Aline Bsaibes

Dominique Courault

Frédéric Baret

Marie Weiss

Albert Olioso

Frédéric Jacob

Olivier Hagolle

Olivier Marloie

Nadine Bertrand

Véronique Desfond

Farzaneh Kzemipour

Albedo and LAI estimates from FORMOSAT-2 data for crop monitoring

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Several applications may exploit remote sensing estimates of land surface variables. They include agriculture, forestry or land management as well as hydrological and meteorological forecasts. Due to the high level of spatial heterogeneity, the size of agricultural fields or natural vegetation patches, and the large dynamic of vegetation, observations made frequently at high spatial resolution are desirable. However, because of technological and economical constraints, only high spatial relationships may either use bidirectional reflectance measurements along with parametric inverse models such as multiple linear regression [START_REF] Eklundh | Investigating the use of Landsat thematic mapper data for estimation of forest leaf area index in southern Sweden[END_REF] and neural networks [START_REF] Baret | The robustness of canopy gap fraction estimates from red and near infrared reflectances: a comparison of approaches[END_REF], or combine bands into vegetation indices used as input for parametric modeling [START_REF] Baret | Potentials and limits of vegetation indices for LAI and PAR assessment[END_REF][START_REF] Walthall | A comparison of empirical and neural network approaches for estimating corn and soybean leaf area index from Landsat ETM+ imagery[END_REF]. Such approaches are limited by data dependence and therefore have a limited extrapolation capacity. Radiative transfer model inversion is potentially a very powerful approach [START_REF] Goel | Inversion of canopy reflectance models for estimation of biophysical parameters from reflectance data[END_REF][START_REF] Weiss | Investigation of a model inversion technique to estimate canopy biophysical variables from spectral and directional reflectance data[END_REF][START_REF] Meroni | Inversion of a radiative transfer model with hyperspectral observations for LAI mapping in poplar plantations[END_REF][START_REF] Schlerf | Inversion of a forest reflectance model to estimate structural canopy variables from hyperspectral remote sensing data[END_REF][START_REF] Darvishzadeh | Inversion of a radiative transfer model for estimating vegetation LAI and chlorophyll in a heterogeneous grassland. Remote Sensing of Environment[END_REF], able to explicitly account for available information such as known peculiarities of targeted canopies thanks to a priori knowledge. However, radiative transfer model inversion is often limited by the realism of canopies structure description, and is known to be severely ill-posed, which induces equifinality problems [START_REF] Combal | Retrieval of canopy biophysical variables from bidirectional reflectance data. Using prior information to solve the ill-posed inverse problem[END_REF][START_REF] Durbha | Support vector machines regression for retrieval of leaf area index from multiangle imaging spectroradiometer[END_REF].

Albedo can also be estimated from remote sensing by inverting radiative transfer models, but the difficulties are the same than those faced when retrieving LAI. Another possibility is using statistical relationships to perform a spectral extrapolation, so called Narrowband-To-Broadband (NTB) conversion. NTB conversion can be applied to nadir bidirectional reflectance [START_REF] Brest | Deriving surface albedo measurements from narrow band satellite data[END_REF][START_REF] Russell | Conversion of Nadir, narrow-band reflectance in red and near-infrared channels to hemispherical surface albedo[END_REF][START_REF] Liang | Retrieval of land surface albedo from satellite observations: a simulation study[END_REF][START_REF] Song | An improved method to derive surface albedo from narrowband AVHRR satellite data: Narrowband to broadband conversion[END_REF][START_REF] Liang | Narrowband to broadband conversions of land surface albedo I: Algorithms[END_REF][START_REF] Liang | A direct algorithm for estimating land surface broadband albedos from MODIS imagery[END_REF][START_REF] Liang | VIIRS narrowband to broadband land surface albedo conversion: formula and validation[END_REF][START_REF] Susaki | Validation of MODIS Albedo Products of Paddy Fields in Japan[END_REF] or, more adequately, on hemispherical reflectance [START_REF] Wanner | Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm[END_REF][START_REF] Weiss | Hemispherical reflectance and albedo estimates from the accumulation of across track sun synchroneous satellite data[END_REF]Jacob et al., 2002a;van Leeuwen and Roujan, 2002;[START_REF] Greuell | Narrowband-to-broadband albedo conversion for glacier ice and snow: equations based on modeling and ranges of validity of the equations[END_REF], where the latter is derived from Bidirectional Reflectance Distribution Function (BDRF) parametric modeling along with directional integration over the upper hemisphere [START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF][START_REF] Lucht | Considerations in the parametric modeling of BRDF and albedo from multi-angular satellite sensor observations[END_REF][START_REF] Jacob | Mapping short-wave albedo of agricultural surfaces using airborne PolDER data[END_REF][START_REF] Pokrovsky | Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison[END_REF]. Although proved efficient when the directional dimension is sufficiently sampled, BRDF modeling can not be applied to sensors such as FORMOSAT-2 or Venµs because the latter have single viewing configurations. Besides, applying NTB conversion to FORMOSAT-2 or Sentinel data is not straightforward regarding limited spectral samplings but especially single off nadir viewing angles. Indeed, NTB conversion has been widely used for multidirectional observations or single nadir viewing directions as abovementioned, but never for single off nadir viewing angles.

In the context of the high spatial resolution and revisit frequency offered by the FORMOSAT-2 sensor, the objective of this study was to explore its potentialities for the retrieval of solar albedo and LAI, regarding the specificities of its spectral and directional configurations. Rather than elaborating complex approaches based on radiative transfer model inversion, we concentrated on empirical approaches based on continuous ground measurements over few representative fields.

