3.7 Model Development
Ordinary Least Squares (OLS) regression was used for modelling and estimation of soil salinity. The parameters chosen were soil moisture, soil temperature and root zone electrical conductivity from field and RADAR backscatter for VH and VV polarisations, NDSI from optical Sentinel -2 data.
The OLS model is robust for estimation of parameters that are unknown in a linear regression model. The OLS is a type of multiple linear regression model and is expressed as(Ferreyra, Curci, & Lanfri, 2016)-
Yn =\(\sum_{i=0}^{k}\beta\)ixni + εn (6)
And Yi = β01xii(7)
Where, Yi is the dependent variable whereas, β0 is intercept of y and β1 is coefficient of slope and εi is term denoting random error(Reynolds et al., 2018).
It was aimed to ascertain the dependency of various parameters since an OLS model performs better with more than one predictor, on the soil salinity in root zone that affects the crop growth. The model did not use RADAR brightness term and volume Scatterers since they had high dependence on each other and Had nearly equal values. Using them would lead to overfitting the model giving exceptionally high values of R2-statistics in training phase. Thirty -two different locations in various agricultural zones of Rupnagar district were chosen to collect field data for the three dates as mentioned earlier. The RADAR backscatter values for the same locations were used in the model. The model is as follows-
Soil_Salinity =\(\text{\ β}0\ +\beta 1\ \times\ \sigma\text{VH\ }+\ \beta 2\ \times\ \sigma\text{VV\ }+\ \beta 3\ \times\ Soil\ Moisture\ +\ \beta 4\ \times\ NDSI+\ \beta 5\ \times\ EC\text{ROOT\ ZONE}\ +\ \beta 6\times Temperature\ in\ F\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8)\text{\ \ \ \ \ }\)
Where, β0, β1…. β5 are all regression coefficients, NDSI is Normalized Differential Soil Salinity Index, EC is electrical conductivity in milli siemens per centimetre and σVH and σVV are backscatter coefficients for VH and VV polarization channels.
Field data collection for soil electrical conductivity and soil moisture was collected from an instrument of field Scout USA which was well calibrated in distilled water (EC=0 mS/cm) and thermal data was collected from thermal imaging camera sensor from Seek Thermal. The field photographs are shown in Figure 6-