Keywords: Remote sensing, spatial heterogeneity, upscaling, downscaling, agricultural landscape, forestry

This paper closes a special Stream that focuses on spatial heterogeneity when mapping biophysical variables over agricultural landscape from solar and thermal infrared remote sensing. We propose an overview of the highlights from prior research, we report the main results of the special stream, and we discuss future directions. The main outcomes of the special stream are related to: 1) the impact on the remotely sensed signal of canopy vertical distribution, shadowing effects, and multiple scattering; 2) the notion of spatial resolution limit in relation to spatial heterogeneity; and 3) the definition of an optimal sampling strategy to spatialize ground measurements.

I. INTRODUCTION

GRICULTURAL landscapes, including crops, rangelands and managed forests, are typical instances for studying global changes. Their evolution is influenced by several factors, either natural (e.g., climate) or anthropogenic (e.g., farmer practices, regional management, governmental incentives). Adapting anthropogenic forcing requires decisionmaking systems that rely on diagnostic and prognostic tools. In this context, land surface processes are described with biophysical models that must be parameterized, calibrated and validated. This can be achieved with Earth observation data.

Remote sensing is one of the most efficient means to capture spatial patterns related to land surface processes, at given temporal sampling and spatial resolution. The remote sensing technique is usually chosen according to the targeted variable: solar domain to retrieve 1 fraction of absorbed photosynthetically active radiation (fAPAR), leaf area index (LAI) and gross primary production (GPP), or thermal infrared (TIR) domain to retrieve land surface temperature (LST).

A large part of the literature has addressed this topic [START_REF] Baret | Estimating Canopy Characteristics from Remote Sensing Observations: Review of Methods and Associated Problems[END_REF][START_REF] Jacob | Modeling and Inversion in Thermal Infrared Remote Sensing over Vegetated Land Surfaces[END_REF]. Due to technical and methodological limitations, most investigations have been conducted under quite homogeneous and flat conditions, with the use of decametric to kilometric spatial resolution sensors. However, agricultural landscapes are highly heterogeneous, due to crop mosaics and canopy structures. F. Jacob is with IRD -UMR LISAH, Montpellier, France (e-mail: frederic.jacob@ird.fr). M. Weiss is with INRA -UMR 1114 EMMAH, Avignon, France (e-mail: marie.weiss@paca.inra.fr).

Financial supports were provided by Agropolis Foundation (contract 0901-013), ANR TRANSMED (contract ANR-12-TMED-0003-01) and the MISTRALS / SICMED program.

Recent observing systems and modeling improvements now allow the investigation of such complex terrains and canopies.

The IEEE Geoscience and Remote Sensing Letters (IEEE-GRSL) opened a call for submission of research papers, through a Special Stream devoted to solar and thermal infrared remote sensing of biophysical variables in agricultural landscapes characterized by spatial heterogeneity. Among 23 submissions, eight papers were accepted for publication, temporally distributed from July 2013 to January 2014. The papers addressed the implications of spatial heterogeneity when mapping a panel of biophysical variables (surface reflectance, chlorophyll fluorescence, LST, LIDAR waveform, GPP, and fAPAR), over various agrosystems (forests, orchards, vineyards, crops, and grasslands), using different remote sensing techniques (active and passive sensors over the solar and thermal infrared spectral domains), onboard different platforms (airborne and satellite).

This paper concludes the Special Stream by focusing on the main outcomes in light of prior research. Section II discusses how spatial heterogeneity is considered in the literature. Section III presents the methodological strategies that have been developed to overcome the difficulties induced by spatial heterogeneity. Section IV provides an overview of the highlights from prior research. Section V details the outcomes from the Special Stream. Section VI concludes the paper by identifying some critical issues to be addressed in the future.

II. SPATIAL HETEROGENEITY IN REMOTE SENSING

In relation to technological constraints and intrinsic characteristics, any remotely sensed measurement corresponds to a mixed pixel that depicts horizontal and vertical heterogeneities. As stated by [START_REF] Marceau | Remote sensing contributions to the scale issue[END_REF], there is no single definition of spatial heterogeneity, because it is usually regarded according to the considered scales and the targeted variables.

Spatial heterogeneity results from the patterns observed at a given scale that is driven by the sensor sampling capabilities [START_REF] Duveiller | A conceptual framework to define the spatial resolution requirements for agricultural monitoring using remote sensing[END_REF][START_REF] Tarnavsky | Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products[END_REF]. At the landscape scale, spatial heterogeneity is characterized either by the length scale beyond which it cannot be captured (textural features) or by the sizes and shapes of landscape elements (contextural features) [START_REF] Chen | Spatial Scaling of a Remotely Sensed Surface Parameter by Contexture[END_REF]. In this case, spatial heterogeneity can be described with land use maps [START_REF] Plexida | Selecting landscape metrics as indicators of spatial heterogeneity-A comparison among Greek landscapes[END_REF] or geomorphological maps [START_REF] Gomez | Regional predictions of eight common soil properties and their spatial structures from hyperspectral Vis-NIR data[END_REF]. It can also be characterized through semi-empirical parameters derived from the angular signature of the bidirectional reflectance [START_REF] Chen | Global mapping of foliage clumping index using multi-angular satellite data[END_REF][START_REF] Pinty | Uniqueness of multiangular measurements. I. An indicator of subpixel surface heterogeneity from MISR[END_REF]. At the field scale, spatial heterogeneity is usually defined according to canopy vertical structure [START_REF] Wang | Canopy vertical heterogeneity plays a critical role in reflectance simulation[END_REF], horizontal structure [START_REF] Widlowski | Horizontal radiation transport in 3-D forest canopies at multiple spatial resolutions: Simulated impact on canopy absorption[END_REF], or both [START_REF] Stenberg | Modeling the Spectral Signature of Forests: Application of Remote Sensing Models to Coniferous Canopies[END_REF].

Spatial heterogeneity also results from radiative transfer

Mapping biophysical variables from solar and thermal infrared remote sensing: focus on agricultural landscapes with spatial heterogeneity.

Frederic Jacob, Member, IEEE and Marie Weiss, Member, IEEE A processes that are driven by spatial structures and land surface processes. The solar observations are influenced by several factors such as shadowing effects or multiple scattering [START_REF] Widlowski | Horizontal radiation transport in 3-D forest canopies at multiple spatial resolutions: Simulated impact on canopy absorption[END_REF]. The thermal observations are also affected by multiple scattering and shadowing effects, as well as by vegetation and soil water status [START_REF] Van Der Tol | An integrated model of soil-canopy spectral radiances, photosynthesis, fluorescence, temperature and energy balance[END_REF].

As driven by spatial patterns and land surface processes, spatial heterogeneity varies with scale and time. It decreases with larger scale [START_REF] Tarnavsky | Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products[END_REF], and varies with the temporal evolution of the elements within the spatial patterns or vertical strata [START_REF] López-Lozano | Sensitivity of gap fraction to maize architectural characteristics based on 4D model simulations[END_REF].

III. METHODOLOGICAL STRATEGIES

In the context of using solar and thermal remote sensing to map biophysical variables over agricultural landscapes, several methods were developed to account for spatial heterogeneity. We provide an overview of these approaches by dividing them into two types: bottom-up and top-down approaches.

Bottom-up approaches aim to estimate biophysical variables over a given extent by accounting for spatial heterogeneity within this extent. This includes simulating remotely sensed measurements with radiative transfer models (RTM, Section III.A), spatializing local ground measurements (Section III.B), and correcting errors induced by spatial heterogeneity within coarse-resolution pixels (Section III.C).

Top-down approaches use ancillary information to retrieve biophysical variables for scene components horizontally or vertically distributed within the pixel. They rely on unmixing methods (Section III.D). Spatial heterogeneity is characterized by both the description level (e.g., the number of components) and the type of ancillary information used for unmixing (e.g., LAI, temperature, land use).

A. Spatial heterogeneity and radiative transfer modeling

Radiative transfer models (RTM) simulate the remotely sensed signal according to a given representation of the scene within the pixel. The representation accounts for spatial heterogeneity with different levels of complexity in terms of spatial structures and radiative transfer processes.

At the basic level of complexity, spatial heterogeneity can be described by considering few scene components that are distributed vertically (e.g., soil and vegetation, eventually shaded and sunlit) or horizontally (e.g., land use classes). The radiative transfer modeling is then restricted to linear or quadratic combinations of radiative properties such as reflectance or temperature [START_REF] Li | A practical algorithm to infer soil and foliage component temperatures from bi-angular ATSR-2 data[END_REF][START_REF] Pisek | Retrieval of seasonal dynamics of forest understory reflectance in a Northern European boreal forest from MODIS BRDF data[END_REF].

At the intermediate level of complexity, 1-D structures are associated to turbid RTM to describe vertical heterogeneity. They encompass several layers, including the soil, and each layer can include several elements with different radiative properties [START_REF] Jacquemoud | PROSPECT + SAIL models: A review of use for vegetation characterization[END_REF][START_REF] Van Der Tol | An integrated model of soil-canopy spectral radiances, photosynthesis, fluorescence, temperature and energy balance[END_REF]. 2-D structures are associated to geometricoptics models with a limited number of inputs, to describe both horizontal and vertical heterogeneity. They include geometrical elements such as parallelepipeds, cylinders, or ellipsoids in relation to the shapes of trunks, stems, or foliage [START_REF] Yu | Modeling directional brightness temperature over a maize canopy in row structure[END_REF].

At the highest level of complexity, 3D mock-ups are associated to radiosity or ray tracing methods with a large number of inputs [START_REF] Disney | Monte Carlo ray tracing in optical canopy reflectance modelling[END_REF][START_REF] Kotchenova | Modeling lidar waveforms with time-dependent stochastic radiative transfer theory for remote estimations of forest structure[END_REF]. They describe the scene as an ensemble of elements such as triangles or cells.

