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Study About the Use of SPOT
Data for the Estimation of Pastoral
Areas in Morocco
Philippe Brionl
Abstract.-In order to provide information on land use for a whole
country, it is often impossible to have a complete cover of the land with
remote sensing data, and it is necessary to use a sampling method. This
paper presents an approach of this problem, relatively to the estimation
of pastoral areas in Morocco : selection of SPOT images, and then
selection of "segments" inside the images. The different options of the
sampling plan are discussed.
INTRODUCTION
In order to provide information on land use, remote sensing brought many
hopes. In some cases, it has been used jointly with ground surveys, and the
exhaustive cover of the satellite image has given an auxiliary information,
combined with the results of the ground survey in order to produce an improved
estimate (by the method of the regression estimate, see for example Pastorelli,
1992). But, often, the number of images required for having an exhaustive cover is
too high, and financial reasons lead to the use of a sample of images : this is, for
example, the case of the MARS program (of the European commission, for the
estimation of crop areas as cereals) ; however, there are no established rules for
the sampling plan to be used for that kind of problems.
The object of this paper is to propose an a priori approach to this problem,
concerning estimation of pastoral areas in Morocco. This work was done jointly
with CNES (Centre National dlEtudes Spatiales, Toulouse) and CRTS (Centre
Royal de Tdkdktection Spatiale, Rabat).
'statistician,INSEE,paris,~ r a n c e
PRINCIPLES OF THE PROPOSED APPROACH
Constraints and method
The first constraint concerns the purchase of satellite data (here, SPOT images).
The impossibility to have a complete cover of Morocco leads us to have a sample
of images. Then, since the classification of images does not presently give quite
perfect results (there still remains confusions for some types of land use), we are
led to having more complete investigations for portions of the images (by
photointerpretation for example).
So, we propose a two-stage sampling plan for the estimation of pastoral areas:
- first, selection of SPOT images ;
- second, selection of "segments" inside the selected images.
These segments are "surveyed" by photointerpretation, or by a ground survey.
They have, for practical reasons, a square shape.
Which items of the sampling plan are to be studied ?
- The size of the segments has to be chosen. In France, for example, a size of 50
hectares is used for ground surveys because of practical reasons (work of the
enumerator). What should be proposed in the context of pastoral areas in
Morocco?
- Another question concerns the number of segments to be selected inside a SPOT
image.
- Third, the sample of segments may be selected using a systematic sampling
method. Is this method efficient, and if so, what is the gain of precision to be
expected ?
- The selection of SPOT images is another problem : how many should be
selected, and is it possible to use a stratification of the country for the sampling
plan ?
Then, once the former points have been treated, what global precision is to be
expected ?
An experimental approach
This approach consists in using some existing materials in order to produce, a
priori, some quantified results to the former questions.
First, three SPOT images, belonging to regions of Morocco with different
characteristics (in the upper Atlas, near the Sahara and on arid plateaux) have been
classified, especially isolating the item "pastoral area" ; these images have been
used for the study of the second stage of the sampling plan.
The study of the first stage was realized using data proceeding from a SPOT
"Quick-Look-Numerical" (QLN) : these data are obtained by sampling one pixel
for six, on row and column, and give a global view of the country, much bigger
than a single image. These data were also classified, particularly using the item
"pastoral area".
The use of these materials permits to have quantified data to study the sampling
system before the actual survey : this approach is rather a new one for the problem
studied, because until now, we have had at our disposal experiences where the
precision is evaluated a posteriori, once the survey has been conducted.
At last, it is also important to mention that the subject discussed in this paper is
a statistical one, and not a cartographic one.
RESULTS
First, we will discuss the results concerning the second stage (selection of
segments inside the images), and integrate them to those obtained for the first
stage (selection of SPOT images).
Sample of segments inside the images
The three images classified were cut up in segments, using six different grids to
define the segments : 200*200m, 400*400m, 600*600m, 800*800m,
1000*1OOOm, 1200*1200m.
Size of the segments
The variance of the estimate of the mean of a variable Y, using a simple random
sample of m segments is approximately equal to :
V(estimate ofthe mean)
=
V(Y) / m (1)
if V(Y) is the variance of the variable in the population, and if we do not take
into account the sampling fraction f that is very small, so the quantity ( I - - is
approximately equal to 1.
Table 1 displays the value of V(Y) for the variable "proportion of pastoral areas
inside the segments", regarding the three images and the different sizes of
segments.
Table 1.- V(proportion of pastoral areas inside the segments)
Midelt
Oujda
Segment size
0.132
200 * 200
0.078
Ktaoua
0.165
When the size of the segment increases, the variance V(Y) decreases, because the
bigger segments are more homogeneous. But, if we introduce cost elements
(corresponding to the time needed to "survey" the segments, e.g. proportional to
the area of the segments, or at least to the square root of this area), we see that the
decrease of variance is not sufficient enough to compensate cost increase. So,
according to the results obtained for these three images located in different regions
of Morocco, it seems better to use small segments (200*200m).
