Use of a Dielectric Sensor for Salinity Determination on an Extensive Green Roof Substrate

The irrigation of extensive green roofs with recycled or saline water could contribute to the conservation of valuable drinking water supplies. In such cases, the continuous monitoring of substrate electrical conductivity (ECsw) is of immense importance for the sustainable growth of the plants growing on the green roof. The present study aimed to estimate the ECsw (pore water EC) of an extensive green roof substrate in lysimeters with the use of the WET-2 dielectric sensor. Half of the 48 lysimeters that simulated extensive green roofs had a substrate depth of 7.5 cm, while the other half had a 15 cm substrate depth. The warm season turfgrass Paspalum vaginatum ‘Platinum TE’ was established at the lysimeters, and during the summer period, it was irrigated every two days at a rate of 14 mm with NaCl solutions of various electrical conductivities (ECi): (a) 3 dS m−1, (b) 6 dS m−1, and (c) 12 dS m−1, while potable water of 0.3 dS m−1 ECi served as the control. The relation between bulk electrical conductivity, σb, and bulk dielectric permittivity, εb, of the substrate was observed to be linear for all ECi levels up to σb values of 2–2.5 dS m−1. The ECsw was predicted by employing the salinity index method which was modified to be applied to the particular case of a green roof substrate. Knowing the salinity index and organic portion (%, v/v) for a given green roof substrate, we could calculate the ECsw. It was found that the use of the salinity index method predicts reliably the ECsw up to 10–11 dS m−1, while the method overestimates ECsw at very low levels of electrical conductivity.


Introduction
In recent decades, green roofs are considered a common practice for reintroducing open green spaces in the densely built fabric of contemporary large cities. Green roofs, regardless of their type, comprise a multi-layered system that commonly includes a protection mat for the waterproofing membrane, a drainage layer, a filtering sheet, a plant growth substrate comprised of lightweight materials, and vegetation [1]. According to existing guidelines [2], green roofs with a substrate depth of up to 15 cm are classified as extensive types, and their vegetation consists of low-maintenance and drought-resistant plants.
Numerous requirements must be met by the growing substrate for extensive green roofs, including maintaining the necessary substrate moisture for plant growth, enabling the quick removal of excess water, providing support and anchoring for the plants, providing nutrients, and having a pH and substrate electrical conductivity (EC sw ) that are suitable for plant growth [3]. The constituents of extensive green roof substrates are mainly inorganic [4], lightweight, and coarse, and possess significant internal porosity, such as pumice [5], crushed bricks or tiles [6], zeolite [7], heat-expanded shale, clay or slate [8], perlite [9], and lava [10]. Organic substances, such as peat and composts, are also used to improve the physical and chemical properties of the substrate, but at smaller participation percentages to prevent substrate subsidizing as a result of decomposition [11].
The benefits of green roofs are numerous, including the amelioration of the urban heat-island effect [12], a reduction in air pollution [13], and stormwater management [14]. However, the implementation of green roofs on a large scale is required to significantly improve urban microclimates [15]. As a result, to meet this increased demand for the irrigation of green roofs, especially in arid or semi-arid areas, such as the Mediterranean region, alternative water irrigation sources should be explored. Saline groundwater, brackish surface water, grey water, or recycled water could all be used for green roof irrigation [16,17]. A significant disadvantage of the aforementioned alternative water sources is the increased electrical conductivity (EC). Hence, to ensure the long-term viability of the plants growing on green roofs, the EC sw must be precisely determined and continuously monitored.
The salinity in a soil environment is mainly estimated by measuring the EC of the saturated soil paste extract (EC e ) [18], which is now established as a standard method. However, this method is laborious and time-consuming since it involves soil sampling, the creation of saturated paste, the collection of extract, and the measurement of the EC e [19]. As a result, instead of EC e , in many cases, electrical conductivity is determined using soil-water solutions in various ratios. This method of indirect estimation of EC e is practically easier but requires that the relationship between EC e and the EC of the specific soil/water ratio be known in advance to be able to estimate EC e .
Dielectric devices, such as time domain reflectometry (TDR) sensors and frequency domain reflectometry (FDR) sensors, have made it possible to simultaneously measure the bulk dielectric permittivity (ε b ), the bulk electrical conductivity (σ b ), and the temperature at the same point in the soil. From the measurement of σ b , the electrical conductivity of the pore water solution of the soil or growing substrate (EC sw ) can be calculated with the help of various models [20][21][22][23][24][25][26].
