Agnes Begue
email: agnes.begue@cirad.fr

Valentine Lebourgeois

Eric Bappel

Pierre Todoroff

Anne Pellegrino

Florence Baillarin

Bernard Siegmund

A Bèguè

Spatio-temporal variability of

Keywords: spatial variability, time series, NDVI, Sugarcane, Spatio-temporal, Crop management, Yield, Production, LAI, sucrose

and research institutions in France or abroad, or from public or private research centers.

Introduction

The main advantage of satellite or aerial imagery over traditional systems is that it provides objective and spatially explicit observations of crop productivity over large areas. Crop yield estimation has been studied by the remote sensing community for many years now (e.g. [START_REF] Pinter | Remote Sensing for Crop Management[END_REF][START_REF] Lamb | The use of qualitative airborne multispectral imaging for managing agricultural crops -a case study in south-eastern Australia[END_REF], especially for cereals, which are major food crops.

Unlike other gramineous crops, estimation of sugar cane yield has been the subject of little remote sensing-oriented research, despite the worldwide importance of the crop with 20 million hectares harvested every year [START_REF] Fao | FAOSTAT[END_REF]. The few studies that have dealt with sugarcane were largely inspired by what was being done for cereal crops. Direct approaches that link crop biomass to multispectral measurements or vegetation indices were developed from field radiometry (Simoes et al. 2005a), aircraft measurements [START_REF] Schmidt | Application of remote sensing technology in the South African sugar industry : Review of recent research findings[END_REF], high resolution satellite images [START_REF] Almeida | ASTER and Landsat ETM+ images applied to sugarcane yield forecast[END_REF][START_REF] Ueno | Combined applications of NIR, RS and GIS for sustainable sugarcane production[END_REF][START_REF] Rao | Remote sensing : A technology for assessment of sugarcane crop acreage and yield[END_REF], and low resolution satellite images [START_REF] Bastidas-Obando | Evaluating the applicability of MODIS data for forecasting sugarcane yields in Colombia[END_REF][START_REF] Schmidt | Application of remote sensing technology in the South African sugar industry : Review of recent research findings[END_REF]. Other indirect approaches that combine multispectral data with agrometerological, production or ecophysiological crop growth models [START_REF] Rudorff | Yield estimation of sugarcane based on agrometeorologicalspectral models[END_REF][START_REF] Bastiaanssen | A new crop yield forecasting model based on satellite measurements applied across the Indus Basin, Pakistan[END_REF][START_REF] Bappel | Assimilation in a sugarcane yield forecasting model of biophysical parameter estimated by remote sensing using SPOT4&5 data[END_REF] have also been explored. However, research in this field is still young and few experiments have been conducted, so it is difficult to draw conclusions about the reliability and possible generalization of results. Furthermore, except for [START_REF] Bastiaanssen | A new crop yield forecasting model based on satellite measurements applied across the Indus Basin, Pakistan[END_REF], who used a rough harvest index, none of these studies estimated sucrose yield.

Although remote sensing is potentially very useful for sugarcane (see review by [START_REF] Bèguè | The application of remote sensing technqiues to sugarcane (Saccharum spp. hybrid) production: a review of the literature[END_REF], Simoes et al. (2005a) linked the paucity of publications of experimental results to the difficulty in collecting data for a large crop and to the length of the growing period. [START_REF] Almeida | ASTER and Landsat ETM+ images applied to sugarcane yield forecast[END_REF] reported that predictions of sugarcane yield using remote sensing are rarely discussed in the specialized literature owing to the proprietary nature of past work, which has mainly been conducted by sugarcane industry research institutes. In addition, we believe that the length of the harvest season, the lack of direct links between sugar yield and crop radiometry, and the uncertainty of the growth models [START_REF] Promburom | Estimating sugarcane yields with Oy-Thai interface[END_REF], Inman-Bamber et al. 2005b) are largely responsible for the difficulties involved in using remote-sensing data to forecast sugarcane yield.

-The length of the harvest season (4-12 months) means ratoon crops start their growth in a wide range of different conditions even in the same location (Inman-Bamber et al. 2005b), resulting in very high spatio-temporal variability at the field scale. Only fine time series of images with decametric resolution enable this variability to be captured at the scale at which it appears. -The lack of direct links between radiometry and sugar yield cannot be easily compensated by the use of growth models. Sugarcane is for the most part indeterminate and sucrose is accumulated in a vegetative organ that is harvested over an extended period of the year (Inman-Bamber et al. 2005a, Inman-Bamber et al. 2005b). Consequently, forecasting sugarcane yield is harder than for most other crops that accumulate the product of value in sexual reproductive organs under relatively predictable patterns of development.

-Finally, it is very difficult to use sugarcane growth models to simulate extreme situation due to the lack of basic physiological information available (Inman-Bamber et al. 2005b) as well as to difficulties in calibrating the model at the field or farm scale [START_REF] Promburom | Estimating sugarcane yields with Oy-Thai interface[END_REF]. Considering the particularities of sugarcane physiology and cultivation, the objectives of this study were to 1. characterize and understand the spatio-temporal variability of the sugarcane crop by analyzing the effects of management practices and climate on the spectral properties of sugarcane over time, and 2. use the results of our analysis and ground measurements made during the experiment to draw conclusions and make recommendations concerning direct remote sensing methods to forecast the sucrose yield (product of biomass and sucrose fraction). To do this, we used NDVI time series of SPOT4 and SPOT5 images acquired monthly over a 2-year period over Guadeloupe and Reunion Islands.

Sugarcane -background information

Sugarcane (Saccharum officinarum L.) is a semi-perennial tall grass in the Poaceae, whose stalk sap is rich in sugar. It is a tropical crop which grows between latitude 35°N and latitude 30°S. The ideal climate for sugarcane is a long, warm growing season and a fairly dry, sunny, cool, but frost-free ripening and harvest season [START_REF] Humbert | The Growing of Sugarcane[END_REF]).

The growth of sugarcane is characterized by three development stages: sprouting and tillering, stalk growth, and maturation. The maturation is triggered by a decrease in soil water content, in temperature, and in nitrogen availability and is characterized by the end of stalk growth and modifications in the stalks and leaves; sucrose accumulates and chlorophyll, leaf water content and turgor decline [START_REF] Hsiao | Plant responses to water stress[END_REF]. We are hypothesizing an inverse correlation between sucrose content and chlorophyll content can be used to estimate yield by remote sensing.

Sugarcane stem cuttings are used as planting material. After 18 and 24 months, the sugarcane is cut and harvested; buds on the underground stubble that remains germinate again and give rise to another crop. This is called the ratoon crop which is harvested at about 12-month intervals for four years or more, before the crop is renewed due to decreasing yield. The crop is harvested when it has fully matured and ripened. Early varieties and ratoon crops are the first to be harvested either mechanically (usually green) or by hand (either burnt or green). The harvest season generally lasts several months; the exact time of harvest depends on the tonnage of cane to be processed, the capacity of the mills, and the climate (there is no harvest during the rainy season).

Data acquisition

Study sites

The experimental sites are located in two French overseas territories -Guadeloupe (16° 17' N; 61° 25' W) in the French West Indies, and Reunion Island (21° 07' S; 55° 31' E) in the southern Indian Ocean -and represent a wide range of agronomic, climatic and socio-economic conditions. On these islands, most growers are smallholders, and the mean size of the sugarcane fields is about 0.9 ha. Sugarcane harvest is done during the dry season, and lasts from February to July in the northern hemisphere, and from July to December in the southern hemisphere.

In Guadeloupe, sugarcane covers about 14 300 ha (Source: Agriculture and Forestry Office, 2006). Sugar production is generally low (~ 60 t ha -1 ), mainly because most crops are rainfed and large areas are frequently subjected to water stress. Image analysis and ground experiments in Guadeloupe were carried out on the Gardel estate site, which covers about 1 000 ha and is run by the only planter-miller on the island. Recorded rainfall on the Gardel estate was respectively 1185 mm and 1905 mm in the 2002-03 and 2003-04 growing seasons (recorded between June and May) for an average annual rainfall of 1325 mm during the period 1977-2000.

In Reunion, 25 500 ha of sugarcane are cultivated along the coast (Source: Agriculture and Forestry Office, 2006). In the wet north-eastern part of the island, where most of our field experiments were conducted, sugarcane is rainfed but production is generally high (~ 90 t ha -1 ). In meteorological stations located close to our field experiment, recorded rainfall was respectively 2028 mm, 1697 mm, and 1626 mm in the 2002, 2003, and 2004 growing seasons (recorded between January and December).

