Yves Mahéo
email: yves.maheo@univ-ubs.fr

Romeo Said
email: romeo.said@univ-ubs.fr

Frédéric Guidec
email: frederic.guidec@univ-ubs.fr

Middleware Support for Delay-Tolerant Service Provision in Disconnected Mobile Ad Hoc Networks

The service-oriented approach is known to be adequate for building distributed applications for mobile ad hoc networks, and a number of successful research works using this approach in routed MANETs have already been conducted. Yet, providing support for service-oriented applications poses specific problems in disconnected MANETs where end-to-end connectivity is not guaranteed. This paper presents a prototype Java middleware support for delaytolerant service provision in disconnected MANETs. It first describes the lower layer of this middleware, which implements a protocol for document dissemination that leverages on delay-tolerant, opportunistic and content-based communication. It then explains how service discovery and service invocation mechanisms can be implemented on top of this protocol. Finally, simulation results are presented, which show that this approach gives good results compared with an alternative approach that consists in exploiting single-hop interactions between service providers and service clients.

Introduction

The service-oriented approach becomes more and more popular for building distributed applications. Serviceoriented applications involve distributed components that can either play the role of service providers or service consumers. Service provision is generally performed in two steps: service discovery, during which services advertised by providers can be discovered by potential consumers, and service invocation, during which a given consumer actually interacts with the provider of a previously discovered service.

This decoupling between interacting entities makes this model suitable for mobile ad hoc networks (MANETs) as it can help cope with their dynamicity. Indeed, in contrast with an infrastructure-based wireless network (such as one relying on fixed access points), a MANET is a network formed spontaneously by a group of mobile, wireless devices.

In the literature MANETs are often assumed to be dense enough, so they can be modelled as connected graphs in which end-to-end dynamic routing algorithms can be implemented [START_REF] Liu | A Survey of Mobile Ad Hoc network Routing Protocols[END_REF]. For such networks, the research on service delivery mainly focuses on supporting service discovery, for service invocation can be performed just like in wired networks. A number of discovery protocols have indeed been developed for connected MANETs, most of them being closely related to the underlying routing protocols [START_REF] Chakraborty | Integrating service discovery with routing and session management for ad-hoc networks[END_REF].

Yet, in MANETs showing a low density and/or a high mobility of hosts, there is no guarantee that a temporaneous path can ever be established between any pair of nodes in the network. Figure 1 shows a typical example of such a disconnected MANET,in which some laptops and hand-held devices with Wi-Fi interfaces are scattered in several buildings. In this figure empty circles denote inactive hosts (typically hosts in suspend-mode) and edges represent connectivity (and thus some potential for communication) between neighbour hosts. Because of their mobility, their limited radio-range and their volatility (they are not active all the time), the devices in this network form so-called "islands" whose topology evolves continuously. Temporaneous communication between two islands is not possible. As a consequence, network-wide communication itself in this kind of network is still a challenge, as routing techniques designed for fully connected MANETs cannot be applied. A method must thus be devised in order to bridge the gap between network islands. Delay-tolerant networking (DTN) is an approach that can help with this respect [START_REF] Fall | A Delay-Tolerant Network Architecture for Challenged Internets[END_REF]. In a delay-tolerant network, a message can be stored temporarily on a host, in order to be forwarded later by this host when circumstances permit. Moreover, mobility can facilitate message propagation, as devices can carry a message when moving from an island to another. Disconnection also has an impact on the way service provision can be implemented. Both service discovery and service invocation must thus be revisited in such conditions.

This paper presents a two-layer middleware support for The remainder of this paper is organized as follows: Sections 2 and 3 respectively describe the communication layer and the service layer of our middleware support. Simulation results are described in Section 4. Finally, Section 5 discusses related research works, and Section 6 concludes the paper.

DTN communication layer

Model and Protocol

Our communication middleware is called DoDWAN (Document Dissemination in Wireless Ad Hoc Network). It supports the content-driven, opportunistic dissemination of structured pieces of information in the network. Content-based communication is a style of communication whereby the flow of information is interest-driven rather than destination-driven [START_REF] Carzaniga | Content-based Networking: A New Communication Infrastructure[END_REF]. Receivers specify the kinds of information they are interested in, without regard to any specific source. Senders can send information in the network without addressing it to any specific destination. In our model, the structured pieces of information we consider are referred to as "documents". A document is composed of two parts: its descriptor, and its content. The descriptor can be perceived as a collection of attributes, which can provide any kind of information about the corresponding document, such as its origin, its topic, a list of keywords, the type of its content, etc. DoDWAN provides support for storing documents in a host's local cache, so this host can serve as a mobile carrier for these documents while moving in the network. Each host is associated an "interest profile", that determines the kind of information it is interested in, and thus implicitly the kinds of documents for which it is willing to serve as a mobile carrier. DoDWAN also defines a gossip-like communication protocol to orchestrate interactions between neighboring hosts, allowing them to exchange documents according to their respective interest profiles. Interaction between mobile hosts relies on a simple model, whereby each host periodically broadcasts its own interest profile and a catalog of document descriptors that are currently available in its local cache. When a host discovers that one of its neighbors can provide a document it is interested in (that is, a document descriptor that matches its own interest profile and that is not already available in its own cache), it can request a copy of this document from this neighbor. Upon receiving one or several requests for a particular document from its neighbours, the owner of this document broadcasts it on the wireless medium, so it can be received by all requestors simultaneously. Transient contacts between mobile hosts are thus exploited opportunistically for exchanging documents between these hosts, based on their respective interest profiles, and based on the documents they can provide each other on demand.

DoDWAN has been designed so as to maximize the document delivery ratio while remaining very frugal as far as the number and the volume of messages are concerned. It has been implemented in Java, in such a way that it can notably exploits the broadcast capabilities of different MAC layers, such as that of 802.11 (Wi-Fi). Further information about DoDWAN and about the content-based dissemination protocol it implements can be found in [START_REF] Guidec | Opportunistic Content-Based Dissemination in Disconnected Mobile Ad Hoc Networks[END_REF].

Publish/subscribe API

DoDWAN provides several kinds of API, including a publish/subscribe API we used to construct our service platform. With this API the programmer is provided a number of interfaces that allow to perform the following tasks:

• Create and manipulate transfer documents A transfer document contains an arbitrary payload and a descriptor consisting of a number of attributes (couples key/ string value). Some attributes are predefined (such as one that specifies the expiration date of a document) and new ones can be added as reqired by the programmer. Attributes can be manipulated with traditional getters/setters.

• Publish documents Transfer documents that are supposed to be delivered to others hosts are published, that is, they are simply "pushed" into the network. According to the model described above, the effect of publishing a document is that this document is simply deposited in the local cache of the sender. It will subsequently be automatically and opportunistically transmitted to other hosts that have subscribed for this kind of document.

• Subscribe for documents In order to specify what kind of transfer documents a host wishes to receive from the network, this host provides a document pattern. A document pattern is simply a descriptor that contains a number of attributes (those attributes one wishes to base the selection upon), each of them carrying a value that is a standard regular expression that will be matched against actual values in the descriptors of accessible documents. The above-mentioned interest profile of a host is directly generated by DoDWAN from the different subscription patterns.

• Receive documents Document subscription triggers the installation of an event listener. When subscribing for a particular kind of documents, one specifies a handler (actually an object with an implicit handler method) that should be called when a matching document is received and deposited in the local cache. Handlers are therefore automatically invoked upon reception of "interesting" documents, that is documents that match the local host's interest profile.

Service Layer

The upper-layer of our middleware support is an aggregation of service-oriented concepts and techniques forming what we refer to as "a service platform". This service platform was built while always trying to take into account all the specificities of disconnected mobile ad hoc networks. The two main characteristics that have to be taken into account are the communication delays and the absence of endto-end connectivity, the latter leading to an unpredictable availability of service providers. These aspects have obviously an impact on the application logic. But because this impact is essentially application-specific, it will not be discussed further in this paper. Instead our aim is rather to show how middleware mechanisms can be implemented at the service-level so we can cope with the induced delays on both the provider and the client sides, and how we can give the client the means to be aware of the available services in its environment (discovery) and the means to asynchronously interact with these discovered services (invocation).

Architecture

The service platform we developed covers the main aspects of service-oriented programming. It therefore implements protocols for service description, service discovery, and service invocation. This platform is implemented in Java. Each mobile node in the network is meant to run only one instance of the service platform, that will take care of the needs of both service providers and service clients.

The architecture of our service platform is depicted in Figure 2. It is composed of the following modules:

• The Service Manager module exposes a service logic to be consumed by remote Client modules. A Service Manager is a service container. It includes service business classes and their descriptions, and it supplies translation between local and remote method invocations. Many instances of Service Manager modules can be operational, each instance corresponding to one installed service.

• The Client module wraps a service discovery pattern and supplies a user interface and remote method invocation functionality. Many Client modules can be operational, each module corresponding to a declared service pattern.

• The Repository module is a self managing storage space for service descriptors. It is also responsible for a platform-wide application of the advertising and discovery policies.

• The Controller module mainly handles the life-cycles of the Service Manager and Client modules.

Communications are carried out by message passing. Messages encapsulate transfer documents that can be sent or received using the publish/subscribe API detailed in Section 2. The content-based nature of the publish/subscribe paradigm is clearly appropriate for service advertisement and discovery. It namely allows semantic discovery when matching a client service pattern against service descriptors. Besides using the publish/subscribe model for service advertisement and discovery, we also rely on this model to support invocation requests and responses. Indeed, the underlying support for content-based communication makes it possible to address a document to a specific host by inserting a destination attribute in the document's descriptor.

Behavior of Service Providers

On the service provider side, the administrator of the host installs for each service the needed service business classes and supplies the corresponding service descriptor. The descriptor of a service is an XML document containing all the information needed by the Client modules to select and then invoke this service. The functional interface of the service is described using the WSDL description language [START_REF] Chinnici | Web Services Description Language (WSDL) Version 2.0[END_REF]. Nonfunctional properties (such as the service name, description, author, etc.) and context-aware properties (e.g. availability, reliability, trust) can be taken into account in the selection process.