Malicki and Walczak [21] introduced the concept of the salinity index (X s ), utilizing measurements of ε b and σ b obtained by the TDR device. Then, Wilczak et al. [26] used the salinity index method to calculate EC sw from ε b and σ b data acquired by an FDR sensor operating at a frequency of up to 500 MHz.
The salinity index (X s ) is defined as the partial derivative of σ b to ε b , where both parameters are determined by a dielectric sensor at the same time and the same point in the soil.
Additionally, Malicli and Walczak [21] reported that the X s is independent of soil water content (θ) when it is above 0.2 cm 3 cm −3 and that X s depends on soil salinity and texture. The relationship between σ b and ε b was proved to be linear, and the slope, which equals the X s , increases with the increasing EC of the irrigation water (EC i ) in the same porous medium but is different for the same value of EC i in different porous media. The constant term (y-intercept) of the linear relationship also depends on the type of medium and the value of EC i .
When the value of X s and the slope (l) of the relationship X s -EC i are known, then it is possible to calculate the value of EC sw from the equation [21]: Malicki and Walczak [21], for the case of inorganic soils, proposed an equation (Equation (3)) to calculate X s (for values of σ b > 0.08 dS m −1 and ε b > 6.2). where σ b = 0.08 dS m −1 and ε b = 6.2 is the common point where the lines converge σ b (ε b , EC sw ). They also showed that slope l can be calculated from an empirical relationship based on the sand content of the soil. The final suggested EC sw calculation equation is: where S is the % (w/w) sand content of the soil. Equation (4) is valid for values of θ langer than 0.2 cm 3 cm −3 because, as mentioned by Malicki and Walczak [21], above this limit, X s is independent of the θ value. The existence of a linear relationship between σ b and ε b from data obtained from the WET-2 sensor (Delta-T Devices, Cambridge, UK), which operates at a frequency of 20 MHz, has been confirmed in many cases of inorganic porous media [23,24,27]. However, the relationship between σ b and ε b has not been investigated in depth until now for coarse textured growing substrates suitable for extensive green roofs [28], as well as the possibility of using the empirical model of Malicki and Walczak [21] (Equation (4)) for EC sw prediction on such substrates. However, to implement this model, it is necessary to know the point of intersection of the linear relationships σ b -ε b, as in inorganic soils, but also a corresponding correlation of l with the substrate properties. However, in the case of green roof substrates, there is zero sand content, so Equation (4) cannot be used. In these cases, an empirical relationship must be found that relates l to another property of the substrate, for instance, the volumetric portion of clay, pumice, perlite, or of organic substances. To be able to find such a relationship requires much more experimental data from different substrates. Such relations for the case of soils have been presented by Wilczak et al. [26] and Kargas and Kerkides [29].
The primary aim of this investigation was to evaluate the EC sw of a green roof substrate, at two different substrate depths, when irrigation was applied with water of EC i of 0.3 dS m −1 , 3 dS m −1 , 6 dS m −1 , and 12 dS m −1 , employing a modified salinity index method suitable for extensive green roof substrates. Specifically, the objectives of this study were, (a) to verify the linear relationship between σ b -ε b for EC i values, (b) to establish, if there is a limit to the value of σ b , above which the relationship σ b -ε b is not linear, and (c) to find an empirical relationship that relates l with the organic portion (%, v/v) of the green roof substrate.

Experimental Setup
The outdoor study was conducted at the experimental field of the Laboratory of Floriculture and Landscape Architecture, Agricultural University of Athens, Greece (37 • 59 N, 23 • 42 E, 35 m above sea level) from 19 July 2014 until 23 October 2014. It comprised 48 PVC lysimeters with a 300 mm inner diameter placed on leveled benches. Within each lysimeter, a complete layered simulation of an extensive green roof system was constructed. More specifically, the bottom of the lysimeter was covered with a protective mat made of nonrotting synthetic polyester fibers with a 3 mm thickness, a dry weight of 0.32 kg m −2 , and a capacity to retain 3 L m −2 of water (TSM32, Zinco, Egreen, Athens, Greece). A drainage board layer made of recycled polyethylene with a height of 25 mm and a weight of 1.5 kg m −2 (FD25, Zinco, Egreen, Athens, Greece) was placed on top of the protective cloth. The drainage layer, which was equipped with water-retaining troughs, could store 3 L m −2 . The drainage layer was covered with a non-woven geotextile (SF, Zinco, Egreen, Athens, Greece) made of thermally strengthened polypropylene, with a thickness of 600 µm, a weight of 100 g m −2 , a 90% apparent opening size of 95 mm, and a water flow rate of 0.07 m s −1 . A 10 mm diameter outflow opening was constructed at the bottom center of each lysimeter. The leachate was directed into a 2 L tank which was kept beneath the lysimeter by a flexible hose that was connected to the outlet.