Geospatial data acquisition

3.2.1 Satellite images. At each study site, image time series were acquired using SPOT4 and SPOT5 satellites. The most complete time series was available for the Reunion Island site, with 25 images acquired between May 2002 andNovember 2004 (Appendix A). This time series belongs to the ISLE-Reunion data base set up by CNES [START_REF] De Boissezon | Reference remote sensing data bases: temporal series of calibrated and orthorectified satellite images for scientific use[END_REF]. For the Guadeloupe site, the image time series comprised 17 images acquired between September 2002 and May 2004 (Appendix B). The images in both time series were as evenly spaced as possible, depending on the cloud cover.

The four spectral bands on SPOT4 and SPOT5 are Green (G: 0.50 -0.59 µm), Red (R: 0.61 -0.68 µm), Near Infrared (NIR: 0.78 -0.89 µm) and Shortwave Infrared (SWIR: 1.58 -1.75 µm). SPOT4 images are acquired at a resolution of 20 m , and SPOT5 images at a resolution of 10 m (except the SWIR band which is 20 m). In addition, a 2.5 m resolution multispectral image (Supermode®) was acquired every year over Reunion Island. All the images were acquired in raw format (level 1a) with no geometric pre-processing.

Digital Elevation Models.

In order to apply accurate geometric correction to the satellite images, we used a Digital Elevation Model (DEM) at a resolution of 25 m in x and y purchased for Reunion Island (TOPO® DB, IGN). In Guadeloupe, a 10 m resolution DEM was processed from aerial photos ordered by the French Ministry of Agriculture.

Cane field boundaries.

Since 2002, data concerning the expansion and localization of sugarcane fields in Guadeloupe and Reunion has been recorded and updated annually by the Agriculture and Forestry Office in conformity with the European Union Common Agricultural Policy (CAP). Based on farmers' declarations, the boundaries of agricultural fields are digitized on 0.5 m resolution aerial ortho-photographs (ORTHO® DB, IGN) acquired every five years. On Reunion Island, farmers only declare blocks of plots. To supplement this block database, a map of field boundaries is produced regularly by photo-interpretation of a SPOT5 image acquired at a resolution of 2.5 m [START_REF] Lebourgeois | Improving sugarcane harvest and planting monitoring for smallholders with geospatial technology: the Reunion Island experience[END_REF]. This is less accurate than using aerial photographs but enables annual updating, which is necessary for a crop like sugarcane with a high rotation rate in a region with highly dynamic land use.

Agronomic data acquisition

In 2002 and 2003, different sets of ground measurements were collected at the experimental sites to characterize the structure and biochemical composition of sugarcane canopies. The measurements were averaged at the field scale so they could later be related to SPOT spectral data. 1. The Leaf Area Index (LAI) was estimated on twenty ratoon fields sampled in irrigated and rainfed areas in Reunion only. The measurements were repeated two or three times during the crop season. For not fully developed cane canopies, LAI was calculated using allometric functions, by measuring the stalk height from the soil to the last ligule, along a 3-m segment of one row in each field (Martiné 2003). For closed canopies, LAI was measured with a Licor LAI-2000 sensor. Both measurements were compared and intercalibrated. 2. The nitrogen and water conditions of the plants were estimated by measuring the greenness of plant leaves. Relative greenness was measured throughout the sugarcane cycle in sampled fields in Reunion and Guadeloupe using a handheld chlorophyll meter (SPAD-502, Konica Minolta). In each field, three SPAD measurements were made on the upper side of the third leaf of 30 plants. 3. The sugar content of cane juice was measured with a handheld refractometer (BRIX ATC-1, Atago). The refractometer measures the total soluble solid content of the juice; the BRIX scale, calibrated to the number of grams of sugar contained in 100 g of water, enables direct reading of stalk sugar content (%).

At the experimental sites in Reunion and Guadeloupe, BRIX measurements were taken on five primary canes per sampled field during the maturation stage. Each cane was sampled at the bottom, middle and top, and the three values were then averaged. To supplement the ground measurements, we collected field information (plantation date, harvest date, variety) and yield data (fresh biomass and sugar content) from the agronomic databases of the Gardel estate and from cane growers in Reunion.

Methods

Image pre-processing

SPOT images were orthorectified using the geometric SPOT model provided by ERDAS IMAGINE™ software. For the process, we used the DEM and 30 control points scattered over both scenes. The control points were extracted from aerial ortho-photographs (ORTHO® DB, IGN). The SPOT images co-registration accuracy was better than one pixel As we used image time series, the digital counts needed to be converted into reflectances. To do this, we used the following equation:

S S E G DC ) cos(θ π ρ = Equation 1
where ρ is the TOA (Top Of Atmosphere) reflectance, DC is the digital count, G is the sensor absolute calibration gain (provided in the metadata associated with the image), θ S is the solar zenith angle and E S is the solar radiation in the appropriate wavelength. In mountainous terrain, such as on Reunion Island, additional radiometric corrections are necessary to take into account the variation in incident radiation due to the surface slope and aspect [START_REF] Richter | Correction of satellite imagery over mountainous terrain[END_REF]. In this case, the illumination angle β s replaces θ S in Eq. 1:

) cos( ) sin( ) sin( ) cos( ) cos( ) cos( n S n S n S S ϕ ϕ θ θ θ θ β - + = Equation 2
where θ n is the surface zenith angle (slope), ϕ S is the solar azimuth angle and ϕ n the surface azimuth angle (aspect).

Despite the radiometric calibration of each image, some effects due to the atmosphere composition or the sun-view configuration still interfered with the radiometry of the surface. To limit these effects, we normalized the reflectance values in each image using invariant targets [START_REF] El Hajj | Relative radiometric normalization and atmospheric correction of a SPOT 5 time series[END_REF] and we based our analysis on the NDVI (Normalized Difference Vegetation Index) values. On the areas of interest, the clouds and cloud shadows were masked by photo interpretation.

NDVI-based indicators

The study was conducted using NDVI time series of SPOT4 and SPOT5 images. All calculations and analysis were done at the field scale, which is the scale of the cropping operation and the scale of the variability.

Using the time series of satellite images, we calculated common NDVI-based indicators (e.g. [START_REF] Tucker | Red and photographic infrared linear combinations for monitoring vegetation[END_REF][START_REF] Prince | Satellite remote sensing of rangelands in Botswana[END_REF][START_REF] Du Plessis | Linear regression relationships between NDVI, vegetation and rainfall in Etosha National Park, Namibia[END_REF]: the maximum NDVI and the integrated NDVI over the growing period. The calculation was done after modeling the NDVI values through time.

For all image acquisition dates, we first computed the mean NDVI for each polygon field eroded by one pixel to minimise residual misregistration errors. The NDVI model was made using these field NDVI values.

For each field, two continuous logistic functions were used to represent the crop growth phase G(t) and the senescence phase S(t) [START_REF] Clevers | Using SPOT data calibrating a wheat growth model under mediterranean conditions[END_REF] (Figure 1):

[ ] { } [ ] { } ) ( ) ( 1 / ) ( 1 / ) ( ) ( ) ( ) ( ts t b ti t a e M t S e M t G t S t G t NDVI - - - - + = + = - = Equation 3
where t is the number of days since the last harvest, M is the maximum value of the logistic curves, a and b are the slopes at the inflexion points of the G and S functions, and ti and ts are time values at these inflexion points. These parameters were obtained by non-linear fitting, minimizing the residual sum of squares. At t = 0 (date of the previous harvest), an initial value for NDVI was set equal to the value of sugarcane field residues calculated from SPOT images acquired within two weeks after the harvest (0.168 and 0.226 for Guadeloupe and Reunion respectively). Once the NDVI was modeled for each field, the maximum value and the integrated NDVI value over the growing period (between two harvests) were calculated. Ratoon NDVI reflects the phenology of the crop [START_REF] Gers | Remotely sensed sugarcane phenological characteristics at Umfolozi, South Africa[END_REF] and can be split into: -A growth phase: After harvest, the soil is covered with crop residues and the value of the NDVI is low, between 0.15 and 0.2, depending on the amount of residues (Figure 2). The NDVI then increases rapidly as the vegetation regrows and, after four to six months, reaches the maximum value (between 0.7 and 0.8) typical of a fully developed dense green canopy. The length of the growing period depends on the climatic conditions after the harvest. In the case of crops harvested early in winter (around June in Reunion, and February in Guadeloupe), sugarcane grows slowly due to low temperatures and low rainfall; the crop canopy needs about six months to reach full cover. When the crop is harvested in summer (around December in Reunion, and July in Guadeloupe), crop growth is faster due to high temperatures and higher rainfall; in these conditions the crop canopy reaches full cover in about four months. -The maturation phase: When there is no water stress (e.g. in Reunion), the NDVI remains stable during the maturation phase, and remains and right up to harvest (Figure 2a). In cases of severe water stress (in Guadeloupe in [2002][2003], NDVI can decrease all the way down to 0.25 (Figure 2b) due to the senescence of the leaves. In such extreme cases, a senescent standing cane and crop residues on the surface of the soil have similar NDVIs and consequently cannot be satisfactorily distinguished using NDVI alone. Only the use of an additional spectral band, such as the short wave infrared band, can help avoid confusing the two surface conditions [START_REF] Lebourgeois | Improving sugarcane harvest and planting monitoring for smallholders with geospatial technology: the Reunion Island experience[END_REF].

