5% clay. However, application of the CCF to soils with clay content between 28% and 69% improved the RMSE. It decreased from 0.136 to 0.132 for soils with 28% clay, from 0.048 to 0.041 for soils with 36.7% clay, and from 0.046 to 0.028 for soils with 68.9% clay. This confirms that the CCF may not be an appropriate correction for soils with clay content less than 30%, but that using CCF may be beneficial for soils with higher clay content.Fig. 7 shows the measurement errors (EM) as a function of θgrav for the MCF, the CCF and the SSCF. The reduction in errors when the CCF is applied to SM150T is observed for soil type C. After applying the CCF for TRIME-Pico 32, there is a reduction in errors for most soil types; however, for some soils (SiCL, CL1, and CL2), the errors increase at high θ. The SSCF reduced errors the most when applied to the data set.SM150TThe measurement error of the SM150T sensor oscillated close to zero when the MCF was used in soil types CL1, CL2, SiC, SaL, and LCL. Therefore, the application of the CCF did not reduce the errors much except in soil type C. The θMCF values in soil type C with 72% clay were higher than actual under more saturated conditions, with the maximum EM of 0.10 m3 m−3 and the RMSE of 0.051 m3 m−3. Overestimation could be explained by enhanced ionic conductivity and dielectric dispersion caused by a large surface area and the cation exchange capacity of clay particles. Because SM150T operate in a lower frequency range (100 MHz), the effect of dispersion is more pronounced, resulting in an increased permittivity (Evett and Parkin 2005; Singh et al. 2019; González-Teruel et al. 2020). Similarly, in organic soil SM150T θMCF consistently overestimated the actual water content, with the maximum EM of 0.09 m3 m−3 and the RMSE of 0.051 m3 m−3. The overestimation was greater at higher θ values and can be explained by the same mechanism as for soil type C. However, in a study by Vaz et al. (2013), SM300 (Delta-T Devices) similar to SM150T performed better in their studied organic soil (RMSE of 0.035 m3 m−3). On the other hand, Kassaye et al. (2019) found that 5TM (Decagon Devices, US) capacitance sensors consistently underestimated soil moisture content in Andisol volcanic origin soils with high organic matter content (RMSE of 0.092 m3 m−3).θMCF showed higher-than-actual values for soil types L (ρb=1.70 g cm−3 and 19% clay) and SiCL (ρb=1.54 g cm−3 and 33% clay) in drier conditions, with the maximum EM of 0.06 m3 m−3 and the RMSE of 0.042 m3 m−3 for L, and the and maximum EM of 0.04 m3 m−3 and the RMSE of 0.023 m3 m−3 for soil type SiCL. For these two soils, ρb seems to have the greatest impact on errors; consequently the application of the CCF did not greatly improve the values of the RMSE. Parvin and Degre (2016), who calibrated capacitance sensors in silty clay soils, concluded that measurement in soils with high clay content and a high ρb can lead to an increase of raw outputs resulting in overestimation of θ when using capacitance sensors, which is consistent with our results.Using the MCF, the maximum measurement error was within the manufacturer-specified value range (±0.03 m3 m−3) for soil types CL1 (RMSE of 0.012 m3 m−3), SaL (RMSE of 0.011 m3 m−3) and LCL (RMSE of 0.011 m3 m−3). In soils of lighter texture, similar to SaL, Kim et al. (2020) found that the SM150 sensor, similar to the SM150T, underestimated θ at values below 0.25 m3 m−3; however, their reported RMSE (0.028 m3 m−3) was higher than ours (0.013 m3 m−3). In contrast, Zhu et al. (2019) who compared the measurement of θ using different sensors with the neutron probe, found that SM150 overestimated θ in loamy sand over the entire range (RMSE of 0.050 m3 m−3). Overestimation also occurred in silt loam in the range from saturated conditions to about 0.2 m3 m−3 (RMSE of 0.147 m3 m−3).When applying the two-point calibration function to the SM150T data set, the RMSE greatly improved. Therefore, the two-point calibration procedure, recommended by the manufacturer can be used as an easy and fast calibration of SM150T sensors. However, applying the SSCF even additionally improved the RMSE of all studied soil types.TRIME-Pico 32The TRIME-Pico 32 sensor measurement error of θMCF showed a larger overestimation as the soil dried. The exceptions are SiC and C soils with high clay content