Remote sensing and ground based datasets were collected over the Crau-Camargue experimental site. The latter embraced a wide range of vegetation and soil moisture conditions, from dry wheat and bare soil fields to irrigated meadow and flooded rice plantations. This allowed investigating the robustness of the empirical methods considered for albedo and LAI retrieval. Furthermore, the high revisit frequency of the collected FORMOSAT-2 dataset provided unique and detailed information about evolution of land surface variables, over a large period ranging from the growing season to post-harvest of major crops. From these chronicles of spatialized measurements, it was therefore interesting to characterize the dynamics of albedo and LAI over different crop cycles, to analyze possible links between these two variables, and to detect possible characteristic trends for different vegetation covers according to anthropogenic forcing such as agricultural practices.

The paper is structured as follows. Section 2 describes the experiment and the resulting data set.

Section 3 presents the empirical methods developed to retrieve albedo and LAI from FORMOSAT-2 data. Section 4 provides the performances of albedo and LAI retrieval methods, and discusses the temporal dynamics of both variables for the several crops we considered. The best performing methods for albedo and LAI retrieval are next selected and applied to the whole image set. This allows analyzing the possible relationships between albedo and LAI for several crops throughout their cultural cycles. Finally, conclusions are drawn with due attention to potential applications and need for further investigations.

Materials

The Crau-Camargue experimental site

The study area was located in the "Crau-Camargue" area, South Eastern France (43.53°N; 4.66°E;

3 m above sea level, see Figure 1). Climate was typically Mediterranean, with irregular precipitations, long dry periods in spring and summer, and strong winds. This flat area was characterized by a wide range of soil and irrigation practices. The experiment took place in 2006, including intensive ground measurements simultaneously collected with satellite data on various crop types [START_REF] Courault | Assessing the Potentialities of FORMOSAT-2 Data for Water and Crop Monitoring at Small Regional Scale in South-Eastern France[END_REF]. Low cumulative precipitation was observed in 2006 (456 mm) as compared to the regional average (548 mm in 2005). The weather was especially dry from April 1 st to mid-September, with one rainfall event only occurring in early June (28 mm).

[Figure 1] The land cover was classified using a maximum likelihood supervised classification. The latter relied on 1/ the four FORMOSAT-2 wavebands, 2/ five images distributed along the experimental period, and 3/ reference areas of known field occupation within the study area. Image number and repartition was driven by the temporal dynamics of vegetation cover, especially that resulting from anthropogenic forcing such as meadow cuts throughout the cultural cycle (three to four cuts per season, leaving 10 cm vegetation height). Twelve classes were identified, which included the main vegetation covers, free water and bare soil surfaces. Although this map was improved with ground based information, it was undeniably subject to uncertainties, with a 20% training residual error.

Figure 1 displays the major vegetation classes that represented about 40% of the whole study area.

The remaining 60% included natural marshlands, the Rhone River and other minor cultures.

The five sampled fields

Five fields that corresponded to the major crops within the region of interest (Figure 1) were chosen for intensive ground based measurements. The two wheat fields (#1 and #2) were sown on November 11 th and December 15 th , and harvested on June 27 th and July 4 th , respectively. They were not irrigated, and turned to bare soils after harvest around DOY 179 (28 th of June). The meadow field (#3) was flooded every 11 days according to a regional water management designed for high yields and quality. Three cuts were performed during the growing season, on May 5 th , July 7 th , and August 11 th . The maize field (#4) was sown on May 5 th , was intermittently irrigated by sprinklers depending on weather conditions, and was finally harvested on August 8 th . This field was located on poor soils that were very stony at some locations, which induced large heterogeneities in vegetation cover that affected the representativeness of ground based measurements. The rice field (#5) was sown on dry soil on April 27 th , then continuously submerged from May 5 th till October 6 th with a 0.10 ± 0.05 m water height, and finally harvested on October 18 th . Due to stem lodging within the rice field after August 30 th caused by strong winds, LAI measurements and FORMOSAT-2 reflectances were biased. Therefore, the data collected afterwards were discarded from analysis.

Ground based measurements

Albedo was measured with Kipp & Zonen CM7 sensors mounted between 1.5 m and 2 m above top of canopy. Measurements were averaged over 10 minute periods throughout vegetation cycles. The measurement footprints were circular, with radii between 25 and 35 m. Albedometers were calibrated to measure incoming radiation over the whole solar spectrum (300 to 3000 nm).

Leaf Area Index (LAI) was derived from hemispherical images that provided Effective LAI. The latter was closer to remote sensing estimates than the true LAI because of leaf clumping [START_REF] Weiss | Methods for in situ leaf area index measurement, part II: from gap fraction to leaf area index: retrieval methods and sampling strategies[END_REF]. The hemispherical images were collected with time intervals of about 10 days, for capturing canopy structure dynamics. In order to represent field average LAI, a cross-pattern sampling protocol was adopted. It consisted of 50 hemispherical images acquired within each study field at each date of measurement. Table 1 gives the main characteristics of the ground measurements performed within the different above mentioned fields.

[Table 1]

The CAN-EYE software (http://www.avignon.inra.fr/can_eye/page5.php) was used to process the hemispherical images. CAN-EYE allowed computing the gap fraction from a series of RGB color images through a simple interactive supervised classification process. LAI was then derived from the resulting gap fractions, using look-up-table techniques based on the Poisson model [START_REF] Nilson | A theoretical analysis of the frequency of gaps in plant stands[END_REF]. A strong correlation (R²=0.98) was observed when comparing those estimates against planimetry based destructive LAI measurements that were simultaneously collected over few locations. However a systematic underestimation of LAI due to leaf clumping was observed, with a clumping coefficient of 0.68. This was consistent with the study from [START_REF] Demarez | Estimation of leaf area and clumping indexes of crops with hemispherical photographs[END_REF] who reported a value of 0.71 over wheat, maize and sunflower.