B. Spatial heterogeneity and spatialization methods

Spatialization methods aim to produce biophysical variable maps from a limited number of local measurements distributed over a given extent. This requires two steps: first to develop spatial sampling strategies and second to apply spatialization methods. Both steps rely on using ancillary information to characterize the spatial heterogeneity.

The ancillary information must be strongly correlated with the biophysical variable of interest. Different sources of information are used and can be related to anthropogenic factors (e.g., land use), biophysical variables (e.g., GPP), or geomorphological drivers (e.g., soil properties).

Sampling strategies generally use classification maps to optimize the number and location of the measurements [START_REF] Martínez | Derivation of high-resolution leaf area index maps in support of validation activities: Application to the cropland Barrax site[END_REF]. Spatialization methods rely on either transfer functions (e.g., relationships between the measurements and the ancillary information), or geostatistics with or without ancillary information (e.g., ordinary or collocated kriging) [START_REF] Berterretche | Comparison of regression and geostatistical methods for mapping Leaf Area Index (LAI) with Landsat ETM+ data over a boreal forest[END_REF].

C. Spatial heterogeneity and coarse resolution pixel

The biophysical variable value at coarse resolution is the arithmetic average of the biophysical variable at finer resolution. When estimating the biophysical variable from remote sensing data, this is still the case when the surface is homogeneous or when the surface is heterogeneous and the relationship F between the remotely sensed signal and the variable is linear. However, when F is nonlinear and the surface is heterogeneous, arithmetic averaging is not valid [START_REF] Liang | Numerical experiments on the spatial scaling of land surface albedo and leaf area index[END_REF]. The associated biases have been quantified in different ways: by comparing the biophysical variable value obtained by averaging the fine resolution estimates with the one issued from the coarse resolution [START_REF] Liu | Scaling of land surface temperature using satellite data: A case examination on ASTER and MODIS products over a heterogeneous terrain area[END_REF][START_REF] Weiss | Investigation of a model inversion technique to estimate canopy biophysical variables from spectral and directional reflectance data[END_REF], or by combining F non-linearity derived from Taylor decomposition with spatial heterogeneity quantified from variogram analysis [START_REF] Garrigues | Influence of landscape spatial heterogeneity on the non-linear estimation of leaf area index from moderate spatial resolution remote sensing data[END_REF]. As heterogeneity is scale dependent, the biases depend upon the resolution difference between the coarse and fine pixels [START_REF] Tian | Multiscale analysis and validation of the MODIS LAI product: I. Uncertainty assessment[END_REF].

D. Spatial heterogeneity and unmixing methods

Unmixing methods consist of retrieving the biophysical variable for each homogeneous scene component within the pixel. These components are horizontally (e.g., crop mosaic) or vertically (e.g., understory and trees) distributed.

Vertical heterogeneity is commonly addressed by inverting linear RTM to retrieve biophysical variables for canopy strata (e.g., the LAI for understory and tree crown [START_REF] Pisek | Retrieval of seasonal dynamics of forest understory reflectance in a Northern European boreal forest from MODIS BRDF data[END_REF] or the temperature for soil and vegetation [START_REF] Li | A practical algorithm to infer soil and foliage component temperatures from bi-angular ATSR-2 data[END_REF]). Linear RTMs consider only single scattering, which assumes that the vertically distributed elements do not interact. This is equivalent to projecting the vertical distribution on a horizontal plane in the viewing direction. The inversion of nonlinear RTM has been mainly conducted using LIDAR data, in order to characterize forest canopy structure [START_REF] Koetz | Inversion of a lidar waveform model for forest biophysical parameter estimation[END_REF].

Horizontal heterogeneity in unmixing methods is commonly addressed by disaggregating pixels, with ancillary information at finer spatial resolution. The goal is to use fine spatial infor-mation from high-resolution sensors and high revisit frequency of coarse-resolution sensors. Disaggregation is usually achieved by fitting multi-linear regressions between the biophysical variable at coarser resolution and the ancillary information at finer resolution. Ancillary information can be the same biophysical variable at the resolution of homogeneous land units [START_REF] Busetto | Combining medium and coarse spatial resolution satellite data to improve the estimation of sub-pixel NDVI time series[END_REF], or a panel of other variables [START_REF] Merlin | Multidimensional Disaggregation of Land Surface Temperature Using High-Resolution Red, Near-Infrared, Shortwave-Infrared, and Microwave-L Bands[END_REF]. This assumes that the biophysical variable of interest is spatially correlated with the ancillary information [START_REF] Zhan | Disaggregation of remotely sensed land surface temperature: Literature survey, taxonomy, issues, and caveats[END_REF].

IV. RESULTS FROM PRIOR RESEARCH

In relation to the topics addressed in Section III, we discuss here breakthroughs from prior research. Therefore, some outcomes are not considered, because they have been widely published. Most of them stated that applying methods designed for homogeneous surfaces over heterogeneous areas is not adequate.

Before designing methods for mapping biophysical variables over heterogeneous surfaces, it is necessary to characterize spatial heterogeneity, according to the limited capabilities of existing sensors. Capturing spatial heterogeneity requires that the pixel size is lower than the length scale of the biophysical variable [START_REF] Garrigues | Quantifying spatial heterogeneity at the landscape scale using variogram models[END_REF]. Furthermore, pixel shape could be optimized a function of spatial heterogeneity [START_REF] Stoy | Using Information Theory to Determine Optimum Pixel Size and Shape for Ecological Studies: Aggregating Land Surface Characteristics in Arctic Ecosystems[END_REF].

The signal simulated by RTM depends on both the degree of the scene heterogeneity and the ability of the model to describe this heterogeneity. Many models have been improved to account for specific heterogeneities (e.g., leaf or plant clumping, rows, or shadowing effects) [START_REF] López-Lozano | Sensitivity of gap fraction to maize architectural characteristics based on 4D model simulations[END_REF][START_REF] Ren | Impact of sensor footprint on measurement of directional brightness temperature of row crop canopies[END_REF]. However, when comparing models with different complexities over a range of spatial heterogeneity, [START_REF] Widlowski | Third Radiation Transfer Model Intercomparison (RAMI) exercise: Documenting progress in canopy reflectance models[END_REF] showed that concluding on the best model is difficult because of differences in model assumptions.

When spatializing ground measurements to validate biophysical variable products at coarse resolution, it is necessary to associate an error estimate to the spatialized and/or upscaled variable. Only few studies investigated the quantification of this error, and they all rely on kriging methods ( [START_REF] Williams | Upscaling leaf area index in an Arctic landscape through multiscale observations[END_REF]).

When considering spatial heterogeneity within the coarse resolution pixel, [START_REF] Garrigues | Influence of landscape spatial heterogeneity on the non-linear estimation of leaf area index from moderate spatial resolution remote sensing data[END_REF] showed that the biases induced by the F non-linearity (Section III-C) can reach up to 20% for LAI at 1 km spatial resolution. The largest biases are observed for agricultural areas due to crop patches. These biases are scale dependent, and decrease with pixel resolution [START_REF] Liang | Numerical experiments on the spatial scaling of land surface albedo and leaf area index[END_REF], similarly to spatial heterogeneity (Section II). They result from observation conditions [START_REF] Duveiller | Crop specific green area index retrieval from MODIS data at regional scale by controlling pixel-target adequacy[END_REF][START_REF] Tarnavsky | Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products[END_REF], including landscape patterns that change with time, radiative transfer processes such as multiple scattering and adjacency effects, and instrumental effects such as the point spread function (PSF). Finally, the impact of spatial heterogeneity on biophysical variable retrieval depends on the degree of the F non-linearity: for LST, [START_REF] Liu | Scaling of land surface temperature using satellite data: A case examination on ASTER and MODIS products over a heterogeneous terrain area[END_REF] reported that it is moderate, with uncertainties ranging from 0.5 K to 1 K. Unmixing methods from RTM inversion usually rely on linear RTM, and address the retrieval of biophysical variables for a few scene components only. A critical issue is to make a compromise between the number of components describing the spatial heterogeneity and the retrieval accuracy of the corresponding biophysical variables. It is possible to increase the number of scene components by using multi-angular observations. Thus, [START_REF] Pisek | Retrieval of seasonal dynamics of forest understory reflectance in a Northern European boreal forest from MODIS BRDF data[END_REF] retrieved LAI of understory and crowns, and [START_REF] Timmermans | Retrieval of canopy component temperatures through Bayesian inversion of directional thermal measurements[END_REF] estimated temperature of sunlit and shaded components, additionally to soil and vegetation.

Unmixing methods based on pixel disaggregation mostly deal with surface temperature [START_REF] Zhan | Disaggregation of remotely sensed land surface temperature: Literature survey, taxonomy, issues, and caveats[END_REF]. This is motivated by the low revisit frequency of high-resolution sensors in relation to the high temporal variability of temperature, compared to other variables that monotonously and slowly change with time (e.g., LAI). Throughout the last decade, an increasing amount of ancillary information has been included in the disaggregation schemes (e.g., NDVI, emissivity, and microwave brightness temperature) [START_REF] Inamdar | Disaggregation of GOES land surface temperatures using surface emissivity[END_REF][START_REF] Merlin | Multidimensional Disaggregation of Land Surface Temperature Using High-Resolution Red, Near-Infrared, Shortwave-Infrared, and Microwave-L Bands[END_REF]. This requires characterizing the relationships between surface temperature and ancillary information. However, [START_REF] Xuehong | Scale Effect of Vegetation-Index-Based Spatial Sharpening for Thermal Imagery: A Simulation Study by ASTER Data[END_REF] questioned the scale invariance of these relationships. Overall, the obtained accuracy, between 2 K and 3 K, is still far from the requirements.

