PCA based index to measure the soil fertility status of panchayats in Pathanamthitta district, Kerala

Introduction

Agricultural production is one of the major factors on which life on earth is relied upon. It possesses a direct relationship with soil productivity, which is the capacity of a soil to produce crop per unit area. This productivity is in turn influenced by soil fertility, it is nothing but the ability of soil to provide adequate soil nutrients (Kanwar,1976) [7] . Hence in order to manage the agricultural production, an idea regarding the soil fertility is mandatory. In order to probe soil fertility, knowledge about the available soil nutrient content is required. An idea of fertility status of different regions will give a way to have a comparison among the regions and will help in classifying the regions according to fertility status (Khokhar, 2008) [10] . It also helps to identify the difference between actual productivity and potential productivity of each region. This can be made use in adopting necessary steps to improve the regional production. But the assessment of fertility based on single nutrients alone is not exactitude (Kavitha and Sujatha, 2015) [8] . Hence an attempt was made in this paper to assess the soil fertility status of 50 panchayats in Pathanamthitta district in Kerala state using 12 soil parameters namely, pH, EC, OC, P, K, Ca, Mg, S, B, Cu, Fe and Mn by constructing a single value fertility status index corresponding to each panchayats. Study on soil fertility status of RARS, Tarahara, Nepal by Khadka et al. (2017) [9] necessitates the adoption of proper nutrient management during crop cultivation where the nutrient index was constructed using various soil parameters like pH, organic matter, N, P2O5, K2O, Ca, Mg, S, B, Fe, Zn, Cu and Mn.

Materials and Methods

The present study is based on secondary data on soil pH, EC, macro and micronutrients of 50 panchayats in Pathanamthitta district. Initially Box plot for the soil nutrient parameters were constructed to detect and remove the outliers in the observations. The descriptive statistics including mean and coefficient of variation calculated to get an idea about the variability of the parameters. In order to identify areas having low to high soil fertility, the study has tried to estimate a soil fertility status index using available nutrient parameters of the soil by PCA. Secondary data on available soil parameters of Pathanamthitta district of Kerala were obtained from Kerala State Planning Board Project conducted in 2013 [12] . PCA is a multivariate technique mainly used for dimensionality reduction of large data set to a small number of linear combinations. PCA will convert large number of dependent variables into new set of variables called as principal components, which are the linear combination of the original variables and are orthogonal to each other (Abdi and Williams, 2010) [1] . The first principal component is the one which account for more amount of variation in the data and second one will be orthogonal to the first principal component and will explain the next highest variation which is not explained by the first one so on. Principal components are selected in the dimension where the variance can be maximized. It can be obtained by rotating the axes. Let Z i = a i T y i , A= (a 1, a 2,… , a p ) T , A is an orthogonal matrix. Here y i changed to Z i , having same distance from origin but the axis have rotated (Rencher, 1934) [13] . Likewise, the suitable dimensions can be identified. The new points Z 1, Z 2, …. Z p thus obtained represent the principal components such that S T = ASA T is the dispersion matrix of Z S = Dispersion matrix of y i a i is chosen such that a i T a i = 1. The diagonal elements of dispersion matrix represent the eigen values. i.e., tr(S) = (Chatfield and Collins, 1980) [5] This eigen value corresponds to each principal component represents the variance explained by that principal components. So the proportion of variance explained by i th principal component, In order to construct the index only those principal components having eigen value more than one will be used. From the extracted PCs, principal component scores are obtained by multiplying the data matrix with the coefficient matrix of extracted PCs. Weighted aggregation of these principal component scores produce the index. SFI Soil Fertility Index of i th panchayath is estimated as:

Which is the weight of j th principal component. V j = Coefficient matrix of extracted principal components. X i = Mean vector of soil fertility parameters of i th panchayat Index thus constructed will be normalized by min-max normalization given by the equation