The service descriptor is submitted to the advertising policy of the local Repository module. This module regularly publishes all local descriptors. The Controller module reads the business classes implementing the service and creates a new instance of the Service Manager module. This module subscribes for incoming invocation requests. When receiving such requests it will translate them into local method invocations, and it will then translate the local results back by publishing responses containing these results. The payload of the invocation message is implemented in SOAP [START_REF] Gudgin | SOAP version 1.2[END_REF].

Behavior of Service Clients

On the service client side, the user defines a service pattern (written in XML) that is meant to match a service descriptor published by a provider. The Controller module creates a corresponding Client module instance that updates the discovery policy of the Repository module by submitting its service pattern in order to convey its wishes in the discovery process. The Repository module submits the service pattern for subscription and stores all the matching service descriptors it receives from the network. Thus, at any time, and for a given service pattern, the client has access to a list of matching services collected in the local repository.

The client can invoke the desired service by publishing a method invocation (with a SOAP message payload). It then subscribes and waits for the service response.

Simulation Results

In order to evaluate the applicability of our approach, we have conducted a series of simulations. We focus here on one particular experiment whose objective was to measure the ability of our service platform to satisfy client service discovery requests and service invocations. In this perspective, we compared our approach to one consisting in restricting communication to one-hop transmissions. In this alternative model, a service client must move within the radio range of a service provider in order to be able to discover the services it provides, and possibly invoke these services. In the remainder of this section, we will call this model PROX-IMITY-based as opposed to the DODWAN-based model described in this paper.

We ran two simulations to establish this comparison. We first simulated our service platform stack running over DoDWAN as depicted in Figure 2, and second we simulated the same service platform stack running over a proximity module that replaced the DoDWAN module. This proximity module implements one-hop discovery and invocation. We tuned the parameters of the implementation (such as the advertisement frequency) so as to remain consistent with the DoDWAN implementation.

In both simulation runs, the simulation starts by the client defining its service discovery criteria. These criteria are assembled into a service pattern. Then, the scenarios slightly differ depending on the chosen model.

• DODWAN-based: The client sends a discovery request (i.e. it injects the service pattern in the network) and then waits for a discovery response (i.e. it waits for being notified when a matching service description issued by a provider has arrived). After processing a discovery response, the client sends an invocation request to the provider and waits until the invocation response is received. All along these interactions, the client and the provider do not necessarily have to be close neighbors, as messages are exchanged network-wide using the DoDWAN dissemination protocol.

• PROXIMITY-based: After the client has defined its service pattern, it waits for an encounter with a matching service provider (which regularly broadcasts service advertisements). When such a provider is in radio range, the client processes the advertised service description, sends its invocation request and waits until it receives a response. Of course, in this scneario the client and the provider must stay in radio range during the whole duration of the transaction.

The simulation environment is an open 1 km 2 simulation area, populated with hosts equipped with Wi-Fi interfaces evolving according to a random waypoint mobility model at speeds varying between 2 m/s and 3 m/s. We created a scarcely populated environment with 100 hosts. Among these hosts, only one is a service provider (which provides a unique service) and 20 of the remaining hosts are potential clients of this service. The remaining 79 hosts are neither producers nor consumers of the single service considered in this scenario. Yet they can serve as message forwarders and carriers, thus helping documents to disseminate networkwide. At time zero, all the clients begin searching for a provider of the desired service. Each of them will send an invocation request as soon as it receives the service description. We ran the simulations in the same environmental conditions for both the PROXIMITY-based and the DODWANbased communication models. The simulations were performed with the MADHOC network simulator [START_REF] Hogie | The MADHOC simulator[END_REF], which allows us to run the actual code of the service platform and the underlying communication middleware.

Figure 3 gives some information about the performance of the discovery process and the overall process (involving a discovery and an invocation) for the PROXIMITY-based and the DODWAN-based communication models. The curves show the percentage of client hosts that have received a response against time. A response is a discovery response (dashed curves) or an invocation response obtained after a discovery process (full-line curves). As expected, the two PROXIMITY-based curves are almost superimposed. This is because of the synchronous interactions of requests and responses this model permits. However, the global performance remains low: no more than 20% of the clients are satisfied, even after a 1200 s pe-riod of time. The fact that a client and a provider can only count on their own move to be able to interact is indeed very penalizing.

With the DODWAN-based model, we observe a delay between the discovery and the invocation due to the very nature of the communications. This delay increases (before the curve flattens) because of the two-way transmissions induced by the service invocation. Yet clients discover the service provider much faster than with the PROXIMITY-based model: the first client receives a service description in approximately 50 s (against 130 s with the PROXIMITY-based model). And after 550 s, all the clients have completed the discovery phase. The same kind of observation can be made when studying invocation responses: performance is comparable with the PROXIMITY-based until 200 s but the the curve clearly arises afterwards. After approximately 17 mn (1030 s), all the clients have received their invocation response (against only 20% for the PROXIMITY-based model).

These results confirm that using DoDWAN can effectively help in allowing interaction between service providers and service clients, especially as the network gets sparser. The global cost in messages has not been taken into account in the work reported here. However, several other simulations -not detailed for the sake of brevity-show that, when considering a greater number of service providers, the relative cost induced by the participation of relaying hosts in the DODWAN-based model decreases.

Related Work

Service-oriented programming in pervasive environments has been the object of many research activities. Most of them primarily focused on service discovery [START_REF] Zhu | Service Discovery in Pervasive Computing Environments[END_REF] and tried to use traditional centralised directory services in infastructure-based wireless networks.

Recently, the characteristics of MANETs (dynamicity, low resources, unreliable transmissions) have been taken into account, with the development of specific discovery protocols. For many of these protocols, communications are still considered achievable and to some extent sustainable (routes between hosts can always be established) [START_REF] Varshavsky | A cross-layer approach to service discovery and selection in MANETs[END_REF][START_REF] Engelstad | Service Discovery Architectures for On-Demand Ad Hoc Networks[END_REF][START_REF] Lenders | Service Discovery in Mobile Ad Hoc Networks: A Field Theoretic Approach[END_REF][START_REF] Chakraborty | Integrating service discovery with routing and session management for ad-hoc networks[END_REF]. Konark [START_REF] Helal | Konark : Service Discovery and Delivery Protocol for Ad-hoc Networks[END_REF] uses a fully distributed advertisement/discovery scheme but relies on a multi-hop multicast and implements session-based invocations.

Other efforts try to create a virtual upper layer in MANETs where some selected hosts are assigned special capabilities. Some of them implement decentralized directories for discovery [START_REF] Sailhan | Scalable Service Discovery for MANET[END_REF] where each interconnected network (small connected network group) has one directory, while others assign network service brokers [START_REF] Nedos | Service*: Distributed Service Advertisement for Multi-Service, Multi-Hop MANET Environments[END_REF] or create network backbones [START_REF] Kozat | Network Layer Support for Service Discovery in Mobile Ad Hoc Networks[END_REF]. Our prototype does not assume any viable interconnections so each host is responsible for its own ser-vice repository. We do not use overlay network structures nor maintain discovery routes.

Conclusion

We presented in this paper the implementation of a twolayer service provision middleware targeted at disconnected mobile ad hoc networks. It provides service discovery and service invocation mechanisms that are built upon a communication layer called DoDWAN. DoDWAN implements a frugal protocol for disseminating documents networkwide, freeing itself of the presence of independent communication islands through the exploitation of the storecarry-and-forward paradigm. DoDWAN offers a publish/subscribe API that is used in a service platform (the upper layer of our middleware) for exchanging service advertisements and discovery messages as well as for invocation and response messages.

We briefly described a simulation experiment that shows that this approach allows interesting service satisfaction ratios when compared to the alternative that consists in relying only on one-hop transmissions for service discovery and service invocation.

These preliminary results demonstrate the feasibility of service provision in a disconnected network built upon an opportunistic content-based dissemination middleware like DoDWAN. As future work, we plan to investigate how the fact that a group of hosts provides the same service can be exploited to speed up service discovery as well as service invocation. Indeed, the ability to take benefit of the redundancy of service providers could be crucial in sparsely populated networks.

Figure 2 .

 2 Figure 2. Architecture of the service platform

Figure 3 .

 3 Figure 3. Discovery and invocation satisfaction ratios for the DODWAN-based and the PROXIMITY-based models

Acknowledgements. This work is supported by the French Agence Nationale de la Recherche under contract ANR-05-SSIA-0002-01.


domain: sdv sde

text:
JACOB AND OLIOSO: DIURNAL COURSE OF ALBEDO FROM POLDER DATA

Knowledge of the diurnal course of land surface albedo is needed for monitoring radiative transfers between soil, vegetation and atmosphere. These transfers are of interest for crop monitoring, hydrological cycle modeling, weather forecast and climate modeling. The required absolute accuracy ranges between 0.02 and 0.05. At the present time, it is possible to derive the diurnal course of albedo from geostationary satellites. Sun -synchronous sensors, with higher spatial resolutions, allow retrieving surface radiative properties by both discriminating different types of land cover and capturing the subclass variability. However, the current possibilities for deriving the diurnal course of albedo from sun synchronous observations are empirical or mathematically complex. We proposed in this paper a physically based method, which is candidate for operational use along with multiangular sun -synchronous sensors, under clear sky conditions. This method uses both reciprocal Kernel -Driven Bi -directional Reflectance Distribution Function (KD BRDF) models and Narrowband To Broadband (NTB) conversion. It was implemented and validated using the Alpilles / ReSeDA database which was collected over agricultural areas. The implementation was performed using the 20 m spatial resolution airborne PolDER data acquired near midday.