The lysimeters were filled with a specialized and patented green roof substrate (Patent No. 1008610), which comprised 65% pumice, 15% thermally treated attapulgite clay, 15% Sensors 2023, 23, 5802 4 of 13 grape marc compost, and 5% clinoptilolite zeolite by volume. The physical and chemical properties of the substrate are presented in Table 1. The substrate depth in half of the lysimeters was 7.5 cm, whereas, in the other half, it was 15 cm. After substrates were placed into the lysimeters, light compression and leveling were applied.

Turfgrass Establishment and Irrigation
The warm season turfgrass species Paspalum vaginatum 'Platinum TE' was established in the plots 45 days before the initiation of the study on 2 June 2014 using washed sod. Paspalum vaginatum (seashore paspalum) was selected because it exhibits several desirable characteristics including increased tolerance to irrigation with water of high salinity up to seawater levels [8,30].
After sodding, the lysimeters were irrigated daily with potable water (EC of 0.3 dS m −1 ) until the initiation of increased salinity irrigation treatments. Increased salinity treatments were initiated on 19 July and ended on 23 October 2014, totaling 97 d. At the initiation of the study (17 July 2014), all lysimeters were irrigated with ample potable water (EC of 0.3 dS m −1 ) to produce uniform substrate moisture conditions. From then on, seashore paspalum was irrigated every other day at the depth of 14 mm (7 mm per day) with three NaCl irrigation solutions (EC i ) of 3 dS m −1 , 6 dS m −1 , and 12 dS m −1 , while potable water of 0.3 dS m −1 electrical conductivity served as the control.
The lysimeters were hand-irrigated with a watering can with a nozzle to ensure even water distribution. During the first three irrigation events of the study (19,21, and 23 July 2014), irrigation solution of 3 dS m −1 was used for all salinity treatments to avoid salinity shock of the turfgrass. From then on, irrigation was applied according to the experimental setup with all three salinity solutions (3 dS m −1 , 6 dS m −1 , and 12 dS m −1 ).

Meteorological Data
During the study period (17 July 2014 until 23 October 2014), air temperature and precipitation were monitored by the weather station of the Laboratory of General and Agricultural Meteorology of the Agricultural University of Athens, Athens, Greece, located 15 m away from the experimental site ( Figure 1). No precipitation was observed during the summer period of the study (17 July-31 August 2014), having an average air temperature of 27.7 • C. The first autumn rainfall was recorded on 9 September 2014 (11.8 mm). Rainfall was also recorded on 16 September (1.8 mm), 7 October (4.6 mm), 22 October (4 mm), and 23 October (26.6 mm), marking the end of the study. The mean air temperature during the autumn months of the study (1 September-23 October 2014) was 22.0 • C. temperature of 27.7 •C. The first autumn rainfall was recorded on 9 September 2014 (11.8 mm). Rainfall was also recorded on 16 September (1.8 mm), 7 October (4.6 mm), 22 October (4 mm), and 23 October (26.6 mm), marking the end of the study. The mean air temperature during the autumn months of the study (1 September-23 October 2014) was 22.0 °C.

Measurements
Throughout the study, the volume and salinity of the leachate, which was collected in tanks beneath each lysimeter, were determined every two days just before irrigation events. The collected leachate in the tanks referred to the previous irrigation application and was discarded after the determination of its volume and EC. For the electrical conductivity of the leachate (ECL) measurements, a handheld conductivity meter (CyberScan 200, Eutech Instruments Pte Ltd., Singapore) was used, which automatically corrected the EC to 25 °C. The outflow runoff volume from each lysimeter was divided by the inflow irrigation water volume to estimate the leaching fraction (LF).
