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 This contribution illustrates results from a large-scale application of the Joint Research Centre Two-stream Inversion Package (JRC-TIP), using MODIS broadband visible and near-infrared white sky surface albedos as inputs. The discussion focuses on products (based on the mean and one-sigma values of the probability distribution functions (PDFs)) obtained during the summer and winter. This paper discusses the retrieved model parameters including the effective leaf area index (LAI), the background brightness, and the scattering efficiency of the vegetation elements. The similarity between the derived LAI seasonal maps and earlier distributions of this variable comforts us in the quality of the albedo products as well as in the ability of the JRC-TIP to interpret the latter meaningfully. The opportunity to generate global maps of new products, such as the background albedo, underscores the advantages of using state of the art algorithmic approaches capable of fully exploiting accurate satellite remote sensing data sets. The detailed analyses of the retrieval uncertainties highlight the central role and contribution of the LAI, the main process parameter to interpret radiation transfer observations over vegetated surfaces. The estimation of the radiation fluxes that are absorbed, transmitted, and scattered by the vegetation layer and its background is achieved on the basis of the retrieved PDFs of the model parameters. Results from this latter step are discussed in a companion paper.
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 The fraction of solar radiation scattered backward by land surfaces, i.e., the surface albedo, results from complex nonlinear radiation transfer processes determining the amount of radiation that is scattered by the vegetation and its background, transmitted through the vegetation layer or absorbed by the vegetation layer and its background. This residual quantity thus incorporates information about the distribution and partitioning of solar radiation between the vegetation layer and the background. Accessing this information is relevant to understand and accurately model land surface processes and related cycles, but this requires solving a series of inverse problems, i.e., analyzing surface albedo products with a radiation transfer model able to simulate the flux partitioning. Thanks to a large-scale effort of the land community, benchmarked radiation transfer models [Pinty et al., 2004b; Widlowski et al., 2007] together with modern and high-performance inverse techniques can be exploited to leverage the high-quality surface albedo products routinely delivered by space agencies.
 The present investigation reports on results obtained from the processing of MODIS collection 5 white sky surface albedo products at 0.01° (≈1 km) resolution over the globe [Schaaf et al., 2002]. The two-stream model developed by Pinty et al.  simulates accurately the partitioning of the solar fluxes based on a one-dimensional approach using effective state variables to overcome the unavoidable difficulties arising from the significant subpixel unresolved spatial variability. This model, originally designed to run forward in large-scale host models, can effectively be exploited to interpret surface albedo observations (white sky and/or black sky albedos) and thus to ensure the consistency between the retrieved information and the forward step. The white sky (equivalent to a BiHemispherical Reflectance) and black sky (equivalent to a Directional Hemispherical Reflectance) albedo values predicted by this model have been validated extensively against very realistic complex three-dimensional canopy scenario, including in the presence of snowy backgrounds [Pinty et al., 2006, section 3 and Figure 7] as well as in the context of the RAdiation transfer Model Intercomparison (RAMI) exercise [Widlowski et al., 2007]. This class of model must help bridging the gap between the exploitation of remote sensing measurements to generate a set of meaningful and physically consistent products that are required by these large-scale host models.
 The effective state variables determine the radiative properties of the modeled soil vegetation system: from a given set of effective state variables, the two-stream model simulates the vertical components of the scattered, transmitted and absorbed radiant fluxes. The latter are important drivers for representing, in regional and large-scale models, the complex processes of exchanges of energy, mass and momentum between the atmosphere and the terrestrial environments. Typically these models implement their own radiative transfer schemes using their own set of state variables. As elaborated by Verstraete and Pinty  and Pinty et al. , the radiation transfer schemes that are used to simulate these processes in climate models and to retrieve the required state variables from remote sensing data must be compatible with each other or at least physically equivalent with respect to the radiant fluxes they generate. Incompatibilities between the assumptions and approximations implicitly made by using different models, for example, one-dimensional (1-D) versus three-dimensional (3-D) radiation transfer models, may generate discrepancies and biases when remote sensing products are heedlessly ingested by the climate models. As a matter of fact, the same class of radiation transfer schemes should be used in forward (when simulating surface processes in climate models) and inverse (when retrieving state variables from remote sensing data) mode.
