A two phase sampling method and the optimal sampling segment dimensions for the estimation of sugar cane cultivated area were developed. This technique employs visual interpretations of LANDSAT images and panchromatic aerial photographs considered as the ground truth. The estimates, as a mean value of 100 simulated samples, represent 99.3% of the true value with a CV of approximately 1%; the relative efficiency of the two phase design was 157% when compared with a one phase aerial photographs sample

Cappelletti, C. A.

Lee, D. C. L.

Mendonca, F. J.

Parada, N. D. J.

Shimabukuro, Y. E.

English

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ESA - SDS p AMA
(E83-10077) ESTIMATION OF THE SUGAR CLUE	 M83-14586   
COLTIiiATID AREA FROM LANDSAT IMAGES USING
SHE THO PHASE SAMPLING METHOD (Institato de
Pesgnisas Espaciais, Sao Jose) 6 p	 Unclas
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1. Publication NQ 2. Version 3. Date 5. Distribution
INPE--2489	 /178 July, 1988 0 Internal ® Extern
0 Restricted4. Origin	 Program
DM/DES	 AREA
6. Key words - selected by the author(s)
TWO PHASE SAMPLING
SEGMT DIMENSIONS
7. U. D.	 528.711.7; 833.82
8. Title
	
INPE-2489-PREW2
10. NQ Of. pages: 05
ESTIMATION OF THE SUGAR CANE 11. Last page: 04
CULTIVATED AREA FRAM LANDSAT IMAGES USING
28E TW PHASE SAMPLING SOD 12. Revised by
9. Authorship	 Carlos Alberto CappetUti
Francisco Jose Mendonva
tea Teixei
	 DiasDavid Chung Lsang Lee
-Yosio Edemir Shzmabukurn 13. Authorized by
Responsible authcr
	 a_4 '
Nelson
	 Jesus P^mda
Director
14. Abstract/Notes
A two phase sampling method and the optimal sampling segment
dimensions are developed for the estimation of the sugar cane cuZtivate4
area. This technique employs visual interpretations of LANDSAT images and
panchromatic aerial photographs considered as the ground truth. The
estimates, as a mean value of 100 simulated samples, represent 99.3% of the
true value with a CV of approximately 1%; the relative efficiency of the
two phase design was 157% when compared with a one phase aerial photographs
sample.
OF
OF POOR QUALLIY
15. Remarks	 This paper was accepted for presentation at the Sixteenth
International Symposium on Remote Sensing of Environment,'
Buenos Aires, Argentina, June 2-9, 1982.
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1
MOM PAGE 0
Of POOR QUALITY
ESTIMATION OF THE SUGAR CANE CULTIVATED AREA FROM LANDSAT
IMAGES USING THE TWO PHASE SAMPLING KETHOD•
t'
V
Carlos Alberto Cappelletti
Francisco Jose MendonCa
David Chung I-iang Lee
7osio Edemir Shiwabukuro
lbistituto de Pesquisas Espaciais - INPE
Conselho National de Desenvolvimento Cientifico a Tecnologico - CNPq
Caixa Postal S15, 12200 - Sio Jose dos Campos, SP, Brasil
ABSTRACT
A two phase sampling method and the
optimal sampling segment dimensions are devel-
oped for the estimation of the sugar cane
cultivated area. This technique employs visual
interpretations of LANDSAT images and pan-
chrow.tic aerial photographs considered as the
ground truth. The estimates, as a mean value
of 100 simulated samp les, represent 99.31 of-
the true value with a CV of approximately 1t;
the relative efficiency of the two phase design
was 1571 when compared with a-one phase aerial
photographs sample.
Ll
D
1. INTRODUCTION
In this paper a statistical system to estimate the sugar cane (Saccharum
spp.) cultivated area in a subregion of Sao Paulo State, Brazil, is presented.
The region under study is known as the Great Region of Jau, , located in the
central part of the state, within the par:.ilels 22 000 1 and 23000 , South, and
meridian 48000' and 49000' West, covering SO46 kma.
For this region, the sugar cane acreage was determined by two different
a1pproaches. In the first approach, Koffler at al., ( 1980) made interpretations
of panchromatic aerial photographs in the scale of 1:3S000 and 1 : 45000,
complemented with a rigorous field control. This information is considered as
the ground truth.
In the second approach, Mendonca et al. ( 1981) used LANDSAT images in the
scale of 1 : 250000 and visual interpretation, associating the spectral
variations of the crop with temporal variations in different satellite pass.
Channels S and 7 were used.
With this basic information, a sampling experiment was designed to
estimate the sugar cane acreage and measure the error rate in relation to the
ground truth. The applied sampling method was a two phase sampling with
regression estimates.
• Presented at the Sixteenth International Symposium on Remote Sensing of
Environment, Buenos Aires, Argentina, June 2-9, 1982.
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iORIGINAL PAGE 1U
OF POOR QUAL Y
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2. STUDY OBJECTIVES
a) To determlae segments size in order to have the maximum correlation
between LANDSAT data and grou p. truth.
b) To estimate the sugar cane acreage with a sampling design using
LANDSAT data and ground truth and considering the cost of each source
of data.
3. SEGMENTS SIZE AND SAMPLING METHOD
	