and low soil bulk density. The sensors underestimated the actual water content with a maximum negative EM for SiC of −0.09 m3 m−3 and the RMSE of 0.044 m3 m−3 (ρb=1.00 g cm−3), and EM −0.08 m3 m−3 and the RMSE of 0.039 m3 m−3 for C (ρb=1.22 g cm−3). The underestimation could be attributed either to bound water molecules being less polarized and leading to a lower dielectric permittivity (Hilhorst et al. 2001; Li et al. 2019) or to a lower bulk density causing a higher ratio of air to solids and water, resulting in a lower permittivity in unsaturated conditions (Vaz et al. 2013). An underestimation of actual θ was also observed for organic soil (ρb=0.45 g cm−3), with a maximum negative EM of −0.07 m3 m−3 and the RMSE of 0.047 m3 m−3. Similarly, lower θ values than actual are reported in organic soils with a large specific surface area due to the bound water effect (Bircher et al. 2016; Kassaye et al. 2019). Sensors consistently overestimated actual θ for soil type L (ρb=1.70 g cm−3), EM of 0.11 m3 m−3, the RMSE of 0.060 m3 m−3 and SiCL (ρb=1.54 g cm−3), the EM of 0.08 m3 m−3, and the RMSE of 0.045 m3 m−3.Laurent et al. (2005) calibrated the TRIME-FM3 access tube sensor, which has the same operating principle as the TRIME-Pico 32. When using the MCF, they reported an overestimation of θ in different soil types, at the tp between 400 and 600, corresponding to θMCF values between 0.2 and 0.4 m3 m−3. This is in agreement with our results, except for soil types C and SiC. The RMSE values obtained in their study ranged from 0.023 to 0.097 m3 m−3, while in our study, the RMSE values ranged from 0.030 to 0.060 m3 m−3. Kim et al. (2020) also reported an overestimation of θ at values below 0.25 m3 m−3 by TRIME-Pico 64 in sandy loam, which is similar to our SaL. In our study, an overestimation occurred at θ below 0.3 m3 m−3. The RMSE using the MCF in their study was, however, lower (0.022 m3 m−3), compared to ours for SaL (0.040 m3 m−3). This finding of overestimation by TRIME-Pico is also consistent with our results from measurement in reference liquids, where overestimation of θMCF also occurred.Due to the strong dependence of the coefficients a0 and a1, on clay content, the application of the CCF resulted in a reduction of the RMSE for all soil types and can be recommended for some improvement in data accuracy compared to the MCF. But as was noted by Singh et al. (2019), who also developed the clay content correction function, while the CCF may be a good fit to current data, its transferability is somehow questionable because the mineralogy and the specific surface area of the clay particles are a more direct factor causing the “clay effect” rather than the actual percentage of clay. However, clay content is a more convenient parameter to use because it is easier to measure clay content than it is to determine mineralogy.The application of the two-point calibration function, otherwise recommended by Delta-T Devices, was also found to be appropriate for TRIME-Pico 32. An additional reduction in the RMSE was observed after it was applied to the data set.Water Content Measurement AccuracyIncorrect θ measurement can have a significant negative effect on studies of drainage, soil water dynamics, and irrigation management. Soulis et al. (2015), who simulated and investigated the effect of dielectric sensor positioning and accuracy on sensor-based irrigation scheduling system efficiency, reported that accuracy is more important than positioning. If the error rate was ±0.03 m3 m−3, which is generally optimistic for many dielectric sensors using the manufacturer’s calibration equations, this already has a significant impact on the efficiency of the irrigation scheduling system. Therefore, the sensors require the highest level of accuracy, which is often not achieved using the calibration equations provided by the manufacturer (Matula et al. 2016; Parvin and Degre 2016; Datta et al. 2018; Roberti et al. 2018).The presented calibration approach is suitable for the calibration of an undisturbed soil sample, whereby the additional sampling cylinder is required to obtain a soil sample. Such procedure is seen as advantageous because it preserves natural soil structure (Holzman et al. 2017), and is preferred when greater accuracy is required (Holzman et al. 2017; Singh et al. 2020).Evaporation