FORMOSAT-2 Data

FORMOSAT-2 is a high spatial resolution satellite that collects images with an 8 m nadir spatial resolution over a 24 km swath, in four 90 nm width wavebands centered at 488, 555, 650 and 830 nm. The orbital cycle is completed within one day. The sensor may deviate from nadir in order to point at sites close to the ground track. Therefore, accessible locations at Earth's surface are observed under a unique viewing direction. In our case, the Crau-Camargue site was targeted with zenith (relative to nadir) and azimuth (relative to north) viewing angles around 41° and 239°, respectively. Images were collected every three to four days at 10:30 UTC from March to October 2006. They were processed for geolocation, radiometric calibration and atmospheric perturbations following [START_REF] Hagolle | Correction of aerosol effects on multitemporal images acquired with constant viewing angles: Application to Formosat-2 images[END_REF]. Clouds and related shadows were discarded following [START_REF] Baillarin | Validation of an automatic image orthorectification processing[END_REF]. Over the 36 images collected between March and October, 30 images were cloudless, with a temporal gap spanning from April 17 th to May 14 th because of cloudy conditions.

Matching ground measurements with FORMOSAT-2 data

To consistently calibrate and validate the empirical methods we considered; it was necessary performing spatial and temporal matching between ground based and FORMOSAT-2 data.

For albedo, the four FORMOSAT-2 pixels included in each albedometer footprint were extracted and averaged. Albedo values acquired at 10:30 UTC were selected for comparisons, since they matched satellite overpasses. According to the starting and ending dates of data collection that varied from one field to another, the resulting dataset included 130 ground samples. Table 1 shows very low values for the albedo coefficient of variation (CV, equal to the ratio of standard deviation to mean value) derived from FORMOSAT-2 retrievals (retrieving method explained in Section 3) over the albedometer footprints. Albedo could therefore be considered quite homogeneous, even for the maize field that depicted an albedo CV twice larger than those depicted by the other fields.

For LAI, ground based measurements and FORMOSAT-2 pixels were collected or selected in order to consider representative values at the field scale. Ground samples were collected within each field according to a cross-pattern protocol, and next averaged. For each field, FORMOSAT-2 overlaying pixels were selected by excluding borders, and the corresponding waveband reflectances were averaged. Table 1 shows the LAI CV over the field extensions, derived from FORMOSAT-2 retrievals on a pixel basis (retrieving methods explained in Section 3). The low LAI CV values for the wheat, meadow and rice fields confirmed that comparing ground based and satellite data was consistent. However, the LAI CV for the maize field was significantly larger than those for the other fields, due to large heterogeneities for soil properties (Section 2.1.2). Calibration and validation results for this field were therefore carefully analyzed (Section 4 and 5). Overall, because of low heterogeneities for four fields over the fives, we expected calibration and validation results would not be affected by non linearity between LAI and reflectance values [START_REF] Garrigues | Using first-and second-order variograms for characterizing landscape spatial structures from remote sensing imagery[END_REF].

The quite low 10 day frequency of LAI ground based measurements induced a temporal interpolation was necessary, in order to obtain concurrent ground and satellite LAI estimates. For this purpose, the LAI dynamic model proposed by [START_REF] Koetz | Use of coupled canopy structure dynamic and radiative transfer models to estimate biophysical canopy characteristics[END_REF] was applied:

) Ts T ( a ) Ti T ( b e e . k LAI 1 1 (1)
T is the cumulated daily mean air temperature above vegetation zero, starting from the sowing date.

The growth period is defined by a logistic equation which parameter b is the relative growth rate at the inflexion point T i . The senescence is determined by an exponential equation which parameter a is the relative growth rate at the cumulated temperature T s when all leaves are senescent. The k parameter is the maximal leaf area. These parameters were estimated using the simplex iterative optimization method (Nelder and Mead, 1965), with a 5% residual calibration error. For irrigated meadow, this empirical model did not allow representing the cuts. Therefore, a simple linear interpolation was applied, benefiting from more frequent ground based data on this field. Figure 9 (later in the result section) illustrates LAI chronicles for the five fields. According to the starting and ending dates of data collection that varied from one field to another, the resulting dataset included 72 ground based estimates that matched FORMOSAT-2 retrievals, completed with 25 data for which the background was bare for sure, corresponding to LAI=0.

A summary on the available albedo and LAI ground measurement datasets is given in Table 2. It is shown albedo values were within the range of usual values reported in the literature, for both bare soil and vegetation cover conditions. Values for LAI were up to almost seven, which yielded us expecting saturation problems when retrieving LAI from FORMOSAT-2 reflectances, especially for these specific situations of large vegetation cover.

[Table 2] 3 Methods

When choosing the methods to be implemented for the retrieval of albedo and LAI from FORMOSAT-2 data, we concentrated on empirical approaches based on continuous ground based measurements over few representative fields. The motivations for choosing empirical approaches were multiple. In the context of exhaustively describing the spatiotemporal variability of surface properties, the FORMOSAT-2 spatial and temporal configurations allowed assessing the potentials of synergy between 1/ ground based web-sensors that continuously monitor specific biophysical variables over few locations, and 2/ high revisit frequency and high spatial resolution satellite images. Second, although using deterministic approaches has more portability, it required first inversion strategies that face the ill-posed problem and related equifinality troubles. Finally, the FORMOSAT-2 spectral and especially directional configurations allowed enlarging the assessment of empirical approaches that have been widely used for usual configurations (i.e. nadir viewing).