Topography is another source of spatial heterogeneity that has been addressed in few studies. Over the solar domain, [START_REF] Combal | Extending a turbid medium BRDF model to allow sloping terrain with a vertical plant stand[END_REF] showed the benefit of including topographic correction within turbid RTM. Over the TIR domain, [START_REF] Liu | Scaling of land surface temperature using satellite data: A case examination on ASTER and MODIS products over a heterogeneous terrain area[END_REF] reported an increase in accuracy of 1 K when accounting for terrain-induced angular effects in surface temperature aggregation scheme. Finally, an original direction was explored by [START_REF] Lauvernet | Multitemporal-patch ensemble inversion of coupled surface-atmosphere radiative transfer models for land surface characterization[END_REF], who took advantage of the temporal dynamics of spatial heterogeneity. They used the scene component dynamics as a priori information to constrain the inversion of an RTM. Similarly, [START_REF] Atzberger | Spatially constrained inversion of radiative transfer models for improved LAI mapping from future Sentinel-2 imagery[END_REF] constrains RTM inversion by assuming different spatial variabilities for each model variable (e.g., unique value within the field or within an pixel window).

V. OUTCOMES FROM THE SPECIAL STREAM Among the four types of methodological strategy discussed in Section III and IV, the eight papers published in the Special Stream dealt with the bottom-up approach: seven papers addressed the simulation of remotely sensed measurements, and one focused on the spatialization of local ground measurements. The top-down approach was not addressed. Table I summarizes the content of the papers in relation to the different items discussed in Sections II and III.

Four papers of the Special Stream addressed the shadowing effect on remotely sensed measurements. [START_REF] Lagouarde | Directional anisotropy of brightness surface temperature over vineyards: case study over the Medoc region (SW France)[END_REF] and [START_REF] Guillevic | Directional Viewing Effects on Satellite Land Surface Temperature Products Over Sparse Vegetation Canopies -A Multisensor Analysis[END_REF] brought up the influence of these effects on the angular signature of LST. [START_REF] Guillevic | Directional Viewing Effects on Satellite Land Surface Temperature Products Over Sparse Vegetation Canopies -A Multisensor Analysis[END_REF] showed the consequences when intercomparing and validating coarse resolution LST. In the solar domain, [START_REF] Zarco-Tejada | Spatial Resolution Effects on Chlorophyll Fluorescence Retrieval in a Heterogeneous Canopy Using Hyperspectral Imagery and Radiative Transfer Simulation[END_REF] identified shadowing effects as the cause of discrepancies between fluorescence estimates at the tree level and those at lower spatial resolutions (≥50 m). Finally, [START_REF] Guillen-Climent | Estimating Radiation Interception in Heterogeneous Orchards Using High Spatial Resolution Airborne Imagery[END_REF] took advantage of the very high spatial resolution to identify shadowed and sunlit soil to improve fAPAR estimates.

Three papers of the Special Stream addressed the notion of spatial resolution limit in relation to spatial heterogeneity. On the one hand, [START_REF] Kobayashi | Spatial Scale and Landscape Heterogeneity Effects on FAPAR in an Open-Canopy Black Spruce Forest in Interior Alaska[END_REF] and [START_REF] Ristorcelli | Simulating Space Lidar Waveforms From Smaller-Footprint Airborne Laser Scanner Data for Vegetation Observation[END_REF] showed that multiple scattering can no longer be neglected when refining the spatial resolution up to a few meters. On the other hand, [START_REF] Zarco-Tejada | Spatial Resolution Effects on Chlorophyll Fluorescence Retrieval in a Heterogeneous Canopy Using Hyperspectral Imagery and Radiative Transfer Simulation[END_REF] investigated the impact of degrading the spatial resolution when mapping vegetation fluorescence. They showed that spatial heterogeneity, induced by vegetation cover fraction, strongly affects the fluorescence signal within a mixed pixel.

Vertical heterogeneity was addressed by [START_REF] Rautiainen | Seasonal Contribution of Understory Vegetation to the Reflectance of a Boreal Landscape at Different Spatial Scales[END_REF] only. The authors showed that, for boreal forests, the understory could contribute up to 40% to the canopy reflectance. They concluded that it is necessary to account for the understory contribution when monitoring the temporal dynamics of tree LAI.

In the unique paper dealing with the spatialization of local ground measurements [START_REF] Wang | Spatial Sampling Design for Estimating Regional GPP With Spatial Heterogeneities[END_REF], the benefit of using geostatistical methods with remote sensing data was investigated. To optimize ground sampling, the authors showed the interest of considering the anisotropic feature of horizontal heterogeneity.

VI. FUTURE DIRECTIONS

Each of the studies cited in this paper addressed a specific heterogeneity. Therefore, the proposed methods and associated outcomes are not general since they are not representative of any range of agricultural landscapes.

There is a lack of studies dealing with vertical heterogeneity. Unmixing methods that rely on RTM inversion must focus on multi-layer models rather than simple linear models. This requires using multispectral and multiangular observations. We recommend accounting for the difference between temporal dynamics of canopy elements (e.g., understory or tree crown). A possible solution is to exploit these dynamics as a priori information for RTM inversion, or to decompose the time series of the composite signal through wavelet analysis.

The influence of inherent measurement factors is rarely investigated when addressing spatial heterogeneity. Multiple scattering or topography must be taken into account in both RTM direct and inverse modes. We also suggest developing correction methods for sensor PSF and gridding artefacts [START_REF] Tan | The impact of gridding artifacts on the local spatial properties of MODIS data: Implications for validation, compositing, and band-to-band registration across resolutions[END_REF].

Forthcoming sensors with high spatiotemporal resolution [START_REF] Drusch | Sentinel-2: ESA's Optical High-Resolution Mission for GMES Operational Services[END_REF][START_REF] Lagouarde | The MISTIGRI thermal infrared project: scientific objectives and mission specifications[END_REF] will offer new possibilities to address these issues. Thus, the scientific community can benefit from observations compatible with the temporal dynamics and spatial patterns of agricultural landscapes.

  Manuscript received December 16, 2013; revised March 01, 2014; accepted March, 21, 2014. Date of publication Month, DD, YEAR; date of current version Month, DD, YEAR.

TABLE I :

 I OVERVIEW OF THE SPECIAL STREAM PAPER CONTENT.

	Paper	Spatial Heterogeneity	Scale	Agrosystem	Type of Scene	Radiative Transfer Modeling	Spectral Domain	Variable of Interest	Scientific Question
	[45]	Horizontal	Field	Vineyards	2D	Linear aggregation	TIR	LST	Directional effect
									on mixed pixel
	[46]	Horizontal	Landscape	Sparse	2D	Linear aggregation	TIR	LST	Directional effect
				Vegetation					on mixed pixel
	[47]	Horizontal	Field	Orchard	2D	Linear aggregation	Solar	Fluorescence	Fluorescence
						Hybrid model			of mixed pixel
	[48]	Horizontal	Field	Orchard	2D	Linear aggregation	Solar	fAPAR	Spatial information
									from high resolution data
	[49]	Both	Landscape	Spruce	3D	Ray tracing	Solar	fAPAR	Multiple scattering
									& spatial resolution
	[50]	Both	Field	Corn, Forest,	3D	Ray tracing	LIDAR	LIDAR	Multiple scattering
				Orchard				Waveform	& spatial resolution
	[51]	Vertical	Field &	Forest	2D	Linear	Solar	Reflectance	Understory impact
			Landscape			aggregation			on signal
	[52]	Horizontal	Landscape	Grassland	2D	-	Solar	GPP	Ground sampling
				Forest					strategy

ACKNOWLEDGMENT

The editors of this Special Stream thank the scientists who contributed as authors and reviewers. We also thank Paolo Gamba for his strong and continuous support as Editor-In-Chief. Our contributions as editors and authors of this manuscript were equal, regardless of author list.


Mauricio Galleguillos

Frédéric Jacob
email: frederic.jacob@supagro.inra.fr

Laurent Prévot
email: lau-rent.prevot@supagro.inra.fr

Philippe Lagacherie
email: philippe.lagacherie@supagro.inra.fr

Shunlin Liang
email: sliang@umd.edu

Mapping daily evapotranspiration over a Mediterranean vineyard watershed

Keywords: Vineyard watershed, daily evapotranspiration, ASTER, HYDRUS-1D, S-SEBI

published or not. The documents may come

I. INTRODUCTION

Land surface evapotranspiration (ET) is a key variable in hydrology and agronomy, where the involved processes are driven by micrometeorology and soil moisture, amongst others. Knowledge of daily ET is paramount for determining crop water use which represents up to 70% of the yearly water balance within semiarid watersheds [START_REF] Moussa | Distributed hydrological modelling of a mediterranean mountainous catchment -model construction and multi-site validation[END_REF]. Since they are mostly rainfed, Mediterranean vineyards experience severe water stress, especially in summer when evaporative demand is maximal and rainfalls are negligible. Water stress is needed to regulate vine metabolism, but excessive stress can cause severe damage to production. Vineyard daily ET and vine water status should therefore be diagnosed at appropriate growth stages and forecasted under expected climate changes.

Most attempts to estimate vineyard daily ET addressed the field scale [START_REF] Ortega-Farias | Latent heat flux over Cabernet Sauvignon vineyard using the Shuttleworth and Wallace model[END_REF], whereas the consideration of larger scales from remote sensing focused on vine physiological conditions only [START_REF] Zarco-Tejada | Assessing vineyard condition with hyperspectral indices: Leaf and canopy reflectance simulation in a row-structured discontinuous canopy[END_REF]. On the other hand, the numerous models that have been developed to map daily ET from optical remote sensing have been mostly used over full cover homogeneous canopies [START_REF] Courault | Review on estimation of evapotranspiration from remote sensing data: From empirical to numerical modeling approaches[END_REF], with a desired accuracy of 0.8 mm.d -1 [START_REF] Kalma | Estimating Land Surface Evaporation: A Review of Methods Using Remotely Sensed Surface Temperature Data[END_REF].