Besides ECL measurements, the substrate bulk dielectric permittivity (εb) as well as the bulk electrical conductivity of the substrate (σb) were determined. The determination was made every four days, before irrigation, using the WET-2 sensor (Delta-T Devices, Cambridge, UK). The WET-2 sensor is an inexpensive frequency domain dielectric soil moisture sensor, which is not able to automatically record data, and its probe consists of three metal rods. The rods are 6.8 cm long and spaced 1.5 cm apart, creating a cylindrical sampling area 65 mm deep and 45 mm wide [31]. The sensor was connected to an HH2 portable moisture meter (Delta-T Devices), in which the Hilhorst [22] model (Equation (5)) is installed for ECsw determinations.

Experimental Methodology and Statistics
The experimental design was multi-factorial and involved two factors: two green roof substrate depths (7.5 cm or 15 cm) and four irrigation water salinities (0.3 dS m -1 , 3 dS m -1 , 6 dS m -1 , and 12 dS m -1 ). The plot arrangement followed a completely randomized

Measurements
Throughout the study, the volume and salinity of the leachate, which was collected in tanks beneath each lysimeter, were determined every two days just before irrigation events. The collected leachate in the tanks referred to the previous irrigation application and was discarded after the determination of its volume and EC. For the electrical conductivity of the leachate (EC L ) measurements, a handheld conductivity meter (CyberScan 200, Eutech Instruments Pte Ltd., Singapore) was used, which automatically corrected the EC to 25 • C. The outflow runoff volume from each lysimeter was divided by the inflow irrigation water volume to estimate the leaching fraction (LF).
Besides EC L measurements, the substrate bulk dielectric permittivity (ε b ) as well as the bulk electrical conductivity of the substrate (σ b ) were determined. The determination was made every four days, before irrigation, using the WET-2 sensor (Delta-T Devices, Cambridge, UK). The WET-2 sensor is an inexpensive frequency domain dielectric soil moisture sensor, which is not able to automatically record data, and its probe consists of three metal rods. The rods are 6.8 cm long and spaced 1.5 cm apart, creating a cylindrical sampling area 65 mm deep and 45 mm wide [31]. The sensor was connected to an HH2 portable moisture meter (Delta-T Devices), in which the Hilhorst [22] model (Equation (5)) is installed for EC sw determinations.

Experimental Methodology and Statistics
The experimental design was multi-factorial and involved two factors: two green roof substrate depths (7.5 cm or 15 cm) and four irrigation water salinities (0.3 dS m −1 , 3 dS m −1 , 6 dS m −1 , and 12 dS m −1 ). The plot arrangement followed a completely randomized design, and each treatment was replicated 6 times resulting in 48 lysimeters (4 irrigation treatments × 2 substrate depths × 6 replications = 48 lysimeters).
In the initial stage of the current study, regressions were conducted between σ b and ε b , which were determined using the WET-2 sensor. These regressions were performed for both substrate depths and each level of EC i using the JMP®ver.11 statistical software (SAS Institute Inc., Cary, NC, USA). Based on the outcomes of these regressions, the viability of utilizing Equations (3) and (4) proposed by Malicki and Walczak [21] for X s and EC sw value calculation was assessed in the context of a green roof substrate.
Subsequently, the feasibility of employing Equation (2), using the value of X s and the slope (l) of the relationship X s -EC i to estimate the EC sw value of the green roof substrate utilized in the study was examined. This investigation was carried out for each value of EC i , for both substrate depths. The calculated average EC sw value was then compared to the measured average EC L value for each level of EC i . Considering the shallow substrate depths, substrate characteristics, high EC i values, and the uniform development of the root system, it is reasonable to argue that the actual salinity of the substrate closely resembles the salinity of the leachate. These factors contribute to a more homogenous distribution of salinity within the substrate, minimizing potential variations and ensuring that the leachate represents the substrate's salinity levels.
In conclusion, a modification of the Malicki and Walzczak [21] model for green roof substrates is presented. This modification is based on the proposed empirical relationship linking l with the organic portion (%, v/v) of the green roof substrate, as well as the new version of the salinity index (Xs) for green roof substrates. To assess the accuracy of the modified Malicki and Walczak model in predicting EC sw for green roof substrates, the root-mean-square error (RMSE) was utilized. By comparing the predicted EC sw values with the measured EC L values, the effectiveness of the model was evaluated.

