2.2. Soil quality assessment
The method used to determine soil quality index following by four steps: (i) setting the goal, (ii) picking minimum data set (MDS) of indicators which depict the best soil function, (iii) scoring the MDS indicators, and (iv) the integration of an indicator score into a relative soil quality index (Masto et al., 2007). Cane productivity was considered as the goal due to variations in different cane producing zones. A total of 25 soil attributes were analyzed using principal component analysis (PCA) for selecting as representative MDS (Andrews et al., 2002). PCs that had high eigenvalues and variables with greater factor loading were pondered as the best delineated attributes. Hence, PCs with eigenvalues >1 and those illustrated at least 5% variations in the data were examined (Bregda et al., 2000). The factor loading of each variable in a particular PC represents the contribution of that variant to the composition of the PC. Highly weighted variable were categories as per the absolute values existed within 10% of the highest factor loading. Correlation coefficient was employed among the indicators for selecting ideal indicator if any variable was redundant as more than one variable was retained within a single PC and hence, eliminated from the minimum data set (MDS). In terms of soil function, the indicators were put in order depending on whether a higher value was considered as ‘good’ or ‘bad’. Indicators like Na, Pa, Ka, Sa, Fe, Zn, ALP and BSR in the MDS were considered “good” and were scored as ‘more is better’. However, Fe content was pondered “good” as existed in the optimum range, hence scored as ‘optimum is better’. A value between 0 and 1 is used as a standard scoring function for transmission and normalized of each indicator (Fig. S1) which were calculated by using non-linear scoring function (NLSF): NLSF (Y) = 1/ [1+ e-b(x-A)].
where, ‘x’ is value of soil attributes, ‘A’ the baseline or value of soil property where score equal to 0.5 and ‘b’ is slope.
Once indicator transformed based on soil functions, the MDS attributes for each observation were weighted by applying the PCA outcome. Each PC incites a certain amount (%) of the variation in the total data set. This percentage divided by the total percentage of variance explained by all PCs with eigenvectors >1, given the weighted factor for variants selected under a given PC. Then the weighted MDS variables scores were summed up for each observation using the following equation as suggested by Li et al. (2013): SQI =\(\sum_{i=1}^{n}{\text{Wi}\times\text{Si}}\)
Where, ‘Wi’ is denoting weighing value of each indicators; ‘Si’ is the indicator score; ‘n’ is the number of indicators in the MDS.
The SQ indexing methods were also measured by employing sensitivity analysis as suggested by Masto et al. (2008): Sensitivity (𝑆) = SQI(max)/SQI(min), where SQI(max) and SQI(min) are the maximum and minimum SQI observed under each cane producing zones of Uttar Pradesh. The higher value of sensitivity is more preferable and sensitive to perturbations and management practices.