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 =
β0+β1xi+εi(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-