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RELATIONSHIP BETWEEN THE SPECTRAL RESPONSE OF SUGAR CANE, BASED ON
AVHRR/NOAA SATELLITE IMAGES, AND THE CLIMATE CONDITION, IN THE STATE
OF SAO PAULO (BRAZIL), FROM 2001 TO 2008
R. R. V. Gonçalves, C. R. Nascimento,
Phd student at Feagri, State University of Campinas
CP 6011 - 13083-875 Campinas, Brazil
{renata, cristina}@cpa.unicamp.br
J. Zullo Jr.
Researcher at Cepagri, State University of Campinas
13083-970 Campinas, Brazil
jurandir@cpa.unicamp.br
L. A. S. Romani
Researcher at Embrapa Agriculture Informatics and Phd student at University of Sao Paulo
CP 668 - 13560-970 Sao Carlos, Brazil
luciana@cnptia.embrapa.br
The objective of this work was analyze the correlation between time series of an agroclimatic index
(WRSI) and the spectral response (NDVI) of sugar cane based on images of AVHRR/NOAA satellites, in
producing regions of the state of Sao Paulo (Brazil), from 2001 to 2008. The use of time series of
AVHRR/NOAA images having subsequent growing seasons improved the correlation between WRSI and
NDVI, when compared to analysis of individual crop seasons. These results can be very useful in
developing more accurate, objective, automatic and anticipated methods of harvest forecasting.
INTRODUCTION
Brazil has an important position in the world market of renewable fuels due to three main factors: a) Its
experience in the use of alcohol fuel for more than 35 years; b) Possibility of increasing the production in next years
based on the availability of new areas and agricultural technology, and c) Production distributed over the year,
mainly from March to November, strategic for global markets. The production is heavily concentrated in the state of
Sao Paulo, located in the southeast region of Brazil, contributing to more than 59% of national production, being
91.3% processed by the sugar-alcohol sector. The increasing world interest in the use of renewable fuels, such as
alcohol, emphasizes the importance of accurate estimates of sugar cane production to support the planning needed
from production to national and international markets.
The use of remote sensing data can improve the objectivity of harvest forecasting methods, both in estimation of
cultivated areas as productivity of crop fields, for the following main reasons: i) Variety of sensor systems currently
available, having the most different spatial, temporal, spectral and radiometric resolutions, suitable for use in
agricultural applications such as the harvest forecasting; ii) Experience of several Brazilian research groups in this
subject; iii) Reduction of costs to acquire and process satellite images.
Spectral vegetation indices are quantities calculated through the ratio, difference or other mathematical
operations, that are useful to monitor the plant development in regional and global scales since they are correlated to
characteristics such as: leaf area index (Prince, 1993), biomass (Justice & Hiernaux, 1986; Tucker, 1979), wet and
dry weight and percentage of vegetation cover (Senay & Elliot, 2002). Impacts of climate in production of
agricultural crops, such as sugar cane, can be assessed by agroclimatic indices since they use the main atmospheric
parameters simultaneously rather than each one at a time. WRSI (Water Requirement Satisfaction Index) is an
example of an index calculated thorough simulations of water balance during the whole cycle of an agricultural
crop.
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Considering the importance of accurate and anticipated estimates of sugar cane production, this work has the
main objective to assess the correlation between an agroclimatic index (WRSI) and a spectral index (NDVI) based
on time series of AVHRR/NOAA satellite images, in producing regions located in the state of Sao Paulo (Brazil),
from 2001 to 2008.
MATERIAL AND METHODS
Ten cities located in a producing area of sugar cane (the northeast region of the state of Sao Paulo, Brazil) were
chosen as test area: Araraquara, Araras, Jaboticabal, Jardinopolis, Jau, Luis Antonio, Pitangueiras, Pontal, Ribeirao
Preto and Sertaozinho. The state of Sao Paulo is located between the geographical coordinates 54°00’ and 43°30’ of
west longitude and 25°30’ and 19°30’ of south latitude.