Results and discussion

Spatio-temporal variability of sugarcane NDVI

Planted sugarcane crops grow more slowly than ratoon crops. When the field is ploughed before planting, it takes between 10 months (in normal water conditions, Figure 2a) and 16 months (in stressed conditions, Figure 2b) for the NDVI to increase from the value of bare soil (between 0.10 and 0.15) to its maximum (between 0.7 and 0.8). This additional time (compared to ratoon crops) is due to the fact that a plant crop has fewer buds available to produce primary shoots and the buds are located deeper in the soil than in the ratoon crop [START_REF] Thompson | Comparison of the growth of a plant and a first ratoon crops at Pongola[END_REF]. 5.1.2 Spatial variability of sugarcane NDVI at the farm or regional scale. The main driving factor of the spatial variability of sugarcane at the farm or regional scale is cropping practices. However, in Reunion and Guadeloupe, one can observe synchronized development of the sugarcane fields at the regional scale, at the beginning of the dry season before the harvest period.

The length of the harvest and planting seasons, and the resulting time lag in sugarcane phenology at the scale of the individual field, are responsible for the high spatial variability in the spectral properties of the cropped area. This variability is illustrated by a boxplot representation of NDVI over the course of the growing season (Figure 3). Such inter-field variability has been reported by many authors, for example [START_REF] Xavier | Multi-temporal analysis of MODIS data to classify sugarcane crop[END_REF], who had difficulty selecting homogeneous samples from the MODIS time series suitable for supervised classification of the cane cropped area in Brazil. However, at our study sites, climatic factors such as rain and temperature play the role of regulators, resulting in synchronization of the vegetative growth of the ratoon crops with a NDVI peak and minimal inter-field variability at the end of the rainy season (Figure 3) about two months before the harvest season (around May in Reunion, and December in Guadeloupe). At this vegetation peak, the new plantations are still at an early stage of development and appear as outliers in the boxplot representation (Figure 3a,b).

In conclusion, during the pre-harvest period, ratoon NDVI is maximal, inter-ratoon-field variability is minimal, and the sugarcane fields are comparable in terms of vegetative development with a completely closed canopy. However, in regions with a longer harvest season (> 8 months) or a different harvest calendar, such synchronization of plantation growth should not occur, as a crop harvested late would not have the physiological time necessary to reach full development before the following harvest.

Relationships between NDVI and crop variables

It is well known that the main driving factors of variations in the NDVI are the amount of vegetation (generally expressed by LAI) and the color of the leaves. Using our experimental data set, we studied the links between these two variables and the NDVI for sugarcane ratoons. To do this, we split our experimental data set into two data sets, one corresponding to the growing phase and the other corresponding to the maturation phase. We confirmed that, during the growing stage, variations in the NDVI were mainly explained by variations in the LAI, and that, during the maturation phase, variations in the NDVI were mainly explained by changes in the color of the leaves. The transition period between these two stages corresponded to the maximum NDVI.

Relationship between NDVI and LAI.

In Reunion, the range in measured LAI values was particular wide (from 0.1 to 7), and enabled us to build a field-scale relationship between the NDVI derived from SPOT images and the measured LAI (Figure 4). This relationship was only established for data acquired during the growth phase of the crop (before and during the period of maximum NDVI), and is consequently only valid for green LAI:

NDVI LAI 9336 . 7 exp 0211 . 0 = Equation 4
As expected, the relationship between NDVI and LAI at field-scale was strong (r² = 0.94), exponential and began to saturate for LAI values above 3. The RMSE was 0.98, which could be related to (a) the imprecision of the LAI estimation caused by the field sampling techniques, and (b) sun-view configuration noises affecting the satellite radiometric signal. This relationship was strong (r² = 0.79) and valid for a large range of SPAD values, from 10 to 40. Values of 40 corresponded to very green leaves (irrigated, healthy canopy) while SPAD values of 10 corresponded to senescent leaves.

During the maturation stage, the leaves are more or less senescent and generally turn yellowish due to degradation of the chlorophyll. This change in color has an impact on reflectances in the visible bands, leading to a decrease in NDVI values. Equation 5 is valid when spectral variations in the canopy can be linked only to variations in leaf color. This assumes that the vegetation canopy is fully developed (no soil visible) and that the structure of the canopy is not modified by any other factors.

Use of NDVI-based indicator for yield forecast

As mentioned above, NDVI could be related to the LAI during the growth stage, and to the color of the leaves during the maturation stage. The LAI is known to be linked to one yield component, cane biomass (e.g. Simoes et al. 2005b); we assumed and confirmed in this study that the color of the leaves can be linked to the other yield component, sugar content. Based on these assumptions and observations, in the following section, we describe the relationships we obtained between sugarcane yield components and NDVI-based indicators.

5.3.1

Relationship between NDVI and cane yield. SPOT time series acquired during the cropping season in Reunion and Guadeloupe were used to derive regressions between cane yield (biomass) measured at the field scale and 1. the maximum NDVI, and 2. the time integral of NDVI (Figure 1), for a large set of sugarcane ratoon fields. Our results show that maximum NDVI and integrated NDVI methods gave comparable RMSE at the field-scale, i.e. 13.2 t/ha and 15 t/ha respectively (Figure 6). As mentioned above, at our sites, the maximum NDVI is reached about two months before harvest begins. At this time, at the end of stalk growth, the yield tendencies of the crop are already established, and the NDVI can be a good indicator of biomass as shown in Figure 6a. This result is in agreement with results of [START_REF] Rudorff | Yield estimation of sugarcane based on agrometeorologicalspectral models[END_REF] and [START_REF] Ueno | Combined applications of NIR, RS and GIS for sustainable sugarcane production[END_REF] who concluded that the best acquisition period of satellite images for the assessment of sugarcane yield is about two months preceding the beginning of harvest. [START_REF] Almeida | ASTER and Landsat ETM+ images applied to sugarcane yield forecast[END_REF] recommended deriving the NDVI-yield relationship at 8-10 months of growth, which is also consistent with our observations. Not using this period could explain the bad results obtained by some authors who related the NDVI or spectral reflectances to yield without questioning the image acquisition dates in their specific agronomic context [START_REF] Kirchner | Limitations of Landsat TM data in monitoring growth and predicting yields in sugarcane[END_REF][START_REF] Schmidt | Application of remote sensing technology in the South African sugar industry : Review of recent research findings[END_REF]. In theory, with a single observation, the reliability of imagery as a means of estimating final yields decreases the earlier the image is taken before harvest because there are more opportunities for factors, such as drought or nutrient deficiency, to influence yield. However, the advantage of the maximum NDVI method is that it can be used with only a few images, even a single image may suffice if it is acquired about two months before the beginning of the harvest season when the growth of different cane fields has reached maximum (Figure 3). However, the relationship is not linear and may not be accurate for high yields due to NDVI saturation.

The integrated NDVI method provides linear regressions with yield (Figure 6b) with is an important feature. However, it is more difficult to implement as it requires a larger number of inter-calibrated images acquired throughout the growing season, along with a good approximation of the harvest dates for each field (which is only possible for large estates, where cropping operations are recorded). Generally, the relationship between integrated NDVI and yield depends on the variety and on environmental conditions [START_REF] Bastidas-Obando | Evaluating the applicability of MODIS data for forecasting sugarcane yields in Colombia[END_REF]. We thus recommend that this approach be used in combination with field measurements to calibrate the regressions. 5.3.2 Relationship between NDVI and sugar content. Our results showed that during the maturation phase (during and after the period of maximum NDVI), a relationship exists between the NDVI derived from SPOT images and BRIX values measured in the field (Figure 7). This relation, which was established from the Guadeloupe and Reunion 2002-2003 data sets, was rather linear between BRIX [12%-25%] and NDVI [0.4-0.7]; below an NDVI value of 0.4, the variations in the NDVI did not correspond to variations in BRIX values that stay constant around 25%. Globally the relation was good with r² = 0.75 and RMSE = 1.87%.

As mentioned above, during the maturation stage the leaves are senescing, the chlorophyll is degraded and the leaves turn yellowish. Generally, leaf senescence corresponds to water loss in the plant and, consequently, to an increase in the sugar content of the stalk juice. The link between extended drying-off periods and enhanced sucrose content has often been demonstrated experimentally (Inman-Bamber et al. 2005a). However, this relationship is valid when the spectral variations of the canopy can be linked only to variations in the color of the leaves. This assumes that the vegetation canopy is fully developed (no soil visible) and that the structure of the canopy is not modified by any other factors.