The validation was conducted using field measurements of albedo, recorded over the diurnal cycle. The retrievals of the diurnal course of albedo were good, with errors ranging from 0.026 to 0.029. Better results were observed for instantaneous values at solar noon and times close to satellite overpasses, as well as for the daily mean value, with errors ranging between 0.014 and 0.022. Amongst the selected reciprocal KD BRDF models, Li -Ross systematically provided the best results, regardless of considered albedo product. Further, using instantaneous values at times close to satellite overpasses, in place of the daily mean value, did not yield significant differences, with errors ranging around 0.01. Finally, we assessed the interest of deriving the diurnal course of reflected solar irradiance by using the several albedo products aforementioned. For the environmental conditions of the Alpilles / ReSeDA experiment, the resulting differences were not significant, with accuracies better than 20 W.m -2 .

Introduction

Land surface albedo is defined as the fraction of solar irradiance reflected within the upper hemisphere and over the whole solar spectrum [START_REF] Dickinson | Land surface processes and climate-surface albedos and energy balance[END_REF][START_REF] Pinty | On the design and validation of surface bidirectional reflectance and albedo model[END_REF].

Since it directly drives the amount of solar irradiance absorbed by natural surfaces, its knowledge is of prime interest when studying surface net radiation budget and further energy transfers at the soil -vegetation -atmosphere interface. These transfers are of interest for crop monitoring [START_REF] Bastiaanssen | Water balance variability across Sri Lanka for assessing agricultural and environmental water use[END_REF], hydrological cycle modeling [START_REF] Ottlé | Assimilation of soil moisture inferred from infrared remote sensing in a hydrological model over the HAPEX-MOBILHY region[END_REF], weather forecast and climate modeling [START_REF] Noilhan | GCM grid-scale evaporation from mesoscale modeling[END_REF][START_REF] Courault | Estimation of surface fluxes in a small agricultural area using the three-dimensional atmospheric model Meso-NH and remote sensing data[END_REF]. Retrieval of instantaneous albedo can be used to compute instantaneous surface energy fluxes [START_REF] Kustas | Spatially distributed sensible heat flux over a semiarid watershed. Part II : use of a variable resistance approach with radiometric surface temperatures[END_REF][START_REF] Kustas | Evaluation of soil and vegetation heat flux predictions using a simple two-source model with radiometric temperatures for partial canopy cover[END_REF]Jacob et al., 2002a]. However, albedo is not constant during the day, mainly because of changes in solar position [START_REF] Dickinson | Land surface processes and climate-surface albedos and energy balance[END_REF][START_REF] Dickinson | Relating surface albedos in GCM to remotely sensed data[END_REF][START_REF] Barnsley | Characterizing the spatial variability of broadband albedo in a semi desert environment for MODIS validation[END_REF]Grant et al., 2000]. This albedo variation has to be inferred for monitoring surface energy fluxes and evapotranspiration throughout the day [Soer, 1977;[START_REF] Dickinson | Land surface processes and climate-surface albedos and energy balance[END_REF]Henderson-Sellers and Wilson, 1983;Jackson, 1985;[START_REF] Moran | Use of groundbased remotely sensed data for surface energy balance evaluation of a semiarid rangeland[END_REF]. It is also required for the derivation of the daily mean value of albedo [Grant et al., 2000]. Daily mean value of albedo is needed for monitoring daily evapotranspiration using the simplified relationship [START_REF] Seguin | Using midday surface temperature to estimate daily evaporation from satellite data[END_REF][START_REF] Brasa-Ramos | Comparison of evapotranspiration estimates by NOAA-AVHRR images and aircraft flux measurements in a semiarid region of Spain[END_REF], as well as for the computation of the monthly value of albedo. Accurate values of albedo at daily or monthly scales are of interest for General Circulation Models (GCM) devoted to climate studies [START_REF] Dickinson | Relating surface albedos in GCM to remotely sensed data[END_REF][START_REF] Sellers | Remote sensing of the land surface for the global change: models -algorithmsexperiments[END_REF][START_REF] Myhre | Uncertainties in radiative forcing due to surface albedo changes caused by land-use changes[END_REF]Tian et al., 2004].

When dealing with accuracy requirements for GCM studies and weather forecast modeling, Henderson- Sellers and Wilson [1983] and [START_REF] D R A F T Cihlar | GCOS/GTOS plan for terrestrial climate-related observations[END_REF] proposed that an absolute accuracy of ±0.05 is required. On the other hand, [START_REF] Sellers | Remote sensing of the land surface for the global change: models -algorithmsexperiments[END_REF] suggested an absolute accu-D R A F T January 26, 2005, 2:58pm D R A F T racy of ±0.02, which corresponds to an accuracy on monthly averaged reflected solar irradiance of ±10 W.m -2 . Estimating albedo at the hourly scale is of prime interest for the computation of the daily mean value of albedo. Indeed, Grant et al. [2000] showed that not considering the diurnal course of albedo yields an absolute error on the daily mean value up to 0.03, corresponding to 15% in relative terms. Similarly, [START_REF] D R A F T Kimes | Hemispherical reflectance variations of vegetation canopies and implications for global and regional energy budget studies[END_REF] reported a 18% relative error on the daily mean value of reflected solar irradiance.

Visible -Near Infra Red (Vis -NIR) remote sensing is an attractive tool for estimating albedo under clear sky conditions. Indeed, it can provide maps at different spatial and temporal scales, whereas field measurements are not representative of the spatial variability depicted by land surfaces. Over the last two decades, several studies focused on estimating accurately land surface albedo from remotely sensed data. The proposed models have different degrees of complexity, leading to different types of approach: empirical, parametric, radiative or geometric (see the review by [START_REF] Pinty | On the design and validation of surface bidirectional reflectance and albedo model[END_REF]). Most of these approaches were devoted to the estimation of instantaneous albedo [START_REF] Brest | Deriving surface albedo measurements from narrow band satellite data[END_REF][START_REF] Dedieu | Satellite estimation of solar irradiance at the surface of the Earth and of surface albedo using a physical model applied to Meteosat data[END_REF]Wanner et al., 1997;Weiss et al., 1999;Song and Gao, 1999;Lucht et al., 2000;[START_REF] Liang | Narrowband to broadband conversions of land surface albedo I Algorithms[END_REF][START_REF] Zhao | Atmospheric and spectral corrections for estimating surface albedo from satellite data using 6S code[END_REF]Pinty et al., 2000a;Jacob et al., 2002b, c]. When the diurnal course is required, there are two possible approaches according to the use of geostationary or sun -synchronous sensors. For geostationary satellites which monitor a given location over the diurnal cycle, it simply consists of estimating instantaneous albedo within each interval of the temporal sampling [START_REF] Dedieu | Satellite estimation of solar irradiance at the surface of the Earth and of surface albedo using a physical model applied to Meteosat data[END_REF][START_REF] Pinty | The relationship between incident and double-way transmittances: an application for the estimate of surface albedo from satellite over the African Sahel[END_REF][START_REF] Minnis | Assymetry in the diurnal variation of surface albedo[END_REF]Pinty et al., 2000a, b]. Sun synchronous sensors, with higher spatial resolution, allow retrieving surface radiative properties by both discriminating different types of land cover and capturing the subclass variability. This is of interest for agricultural applications [START_REF] Baret | Proceedings of the International Conference "Soils under Global Change -a Challenge for the 21st Century[END_REF]. Since these sensors collect, over D R A F T January 26, 2005, 2:58pm D R A F T a given location, one observation a day when the platform overpasses, it is necessary to perform a temporal extrapolation. This can be done by empirically modeling the dependence of instantaneous albedo upon the sun position [START_REF] Barnsley | Characterizing the spatial variability of broadband albedo in a semi desert environment for MODIS validation[END_REF]Grant et al., 2000;Lucht et al., 2000]. However, Grant et al. [2000] showed that this requires previous calibrations, whereas the solar dependence may vary significantly according to the observed target. Another possibility for the temporal extrapolation consists of using radiative transfer models [START_REF] Dickinson | Relating surface albedos in GCM to remotely sensed data[END_REF][START_REF] Liang | An analytic BRDF model of canopy radiative transfer and its inversion[END_REF][START_REF] Kimes | Inversion methods for Physically-Based Models[END_REF]. However, inverting such models is mathematically complex and requires tedious numerical procedures, which is not appropriate for operational applications [Wanner et al., 1997;[START_REF] Pragnère | Comparison of three radiative transfer model inversion techniques to estimate canopy biophysical variables from remote sensing data[END_REF][START_REF] Kimes | Inversion methods for Physically-Based Models[END_REF].

Regarding limitations of the current possibilities for sun -synchronous sensors, reciprocal Kernel -Driven Bi -directional Reflectance Distribution Function (KD BRDF) models offer the opportunity to investigate new approaches devoted to the retrieval of the diurnal course of albedo. These models are physically based and designed for operational use. Both their basic concepts and features are reviewed in [START_REF] Lucht | Considerations in the parametric modeling of BRDF and albedo from multiangular satellite sensor observations[END_REF], and will be summarized in this paper ( § 4.1 and § 4.2). Promising results were already reported when using reciprocal KD BRDF models, along with single directional data collected from geostationary sensors at different solar positions during the day [van Leeuwen and Roujean, 2002;Pokrovsky et al., 2003a, b]. For multidirectional sun -synchronous sensors, these models have been used to retrieve instantaneous albedo products from multiangular data collected at a given solar position of the day [START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF]Weiss et al., 1999;[START_REF] Schaaf | First operational BRDF, albedo nadir reflectance products from MODIS[END_REF]Jacob et al., 2002b, c].

This study focused on implementing and validating a new approach devoted to the derivation of the diurnal course of albedo from multidirectional data collected at a given time of the day. The method we propose is candidate for operational use along with multiangular sun - et al. [1999, 2002b]; Jacob et al. [2002b, c], and will be summarized in this paper (see § 4.5).