Row structured vineyards present specific problems for estimating ET, such as the impact of turbulence within canopy and inter-row on convective fluxes, or the influence of shade effects on remote sensing data. It seems relevant to use a two source model that splits soil and vegetation, with additional differentiating between sunlit and shaded parts [START_REF] Van Der Tol | An integrated model of soil -canopy spectral radiances, photosyntesis, fluorescence, temperature and energy balance[END_REF], but parameterization complexities can induce large errors. An alternative is to derive ET from surface temperature differences rather than from absolute values, thus minimizing data and parameterization errors. Based on spatial contrasts, such differencing methods benefit from variations captured with high spatial resolution sensors [START_REF] Jacob | Mapping surface fluxes using airborne visible near infrared, thermal infrared remote sensing data and a spatialized surface energy balance model[END_REF], where Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) uniquely offers high quality spaceborne data of surface temperature [START_REF] French | Detecting land cover change at the Jornada experimental range, New Mexico with ASTER emissivities[END_REF].

Amongst differencing methods, such as the Surface Energy Balance Index (SEBI) [START_REF] Menenti | In: Exchange Processes at the Land Surface for a Range of Space and Time Scales[END_REF] or the Water Deficit Index (WDI) [START_REF] Moran | Estimating crop water deficit using the relation between surface-air temperature and spectral vegetation index[END_REF], the Simplified-SEBI (S-SEBI) [START_REF] Roerink | S-SEBI: A simple remote sensing algorithm to estimate the surface energy balance[END_REF] is characterized by its simplicity and feasibility, and is therefore a good candidate for operational purposes. It has been applied over various agrosystems [START_REF] Gomez | Retrieval of evapotranspiration over the Alpilles/ReSeDA experimental site using airborne POLDER sensor and a thermal camera[END_REF], [START_REF] Sobrino | Application of a simple algorithm to estimate daily evapotranspiration from NOAA-AVHRR images for the Iberian Peninsula[END_REF] and at different spatial resolutions [START_REF] Sobrino | A simple algorithm to estimate evapotranspiration from DAIS data: Application to the DAISEX campaigns[END_REF], [START_REF] Verstraeten | Estimating evapotranspiration of European forests from NOAA-imagery at satellite overpass time: Towards an operational processing chain for integrated optical and thermal sensor data products[END_REF]. Its assessment over vineyards is of interest since the model relies on temperature differences and albedo only, thus avoiding delicate computations of biophysical variables.

This paper reports the first results obtained when mapping daily ET over vineyards by using S-SEBI along with ASTER optical imagery over two growth cycles. Validation relies on ground based estimates at sites that differ in canopy structure, soil properties and watertable level. We first present the study site ( § II-A), methodology for both the ground based and the remotely sensed estimations ( § II-B & II-C) and the validation strategy ( § III). We next report results from the ground based ( § IV-A) and the remotely sensed ( § IV-B) estimations.

II. MATERIALS AND METHODS

A. Study site

The Peyne watershed (43.49 • N, 3.37 • E, 80 m asl) is located in the Languedoc -Roussillon region of southern France. This 65 km 2 size watershed contains vine mono-cultures (70%) over flat terrains, mostly rainfed (>95%), while the remaining 30% includes olive and wheat crops, forests, native scrubland and urban zones. Yearly Penman ET is close to 1100 mm, and annual rainfalls range between 400 and 1300 mm [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF].

The area is heterogeneous in soil type (with various parent materials) and watertable level. To capture this variability for validation purposes, seven sites were selected, corresponding to rainfed vineyards with similar trellis structures apart from row orientation (Tab. I). Each of Site 1 to 5 and 7 spread over one field, with size ranging from 0.03 to 0.09 km 2 . Site 6 had a 0.15 km 2 size and spread over nine fields that included vineyards by 90% in surface area. It was split into a north (6N) and a south (6S) sub-site for validation purposes.

B. Ground based estimates of daily ET

Amongst the possibilities for in-situ estimation of daily ET, we chose an alternative that minimized experimental efforts. It made use of the HYDRUS-1D model that simulates water transfers in the vadose zone after calibration against soil moisture profiles, provided meteorological forcing is known.

1) Field data: Hourly values of air temperature, wind speed, relative humidity, solar irradiance and rainfall were collected at Site 6 with a CIMEL ENERCO 400 station, following meteorological standards apart from wind speed (measured at 2 m height rather than 10 m). Hourly net radiation was measured over a representative vineyard within Site 6 using a Campbell NRlite device whose footprint was up to 66% vine canopy.

Each site was monitored for vegetation, watertable and soil moisture, biweekly and after rainfalls. Vegetation was monitored for canopy height and width. Watertable level was monitored down to 2.5 m with manual piezometric devices. The number of locations for collecting soil moisture profiles varied according to soil heterogeneity from a pedological map and to site size: one location for Site 1, 2, 4, 7; two locations for Site 3 and 5; and nine locations for Site 6. Profiles were sampled every 0.2 m down to 2.5 m with a Vectra 503-DR CPN Neutron Probe (NP) device, and completed for the top 0.15 m using a Soil Moisture Equipment TRASE 6050 TDR.

Eddy Covariance (EC) devices were setup within two sites that differed in soil properties and watertable level: a permanent flux tower (Site 6) and a temporary flux tower for three day windows around ASTER overpasses (Site 7). Each tower included a R.M. Young 81000 3D sonic anemometer and a fast hygrometer (Licor LI7500 for Site 6 and Campbell KH2O for Site 7). For Site 6 (resp. Site 7), that spread over nine (resp. one) fields, the sensors were setup 5.7 m (resp. 1.5 m) above canopy and acquisition frequency was 10 Hz (resp. 20 Hz). Sensible and latent heat fluxes were calculated over hourly intervals by applying double rotation and instrumental corrections from the ECPACK 2.5.20 library [START_REF] Dijk | The principle of surface flux physics: theory, practice and description of the ECPACK library[END_REF]. Fluxes were calculated with tolerance intervals, about 20% and 12% for Sites 6 and 7. For energy balance closure, convective fluxes and available energy agreed within 80% in relative. Daily ET was finally calculated as the sum of hourly ET.

Ground based data were collected from August 2007 to October 2008. Each instrument was manufacturer calibrated. The NP device was calibrated by accounting for soil type and moisture. Calibration was performed against gravimetric soil moisture data at each measurement depth (soil density was estimated using a Campbell DR 501 gamma probe), with a residual error of 0.04 m 3 .m -3 (15% relative error).

2) The HYDRUS-1D model: HYDRUS-1D is a deterministic model that simulates water transfers in the vadose zone from Richards equation [START_REF] Simunek | Modeling Nonequilibrium Flow and Transport Processes Using HYDRUS[END_REF]. Actual plant transpiration is estimated as the sum, over soil layers, of water uptake by roots, where the latter is derived from maximum transpiration through a reduction coefficient that depends on moisture. Actual soil evaporation is derived from potential evaporation according to surface pressure head.

Rainfalls were measured at the meteorological station ( § II-B1). Maximum transpiration and potential evaporation were derived from reference ET using Riou's model designed for vineyards [START_REF] Riou | Consommation d'eau de la vigne en conditions hydriques non limitantes. Formulation simplifiée de la transpiration[END_REF], [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF], [START_REF] Bsaibes | Évaluation d'une approche multi-locale d'estimation spatiale de l'évapotranspiration[END_REF]. Following [START_REF] Riou | Consommation d'eau de la vigne en conditions hydriques non limitantes. Formulation simplifiée de la transpiration[END_REF], reference ET was derived from meteorological data by using the Penman formulation under standard conditions. Then Riou's model inferred potential transpiration as a fraction of reference ET (potential evaporation was the residual), by assuming this fraction almost equals the ratio of solar radiation absorbed by vine leaves to that absorbed by the whole vineyard. For this, solar irradiance absorbed by leaves was geometrically derived from solar position and canopy structure (see Tab. I), and vegetation albedo was set to 0.2. Maximum transpiration was set to potential transpiration, which was within the confidence interval reported by [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF] who suggested a 10% larger value.

The soil was split into N horizons including topsoil (N ∈ [2 -4] following in-situ observations and expert knowledge), and discretized into 251 layers between 0 and 2.5 m depth. Root density was distributed according to in-situ observations and previous studies [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF], [START_REF] Bsaibes | Évaluation d'une approche multi-locale d'estimation spatiale de l'évapotranspiration[END_REF]. The resulting averaged profile considered 75% of roots between 25 and 125 cm, with a 2.2 m maximum depth. The reduction coefficient for transpiration was parameterized using the Feddes functions [START_REF] Feddes | Simulation of field water use and crop yield[END_REF], along with threshold pressures of -0.1 and -1.5 mbar for potential root water uptake [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF]. Lower boundary conditions were set to free outflow when piezometric data indicated watertable absence, and to the fixed pressure head at the watertable level otherwise.