For albedo, the considered empirical approaches were the Narrowband-To-Broadband (NTB) conversion and the NNT based method. NTB conversion has been widely used for recovering albedo. NNT based method has been extensively employed for the retrieval of biophysical variables (fraction cover, chlorophyll content…) as reviewed by [START_REF] Baret | Estimating canopy characteristics from remote sensing observations. Review of methods and associated problems[END_REF], and was therefore considered as a candidate method for albedo retrieval. When dealing with LAI, we considered multiple linear regressions similar to NTB conversion and recently proposed by [START_REF] Eklundh | Investigating the use of Landsat thematic mapper data for estimation of forest leaf area index in southern Sweden[END_REF] for application over forests. We also assessed NNT based methods that have been widely used for retrieving LAI. In this last case, we considered to ways for applying NNT, either from reflectances to LAI, or from NDVI to LAI given NDVI has efficient normalization properties.

Stepwise multiple regression method

For a given sun direction s , albedo a( s ) over a considered spectral range can be approximated as the weighed summation of hemispherical reflectances s h j [START_REF] Jacob | Derivation of diurnal courses of albedo and reflected solar irradiance from airborne POLDER data acquired near solar noon[END_REF]:

s n j h j s j s s a 1 0 .
(2)

A specific spectral band amongst n is labeled j. The weighting coefficients j ( s ) may vary as a function of s , and have to be adjusted through stepwise multiple regressions. As explained in , , where the latter are collected with close nadir viewing:

Introduction, hemispherical reflectances

n j o s j s j s s 1 0 ) , ( ). ( ) ( (3)
This relies on assuming hemispherical and nadir bidirectional reflectances are linearly related, either because spatial variabilities do not significantly affect the ratio of nadir to hemispherical reflected radiances, or because it is possible considering a constant BRDF shape that is scaled to the observed bidirectional reflectance. This strong assumption was directly validated over a limited range of environmental conditions only [START_REF] Russell | Conversion of Nadir, narrow-band reflectance in red and near-infrared channels to hemispherical surface albedo[END_REF]Weiss et al. 2002a;Schaaf et al. 2002).

However, indirect validations were performed over a large range of environmental conditions, through the comparisons of albedo products derived from Equation 3 against reference estimates [START_REF] Brest | Deriving surface albedo measurements from narrow band satellite data[END_REF][START_REF] Russell | Conversion of Nadir, narrow-band reflectance in red and near-infrared channels to hemispherical surface albedo[END_REF][START_REF] Liang | Retrieval of land surface albedo from satellite observations: a simulation study[END_REF][START_REF] Song | An improved method to derive surface albedo from narrowband AVHRR satellite data: Narrowband to broadband conversion[END_REF][START_REF] Liang | Narrowband to broadband conversions of land surface albedo I: Algorithms[END_REF][START_REF] Liang | Narrowband to broadband conversions of land surface albedo: II Validation[END_REF][START_REF] Liang | A direct algorithm for estimating land surface broadband albedos from MODIS imagery[END_REF][START_REF] Liang | VIIRS narrowband to broadband land surface albedo conversion: formula and validation[END_REF][START_REF] Susaki | Validation of MODIS Albedo Products of Paddy Fields in Japan[END_REF]. For the current study, the additional difficulty was using off nadir bidirectional reflectance (zenith and azimuth angles of 41° and 239°, respectively), which yielded foreseeing NTB conversion may perform poorly.

The stepwise multiple linear regression method has been applied by several authors for different spectral and angular configurations. Given no coefficient set were available for the FORMOSAT specific configuration over the Crau-Camargue study site, we assessed the performances of a coefficient set calibrated over the collected dataset, and compared against existing coefficient sets proposed by [START_REF] Weiss | Hemispherical reflectance and albedo estimates from the accumulation of across track sun synchroneous satellite data[END_REF], [START_REF] Liang | Retrieval of land surface albedo from satellite observations: a simulation study[END_REF]Jacob et al. (2002a). These coefficients sets were obtained by considering different spectral configurations (waveband locations and widths), different directional configurations (using Equation 2 and 3 for hemispherical or nadir reflectances respectively), and by considering or not the diffuse component of solar irradiance.

LAI was derived from multiple linear regression applied over bidirectional reflectances by using the same formalism as Equation 3. As compared to [START_REF] Eklundh | Investigating the use of Landsat thematic mapper data for estimation of forest leaf area index in southern Sweden[END_REF] who validated the concept with Landsat data over coniferous and deciduous forest canopies, assessing this approach was interesting with regards to the large differences in experimental conditions, whether it was the considered biomes (agricultural lands versus forests), the directional configuration (off nadir versus nadir viewing), or the spectral configuration (no shortwave infrared band with FORMOSAT-2).

For both LAI and albedo retrievals, we suspected a significant limitation when using the coefficient set calibrated over the whole Crau-Camargue dataset, with regards to changes in solar direction at the time of satellite overpass. Indeed, solar zenith (respectively azimuth) angle varied throughout the experimental period from 25° to 45°(respectively from 135° to 160°). Equation 3 was therefore adjusted for each individual date, using the five pairs of matching ground albedo measurements / FORMOSAT-2 bidirectional reflectances. Results displayed in Figure 2 showed that coefficients j ( s ) devoted to albedo did not exhibit specific features as a function of solar direction, indicating these coefficients could be assumed independent on s . The same independency was observed for the coefficients devoted to LAI (results not shown for sake of brevity). Therefore, coefficients were also assumed independent on s for LAI in Equation 3.