Results and Discussion
The electrical conductivity of the leachate collected in tanks beneath the lysimeters started to increase immediately after the initiation of high-salinity irrigation treatments ( Figure 2). When irrigation was applied with the 3 dS m −1 solution, the equalization of EC L with that of the EC i was recorded 10 days after initiation (DAI) of the study for the 7.5 cm substrate depth and 16 DAI for the 15 cm substrate depth. Accordingly, when irrigation was applied to 6 dS m −1 and 12 dS m −1 solutions, the equalization of EC L with EC i occurred on 16 and 20 DAI for 7.5 cm and 15 cm substrate depth, respectively, since an irrigation solution of 3 dS m −1 was used for all salinity treatments during the study's first three irrigation events to prevent the salinity shock of the turfgrass. During August, successive irrigation events gradually increased EC L , reaching values of 13-14 dS m −1 for EC i = 3 dS m −1 , 20-21 dS m −1 for EC i = 6 dS m −1 , and 31-32 dS m −1 for EC i = 12 dS m −1 . In contrast, the EC L values of the experimental plots irrigated exclusively with potable water remained relatively constant throughout the study at relatively low levels (<1.5 dS m −1 ), above the potable water's EC value (0.3 dS m −1 ). This sharp increase in EC L is attributed to the very low LF which favored the continuous accumulation of salts at the substrate and the drainage layers of the simulated green roofs in the lysimeters. More specifically, from the beginning of the study until the end of August, the LF had an average value for all irrigation treatments less than 0.1 (≈0.09), which even prevented EC L determination during several sampling periods (18-22 August and 28 August-1 September). The reduction in temperatures throughout September and the presence of light rains (Figure 1) favored an increase in LF, with a mean value of 0.55, resulting in an EC L gradual decrease. The increase in LF continued during October with a mean value of 0.75, promoting further EC L reduction, which by the end of the study (23 October 2014), reached values of approximately 5 dS m −1 for EC i = 3 dS m −1 , 8.5 dS m −1 for EC i = 6 dS m −1 , and 16.5 dS m −1 for EC i = 12 dS m −1 , for both substrate depths. It is apparent that whenever green roof irrigation is applied using high-salinity water, leaching requirements are expected to be high enough for EC L to remain close to the EC i [8].
An important observation from the study was that the green coverage of the P. vaginatum turfgrass consistently remained high, exceeding 90% across all treatments. This finding demonstrates the remarkable resilience of seashore paspalum to elevated salinity levels [32,33] and highlights the potential for irrigating P. vaginatum turfgrass in extensive green roofs with water with an EC of up to 12 dS m −1 for extended periods without a significant deterioration in visual quality. According to Figure 3, the relationship between σb and εb is strongly linear for al levels of ECi for both substrate depths of 7.5 cm and 15 cm, and the correlation coefficient R 2 decreases with increasing ECi. For the substrate depth of 7.5 cm the values of R 2 are equal to 0.84, 0.90, 0.77, and 0.57 for irrigation with potable water and solutions with EC of 3 dS m -1 , 6 dS m -1 , and 12 dS m -1 , respectively, while for the depth of 15 cm, they are equal to 0.74, 0.87, 0.80, and 0.70, respectively. The large decrease in the R 2 value for ECi = 12 dS m -1 , when the substrate depth was 7.5 cm, is probably because several values of σb were greater than 3 dS m -1 . According to Kargas et al. [34], the values of εb from the WET-2 sensor for soils are reliable up to about the value σb = 3 dS m -1 since for higher values of σb, there is a decrease in the value of εb. As can be observed from the results of this present study, for a reliable estimate of εb in the case of green roof substrates, it is better to limit σb up to about values of 2-2.5 dS m -1 . Additionally, from Figure 3, the point of intersection of the relations σb-εb is quite different from that of inorganic soils, so the proposed Equation (3) of Malicki and Walczak [21] for Xs value calculation cannot be used in the case of green roof substrates. Roughly, it can be seen that the intersection point has values of εb = 12 and σb = 0.125 dS m -1 , which are very different from the intersection points of inorganic soils, εb =6.2 and σb = 0.08 dS m -1 .