For each soil horizon, unsaturated hydraulic conductivity and retention curves were characterized using van Genuchten functions that depend on residual θ r and saturated θ s soil moisture, on saturated hydraulic conductivity K s , on bubbling pressure α and on the pore-size distribution index n [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[END_REF]. θ r and θ s were set to maximal and minimal moisture values observed from NP data. Topsoil α, K s and n were estimated following former studies over the Peyne watershed [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF], [START_REF] Bsaibes | Évaluation d'une approche multi-locale d'estimation spatiale de l'évapotranspiration[END_REF]. For deeper horizons, they were estimated using the HYDRUS-1D calibration mode that minimized the differences between measured and simulated soil moisture profiles over the simulation period. Initial guesses were derived from literature values proposed for similar soils when possible [START_REF] Trambouze | Measurement and modelling of the transpiration of a Mediterranean vineyard[END_REF], [START_REF] Bsaibes | Évaluation d'une approche multi-locale d'estimation spatiale de l'évapotranspiration[END_REF], and from the HYDRUS-1D ROSETTA module otherwise.

For each location of NP measurements ( § II-B1), HYDRUS-1D was calibrated against the NP data collected between August 2007 and October 2008. Hourly simulations accounted for changes in illumination, and the resulting ET was totaled at the daily scale. Calibration relied on noon values, since NP data acquisition periods were centered on noon.

C. Remote sensing estimates of daily ET 1) ASTER estimates of land surface radiative variables:

We used ASTER official products for surface reflectance, waveband emissivity and radiometric temperature, whose accuracies were 5%, 0.01 and 1.5 K respectively [START_REF] Thome | ASTER preflight and inflight calibration and the validation of Level 2 products[END_REF], [START_REF] Jacob | Modeling and inversion in thermal infrared remote sensing over vegetated land surfaces[END_REF]. These products resulted from 11 cloud-free sets of images sunsynchronously collected around nadir viewing at 11:00 UTC in 2007 (DOY 226, 258, 306) and 2008 (DOY 174,190,197,206,213,245,270,277). Reflectances at 15 m (visible and near infrared) or 30 m (shortwave infrared) were averaged at the 90 m resolution of emissivity and radiometric temperature. Images were carefully geolocated against aerial orthophotos.

ASTER albedo was computed as a linear combination of reflectances. Due to deficient shortwave infrared channels in 2008, the generic two channel formulation from [START_REF] Jacob | Mapping short-wave albedo of agricultural surfaces using airborne PolDER data[END_REF] was linearly corrected against the ASTER seven channel formulation from [START_REF] Liang | Narrowband to broadband conversions of land surface albedo I: Algorithms[END_REF]. The correction was calibrated over the 2007 dataset (relative residual error of 6%). ASTER broadband emissivity was computed as a linear combination of channel emissivities following [START_REF] Ogawa | Estimation of land surface window (8-12 µm) emissivity from multi-spectral thermal infrared remote sensing -A case study in a part of Sahara Desert[END_REF]. Finally, ASTER net radiation was classically computed following [START_REF] Jacob | Mapping surface fluxes using airborne visible near infrared, thermal infrared remote sensing data and a spatialized surface energy balance model[END_REF]. In addition to albedo, broadband emissivity and radiometric temperature, this required meteorological data about solar irradiance, and about air temperature and humidity for deriving atmospheric irradiance [START_REF] Bsaibes | Évaluation d'une approche multi-locale d'estimation spatiale de l'évapotranspiration[END_REF].

2) The S-SEBI model: Below is a model overview, see [START_REF] Roerink | S-SEBI: A simple remote sensing algorithm to estimate the surface energy balance[END_REF], [START_REF] Gomez | Retrieval of evapotranspiration over the Alpilles/ReSeDA experimental site using airborne POLDER sensor and a thermal camera[END_REF], [START_REF] Sobrino | A simple algorithm to estimate evapotranspiration from DAIS data: Application to the DAISEX campaigns[END_REF], [START_REF] Verstraeten | Estimating evapotranspiration of European forests from NOAA-imagery at satellite overpass time: Towards an operational processing chain for integrated optical and thermal sensor data products[END_REF] for detailed descriptions. Deriving daily ET ET d from S-SEBI along with optical imagery, where the latter captures contrasts driven by evaporation processes, is twofold. Evaporative fraction Λ, the ratio of latent heat flux to available energy, is computed from the differences between pixel temperature T S and maximum (T max ) and minimum (T min ) temperatures within the corresponding albedo class. Next, assuming the instantaneous Λ at satellite overpass is equal to the daily Λ, and neglecting daily soil heat flux, ET d is derived by extrapolating, at the daily scale, instantaneous net radiation at satellite overpass R ni , through the ratio Cd i =R nd /R ni where R nd is daily net radiation (L is latent heat of vaporization):

ET d = Λ R nd L = T max -T S T max -T min Cd i R ni L (1)
To implement S-SEBI with the ASTER data, the temperature -albedo space was characterized by calculating, for each 10 -3 width albedo class, albedo mean value and extreme temperatures. Next, T max upper (resp. T min lower) limit was determined from the linear regression between albedo class mean value and maximum (resp. minimum) temperature. As originally proposed by [START_REF] Roerink | S-SEBI: A simple remote sensing algorithm to estimate the surface energy balance[END_REF], T max upper limit was computed by excluding albedoes below the threshold value corresponding to the maximum temperature of the concave temperaturealbedo relationship [START_REF] Bastiaanssen | A remote sensing surface energy balance algorithm for land (SEBAL). 1. Formulation[END_REF]. To reduce noise influence, T min lower limit was computed by including all albedoes [START_REF] Verstraeten | Estimating evapotranspiration of European forests from NOAA-imagery at satellite overpass time: Towards an operational processing chain for integrated optical and thermal sensor data products[END_REF]. To include all (temperature, albedo) pairs within the outer limits, an offset was added to T max (resp. subtracted to T min ) regression line, where the offset corresponded to the variability of maximum (resp. minimum) temperature over albedo classes.

Following [START_REF] Gomez | Retrieval of evapotranspiration over the Alpilles/ReSeDA experimental site using airborne POLDER sensor and a thermal camera[END_REF], coefficient Cd i was calibrated on a daily basis from in-situ measurements of net radiation within Site 6 ( § II-B1). Calibrated Cd i depended on satellite overpass time, and was assumed to be uniform within the Peyne watershed.

Capturing spatial contrasts within the watershed was consistent with the presence of bare soils, forests, rivers and water bodies. Thus, deriving evaporative fraction from temperature differencing assumed similar micrometeorological and aerodynamic conditions for all surfaces, in spite of differences in roughness length, wind speed and air temperature. The resulting errors were expected to be low, according to previous works on heterogeneous patchworks [START_REF] Gomez | Retrieval of evapotranspiration over the Alpilles/ReSeDA experimental site using airborne POLDER sensor and a thermal camera[END_REF], [START_REF] Verstraeten | Estimating evapotranspiration of European forests from NOAA-imagery at satellite overpass time: Towards an operational processing chain for integrated optical and thermal sensor data products[END_REF], [START_REF] Sobrino | Application of a simple algorithm to estimate daily evapotranspiration from NOAA-AVHRR images for the Iberian Peninsula[END_REF].

III. ASSESSMENT AND VALIDATION STRATEGY Fig. 1 displays an example of the daily ET maps we obtained. A large range of ET values (1 to 7 mm.d -1 ) was observed in time and space for validation sites, which confirmed the latter were appropriate for capturing variations ( § II-A). First, we inspected HYDRUS-1D simulations, by 1/ quantifying residual error on model calibration, and 2/ comparing simulations against EC measurements. For comparison over Site 6, we averaged the nine HYDRUS-1D simulations that corresponded to the locations of NP measurements within the footprint of EC measurements. Second, we compared the ASTER / S-SEBI estimates against the HYDRUS-1D simulations, by differentiating years and sites. For comparison over sites with two locations of NP measurements, we averaged the HYDRUS-1D simulations. For comparison over Site 6, HYDRUS-1D simulations were averaged for each sub-site 6N and 6S ( § II-A). From an ASTER viewpoint, we extracted each pixel matching to a site or a sub-site.

IV. RESULTS AND DISCUSSION

A. Assessing quality of ET ground based estimates

When averaged over all dates and locations of NP measurements, the profile of Root Mean Square Error (RMSE) between measured and simulated soil water content showed a decrease with depth from 0.06 to 0.03 m 3 .m -3 (30 and 10% in relative), which was ascribed to temporal stability of deep soil moisture. Largest values around 1 m depth were imputed to moisture variations in relation to root water uptake. When averaged over each profile, RMSE between measured and simulated soil water content varied between 0 and 0.15 m 3 .m -3 (0% and 60% in relative) from one date and one location to another. For a given location, RMSE diminished with simulation time, which may result from errors in HYDRUS-1D initialization. Lowest (resp. largest) RMSE was observed within Site 4 (resp. Site 1), but no link was found with watertable conditions or soil types (Tab. I). When focusing on temporal changes in soil water storage (i.e. integrated soil moisture profile) at noon, relative RMSE between measurements and simulations was lower than 10% regardless of date and location. This was acceptable, given i) the large suite of conditions in soil and watertable, and ii) the errors on NP data, about 15% in relative ( § II-B1).

For Site 7, characterized by a strong water constraint related to a clay soil with no watertable (Tab. I), RMSE between HYDRUS-1D estimates and EC measurements of daily ET was 0.4 mm.d -1 (18% in relative). For Site 6 with a moderate water constraint, RMSE was 0.57 mm.d -1 (33% in relative). The larger RMSE observed for Site 6 was ascribed to a larger amount of data (nine locations of NP measurements). Over both sites, HYDRUS-1D simulations overestimated EC estimates for large ET values after lengthy and large rainfalls, whereas absolute RMSE was quite stable over the simulations. Overall, these results were acceptable, since the two estimates were independent, based either on near surface turbulent fluxes or on vadose-zone water transfers.

From i) calibration results that involved various hydrodynamic conditions, and ii) comparison against independent EC data, we underlined the consistency of HYDRUS-1D simulated daily ET. This made it possible to use the latter as ground based reference for validating remotely sensed estimates.