Efficiency of the systematic sampling method
This method consists in selecting segments located on a grid, rather than taking
them completely randomly. The size of the grid may vary, and is related to the
sampling fraction. Having cut up three images in segments makes it possible to
calculate exactly the variance of the estimate with this method (by calculating the
results of all possible systematic samples, which are in limited number), and to
compare it to the one obtained by Eq. 1, for the three sites, different sizes of
segments and for different sampling rates.
The results are that, generally, the systematic method is more efficient that
simple random sampling, and, on an average, the gain of variance of the estimate
is between 30% and 40%. These results are similar to those obtained by Dunn and
Harrison (1993).
Precision of the estimation inside the images
Table 2 gives the coefficient of variation for the estimate of the proportion of
pastoral areas inside each image for a systematic sampling of segments of
200*200m, the sampling fraction being 11100.
Table 2.-Precision of the estimates inside the images
1mag.e
coefficient of variation
Midelt
2.3 %
Oujda
1.1 %
Ktaoua
9.9 %
-
The coefficient of variation is defined as the ratio from the square root of the
variance of the estimate of a characteristic to the value of this characteristic.
Selection of SPOT images
Using the QLN makes it possible to reconstruct "approximate" SPOT images for
the whole country. The values obtained from these images constitute the basis to
evaluate the global precision of the sampling plan.
Variance of the estimate for a two-stage sampling plan
If the selection for the first stage is with equal probabilities, the variance of the
estimate f of the total is :
T. (Y) pastoral area of the image a
Z, is the variance of the estimate of the total
T, (Y) according to the method of selection
of segments inside the image
Results from the first part (selection of segments inside the images) are used for
the estimation of the Za , and the data of QLN give information about Sf.
Results
Average results (calculated with the three images) for the second stage were
used, and Table 3 gives the precision of the global estimate of pastoral areas for
Morocco, with different numbers of images selected at the first stage, and 400
segments of 200*200m selected in each image.
Table 3.-Precision of the estimate of pastoral area for Morocco
Number of surveyed images
Coefficient of variation of Relative share of the second
the estimate (%)
stage in the total variance of
the estimate (%)
20
12.0
2.1
The share of the variance which depends from the second stage is small, that
means that the variance between images brings the most important part of this
variance. So, it is possible to have, for the second stage, a smaller sample. If we
take 30 images and 30 segments inside each image, we obtain a coefficient of
variation of 10.5%.
The second result of Table 3 is that, even when the sampling rate for the first
stage is high, for example 100 images selected within the 115 "possible" which
cover the whole country, there still remains a consistent value of the variance of
the estimate.
Use of a stratification
A "rough" stratification was used, classifying all 115 images in 9 classes :
selecting 30 images using this stratification (and 30 segments inside each image),
the coefficient of variation of the estimate for pastoral areas is 8.9% (instead of
10.5% without stratification).
CONCLUSION
The most important result of this study is the great part of the variance of the
estimate due to the first stage of the sampling plan, that is the fact of selecting
images among the 115 images covering the country.
This result is well known for sampling questions, and one way to take it into
account and to improve the efficiency of the method might be to have smaller
primary units : using portions of SPOT images for the first stage could be a
response to that problem.
Then, the results obtained in this paper should not be considered as exact values
of the precision to be obtained with such a method, but rather as approximations
based on an experimental approach.
Finally, we considered this problem as an "instantaneous" estimation, trying to
evaluate the pastoral areas of the country for one year. To evaluate the evolution
between two years, or more, should lead to other propositions and results for the
sampling plan.
REFERENCES
Cochran, W.G., 1977, Sampling techniques, 3rd ed, Wiley, New York
Dunn, R., Harrison, A.R., 1993, Two-dimensional systematic sampling of land
use, Applied Statistics 42 n04
Pastorelli, R, 1992,Superficies agricoles a partir d'images satellite, Courrier des
statistiques n061-62, Paris
Rapport CNES, 1995, Projet Geostat Maroc, etude statistique, CNES, Toulouse
BIOGRAPHICAL SKETCH
Philippe Brion graduated from Ecole Polytechnique (Paris) and ENSAE (Ecole
Nationale de la Statistique et de llAdministrationEconomique, Paris). He was in
charge of the sampling methodology in SCEES (statistical department of the
French Ministry of Agriculture) from 1980 to 1989, and is now working in INSEE
(Institut National de la Statistique et des Etudes Economiques) on methodological
problems for statistical cooperation (developing and transition countries).