[Figure 2]

Neural network based method (NNT)

Neural networks enabled relating the FORMOSAT-2 Green, Red and NIR waveband reflectances to either ground based albedo values or interpolated LAI (labeled NNT Ref ). The Blue waveband was omitted because it considerably degraded the performances of both albedo and LAI estimations (results not reported here). Moreover, [START_REF] Jiang | Development of a 2-band Enhanced Vegetation Index without a blue band[END_REF] demonstrated that, for a large range of vegetation conditions at the global scale, the inclusion of the Blue band does not significantly improve the vegetation characterization. We used the feed-forward back-propagation algorithm detailed in [START_REF] Hagan | Training feed-forward networks with the Marquardt algorithm[END_REF]. It was made of made of a single hidden layer with two tangent-sigmoid neurons, and one output layer with a single linear neuron (Figure 3). Prior to training, inputs and outputs were normalized by their minimum and maximum values. The learning process was achieved using the Levenberg-Marquardt back-propagation method. Twenty random initializations were tested and the one providing the best performance was selected. Implementing the neural network required 11 coefficients to be tuned over the training data set (eight weights and three biases, Figure 3a). Hyper specialization was not evaluated due to the lack of independent data.

It was however reduced by the minimal architecture selected for the network.

[Figure 3]

Neural networks were also used for relating NDVI to interpolated LAI (labeled NNT NDVI ). In this case, the implementation of the neural network required seven coefficients only to be tuned over the training data set (four weights and three biases, Figure 3b). Indeed, this implementation was based on a unique NDVI independent variable, whereas the previous NNT design was based on three independent variables as inputs, i.e. the Green, Red and NIR reflectances (Figure 3a).

Exponential law based method

Among the various relationships between NDVI and LAI proposed in the literature, we considered for the current study the exponential law derived from the studies of [START_REF] Asrar | Estimating absorbed photosynthetic radiation and leaf area index from spectral reflectance in wheat[END_REF], [START_REF] Baret | Potentials and limits of vegetation indices for LAI and PAR assessment[END_REF] and Wilson and Meyer (2007), and which has been widely used.

NDVI NDVI NDVI NDVI ln . K LAI s LAI 1 (4)
NDVI is the asymptotic value of NDVI when LAI tends towards a maximum value, NDVI s is the bare soil NDVI value and K LAI is an extinction coefficient. The simplex optimization approach was used to adjust parameters NDVI , NDVI s, and K LAI by minimizing the Root Mean Square Error (RMSE) between measured and estimated LAI.

Calibration and validation procedures and performance metrics

The experimental data set (sample number N=130 for albedo and 97 for LAI) was not large enough to be split into independent calibration and validation datasets. Therefore, a "leave-one-out" crossvalidation method [START_REF] Stone | Cross-validatory choice and assessment of statistical predictions[END_REF][START_REF] Geisser | The predictive sample reuse method with applications[END_REF]) was used for validation. It consisted in calibrating over n-1 data, and validating over the remaining "left-out" data. This process was repeated N times to cover the whole dataset. Then, performances were assessed using standards metrics:

Absolute Mean Error (ME A ), was the bias between measured (M i ) and estimated (E i ) values,

n i i i A ) M E ( n ME 1 1 (5)
Absolute Root Mean Square Error (RMSE A ) quantified the scatter between measured and estimated values, and Relative Root Mean Square error (RMSE R ) was the ratio of RMSE A to the mean of measured values M i .

n i i i A ) M E ( n RMSE 1 2 1 i A R M RMSE RMSE (6)

LAI versus Albedo

The large dataset of albedo and LAI, that included spatialized estimates spreading over entire crop cycles, allowed analyzing a possible relationship between these two biophysical variables. To be able to compare and understand such a possible relationship, radiative transfer simulations were carried out for conditions similar to those prevailing during the experiment. LAI and albedo values were simulated using the canopy reflectance model PROSAIL [START_REF] Jacquemoud | PROSPECT + SAIL Models: a review of use for vegetation characterization, Remote Sensing of Environment[END_REF] for three types of ground surfaces (water, dry soil and wet soil), and a range of leaf inclination angles (20°, 58° and 70°) under a constant zenith angle of 30°. These values corresponded to averaged values that were representative of the experimental conditions. Diffuse fraction and spectral irradiance were simulated using the 6S atmosphere radiative transfer model [START_REF] Vermote | Second simulation of the satellite signal in the solar spectrum, 6S: an overview[END_REF] with midlatitude summer atmosphere and clear conditions (aerosol optical thickness at 550 nm set to 0.2347). All the other variables used for the simulations corresponded to typical average values representative of soil and vegetation conditions similar to the Crau-Camargue conditions (Table 3).