D R A F
The method we propose was tested over the data set gathered in the framework of the Remote Sensing Data Assimilation (ReSeDA) program [START_REF] Prévot | Assimilation of multi-sensor and multi-temporal remote sensing data to monitor vegetation and soil: the Alpilles ReSeDA project[END_REF][START_REF] Olioso | Spatial aspects in the Alpilles-ReSeDA project[END_REF][START_REF] Baret | Assimilation of multisensor and multitemporal remote sensing data to monitor soil and vegetation functioning[END_REF]. The Alpilles -ReSeDA experiment combined acquisition during one year of 1/ multiangular Vis -NIR remote sensing data collected near midday twice a month with the airborne POLDER sensor, and 2/ ground based measurements of albedo recorded throughout the day within several agricultural fields ( § 3). The use of high spatial resolution and multitemporal remotely sensed data allowed us to validate albedo retrievals over cycles of several crops.

The current paper is structured as following. In a first part, we detail:

• the definitions to be used in the paper ( § 2),

• the Alpilles / ReSeDA project, its goals and experimental support ( § 3.1),

• the acquisition and preprocessing of the ReSeDA / PolDER dataset ( § 3.2),

• the ground based measurements of albedo used for validation exercises ( § 3.3).

Implementing the method we propose over the ReSeDA data set was performed as following.

• According to performance studies reported in the literature, we selected reciprocal Kernel -Driven (KD) BRDF models ( § 4.1 and 4.2).

• The models were inverted over the PolDER BRDF angular samplings near midday ( § 4.3).

D R A F T January 26, 2005, 2:58pm D R A F T X -7
• The inverted models were forwardly run to compute, within each PolDER channel, hemispherical reflectance (also called spectral or narrowband albedo) for different solar positions over the diurnal cycle ( § 4.4).

• The diurnal course of broadband albedo was derived from those of hemispherical reflectance by using Narrowband To Broadband (NTB) conversion ( § 4.5).

Section 5 presents the strategy used to analyze and validate the method we propose over the Alpilles -ReSeDA data set. The results are presented as following.

• The analysis of field data of albedo are reported in § 6.1.

• We assessed the robustness of the reciprocal KD BRDF models regarding the temporal extrapolation, by considering hemispherical reflectance ( § 6.2) and albedo ( § 6.3).

• We next focused on reflected solar irradiance which is the albedo -linked component of land surface radiation budget ( § 6.4).

Retrievals of albedo and reflected solar irradiance were validated by considering specific albedo products: the diurnal course, the daily mean value, and typical instantaneous values (10:00, 12:00 and 14:00 local solar time). Finally, the results are discussed regarding observations reported in previous studies ( § 7).

Definitions and nomenclature

Over the last decade, several studies focused on albedo retrieval from remote sensing, which yielded the existence of different nomenclatures. In this section, we first define the variables of interest: surface radiative properties and remote sensing measurements. These definitions are given by linking them to nomenclatures proposed in the literature.

D R A F T January 26, 2005, 2:58pm D R A F T
The definition of albedo a(θ s , ϕ s ) as the fraction of solar irradiance reflected within the upper hemisphere and over the whole solar spectrum may be expressed as [Weiss et al., 1999]:

a(θ s , ϕ s ) = 3000 nm 300 nm ρ h,λ (θ s , ϕ s ) R g,λ (θ s , ϕ s ) dλ 3000 nm 300 nm R g,λ (θ s , ϕ s ) dλ (1)
This definition accounts for the reflected fractions of diffuse and direct solar irradiances, and can be labeled shortwave apparent albedo [START_REF] Liang | Retrieval of land surface albedo from satellite observations: A simulation study[END_REF][START_REF] Liang | Narrowband to broadband conversions of land surface albedo I Algorithms[END_REF]Liang et al., 2002b]. Hemispherical reflectance ρ h,λ (θ s , ϕ s ) represents the fraction of spectral solar irradiance R g,λ (θ s , ϕ s ) reflected within the upper hemisphere, for a given wavelength λ, and a given solar direction characterized by zenith and azimuth angles (θ s , ϕ s ). Spectral solar irradiance R g,λ (θ s , ϕ s ), also called incoming solar radiation, includes diffuse and direct components. Consequently, hemispherical reflectance ρ h,λ (θ s , ϕ s ) includes reflected fractions of solar direct and diffuse irradiances: it corresponds to the weighted sum of directional -hemispherical and hemispherical -hemispherical (bi -hemispherical) reflectances, the weighting coefficients being the fractions of direct and diffuse solar irradiances [Lucht et al., 2000]. Directional -hemispherical and hemispherical -hemispherical reflectances are also called black -sky and white -sky albedos [START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF]Wanner et al., 1997;Lucht et al., 2000;[START_REF] Schaaf | First operational BRDF, albedo nadir reflectance products from MODIS[END_REF]Pokrovsky et al., 2003a]. Hemispherical reflectance ρ h,λ (θ s , ϕ s ) is also labeled spectral albedo, or spectral apparent albedo [Kimes and Sellers, 1985;[START_REF] D R A F T Kimes | Hemispherical reflectance variations of vegetation canopies and implications for global and regional energy budget studies[END_REF][START_REF] Privette | Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data[END_REF]Toll et al., 1997;Weiss et al., 1999;[START_REF] Liang | Retrieval of land surface albedo from satellite observations: A simulation study[END_REF][START_REF] Lucht | Considerations in the parametric modeling of BRDF and albedo from multiangular satellite sensor observations[END_REF]Liang et al., 2002b].

Hemispherical reflectance ρ h,λ (θ s , ϕ s ) can be expressed as the integration over viewing zenith and azimuth angles

(θ v , ϕ v ) of apparent bi -directional reflectance ρ λ (θ s , ϕ s , θ v , ϕ v ): ρ h,λ (θ s , ϕ s ) = 1 π 2 π 0 π/2 0 ρ λ (θ s , ϕ s , θ v , ϕ v ) cos(θ v ) sin(θ v ) dθ v dϕ v (2) D R A F T January 26, 2005, 2:58pm D R A F T
where apparent bi -directional reflectance ρ λ (θ s , ϕ s , θ v , ϕ v ) is the weighted sum of directionaldirectional (bi -directional) and hemispherical -directional reflectances, the weighting coefficients being the fractions of direct and diffuse solar irradiances. Then, the angular distribution of bi -directional reflectance (respectively apparent bi -directional reflectance) corresponds to BRDF for Bi -directional Reflectance Distribution Function (respectively apparent BRDF).

Remote sensors provide, after atmospheric corrections, data of apparent bi -directional reflectance within given wavebands characterized by filter response functions. The albedo retrievals within these wavebands are often called narrowband albedos, whereas integrated values over given portions of the solar spectrum are usually labeled broadband albedos [START_REF] Russel | Conversion of nadir, narrowband reflectance in red and near infrared to hemispherical surface albedo[END_REF]Song and Gao, 1999;Lucht et al., 2000;[START_REF] Barnsley | Characterizing the spatial variability of broadband albedo in a semi desert environment for MODIS validation[END_REF]Liang et al., 2002a, b].

In the current study, we use the following labels: albedo for shortwave apparent albedo, hemispherical reflectance for narrowband apparent albedo, bi -directional reflectance for the remote sensing measurements of apparent bi -directional reflectance, and BRDF for the angular distribution of apparent bi -directional reflectance (apparent BRDF).

Data acquisition and preprocessing

The experiment

The data were collected during the Alpilles -ReSeDA experiment, which was the first step of the European ReSeDA program. This program aimed at improving the use of multitemporal, multispectral and multidirectional remote sensing data for a better understanding and description of soil and vegetation processes [START_REF] Prévot | Assimilation of multi-sensor and multi-temporal remote sensing data to monitor vegetation and soil: the Alpilles ReSeDA project[END_REF][START_REF] Baret | Assimilation of multisensor and multitemporal remote sensing data to monitor soil and vegetation functioning[END_REF]. It focused on assimilating remotely sensed data into both Soil -Vegetation -Atmosphere -Transfer (SVAT)

and crop simulation models. Moreover, the simultaneous acquisition of remote sensing data at

D R A F T January 26, 2005, 2:58pm D R A F T
different spatial resolutions allowed assessing the scaling issue, i.e. the meaning of aggregated variables when using coarse resolution sensors [START_REF] Olioso | Spatial aspects in the Alpilles-ReSeDA project[END_REF][START_REF] Wassenaar | Estimation of evapotranspiration over heterogeneous pixels[END_REF].

The study area was a Mediterranean agricultural region of 5×5 km 2 size, located in the South East of France (N 43 [2002]. In the current study, we focused on 1/ the visible -near infrared remote sensing data acquired with the airborne PolDER sensor, and 2/ the field measurements of albedo.

PolDER data

The airborne PolDER imaging radiometer flew once to twice a month. Data were collected on clear sky days at a 3000 m flight altitude which yielded a 20 m nadir spatial resolution. For each day of acquisition, four flight lines were parallel to the solar plan, and one was perpendicular. The PolDER data were preprocessed in a similar way to that used by [START_REF] Leroy | Directional parameters, hemispherical reflectances and anglecorrected NDVIs derived at global scale by the spaceborne PolDER[END_REF]. A detailed description can be found at http://www.avignon.inra.fr/ reseda/base/documents/reseda-report/RES-111.pdf. The sensor calibration was performed before, during and after the experiment. Its accuracy was about 5%. Atmospheric effects were removed using the Simplified Method for Atmospheric Correction (SMAC)

algorithm [START_REF] D R A F T Rahman | SMAC : a Simplified Method for the Atmospheric Correction of satellite measurements in the solar spectrum[END_REF]. SMAC computed bi -directional reflectance by ratioing reflected solar radiance in the viewing direction to incoming solar irradiance, the latter including the diffuse and direct components. Using the data collected from the GPS and the GCU, images were superimposed to a Lambert II projection, which corresponded to a 20 m spatial sampling.

All these preprocessing provided, for each day of the experiment, each of the 20 m size pixels within the 5×5 km 2 size study area, and each of the four PolDER channels, an angular sampling of BRDF between 0 and 45 • , each sample corresponding to a solar position.

