#### 3.3.1. ECp Laboratory Calibration

Table 3 presents the RMSE for the different models. All models showed good performance in the 0–3 dS m

^{−1} range, except Hilhorst with (K

_{0} = 6) and MHK with K

_{0} = 4.1. Moreover, RMSE results (

Table 3), showed an increase of the range of default H model validity until ECp = 6.8 dS m

^{−1}. This finding can be linked to the higher operating frequency of 5TE (70 MHz) compared to the capacitance sensor used by Hilhorst (30 Mhz). Hilhorst reported that the model assumption ceases to be accurate at higher salinity as ECp significantly deviates from that of free water.

From the results presented in

Table 3, the ECp limit for accurate measurements seems to be 6.8 dS m

^{−1}. Similar results were reported by Scudiero et al. [

40], using the 5TE sensor and ECp limit <10 dS m

^{−1} with RMSE equal to 0.68 dS m

^{−1}. Using the H model with K

_{0} value recommended in the Decagons manual (K

_{0} = 6) showed a larger RMSE for all salinity levels compared the default parameter (K

_{0} = 4.1). The H model with K

_{0} = 3.3 (determined experimentally according to the WET manual) gave better results for the three salinity ranges. Persson [

13] stated that the H model using a fitted soil parameter gives ECp values statistically similar to other model results (e.g., [

3,

10,

46]).

Focusing on the modified Hilhorst model using the MHK approach with K

_{0} = 4.1, one can observe that the RMSE is at maximum, especially for ECp ≥ 6.8 dS m

^{−1}. Kargas el al. [

6] validated this approach using a lower salinity level (ECp ≤ 6 dS m

^{−1}). According to our results (Figure 7), an overestimation of the H model, especially at ECp ≥ 3 dS m

^{−1}, is observed. Similarly, Visconti et al. [

19] showed an overestimation of ECp in the range of 0–10 dS m

^{−1} and Scudiero et al. [

40] showed an overestimation of ECp in the range 3–10 dS m

^{−1}, both working with the 5TE sensor and the H model. In the present study, the H model overestimated ECp, thus using the MHK approach will not improve results.

The observed overestimation by the H model might be due to K

_{0}, which was assumed to be equal to 4.1. In addition, one should note that the H model does not consider solid particle surface conductivity, which could contribute to the ECp error [

17]. From

Table 3, decreasing K

_{0} from 4.1 to 3.3 for both the H and MHK model leads to a significant decrease of RMSE, two times lower than the default. The H model seems to be more dependent on the soil parameter K

_{0} than on Ka and ECa.

K

_{0} estimated from the best fit approach for the different salinity levels is plotted against ECa in

Figure 6. The K

_{0} range varied between 1.29 and 3.2 with a mean of 3.0, which is similar to the K

_{0} determined experimentally using distilled water (K

_{0} = 3.3).

At saturation, ECa was equal to 0.32 dS m

^{−1} and 2.4 dS m

^{−1} and Ka was equal to 15 and 19 for the lowest (2 dS m

^{−1}) and the highest (10.5 dS m

^{−1}) observed ECp, respectively. According to

Figure 6, K

_{0} decreases with increasing salinity. Similar to [

18], our results showed that K

_{0} is not constant, but depends on ECa and that a third-order polynomial fitted the K

_{0}–ECa relationship rather well (R

^{2} ≥ 0.95). K

_{0} = f (ECa) in

Figure 6, was used in the H model to predict ECp. Compared to the H model, for the individual ECp levels, using the MHB model, RMSE decreased significantly.

Figure 7 shows observed and predicted ECp using the H model with three different K

_{0} and the MHK and MHB approaches, respectively. All model performances, are approximately the same for ECp ≤ 3 dS m

^{−1}, except when using K

_{0} = 6 and K

_{0} = 4.1 for H and MHK models, respectively.

Based on the laboratory results, the MHB approach improved the H model and gave accurate estimation of ECp with R^{2} = 0.99 for all salinity levels. Thus, for high soil salinity (6.8 dS m^{−1} ≤ ECp ≤ 10.5 dS m^{−1}), the MHB approach is recommended for achieving optimal accuracy of ECp measurements. For lower ECp (≤3 dS m^{−1}), the standard H model is sufficient. For high ECp, the MHK approach failed to reproduce the observed ECp correctly and the approach is not recommended based on the results of our study. Further studies for different soil types are needed so that this combined approach in predicting ECp can be validated.

#### 3.3.2. Field Validation of ECp Models

Unfortunately, we do not have field observed ECp to validate and statistically compare the different models. Instead, we determined a linear relationship (ECp = f (ECe)) for different calculated ECp, using the H, MHK, and MHB models and 5TE measurements, with observed field ECe. Several researchers have studied relationships between ECe and ECp, e.g., [

3], showing that the relationship is strongly linear. The relationship (ECp = f (ECe)) with the highest R

^{2} = 0.9 was chosen to predict the field ECp values (ECp

_{obs}). During the investigation period, ECe was determined from soil samples, according to the USDA standard (collected at the same depth as the location of the 5TE sensors), ranging between 1.7 and 4.1 dS m

^{−1}. The relatively low soil salinity is due to a rainfall observed in the field one day before soil sampling.

The observed ECp

_{obs} obtained from the best fit relationship is plotted against the estimated ECp for the different models in

Figure 8. The H model with K

_{0} = 6.6 was not included in the figure since it gave out of range values. The ECp estimation with MHB approach appears uniformly scattered about the 1:1 line. On the other hand, the H model with K

_{0} = 3.3 shows a cloud of points near the 1:1 line.

Compared to laboratory results, for the same ECa range (ECa ≤ 0.7 dS m

^{−1}) (

Table 4), observed errors are higher for the field validation. The RMSE increased for all models. Errors are mainly related to a number of factors absent in the laboratory but present under field conditions. Due to this reason, a methodological approach composed by laboratory calibration and field validation is optimal.

The MHB approach presents a significant improvement of the H model, especially at high ECp (

Table 4). The H and MHK model fit is acceptable for field and laboratory conditions only for ECp ≤ 3dS m

^{−1} while the MHB approach is acceptable for field conditions and it can be safely used for sandy soil and ECp ≤ 7 dS m

^{−1}.

Since variation and uncertainties in the field are higher, it is recommended to validate the calibrated models with field data. According to our results, the H model with K_{0} = 6 is not recommended either with laboratory nor field data. However, the reduction of K_{0} to 3.3 increased the performance of the model and it can be safely used for ECp < 3 dS m^{−1}. For ECp > 3 dS m^{−1}, the MHK approach did not improve the H model with RMSE more than 1 dS m^{−1} and it is not recommended. Thus, for achieving optimal accuracy of ECp measurements, the MHB approach is recommended for ECp ≤ 7dS m^{−1}.