Conclusions

Until recently, remote sensing was less often used for sugarcane than for other gramineous crops mainly because sugarcane cycles are highly variable in time and space, and consequently difficult to capture on, and interpret from, single satellite images. Based on two examples in Reunion and Guadeloupe, and thanks to a large time series of high-resolution SPOT images, we were able to show that the variability was the result of the interaction between the sugarcane crop calendar (which is spread out over a period of several months), the phenology of the plant, and the climate. We linked these variations to crop variable dynamics, in particular LAI and leaf color, in order to derive a simple NDVI-based indicator of sugar yield (cane yield and sugar content). Our main finding is that understanding sugarcane physiology and cultural practices is crucial if remote sensing applications are to succeed in yield predictions. We wish to emphasize the importance of identifying the period in which the NDVI was acquired before interpreting and analyzing images.

In conclusion, the results obtained in this study should facilitate the assessment of satellite remote sensing for sugarcane yield forecast. The arrival of a new generation of high resolution satellites with a high capacity of revisit will surely help to develop remote sensing applications for sugarcane management.

Appendix A: List of SPOT images acquired over the Reunion site (KALIDEOS ISLE-Reunion).

Acquisition Date

Satellite Mode (a) Incidence angle (b) 24.9 (a) J is the SPOT5 multispectral mode (10 m resolution); THX is the pan-sharpened mode (2.5 m resolution) of SPOT5 multispectral images; PXI is the pan-sharpened mode (10 m) of SPOT4 multispectral images. (b) Right incident angle is negative, left is positive.

Figure 1 .

 1 Figure 1. Example of temporal profile of NDVI measured with SPOT satellites over a sugarcane field in Guadeloupe. The points correspond to SPOT measurements acquired on different dates, and the curve is a fitted logistic-based function (see text). The maximum and time-integral of the fitted function are given.

  Temporal variability of sugarcane NDVI at the field scale. The time variations in sugarcane fieldbased NDVI were shown to be mainly related to the phenology of the crop and to climatic conditions. The examples given in Figure 2 are typical of the time variations in field-based NDVI in wet rainfed conditions (Reunion) and in dry rainfed conditions (Guadeloupe).

Figure 2 .

 2 Figure 2. Time series of SPOT NDVI illustrating the sugarcane crop cycles of three fields in (a) a rainfed area with no water stress on Reunion Island, and (b) a rainfed area with limited water in Guadeloupe (Gardel). The shaded areas correspond to the harvest seasons. The dotted lines represent the harvest.

Figure 3 .

 3 Figure 3. Box plot of SPOT NDVI of rainfed sugarcane fields over time (a) ratoons and plantations under wet conditions in Reunion, (b) ratoons and plantations under dry conditions in Guadeloupe, (c) ratoons only in Reunion, (d) ratoons only in Guadeloupe. The shaded areas correspond to the harvest seasons.

Figure 4 .

 4 Figure 4. Relationship between LAI measurements and SPOT NDVI calculated at the field scale for the Reunion data set. For each field, only the NDVI values acquired before or during the maximum NDVI were selected.

Figure 5 .

 5 Figure 5. Relationship between SPAD measurements and SPOT NDVI calculated at the field scale for the Reunion (open symbols) and Guadeloupe (solid symbols) data sets. For each field, only the NDVI values acquired during or after the maximum NDVI were selected.

Figure 6 .

 6 Figure 6. Regressions between ratoon field yields in Guadeloupe (solid symbols) and Reunion (open symbols), and SPOT NDVI indicators: (a) NDVI maximum (see text) and (b) NDVI time integral (see text).

Figure 7 .

 7 Figure 7. Relationship between BRIX values measured on sugarcane ratoon fields in Guadeloupe (solid symbols) and Reunion (open symbols) and field NDVI calculated from SPOT images. For each field, only the NDVI values acquired during or after the maximum NDVI were selected.

Acknowledgments

o Most of the results presented here come from the SUCRETTE project funded by the French Ministry of Research through the Earth and Space Program (RTE). o CNES (Centre National d'Etudes Spatiales), in particular to Hélène De Boissezon, for access to the ISLE-REUNION KALIDEOS data base which is a satellite image reference database developed for scientific studies.

o Many thanks to the students who participated in the data collection and processing, namely Marie Guitton, Stéphanie Catsidonis, and Yann Buchon.

Appendix B: List of SPOT images acquired over the Guadeloupe site.

Acquisition Date

Satellite Mode (a) Incidence Angle (b) (a) J is the SPOT5 multispectral mode (10 m resolution); XI is the SPOT4 multispectral mode (20 m resolution). (b) Right incident angle is negative, left is positive.


Valentine Lebourgeois
email: valentine.lebourgeois@cirad.fr

Agnès Begue
email: agnes.begue@cirad.fr

Pascal Degenne
email: pascal.degenne@cirad.fr

Eric Bappel
email: eric.bappel@teledetection.fr

Improving harvest and planting monitoring for smallholders with geospatial technology: the Reunion Island experience

With the recent development of geospatial technologies, remote sensing data are more and more integrated in the information systems of crop industries. The satellite's ability to collect "snapshots" over large cropped areas at once makes it a unique tool able to acquire localized and objective data in real-time.

In this paper, we present how this technology can provide reliable information for sugarcane planting and harvest monitoring by updating information on field/blocks boundaries and cane status using time series of satellite images. Through the experience conducted on Reunion Island (Indian Ocean) where the sugar industry has difficulty collecting updated localized information on smallholders fields, we show how SPOT satellite images can be interpreted and processed in order to produce thematic maps and statistics. These maps can then be integrated in a Geographic Information System (GIS) designed for decision makers. This on-the-shelf GIS permits one to visualize maps and edit monthly statistics of the management practices in each production area.

Introduction

Sugarcane on Reunion Island

Reunion Island is an overseas department of France situated in the Southern Indian Ocean, about 700 km east of Madagascar. The island is mostly rugged and mountainous, with fertile lowlands along the coast cultivated mainly with sugarcane (60% of the cropped area). Sugarcane covers 26,000 hectares (Figure 1; Source: DDAF 2005), cultivated by 4,200 smallholder growers supplying two mills: Bois Rouge (Sucreries de Bois Rouge) and Le Gol (Sucrière de La Réunion). The harvest season is from July to December.

Needs of the sugarcane industry considering cane fields status

As for other regions in the world, where sugarcane is cultivated by smallholder growers, data on the extension of the cropped area and crop status are not always recorded and centralized, and the sugar industry has difficulty obtaining updated localized information on the cane fields/blocks boundaries and status. In Reunion, the yield and sugar content are measured when the cane is delivered to the mill and the name of the farmer is consigned. However, no information is given on the field provenance of the cane, making it impossible during harvest season to keep track of progress in terms of area harvested.

A collection of updated and extensive information on the cane fields/blocks over the whole area serviced by the mill may help to optimize the activities of the sugar industry. In addition to yield forecast, the principal need expressed by the industry is information on the harvest progress throughout the harvesting season. This information could be used to improve efficiency in both factory and field, in particular through:

• a better estimation of the effective yield (via the ratio between the cumulative cane biomass delivered to the mill and the cumulative harvested cane area over the same period);

• a better assessment of the standing cane area still to be harvested, in order to optimize cutters deployment and transport operations (harvest rate of the different areas serviced by the mill);

• support to update information on the field boundaries and status in the mill/institution databases.

Another need expressed by the industry is information on the planted area. Maps of the planted fields, and the planting rate associated, can be a new source of information in a region where the planting rate is only based on farmer declarations for planting subsidies. This information could be used for:

• better knowledge of sugarcane management practices (plant rate, geographic disparities, …);

• estimating production of the coming harvest season (according to cropped area) and to plan corresponding transport operations.

Geospatial technology as a tool for real-time monitoring

With the recent development of geospatial technologies, many researchers have studied the potential of satellite images to capture information about large areas of cane at once. First used for crop area mapping (e.g. [START_REF] Narciso | Identification and classification of sugarcane based on satellite remote sensing[END_REF][START_REF] Hadsarang | Utilization of Landsat-5 (TM) imagery for sugarcane area survey and mapping in Thailand[END_REF], the applications became more and more diversified and specialized due to continuous research efforts in the agricultural domain, but also to a larger technological offering in satellite services [START_REF] Bégué | Review of the current and potential remote sensing applications for the sugarcane industry[END_REF]. The use of remote sensing for cutting surveys is recent [START_REF] Mc Donald | Landsat TM imagery and GIS can be used to detect harvested and fallow cane blocks in the Herbert[END_REF][START_REF] Gers | Using SPOT4 satellite imagery to monitor area harvested by small scale sugarcane farmers at Umfolozi[END_REF][START_REF] Bégué | Application of remote sensing technology to monitor sugar cane cutting and planting in Guadeloupe (French West Indies)[END_REF] and linked to the evolution of satellite solutions which are now able to provide a large number of high resolution image acquisitions during several consecutive months. This paper presents the experience acquired on Reunion Island on geospatial technology applied to planting and harvest survey. The products and tools (methodology) presented here have been developped during the SUCRETTE1 research project [START_REF] Ribbes | Potentialités de la télédétection satellitaire pour la filière canne à sucre (Projet SUCRETTE)[END_REF], conducted by CIRAD (Centre de coopération Internationale en Recherche Agronomique pour le Développement) and Spot Image. This project explored the potentials of remote sensing and GIS technologies to provide geospatial products and tools for decision support in the sugarcane industry. The structure of an operational service derived from these developments is currently in discussion with the industry.