Results and Discussion

Descriptive statistics

Mean value and CV of 12 soil parameters corresponds to each panchayat were obtained from sample data. pH showed highest consistency with a CV of 8.92 per cent. EC ranges from 0.06 dS m -1 to 2.75 dS m -1 with a CV of 159.30 per cent. CV of OC was 27.70 per cent with a mean value of 1.65 per cent. CV of 61.85 per cent was noticed in P with a mean value of 66.62 kg ha -1 . Availability of K varied between 148.32 to 475.67 kg ha -1 with a CV of 28.80 per cent. Lowest amount of observed Ca content was 82.10 mg kg -1 and highest was 1000 mg kg -1 with a CV of 48.60 per cent. CV of Mg was 94.30 per cent. Mean value of S was 20.60 mg kg -1 showing a CV of 36.89 per cent. B was found to be deficient in most of the panchayats with a CV of 102.39 per cent. CV of Cu was 35.86 per cent with a mean value of 2.73 mg kg -1 . Fe also exhibited a similar CV of 41.56 per cent. Mean value corresponds to Mn was 28.80 mg kg -1 with a CV of 63.17 per cent.

Principal component analysis

Principal component analysis was performed as the basic method to identify the variation in soil fertility status of 50 panchayats in Pathanamthitta district. An index corresponds to each panchayat, which was constructed by the method of PCA is supposed to represent its fertility status. The results of PCA on mean vector of 50 panchayats in Pathanamthitta are presented in Table 1. The first four principal components having eigenvalue more than one and accounted for more than 68 per cent variation in the data were retained for the construction the index. the data. In PC 1 highest coefficient was for Fe (0.85) followed by pH (0.80). While considering PC 2, Ca possessed highest coefficient value of 0.79 and S had a coefficient loading of 0.12 on PC 2. S was reported to have high loading on PC 3 and PC 4.

The four PCs which were extracted based on KMO criteria were retained for index construction. Based on the first and second principal components, score plot was obtained to identify the soil fertility similarities among the panchayats (Fig. 1).

Construction of index

After extracting the PCs, the PC scores were obtained by multiplying the mean vector of 50 panchayats with the eigenvector matrix (Coefficient matrix) of extracted four PCs. Thus four PC scores were obtained and each of these scores can be considered as an indication of soil fertility status. But a more reliable index of soil fertility can be obtained as the weighted aggregation of the PC scores. Weight correspond to each PC score was calculated as the proportion of variance explained by each PC to the cumulative variance of all the four PCs. Thus the weight of four PC scores were estimated as 0.425, 0.286, 0.157 and 0.132 respectively. The Soil Fertility Index was calculated as the weighted aggregation of PC scores followed by min-max normalization. The estimated SFI and normalized index are given in Table 2. Based on the score plot, the panchayats which comes closer in the same quadrant can be grouped under same soil fertility category. The panchayats which are at long distance from origin can be considered as the predominantly different ones. The inference obtained from score plot is on par with the classification of panchayats (Table 3). It is evident from Table 3 that

Conclusion

This study implies the relatively good soil fertility of the district under study. With regard to the soil fertility index, Aruvappulam panchayat in Pathanamthitta district shows higher soil fertility and Thottapuzhaserry panchayat is poor in all among them. Physiographically, the district is divided into coastal plain, mid land region and hill ranges with major area come under hill ranges and is thickly forested. Major soil type in Pathanamthitta is forest loam which is formed as a result of weathering of country rock under forest cover (KSPB, 2013) [12] . This forest soils are rich in organic matter content with good water retention capacity. This influence positively to the availability various plant nutrients in the soil. This may be the reason for observed good soil fertility of Pathanamthitta district. Along with this adequate fertility management practices have to be adopted to maintain the district agriculturally productive. PCA as a multivariate technique is very useful in reducing the dimension of large data set and also in construction of index in order to measure the latent variables.

Acknowledgement

AcknowledgementAuthors are thankful to the University faculties for providing data.

References

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