B. Validating ASTER / S-SEBI estimates of daily ET

The first step focused on net radiation which is a key variable in S-SEBI calculation ( § II-C2). Validation of ASTER estimates against in-situ data collected within Site 6 ( § II-B1) provided a RMSE of 45 W.m -2 , which may be explained by differences between soil and vegetation portions within the NR-lite footprint and ASTER pixels (66% versus 40%). The second step aimed to quantify the standard deviation of daily ET within 3×3 pixel windows centered on the validation sites. The result (0.4 mm.d -1 ) indicated that the spatial variability of the ASTER data in the neighborhood of the validation sites had no significant influence on the validation exercise.

Validation of ASTER / S-SEBI predictions against HYDRUS-1D estimates for the seven sites are displayed in Fig. 2. For daily ET ranging between 0 and 5 mm.d -1 throughout two vineyard growth cycles, RMSE was 0.8 mm.d -1 (30% in relative), and R 2 was about 0.74. This was better than reports from [START_REF] Gomez | Retrieval of evapotranspiration over the Alpilles/ReSeDA experimental site using airborne POLDER sensor and a thermal camera[END_REF], [START_REF] Sobrino | A simple algorithm to estimate evapotranspiration from DAIS data: Application to the DAISEX campaigns[END_REF], [START_REF] Sobrino | Application of a simple algorithm to estimate daily evapotranspiration from NOAA-AVHRR images for the Iberian Peninsula[END_REF] for finer (≤ 20 m) and coarser (∼ 1 km) spatial resolutions (between 1 and 1.5 mm.d -1 ). RMSE was lower (0.6 mm.d -1 ) when replacing HYDRUS-1D estimates by EC measurements. These errors were ascribed to the assumptions S-SEBI relies on, such as similar micrometeorological and aerodynamic conditions for all surfaces, or equivalence between daily and instantaneous values of Λ.

On a yearly basis, remote sensing and in situ estimates agreed better in 2008 (Tab. II). On a daily basis, relative RMSE was better (27%) in spring than in summer (38%) and autumn (44%). These results were ascribed to poorer S-SEBI performances when variability in water conditions was lower.

Validation results on a site basis indicated low unsystematic and large systematic errors. Statistical indicators (Tab. II) were compared against watertable conditions, soil type, row orientation, and soil color. First, RMSE decreased when row orientation changed from -50 • West to +90 • East (North being 0 • ), with a 0.5 R 2 value. This was ascribed to shade effects on the ASTER data, and may also result from coupling between wind direction and row orientation [START_REF] Heilman | Soil and canopy energy balances in a west Texas vineyard[END_REF]. Second, slope and offset were correlated (R value of 0.63) with the HYDRUS-1D calibration residual error, where the latter was averaged for each site over temporal chronicles.

Overall, although there were doubts about using a very simple model over a complex vineyard landscape, the first results reported here showed S-SEBI performances were similar to those obtained over simpler canopies with full covers. Partial influences from row orientation suggested probable (resp. possible) radiative (resp. aerodynamic) behaviors induced by row structure. Furthermore, S-SEBI performances depended on agreement between supposed and captured spatial variabilities. However, theoretically deriving outer limits would require characterizing micrometeorological and aerodynamic

Fig. 1 .

 1 Fig. 1. Daily ET map over the Peyne watershed on July, 15, 2008. Validation sites are numbered 1 to 7, and those with EC devices are double circled.

Fig. 2 .

 2 Fig. 2. Comparison, over the seven sites, of ASTER / S-SEBI daily ET estimates against those derived from HYDRUS-1D. R 2 is coefficient of determination, Slope and Offset are from linear regression between predictions and references (continuous line). RMSE and RRMSE are absolute and relative Root Mean Square Error, respectively. Dashed line is the 1:1 line.

TABLE I VALIDATION

 I SITE FEATURES WITH PREDOMINANT SOIL TEXTURE, WATERTABLE CONDITIONS, AND ROW ANGLE (NORTH AS ORIGIN).

	Site Soil	Watertable	Row	Canopy
		texture	conditions	angle ( • )	structure
	1	Sandy, Silty	Absent	-17 West Row spacing:
	2	Clay, Gravels Intermittent + 42 East	2.5 m
	3	Silty, Sandy	Absent	-34 West
	4	Clay Loam	Permanent	+ 24 East	Row width
	5	Clay	Intermittent + 35 East	(max): 1 m
	6N	Clay loam	Intermittent + 85 East
	6S	Silty	Absent	-01 West Row height
	7	Clay	Absent	-42 West 1.22 -1.75 m

TABLE II STATISTICAL

 II INDICATORS WHEN COMPARING HYDRUS-1D AND S-SEBI ESTIMATES: ABSOLUTE (MM.D -1 ) AND RELATIVE (%) RMSE, SLOPE (-) AND OFFSET (MM.D -1 ) FROM LINEAR REGRESSION BETWEEN PREDICTIONS AND REFERENCES, COEFFICIENT OF DETERMINATION (-). COLUMNS 2-9 ARE RELATED TO YEARS 2007 AND 2008 FOR EACH VALIDATION SITE. COLUMNS 10-11 ARE RELATED TO ALL VALIDATION SITES FOR 2007 AND 2008 YEAR.

	Site	1	2	3	4	5	6N 6S	7	2007 2008
	ARMSE 0.99 0.54 0.59 0.64 0.98 0.69 0.72 1.30 0.69 0.88
	RRMSE 40	26	28	23	23	31	26	60	57	30
	Slope	0.55 0.74 0.77 0.94 0.62 0.65 0.80 0.45 0.76 0.68
	Offset	0.85 0.32 0.51 0.01 0.41 0.56 0.77 0.62 0.52 0.49
	R 2	0.76 0.86 0.90 0.71 0.96 0.79 0.86 0.83 0.52 0.69
	conditions (e.g. WDI, SEBI), and would be therefore subject
	to errors in such characterizations.

ACKNOWLEDGMENTS

The authors thank LISAH technical staff for the experiment, and Jet Propulsion Laboratory for ASTER data collection. This study was funded by Chilean National Commission for Scientific and Technological Research, by French National Institute for Agricultural Research, and by French National Program for Remote Sensing.


Majid Mehrasa
email: majid.mehrasa@g2elab.grenoble-inp.fr

Reza Razi
email: reza.razi@grenoble-inp.fr

Khaled Hajar
email: khaled.hajar@grenoble-inp.fr

Antoine Labonne
email: antoine.labonne@g2elab.grenoble-inp.fr

Ahmad Hably
email: ahmad.hably@gipsa-lab.grenoble-inp.fr

Seddik Bacha
email: seddik.bacha@g2elab.grenoble-inp.fr

Power Management of a Smart Vehicle-to-Grid (V2G) System Using Fuzzy Logic Approach

Keywords: Smart Charging, Plug-in Electric Vehicles (PEVs), Fuzzy Logic Control, State-of-Charging (SOC)

Smart charging/discharging of Plug-in Electric

Vehicles (PEVs) is definitely able to bring a significant cost benefit for both EV station owners and EV owners as well. To this end, this paper develops a Mamdani-based fuzzy strategy with the inputs including the forecasted and real PV generation data, electricity price, and the instantaneous state-of-charging (SOC). Moreover, the output power of PEVs is considered as the output of the proposed strategy. In order to attain further smooth and accurate power sharing for PEVs, varied output rules are assigned commensurate with the rated power of each PEVs. In addition, another fuzzy strategy is developed using the instantaneous SOC error to establish a specified SOC for PEVs at the departure time. While two PV panel profiles are taken into account, Simulation in MATLAB/Simulink environment presents accurate and acceptable results from SOCs of PEVs, PEVs output power, prices and grid power.

I. INTRODUCTION

The numbers of electric vehicles (EVs) have been estimated to globally surpass 35 million [START_REF] Liu | A Review on Electric Vehicles Interacting with Renewable Energy in Smart Grid[END_REF] and 100 million [START_REF] Bindra | Electric Vehicle Batteries Eye Solid-State Technology: Prototypes Promise Lower Cost, Faster Charging, and Greater Safety[END_REF] by 2022 and 2028, respectively. It provides this opportunity for researchers and industrial companies to deeply deal with smart charging of EVs especially based on the cost-benefit criteria in both Vehicle-to-Grid (V2G) and Grid-to-Vehicle (G2V) applications [START_REF] Hajar | Smart Charging Impact on Electric Vehicles in Presence of Photovoltaics[END_REF][START_REF] Turker | Modelling of System Components for Vehicle-to-Grid (V2G) and Vehicle-to-Home (V2H) Applications with Plug-in Hybrid Electric Vehicles (PHEVs)[END_REF]. Among different optimal strategies for Electric Vehicles (EVs) [START_REF] Ovalle | Grid Optimal Integration of Electric Vehicles: Examples with Matlab Implementation[END_REF], researches worked on techniques such as Escort Evolutionary Game [START_REF] Ovalle | Escort Evolutionary Game Dynamics Application on a Distribution System with PV, BSS and EVs[END_REF], Reinforcement Learning Technique [START_REF] Ding | Optimal Electric Vehicle Charging Strategy With Markov Decision Process and Reinforcement Learning Technique[END_REF], Mixed Strategy [START_REF] Ovalle | Mixed Strategist Dynamics Application to Electrical Vehicle Distributed Load Scheduling[END_REF], Linear Quadratic Gaussian [START_REF] Florescu | LQG Optimal Control Applied to On-Board Energy Management System of All-Electric Vehicles[END_REF], and Linear Programing [START_REF] Razi | A User-Friendly Smart Charging Algorithm Based on Energy-Awareness for Different PEV Parking Scenarios[END_REF].

