Abstract
A study was conducted to improve precision of crop acreage adopting stratified random sampling approach. Remotely sensed data was used to classify mustard crop for the states of Rajasthan, Madhya Pradesh, Uttar Pradesh, Gujarat and Haryana covering 81% of mustard area of India. A grid of size 5 × 5 km was super-imposed on classified image of study area and proportion of mustard crop within the grid was ascertained. Crop proportion was used to determine strata. Stratification was done based on equal interval of proportion, equal sample number and cumulative square root of frequency method. Cumulative square root of frequency method gave highest precision in all the cases.
Similar content being viewed by others
References
Allen, R., Hanushchak, G., & Craig, M. (2002). History of remote sensing for crop acreage in USDA’s National Agricultural Statistics Service. Available online at: www.usda.gov/nass/nassinfo/remotehistory.htm#2
Aoyama, H. (1954). A study of stratified random sampling. Annals of the Institute of Statistical Mathematics, 6, 1–36.
Bhagia, N., Bhuyan, M. R., Oza, M. P., Patel, N. K., Parihar, J. S., Mehmood, K., et al. (2006). Cotton area estimation using multi-temporal AWiFS data-A feasibility study. Scientific Note: EOAM/SAC/RESA/FASAL-TD/SN/26/2006, Space Applications Centre, Ahmedabad
Bhagia, N., Patel, N. K., Singh, V., Chodvadiya M., Narendra Babu, T., & Ramesh, K. V. V. (2008). Classification accuracy of cotton crop using multi-date AWiFS data and ground information. Scientific Note: EOAM/SAC/RESA/FASAL-TD/SN/36/2008, Space Applications Centre, Ahmedabad.
Cochran, W. G. (1961). Comparison of methods for determining stratum boundaries. Bulletin of International Statistical Institute, 38(2), 345–358.
Cochran, W. (1992a). Stratified random sampling. In: Sampling techniques (pp. 89–114). New Delhi: Wiley Eastern Ltd.
Cochran, W. (1992b). Further aspects of stratified sampling. In: Sampling techniques (pp. 115–149). New Delhi: Wiley Eastern Ltd.
Dalenius, T. (1950). The problem of optimum stratification–I. Skandinavisk Actuarietidskrift, 33, 203–213.
Dalenius, T., & Gurney, M. (1951). The problem of optimum stratification–II. Skandinavisk Actuarietidskrift, 34, 133–148.
Dalenius, T., & Hodges, J. L. Jr. (1957). The choice of stratification points. Skandinavisk Actuarietidskrift, 40, 198–203.
Dalenius, T., & Hodges, J. L., Jr. (1959). Minimum variance stratification. Journal of the American Statistical Association, 54, 88–101.
Durbin, J. (1959). Sampling in Sweden. Journal of the Royal Statistical Society. Series A, 22, 246–248.
Ekman, G. (1959). An approximation useful in univariate stratification. The Annals of Mathematical Statistics, 30, 219–229.
Feiveson, A. H., Chhikara, R. S., & Hallum, C. R. (1978). LACIE sampling design. In: R. B. MacDonald (Eds.), Proc. LACIE Symposium, held at NASA Johnson Space Centre in Texas, USA from Oct. 23–26, 1978. (Vol. 1, pp. 47–52).
Hansen, M. H., Hurwitz, W. N., & Madow, W. G. (1953). Sample survey methods and theory (Vol. I and II). New York: Wiley.
Hess, I., Sethi, V. K., & Balakrishnan, T. R. (1966). Stratification-A practical investigation. Journal of the American Statistical Association, 61, 74–90.
Hiederer, R., Favard, J. C., Guedes, D., & Sharman, M. (1993). Estimating European Crop Surfaces from SPOT and Landsat TM data. In: J. L. van Genderen, R. A. van Zuidam, & C. Pohl (Eds.), Proc. of International Symposium on Operationalization of Remote Sensing, held at Netherlands, Europe from April 19–23, 1993 (pp. 116–127).
Houston, A. G., Feivesen, A. H., Chhikara, R. S., & Hsu, E. M. (1978). Accuracy assessment: The statistical approach to performance evaluation. In R. B. MacDonald (Eds.), Proc. of LACIE Symposium held at Texas, USA, from Oct. 23–26, 1978 (Volume 1, pp. 115–130).
Klersy, R., & Churchill, P. N. (1993). Application of remote sensing to operational problems within European Communities sectoral policies. In J. L. van Genderen, R. A. van Zuidam, & C. Pohl (Eds.), Proc. of International symposium on Operationalization of Remote Sensing, held at Netherlands, Europe from April 19–23, 1993 (pp. 1–15).
Mahalanobis, P. C. (1952). Some aspects of design of sample surveys. Sankhya, 12, 1–7.
Oza, S. R., Ravindran, A., Jayaraman, M., & Rajeev, S. (1993). Determining optimum sampling unit size and sampling fraction size for crop acreage estimation. Asian Pacific remote sensing journal, 5, 85–91.
Oza, M. P., Rajak, D., Bhagia, N., Dutta, S., Vyas, S. P., Patel, N. K. et al. (2006) Multiple production forecast of wheat in India using remote sensing and weather data. In R. J. Kuligowski, J. S. Parihar, & G. Saito (Eds.), Proc. of SPIE Asia-Pacific, held at Goa, India from Nov. 13–17, 2006. No. 6411–02, p. 23.