Satellite images of NOAA-16 and NOAA-17 for seven crop seasons (from April, 2001 to March, 2008) were
obtained in a database available in the Center for Meteorological and Climatic Researches in Agriculture (Cepagri)
at the University of Campinas (Unicamp). These images were processed by the system NAVPRO according to the
following steps: format conversion, radiometric calibration, accurate geometric correction and generation of NDVI
data. NAVPRO is a processing system applied to AVHRR/NOAA images developed by researchers of Colorado
Center for Astrodynamics Research (CCAR) and implemented by Antunes (2005) and Esquerdo (2007). This system
is compatible with Linux platform, implemented in “Shell Script” and process AVHRR/NOAA images
automatically (Esquerdo et al., 2006).
Compositions of maximum value of NDVI (MVC) were calculated to minimize the existents atmospheric effects
daily images of AVHRR/NOAA satellites. The agroclimatic index WRSI (Water Requirement Satisfaction Index)
was calculated based on the water balance methodology proposed by Thornthwaite & Matter (1955) and adapted by
Camargo & Camargo (1983) to Brazil and Sao Paulo.
The analysis of multivariate time series of NDVI and WRSI was made by the software JMulti (Time Series
Analysis with Java), using the Vector Autoregressive (VAR) model based on the following principle: the Xt time
series of nx1 order follows an autoregressive vector model of order p, given by Eq. (1).
(1)
where, at ~ WN(0,∑), ø0 = (ø10, ...., øn0) is a nx1 vector of constants and øk are n x n constant matrices, having
elements ø(k)ij, i,j = 1,..., n, k = 1,..., p.
The autoregressive vector model relates the current values of time series (Xt) with its past values to the order p.
WN (White Noise) means that at is a random variable having mean equal to zero and variance ∑. The term at is
responsible for causing variability in the series. The methodology of Box-Jenkins was used to analyze each
individual component X1t e X2t (Box et al., 1994). This methodology is based on the hypothesis that the behavior of
a given time series may be mainly explained by information available in the time series. Thus, the ARMA (p,d,q)
models do not require, necessarily, other external variables to the time series and it is assumed that the past of a time
series has the most relevant information to explain its behavior by means of a set of components. The models
obtained with these tests were used for two main purposes: i) Assess the behavior and relationship along time
between values of NDVI and WRSI; b) Estimate values of NDVI and WRSI from April to December, 2007. Values
estimated by these models were compared to observed data in the same period.
RESULTS AND DISCUSSION
The tests performed showed significant correlations between agroclimatic data (represented by WRSI) and the
spectral response of sugar cane (described by values of NDVI). The best results obtained by analysis of correlation
between values of NDVI and WRSI were found when using the whole time series, that means, from 2001 to 2007.
Correlations between NDVI and WRSI were not significant when analyzing each year at a time, except in some
cases. These results emphasize the importance of using time series having subsequent years to develop models
applied to monitor the development of sugar cane fields.
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Results for Araraquara and Luis Antonio are described here, as an example. An autoregressive model of order 2
was fitted for Araraquara, based on AIC, BIC, HCQ and FPQ criteria of multivariate time series analysis.
Autocorrelations were significant for lags greater than 2, mainly for 3, 7 and 12, based on residual analysis. The
autoregressive model of ordem 7 was the best fit according to residual analysis among all models tested. The
bivariate fitted model is described by Eq. (2) and Eq. (3).
0.245
0.269
0.187
2
0.077
7
0.056
0.121
0.165
1
0.126
2
7
0.148
1
0.102
0.044
0.238
3
0.133
0.073
0.146
0.054
0.033
(2)
0.698 0.168
7
0.197
0.342
0.284
1
0.735
0.223
0.244
0.214
3
0.665
0.291
0.363
0.138
0.114
0.054
(3)
where Si(month) are seasonality indicators being Si(month) = 1 if month = i and Si(month) = 0 if month ≠ i for i =
January, February, ..., December.