a) Determination of segments size 	 t -
With a grid of size 1 cm by 1 ca (corresponding to 2.S ka by 2.S ka)
applied on a composition of LAhjSAT images and on a mosaic of aerial
photographs, the number of points with sugar cane in each unitary segment was
determined.
From that information, a subarea of 60 km x 37.5 ka was selected and
a uniformity trial (Federer, 1967) was designed.,The response variable was the
number of hectares cultivated with sugar cane by segment of 6.25 kma.
Ten different types of segments were considered:
T ► a	 Size	 Seg`aent
Ix 1	 2.5 x 2.S •	 6.25 kas	360
Ix 2	 2.S x 5.0 = 12.50 ka s	168
Ix 3	 2.S x ?.S = 18.75 kas 	 120
lx 4	 2.S x 10.0 s 25.00 kas	72
2x 2	 S.0 x S.0 . 25.00 kms	84
2 x 3	 S.0 z< 7;S . 37. SO km s	36
2 x 4	 S.0 x 10.0 . S0.00 kms	 36
3 x 3	 7.5 x 7.S . S6.2S ka s 	 .40
3 x 4	 7.5 X 10.0 • 75.00 kas	24
4x .	 10.0 x 10.0 a 100.00 kms	18
The criterion of selection was the maximum correlation between the
variables "response to the LANDSAT images interpretation", X, and "ground
truth", Y.
b) Sampling design
A two phase sampling design with regression estimates was applied
combining the two sources of information.
T1is design takes . advantage of the correlation between X and Y and the
cost tatio for collecting the data in each variable. The sample selection was
done in two steps. In the first step, a relatively lar a sample in the less
expensive %ariable, X in this case, was selected, and in the second step a
small sample in the other variable that is more expensive to be observed, Y,
was selected. This bivariate information permits the calibration of the
Information from, X.
When the correlation between X and Y is sufficiently large, a reduction in
the estimator variance and in the sample size is significant in comparison with
a single phase sampling design on Y alone.
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W POOR qJALM
Before applying the saaplinj design, the re on of study was redefined in
order to eliminate parts of it were sugar cane s not cultivated, and also to
eliminate some geographical . accident as well as some i:.coaplete marginal
segments.
The theoretical considerations of the sampplin methodapplied in this
-study are developed in'Cochran (1963), Loestsch ans Haller (1973) and Jessen
(1978), among other authors.
4. ANALYSIS AND ESTIMATION
The sample size in the two phases was set to achieve a sugar cane acreage
;SS
within S1 of the corresponding complete acreage evaluation with a
9 % confidence level at a minimum cost.
To calculate k and n, the number of segments in the first and second
phase, respectively, it was used cy and p calculated from the complete
enumeration of available ground truth data. When this information is not
availabl y:, it is necessary to select a pilot sample.
With the obtained values of k and n, it was simulated a sequence of one
hundred samples in two phases by means of a simple random selection in each
phase, being the second phase sample a simple random subsample from the first
one.
The simulation produced a sequence of values of the random variables YR9
estimate of the sugar cane acreage; V OR), variance of the estimate; and
.of D - TR - a, where a - 133888 Ha is the total number of hectares cultivated
with sugar cane from the ground truth complete enumeration. This value is
assumed without error.
Finally, the simulated data were analysed statistically.
S. RESULTS
a) The selected segment size in the unifnrmity trial was the one with
dimension 2x 3, corresponding to S.0 km x 7.S km - 37.50 km l or
3750 ha. The maximum correlation coefficient between X and Y was