in porous media is driven by capillary-induced liquid flow and vapor diffusion resulting in a complex drying pattern (Lehmann et al. 2008; Shokri et al. 2008). In an open soil column, there is a gradual movement of the evaporation front and the formation of the drying layer (An et al. 2020). As the sensors are continuously inserted into a soil sample during the calibration procedure, evaporation under the sensor head is prevented. Consequently, this method is preferred for sensors with a larger radius of influence (e.g., capacitance), because the ratio between the exposed soil surface and the area covered by the sensor head is larger, allowing for more homogeneous drying of the soil. The radius of influence of TRIME-Pico 32 is relatively small and higher errors occurred at lower θ when using the MCF, especially for soil samples with high ρb. Apart from the general overestimation of θMCF, observed in reference liquids and reported in the literature (Laurent et al. 2005; Kim et al. 2020), another possible reason for the overestimation may be a nonhomogeneous drying process of soils. Heterogeneity may cause an enhanced electric field in wetter zones and consequently an overall higher detected dielectric permittivity, compared to a uniformly-distributed soil water content (Logsdon 2009). Due to preferential detection of wetter zones (Logsdon 2009), presence of roots (Kang et al. 2019), soil fauna, and temperature variations (Visconti et al. 2014; Kassaye et al. 2019), some authors recommend field validation of measurement data. Another nonnegligible source of uncertainty in sensor data obtained in the field is the interreplicative variability of sensors exposed to the same conditions (Lo et al. 2020).ConclusionIn the current study, we evaluated the performance of two commercially available but not widely studied dielectric sensors, the SM150T (Delta-T Devices) and TRIME-Pico 32 (IMKO). First, we determined the volume of influence in water and air. We evaluated sensor-to-sensor variability in reference liquids, which was generally greater for the TRIME-Pico 32 sensors. For both sensor types, the measurement variability increases with increasing permittivity.We evaluated the accuracy of the manufacturer’s calibration functions (MCF) of both sensors by evaluating their performance in soils with different properties, eight mineral and one organic. The SM150T errors generally oscillated around zero for most soil types, except for C (72% clay), O (46% organic matter), and L (ρb=1.7 cm−3). TRIME-Pico 32 errors were generally larger, especially in the drier range.Based on the linear relationship between θgrav and ε, the coefficients of intercept (a0) and slope (a1) were determined. The two-point calibration procedure was applied to both sensor data sets. We further investigated the relationships between clay content and the two coefficients. For both sensor types, the relationship between each of the coefficients and clay content was linear. Considering clay content, we also analyzed the influence of soil bulk density and organic matter content; however, dependence was not statistically significant. Based on the clay content and the relationship between a0 and a1, we developed sensor-specific clay correction functions (CCF). Because the dependence was stronger for TRIME-Pico 32, the calculated θCCF yielded less error when the CCF was applied to the data set. Therefore, the CCF is recommended to improve the errors when TRIME-Pico 32 is used. The errors did not improve much when applied to the SM150T data set and in some cases the errors actually increased. However, external validation of the CCF using SM300 (Delta-T Devices) showed an improvement in RMSE compared to MCF for soils with clay content of 28% or greater. Two-point calibration resulted in substantial error reduction, especially for SM150T. However, the greatest error reduction for both sensor types was observed when individual soil-specific calibration functions (SSCF) were applied. The two-point calibration function is the second best recommendation because it is easier to determine and less time consuming. The clay correction function is also recommended instead of MCF. However, our CCF lacks soil samples with clay contents between 42% and 72%, so it could be improved. 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