 Without observational information, the effective state variables exhibit large uncertainties which translate into large uncertainties in the simulated radiant fluxes and then further into large uncertainties in simulated future climate [e.g., Friedlingstein et al., 2006; Denman et al., 2007]. Remote sensing measurements from space represent observational information that is capable of reducing these uncertainties in multiple ways. One way consists in performing direct assimilation into climate models. This is a quite complex goal to achieve because it involves the construction of an assimilation system including a so-called observational operator that maps the state of the terrestrial vegetation onto the observed top of atmosphere radiances. By contrast, the assimilation of remote sensing products at the level of top-of-canopy radiant fluxes [e.g., Knorr et al., 2010; Kaminski et al., 2010] represent a slightly less demanding task. To implement such an approach requires, however, that the retrieved products are delivered together with uncertainties in each component of this flux vector as well as documented information about the correlation between these uncertainties.
 The generation of such products from remote sensing information is a highly challenging task in itself, both at the scientific as well as at the technological level. Capitalizing on observational information while, simultaneously ensuring physical consistency between the products requires implementing a two-step procedure. In the first step, i.e., the inversion, the unknown model input quantities, i.e., the state variables, are estimated from the observed scattered fluxes at the top of the canopy, e.g., the MODIS broadband visible and near-infrared white sky albedos. Since the number of model unknowns exceed the number of independent observations, i.e., the inverse problem is underdetermined, additional information has to be included in the procedure. This is achieved explicitly by assigning prior values to the set of model state variables and this state of information is expressed using Probability Density Functions (PDFs) (e.g., Tarantola  for the methodological background). This first step thus delivers posterior PDFs of the model state variables, including the effective LAI (see section 3.1) values. In a second step, the calibrated model is used to approximate PDFs of all radiant fluxes simulated by the two-stream model, including those that are not observed. The model ensures the physical consistency between the optimized posterior PDFs in the parameter and flux spaces. Note that such a two-step procedure (without propagation of the uncertainties in the space and time domains) are currently used in four-dimensional variational assimilation in the context of numerical weather prediction [Courtier et al., 1994], where the unknowns are the components of the initial state.
 The above methodological approach is implemented in the JRC-TIP [Pinty et al., 2007]. The posterior PDFs (approximated by Gaussians) thus result from an optimization of the two-stream model parameters that are required to best fit the observed surface albedos while being constrained by their prior values. The relative weight given to the observations with respect to the prior information is specified by covariance matrices of uncertainties quantifying both contributions independently. The propagation of uncertainties from the observations to the model parameters is achieved via the Hessian of the cost function and yields a covariance matrix of posterior parameter uncertainties. This matrix is propagated to the radiation fluxes via the model's Jacobian matrix of first derivatives. The required derivative information is provided by highly efficient derivative code that is generated automatically from the two-stream code [Giering and Kaminski, 1998; Voßbeck et al., 2008]. In this framework the strength of the observational constraint is quantified by the reduction in uncertainties in the posterior PDFs by comparison with the prior PDFs, in the parameter space or in the flux space, for example, the uncertainty reduction can only occur along two directions in the parameter space if only two broadband albedo observations are used. The generated matrix of correlations in posterior radiant flux uncertainty corresponds precisely to the input required for performing the assimilation into the terrestrial components of the climate models mentioned previously since it specifies accurately the information content at the flux level.
 The intent of this and the companion contribution is to assess the degree to which the challenging objective of devising an inverse modeling system that delivers, in the form of PDFs, a set of global medium-resolution remote sensing products which are physically consistent can be reached. We illustrate results from the JRC-TIP obtained at 1 km resolution at global scale and assess the spatial and seasonal consistency of the retrieved geophysical fields. This investigation was conducted over the full year 2005 of MODIS broadband visible and near-infrared albedos and only some selected snippets are discussed here. Products generated for two periods representative of typical situations occurring during the North Hemisphere summer and winter have been selected to demonstrate the performance of the inversion and the quality of the surface albedo products. The present paper focuses on the model process parameters and discusses the mean and one-sigma PDF values of the retrievals. These PDFs are then used in forward simulations of the two-stream model to estimate the radiation fluxes that are absorbed in the vegetation layer and the background underneath, transmitted through the vegetation layer and finally scattered at the top of the vegetation canopy. Results from this second step are discussed in a companion paper [Pinty et al., 2011a].
