Eurasian Journal of Soil Science

Volume 7, Issue 3, Jul 2018, Pages 238 - 250
DOI: 10.18393/ejss.427189
Stable URL: http://ejss.fess.org/10.18393/ejss.427189
Copyright © 2018 The authors and Federation of Eurasian Soil Science Societies



Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study

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Kalambukattu,J., Kumar,S., Ghotekar,Y., 2018. Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study. Eurasian J Soil Sci 7(3):238 - 250. DOI : 10.18393/ejss.427189
Kalambukattu,J.,Kumar,S.,& Ghotekar,Y. Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study Eurasian Journal of Soil Science, 7(3):238 - 250. DOI : 10.18393/ejss.427189
Kalambukattu,J.,Kumar,S., and ,Ghotekar,Y."Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study" Eurasian Journal of Soil Science, 7.3 (2018):238 - 250. DOI : 10.18393/ejss.427189
Kalambukattu,J.,Kumar,S., and ,Ghotekar,Y. "Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study" Eurasian Journal of Soil Science,7(Jul 2018):238 - 250 DOI : 10.18393/ejss.427189
J,Kalambukattu.S,Kumar.Y,Ghotekar "Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study" Eurasian J. Soil Sci, vol.7, no.3, pp.238 - 250 (Jul 2018), DOI : 10.18393/ejss.427189
Kalambukattu,Justin George ;Kumar,Suresh ;Ghotekar,Yogesh S. Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study. Eurasian Journal of Soil Science, (2018),7.3:238 - 250. DOI : 10.18393/ejss.427189

How to cite

Kalambukattu, J., Kumar, S., Ghotekar, Y., 2018. Spatial variability analysis of soil quality parameters in a watershed of Sub-Himalayan Landscape - A case study. Eurasian J. Soil Sci. 7(3): 238 - 250. DOI : 10.18393/ejss.427189

Author information

Justin George Kalambukattu , Agriculture and Soils Department, Indian Institute of Remote Sensing, ISRO, Dehradun, Uttarakhand, India Uttarakhand, India
Suresh Kumar , Agriculture and Soils Department, Indian Institute of Remote Sensing, ISRO, Dehradun, Uttarakhand, India
Yogesh S. Ghotekar , Agriculture and Soils Department, Indian Institute of Remote Sensing, ISRO, Dehradun, Uttarakhand, India

Publication information

Article first published online : 25 May 2018
Manuscript Accepted : 18 May 2018
Manuscript Received: 29 Jan 2018
DOI: 10.18393/ejss.427189
Stable URL: http://ejss.fesss.org/10.18393/ejss.427189

Abstract

Soil organic carbon (SOC) is a key component in maintaining soil quality. Mapping the local scale variations in the distribution and stratification of SOC and other soil quality parameters across different layers has always been a challenging task, in the current global scenario of changing climates. The study was aimed to investigate the spatial distribution of SOC and other soil quality parameters including SOC stratification ratio and CN ratio in a small hilly watershed (̴ 10 km2) located in the mid Himalayan region of Himachal Pradesh, India. Soil samples were collected in November 2015, from 75 points at two depths (0-15 cm and 15-30cm), along with their geographical coordinates using a Global Positioning System (GPS). The results revealed that SOC concentration (g kg-1) decreased with increasing soil depth, throughout the study area and differed significantly (P

Keywords

Soil quality, Himalaya, IDW interpolation, watershed, soil organic carbon.

Corresponding author

References

Andrews, S.S., Karlen, D.L., Mitchell, J.P., 2002. A comparison of soil quality indexing methods for vegetable production systems in northern California. Agriculture Ecosystems & Environment 90(1): 25–45.

Aparicio, V., Costa, J.L. 2007. Soil quality indicators under continuous cropping systems in the Argentinean pampas. Soil and Tillage Research 96(1-2): 155–165.

Arshad, M.A., Martin, S., 2002. Identifying critical limits for soil quality indicators in agro-ecosystems. Agriculture Ecosystems & Environment 88(2): 153–160.

Bera, T., Collins, H.P., Alva, A.K., Purakayastha, T.J., Patra, A.K., 2016. Biochar and manure effluent effects on soil biochemical properties under corn production. Applied Soil Ecology 107:360–367.