Field data of albedo

The in -situ albedo data were calculated as the ratio of reflected to incoming solar radiation measurements. Solar irradiance was measured using a Kipp & Zonen CM6B pyranometer, setup on a meteorological site located on the center of the study area. Two other measurements on different locations provided very close measurements: correlation coefficient of 0.999, and mean quadratic error of 10 W.m -2 , corresponding to 1% in relative terms.

Data of reflected solar irradiance were available for six of the seven ground measurement stations (Fields 101,102,120,203,214,501). These data were collected near field centers, with a 15 s time step and a 20 mn averaging. Their ground footprint ranged from 1000 to 3000 m 2 , depending on sensor height. [START_REF] François | Conversion of 400 -1100 nm vegetation albedo measurements into total shortwave broadband albedo using a canopy radiative transfer model[END_REF]Jacob et al. [2002b, c].

Deriving the instantaneous value, the diurnal course and the daily mean value of albedo

In this section, we present the implementation of the proposed method over the Alpilles -ReSeDA / PolDER multidirectional dataset. We first give a brief overview of the Kernel -Driven Bi -directional Reflectance Distribution Function (KD BRDF) models, to next select some of them according to the study objectives. Then, we explain the computation of hemispherical reflectance products: instantaneous value and diurnal course. Finally, we present the derivation of PolDER albedo products: instantaneous value, diurnal course and daily mean value.

Kernel -Driven BRDF models: a brief presentation

KD BRDF models aim at deriving the whole BRDF from angular samplings provided by multiangular remote sensing data. These models express the observed BRDF as a superposition of BRDF basic shapes. Each shape correspond to a radiative transfer process: isotropic reflection, surface reflection and volume scattering [START_REF] Roujean | A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data[END_REF]Wanner et al., 1995Wanner et al., , 1997;;[START_REF] Lucht | Considerations in the parametric modeling of BRDF and albedo from multiangular satellite sensor observations[END_REF]Lucht et al., 2000]. The BRDF basic shapes are expressed using mathematical functions (kernels). The bi -directional reflectance is then given as a linear combination of the N kernels K i which depend on the viewing angles (θ v , ϕ v ), and the solar angles (θ s , ϕ s ):

ρ λ (θ s , ϕ s , θ v , ϕ v ) = N i=1 α i,λ K i (θ s , ϕ s , θ v , ϕ v ) (3)
The coefficients α i,λ depend on wavelength λ and the radiative properties of the observed surface. From a multiangular dataset of bi -directional reflectance ρ λ j collected over a given location for a given solar position, and within a given waveband j, inverting a KD BRDF model

D R A F T January 26, 2005, 2:58pm D R A F T
consists of estimating rapidly and unambiguously the coefficients α i,λ j by solving the system

[ρ λ j ] = [K][α i,λ j ] through a pseudo -matrix inversion.
Once inverted, the model can be forwardly run for a given solar position and for several viewing angles within the upper hemisphere, which provides the BRDF retrieval. Both model inversion and forward run are fast and easy to implement, which makes KD BRDF models candidates for operational use.

KD BRDF models can be split in two categories according to their reciprocity properties, i.e. the possibility or not to switch solar and viewing angles. This yields labeling KD BRDF models as "reciprocal" or "non reciprocal". The consequence of reciprocity properties is the independence of inversion coefficients to solar position.

• Non reciprocal KD BRDF models, such as the Walthall model [Walthall et al., 1985], have kernels which do not fully account for the solar position. The inversion procedure provides coefficients which depend on the solar direction. Retrieving the diurnal course of BRDF requires inverting the model over datasets collected at different solar positions over the diurnal cycle.

• Reciprocal KD BRDF models, such as Roujean [START_REF] Roujean | A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data[END_REF] and Li -Ross [Wanner et al., 1995], have kernels which fully account for the solar position. The inversion procedure provides coefficients which do not depend on the solar direction. It is possible to compute BRDF at any solar position, regardless of solar position for model inversion.

Rationale in choosing Kernel -Driven BRDF models

In the current study, the diurnal course of albedo was derived from that of hemispherical reflectance which was inferred from that of BRDF. Therefore, we had to consider reciprocal KD BRDF models only. Choosing models was driven by results reported in previous studies, which dealt with the model performances when 1/ retrieving the observed BRDF, and 2/ deriving hemispherical reflectance. We considered three classical models: Li -Ross [Wanner et al., 1995], Modified Rahman Pinty Verstraete (MRPV) [START_REF] Engelsen | Parametric bidirectional reflectance factor models : evaluation, improvements and applications[END_REF], and [START_REF] Roujean | A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data[END_REF]. These models have three kernels, hence three coefficients α i,λ in Equation 3.

D R A F T January 26, 2005, 2:58pm D R A F T
Four variants were proposed for Li -Ross, according to the canopy density and thickness.

We considered the "Li -Sparse / Ross -Thick" version, which was selected by Wanner et al.

[1997] for its performances over plowed fields and vegetated surfaces, and presented as one of the most accurate models by [START_REF] Privette | Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data[END_REF] and [START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF]. Amongst the two available versions for MRPV, we choose the linearized version which inversion procedure is easier and faster [START_REF] Engelsen | Parametric bidirectional reflectance factor models : evaluation, improvements and applications[END_REF], while this variant provided good results from validation exercises [START_REF] Baret | Impact of surface anisotropies on the observation of optical imaging sensors[END_REF][START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF]Weiss et al., 2002b]. Roujean was previously tested over several measured and simulated data sets, and presented as a robust model [START_REF] Baret | Impact of surface anisotropies on the observation of optical imaging sensors[END_REF][START_REF] Chopping | Testing a LiSK BRDF Model with in Situ Bidirectional Reflectance Factor Measurements over Semiarid Grasslands[END_REF][START_REF] Pokrovsky | Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison[END_REF]Pokrovsky et al., 2003a]. We did not consider the reciprocal version of the Walthall model proposed by [START_REF] Nilson | A reflectance model for the homogeneous plant canopy and its inversion[END_REF], since Lucht [1998] showed this version provided poor retrievals for BRDF and hemispherical reflectance.

The three reciprocal KD BRDF models we selected were already tested over the Alpilles -ReSeDA / PolDER data set for the derivation of instantaneous products at the PolDER data acquisition time. First, Weiss et al. [2002b] showed expressing the observed BRDF from three kernels was sufficient, since they contain up to 95% of the required information. They reported the model fitting performances were better if the inversion was performed over samplings within the solar plan. Second, Jacob et al. [2002b] showed the model performances were not driven by atmospheric conditions. They observed the retrieval quality for the hemispherical reflectance was driven by the model performances for viewing extrapolation outside the PolDER angular sampling. Third, Jacob et al. [2002b, c] showed that these reciprocal KD BRDF models provide

D R A F T January 26, 2005, 2:58pm D R A F T
close retrievals of hemispherical reflectance at the PolDER data acquisition time, with relative discrepancies ranging between 8 and 12% according to the PolDER channel.

Inverting reciprocal KD BRDF models over PolDER data

The selected models were inverted over the multidirectional ReSeDA / PolDER dataset. The latter provided, for each day of the experiment, each of the 20 m size pixels, and each of the four PolDER channels, an angular sampling of BRDF between 0 and 45 • . Model inversion was performed on a pixel by pixel basis, over these multidirectional measurements of bi -directional

reflectance ρ λ (θ s , ϕ s , θ v , ϕ v ).
The models fully accounted for the solar position ( § 4.1). Therefore, their inversion was performed considering the solar position for each of the measurements collected within the PolDER data acquisition period (45 minutes, see § 3.2).

In this paper we used the label bidirectional reflectance for PolDER measurements of apparent bidirectional reflectance ( § 2). Following standard procedures reported in the literature [START_REF] Roujean | Retrieval of land surface parameters from airborne PolDER bidirectional reflectance distribution function during HAPEX-Sahel[END_REF]Wanner et al., 1997;[START_REF] Privette | Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data[END_REF][START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF][START_REF] Chopping | Testing a LiSK BRDF Model with in Situ Bidirectional Reflectance Factor Measurements over Semiarid Grasslands[END_REF]Weiss et al., 2002b], we inverted the reciprocal KD BRDF models over the angular samplings of apparent BRDF. The latter included directional -directional and hemispherical -directional reflectances, each weighted by the direct and diffuse solar irradiances at the PolDER data acquisition time ( § 2). From our understanding of the considered processes, integrating the retrieved apparent BRDF provided apparent albedo, although it corresponded to black-sky albedo, according to literature. This yield assuming, when deriving the diurnal course of albedo, a constant diurnal course for the ratio of diffuse to direct solar irradiances, equal to that for PolDER data acquisition. This assumption relied on close values for black sky and apparent albedo, as discussed further: the environmental conditions corresponded to low diffuse solar irradiance ( § 6.1), whereas the latter did not significantly influence albedo computation ( § 7).

D R A F T January 26, 2005, 2:58pm D R A F T

Deriving the diurnal course of hemispherical reflectance

The inverted models were next forwardly run, to retrieve bi -directional reflectance at any solar and viewing directions. BRDF was then computed for different solar positions between sunset and sunrise, with a 20 mn time step corresponding to that of field data acquisition ( § 3.3).

Solar zenith and azimuth angles were calculated from astronomical rules using the latitudelongitude of the site and the local solar time. The calculations were actually limited to solar zenith angles ranging from 0 to 80 • , because of unrealistic retrievals for larger solar zenith angles. This was ascribed to the model physics which become questionable for such angles [START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF]. The 80 • limitation on sun zenith angle could be applied since solar irradiance was low for these angles: according to field measurements, solar irradiance integrated over sun zenith angles larger than 80 • was about 5% of that integrated over the diurnal cycle.

Hemispherical reflectance within each PolDER channel ρ h,λ j (θ s , ϕ s ) was derived by integrating the retrieved BRDF over viewing angles (θ v ,ϕ v ) (see Equation 2). According to the model used, the integration was analytical, or numerical over a 24×24 direction Gaussian quadrature [Weiss et al., 1999]. These calculations provided, for each day of the experiment, each of the 20 m size pixels, and each of the four PolDER channels, the diurnal course of hemispherical reflectance, with a 20 mn time step, and for solar zenith angles ranging between 0 and 80 • .