Observing the slopes of the σb-εb relationships, which are equal to the value of the salinity index (Xs), for both substrate depths, they increase with the increase in the EC An important observation from the study was that the green coverage of the P. vaginatum turfgrass consistently remained high, exceeding 90% across all treatments. This finding demonstrates the remarkable resilience of seashore paspalum to elevated salinity levels [32,33] and highlights the potential for irrigating P. vaginatum turfgrass in extensive green roofs with water with an EC of up to 12 dS m −1 for extended periods without a significant deterioration in visual quality. According to Figure 3, the relationship between σ b and ε b is strongly linear for all levels of EC i for both substrate depths of 7.5 cm and 15 cm, and the correlation coefficient R 2 decreases with increasing EC i . For the substrate depth of 7.5 cm the values of R 2 are equal to 0.84, 0.90, 0.77, and 0.57 for irrigation with potable water and solutions with EC i of 3 dS m −1 , 6 dS m −1 , and 12 dS m −1 , respectively, while for the depth of 15 cm, they are equal to 0.74, 0.87, 0.80, and 0.70, respectively. The large decrease in the R 2 value for EC i = 12 dS m −1 , when the substrate depth was 7.5 cm, is probably because several values of σ b were greater than 3 dS m −1 . According to Kargas et al. [34], the values of ε b from the WET-2 sensor for soils are reliable up to about the value σ b = 3 dS m −1 since for higher values of σ b , there is a decrease in the value of ε b . As can be observed from the results of this present study, for a reliable estimate of ε b in the case of green roof substrates, it is better to limit σ b up to about values of 2-2.5 dS m −1 . Additionally, from Figure 3 values and are therefore proportional to the salinity regime established in the substrate. More specifically, the values of Xs vary from 0.0593 to 0.0109 for the depth of 7.5 cm and from 0.0544 to 0.0109 for the depth of 15 cm, depending on the value of ECi (Figure 3). Moreover, the value of the constant term of the linear relationships decreases with increasing ECi value. Thus, for ECi = 0.3 dS m -1 , the constant term has a value of -0.0570, while for ECi = 12 dS m -1 , it has a value of -0.2749 for the depth of 7.5 cm, whereas, for the depth of 15 cm for ECi = 0.3 dS m -1 , the constant term has a value of -0.0409, while for ECi = 12 dS m -1 , it has a value of -0.4425. Figure 3. Relationship between bulk electrical conductivity (σb, dS m -1 ) and substrate dielectric permittivity (εb) as determined using the WET-2 dielectric sensor during the study period for the substrate depths of 7.5 cm and 15 cm when irrigation was applied with water of electrical conductivity 0.3 dS m -1 (potable water), 3 dS m -1 , 6 dS m -1 , and 12 dS m -1 .
In Figure 4, the relationship between Xs and ECi for the two substrate depths of 7.5 cm and 15 cm is presented. These relationships are strongly linear with R 2 = 0.90 and a slope of 0.0040 for a depth of 7.5 cm and R 2 = 0.95 and a slope of 0.0035 for a depth of 15 cm. The slope value for the green roof substrate used in the study at both depths is completely different (lower) from those presented by Malicki and Walczak [21] for various soil types. For sandy soil, they reported values of 0.0136 and 0.0126; for loamy sand soil, Figure 3. Relationship between bulk electrical conductivity (σ b , dS m −1 ) and substrate dielectric permittivity (ε b ) as determined using the WET-2 dielectric sensor during the study period for the substrate depths of 7.5 cm and 15 cm when irrigation was applied with water of electrical conductivity 0.3 dS m −1 (potable water), 3 dS m −1 , 6 dS m −1 , and 12 dS m −1 .
Observing the slopes of the σ b -ε b relationships, which are equal to the value of the salinity index (X s ), for both substrate depths, they increase with the increase in the EC i values and are therefore proportional to the salinity regime established in the substrate. More specifically, the values of X s vary from 0.0593 to 0.0109 for the depth of 7.5 cm and from 0.0544 to 0.0109 for the depth of 15 cm, depending on the value of EC i (Figure 3). Moreover, the value of the constant term of the linear relationships decreases with increasing EC i value. Thus, for EC i = 0.3 dS m −1 , the constant term has a value of −0.0570, while for EC i = 12 dS m −1 , it has a value of −0.2749 for the depth of 7.5 cm, whereas, for the depth of 15 cm for EC i = 0.3 dS m −1 , the constant term has a value of −0.0409, while for EC i = 12 dS m −1 , it has a value of −0.4425.