Bernoux, M., Carvalho, M.D.S., Volkoff, B., Cerri, C.C., 2002. Brazil’s soil carbon stocks. Soil Science Society of America Journal 66(3): 888-896.

Bhatti, J.S., Apps, M.J., Jiang, H., 2002. Influence of nutrients, disturbances and site conditions on carbon stocks along a boreal forest transect in central Canada. Plant and Soil 242(1): 1-14.

Bouyoucos, G.J., 1962. Hydrometer method improved for making particle size analysis of soils. Agronomy Journal 54(5): 464-465.

Burrough, P.A., 1989. Fuzzy mathematical methods for soil survey and land evaluation. European Journal of Soil Science 40(3): 477–492.

Chandio, I.A., Matori, A.N., Lawal, D.U., Sabri, S., 2011. GIS based Land suitability Analysis using AHP for public parks planning in Larkana city. Modern Applied Science 5(4): 177-189.

Diack, M., Stott, D., 2001. Development of a soil quality index for the Chalmers Silty Clay Loam from the Midwest USA. Purdue University: USDA-ARS National Soil Erosion Research Laboratory. In: Sustaining the global farm. Selected papers from the 10th International Soil conservation Organization Meeting (ISCO99). Stott, D.E., Mohtar, R.H., Steinhardt, G.C. (Eds.). International Soil Conservation Organization in cooperation with the USDA and Purdue University. West Lafayette, USA. pp. 550-555.

Diacono, M., Montemurro, F., 2010. Long term effects of organic amendments on soil fertility. A review Agronomy for Sustainable Development 30(2): 401-422.

Ditzler, C.A., Tugel, A.J., 2002. Soil quality field tools : Experiences of USDA-NRCS soil quality institute. Agronomy Journal 94(1): 33–38.

Dobermann, A., Oberthur, T., 1997. Fuzzy mapping of soil fertility — a case study on irrigated riceland in the Philippines. Geoderma 77(2-4): 317–339.

Doran, J.W., Parkin, T.B., 1994. Defining and assessing soil quality. In: Defining Soil Quality for a Sustainable Environment. Doran, J.W., Coleman, D.C., Bezdicek, D.F., Stewart, B.A. (Eds.). Soil Science Society of America, Special Publication, Madison, Wisconsin, USA. 35:1-21.

Doran, J.W., Parkin, T.B., 1996. Quantitative indicators of soil quality: a minimum data set. In: Methods for assessing soil quality. Doran, J.W., Jones, A.J. (Eds.). Soil Science Society of America, Special Publication, Madison, Wisconsin, USA. 49: 25–38.

Doran, J.W., Jones, A.J., 1996. Methods for assessing soil quality. Soil Science Society of America, Special Publication Number 49, Madison, Wisconsin, USA. 410p.

Doran, J.W., Coleman, D.C., Bezdicek, D.F., Stewart, B.A., 1994. Soil Science Society of America, Special Publication Number 35, Madison, Wisconsin, USA. 244p.

Fang, X., Xue, Z., Li, B., An, S., 2012. Soil organic carbon distribution in relation to land use and its storage in a small watershed of the Loess Plateau, China. Catena 88(1): 6–13.

Franzluebbers, A.J., 2002. Soil organic matter stratification ratio as an indicator of soil quality. Soil and Tillage Research 66(2): 95-106.

Fu, B., 1991. Theory and practice of land evaluation. China Science and Technology Press, Beijing.

Gong, G., Mattevad, S., O'Bryant, S.E., 2010. Comparison of the accuracy of kriging and IDW interpolations in estimating groundwater arsenic concentrations in Texas. Environmental Research 130: 59–69.

Heal, O.W., Anderson, J.M., Swift, M.J., 1997. Plant litter quality and decomposition: An historical overview. In Driven By Nature: Plant Litter Quality and Decomposition. Cadisch, G., Giller, K.E. (Eds.), CAB International, Wallingford. pp 3-30.

Herrick, J.E., Brown, J.R., Tugel, A.J., Shave, P.L., Havstad, K.M., 2002. Application of soil quality to monitoring and management: paradigms from rangeland ecology. Agronomy Journal 94(1): 3–11.