For assessing the method proposed in this paper, we also considered the retrieval of instantaneous hemispherical reflectance at the PolDER data acquisition time. We forwardly run the inverted models, to compute instantaneous BRDF over the data collection period which lasted 45 minutes around solar noon ( § 3.2). This required averaging, over this period, the solar position to be used for the calculation of BRDF [Jacob et al., 2002b, c].

Computing PolDER albedo products

D R A F T January 26, 2005, 2:58pm D R A F T
Integrated values of broadband albedo can be expressed as linear combinations of narrowband multispectral observations using Narrowband To Broadband (NTB) conversion (see Introduction). Therefore, the diurnal course of albedo was derived applying NTB conversion to those of hemispherical reflectance within the four PolDER channels. The integrated value of albedo over the whole solar spectrum was expressed as a linear combination of hemispherical reflectance ρ h,λ j (θ s , ϕ s ) within the four PolDER channels j centered at 443, 550, 670 and 865 nm:

a(θ s , ϕ s ) = j=4 j=1 β λ j ρ h,λ j (θ s , ϕ s ) (4)
No coefficient set β λ j was proposed for the airborne PolDER sensor. From the retrieved diurnal course of albedo, we finally derived the daily mean value of albedo < a > by weighting each instantaneous estimate a(θ s , ϕ s ) with the corresponding solar irradiance Rg(θ s , ϕ s ):

[6] ARMSE is the mean quadratic difference between predictions and observations for a given variable.

[7] RRMSE is the ratio of ARMSE to the mean value of the observations.

Rg(θ si , ϕ si ) a(θ si , ϕ si ) i=M i=1 Rg(θ si , ϕ si ) (5)
where dt is the time step equal to 20 minutes ( § 4.4), (θ s1 , ϕ s1 ) are solar zenith and azimuth angles (θ s , ϕ s ) at sunrise time t = t r , and (θ sM , ϕ sM ) are (θ s , ϕ s ) at sunset time t = t s .

Strategy for analyzing and validating the proposed method

In the context of deriving the diurnal course of albedo from multiangular data set collected at a given time of the day, we assessed the abilities of the reciprocal KD BRDF models to perform a temporal extrapolation. Since the diurnal course of albedo was derived from that of hemispherical reflectance ( § 4.5), we analyzed the retrievals of first hemispherical reflectance ( § 6.2), and second albedo ( § 6.3). Finally, we focused on the diurnal course of reflected solar irradiance ( § 6.4), which is the albedo linked component for land surface radiation budget.

When focusing on albedo and reflected solar irradiance, we assessed the utility of considering either the diurnal course of albedo, the daily mean value, or instantaneous values at specific times (10:00, 12:00 and 14:00 local solar time). These times were close to satellite overpasses:

SPOT, Landsat, Terra on morning, and Aqua, NOAA on afternoon. The resulting albedo products were first validated against ground based measurements. Next, they were used for the derivation of the diurnal course of reflected solar irradiance, the latter being then validated.

We also considered the albedo retrievals at the PolDER data acquisition time ( § 4.4). This aimed at linking the retrieval quality for the diurnal course of albedo to that for instantaneous values over the information collection period (45 minutes around solar noon, see § 3.2). For this, instantaneous albedo was retrieved by averaging over this period 1/ field measurements of albedo recorded with a 20 minute step ( § 3.3), and 2/ the solar position to be used for the calculation of the hemispherical reflectance ( § 4.4).

D R A F T January 26, 2005, 2:58pm D R A F T
The investigations listed above were conducted considering the six PolDER pixels which matched the ground based measurement locations ( § 3.3). Therefore, we compared 20 m 2 size PolDER pixels against field measurements with footprints ranging from 1000 to 3000 m 2 . This was possible since the spatial variability of the PolDER albedo products within the field measurement footprints was not significant [Jacob et al., 2002b].

Results

Field data of albedo

First subplot of Figure 1 displays the diurnal courses of incoming and reflected solar radia-Figure 1 tion measured inside Field 203 (alfalfa crop). The considered days were those corresponding to PolDER data acquisition. The curves showed measurements were fluctuating on days 05/22, 06/09 and 06/24, the corresponding diurnal courses of albedo being perturbed (see second subplot). This was ascribed to atmospheric perturbations such as clouds overpassing the study area.

Reciprocal Kernel -Driven (KD) BRDF models were not designed to account for such atmospheric perturbations occurring throughout the day. Therefore, the data collected during these three days were removed, which yielded selecting days with low diffuse solar irradiances.

Second subplot of Figure 1 displays asymmetries between morning and afternoon albedo profiles. Such asymmetries were observed with previous experiments by, for instance, Minnis et al.

[1997] and Song [1998]. • Absolute and Relative Root Mean Square Difference (ARMSD 1 and RRMSD 2 ) of 0.009 and 4.3% respectively,

• Absolute and Relative Bias (ABias 3 and RBias 4 ) of 5e-4 and 0.2% respectively,

• offset / slope values of 0.03 and 0.88 respectively, if expressing the 14:00 value as a linear function of the 10:00 value.

Finally, we assessed the uncertainties induced by using, in place of the daily mean value of albedo, the instantaneous values at 12:00, 10:00 and 14:00 local solar time (Figure 3). The noon Figure 3 and daily mean values were different (right subplot), with ARMSE and ABias values of 0.021 and -0.019, respectively. The instantaneous values at 10:00 agreed very well with the daily mean value (bottom left subplot). Using the instantaneous values at 10:00 and 14:00 local solar time, rather than the daily mean value, induced low errors (left subplots): ARMSE = 0.007 / ABias = -0.006 and ARMSE = 0.010 / ABias = -0.007, respectively.

Hemispherical reflectance within the PolDER channels

We next assessed the consistencies of the reciprocal KD BRDF models for extrapolating, over the diurnal cycle, the remote sensing information collected at a given time of the day. For this, we analyzed the retrieved diurnal courses of hemispherical reflectance. Figure 4 displays Figure 4 examples of diurnal courses of hemispherical reflectance retrieved from Li -Ross and Roujean over a bare soil and a wheat crop. The bowl shape of the diurnal course of hemispherical reflectance at 865 nm was more pronounced for the wheat crop (right subplots), than for bare soil (left subplots). A converse behavior was observed for the other channels. For both surfaces,

[1] ARMSD is the mean quadratic difference between two different predictions for a given variable.

[2] RRMSD is the ratio of ARMSD to the mean value of the two predictions.

[3] ABias is the mean difference between two different predictions for a given variable.

[4] RBias is the ratio of ABias to the mean value of the two predictions.

D R A F T January 26, 2005, 2:58pm D R A F T hemispherical reflectance was larger at 865 nm than for the other PolDER channels. This trend was more pronounced for the wheat crop. The diurnal courses of hemispherical reflectance retrieved from Li -Ross and Roujean could be significantly different. For NIR hemispherical reflectance over bare soil, the absolute difference ranged from 0.04 at noon to 0.1 at sunrise and sunset, which corresponded to relative differences of 25% and 40%, respectively.

The four subplots on Figure 4 showed the differences between model retrievals depended on the surface type, the wavelength, and the solar direction. To characterize these differences as functions of the wavelength and the solar direction, we used the following protocol. For each day, each of the 6 validation pixels, and each PolDER channel, the discrepancies between model retrievals were characterized as a functions of the local solar time. By using three reciprocal KD BRDF models, there were three hemispherical reflectance retrievals to be compared for a given solar time i. The discrepancy was characterized using the Absolute Range (AR) and the Relative Range (RR) for the hemispherical reflectance retrievals ρ hi : AR i = max(ρ hi ) -min(ρ hi ), and

RR i = AR i ρ hi
, where ρ hi is the averaged value of the three model retrievals.

Figure 5 displays, for the alfalfa crop, variations of the Absolute Range (AR) and the Relative Figure 5 Range (RR) versus the local solar time. The main trend was an increase of the AR and RR values, as the solar zenith angle increased. A decrease of the AR and RR values for the same solar changes was sometimes observed at 550 and 670 nm, on summer days. For a better understanding of the trends we observed with the alfalfa crop, we next considered all fields for a given day and all days for a given field. The trends were similar, but we did not observed any systematical behavior. Overall, the averaged values of the Relative Range over the experiment were 70%, 20%, 23%, and 9%, for PolDER channels at 443, 550, 670, and 865 nm, respectively.

PolDER albedo products

D R A F T January 26, 2005, 2:58pm D R A F T
The diurnal course of albedo were derived using the three reciprocal KD BRDF models along with the NTB conversion coefficient set designed for MISR observations ( § 4.5). This yielded three different retrievals for the diurnal course of albedo. Their intercomparison was performed using a similar protocol to that used for hemispherical reflectance. The discrepancy between the retrievals was analyzed through Absolute Range (AR) and Relative Range (RR) as functions of the local solar time ( § 6.2). The trends were similar to those observed for hemispherical reflectance. Nevertheless, we noted a significantly lower occurrence of decreasing AR and RR values as the solar zenith angle increased (figure not shown). The AR values ranged between 0.005 and 0.04, i.e. from 3 to 25% in relative terms. Overall, the RR averaged value over the experiment was 0.016, i.e. 10% in relative.

Examples of comparison of PolDER retrievals against field measurements for the diurnal course of albedo are displayed in Figure 6. Despite some differences between predictions and Figure 6 observations, the proposed method provided consistent estimates. The general trend was an increase of the difference between PolDER retrievals and field data, as the solar zenith angle increased. The diurnal courses retrieved with the Li -Ross model were systematically flatter than those derived from the other models. These scatterplots suggested the bias between PolDER retrievals and field measurements over the diurnal cycle might be driven by that occurring at the PolDER data acquisition time. This was verified through a 0.8 correlation coefficient. we removed a part of the days and fields considered in these studies ( § 3.3 and 6.1).