[Table 3]

Results and discussion

This section presents the results we obtained when retrieving albedo ( § 4.1) and LAI ( § 4.2), as well as when analyzing a possible relationship between both ( § 4.3). For the retrieving of albedo and 4.1 Albedo estimates from FORMOSAT-2 data

Comparison of the different method performances

Table 4 displays the results we obtained for the retrieval of albedo, when calibrating NTB conversion and NNT method over the Crau-Camargue dataset (Set 1 and NNT), and when validating coefficient sets proposed by previous studies for other sensors with different spectral and direction configurations. Set 2 and 3 were calibrated over a simulated dataset, and designed for hemispherical reflectances collected within generic wavebands [START_REF] Weiss | Hemispherical reflectance and albedo estimates from the accumulation of across track sun synchroneous satellite data[END_REF]. Set 4 was calibrated over a measured dataset, and designed for hemispherical reflectances collected within PolDER wavebands (Jacob et al., 2002a). Set 5 was calibrated over a measured dataset, and designed for nadir bidirectional reflectances collected within MISR waveband [START_REF] Liang | Retrieval of land surface albedo from satellite observations: a simulation study[END_REF].

[Table 4]

The stepwise multiple regression (Equation 3) calibrated over the Crau-Camargue dataset was obtained by selecting positive and statistically significant bands only (Set 1). Best performances were obtained when using the Red and NIR bands only, with a corresponding offset equal to 0.

Thus, absolute bias ME A was almost negligible and Relative Root Mean Square Error RMSE R was acceptable, around 7.5%. These validation results were comparable to calibration residual errors reported by [START_REF] Weiss | Hemispherical reflectance and albedo estimates from the accumulation of across track sun synchroneous satellite data[END_REF], [START_REF] Liang | Retrieval of land surface albedo from satellite observations: a simulation study[END_REF] and Jacob et al. (2002a), and were close to relative accuracy of albedometer measurements and FORMOSAT-2 corrected data (around 5%).

Similarities in performances for Set 1 versus Set 2 and 4 were explained by similarities in coefficient values, the latter varying of about 8 and 14% in relative for the red and near infrared bands, respectively. When applying coefficients Set 3 and 5 that included the Green band; performances were even worse as compared to Set 2 that included Red and NIR bands only. This indicated the Green band could have added more noise than information in albedo estimation.

We could not discriminate performances according to the consideration of hemispherical or nadir bidirectional reflectances, whereas the best performances were observed with the data set of FORMOSAT-2 off nadir bidirectional reflectance. These both elements contributed to strengthen the directional approximations formulated in Section 3.1, when assuming NTB conversion could also be applied to off nadir bidirectional reflectances. However, this positive report ought to be moderated because of additional complexities when comparing the different coefficient sets, such as the combined effects between differences in spectral configurations and land surface properties.

When dealing with the coefficient Set 1 that was calibrated over the Crau-Camargue dataset, the sum of the coefficients appeared to be almost equal to one (column in Table 4). This was in agreement with [START_REF] Brest | Deriving surface albedo measurements from narrow band satellite data[END_REF][START_REF] Brest | Deriving surface albedo measurements from narrow band satellite data[END_REF]Jacob et al. (2002a). Indeed, the whole solar spectrum could be split into nominal spectral intervals, and supposedly fully scanned through the corresponding wavebands. Then, the associated weighting coefficients corresponded to the fractions of solar irradiance over these intervals. However, this physical assumption might be far from reality when characterizing the whole spectral domain by using a visible and a near infrared band only.

The Blue band was never significant in the considered coefficient sets: its weight might be relatively small due to the low radiation level. Further, it might also be considerably disturbed by residual atmospheric effects due to inappropriate aerosol corrections. Moreover, this band might not provide additional information. Indeed, [START_REF] Jiang | Development of a 2-band Enhanced Vegetation Index without a blue band[END_REF] reported strong correlations with the Red band for a for a large range of vegetation conditions at the global scale.

Inspecting performances from one field to another showed that those were lower over rice and meadow, with RMSE R of 10.5% and 10.1% respectively. Figure 4a emphasizes the difficulties for the regression to fit the scattering induced by very different situations between meadow and rice, with an overestimation (respectively underestimation) for rice albedo (respectively freshly cut meadow albedo). These poor performances could be explained by the lack of water sensitive shortwave infrared (SWIR) wavebands within the FORMOSAT-2 configuration. Indeed, inclusion of such bands might improve albedo estimation under conditions of wet soil and free water background. To our knowledge, very few studies tried to estimate rice albedo from remote sensing, probably because of additional difficulties induced by the presence of water background. Very recently, [START_REF] Susaki | Validation of MODIS Albedo Products of Paddy Fields in Japan[END_REF] obtained a RMSE R of 15.1 % with ASTER data over rice cultures in Japan, when applying the appropriate coefficient set proposed by [START_REF] Liang | Narrowband to broadband conversions of land surface albedo I: Algorithms[END_REF]. This error was 20 larger than that obtained here, indicating our calibrated coefficient set was acceptable, despite 1/ the consideration of complex surfaces that combined water and vegetation, 2/ the absence of FORMOSAT-2 SWIR waveband, and 3/ the consideration of off nadir bidirectional reflectances.

[Figure 4] Table 4 also indicates the NNT method had the best performance. The improvement mainly occurred for meadow (RMSE R decreasing from 10.3% to 4.3%), and in a lesser extent for rice and maize (Figure 4b). Performance improvement systematically corresponded to albedo values lower than 0.2, i.e. for crops with low amount of vegetation and wet or dark soil background. As compared to the simple linear multiple regression, the NNT were more flexible, thanks to both their non linear character and their larger degree of freedom (number of coefficients to be tuned, see last column of Table 4). This could explain the better performances observed in complex situations, with variable background properties and low amount of vegetation. Even if the obtained RMSE R was 3.5%, it could be set to 5%, which corresponded to the accuracy of both albedometer measurements and FORMOSAT-2 corrected data. It is worth noting this NNT based empirical approach has never been applied to albedo estimation, and such results are quite encouraging.