Parihar, J. S., & Dadhwal, V. K. (2002). Crop production forecasting using remote sensing data: Indian experience. The International archives of Photogrammetry, Remote Sensing and Spatial Information Sciences. Proceedings ISPRS Comm. VII Symposium: Resource and Environmental Monitoring, held at Hyderabad, India, from Dec. 3–6, 2002. Volume 34 (7), pp. 313–318.
Parihar, J. S., & Oza, M. P. (2006). FASAL: an integrated approach for crop assessment and production forecasting. In: (R. J. Kuligowski, J. S. Parihar, & G. Saito), Proc. of SPIE Asia-Pacific, held at Goa, India from Nov. 13–17, 2006. No. 6411–01, p. 01.
Raj, D., & Chandhok, P. (1999). Stratification. In: Sample survey theory (pp. 97–113). New Delhi: Narosa Publishing House.
Sethi, V. K. (1963). A note on optimum stratification of populations for estimating the population means. Australian Journal of Statistics, 5, 20–33.
Sukhatme, P. V., & Sukahtme, B. V. (1970). Stratified sampling. In Sampling theory of surveys with applications (pp. 80–134). Bombay: Asia Publishing House.
Acknowledgement
Authors are thankful to Dr. R.R Navalgund, Director, Space Applications Centre for his support and encouragement. Authors are grateful to Dr. J.S. Parihar, Deputy Director, Earth, Ocean, Atmosphere, Planetary Sciences and Applications Area (EPSA) for his keen interest and encouragement. Authors also thank Dr. Sushma Panigrahy, Group Director, Agriculture, Terrestrial Biosphere and Hydrology Group (ABHG) for her guidance and support in carrying out this work. This work was carried out under FASAL project sponsored by Department of Agriculture and Co-operation.
Author information
Authors and Affiliations
Corresponding author
Annexure
Annexure
Mathematical basis for construction of strata by frequency method (Cochran 1992b)
The variance of estimate in stratified random sampling is given by
where Nh is population size and nh is sample size in stratum h, N is total population value given by \( {\text{N}} = \sum\limits_{{{\text{h}} = 1}}^{\text{L}} {{{\text{N}}_{\text{h}}}} \)
where yhi is the ith observation in the stratum h, yh is mean of stratum h and Sh 2 is the variance within the stratum h
Under Neyman allocation and ignoring finite population correction \( {\text{V}}\left( {{{\overline {\text{y}} }_{\text{st}}}} \right) \) is given as \( {\text{V}}\left( {{{\overline {\text{y}} }_{\text{st}}}} \right) = \left( {{1}/{\text{n}}} \right)*{\left( {\Sigma {{\text{W}}_{\text{h}}}{{\text{S}}_{\text{h}}}} \right)^{{2}}} \) where \( {{\text{W}}_{{{\text{h}} = }}}{{\text{N}}_{\text{h}}}/{\text{N}} \) is stratum weight, S 2h is stratum variance, Minimizing \( {\text{V}}\left( {{{\overline {\text{y}} }_{\text{st}}}} \right) \) amounts to minimizing WhSh
Under assumptions of large number of strata and rectangular distribution within stratum \( {{\text{W}}_{\text{h}}}\sim {{\text{f}}_{\text{h}}}\left( {{{\text{y}}_{\text{h}}} - {{\text{y}}_{{{\text{h}} - {1}}}}} \right)\quad {{\text{S}}_{\text{h}}} = \left( {{{\text{y}}_{\text{h}}} - {{\text{y}}_{{{\text{h}} - {1}}}}} \right)/\surd \left( {{12}} \right)\,{{\text{y}}_{\text{h}}} \) and yh−1 are bounds & fh is frequency
\( \surd \left( {{12}} \right)\;\left( {\sum\limits_{{{\text{h}} = 1}}^{\text{L}} {{{\text{W}}_{\text{h}}}{{\text{S}}_{\text{h}}}} } \right) = \sum\limits_{{{\text{h}} = 1}}^{\text{L}} {{{\left( {{\text{G}}\left( {\text{h}} \right) - {\text{G}}\left( {{\text{h}} - {1}} \right)} \right)}^{{2}}}} \) where \( \sum\limits_{{{\text{h}} = 1}}^{\text{L}} {{{\left( {{\text{G}}\left( {\text{h}} \right) - {\text{G}}\left( {{\text{h}} - {1}} \right)} \right)}^{{2}}}} \) is constant \( \left( {\sum\limits_{{{\text{h}} = 1}}^{\text{L}} {{{\text{W}}_{\text{h}}}{{\text{S}}_{\text{h}}}} } \right) \) is minimized when G (h)-G (h-1) is constant i.e. Variance is minimized when \( {\text{cum}}.\surd \;\left. {\left( {{{\text{f}}_{\text{h}}}} \right)\left( {{{\text{y}}_{\text{h}}} - {{\text{y}}_{{{\text{h}} - {1}}}}} \right)} \right) \) is constant
About this article
Cite this article
Bhagia, N., Rajak, D.R. & Patel, N.K. Improvement in Precision of Crop Acreage Estimation by Remote Sensing Using Frequency Distribution Based Stratification. J Indian Soc Remote Sens 39, 153–160 (2011). https://doi.org/10.1007/s12524-011-0098-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12524-011-0098-y