This is a stationary process. NDVI was influenced by its own past values (lags 1, 2, 3 and 7) and past values of
WRSI (lags 1, 2, 3 and 7). WRSI was influenced by its past values (lag 1) and past values of NDVI (lags 3 and 7).
Residues did not have correlation structure according Portmanteau test and multivariate version of Box-LjungPierce statistics, with P-value = 0.9201 and P-value = 0.7527, respectively. The normality hipothesis of residues
were not refused by Bera and Jarque normality tests, with P-value = 0.5663 and P-value = 0.7204, from Eq. (2) and
Eq. (3), respectively.
Relative errors were lower than 20% (being 13% in eight of nine months analysed) to estimate NDVI, according
Table 1. The mean relative error was 9.43%. The mean relative error was 19.13% to estimate WRSI in nine months,
according to Table 2. These two values (9.43% and 19.13%) explain the distance between estimated and observed
lines in Figures 1 (closer) and 2 (distant). The largest difference in estimates of WRSI may have been caused by a
possible mismatch between periods of observation and prediction that was not precisely described by Eq. (3).
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Figure 1. Observed
O
and estimated
e
valuees of NDVI forr Araraquara.
Figure 2. Observed
O
and estimated
e
valuees of WRSI forr Araraquara.
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Table 1. Observed and estimated values, lower and upper limits of confidence interval and relative errors of NDVI
from April to December 2007 for Araraquara.
NDVI
Limits
Month
Errors (%)
Observed Estimated Lower Upper
April
0.6023
0.6107
0.5506 0.6708
1.4
May
0.6003
0.5963
0.5262 0.6663
0.7
June
0.5819
0.5239
0.4516 0.5962
10.0
July
0.5015
0.4579
0.3839 0.5320
8.7
August
0.4601
0.4108
0.3349 0.4866
10.7
September
0.4042
0.3254
0.2489 0.4020
19.5
October
0.3364
0.3065
0.2295 0.3835
8.9
November
0.4702
0.4089
0.3307 0.4870
13.0
December
0.5508
0.4847
0.4064 0.5629
12.0
Table 2. Observed and estimated values, lower and upper limits of confidence interval and relative errors of WRSI
from April to December 2007 for Araraquara
WRSI
Limits
Month
Errors (%)
Observed Estimated Lower Upper
April
0.8767
0.8607
0.6391 1.0822
1.8
May
0.8365
0.9085
0.6839 1.1331
8.6
June
0.8523
0.7307
0.5059 0.9554
14.3
July
0.8785
0.5998
0.3707 0.8288
31.7
August
0.7795
0.5363
0.3050 0.7676
30.3
September
0.4023
0.5192
0.2873 0.7511
29.0
October
0.4931
0.7087
0.4763 0.9411
43.5
November
0.9674
0.8514
0.6176 1.0852
12.0
December
0.9779
0.9686
0.7339 1.2032
0.9
An autoregressive model of order 3 was fitted for Luis Antonio, based on AIC, BIC, HCQ and FPQ criteria of
multivariate time series analysis. Autocorrelations were significant for lags greater than 3, mainly for 7, 10 and 12,
based on residual analysis. The autoregressive model of ordem 10 was the best fit according to residual analysis
among all models tested. The bivariate fitted model is described by Eq. (4) and Eq. (5).
0.383
0.068
0.306
0.041
1
0.110
3
0.147
9
0.034
0.029
0.092
1
0.041
4
9
0.073
0.322
0.042
0.324
2
0.112
4
10
0.052
(4)
0.282
0.622
1
0.355
7
0.406
0.831
3
0.249
10
0.185
0.248
0.152
3
0.286
(5)
where Si(month) are seasonality indicators being Si(month) = 1 if month = i and Si(month) = 0 if month ≠ i for i =
January, February, ..., December.