In Figure 4, the relationship between X s and EC i for the two substrate depths of 7.5 cm and 15 cm is presented. These relationships are strongly linear with R 2 = 0.90 and a slope of 0.0040 for a depth of 7.5 cm and R 2 = 0.95 and a slope of 0.0035 for a depth of 15 cm. The slope value for the green roof substrate used in the study at both depths is completely different (lower) from those presented by Malicki and Walczak [21] for various soil types. For sandy soil, they reported values of 0.0136 and 0.0126; for loamy sand soil, a value of 0.011; for silty loam soil, a value of 0.0098; and for silt, a value of 0.0081. Therefore, the X s -EC i relationship, like the point of intersection of the σ b -ε b lines, depends on the special characteristics of the porous medium. Due to the aforementioned information, Equation (4) proposed above for calculating the EC sw cannot be used in the case of green roof substrates because they have completely different characteristics. As a first approach, Equation (2) could be used to estimate the EC sw value, which will be built up in the substrate for each value of EC i .
Sensors 2023, 23, 5802 9 of 13 a value of 0.011; for silty loam soil, a value of 0.0098; and for silt, a value of 0.0081. Therefore, the Xs-ECi relationship, like the point of intersection of the σb-εb lines, depends on the special characteristics of the porous medium. Due to the aforementioned information, Equation (4) proposed above for calculating the ECsw cannot be used in the case of green roof substrates because they have completely different characteristics. As a first approach, Equation (2) could be used to estimate the ECsw value, which will be built up in the substrate for each value of ECi. For the substrate depth of 7.5 cm, the estimated mean ECsw, using Equation (2) for the corresponding salinity indices, is 2.73 dS m -1 for irrigation with potable water, 7.80 dS m -1 for ECi = 3 dS m -1 , 12.08 dS m -1 for ECi = 6 dS m -1 , and 14.83 dS m -1 for ECi = 12 dS m -1 , while for the 15 cm substrate depth, the estimated mean ECsw is 3.11 dS m -1 for irrigation with potable water, 8.57 dS m -1 for ECi = 3 dS m -1 , 9.83 dS m -1 for ECi = 6 dS m -1 , and 15.54 dS m -1 for ECi = 12 dS m -1 ( Table 2). For both substrate depths, from the measurement of mean ECL for the study period, it can be claimed that the salinity index model accurately predicts the ECsw for irrigation with an ECi of 3 dS m -1 and 6 dS m -1 , while it significantly overestimates for small values of the salinity index such as 0.0109, which corresponds to potable water (ECi = 0.3 dS m -1 ) ( Table 2). For those cases where irrigation is applied with low ECi values, ECsw can be predicted with the Hilhorst [22] model (Equation (5)), which is installed into the HH2 meter, to which the WET-2 sensor is connected. The mean value of ECsw for the study period for irrigation with potable water as measured with the WET-2 sensor and using the Hilhorst model is 0.67 dS m -1 for the 7.5 cm substrate depth and 0.85 dS m -1 for the 15 cm substrate depth, which is close to the measured mean values of  Table 2). For both substrate depths, from the measurement of mean EC L for the study period, it can be claimed that the salinity index model accurately predicts the EC sw for irrigation with an EC i of 3 dS m −1 and 6 dS m −1 , while it significantly overestimates for small values of the salinity index such as 0.0109, which corresponds to potable water (EC i = 0.3 dS m −1 ) ( Table 2). For those cases where irrigation is applied with low EC i values, EC sw can be predicted with the Hilhorst [22] model (Equation (5)), which is installed into the HH2 meter, to which the WET-2 sensor is connected. The mean value of EC sw for the study period for irrigation with potable water as measured with the WET-2 sensor and using the Hilhorst model is 0.67 dS m −1 for the 7.  (Table 2). Similar behavior of the Hilhorst model was also observed by Bañón et al. [28] in measurements with the dielectric soil moisture sensor GS3 on a substrate comprised of 60% sphagnum peat, 30% coconut fiber, and 10% perlite by volume. In particular, the deviations (underestimation) increased when the substrate water content was very low and salinity was high. For irrigation with EC i = 12 dS m −1 , the salinity index model significantly underestimates EC sw for both substrate depths by calculating an EC sw value equal to 14.83 dS m −1 for the 7.5 cm substrate depth and 15.54 dS m −1 for the 15 cm substrate depth, while the measured mean values of the EC L were equal to 19.73 dS m −1 and 18.56 dS m −1 for the substrate depth of 7.5 cm and 15 cm, respectively. This can be attributed to the fact that several values of σ b were greater than 3 dS m −1 when irrigation was applied with EC i = 12 dS m −1 resulting in false ε b values ( Figure 3) [34]. This is also confirmed by the low R 2 values (0.57 for the 7.5 cm substrate depth and 0.70 for the 15 cm substrate depth) of the σ b -ε b relationships, and, as a consequence, the slope of these regression lines, which equals the X s , is unreliable.