Jackson, M.L., 1973. Soil Chemical Analysis, Prentice Hall of India Pvt. Ltd., New Delhi.

Jague, E.A., Sommer, M., Saby , N.P.A., Cornelis, J.T., Wesemael, B., Van Oost, K., 2016. High resolution characterization of the soil organic carbon depth profile in a soil landscape affected by erosion. Soil & Tillage Research 156: 185–193.

Karlen, D.L., Ditzler, C.A., Andrews, S.S., 2003. Soil quality: why and how? Geoderma 114(3-4): 145-156.

Karlen, D.L.K., Gardner, J.C., Rosek, M.J., 1998. A soil quality framework for evaluating the impact of CRP. Journal of Production Agriculture 11(1): 56–60.

Karlen, D.L., Mausbach, M.J., Doran, J.W., Cline, R.G., Harris, R.F., Schuman, G.E., 1997. Soil quality: A concept, definition, and framework for evaluation. Soil Science Society of America Journal 61(1): 4-10.

Klingebiel, A.A., Montgomery, P.H., 1961. Land capability classification. U.S.Department of Agriculture, Soil Conservation Service, Agriculture Handbook No. 210, Washington DC, USA. Available at: https://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/nrcs142p2_052290.pdf

Kumar, P., Verma, T.S., 2005. Characterization and classification of some rice growing soils of Palam Valley of Himachal Pradesh. Agropedology 15(2): 80-85.

Larson, W.E., Pierce, F.J., 1994. The dynamics of soil quality as a measure of sustainable management. In: Defining Soil Quality for a Sustainable Environment. Doran, J.W. Coleman, D.C. Bezdicek, D.F., Stewart, B.A. (Eds.). Soil Science Society of America Special Publication, Madison, Wisconsin, USA. 35:37-51.

Li, F.B., Lu, G.D., Zhou, X.Y., Ni, H.X., Xu, C.C., Yue, C., Yang, X.M., Feng J.F., Fang, F.P., 2015. Elevation and land use types have significant impacts on Spatial variability of soil organic matter content in Hani terraced field of Yuanyang county, China. Rice Science 22(1): 27-34.

Lin, G.F., Chen, L.H., 2004. A spatial interpolation method based on radial basis function networks incorporating a semivariogram model. Journal of Hydrology 288(3-4): 288–298.

Liu, S., An, N., Yang, J., Dong, S., Wang, C., Yin, Y., 2015. Prediction of soil organic matter variability associated with different land use types in mountainous landscape in southwestern Yunnan province, China. Catena 133: 137–144.

Mandal, D., Singh, R., Dhyani, S.K., Dhyani, B.L., 2010. Landscape and land use effects on soil resources in a Himalayan watershed. Catena 81(3): 203–208.

McBratney, A.B., Odeh, I.O.A., 1997. Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions. Geoderma 77(2-4): 85–113.

Mishra, A.K., Deep, S., Choudhary, A., 2015. Identification of suitable sites for organic farming using AHP & GIS. The Egyptian Journal of Remote Sensing and Space Science 18(2): 181-193.

Munson, S.A., Carey, A.E., 2004. Organic matter sources and transport in an agriculturally dominated temperate watershed. Applied Geochemistry 19(7): 1111–1121.

Murphy, J., Riley, J.P., 1962. A modified single solution method for the determination of phosphate in natural waters. Analytica Chimica Acta 27: 31-36.

Diodato, N., Ceccarelli, M., 2014. Multivariate indicator kriging approach using a GIS to classify soil degradation for Mediterranean agricultural lands. Ecological Indicators 4(3):177–187.

Parras-Alcántara, L., Lozano-García, B., Galán-Espejo, A., 2015. Soil organic carbon along an altitudinal gradient in the Despeñaperros Natural Park, southern Spain. Solid Earth 6: 125–134.

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Prescott, C.E., Maynard, D.G., Laiho, R., 2000. Humus in northern forests: friend or foe? Forest Ecology and Management 133(1-2): 23–36.

