Estimation of Wheat Crop Height Using Multivariate Regression and Sentinel-1-Derived Radar Backscatter Response

In this study, we used time-series radar backscatter response in VV and VH polarizations (i.e. σ°
VV
and σ°
VH
) and ground-based wheat height data to establish the multivariate regression models for wheat height estimate. For generating time-series σ°
VV
and σ°
VH
, the C-band Sentinel-1 satellite data were used. The ground height observation was obtained from the farm having Durum wheat variety HI 8759 (also known as Pusa Tejas). We experimented with five different multivariate regression models (MVRM) using combinations of independent variables i.e. σ°
VV
, σ°
VH
, σ°
VV
/σ°
VH
ratio, and days after sowing (DAS). Based on the combination of variables, the five models can be depicted as MVRM1 (σ°
VV
, σ°
VH
, and DAS), MVRM2 (σ°
VH
and DAS), MVRM3 (σ°
VV
and DAS), MVRM4 (σ°
VV
and σ°
VH
) and MVRM5 (σ°
VV
/σ°
VH
ratio and DAS). Based on statistical observation, it is found that although the model R
²
for MVRM1 and MVRM2 was about 0.90, the condition number is very high in both cases, which causes multicollinearity. This leads to model overfitting. On the other hand, model R
²
obtained for MVRM3, MVRM4, and MVRM5 are 0.94, 0.65, and 0.93 respectively and all the models are free from multicollinearity as the condition number is low. Another observation shows that DAS is an important variable in the regression model along with the backscatter response. Overall, based on the statistical parameters, MVRM3 and MVRM5 were found suitable for wheat height estimation. This particular model was validated on an independent wheat farm and found encouraging results.