 The examples peppering these two companion papers have been selected to illustrate the main features and key advantages of the JRC-TIP approach, namely (1) the production of physically consistent products, (2) the generation of new geophysical fields in accordance with the two-stream model, such as the brightness of the background under the vegetation layer, the leaf canopy absorption efficiency or the complete set of associated radiation surface fluxes in and out of the vegetation and background layers, (3) a comprehensive documentation of the uncertainties of the products using a rigorous mathematical framework, and (4) the capacity of delivering such products under rather exacting and diverse conditions, so that no back-up solution or alternate method is necessary to fill in the gaps.
2. Data Sets
 The current investigation uses the visible (0.3–0.7 μm) and near-infrared (0.7–3.0 μm) broadband white sky albedo values (calculated under the assumption of an isotropic illumination of the surface [Schaaf et al., 2002]) available from MODIS collection V005 products (MCD43B3) at 1 km (0.01°) spatial resolution for successive 16 day periods (https://lpdaac.usgs.gov/). The main motivation for selecting this particular product is twofold: (1) focusing on surface albedo quantities that depend on intrinsic surface properties only and (2) exploiting products at the most integrated/averaged level in both the angular, i.e., albedo quantities instead of bidirectional reflectance factors, and spectral, i.e., broadband instead of narrow bands, domains. Moreover, as discussed by Pinty et al. , the bulk of the information that is desired for the vast majority of land application activities is actually contained in albedo, e.g., angularly integrated quantities, in the visible and near-infrared spectral domains. Note that the retrieval scheme described here can be used as well with black sky albedo quantities provided that their uncertainties are documented and validated over a range of surface types for each relevant Sun angle.
 To benefit from an appropriate spatial and temporal sampling, albedo values associated with quality flags 0 (best quality) and 1 (good quality) (MCD43B2) at the same (1 km) spatial resolution, were considered. In the context of the present application, relative uncertainty values of 5% and 7% were attributed to products with flag values 0 and 1, respectively. In addition, a lower limit for the absolute uncertainty value was set at 2.5 10−3 to avoid specifying unrealistically low uncertainties with the occurrence of small albedos as may happen in the visible domain over dense vegetation canopies. These uncertainty values are entering the measurement error covariance matrix discussed in section 3. Associating quality flags with quantitative uncertainty values is a quite challenging task. The 5% and 7% relative values selected here to conduct global-scale applications are based on a literature survey dealing with calibration issues [e.g., Bruegge et al., 2004; Thome et al., 2004; Xiong et al., 2005], advanced validation exercises [e.g., Lyapustin et al., 2007; Vermote and Kotchenova, 2008] as well as comparison studies using albedo products derived from the Multiangle Imaging SpectroRadiometer (MISR) instrument [e.g., Taberner et al., 2010].
 The MODIS surface albedo products delivered at 1 km spatial resolution (from MCD43B) result from an averaging of the underlying 500 m resolution retrievals and the quality flags associated with the 1 km products represent the majority of the quality flags at the spatial resolution of 500 m. Although MODIS collection V005 products are generated every 8 days using a 16 day accumulation period, the present application considers the products available every 16 days to avoid the temporal correlation inherent to the overlapping 16 day accumulation periods.
 The MODIS snow indicator associated with the 16 day composite MODIS surface albedo product has been used here to identify snow events. Ephemeral snow conditions occurring during a 16 day period are discarded by the MODIS algorithm when the majority of the 16 day accumulation period for MODIS are snow free and the MODIS product at 500 m resolution is then flagged as snow free.
3. Setup of the Retrieval Scheme
 The retrieval scheme adopted here, namely the Joint Research Centre Two-stream Inversion Package (JRC-TIP), has been described in detail and its performance assessed in previous studies [Pinty et al., 2007, 2008; Lavergne et al., 2006; Clerici et al., 2010; Voßbeck et al., 2009]. It is based on a generic formulation of the inverse problem such that the optimal solutions result from the minimization of the cost function J(X),
 This cost function balances the mismatch between the albedo (1) measured d (by MODIS visible and near-infrared broadband white sky surface albedos) and modeled (using the two-stream model M(X) described by Pinty et al. ) surface albedo with associated uncertainties specified in the covariance matrix Cd and (2) the deviation of the model parameters X from their prior PDF values represented by the mean value Xprior of a prior Gaussian PDF with covariance matrix The solutions are given as a Gaussian approximation of the multidimensional PDFs of the model parameters together with a covariance matrix documenting the uncertainties associated with these solutions.