Qi, Y., Darilek, J.L., Huang, B., Zhao, Y., Sun, W., Gu, Z., 2009. Evaluating soil quality indices in an agricultural region of Jiangsu Province, China. Geoderma 149(3-4): 325–334.

Roy, S., Kumar, S., 2014. Developing a framework for soil quality assessment in a watershed of mountainous ecosystem using geo-spatial approach. M.Tech Thesis, IIRS, Dehradun

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Abstract

Soil organic carbon (SOC) is a key component in maintaining soil quality. Mapping the local scale variations in the distribution and stratification of SOC and other soil quality parameters across different layers has always been a challenging task, in the current global scenario of changing climates. The study was aimed to investigate the spatial distribution of SOC and other soil quality parameters including SOC stratification ratio and CN ratio in a small hilly watershed (̴ 10 km2) located in the mid Himalayan region of Himachal Pradesh, India. Soil samples were collected in November 2015, from 75 points at two depths (0-15 cm and 15-30cm), along with their geographical coordinates using a Global Positioning System (GPS). The results revealed that SOC concentration (g kg-1) decreased with increasing soil depth, throughout the study area and differed significantly (P<0.01) between the two depths in vertical soil profile. The SOC stratification ratio values were greater than 1.2 in major portion of watershed indicating a spatial improvement in soil quality. C: N ratio, another important soil quality attribute values were found to be <12:1, indicating high degree of soil quality and increased rate of organic matter mineralization.  The spatial distribution maps of SOC content (g kg-1), SOC stratification ratio as well as CN ratio of study area were generated using Inverse Distance Weighted (IDW) interpolation approach. Additionally soil quality index (SQI) was also computed using various soil quality parameters based on Analytical Hierarchy Process (AHP) and their spatial distribution was analyzed in the watershed. Nearly 76% of the study area had SQI values in the range of 60-75, whereas 22.16% of the area had SQI<60 and 2.59% had SQI>75. The overall results indicated that a higher degree of soil quality existed at the higher elevation regions of the watershed. Majority of the soils in the watershed accounted for only 60% of the maximum possible value of SQI, which necessitates the adoption of better management practices for improving the soil quality.

Keywords: Soil quality, Himalaya, IDW interpolation, watershed, soil organic carbon.

References

Andrews, S.S., Karlen, D.L., Mitchell, J.P., 2002. A comparison of soil quality indexing methods for vegetable production systems in northern California. Agriculture Ecosystems & Environment 90(1): 25–45.

Aparicio, V., Costa, J.L. 2007. Soil quality indicators under continuous cropping systems in the Argentinean pampas. Soil and Tillage Research 96(1-2): 155–165.

Arshad, M.A., Martin, S., 2002. Identifying critical limits for soil quality indicators in agro-ecosystems. Agriculture Ecosystems & Environment 88(2): 153–160.

Bera, T., Collins, H.P., Alva, A.K., Purakayastha, T.J., Patra, A.K., 2016. Biochar and manure effluent effects on soil biochemical properties under corn production. Applied Soil Ecology 107:360–367.

Bernoux, M., Carvalho, M.D.S., Volkoff, B., Cerri, C.C., 2002. Brazil’s soil carbon stocks. Soil Science Society of America Journal 66(3): 888-896.

Bhatti, J.S., Apps, M.J., Jiang, H., 2002. Influence of nutrients, disturbances and site conditions on carbon stocks along a boreal forest transect in central Canada. Plant and Soil 242(1): 1-14.

Bouyoucos, G.J., 1962. Hydrometer method improved for making particle size analysis of soils. Agronomy Journal 54(5): 464-465.

Burrough, P.A., 1989. Fuzzy mathematical methods for soil survey and land evaluation. European Journal of Soil Science 40(3): 477–492.

Chandio, I.A., Matori, A.N., Lawal, D.U., Sabri, S., 2011. GIS based Land suitability Analysis using AHP for public parks planning in Larkana city. Modern Applied Science 5(4): 177-189.