Further applications on other datasets would be necessary for additional validations. Both wheat fields had comparable albedo dynamics, while bare soils exhibited contrasted time courses after harvesting (DOY 179), and especially after DOY 220 (pointed by an arrow in bottom left subplot of Figure 5). This was mainly due to green vegetation re-emergence in wheat Field #1.

Dynamics of Albedo as estimated from FORMOSAT-2 data

Maize field dynamics showed limited amplitudes of variation, the few large changes being ascribed to irrigation practices. Dynamics of albedo for rice showed a significant increase when the canopy developed. This was in agreement with observations from [START_REF] Maruyama | Dependence of solar radiation transport in rice canopies on developmental stage[END_REF] over rice crops.

Indeed, they reported a first period with low albedo values (around 0.10) that corresponded to low vegetation cover overlaying a water or very wet soil background, and followed by an albedo increase during vegetation growth, until it stabilized around a value of 0.18 to 0.20.

[Figure 5] variations. This was mainly explained by irrigation or rainfall events, which induced a systematic albedo drop (between 0.01 and 0.04) that vanished after two or three days. Note that the cuts did not induce large albedo variation, probably because a significant fraction of green vegetation was kept.

[Figure 6]

4.2 LAI estimates from FORMOSAT-2 data

LAI as a function of individual reflectances

Table 5 displays the parameters we obtained when calibrating the various empirical methods to be considered when retrieving LAI from FORMOSAT-2 data. Are also indicated the corresponding performances in terms of absolute bias, absolute and relative root mean square errors. We recall LAI references were obtained from ground based measurements through a temporal interpolation ( §2.1.5). Statistical analysis through stepwise regression retained the Red and NIR wavebands only.

As illustrated by Figure 7a that displays the "leave-one-out" cross-validation, the corresponding performances were significantly poor. Further, the RMSE R values displayed in Table 5 were larger than those obtained by Fassnacht et al. (1995), [START_REF] Eklundh | Investigating the use of Landsat thematic mapper data for estimation of forest leaf area index in southern Sweden[END_REF] and Jensen and Binford (2004).

[Table 5]

[Figure 7]
As compared to the previous studies abovementioned, the lower performances we observed were explained by differences in land surface properties and remotely sensed information. Indeed, these former studies were devoted to the monitoring of forests from Landsat Thematic Mapper (TM), thus benefiting from both lower spatial heterogeneities, and from additional spectral information through shortwave infrared (SWIR) wavebands. For the current study, the significantly poor performances were ascribed to several factors. The first one was the large variabilities of canopy structure and soil background properties, to be both taken into account with three freedom degrees only (Table5).

Second, the absence of FORMOSAT-2 SWIR waveband may contribute to the poorer performances in LAI estimation. Indeed, [START_REF] Eklundh | Investigating the use of Landsat thematic mapper data for estimation of forest leaf area index in southern Sweden[END_REF] obtained a significant contribution of the SWIR wavebands while estimating the LAI over a forest using the multiple regression approach.

Rice was the unique field for which albedo was reasonably well estimated, all the other fields corresponding to large scattering between measured and estimated values. Although stepwise multiple linear regression could have been independently applied over each of the four land cover classes, the restricted data set would have prevented from obtaining robust relationships.

Additionally, the maize field was quite heterogeneous, and the ground sampling was probably too small to obtain a representative value of the field LAI.

Training of neural networks over individual reflectances (NNT Ref ) showed significant improvements of retrieval performances. The RMSE values were indeed twice lower (Table 5 first line as compared to second one, and Figure 7c as compared to Figure 7a). This was ascribed to the larger number of coefficients to be tuned (Table 5). Regardless of the considered field, the scattering between estimated and measured LAI values (Figure 7c) was similar.

LAI as a function of NDVI

Table 5 and Figure 7b show that both the NDVI based heuristic formulation (exponential shape) approach and the NDVI based neural network approach NNT NDVI performed better than the reflectances based approaches, whether it was NTB conversion or NNT.

A unique set of parameters for the heuristic formulation (Equation 4) was adjusted over the whole set of (ground based LAI, FORMOSAT-2 NDVI) pairs. Value of NDVI (Table 5) was very comparable to those obtained by [START_REF] Weiss | Validation of neutral techniques to estimate canopy biophysical variables from remote sensing data[END_REF] and [START_REF] Wilson | Determining vegetation indices from solar and photosynthetically active radiation fluxes[END_REF] over similar vegetation types but with different viewing angles (nadir looking with these former studies, against 41°zenith / 239°azimuth with the current study), and probably different solar directions. This may explain why K LAI value obtained in the current study (0.71) was slightly larger than that obtained (0.67) by [START_REF] Weiss | Validation of neutral techniques to estimate canopy biophysical variables from remote sensing data[END_REF]. The NDVI normalization properties appeared to be efficient. With three freedom degrees only, better performances were obtained than with the 11 freedom degree of the reflectance based NNT method, the RMSE R dropping down by 20% in relative.

Training a neural network with measured LAI and NDVI values allows more flexibility in the shape of the relationship between these two variables. Seven parameters had indeed to be tuned, as compared to three parameters when using heuristic formulation (Equation 4). Results show this method performed best, with a RMSE R value of 27.54% (Table 5 and Figure 7d). These good performances were ascribed to the combined effect of NDVI efficient normalization properties and the NNT flexibility. However, saturation problems still were observed for LAI values larger than 4, a problem that may result from the saturation of the remotely sensed signal over the optical domain.