What information about vegetation status can remote sensing provide?

The optical properties of a sugarcane field Most of the Earth observation satellites measure solar radiation reflected by the Earth's surface. This radiation is measured separately in visible (generally blue, green and red), for normal colour photographs, and infrared IR (near and middle) spectral bands.

When radiation is intercepted by a vegetation canopy, different processes occur depending on the wavelength (mainly biochemistry of the leaves in the visible, structure of the canopy in the near infrared, and water content in the middle infrared). These specific interactions between vegetation and spectral radiation are the basis of remote sensing applied to vegetation monitoring as they permit to retrieve surface characteristics from the measurement of the reflectance in the different spectral bands.

Figure 2 shows how the spectral reflectance of a cane field varies according to the crop status and conditions; for example, in the visible bands (red and green), because of radiation absorption by the leaf pigments, the reflectance of a vegetation canopy is lower than that of bare soil; in the near infrared, vegetation and bare soil have very different reflectances, while they are close in the middle infrared. At the opposite, the middle infrared band is important to separate residues from the other status.

Figure 2 : Mean and standard deviation of the spectral response of cane fields with different status: green standing cane (full vegetation cover), residues (harvested field) and bare soil (planted field). Given for SPOT satellite bands (IR stands for InfraRed).

The main current satellite sensors

Satellite imaging systems are mainly characterized by the spatial resolution (size of the pixels), the number and position of the spectral bands, the satellite revisit time, and the size of the image (foot print). The list of the main commercial satellite systems and their characteristics are given in Table 1.

Product catalogue, image browser and prices can be found on the Companies' web sites. Tasked products delivered in a nominal map geometry are generally priced between 0.9 USD (20 m resolution) and 28 USD (0.65 m resolution) per km² for a minimum scene acquisition of 3,600 km² and 64 km² respectively, while archived products are priced between 0.01 USD (30 m resolution) and 17 USD (0.65 m resolution) per km² for a minimum order size of 32,400 km² and 25 km² respectively.

High spatial resolution images (decametric resolution) can be used to monitor crop growth (seasonal monitoring), while very high spatial resolution images (metric resolution), which are more expensive and acquired on a smaller region, are suitable to map infrastructures or field boundaries (scales of 1:25,000 to 1:5,000).

Table 1: List and characteristics of the main current commercial Earth Observation satellites.

Production of thematic maps

This section presents the image processing techniques that permit transformation of a sequence of satellite images into harvest or plantation progress maps. In the SUCRETTE project, we used a time series of SPOT images (Table 1) at 20 m (SPOT4) and 10 m (SPOT5) spatial resolution; these images were geometrically (orthorectified) and radiometrically (reflectance values) corrected.

According to the scale at which the method is carried out ("block parcel" or "cane field"), two methodologies are proposed. In both cases, these methods result in maps of harvested and planted cane area, and evaluate harvest progress or planting rates. boundaries are digitized on 0.5 m resolution aerial orthophotos (ORTHO® DB, IGN) that must be less than five years old (Figure 3a). For each block, such information as "grower's number", "irrigation mode" or "delivery zone" is given. By grouping all the areas identified in the bare soil class during the planting period (from September to April), a map of ploughed areas can also be produced. If we make the hypothesis that all ploughed areas will be replanted with sugarcane during the next months, this map can be considered as that of replanted cane, from which a replanting rate can be calculated.

However, concerning planting map production, the use of a block parcel map is limited by the presence of tracks surrounding most of the fields. In fact, those tracks have the same spectral response as the bare soil resulting in errors on the planting rate. Therefore, to produce the planting map, a digitized field map is more appropriate.

Cane status mapping at the cane field scale

We saw previously the limitations of using a block parcel map to obtain reliable area statistics on the cane status. Furthermore, cane status is not homogeneous within the block parcels (different farming operation dates) resulting in difficulties to calculate field indicators to support crop management decisions. To overcome these limitations, we created a classification based on a cane field mask derived from very high spatial resolution images (metric our sub-metric resolution).

1. Mapping the cane field boundaries: We used a SPOT5 image at 2.5 m resolution to draw the individual field boundaries by visual interpretation (Figure 3b). This technical solution is less accurate than the use of aerial photo at the field scale (respectively ± 2.8% and ± 0.5%, calculated on an hypothetical square field having an area equal to the Reunion mean cane field area), but it guarantees an annual update, compared to the five years update resulting from aerial photo survey on Reunion Island. A yearly update is necessary for a crop with a high rotation rate like sugarcane, in particular in a region with high land use dynamic.

Classification per field:

In this case, we used the cane field boundaries to create a mask before the multispectral classification. In order to eliminate mixed border pixels, a 10 m or 20 m buffer (for SPOT5 and SPOT4 respectively) was created around each field polygon. The buffers were subtracted from the original edge of the field polygon to create the mask.

Then, as previously, we proceeded with the classification of the pixels inside the mask. On the classified image, the number of pixels belonging to each class (green standing cane, crop residues, bare soil and unclassified pixels) is counted for each field (polygon) resulting in a harvest or planting rate at the field scale. According to rate thresholds, each field can be finally classified into four farming operation classes: not harvested, harvested, harvest in progress, planted cane and unprocessed (Figure 4c).

This more flexible method has the advantage of allowing the creation of new classes and can be adapted more easily to the needs expressed by the end user. Furthermore, the results can be provided in vector format and directly integrated in any GIS.

3. Statistics: Harvest maps and statistics can be generated about one week after image acquisition. If one considers that fields in which cutting has begun are generally completely harvested during the following week, those fields can be counted as harvested, and the statistical results are closer to the reality of the harvest progress one week after the image acquisition.

At the end of the planting period, by grouping together all the planted fields monthly identified, a planting map can also be produced. However, a field-based approach (vector map) is not the most appropriate to represent planted areas as a planting operation is often an opportunity for the farmer to reorganise the distribution of the fields in his own land. In that case, a raster (image) map of planted cane seems to be more appropriate (Figure 4b).

Validation and limits

Regarding harvest monitoring, results obtained from the classification of three SPOT images acquired during the harvest season have been compared to a database of a sugar farm composed of 81 fields situated in the North-East of the Island. In this database, harvest dates correspond approximately to the middle of field cutting period. Therefore, in our classification, fields with a harvest progress rate higher than 50% were classified in the harvested class, and the other fields in the not harvested class.

According to the error matrix (Table 2), the overall accuracy of the classification reaches 96.5 % of well classified fields on the image acquired 2 months after the harvest start (August 19, 2004). This percentage is quite constant throughout the harvest season, with 93.8% and 95.1% of well classified fields calculated from September 11 and October 26 images, respectively. In most cases, the errors correspond to the fields that were classified as harvest in progress.

When applied to the entire cane cropped area, it may happen that the unclassified class is not negligible due to a high presence of clouds. In that case, the harvest and planting rates will be calculated on a sample area (Figure 5). Another classification limit occurred when the delay between two cloud-free images is too large, resulting in errors when distinguishing standing crop from cane regrowth of fields harvested previously in the season. This delay can be estimated at 3 months during the winter when cane growth is slow (at the beginning of the harvest season), and at 2 months during the summer when cane growth is rapid (at the end of the harvest season). In some cloudy regions, we recommend a frequency of the image acquisition higher than these delays in order to reduce the delay between cloud-free data acquisition over the cane-cropped area.

In order to improve classification results and in order to be able to map real planted cane (and not ploughed field), current research at CIRAD is focusing on the development of a classification driven by expert systems and crop growth modelling.

Distributing Cartographic Results to the Sugar Cane Industry

One objective of the SUCRETTE project was to study appropriate methods for distributing the thematic maps and statistical results to the members of the sugar cane industry. The analysis of needs and requirements of the industry in that domain revealed a wide diversity of situations and technical backgrounds. We have tried to imagine solutions taking advantage of recent developments in web mapping techniques, that can adapt to that diversity of situations and constraints, and that can be used and understood with as little training as possible.

Printed bulletin

One convenient way to distribute cartographic maps is on printed-paper. It has the advantage of simplicity and in some cases there is no alternative. Successful trials resulted in distributing a crop situation report. This report included a cartographic map and the associated statistics on a single sheet of paper (Figure 5).