Figure 7 displays the validation scatterplots for two PolDER / Li -Ross albedo products: Figure 7 the instantaneous value at solar noon and the daily mean value. The trends were very similar for both products: large correlations, low discrepancies, and underestimations of field data by PolDER retrievals. These two albedo products were finally intercompared (Figure 8). The results were very consistent with those obtained for field data ( § 6.1 and Figure 3). The noon and daily mean values were different, with ARMSE and ABias values of 0.015 and 0.013.

PolDER products of reflected solar irradiance

The method we propose here was finally validated considering the diurnal course of reflected solar irradiance. We assessed its accuracy by validating, against field measurements, retrievals derived from the following albedo products: 1/ the diurnal course, 2/ the daily mean value, 3/ instantaneous values at 10:00, 12:00 and 14:00 local solar time. Since validation results for D R A F T January 26, 2005, 2:58pm D R A F T albedo retrievals were systematically better with Li -Ross ( § 6.3), the investigations dealing with reflected solar irradiance were conducted considering the Li -Ross albedo products only. Table 3 displays ABias and ARMSE when comparing, against field measurements, reflected Table 3 solar irradiance retrieved from PolDER by using the several Li -Ross albedo products previously listed. ARMSE ranged from 11.5 W.m -2 to 17 W.m -2 , corresponding to a 30% variation, in relative terms. Regardless of albedo product used, field data were systematically underestimated by PolDER retrievals. The lowest underestimation corresponded to the use of diurnal course, with an ABias of -5.5 W.m -2 . A similar bias was observed with the daily mean value. The largest underestimation corresponded to the use of albedo at solar noon (ABias of-12.5 W.m -2 ).

As compared to the use of either noon or daily mean value, intermediary underestimations were observed with instantaneous values at 10:00 and 14:00 local solar time, the latter providing very similar ARMSE and ABias.

Discussion

The intercomparison of the Li -Ross and Roujean retrievals for the diurnal course of hemispherical reflectance was consistent with our knowledge of the considered processes. Curves and solar direction, which may be explained by the different ways the models described the reflection / scattering processes through their kernel formulations.

The intercomparison of the three model retrievals for the diurnal course of hemispherical reflectance mainly showed lower agreements as the solar zenith angle increased (Figure 5). This resulted from 1/ intrinsic capabilities of the reciprocal KD BRDF models for solar extrapolation, especially at large solar zenith angles [START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF] and 2/ errors in model fitting of PolDER BRDF during the inversion procedure [Jacob et al., 2002b], which drove solar extrapolation performances. We expected in a first time that model retrievals would agree more for the solar positions corresponding to PolDER data acquisition, since they were inverted for these solar positions (see § 3.2). However, the best agreements between model retrievals did not corresponded the PolDER overpass times. This showed that the discrepancies between model retrievals were mainly driven by the different ways the models characterized the BRDF solar dependence.

When intercomparing the model retrievals for the diurnal course of albedo, we observed similar trends to those reported for the diurnal course of NIR hemispherical reflectance. First, the diurnal courses for both variables were bowl curved. Second, the discrepancy between models retrievals were very close: 10% for albedo, and 9% for NIR hemispherical reflectance. Third, the intercomparison scatterplots for both variables were very similar. These results showed the strong link between the two variables, which was explained by two factors. First, the largest hemispherical reflectance values occurred at 865 nm, as shown by Figure 4. Second, the coefficient set to be applied for NTB conversion yielded a large weight to the NIR hemispherical D R A F T January 26, 2005, 2:58pm D R A F T reflectance (Table 1). These two combined factors induced a larger contribution for NIR hemispherical reflectance to the albedo calculations.

The comparison of the retrieved diurnal courses of albedo against field measurements showed larger differences for larger solar zenith angles (Figure 6). This was explained by three factors.

The first one was the performances of the reciprocal KD BRDF models for extrapolating BRDF at large solar zenith angles, also driven by model performances for fitting the observed BRDF.

The second factor was the use of models assuming constant surface and meteorological conditions over the diurnal cycle, whereas these conditions could change [START_REF] Minnis | Assymetry in the diurnal variation of surface albedo[END_REF]Song, 1998;Grant et al., 2000]. The third factor was assuming a constant diurnal cycle for the ratio of diffuse to direct solar irradiances, when inverting the reciprocal KD BRDF model ( § 4.3). This was different from actual situations, especially for largest solar zenith angles ( § 6.1).

The validation exercises for the several PolDER albedo products we considered indicated the good quality of these products (Table 2). Indeed, Absolute Root Mean Square Error (ARMSE) et al., 2002b]. The second critical point was the performance of NTB conversion for spectral extrapolation, to compute the integrated value of albedo [Jacob et al., 2002c].

By inverting reciprocal KD BRDF models over PolDER directional samplings of apparent BRDF, we assumed a constant diurnal course for the ratio of diffuse to direct solar irradiances ( § 4.3). It was not a critical point, since the diffuse solar irradiance decreased as the wavelength increased, and was low for NIR hemispherical reflectance which was the main component for albedo computation (see third paragraph of this section). This was consistent with analysis of the field data displayed on third subplot of Figure 1. Indeed, we constructed a diurnal course of solar irradiance by assuming a constant diurnal course for the ratio of diffuse to direct solar irradiances, and equal to that for PolDER data acquisition time. Its comparison with actual field data showed a relative difference of 5.2%.

Regardless of considered albedo product, the validation results were systematically better with the Li -Ross model. This was consistent with previous studies focusing on the performances of KD BRDF models for providing BRDF -derived products [Wanner et al., 1997; [START_REF] Privette | Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data[END_REF][START_REF] Lucht | Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling[END_REF]Weiss et al., 2002b;Jacob et al., 2002b, c;[START_REF] Schaaf | First operational BRDF, albedo nadir reflectance products from MODIS[END_REF]van Leeuwen and Roujean, 2002;[START_REF] Pokrovsky | Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison[END_REF]Pokrovsky et al., 2003a].

D R A F T January 26, 2005, 2:58pm D R A F T
Since Li -Ross systematically provided flatter diurnal courses of albedo, the PolDER calculations for the daily mean value of albedo underestimated field data in a larger extent when using this model rather than MRPV or Roujean.

By assessing the interest of using instantaneous values of albedo in place of the daily mean value, we obtained similar results to those reported in the literature. Using the instantaneous value at solar noon yield significant underestimations (Figure 3 and8). This was explained by the increase of the instantaneous albedo when solar zenith angle increased (see Figure 6). On the other hand, using instantaneous values at times close to satellite overpasses (10:00 and 14:00 local solar time) did not yield significant biases. This was in agreement with the suggestion of Henderson- Sellers and Wilson [1983], who proposed 9:00 local solar time as an optimum time,

for using instantaneous values of albedo in place of the daily mean value.

Regardless of PolDER / Li-Ross albedo products used for the derivation of the diurnal course of reflected solar irradiance, field data were systematically underestimated by remote sensing retrievals (Figure 9 and Table 3). The main results are listed below.

• The largest underestimations were observed when using the instantaneous value of albedo at solar noon, since this albedo value was the lowest of the day. The resulting underestimation occurred mainly for intermediary solar zenith angles, since albedo decreased for lower angles and solar irradiance decreased for larger angles.

• The use of the diurnal course of albedo provided the lowest underestimation. This was the best result we could obtain, and corresponded to the accuracy of the method we propose here.

D R A F T January 26, 2005, 2:58pm D R A F T

• Underestimations were similar if using the diurnal course or the daily mean value of albedo, since the latter was calculated as the weighted sum of each instantaneous value (see Equation 5).

Then, the large scatter around solar noon was explained by the combined effect of 1/ usually larger albedos through the daily mean value, and 2/ a larger solar irradiance at solar noon.

• As compared to the use of either the instantaneous value of albedo at solar noon or the daily mean value of albedo, intermediate underestimations were observed with the instantaneous values at either 10:00 or 14:00 local solar time. Indeed, these albedo values were intermediate between the daily mean value and the instantaneous value at solar noon.

• The similar validation results obtained when using 10:00 and 14:00 albedo values were explained by the low differences between the field data for these albedo values (see Figure 2 and § 6.1). Indeed, analyzing field measurements of albedo showed that, for the Alpilles / ReSeDA experiment, the changes in environmental conditions did not dramatically affect the symmetrical nature of the diurnal course of albedo ( § 6.1).

• Using either the diurnal course of albedo, the daily mean value of albedo, or the instantaneous values of albedo did not affect dramatically the accuracy on the diurnal course of reflected solar irradiance. Indeed, the validation results showed accuracies better than that commonly required, i.e. 20 W.m -2 [van Leeuwen [START_REF] Pokrovsky | Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison[END_REF].

Observing similar product qualities for the reflected solar irradiance regardless of considered albedo product was not in agreement with previous studies. Indeed, the latter reported larger errors if not considering the diurnal course [START_REF] D R A F T Kimes | Hemispherical reflectance variations of vegetation canopies and implications for global and regional energy budget studies[END_REF]Grant et al., 2000]. The explanation was then the considered environmental conditions, which may have larger consequences than those observed for Alpilles / ReSeDA [START_REF] Minnis | Assymetry in the diurnal variation of surface albedo[END_REF]Song, 1998;Grant et al., 2000].

D R A F T January 26, 2005, 2:58pm D R A F T

Conclusion

This study aimed at proposing a new method for deriving the diurnal course of albedo, by using remote sensing data collected from multiangular sun -synchronous sensors, under clear sky conditions. The method is based on the use of both reciprocal Kernel -Driven (KD) Bidirectional Reflectance Distribution Function (BRDF) models and Narrowband To Broadband (NTB) conversion. Its interest is not requiring local calibration. Its analysis and validation was possible thanks to the richness of the dataset collected during the ReSeDA experiment, which included 20 m spatial resolution airborne PolDER data collected near solar noon, and field measurements of albedo recorded over the diurnal cycle. The investigations reported in the current paper provide useful information for the modeling of BRDF and albedo, and also for the operational use of multiangular sun -synchronous sensors when retrieving land surface albedo.

