# Sustainable Management of Water Resources in Supplementary Irrigation Management
## 2 Materials and Methods
### Measuring Soil Water Content
In total, SWC was measured 110 times on four soil depths as follows: 10, 20, 30 and 45 cm (Figure 4b). At the same time, 88 disturbed soil samples were taken from the experimental site (22 measurements and four soil depths) for field testing (Figure 3b, x marks represent the location of soil sampling, T represents Tensiometer and W represents Watermark). Edelman auger was driven into the soil to collect soil samples for the same soil depths and location where sensors were placed or where the sensor readings were taken. After taking the soil samples, the sampling holes were immediately refilled with soil from the same location so that the mass flow of soil water would be reduced. The direct method for measuring SWC was done by a thermogravimetric method that refers to the difference in weight before and after drying of the soil sample. Moreover, the thermogravimetric method is a reference method for SWC measurement [28]. After the weighing, the soil samples were dried at 105 \({}^{\circ}\)C for 24 h and weighed again [29]. Gravimetric soil water content was determined as  
\[\theta\mathrm{gwc}=\frac{(\mathrm{Ww}-\mathrm{Wd})}{\mathrm{Wd}}\ \times 100 \tag{1}\]  
where \(\theta\mathrm{gwc}\) is gravimetric water content, \(\mathrm{Ww}\) is the weight of the wet soil and \(\mathrm{Wd}\) is the weight of the dry soil. The gravimetric method expresses gravimetric water content [30], while the Volumetric Water Content (VWC, %) is the volume of water held within a volume of oven-dried undisturbed sample (soil core). VWC was determined as [31]  
\[\theta\mathrm{v}=\theta\mathrm{\rho b} \tag{2}\]  
where \(\theta\mathrm{v}\) is VWC, \(\theta\) is Gravimetric Moisture (GM) and \(\mathrm{\rho b}\) is soil bulk density (g cm\({}^{-3}\)). Factorial analysis of variance (ANOVA) was done to assess the impact of soil layer (depths) on \(\theta\mathrm{v}\). Furthermore, a comparison of the gravimetric method and sensor readings was made by using correlation and regression analysis in STATISTICA 13 (StatSoft, Inc., Tulsa, OK, USA). The following statistical methods were used to examine the differences between the sensor measurements and \(\theta\mathrm{v}\). The degree of similarity between the sensor  
Figure 4: The position of tested sensors regarding the monitoring depth (**a**) and location in the experimental plot (**b**). readings and GM measurements was done by using a coefficient of determination (R\({}^{2}\)) and correlation (r). Root Mean Square Error (RMSE) used for validation of calibration equation and was calculated as the difference between the sensor readings and gravimetric moisture (0v), proposed by [PERSON] [32]:  
\[\text{RMSE}=\left[n^{-1}\sum_{i=1}^{n}(\text{Si}-\text{Oi})^{2}\right] \tag{3}\]  
where Si is the estimated and Oi is the observed value. Mean Absolute Error (MAE) was calculated according to Addicott and Whitmore [33] and was used to quantify the deviation of the estimated 0v means from the observed 0v:  
\[\text{MAE}=\frac{1}{N}\sum_{i=1}^{N}(\text{Si}-\text{Oi}) \tag{4}\]  
where \(N\) is the number of observations and Si and Oi are estimated and observed values, respectively. Mean Difference (MD) was used to describe the average difference between the sensor readings and corresponding VWC measurements [34]:  
\[\text{MD}=\frac{\sum_{i=1}^{n}(\text{Msi}-\text{Mgi})}{n} \tag{5}\]  
where Msi is the sensor reading, Mgi is 0v measurement and \(n\) is the number of samples.