Figure 8 illustrates the LAI -NDVI relationship generated by both the NNT NDVI and the heuristic formulation (Equation 4). Both methods followed a smooth exponential trend in compliance with Equation 4. The figure also shows how the heterogeneous, row-planted maize crop exhibited a different behavior than the other homogeneous vegetation covers. This heterogeneity in structure and field cover could have made the LAI -NDVI relationship quite different over this crop.

Consequently, the latter was not well characterized through the multi-crop calibrated relationship.

[Figure 8]

Dynamics of LAI as estimated from FORMOSAT-2 data

Dynamics of FORMOSAT-2 LAI retrieved from the best performing NNT NDVI approach was very smooth, as expected (Figure 9). Dynamics showed a classical temporal pattern for wheat, maize and rice, with increase LAI during the vegetative growth, followed by a relatively rapid senescence.

Rice and maize crops depicted bare soil conditions (LAI=0) at the beginning. Wheat fields showed significant amount of green vegetation after harvest (LAI 0.4), presumably corresponding to weeds that developed after the rainfall events observed around DOY 255. Dynamics of meadow shows the three cuts and the re-emergence just afterwards. Note that since LAI was around one just after the cuts, this explains why the albedo dynamics was not affected by these cuts.

[Figure 9]

LAI versus Albedo

NNT based FORMOSAT-2 retrievals of both LAI and albedo over the whole study area were matched for all vegetation types and for all acquisition dates. Figure 10 displays the resulting boxplots along with the corresponding statistics (mean value, lower and upper quartiles), and the ground based measurements. It is shown when LAI increases, albedo follows almost the same trend for wheat, meadow and maize. However, rice behaves differently, and especially for LAI values lower than 2.5. The general trend observed over the whole area from FORMOSAT-2 retrievals was similar to that observed over the five fields where measurements were collected. However, most of the field data were outside the 95% confidence interval of albedo variation within each LAI class.

This indicated although ground based data were representative of each field as shown by the low CV values in Table 1, the fields were not representative of the land use classes. Although this was not expected, consequences on the empirical models calibrated for estimating LAI and albedo might be marginal. Indeed, calibrations were performed by including all crops and dates, while LAI and albedo measured values covered most of the ranges observed across the study area and period.

[Figure 10]

Figure 11 displays the LAI -albedo relationship simulated from radiative transfer modeling ( § 3.5).

For the investigated crops, these simulations agree very well with observations displayed on [Figure 11]

Conclusion

This study demonstrated that it is possible accurately retrieving albedo and LAI from the specific FORMOSAT-2 observations, along with empirical approaches based on restricted spatial sampling but continuous monitoring. Although calibrations were performed by including all data collection dates and all crops (wheat, maize, rice and meadow), very good performances were achieved.

Further, the advantages of the neural network techniques (NNT) over linear multiple regressions or heuristic formulations was demonstrated. For the first time an NNT based method was used to retrieve albedo, and the results were quite encouraging.

Due to the relatively small sample size, the empirical models established for retrieving LAI and albedo probably need additional independent evaluation about their robustness, with emphasis on the sampling strategy that optimizes the number, locations and dates of the ground based measurements. When applied over orchards and vineyards, attention should also be paid to row orientations relatively to solar or viewing directions. Furthermore, these relationships were calibrated under the specific FORMOSAT-2 viewing conditions that are latitude / longitude dependent (here, zenith angle = 41°and azimuth angle = 239°). Application to other conditions may require adaptations, either by using radiative transfer models if well calibrated over the considered surfaces, or by replicating the whole experimental process under these new conditions.

Alternative approaches based on radiative transfer model inversion were not considered in this study, and should require further efforts. This might be possible under conditions of well defined prior information, given single multi-date and multi-crop calibration of empirical approaches yielded accurate estimates of LAI and albedo, and this in spite of limited information provided by the FORMOSAT-2 samplings (three wave bands and a single off nadir viewing direction).

Another original output of this study was the possibility to investigate the spatial correlation between albedo and LAI. We observed great consistencies when comparing albedo -LAI 5).

  modeling of BRDF. When observations are available in a single viewing direction only, several studies proposed directly applying Equation 2 on bidirectional reflectances o s j

Figure 5

 5 Figure 5 displays albedo dynamics captured throughout the study period from ground based

Figure 6

 6 Figure 6 displays albedo dynamics captured throughout the study period from ground based

Figure 10 .

 10 Figure 10. The soil background played a major role for low to moderate LAI values (LAI<3), which

Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :Figure 8 :Figure 9 :Figure 10 :Figure 11 :

 34567891011 Figure 3: Neural network architecture when inputs were a) the green, red, and near infrared reflectances ( ) and b) NDVI only. The squares represent the input and output variables, and the circles represent both the two tangent sigmoid neurons of the hidden layer and the single linear neuron of the output layer. The network structure required for a) 11 coefficients to be tuned: eight weights (w1…w8) and three biases (b1…b3) and for b) seven coefficients to be tuned: four weights (w1…4) and three biases (b1…b3).

©NSPO (2006) and distributed by SPOT Image S.A. all rights reserved. We would like to thank farmers for allowing us to make use of their fields for various measurements, Jean-François Hanocq for his technical contribution, Françoise Ruget for her agronomy expertise and Jean-Claude Mouret of INRA Montpellier for providing us with information on rice plantations.

meadow, #4 for maize and #5 for rice.

Acknowledgments

This study was part of projects financed by the MIP-PACA regions in France and by the CNES (DAR 2006 TOSCA). This work was done thanks to the post-doctoral financial support of INRA 'Environnement et Agronomie' department. The FORMOSAT-2 images used in this paper are