Light interactive maps on a web page

Installing a geographic information system (GIS) on a user's desktop offers flexibility and interactivity to the user. Such a system enables one to manipulate and compare several thematic layers on a map, thus improving the capacity for interpretation. However the cost of the software and training are often too high to be considered acceptable by industry members. Therefore, we explored an intermediate solution (between printed paper and full GIS software). This proposition takes advantage of recent important advances in cartographic mapping technologies developed for the World Wide Web. This application is both easy to install and easy to use while still offering an excellent level of interactivity.

Furthermore the same publishing technique can be used when a connection to the internet is available, and when is it not.

The results of remote sensing analysis are presented in a single web page (Figure 6) that contains an interactive map and, when necessary, a table displaying different statistical variables and results associated with the sugar cane parcels (or groups of parcels). It can be viewed by any web browser software (such as Internet Explorer, Netscape, Firefox, Opera, ..) without the need for installing GIS software.

The light mapping program that we chose to embed in the web page is a Java applet named AlovMap [START_REF] Johnson | AlovMap. Archaeological Computing Laboratory[END_REF]. It offers very good interactive features, such as turning on and off different layers, zoom, pan, and object selection by query. It can be highly customized and controlled using Javascript commands, which is a real asset for adapting map layout, content, and behaviour to the different needs among members of the sugar cane industry.

Generating the "light maps"

To help a GIS technician of the sugar industry produce such kinds of "light maps", we developed a prototype software named "Limage" (for LIght MAp GEnerator) that takes the statistical results of remote sensing analysis for input and generates a web page with an interactive mapping applet embedded (Figure 7). Thanks to that tool, it is possible to produce the mapping web pages without being an expert of all the underlying techniques involved in the process.

Limage was designed in such a way that all the files required for viewing a map in a web page are generated inside a unique destination directory. It means that the result is a standalone set of files that can be copied (using a USB key for example) and used locally on a desktop computer, or that can be uploaded on a web server and viewed by numerous final users through the internet.

Conclusions

For small-scale farming systems, information at the field or farm scales is difficult to get because data collection is often a long and non-exhaustive process based on heterogeneous declarative data. Remote sensing can therefore be an exhaustive and objective source of information in near real-time.

In Reunion, we made the demonstration of the technical feasibility and relevance of the use of satellite images and tailored GIS tools to update yearly the sugarcane field boundaries, and to monitor the harvest progress and planting. The operational use of satellite image in the sugar industry is currently being discussed with the agriculture administration and the technical services and sugar factories of the island.

Figure 1

 1 Figure 1 : a) Situation map of Reunion Island in the Indian Ocean (Source: Wikipedia); b) Sugarcane cropped area over Reunion Island: rainfed (green), irrigated (blue) (Source: DDAF 2004).

Figure 3 :

 3 Figure 3 : Example of digitized cane cropped area based on very high resolution images: (a) 1997 aerial photo (ORTHO® DB) and block parcel boundaries (Source: DDAF, 2002); (b) SPOT5 image acquired on July 6, 2002 at 2.5 m resolution (Source: SUCRETTE /BD ISLE-Reunion) and field boundaries.

Figure 4 :

 4 Figure 4: Example of harvest and planting mapping on a SPOT image acquired on August 19, 2004 with 10 m resolution (Source: SUCRETTE ISLE-Reunion): a) False colour composition of a subset (Near IR/Red/Green), on which photosynthetic vegetation appears in red, cane residues in light blue and bare soil in dark blue. b) Classified image of the cane cropped area, inside the block parcel limits in black (Source: DDAF). c) Classified cane fields in a GIS layer.

Figure 5 :

 5 Figure 5 : Example of a printed crop situation bulletin. Note that when the proportion of sample area is low, the harvest statistics are not provided because they are not reliable enough (Source : SUCRETTE/CIRAD).

Figure 6 :

 6 Figure 6 : Interactive map in a web page (Source: SUCRETTE/CIRAD).

Figure 7 :

 7 Figure 7 : The "Light Map Generator" helps a GIS technician producing interactive maps embedded in a web page (Source: SUCRETTE/CIRAD).

  Mapping block parcel boundaries: In Reunion, since 2002, and in conformity with the Common Agricultural Policy (CAP) of the European Union, data concerning the extension and localization of sugarcane fields are recorded and updated each year by the Departmental

	Cane status mapping at the block parcel scale
	1.
		Company Web Site (products, catalog browser, and image order)	Spatial resolution	Spectral bands
	Landsat7	http://edc.usgs.gov/products/sat	30 m	Blue, Green, Red,
		ellite/landsat7.html		Near IR,
		http://glovis.usgs.gov/		Middle IR1,
			15 m	Middel IR2
	SPOT	http://www.spotimage.fr/	20 m	Green,Red,
			10 m	Near IR,
			5 m	Middle IR
			2.5 m
	Formosat	http://www.spotimage.fr/	8 m	12 bands between
			2 m	Blue and Near IR
	Ikonos	http://www.geoeye.com/	4 m	Blue, Green, Red,
			1 m	Near IR
	Quickbird	http://www.digitalglobe.com/	2.6 m	Blue, Green, Red,
			0.65 m	Near IR
	Orbview	http://www.geoeye.com/	4 m	Blue, Green, Red,
				Near IR

Agriculture and Forestry Office (DDAF). Based on farmers' declaration, block parcel

Table 2 :

 2 The cane field classification error matrix (given in number of fields).

SUivi de la Canne à sucRE par TélédéTEction

Acknowledgments

o The results presented here are issued from the SUCRETTE project, funded by the French Ministry of Research through the Earth and Space Program (RTE), and from other research activities supported by the Region REUNION; o Special thanks for the CNES (Centre National d'Etudes Spatiales), in particular to Hélène De Boissezon, for the access to the ISLE-REUNION data base which is a satellite images reference database developed by CNES for scientific studies.


Agnès Begue
email: agnes.begue@cirad.fr

Pierre Todoroff
email: pierre.todoroff@cirad.fr

Johanna Pater

MULTI-TIME SCALE ANALYSIS OF SUGARCANE WITHIN-FIELD VARIABILITY: IMPROVED CROP DIAGNOSIS USING SATELLITE TIME SERIES?

Within-field spatial variability is related to multiple factors that can be time-independent or time-dependent. In this study, our working hypothesis is that a multi-time scale analysis of the dynamics of spatial patterns can help establish a diagnosis of crop condition. To test this hypothesis, we analyzed the within-field variability of a sugarcane crop at seasonal and annual time scales, and tried to link this variability to environmental (climate, topography, and soil depth) and cropping (harvest date) factors. The analysis was based on a sugarcane field vegetation index (NDVI) time series of fifteen SPOT images acquired in the French West Indies (Guadeloupe) in 2002 and 2003, and on an original classification method that enabled us to focus on crop spatial variability independently of crop growth stages.

We showed that at the seasonal scale, the within-field growth pattern depended on the phenological stage of the crop and on cropping operations. At the annual scale, NDVI maps revealed a stable pattern for the two consecutive years at peak vegetation, despite very different rainfall amounts, but with inverse NDVI values. This inversion is linked with the topography and consequently to the plant water status.

We conclude that (1) it is necessary to know the crop growing cycle to correctly interpret the spatial pattern, (2) single-date images may be insufficient for the diagnosis of crop condition or for prediction, and (3) the pattern of vigour occurrence within fields can help diagnose growth anomalies.

INTRODUCTION

Image-based remote sensing can provide spatially and temporally distributed information for precision agriculture [START_REF] Moran | Opportunities and limitations for image-based remote sensing in precision crop management[END_REF][START_REF] Pinter | Remote Sensing for Crop Management[END_REF]. Aerial photographs and crop images, for instance, have been used to draw management zones as portions of a field that express homogeneous combinations of yield-limiting factors (e.g. [START_REF] Anderson | Multispectral videography and geographic information systems for site-specific farm management[END_REF]. In order to optimize the inputs and the cropping schedule, however, it is also necessary to determine the causes of spatial variability in crop vigour.

Crop growth variability is related to multiple factors that can be time-independent or timedependent. The main time-independent factors of variability are linked to the substrate, like topography and soil type and depth, or to previous land use. Annual-linked factors may include anomalies in planting and emergence, or in weather conditions. Seasonal-linked factors may include plant diseases, weed development, severe climatic events or irrigation system mal-function. These time-independent and time-variable factors can also interact, leading to complex spatio-temporal patterns of crop vigour [START_REF] Machado | Spatial and temporal variability of corn growth and grain yield: Implications for site-specific farming[END_REF]. Hyperspectral images, acquired in multiple and narrow spectral bands, can be used to detect crop nutrients and water stress conditions [START_REF] Lelong | Hyperspectral imaging and stress mapping in agriculture : a case study on wheat in Beauce (France)[END_REF]. Unfortunately, most of the satellite or airborne sensors have a small number of broad spectral bands, and typically lack the diagnostic capability to identify a particular type of stress or to determine why biomass is at a certain level. According to [START_REF] Pinter | Remote Sensing for Crop Management[END_REF], historic imagery, at field and farm levels, could be combined with agronomic and climatic data to map areas prone to water stress, nutrient deficiency, or pest problems under a particular environmental scenario.