 The inverse problem of inferring a seven-dimensional parameter vector X (one spectrally independent LAI and three parameters in each spectral domain; see section 3.1) from a two-dimensional observational vector is highly underdetermined. For a given pair of observed albedos there is an infinite number (in fact at least a five-dimensional subspace of the parameter space) of parameter vectors that provide the best match to the observations. The prior information is thus crucial, because it allows us to select one parameter vector within this subspace, namely the one that is as close as possible to the prior parameter vector.
 The solutions are given as a Gaussian approximation of the multidimensional PDFs of the model parameters together with a covariance matrix documenting the uncertainties associated with these solutions. This covariance matrix is approximated by the inverse of the cost function's Hessian matrix, i.e., the matrix containing the partial second derivatives of the cost functions.
 The JRC-TIP implements an inversion scheme which exploits the adjoint, tangent linear and Hessian codes of J(X) generated by the compiler tool Transformation in C++ (TAC++) [Voßbeck et al., 2008] available from FastOpt (http://www.FastOpt.com/). It delivers PDFs of the two-stream model parameters Xpost as well as the radiation fluxes, i.e., scattered, transmitted and absorbed by the vegetation layer and its background, simulated forward by the two-stream model. The uncertainty ranges of the estimated model parameters are propagated toward the radiation fluxes via the two-stream model first derivatives [Voßbeck et al., 2009].
 In practice, look-up tables (LUTs) were generated in the measurement space (here a highly discretized two-dimensional broadband white sky albedo space) to store the JRC-TIP solutions (limited to the mean and the one-sigma PDF values of the covariance matrix obtained off-line from a few selected sets of prior conditions. This LUT-based approach contributes to the computational efficiency of the JRC-TIP while limiting the occurrence of physically nonvalid (or dubious) solutions [Clerici et al., 2010].
 According to equation (1), large J(X) values may arise due to (1) the occurrence of a geophysical situation that cannot be explained by the two-stream model and/or the use of insufficient quality input data and/or (2) large deviations of the retrieved/optimized model parameters from their prior values. It is worth recalling here that adopting slightly less optimistic uncertainty values in the input albedo products (see section 2) would mainly translate nonlinearly into larger uncertainties, i.e., increase the width of the PDFs, in the suite of products retrieved by inversion.
3.1. Two-Stream Model Parameters
 The two-stream model (a 1-D radiation transfer model tailored to represent plane-parallel, homogeneous vegetation canopies in regional and global climate models) probably constitutes the simplest way to simulate accurately radiation fluxes from a given volume of vegetation without simulating explicitly the 3-D local variability exhibited by the model parameters at the subpixel or subgrid cell resolutions. The partition of radiation fluxes between absorption, transmission and scattering fractions, resulting from a complex 3-D environment can, indeed, always be represented accurately by a 1-D model, provided domain-averaged effective variables are used instead of the actual ones [Pinty et al., 2004a, section 3.3]. In other words, an equivalent 1-D representation can always be found to generate radiant fluxes similar to those arising from a 3-D system (averaged over the domain of investigation). The accurate representation of any single 3-D system requires an extremely large number of variables at various spatial scales and multiple (in fact an infinite number) combinations of such variables yield the same set of radiant fluxes. By contrast, this same set can be generated very accurately using 1-D radiation transfer models. The values taken by the 1-D model variables are called effective to indicate that their values are derived from a 1-D homogeneous turbid medium model constrained to yield the same fluxes as those that would be generated by a 3-D heterogeneous canopy [e.g., Davis and Marshak, 2010]. It must be recalled here that the use of a spherical distribution function to account for the orientation of the vegetation scatterers is not mandatory; that is, the two-stream model could be operated with different leaf angle functions. The choice of the spherical distribution here is motivated by the requirement to use the same biome-independent model for global applications.