These investigations underlined the abilities of the reciprocal KD BRDF models to extrapolate the remotely sensed information collected at a given time of the day, for the derivation of land surface albedo over the diurnal cycle. This is an indicator of the model consistencies, and provided new applications, additionally to their operational use for retrieving numerous surface variable products [Weiss et al., 1999;Weiss and Baret, 1999;Weiss et al., 2002a;Liang et al., 2002a;[START_REF] Schaaf | First operational BRDF, albedo nadir reflectance products from MODIS[END_REF][START_REF] D R A F T Petitcolin | Land surface reflectance, emissivity and temperature from MODIS middle and thermal infrared data[END_REF]Jacob et al., 2004]. Amongst the reciprocal KD BRDF models we selected for conducting this study, better results were systematically obtained with the Li -Ross model. This was consistent with previous studies, and encourages the consideration of this model for related investigations.

A possible improvement of the method we propose would be increasing the modeling degree, by discriminating diffuse and direct components of solar irradiance, when inverting the reciprocal KD BRDF models. This would allow accounting for the diurnal cycle of the ratio of D R A F T January 26, 2005, 2:58pm D R A F T diffuse to direct solar irradiances. However, it seems to be of second order, since the retrieval quality for the diurnal course of albedo was mainly driven by that for the instantaneous value at the PolDER data acquisition time. Consequently, it is recommended to focus first on better estimating instantaneous retrievals of BRDF, hemispherical reflectance and albedo, when seeking a better accuracy. Nevertheless, the errors we obtained for the different albedo products we considered (instantaneous values at specific times, diurnal course and daily mean value) were included within the range of required accuracies for further applications.

The instantaneous values of albedo at times close to satellite overpasses agreed very well with daily mean values. On the other hand, the qualities of the instantaneous values were better than those of the daily mean value derived from the diurnal course. Then, it is recommended to use instantaneous values at satellite overpasses for the daily mean value, when the latter is needed.

Regardless of considered albedo product used for the derivation of reflected solar irradiance, the quality of the retrievals was better than that required for further applications. This means that instantaneous values, which corresponded to the best accuracies, can be used in place of more complex products such as the diurnal course and the daily mean value. On the other hand, it may be necessary to use the diurnal course of albedo when describing the energetic exchanges with a hourly time step. Indeed, significant differences were observed for middle morning and middle afternoon values. Finally, the daily mean value (respectively the diurnal course), corresponding to the lowest bias (respectively lowest ARMSE), were the most accurate for applications at the daily scale (respectively hourly scale).

These conclusions were not in agreement with others previously reported in the literature. This is probably due to the environmental conditions during the ReSeDA experiment. Indeed, these conditions did not induce significant asymmetries for the diurnal course of albedo, con- Li -Ross 0.0152 -0.0054 0.0259 -0.0140 0.0141 -0.0029 0.0168 -0.0078 MRPV 0.0179 0.0059 0.0268 0.0029 0.0180 0.0094 0.0258 0.0092 Roujean 0.0190 0.0043 0.0285 -0.0027 0.0201 0.0056 0.0223 0.0070 Table 2. ARMSE and ABias between PolDER albedo retrievals and in -situ measurements.

D
From left to right: the instantaneous value at the PolDER data acquisition time, the diurnal course, the instantaneous value at solar noon, and the daily mean value. ARMSE (Absolute Root Mean Square Error) is the mean quadratic difference between predictions and observations for a given variable. RRMSE (Relative Root Mean Square Error) is the ratio of ARMSE to the mean value of the observations. ABias is the mean difference between predictions and observations for a given variable. RBias is the ratio of ABias to the mean value of the observations.

2 •

 2 They gave as explanations several factors: change in crop architecture, vegetation alignment, minor changes in atmospheric conditions, morning dew, evaporation or wind. To quantify the observed asymmetries, we intercompared the instantaneous albedo values at symmetric times to solar noon, i.e. 10:00 and 14:00 local solar time. These values were very close (see Figure 2), as shown by statistical indicators: Figure coefficient correlation of 0.92, D R A F T January 26, 2005, 2:58pm D R A F T

Figure 9

 9 Figure 9 displays the validation results for the diurnal course of reflected solar irradiance Figure 9

  displayed by Figure 4 were explained by 1/ a larger surface reflection occurring within the visible domain for the bare soil, and 2/ a larger canopy volume scattering occurring within the Near D R A F T January 26, 2005, 2:58pm D R A F T Infra Red (NIR) domain for vegetated surfaces. The volume scattering increased as the solar zenith angle increased, which induced well pronounced bowl curves for NIR hemispherical reflectance. The differences between model retrievals depended on the surface type, wavelength

  ranged from 0.0141 to 0.0285, which overlapped the lowest part of the accuracy interval required for further applications (from 0.02 to 0.05, see Introduction). The lowest ARMSE values corresponded to instantaneous values at solar noon and PolDER data acquisition time. The largest ARMSE values for the diurnal course were explained by the inability of the proposed method to retrieve exactly albedo variation over the diurnal cycle, because of the three factors listed in the previous paragraph. It was not surprising to obtain better validation results for the daily mean value of albedo than for the diurnal course. Indeed, the computation of the daily mean value consisted of weighting each instantaneous value with the corresponding solar irradiance (see Equation 5). This yielded lower weights to instantaneous values at large solar zenith angles, and therefore lower contributions from the corresponding largest inaccuracies. D R A F T January 26, 2005, 2:58pm D R A F T An important result was the 80% correlation coefficient between the retrieval quality for the instantaneous value of albedo at the PolDER data acquisition time and that for the diurnal course of albedo. This underlined the consistency of deriving the diurnal course of albedo by choosing the most adequate coefficient set for the instantaneous value at the PolDER data acquisition time ( § 4.5). More important, it showed the method performances for temporal extrapolation was strongly influenced by those for estimating instantaneous albedo at the data acquisition time. Also, it emphasized the critical points of the method. The first one was the model performances for retrieving the observed BRDF, especially outside of the PolDER angular sampling, since it drove the retrieval quality for the instantaneous value of hemispherical reflectance [Jacob

  R A F T January 26, 2005, 2:58pm D R A F T versely to other experiments. Thus, the method proposed in this study might have lower performances for environmental conditions inducing larger asymmetries for the diurnal course of albedo. Then, the question is the occurrence of these asymmetries at the global scale. Further, it should be interesting to extend the investigations of this study to the retrieval of the other surface variables which drive the diurnal course of net radiation. This may provide new possibilities, when dealing with the strategy of remote sensing data assimilation into SVAT models, such as assimilating net radiation retrievals by considering either instantaneous values at a given time, or diurnal courses. Acknowledgments. The Alpilles / ReSeDA project was funded by the EEC -DG XII (contract ENV4-CT96-0326-PL952071) and the French Programme National de Télédétection Spatiale and Programme National de Recherches en Hydrologie. The airborne PolDER sensor was provided by the Laboratoire d'Optique Atmosphérique, Lille, France. Financial support was provided by EC in the frame of the WATERMED project (contract ICA3-CT-1999-00015). This study was initiated during a post -doctoral position funded by the ASTER project of NASA's EOS -Terra Program thanks to Tom Schmugge. It was finalized during a visiting period at the U.S. Water Conservation Lab (USDA / ARS, Phoenix, AZ, USA), funded by both NASA under Grant EOS03-0057-0459 (P.I. Andrew French), and the Department of Research, Development, and International Relations of the École Supérieure d'Agriculture de Purpan. Special thanks to Frédéric Baret and Jean-Louis Roujean for constructive discussions, and to the reviewers for increasing the manuscript quality through their comments. We are grateful to the GNU / Octave community for providing a free and powerful numerical computation software. D R A F T January 26, 2005, 2:58pm D R A F T

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. First subplot: diurnal courses of incoming and reflected solar radiation over field

Figure 5 .

 5 Figure 5. Variation, versus the local solar time, of Absolute (left subplots) and Relative (right

Figure 6 .

 6 Figure 6. Comparison against field measurements (•) of the diurnal course of albedo retrieved

Figure 7 .Figure 8 .Figure 9 .

 789 Figure 7. Comparison, against field measurements, of albedo products retrieved from the

Table 2

 2 displays the validation results for PolDER products when considering the instanta-

	Table 2

albedo were slightly different from those reported by

Jacob et al. [2002b, c]

. Indeed, by filtering data to select environmental conditions allowing the retrieval the diurnal course of albedo,

X -35

Grant, I., A. Prata, and R. Ceche, The impact of the diurnal variation of albedo on the remote sensing of the daily mean albedo of grassland, Journal of Applied Meteorology, 39, 231-244, 2000. Henderson-Sellers, A., and M. Wilson, Surface albedo data for climatic modeling, Reviews on Geophysics, 23, 1743Geophysics, 23, -1778Geophysics, 23, , 1983. . Jackson, R., Evaluating evapotranspiration at local and regional scale, Proceedings of the IEEE, 73, 1086IEEE, 73, -1096IEEE, 73, , 1985. . Jacob, F., A. Olioso, X. Gu, Z. Su, and B. Seguin, Mapping surface fluxes using visible, near infrared, thermal infrared remote sensing data with a spatialized surface energy balance model, Agronomie: Agriculture and Environment, 22, 669-680, 2002a. Jacob, F., A. Olioso, M. Weiss, F. Baret, and O. Hautecoeur, Mapping short-wave albedo of agricultural surfaces using airborne PolDER data, Remote Sensing of Environment, 80, 36-46, 2002b. Jacob, F., M. Weiss, A. Olioso, and A. French, Assessing the narrowband to broadband conversion to estimate visible, near infrared and shortwave apparent albedo from airborne PolDER data, Agronomie: Agriculture and Environment, 22, 537-546, 2002c