Remote sensing studies using historic images are generally based on the premise that the spatial variability in crop yield is influenced by spatial variability in soil factors at a similar scale, and make use of image time series at an annual scale (e.g. [START_REF] Boydell | Identifying potential within-field management zones from cotton-yield estimates[END_REF]. However, the number of years of consecutive image data required to return an acceptably stable map differs depending on the study, from the recommended five years [START_REF] Boydell | Identifying potential within-field management zones from cotton-yield estimates[END_REF] to a longer term database for crops under variable environmental conditions [START_REF] Lamb | Spatial and temporal stability of corn grain yields[END_REF][START_REF] Schepers | Appropriateness of management zones for characterizing spatial variability of soil properties and irrigated corn yields across years[END_REF]. At the seasonal scale, the dynamics of spectral vegetation indices are generally studied in order to determine the best period to delineate yield potential zones [START_REF] Zarco-Tejada | Temporal and spatial relationships between within-field yield variability in cotton and high-spatial hyperspectral remote sensing imagery[END_REF][START_REF] Yang | Relationships between yield monitor data and airborne multidate multispectral digital imagery for grain sorghum[END_REF], which is not sufficient to establish crop diagnosis.

In this study, since spatial variability is related to multiple factors that can be timeindependent or time-dependent, our working hypothesis is that a multi-time scale analysis of the dynamics of spatial patterns can help to establish diagnosis on crop conditions. To test this original hypothesis, we analyzed the within-field variability of sugarcane crop at two different time-scales, seasonal and annual, and tried to relate this variability to cropping (harvest date) and environmental (climate, topography and soil depth) factors. This analysis is based on a sugarcane field normalized difference vegetation index (NDVI) time series of fifteen SPOT images of the French West Indies (Guadeloupe) from 2002[START_REF] Pinter | Remote Sensing for Crop Management[END_REF], and 2004 (SUCRETTE project; (SUCRETTE project;[START_REF] Ribbes | Potentialités de la télédétection satellitaire pour la filière canne à sucre -Projet SUCRETTE (Potential of satel-lite remote sensing for the sugarcane industry -SUCRETTE project)[END_REF].

MATERIAL AND METHODS

Crop material and study site

Sugarcane (Saccharum officinarum L.) is a semi-perennial grass with fibrous stalks two to six meters tall, belonging to the Graminae family. It is a vegetatively propagated crop, and the propagules are the stem cuttings. After 18-24 months from initial planting, the plant crop is harvested, and the buds on the leftover underground stubbles germinate again and give rise to another crop. This crop, called a ratoon crop, is harvested about every 12 months for up to four years or more, before being renewed due to decreasing yield.

The study site is a 8 ha field named Sahara located in Gardel Estate (16°18'24'' N; 61°20'29'' W), a planter-miller growing sugarcane i n the French West Indies (Guadeloupe).

Cropping data

Sahara field was planted with CO6415 cultivar in 2000, and harvested on June 10, 2002, April 30, 2003(41.9 t) and June 9, 2004 (63.8 t) during the study period. During this period, the crop was rainfed and healthy.

Environmental data acquisition and processing

The climate station closest to Sahara field is Boisvin, less than 2 km away. Soil depth over the reef limestone subsoil was measured on Sahara field in 2004 using the electric resistivity method [START_REF] Hesse | Prospections géophysiques à faible profondeur[END_REF]. Measurements of resistivity r (Ωm) were made at the corners of a 20 m by 20 m grid, localized with a Trimble Pathfinder GPS, and converted into soil depths z (m) with coefficients calibrated for the Gardel vertisols [START_REF] Cabidoche | Distribution des sols à argiles gonflantes sur calcaires récifaux (zone Caraïbe) -Utilisation de mesures de résistivité électrique (Distribution of expanding clay soils over reef limestone in the Caribbean -Use of electric resistivity)[END_REF] :

z = 2 -0.74 ln(r-3) (1)
Soil depth values were then interpolated using kriging and rasterized at 10 m resolution to be compatible with the spatial resolution of SPOT images.

Satellite data acquisition and processing

A time series of SPOT images were acquired in 2002, 2003, and 2004 over Guadeloupe as part of a research project [START_REF] Ribbes | Potentialités de la télédétection satellitaire pour la filière canne à sucre -Projet SUCRETTE (Potential of satel-lite remote sensing for the sugarcane industry -SUCRETTE project)[END_REF]. For this study, a set of fifteen cloud-free images (thirteen SPOT5 images and two SPOT4 images) were selected over Gardel Estate (Table 1). The images were acquired at 20 m and 10 m resolution respectively for SPOT4 and SPOT5 satellites (red and near infrared bands), in raw format (level 1a) with no geometric pre-processing. Image pre-processing SPOT images were ortho-rectified using the SPOT geometric model provided by ERDAS IMAGINE™ software (UTM 20N). For the orthorectification, we used the DEM and thirty control points scattered over the whole island. The control points were extracted from aerial ortho-photos (ORTHO® DB, IGN). The image registration error was less than 10 m (less than 1 SPOT5 pixel).

In order to get comparable physical values between the images, the digital counts were converted to Top of Atmosphere (TOA) reflectances, using the following equation:

S S E G DC ⋅ ⋅ ⋅ = ) cos(θ π ρ (2)
where ρ is the TOA (Top Of Atmosphere) reflectance, DC is the digital count, G is the sensor absolute calibration gain (provided in the metadata associated with the image), θ S is the solar zenith angle and E S is the solar radiation in the appropriate wavelength. To minimize the radiometric residual effects due to varying irradiance conditions, we used a ratio-based vegetation index [START_REF] Tucker | Red and photographic infrared linear combinations for monitoring vegetation[END_REF]. The most commonly used is the Normalized Difference Vegetation Index (NDVI; [START_REF] Rouse | Monitoring vegetation systems in the Great Plains with ERTS[END_REF], calculated as:

RED NIR RED NIR NDVI ρ ρ ρ ρ - - = (3)
where r NIR and r RED are respectively the TOA reflectances in the near infrared and the red bands.

No atmospheric correction was performed since only clear sky images were selected and because the images were mainly processed (classification and correlation) on a daily basis.

Field image classification

To help visualize and summarize field spectral data for each date the field NDVI values were aggregated into five discrete categories. To do this, subset NDVI images corresponding to the boundaries of Sahara field (minus a buffer zone of 20 m) were created from the time series. The aggregation was done according to the equal count (quintiles) or equal-area classification, where approximately the same number of observations (20% of the total) was put into each class. This technique allows focusing on crop spatial variability independent of the crop growth stages.

Correlation between variables

To complement the visual and qualitative result obtained from the image classification, we used the Spearman coefficient to calculate the correlation between the NDVI images, and between NDVI values, elevation, and soil depth. The Spearman coefficient assesses how well an arbitrary monotonic function can describe the relationship between two variables, without making any assumptions about the frequency distribution of the variables or the linearity of the relationship.

RESULTS

Environmental data

The satellite time series covered two consecutive cycles of sugarcane growth with different rainfall amounts (Figure 2a). The 2002-2003 cycle showed a rainfall deficit of 140 mm compared to the 24-year rainfall average, with deficit records in November and December (respectively 112 mm and 87 mm) at the end of the rainy season. In contrast, the rainfall of the 2003-2004 cycle showed a surplus of 580 mm compared to the 24-year average with peaks in November and December (respectively 116 mm and 327 mm), due to particularly strong rainfall events.

NDVI time series of sugarcane

Figure 2b shows the evolution of the mean NDVI of Sahara field throughout the two growing cycles. After harvest, in May and June 2003, when there are only crop residues present on the soil, the value of the NDVI is low, between 0.15 and 0.2. The NDVI then increases rapidly as the vegetation re-grows and reaches its maximum at the end of the rainy season, with values between 0.7 and 0.8, typical of a fully developed dense green canopy. When there is no water stress, as in 2003-2004 in Guadeloupe, the NDVI remains stable or decreases slowly during the maturation phase due to a slight decline in leaf chlorophyll and change in the canopy architecture [START_REF] Almeida | ASTER and Landsat ETM+ images applied to sugarcane yield forecast[END_REF], and continues as such until harvest. In contrast, in cases of severe water stress as in 2002-2003 in Guadeloupe, the NDVI, after reaching its maximum, can decrease all the way down to 0.25 mainly due to the severe senescence of the leaves.