 Three effective variables are required by the two-stream model to represent the radiation transfer processes in the vegetation layer namely (1) the spectrally invariant effective leaf area index (LAI), estimated with a spherical distribution function to account for the orientation of the randomly distributed vegetation scatterers, (2) the effective single scattering albedo of elementary vegetation volumes, including leaves and branches, denoted ωl(λ) = rl(λ) + tl(λ) where rl(λ) and tl(λ) refer to the effective reflectance and transmittance factors, respectively, which mimic the absorption probability of elementary vegetation volumes, and (3) the ratio dl(λ) = rl(λ)/tl(λ), which specifies the preferential forward or backward direction of scattering. One additional piece of information is required by the two-stream model, namely the ‘true’ (by opposition to effective) albedo (or Bi-Hemispherical Reflectance) of the background below vegetation rg(λ).
 As suggested by Pinty et al. [2006, section 2.3.1], the relationship between effective and true LAI requires the introduction of a structure factor at the pixel resolution (sometimes called clumping factor at the stand level [Chen and Cihlar, 1995]) that is associated with the heterogeneous nature of the canopy volume. In the vast majority of cases, the effective LAI value is generally much lower than the pixel-averaged true LAI values of the scenes (provided the proportion of woody material is not too large with respect to the amount of leafy elements of the scene). Note that in the presence of woody elements, for example, as is the case in boreal forests, the value of the effective LAI, which accounts for all leafy and woody elements composing the vegetation canopy, is sometimes called a plant area index. The ratio, mainly in the [0.6–0.8] range, between effective to true LAI was investigated theoretically using a wide range of modeled coniferous forest conditions [Widlowski et al., 2004] based on realistic coniferous forest properties as reported in the literature [Widlowski et al., 2003]. Such relationships between the true and effective LAI values were found to be in good agreement with those deduced from field measurements; the latter result from a careful analysis of multiple estimations collected over various locations and tree species during the international Boreal Ecosystem-Atmosphere Study (BOREAS) that have been assembled by Chen et al. [1997, Table 3].
3.2. Prior Values
 Prior model parameter values, together with their uncertainty ranges, constitute essential ingredients to find unique solutions as they transform an ill-posed into a well-posed mathematical inverse problem. The specification of this information must, however, be implemented carefully to avoid unduly constraining the solution with prior knowledge that may or may not be appropriate or reliable for the particular situation at hand. Specifying a reasonable degree of variability around the priors should allow the retrieval of practical solutions with acceptable levels of uncertainty. The priors specified here represent the information provided to the inversion without specific input from the remote sensing observations or radiation transfer models simulating the observations.
 The strategy adopted in the present investigation is such that the prior values on the parameters characterizing the vegetation layer are time and space invariant; that is, they are not specified as a function of land cover and/or seasons. Moreover, the effective LAI, which is largely unknown and quite variable, is specified with a very large uncertainty allowing the inversion procedure to explore any physically realistic value. The mean values Xprior and associated standard deviations used to set the diagonal of the prior covariance matrix at the broadband visible and near-infrared spectral domains, respectively are provided in Table 1 (remaining entries in not specified in Table 1, are zero). They are the same as those adopted in earlier studies [e.g., Pinty et al., 2008, Table 2 and Figure 1] and are duplicated here for the sake of convenience. These values have been selected on the basis of model-based investigations and detailed time series analysis in previous investigations [Pinty et al., 2004a, 2007; Lavergne et al., 2006].
Table 1. Mean Values Xprior and Associated Standard Deviations Used to Set the Diagonal of the Prior Covariance Matrix a
and correspond to the broadband visible (0.3–0.7 μm) and near-infrared (0.7–3.0 μm) spectral domains, respectively; and refer to the single scattering albedo, asymmetry factor, and background albedo, respectively.
Values associated with the green leaf scenario.