Diack, M., Stott, D., 2001. Development of a soil quality index for the Chalmers Silty Clay Loam from the Midwest USA. Purdue University: USDA-ARS National Soil Erosion Research Laboratory. In: Sustaining the global farm. Selected papers from the 10th International Soil conservation Organization Meeting (ISCO99). Stott, D.E., Mohtar, R.H., Steinhardt, G.C. (Eds.). International Soil Conservation Organization in cooperation with the USDA and Purdue University. West Lafayette, USA. pp. 550-555.

Diacono, M., Montemurro, F., 2010. Long term effects of organic amendments on soil fertility. A review Agronomy for Sustainable Development 30(2): 401-422.

Ditzler, C.A., Tugel, A.J., 2002. Soil quality field tools : Experiences of USDA-NRCS soil quality institute. Agronomy Journal 94(1): 33–38.

Dobermann, A., Oberthur, T., 1997. Fuzzy mapping of soil fertility — a case study on irrigated riceland in the Philippines. Geoderma 77(2-4): 317–339.

Doran, J.W., Parkin, T.B., 1994. Defining and assessing soil quality. In: Defining Soil Quality for a Sustainable Environment. Doran, J.W., Coleman, D.C., Bezdicek, D.F., Stewart, B.A. (Eds.). Soil Science Society of America, Special Publication, Madison, Wisconsin, USA. 35:1-21.

Doran, J.W., Parkin, T.B., 1996. Quantitative indicators of soil quality: a minimum data set. In: Methods for assessing soil quality. Doran, J.W., Jones, A.J. (Eds.). Soil Science Society of America, Special Publication, Madison, Wisconsin, USA. 49: 25–38.

Doran, J.W., Jones, A.J., 1996. Methods for assessing soil quality. Soil Science Society of America, Special Publication Number 49, Madison, Wisconsin, USA. 410p.

Doran, J.W., Coleman, D.C., Bezdicek, D.F., Stewart, B.A., 1994. Soil Science Society of America, Special Publication Number 35, Madison, Wisconsin, USA. 244p.

Fang, X., Xue, Z., Li, B., An, S., 2012. Soil organic carbon distribution in relation to land use and its storage in a small watershed of the Loess Plateau, China. Catena 88(1): 6–13.

Franzluebbers, A.J., 2002. Soil organic matter stratification ratio as an indicator of soil quality. Soil and Tillage Research 66(2): 95-106.

Fu, B., 1991. Theory and practice of land evaluation. China Science and Technology Press, Beijing.

Gong, G., Mattevad, S., O'Bryant, S.E., 2010. Comparison of the accuracy of kriging and IDW interpolations in estimating groundwater arsenic concentrations in Texas. Environmental Research 130: 59–69.

Heal, O.W., Anderson, J.M., Swift, M.J., 1997. Plant litter quality and decomposition: An historical overview. In Driven By Nature: Plant Litter Quality and Decomposition. Cadisch, G., Giller, K.E. (Eds.), CAB International, Wallingford. pp 3-30.

Herrick, J.E., Brown, J.R., Tugel, A.J., Shave, P.L., Havstad, K.M., 2002. Application of soil quality to monitoring and management: paradigms from rangeland ecology. Agronomy Journal 94(1): 3–11.

Jackson, M.L., 1973. Soil Chemical Analysis, Prentice Hall of India Pvt. Ltd., New Delhi.

Jague, E.A., Sommer, M., Saby , N.P.A., Cornelis, J.T., Wesemael, B., Van Oost, K., 2016. High resolution characterization of the soil organic carbon depth profile in a soil landscape affected by erosion. Soil & Tillage Research 156: 185–193.

Karlen, D.L., Ditzler, C.A., Andrews, S.S., 2003. Soil quality: why and how? Geoderma 114(3-4): 145-156.

Karlen, D.L.K., Gardner, J.C., Rosek, M.J., 1998. A soil quality framework for evaluating the impact of CRP. Journal of Production Agriculture 11(1): 56–60.

Karlen, D.L., Mausbach, M.J., Doran, J.W., Cline, R.G., Harris, R.F., Schuman, G.E., 1997. Soil quality: A concept, definition, and framework for evaluation. Soil Science Society of America Journal 61(1): 4-10.