Seasonal variations of NDVI patterns

Within-field growth pattern depends on the phenological stage of the crop and the cropping operations. Figure 3

Annual variations of NDVI patterns

Around the peak of vegetation growth (images 1, 3, and 4 for 2002-2003 -image 2 was eliminated, cf. previous section -and images 11, 12, and 13 for 2003-2004 in Figure 3), the within-field NDVI patterns are comparable for both crop cycles, but the values of the classes are inverted (Figure 4;Table 2). This unexpected feature can be attributed to the interaction between topography and climate conditions. The analysis of the field topography (Figure 1)

indicates that during the dry year (2002/03), the NDVI is maximal in the lower part of the field, while in the rainy year (2003/04), the NDVI is maximal in the higher part of the field.

Similarly, during the wet year, the NDVI is minimal in the lower part of the field, while in the rainy year (2003/04), the NDVI is minimal in the higher part of the field. This observation is confirmed by the correlation values obtained between elevation and NDVI at pixel scale (Figure 2); negative values are obtained for the dry year, while positive values are found for the wet year. The best correlations are obtained with the images acquired around the peak of vegetation growth (between November and February), except for the two outliers (October 24, 2002 andApril 12, 2004).

DISCUSSION

At the seasonal scale, the within-field growth pattern depends on the phenological stage of the crop. During the early growth stages, the within-field spatial variability pattern is erratic and then stabilizes when the crop is fully developed and the soil is no longer visible. This result is in agreement with the studies of [START_REF] Zarco-Tejada | Temporal and spatial relationships between within-field yield variability in cotton and high-spatial hyperspectral remote sensing imagery[END_REF] and [START_REF] Yang | Relationships between yield monitor data and airborne multidate multispectral digital imagery for grain sorghum[END_REF] which showed that the best correspondence between the spatial pattern of NDVI and yield were obtained with airborne images acquired around peak vegetative development, before the maturation stage when the plants are senescing. However, we showed in our data set that even images acquired around the vegetation peak could be outliers, showing unexpected spatial patterns. Our hypothesis is that specific climatic events could be strong enough to momentarily change the architecture of the crop.

At the annual scale, when averaging the NDVI maps around peak biomass, we found a stable pattern for both years, but with very different NDVI values. These potential yield variations can be directly linked to the topography and consequently to the water conditions of the plant, with limited water stress during the dry year in the lower part of the field and water logging during the rainy year. The influence of the topography was previously shown by Marques Da Silva and Alexandre (2005), who proposed topographical indices to help in sitespecific management for delineating areas where crop yields are more sensitive to extreme water conditions. Our results confirmed the observations obtained by yield monitoring; [START_REF] Eghball | Fractal analysis of temporal yield variability of crop sequences: Implications for site-specific management[END_REF] and [START_REF] Lamb | Spatial and temporal stability of corn grain yields[END_REF] showed that, under rainfed conditions, the temporal variability of yields was more dominant than spatial variability, indicating that spatial patterns in grain yields were greatly affected by yearly climatic conditions, particularly by year-to-year changes in seasonal water supply. [START_REF] Schepers | Appropriateness of management zones for characterizing spatial variability of soil properties and irrigated corn yields across years[END_REF] reached the same conclusions on irrigated corn crops and explained it by variations in soil properties affecting water-supplying capacity.

CONCLUSION

From the literature, results from within-field variability studies do not always agree. This may be due to a lack of consistency of the results over a series of years, or because soil properties may not have explained the observed yield. To respond to the difficulties in the interpretation of the studies carried out, the use of high resolution satellite imagery or aerial photography time series could be one solution. In this paper, we showed through an example using satellite remote sensing, how the cropping and environmental factors impact the within-field temporal variability. Our results showed that (1) it is necessary to know the crop phenology in order to interpret correctly the spatial pattern, and that (2) single date images can be insufficient for the diagnosis of crop conditions or for predictions. We concluded that the pattern of crop vigour occurrence within fields could help to diagnose the causes of crop growth anomalies which can then be verified by ground inspection and sampling.

The results obtained in this paper highlight the potential of satellite remote sensing to support crop management decision-making. This contribution is mainly based on multi-temporal NDVI acquired at the field-scale. An increase in the availability of decametric/metric image time series can be expected soon with the launch of satellites with high revisit time such as Formosat or Venµs, or with the growing use of light airborne systems. This contribution should be further improved when NDVI time series are combined with other data sources such as hyperspectral measurements, or when the NDVI times series are analysed with tools such as geostatistics to better characterize crop conditions, hasten crop diagnosis, and improve yield predictions.

  The recorded rainfall was respectively 1185 mm and 1905 mm for the 2002-03 and 2003-04 growing seasons (from June to May); the average annual rainfall (1977-2000 period) on the Gardel area being 1325 mm. The Sahara field Digital Elevation Model (DEM) was extracted from the Guadeloupe DEM. The Guadeloupe DEM was produced in 2002 by DDAF 1 from aerial orthophotos (ORTHO® DB, IGN) and ground control points. The DEM is in UTM 20N projection, and with horizontal and vertical resolutions of 10 m and 1 m respective.

Figure 1 :

 1 Figure 1: Environmental data maps of Sahara field: a) Digital Elevation Model (Source:

Figure 2

 2 Figure 2 (a: top to d: bottom): a) Boisvin monthly rainfall deviation from average over 24

  shows equal-population classes of Sahara field NDVI for each acquisition date during two consecutive growing cycles. During the growth stages (images 7, 8, and 15), the within-field spatial variability is high; at this stage, the vegetation cover is partial and the background is still visible. The within-field variability is linked to background variability factors such as the density and degradation status of cane residues, and to possible development of weeds. From the end of the growing stage to the initial maturation phase (images 1 to 4, for the 2002-2003 season, and images 11 to 14 for the 2003-2004 season), the pattern of within-field variability stabilizes. This visual interpretation is confirmed by the high values of the correlation coefficients (from 0.63 to 0.83) obtained between images 1, 3, 4 for the 2002-2003 season, and between images 11, 12, 13 for the 2003-2004 season (

Figure 3 :

 3 Figure 3: Sahara field images of equal-classified NDVI, for 2 crop cycles, 2002-2003 and

Figure 4 :

 4 Figure 4 : Tercile representation of average NDVI images for the (a) 2002-03 and (b) 2003-

Table 1 :

 1 List of the SPOT images and characteristics used in the study

		Acquisition date	Satellite	Incidence	Solar Elevation	Solar Azimuth	Phase
			(sensor)	Angle 1 (°)	Angle (°)	Angle(°)	Angle (°)
	1	September 19, 2002	SPOT4	6.9	67.2	127.8	29.0
	2	October 24,	SPOT5	-6.8	52.1	143.3	31.7
	3	January 21,	SPOT5	-16.5	46.7	145.7	32.9
	4	February 11, 2003	SPOT5	-23.5	50.1	138.5	24.5
	5	March 29, 2003	SPOT5	7.0	66.3	122.2	30.4
	6	April 30,2003	SPOT5	-23.5	68.9	91.7	4.6
	7	May 4, 2003	SPOT5	22.1	74.7	90.1	37.1
	8	May 25,2003	SPOT5	14.6	73.4	71.5	30.0
	9	July 17, 2003	SPOT5	-25.1	66.5	73.2	11.9
	10 September 12, 2003	SPOT5	-17.6	66.3	117.3	8.0
	11 January 4, 2004	SPOT5	-2.2	45.9	151.0	42.7
	12 January 31,	SPOT4	13.4	50.2	146.9	49.7
	13 March 1, 2004	SPOT5	5.8	57.4	135.5	37.5
	14 April 12, 2004	SPOT5	-10.5	67.9	107.4	11.7
	15 June 19, 2004	SPOT5	-24.9	67.0	68.0	13.8

1 : Negative values for Right viewing

Table 2 ).

 2 However, in this time series, two images display unexpected growth patterns: the October 24, 2002 image (image 2) and the April 12, 2004 image (image 14). Although no particular conditions were noticed when they were acquired (Table1), a heavy rainfall occurring two days before the October 24, 2002 image may have modified the crop architecture significantly enough to induce a change in the growth pattern observed in that image. For the April 2004 outlier, however, no reasonable explanation can be put forward at this point.

	At this stage, the crop is fully developed and the soil is no longer visible. On April 30, 2003
	(image 6), the within-field variability map displays striped patterns, characteristic of the har-
	vest in progress.

Table 2 :

 2 Spearman correlation matrix calculated between the fifteen SPOT NDVI images of Sahara field. Values in bold are significantly different from 0 at P<0.01.

Direction Départementale de l'Agriculture et des Forêts

ACKNOWLEDGEMENTS

Most of the results presented here emanate from the SUCRETTE project funded by the French Ministry of Research (RTE Program). Thanks to Stéphanie Catsidonis for helping with data acquisition and to Dominique Tressens for giving access to Gardel fields and databases.