But, in order to adopt smart charging/discharging algorithms for much more effective control of EVs, two rulebased control strategies have been proposed including Deterministic Rule-Based Methods (DRMs) and Fuzzy-Rule-Based Controllers (FRCs) [START_REF] Wirasingha | Classification and Review of Control Strategies for Plug-In Hybrid Electric Vehicles[END_REF]. In DRMs, the rules are ascertained prior to the actual operation of the system under control. In contrast, FRCs are featured by robustness against uncertainty and easy adjustment as well [START_REF] Ferreira | Energy Management Fuzzy Logic Supervisory for Electric Vehicle Power Supplies System[END_REF]. In addition, FRCs have fast performance with significant computational burden mitigation and the excellent secession capability of multiple controllers [START_REF] Syed | Fuzzy Gain-Scheduling Proportional-Integral Control for Improving Engine Power and Speed Behavior in a Hybrid Electric Vehicle[END_REF]. As a consequence, as one of the most effective strategies for smart charging of EVs, it is highly worthy to investigate various kinds of FRCs in the frame of different industrial applications.

FRCs-based smart charging strategies focused on various industrial challenges [START_REF] Inala | Impact of V2G Communication on Grid Node Voltage at Charging Station in a Smart Grid Scenario[END_REF]- [START_REF] Ghofrani | Smart Scheduling and Cost-Benefit Analysis of Grid-Enabled Electric Vehicles for Wind Power Integration[END_REF]. For instance, a fuzzy control technique was proposed by [START_REF] Singh | A Multi Charging Station for Electric Vehicles and Its Utilization for Load Management and the Grid Support[END_REF] to assign power coordination between EVs and power grid against Point of Common Coupling (PCC) voltage fluctuations. In this technique, the final charging/discharging rate and SOC of EVs battery were taken into account. Also, in [START_REF] Teng | Design of a Fully Decentralized Controlled Electric Vehicle Charger for Mitigating Charging Impact on Power Grids[END_REF], a fully decentralized controller was designed based on fuzzy logic technique with the input parameters driven from the power grid, EV charger and EV battery pack. This technique was aimed to reach a suitable EV charger for regulating the charging current against power grid instability. On the other hand, an adaptive fuzzy was established to accurately execute the EV prioritization process for simultaneously attaining the storage utilization maximization and the charging cost minimization [START_REF] Reddy | A Novel Strategy for Maximization of Plug-In Electric Vehicle's Storage Utilization for Grid Support with Consideration of Customer Flexibility[END_REF]. In order to highly achieve precise charging/discharging points for connected EVs in presence of uncertainties coming from the electric grid and EVs, a fuzzy logic control was proposed in [START_REF] Hussain | Efficient Power Management Algorithm Based on Fuzzy Logic Inference for Electric Vehicles Parking Lot[END_REF] to manage the efficient power available in the EVs of the parking lot. A fuzzy strategy was incorporated by grid constraints to specify the score of each PEV in the charging process aiming to maximize the owner's satisfaction based on the delivered energy [START_REF] Akhavan-Rezai | Online Intelligent Demand Management of Plug-In Electric Vehicles in Future Smart Parking Lots[END_REF]. The FRCs were also employed in energy management of hybrid electric autonomous vehicle [START_REF] Phan | Interval Type-2 Fuzzy Logic Control for Energy Management of Hybrid Electric Autonomous Vehicle[END_REF], the intelligent control of a vehicle-to-grid system [START_REF] Sah | A Fuzzy Logic and Artificial Neural Network-Based Intelligent Controller for a Vehicle-to-Grid System[END_REF], and Big Data Analysis Technology of PEVs [START_REF] Lv | Big Data Analysis Technology for Electric Vehicle Networks in Smart Cities[END_REF].

In this paper , a fuzzy-based smart charging technique is proposed for the smart grid shown in Fig. 1 to attain an accurate charging and discharging states for PEVs. Since V2G discharging challenges [START_REF] Turker | Optimal Minimization of Plug-In Electric Vehicle Charging Cost With Vehicle-to-Home and Vehicle-to-Grid Concepts[END_REF] and minimum peak load [START_REF] Nguyen | Charging Strategies to Minimize the Peak Load for an Electric Vehicle Fleet[END_REF] are two very important targets, in the proposed technique, the PEVs are intended for attaining the cost benefit when both V2G and load consumption are instantaneously taken into account. Hereby, it is aimed to increase the power injection from PEVs to power grid while the price is increasing as well. As another target, each PEV should have a specified SOC at the departure time. Consequently, a new fuzzy strategy is developed through the instantaneous SOC error with the specified SOC as the reference set-point. This paper organizes as the follows. Section I focuses on the literature review. Proposed Fuzzy-based smart charging strategy is developed in Section II. This section consists of two sub-sections including the charging/discharging control of PEVs and SOC setting at the departure time. These sub-sections also investigate the effects of PV power, price and SOC error on the PEVs output power. The simulation results including SOCs of PEVs, PEVs output power, prices and grid power are discussed in Section III. Conclusion is presented in Section IV.

II. PROPOSED FUZZY-BASED SMART CHARGING STRATEGY

In this paper, the smart grid shown in Fig. 1 is taken into account. Based on this figure, the smart grid consists of three PEV, power grid, PV panels and load including both constant and variable loads. The power grid and PEVs are able to provide bidirectional power flow. The PV panels inject an unidirectional power to PCC with the profiles shown in Fig. 2(a). The total load has a profile according to Fig. 2

(b).

A. The Charging/Discharging Control of PEVs

In order to reach the cost benefits, the PEVs in the considered smart grid should be managed through paying attention to minimum and maximum prices. On the other hand, knowing the variation trend of the PV power can facilitate reaching more cost benefit and utilization of PV panel power. Also, when SOC is monitored, it helps highly PEVs make a decision to stay at charging or discharging state. Based on the smart grid in Fig. 1, the proposed smart charging/discharging strategy is aimed to achieve the following targets,

• The PV panels power must be utilized for charging the PEVs as much as possible. • The power injection amount from PEVs to grid must be increased while the price is increasing as well.

• The charging process of PEVs must be prioritized by PV panels. But, the power injection amount from grid to PEVs must be increased while the price is decreasing. Using the aforementioned targets and noticing the price profile depicted in Fig. 2(c), the proposed fuzzy strategy is devised based on the Table I. As it can be seen from this table, the states of Low (L), Medium (M) and High (H) are defined for all SOCs of PEVs, the PV panels power and the price. For the charging (C) and discharging (DC) modes in the output of fuzzy strategy, Very High (VH) and Zero (Z) are taken into consideration as well. The weight factor for each rule is set on "1" in this paper. The Mamdani Fuzzy Inference System (FIS) type with the Trapezoidal membership function are employed. A typical Trapezoidal membership function is illustrated in Fig. 3. Based on Fig. 3, the output of proposed Fuzzy strategy is obtained through (1),

According to Table III, the PEVs with different rated output power are exerted. It can be concluded that the charging and discharging rate differs for each PEVs. This point is employed to determine the Fuzzy rules for PEVs output power based on Table I. As it can be realized from this table, the charging and discharging rate is boosted in order as PEV1, PEV3, and PEV2. Also, in the proposed Fuzzy-based smart charging, the utilization of PV panel power takes priority over cost benefit when the SOC is in low level. This priority is seen in the rules 5, 6, 8 and 9, as given in Table I. In addition, excepted for the rules 6 and 9, all PEVs start discharging with very high rate when the price is high as determined in the rules 12, 15, 18, 21, 24, and 27. Using the Table I, a fuzzy rule-based 3D curve is achieved for each PEV based on the price and the PV panel power as it is depicted in Fig. 4.

In this figure, it can be understood when the price is increasing, all PEVs tend to be discharged more. It should be also noticed that the maximum discharging happens for PEVs when the PV panel power is approximately zero and the price is equal to its maximum value. On the other hand, as it can be figured out from Fig. 4(a), (b) and (c), in the midpoints of the price and PV panels power, all PEVs reach the maximum charging from the proposed strategy point of view. In order to compare the Fuzzy rules performance for three PEVs, the PEV output power is plotted based on PV panel power and price in Fig. 5 In both figures, it is obvious that the same results are achieved for the PEV1 and PEV2. Fig. 5(a) illustrates that there is the same trend for the output power of PEVs in which all PEVs are able to attain the maximum charging point after around Ppv=6kW. According to this figure, the PEV1 and PEV3 keep their discharging state in the interval [0kW 4kW] which is more than the PEV2 within interval [0kW 3.7kW]. Within the mentioned intervals, the discharging rate of PEVs is continuously mitigated with a constant ramp as depicted in Fig. 5(a). It can be observed from Fig. 5(b) when the price is within the interval [0 Cents/kW-h 20 Cents/kW-h], the output power of all PEVs is maximally charged. However, the PEV1 and PEV3 have less charging degree (-0.23 Per-Unit) in comparison with the PEV2 (-0.5 Per-Unit). It means that the PEV1 and PEV3 save more money while the power grid is the responsible of charging the PEVs and the price is medium. Inversely, when the price is low and the power grid is the responsible of charging PEVs, the PEV2 can bring more cost benefit for both PEVs station owner and PEVs owner. But, after the price 20 Cents/kW-h, the discharging degree of all PEVs is increased with constant rate as depicted in Fig. 5

(b).

There is slight difference between the discharging trend of all PEVs, although the PEV1 and PEV3 have higher the discharging degree compared to the PEV2. It is worth mentioning when the price is going ahead its maximum value, all PEVs completely provide maximum power injection to the power grid as achieved in Fig. 5(b).