Klingebiel, A.A., Montgomery, P.H., 1961. Land capability classification. U.S.Department of Agriculture, Soil Conservation Service, Agriculture Handbook No. 210, Washington DC, USA. Available at: https://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/nrcs142p2_052290.pdf

Kumar, P., Verma, T.S., 2005. Characterization and classification of some rice growing soils of Palam Valley of Himachal Pradesh. Agropedology 15(2): 80-85.

Larson, W.E., Pierce, F.J., 1994. The dynamics of soil quality as a measure of sustainable management. In: Defining Soil Quality for a Sustainable Environment. Doran, J.W. Coleman, D.C. Bezdicek, D.F., Stewart, B.A. (Eds.). Soil Science Society of America Special Publication, Madison, Wisconsin, USA. 35:37-51.

Li, F.B., Lu, G.D., Zhou, X.Y., Ni, H.X., Xu, C.C., Yue, C., Yang, X.M., Feng J.F., Fang, F.P., 2015. Elevation and land use types have significant impacts on Spatial variability of soil organic matter content in Hani terraced field of Yuanyang county, China. Rice Science 22(1): 27-34.

Lin, G.F., Chen, L.H., 2004. A spatial interpolation method based on radial basis function networks incorporating a semivariogram model. Journal of Hydrology 288(3-4): 288–298.

Liu, S., An, N., Yang, J., Dong, S., Wang, C., Yin, Y., 2015. Prediction of soil organic matter variability associated with different land use types in mountainous landscape in southwestern Yunnan province, China. Catena 133: 137–144.

Mandal, D., Singh, R., Dhyani, S.K., Dhyani, B.L., 2010. Landscape and land use effects on soil resources in a Himalayan watershed. Catena 81(3): 203–208.

McBratney, A.B., Odeh, I.O.A., 1997. Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions. Geoderma 77(2-4): 85–113.

Mishra, A.K., Deep, S., Choudhary, A., 2015. Identification of suitable sites for organic farming using AHP & GIS. The Egyptian Journal of Remote Sensing and Space Science 18(2): 181-193.

Munson, S.A., Carey, A.E., 2004. Organic matter sources and transport in an agriculturally dominated temperate watershed. Applied Geochemistry 19(7): 1111–1121.

Murphy, J., Riley, J.P., 1962. A modified single solution method for the determination of phosphate in natural waters. Analytica Chimica Acta 27: 31-36.

Diodato, N., Ceccarelli, M., 2014. Multivariate indicator kriging approach using a GIS to classify soil degradation for Mediterranean agricultural lands. Ecological Indicators 4(3):177–187.

Parras-Alcántara, L., Lozano-García, B., Galán-Espejo, A., 2015. Soil organic carbon along an altitudinal gradient in the Despeñaperros Natural Park, southern Spain. Solid Earth 6: 125–134.

Pieri, C., Dumanski, J., Hamblin, A., Young, A., 1995. Land quality indicators. World Bank Discussion Papers, 315. The World Bank, Washington DC, USA. 80p. Available at [Access date :29.01.2018]: http://documents.worldbank.org/curated/en/405971468739495480/pdf/multi-page.pdf

Prescott, C.E., Maynard, D.G., Laiho, R., 2000. Humus in northern forests: friend or foe? Forest Ecology and Management 133(1-2): 23–36.

Qi, Y., Darilek, J.L., Huang, B., Zhao, Y., Sun, W., Gu, Z., 2009. Evaluating soil quality indices in an agricultural region of Jiangsu Province, China. Geoderma 149(3-4): 325–334.

Roy, S., Kumar, S., 2014. Developing a framework for soil quality assessment in a watershed of mountainous ecosystem using geo-spatial approach. M.Tech Thesis, IIRS, Dehradun

Ryals, R., Kaiser, M., Torn, M.S., Berhe, A.A., Silver, W.L., 2014. Impacts of organic matter amendments on carbon and nitrogen dynamics in grassland soils. Soil Biology and Biochemistry 68: 52-61.

Saaty, T.L., 2008. Decision making with the analytical hierarchy process. International Journal of Services Sciences 1(1): 83-98.

Saaty, T.L., 1977. A scaling method for priorities in hierarchical structures. Journal of Mathematical Pscychology 15(3): 234-281.

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