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July 28-30, 2009 Š Groton, Connecticut
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p
NDVII was influenceed by its own past
p values (laggs 1, 2, 4, 9 andd 10) and past values
v
This iss a stationary process.
of WRSI (lags 1, 3, 4 and
d 9). WRSI was
w influenced by its past valuues (lags 1 andd 3) and past values
v
of NDVI (lags
3, 7 and 100).
Residuues did not hav
ve correlation structure according Portmannteau test and multivariate
m
veersion of Box-L
LjungPierce statiistics, P-value = 0.6346 and P-value
P
= 0.32234, respectively. The normallity hipothesis of residues weere not
rejected byy Bera and Jarque normalityy tests, P-valuue = 0.2244 annd P-value = 0.4991,
0
from Eq.
E (4) and Eq. (5),
respectivelly.
Relativve errors weree lower than 155.1% in estimaates of NDVI, according Tabble 3. The meaan relative erroor was
7.69%. Thhe mean relativ
ve error was 20.27%
2
to estim
mate WRSI inn nine months,, according to Table 4. Thesse two
values (7.669% and 20.27
7%) explain thhe distance betw
ween estimated and observed lines in Figuures 3 (closer) and 4
(more distaant). The largeest difference inn estimates of WRSI may haave been causeed by a possiblle mismatch beetween
periods of observation an
nd prediction thhat was not preecisely describeed by Eq. (5).
Figure 3. Observed
O
and estimated
e
valuees of NDVI forr Luis Antonio.
Figure 4. Observed
O
and estimated
e
valuees of WRSI forr Luis Antonio.
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Table 3. Observed and estimated values, lower and upper limits of confidence interval and relative errors of NDVI
from April to December 2007 for Luis Antonio.
NDVI
Limits
Month
Errors (%)
Observed Estimated Lower Upper
April
0.6102
0.6471
0.5916 0.7026
6.1
May
0.6093
0.6263
0.5599 0.6927
2.8
June
0.5877
0.5703
0.4959 0.6448
3.0
July
0.5180
0.5392
0.4547 0.6237
4.1
August
0.4993
0.4238
0.3299 0.5176
15.1
September
0.4297
0.3827
0.2836 0.4818
11.0
October
0.3496
0.3419
0.2387 0.4451
2.2
November
0.4886
0.4389
0.3329 0.5450
10.2
December
0.5713
0.4863
0.3786 0.5939
14.9
Table 4. Observed and estimated values, lower and upper limits of confidence interval and relative errors of WRSI
from April to December 2007 for Luis Antonio.
NDVI
Limits
Month
Errors (%)
Observed Estimated Lower Upper
April
0.8767
0.9161
0.6796 1.1526
4.5
May
0.8365
0.9197
0.6740 1.1654
9.9
June
0.8523
0.7293
0.4828 0.9757
14.4
July
0.8785
0.6153
0.3622 0.8684
30.0
August
0.7696
0.4540
0.1974 0.7105
41.0
September
0.4023
0.4856
0.2275 0.7437
20.7
October
0.4939
0.7001
0.4397 0.9605
41.8
November
0.9674
0.7917
0.5290 1.0544
18.2
December
0.9778
0.9582
0.6950 1.2213
2.0
CONCLUSION
It was possible to estimate the NDVI (that is, the spectral response of sugar cane) and the WRSI (that is, the
agroclimatic conditions related to sugar cane production) in the future (from April to December 2007) using past
values (2001 to 2007) of these indices for ten cities located in the state of Sao Paulo. The models developed can be
used to monitor the development of sugar cane in an objective and systematic way using data acquired by remote
sensors and weather stations, being useful for agricultural planning at regional scale.
ACKNOWLEDGMENTS
To Fapesp (State of Sao Paulo Research Foundation) by financial support.
To Cepagri/Unicamp (Center of Meteorological and Climatic Researches Applied to Agriculture - University of
Campinas) by AVHRR/NOAA satellite images.
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MultiTemp 2009 - The Fifth International Workshop on the Analysis of Multi-temporal Remote Sensing Images
July 28-30, 2009 Š Groton, Connecticut