Values adopted for the bare soil case with a correlation factor between the two spectral domains of 0.8862 set in
Values adopted under occurrence of snow with a correlation factor between the two spectral domains of 0.8670 set in
 The JRC-TIP has been operated with two sets of values for the effective single scattering albedo of the vegetation layer. The ‘standard’ set refers to the general case where limited knowledge is specified on this quantity while the so-called ‘green leaf’ scenario imposes much more constraining reflectance and transmittance factor values (note the very low uncertainty range in the corresponding to typical green leaf properties, for example, high absorption in the visible range where photosynthetic activity takes place and large scattering in the near-infrared domain where multiple scattering effects are enhanced. The corresponding mean values have been estimated from an ensemble of measured [Hosgood et al., 1995] and modeled [Jacquemoud and Baret, 1990] leaf optical properties; they were further modified to best account for the overall effects on the domain-averaged radiant fluxes, of needle clumping into shoots, shoots or leaves clumping into crowns as well as the presence of woody elements in the canopy [Rautiainen et al., 2004; Pinty et al., 2004a]. The lack of confidence in the specification of prior information for these effective parameters is expressed by relatively large uncertainties specified in the covariance matrix Results from these two sets will be analyzed further to assess the impact of the specification of the ‘leaf color’ on the retrievals.
 The prior values associated with the background reflectance acknowledge the well-known visible and near-infrared correlation in the spectral domain (the level of correlation imposed on the uncertainties of the background albedos are given as footnotes of Table 1). These prior values on the background are also modulated to account for the specific changes in the spectral relationships under the occurrence of snow. In the following application, the presence of snow is determined on the basis of information provided by the MODIS snow product (see section 2) and the prior values for the background are switched to snow-like conditions accordingly.
 As discussed by Pinty et al. , the capability to carefully and accurately (through the width of the PDFs) specify the prior knowledge is an asset to the inversion procedure. It allows us to recognize, to take advantage and finally to account explicitly, and in a well-established mathematical frame, for intrinsic correlations between parameters characterizing the vegetation layer and its background. This prior knowledge thus corresponds to the information available and applicable at anytime to most geographical location before using any Earth Observation data sets or products, like surface albedos. This information is used in section 5 as a reference to quantify the knowledge gained from inversion of the two-stream model against MODIS surface albedo products.
Figure 1 provides examples of the mean of the PDF ‘standard’ prior values for the LAI (Figure 1, top left) and the single scattering albedo in the near-infrared domain (Figure 1, bottom left) when operating the inversion of MODIS white sky albedo products for 13–28 August 2005 16 day period. The black points identify the grid cells for which no information is available from the MODIS products mostly due to cloud and/or ephemeral snow occurrence during each 16 day period of accumulation. The prior knowledge on the vegetation parameters does not thus depend on the geographical location by contrast to the background reflectance which acknowledges the occurrence of snow conditions notably at the highest latitudes of the North Hemisphere, e.g., over Greenland, in winter (see Figure 1, right). It is worthwhile recalling that the prior uncertainties of the ‘standard’ scenario provide some freedom for the corresponding model parameters to vary and be optimized as a function of space and time to match the observed albedo products.
 The accuracy of the retrievals of the model process parameters as well as examples of typical covariance matrices have been discussed extensively by Pinty et al. [2007, section 3]. For all practical purposes, it is appropriate to consider three broad categories of vegetation canopies driven by their effective LAI values, the dominant process parameter, namely, high (larger than approximately 3.0), low (lower than approximately 1.0) and intermediate.
 Under conditions where high LAI values dominate, the background albedo cannot be resolved accurately (not enough radiation escapes the canopy with a significant signature from the background). Since the lower boundary condition of the canopy layer cannot be resolved accurately, the canopy optical thickness, the LAI, is retrieved with high uncertainty values. However, high LAI conditions favor the accurate retrieval of the effective single scattering albedo of the elementary vegetation scattering volumes, ωl. Low LAI vegetation canopies exhibit the opposite features that is, the background albedo and LAI are resolved very accurately but there is not enough radiation scattered by the canopy elements only to provide an accurate estimate of the effective single scattering albedo. The accuracy of the retrievals under intermediate LAI conditions depends strongly on the scattering/absorbing properties of the vegetation elements and the background brightness. Bright backgrounds, including snow, contribute positively to an accurate LAI retrieval but also smear the scattering signature due to the vegetation elements, thus yielding uncertain retrievals of the vegetation single scattering albedo.