B. SOC Setting at the Departure Time

Another important target of the proposed smart charging/discharging strategy is to enforce the PEVs to have a specified SOC at the departure time from charging station. For SOC setting at the departure time, a new set of rules based on the instantaneous error of SOC is schemed as presented in Table II. The instantaneous SOC error is defined as the following,

i i i SOC Final e SOC SOC =- (3)
The proposed strategy in this sub-section utilizes the Mamdani FIS type with the Trapezoidal membership function as well. Thus, the output of the fuzzy strategy is achieved through, ( , , , , ) max min ,1, , 0

i i i i i i SOC i i i i SOC SOC i i i i
Where "i" stands for the i th PEV (i=1,2,3). In Table II, the abbreviations of the symbols mean B (Big), M (Medium), L (Low), P (Positive) and N (Negative). As it can be seen from Table II, the same rules are developed for PEV2 and PEV3, and different rules with less charging and discharging rate are made for PEV1 because of its higher-rated power. In order to compare the effects of the fuzzy rules on the charging/discharging degrees of the PEVs output power, Fig. 6 is plotted by using the rules in Table II. In Fig. 6, the inequalities of e i SOC >0 and e i SOC <0 mean that the PEV must be within the charging and discharging modes, respectively. To assess Fig. 6, as it is predicted, when the positive values of e i SOC is increased, the PEVs charging degree of proposed strategy must be increased as well. Moreover, inversely, while the negative values of e i SOC is decreasing, the PEVs output power should start discharging with constant rate.

III. SIMULATION RESULTS

The proposed smart charging/discharging strategy is evaluated through MATLAB/Simulink enviorment while two PV panels profiles are taken into account according to Fig. 2(a). The simulation parameters are demonstrated in Table III. As it can be seen from this table, the final SOC of three PEVs at departure time should be 70 %, 80 % and 60 %, respectively. The end of the simulation is considered as the departure time for all PEVs. According to Table III, the PEV2 has less rated power leading to bigger charging degree in the proposed Fuzzy rules comapred to other PEVs as exhibited in Fig. 5. In addition, the SOC in the rules of proposed fuzzy charging/discharging strategy is chosen between 20% and 90%. This section includes two sub-sections focusing on power analysis as well as the SOC and price analysis.

A. The Power Analysis

Fig. 7 shows the output power of three PEVs for clear and cloudy days. According to Fig. 7, using the proposed strategy, the PEV2 is set to be charged through PV panels much more than the PEV1 and PEV3 in both clear and cloudy days. After the PEV2 is fully charged, the PEV1 and PEV3 still remain at charging mode as depicted in Fig. 7(a) and (b). By noticing Fig. 2(c), the proposed smart charging/discharging strategy can be evaluated at the peak price. When the price is within its peak period, the proposed strategy is able to enforce the discharging mode with very high rate for all PEVs as can be observed from Fig. 7(a) and (b). Based on these figures, the PEV2, PEV3, and PEV1 contribute respectively to transforming power from PEVs to the grid. At the end of the simulation as the departure time of PEVs, all PEVs start charging to reach the finalized SOCs stated in Table III. Fig. 8 illustrates the grid power for both clear and cloudy days. As it can be understood from this figure, when the PV panel power exists, the grid power is attempted to have less power generation and consumption. However, a peak power consuption happens for the grid immediately after full charging state of PEV2, as depicted in Fig. 8. On the other hand, it should be pointed out that the grid power approaches its maximum power consuption when the price is located within its peak period shown in Fig. 2(c).

B. The SOC and Price Analysis

The proposed smart charging/discharging strategy can provide the SOCs for three PEVs according to Fig. 9 when both clear and cloudy days are applied. As it can be seen from this figure, all SOCs are continously increased with the constant ramp within the interval which PV panels power reaches its peak values. Among the PEVs, the PEV2 has more charging rate as it has been assessed through Fig. 5. In comparison with the cloudy day, the PEV3 has been charged more in the cloudy day. In addition, all PEVs in the cloudy day have been more discharged while the price is within its peak values compared to the day. By noticing both Fig. 9(a) and (b), it can be realized that the proposed smart strategy is able to enable all PEVs to reach their finalized SOC at the departure time.

According to these figures, it is obvious that the PEV1, PEV2 and PEV3 can reach the SOCs of 70 %, 80 % and 60 %, respectively with high accuracy and suitable transient time. As another target of this paper, the results of the price for both clear and cloudy days are illustrated in Fig. 10. This figure displays that high cost benefits can be obtained for both PEVs station and PEVs owners in all day. As it has been scheduled in the proposed smart charging/discharging strategy, when the price is within its peak values, the most cost benefits are driven as dipicted in Fig. 10. IV. CONCLUSION A fuzzy-based smart charging/discharging strategy has been proposed in this paper to manage the output power of PEVs in a smart grid structure. The proposed strategy has consisted of two parts. The first part has been developed using a set of Mamdani FIS rules proportional to the rated output power of PEVs. This part has aimed to reach the utilization of PV panel power as well as bring cost benefits for the PEVs station owner and the PEVs owner. Several 3D and 2D curves have been obtained accordingly to assess the effects of the proposed fuzzy smart strategy on each PEV output power. As another main target of this paper, the second part has been allocated for the setting process of all PEVs SOCs at a specified point when the PEVs have departed from the charging station. To this end, the instantaneous SOC errors have been incorporated by the proposed fuzzy rules for PEVs with varying charging/discharging degrees. Simulation results in MATLAB/Simulink environment have been achieved to verify the validity of the proposed strategy in presence of different PV panel profiles.

Fig. 1 .

 1 Fig. 1. The smart grid under study.

Fig. 2 .

 2 (a) PV panel power profiles in two states of clear day and cloudy day, (b) Load power profile, and (c) the price profile.

Fig. 3 .

 3 Fig. 3. Trapezoidal membership function for proposed Fuzzy strategy.

  x and f(.) are the input and output of the fuzzy system, respectively. The parameters a, b, c and d are chosen by the designer and they can highly impact on the final value of the fuzzy system output. The relation (1) can be also stated as the following by using the S-norm function,

  (a) and (b), respectively.

Fig. 4 .

 4 The fuzzy rule-based 3D curves based on the price and the PV panel power for (a) PEV1, (b) PEV2, and (c) PEV3.

Fig. 5 .

 5 Fig. 5. Comparison between the Fuzzy rules of three PEVs output power based on (a) PV panel power, and (b) Price.

Fig. 6 .

 6 Fig. 6. Comparison between the charging/discharging degrees of the PEVs output power.

Fig. 7 .

 7 The output power of three PEVs for (a) clear day, and (b) cloudy day.

Fig. 8 .

 8 Fig. 8. The grid power for clear and cloudy days.

Fig. 9 .

 9 The SOC of three PEVs for (a) clear day, and (b) cloudy day.

Fig. 10 .

 10 Fig. 10. The price for clear and cloudy days.

Table I .

 I The rules of proposed fuzzy charging/discharging strategy for PEVs.

			Inputs			Outputs					Inputs			Outputs
	No SOC Ppv	Price	PEV1	PEV2	PEV3	Weight	No SOC Ppv Price	PEV1	PEV2	PEV3	Weight
								of Rule								of Rule
	1	LS	Lpv	LP	MC	VHC	HC	1	15	MS	Mpv	HP	VHDC VHDC VHDC	1
	2	LS	Lpv	MP	LC	MC	LC	1	16	MS	Hpv	LP	LC	HC	MC	1
	3	LS	Lpv	HP	Z	Z	Z	1	17	MS	Hpv	MP	LC	MC	LC	1
	4	LS	Mpv	LP	MC	VHC	HC	1	18	MS	Hpv	HP	VHDC VHDC VHDC	1
	5	LS	Mpv	MP	MC	VHC	HC	1	19	HS	Lpv	LP	Z	Z	Z	1
	6	LS	Mpv	HP	LC	MC	LC	1	20	HS	Lpv	MP	VHDC VHDC VHDC	1
	7	LS	Hpv	LP	MC	VHC	HC	1	21	HS	Lpv	HP	VHDC VHDC VHDC	1
	8	LS	Hpv	MP	MC	VHC	HC	1	22	HS	Mpv	LP	LC	MC	LC	1
	9	LS	Hpv	HP	LC	HC	MC	1	23	HS	Mpv	MP	LC	MC	LC	1
	10	MS	Lpv	LP	MC	VHC	HC	1	24	HS	Mpv	HP	VHDC VHDC VHDC	1
	11	MS	Lpv	MP	VHDC VHDC VHDC	1	25	HS	Hpv	LP	LC	MC	LC	1
	12	MS	Lpv	HP	VHDC VHDC VHDC	1	26	HS	Hpv	MP	LC	HC	MC	1
	13	MS	Mpv	LP	LC	MC	LC	1	27	HS	Hpv	HP	VHDC VHDC VHDC	1
	14	MS	Mpv	MP	LC	MC	LC	1

Table II .

 II The rules for SOC setting at the departure time

	no	1	2	3	4	5	6	7
	e i	SOC	BP	MP	LP	Z	LN	MN	BN
	PEV1	HC	HC	MC	Z	MDC	HDC	HDC
	PEV2	VHC	VHC	MC	Z	HDC	VHDC VHDC
	PEV3	VHC	VHC	MC	Z	HDC	VHDC VHDC
			TABLE III: THE PARAMETERS FOR SIMULATION TEST
				Definition			Value
		Rated maximum/minimum power of PEV1		22/-22 kV
		Rated maximum/minimum power of PEV2		7.4/-7.4 kV
		Rated maximum/minimum power of PEV3		11/-11 kV
			Maximum/minimum PEVs SOC		90 %, 20 %
			Final SOC for PEV1, PEV2 and PEV2		70%, 80%,60%

This work has been supported by the aVEnir project of the PIA operated by ADEME.