r . .82 for this size, being r - .66 and .73 for segments of size
6.25 kma and 100.00' kma respectively.
b) The sampling frame, after being redefined (3 b), had 86 segments with
an area of 3082 ks 2 , 161 of them incomplete, but with an area greater
than one half of the complete one.
c) The standard deviation of Y was cy - 777.46 ha and the correlation
coefficient pxy - .82. The cost ratio considered cz:c= was 1:13,
where c l and cs are the unit cost of observing one Xi (in phase one)'
and one Yi' (in phase two), respectively. The sample sizes were
k • S8 and n - 11 for a relative variance of 51 with a confidence
level of 951 and a minimum cost of C - 201 monetary units. The
regression equation of ground truth and LANDSAT data was Y n 442 ..69X.
d) The results from the analysis of the simulated data were M (42) .
a 13288h ha (99.3% of the gro4und tru h value). SD YR) - 013 ha
(SDI - 1%). Range (Y ) - max r? - min Y a 29393 ha. 1 - M (YR) - a .
• -999 ha.. The confidence ;nterval for the su ar cane acres a at the
9S% level was (130963; 13e91S) z (.97.7%; 100.I%), 	 and for t e mean
difference wII at the 951 revel was (-3025; 1027).
b.
I4.
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ORMINAL PAGE 4
OF POOR QUALITY
The relative efficiency of the two phase design with respect to a
simple phase was 1571, what means a gain of 571 when LANDSAT data and
ground truth data are jointly used in a regression estimator. Finally,
the total acreage estimate from LANDSAT data only, with a sample of
size k • 58, was R . 140266 ha (104.81 of the ground truth value).
The 9S1 confidence interval was (138924; 141608) = (103.81; 105:8:).
The regression estimate has a tendency to underestimate the true
value, 99.31 of it, while using only LANDSAT data the estimate
represents 104.81. The estimation with aerial photograph data (ground
truth data in this study) is not being taker into consideration
because of high collecting cost. This is the main reason for
implementing a sampling design that minimizes the use of that type
of inforwation.
6. CONCLUSIONS
The samplingg design applied in this study shows the benefits, in cost and
precision, xelative to a complete inventory through a more expensive method
of data collecting like aerial photography.
The authors understand that these results are limited to a small region
like the one selected for this study. Besides that, much work has yet to be
.'doze in this sampling approach.
7. REFERENCES
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1
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Cochran, M.G. Sampling techniques. 2 ad. New York, Wiley, 1963. 413 p.
Federer, M.T. Experimental design, theory and application. New Delh-, Oxford,
1967. 544 p.
Jesson, R.J. Statistical survey techniques. New York, Wiley, 1978. *S20 p.
Koffler I N.F.- Chiarini, J.V. ;Gavalli, A.C.;Nogueita, F.P. Inventario canaviei
TO con auxilio de fotografias aereas — a Grande Regiio de Jau no ano safra
1979/80. 20): 1-22, ago. 1980.
Loestsch, F.; Haller, X.E. Forest inventory. 2 ed. BLV Verlags Gesellschaft
Munchen Bern Wien, 1973. 436 p.
monndonsa, F.J.; Lee, D.C.L.; Tardiu, A.T.; Shimabukuro, Y.E.; Chen. S.C.;
Lucht, L.A.M.; Moreira, N.A.; Lima, A.M.'—do; Haia, F.C.S. Levantamento do
area canavieira do Estado de Sao Paulo, utilizando dados do LANDSAT - ano
safra 1979/80. Sao Jose dos Campos, INPE, mar. 1981. (INPE-2021-RPE/288)
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Estimation of the sugar cane cultivated area from LANDSAT images using the two phase sampling method

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