Use of GIS for sampling designs for agricultural surveys


Randhir Singh, Anil Rai and Prachi Misra
Indian Agricultural Statistics Research Institute,
New Delhi - 110012

Introduction
The last decades witnessed revolutionary changes in the approaches related to spatial problems because of incredible progress in automation and computer technology especially with the introduction of modern Geographic Information System (GIS). It is a powerful tool for storing, retrieving analysing and integrating spatial and non-spatial geographical data apart from drawing any kind of maps. The development of spatial statistical techniques has been accelerated parallel to this rapid growth of GIS technologies and there is a need to integrate the GIS, and spatial statistical techniques and remote sensing.

A number of organisations in India are engaged in developing suitable applications of remote sensing technology. The initial success of these led to the formulation of crop acreage and production estimation (CAPE) project which was firrst major project launched under Remote SENSING Application Mission (RSAM) and Department of Space (DOS) in 1986. First indepenent attempt in the country towards the use of satellite digital data was made in karnal district of Haryana using Landsat MSS data by (1989). Dadhawal and Sridhar (1986), Panikar et al. (1987), Dadhawal et al. (1987), Murthy et al. (1996) etc. have made significant contributions towards acreage and production estimation of rice and wheat in the country. Singh, et al. (1992) and Goyal, et al. (1994) presented the use of satellite data alongwith survey data for improving the efficiency of crop yield estimators. The applications of Remote Sensing and GIS for Land Use Planning under different projects underaken in the country has been considered by Krishnamurthy and Adiga (1987).

In case of spatial analysis the data can be described in three ways

1. point
2. line
3. area or polygons.

A point refers to a single plae and is usually considered as having no dimension or having dimension which is negligible when compared to study area such location of industries, houses etc. Line data or networks can be found in GIS to describe economic features like rivers transportation system etc. Data arranged on polygons have a particular relevance if a GIS is designed to assist agricultural or socio-economic survey with the help of remote sensing data. The sampling units in these surveys are based on the area frame obtained with the help of satellite image or geographical areas like villages, cities, regions etc. There are mainly three important sources of spatial data, census, surveys and satellite image of geographical area.

Sampling Procedure Based on GIS
Sampling design for spatial data have a long tradition starting from Mahalanobis (1940). Hedayat et al. (1988) proposed a sampling plan in which contiguous units are excluded thereby resulting in second order inclusion probabilities being zero corresponding to pairs of contiguous units.

Arabia (1993) described a sampling technique ‘Dependent Area Units Sequential Technique’ i.e. DUST which avoids the inclusion of neighbouring areas in area sample. This technique can be consider as an extension of the technique proposed by Hedayat et. al. (1988) and is described here briefly.

Let there be N non-overlapping area units in the study area.. Let X be a auxiliary character and let Y be the character under study for geographical area units. This sampling design consists of three important steps :

1. Estimation of spatial correlation b with the help of X at various distance lag. For simplicity distance of decay moder b_k b₁^k can be applied.
2. Testing the stationarity at various order correlation's for identifying the zones, and
3. Selecting the first unit by assigning weight 1 and assigning weight     (1-b₁ d_ik) for selecting the k-th unit in the sample of size n where k = 2, 3....n and d_ik is the distance between i-th and k-th area units measured in terms of physical distance between centroids or in terms of order of neighbourhood.

As a consequence of this sampling design area units are not selected with uniform criteria or probability, units closer to a selected unit receive smaller probabilit6y as compared to units distance apart. Thus,. in zones displaying a positive spatial correlation, we can save sampling units by scattering them. It has been demonstrated that most of the traditional techniques can be derived as particular cases of DUST. For example, if b₁= O, it reduces to simple random sampling whereas if area is stratified and within each strata b₁= O, then it reduces to stratified random sampling. Further, setting d_ij=1 if d_ij=d_max and O otherwise will give rise to systematic sampling.

Simulation Study :
In this simulation study village wise data from District Census Hand Book of 1991 for Rohtak district of 492 villages of Haryana has been utilized. The village wise map was digitized using PC-ACR/INFO software and irrigated area of the village has been treated as character under study (Y), whereas, total cultivated area of the village as auxiliary character (X). The whole district has been identified as one zone after testing the spatial correlation coefficients of different order. The over all spatial correlation coefficient for the district was approximately 0.22. The problem is to compare different sampling strategy for estimating population mean = 609.0022 ha. with respect to its accuracy, bias and stability. In this simulation study 100 samples of different sizes has been selected following various sampling procedures and the parameters related to accuracy, bias and stability has been obtained. The results are presented in the following table.

Sample Size Strategy	30			50			100
	R.B.	R.E.	C.V.	R.B.	R.E.	C.V.	R.B.	R.E.	C.V.
STG - I	0.28	-	13.38	0.19	-	10.66	0.12	-	7.72
STG - II	0.74	0.87	14.73	0.73	0.99	10.39	0.15	1.29	6.77
STG - III	0.19	6.26	5.32	0.01	7.00	3.94	0.04	8.16	2.70
STG - IV	3.09	8.38	4.76	1.98	8.60	3.63	0.93	8.79	2.63

STG - I = Simple random sampling without replacement strategy
STG - II = Usual DUST Technique proposed by Arbia with the estimator of SRSWOR
STG - III = Proposed Sampling Strategy with W_hi (1)X_hi=1
STG - IV Proposed Sampling Strategy
R.B. = % Relative Bias.
R.E. = Relative Efficiency.
C.V. = Coefficient of variation.

From the above table it can be seen that the performance of the proposed strategy is far better in all respects expect R.B. It can also be observed that performance is improving with increasing sample size.

Multistage sampling design for crop surveys using satellite data
Presently after launching of IRS-IC and IRS-ID the availability of spectral data at different resolutions has been made available. The Wide Field Sensors (WiFS) with spatial resolution of 189.3 meters and LISS-III data of resolution 23 meter are available. There is need to develop methodologies for different surveys using data pertaining to different resolutions as there is wide difference between the data of both the sensors. The data pertaining to LISS-III is very costly as compared to WiFS.

The WiFS data for the large area (say state) under study is acquired and stratum boundaries based on spatial correlation coefficient are made with the help of digital number values of area unit. The district boundaries within the state are digitized and a sample of districts is selected with the help of DUST technique using proportional allocation. The LISS-III data is now processed for only the selected districts. Again in each of the selected districts villages are digitized and a sample of villages is selected using DUST technique. In this way, the villages are selected by using IRS-IC data using stratified multistage sampling design. The land use classes of each selected village can be obtained using ground truth survey. Further, the yield of the crop under study can be obtained by developing suitable models based on crop cutting experiments data. The basic purpose of this stratified sampling design is to get precise estimates of important crop statistics like crop acreage and crop yield and crop yield forecast models from an integrated survey at a relatively much cheaper cost.

Reference

1. Arabia, G. (1989): Statistical effects of spatial data transformation In: 'Accuracy of spatial data basis'.Eds/ Good Child, M.F. and Gopal, S. Taylor and Frances, London.
2. Arabia, G. (1993): Use of GIS in spatial statistical surveys. Int. Statist. Rev., 61, 2, pp.339-359.
3. Arabia, G. & Haining, R.P. (1989): Error propagation through map operations. Working paper. National Centre of Geographic Information and Analysis, UCSB.
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8. Krishnamurthy, Y.V.N. and Ddiga, S. (1976) Remote sensing and GIS for land use planning. Presented at the National Workshop on land use planning organised by Planning Commission and NCAP, New Delhi.
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