To calculate the value of X s using the method mentioned above, it is necessary to obtain a series of measurements on the same substrate with the same solution at different θ. Obviously, this procedure has little practical value in the calculation of EC sw . However, if the point of convergence of the lines is known then it is possible to calculate the value of X s by determining the value of the partial derivative from a suitable difference quotient. Considering that the convergence point has values of ε b = 12 and σ b = 0.145 dS m −1 , the value of X s can be approximated by the equation: However, to make the model more functional in terms of EC sw estimation, the slope l (Equation (2)) must be related to some property of the green roof substrates, e.g., the volumetric portion of pumice or organic substance, as was performed with the classic Malicki and Walczak model [21], where the slope l of soils was correlated with sand content. For this, similar data are needed from other types of substrates in order to draw safe conclusions [29]. From the literature review, it was found that experimental data from different growing substrates are extremely limited. In a study by Incrocci et al. [35], experimental data of a substrate comprising peat and pumice (1:1, v/v) are presented. After an appropriate transformation of the data, it follows that the relationship σ b -ε b is linear at each EC i value, just like the experimental data in the present study, but also that the relationship between X s and EC i is linear with a slope of 0.0123. If the slope l is related to the organic portion (% v/v) of the two substrates, peat/pumice (1:1, v:v) and the substrate evaluated in the present study comprised pumice/thermally treated attapulgite clay/clinoptilolite zeolite/grape marc compost (65: 15:5:15, v:v), then the relationship is: l = 0.0002OM + 0.0012 (7) where OM is the organic portion (% v/v) of the substrate. Of course, it is important to note that while these results are promising, they are only limited to two growing substrates. It is, therefore, necessary to extend this investigation, also considering other growing substrates which are widely used in horticulture and green roofs.
Thus, from the experimental data up to now, in the case of the two substrates, the model of Malicki and Walczak [21] can acquire the particular form: Therefore, from the measurement of σ b and ε b and the organic portion (% v/v) of the substrate, the value of EC sw can be estimated. Based on the estimated EC sw and EC L measurements during the study, the root mean square error (RSME) was calculated equal to 1.10, 1.69, 2.08, and 4.29 for irrigation with potable water and solutions with EC i of 3 dS m −1 , 6 dS m −1 , and 12 dS m −1 , respectively, when the substrate depth was 7.5 cm, while for the depth of 15 cm, they were equal to 0.96, 1.47, 2.39, and 4.62, respectively. These results indicate that Equation (8) provided adequately reliable results when irrigation was applied with water of 3 dS m −1 and 6 dS m −1 EC i . When irrigation is applied with low EC i values such as those of potable water, the Hilhorst [22] model (Equation (5)), which is installed in the HH2 meter and to which the WET-2 sensor is connected, can be used to predict EC sw .

Conclusions
Based on the results of the study, it was found that the relationship σ b -ε b for an extensive green roof substrate is linear for each level of EC i , and the slope of the linear relationship increases with the increase in EC i . The linearity is maintained up to a level of σ b values, which depends on the characteristics of the dielectric sensor.
However, the empirical relationship presented by Malicki and Walczak [21] for inorganic soils cannot be used to predict EC sw of extensive green roofs because the relationships for calculating the salinity index and the slope l in the green roof substrates differ significantly. Applying the Malicki and Walczak [21] model to the general form showed that the model generally accurately predicts the EC sw of extensive green roofs for EC sw up to 10-11 dS m −1 while significantly overestimating at very low salinity index values.
With the appropriate modification of the Malicki and Walczak model for the case of green roof substrates, to predict EC sw , the determination of the WET-based salinity index (X s ) and organic portion (% v/v) of the substrate is required. The modified Malicki and Walczak model is more effective than the Hilhorst model in all cases except for the cases when the EC sw is lower than 2 dS m −1 .