 The accurate estimation of the predominant scattering direction regime, the dl parameter, is rather challenging over the full range of LAI conditions. The retrieval of this quantity indeed requires a significant signature from the downward scattered transmission to the upward scattered signal at the top of the canopy [Pinty et al., 2004a, section 3.3.3], a condition that is hardly realized for high (low) LAI canopies due to the very limited contribution from the background (from the elements composing the canopy). As a consequence, the vast majority of the retrieved dl parameter values, both the mean and one-sigma PDFs, remain close to their prior values. This situation does not impact significantly the absorbed fluxes at the canopy scale discussed in the companion paper given that the latter are mainly controlled by the effective canopy single scattering albedo that is [1 − (ωl)].
Figure 2 displays the time series of the effective LAI and the near-infrared background albedo over four sites located in the Southern Study Area (SSA) of the international Boreal Ecosystem-Atmosphere Study (BOREAS) experiment. These sites, corresponding to different types of vegetation and environmental conditions, are identified as Old Black Spruce (54°00′18″N; 105°07′30″W) (Figure 2a), Young Aspen trees (53°39′17″N; 105°19′29″W) (Figure 2b), Managed land (53°39′17″N; 105°19′29″W) (Figure 2c) and Young Jack Pine (53°52′30″N; 104°38′41″W) (Figure 2d). The retrieved values shown here are estimated using the 1 km (0.01°) spatial resolution MODIS (red color) and MISR (blue color) BHR–white sky surface albedo. The MISR products are derived from the procedure described by Taberner et al. [2010, section 2]. On all these panels in Figure 2, the MODIS values are reported on day 8 of every 16 day period while the MISR values are associated with day 4 of every 8 day period. The vertical bars display the uncertainty of the retrieval, i.e., the one-sigma value of the PDFs and, in the MODIS case, solid and dashed lines refer to flag values 0 and 1, respectively. Open symbols, for example, in Figure 2b, are identifying solutions associated with relatively high cost function values that is, larger than 3.
 Overall, the retrieved values from the MODIS and MISR suites of products are in good agreement, including when snow has been detected by MODIS (identified by black triangles on top axes) despite the biases that have been identified in the input surface albedo products derived from these two instruments [Pinty et al., 2011b; Wang et al., 2010]. The time series in effective LAI exhibit smooth variability over all four sites, as can be expected from the dominant vegetation type and cover. By contrast, the retrieved background albedo values show large and sudden variations related to the occurrence of snowy and snow-free conditions. These episodes do not, however, translate into abrupt changes in effective LAI and this suggests that the inversion scheme is capable of properly accounting for drastic changes in the measurement (input) albedo products due to the intermittent presence snow and subsequent melting events. This remarkable temporal consistency can be locally perturbed (see for instance the MISR retrievals over the Young Jack Pine at the end of November) by the assignment of a false prior information on the background albedo, i.e., snow-covered versus snow-free conditions. In this particular case, the large retrieved LAI value is masking the background signature to compensate for the low background reflectance (prior values in the absence of snow). Note that the uncertainty of the retrievals is larger than usual (due to the large deviation from the prior background conditions) which provides a useful way to flag such conditions.
 The effective LAI time series are mirroring a diversity of phenological cycles over the BOREAS SSA region. As anticipated, the phenological cycle is the most pronounced over managed land and is much more limited over evergreen needle forests. According to the earlier discussion in this section, the effective LAI dominates the radiation transfer regimes. Large LAI values occurring at the peak of the growing season are retrieved with significant uncertainty given the lack of a significant signature from the background. These conditions are associated with large uncertainties in the retrieved background values. By contrast, at intermediate and low effective LAI conditions, the albedo of the background is well-resolved and the posterior uncertainties are smaller than the prior value (highlighted by the grey shaded area for snow-free cases). The spatiotemporal variability in the background albedos is a prominent feature in this boreal region. The presence of spatially unresolved water bodies (at the 1 km resolution) reduces the grid cell-averaged background albedo values (with respect to the mean priors) notably in the near-infrared domain where absorption of solar radiation by water is very significant.
 The global maps shown in this paper were generated using the average values over 20 × 20 grid cells, i.e., ≈20 km, of the mean and the one-sigma values (the latter are not reduced by the spatial averaging procedure and are thus representative of a single pixel value) of the PDFs retrieved at the 1 km (0.01°) MODIS spatial resolution. One must recall that when performed over regions including vegetation-free grid cells, the averaging procedure may yield apparently biased low effective LAI and background albedos values (especially in presence of water bodies as shown in Figure 2). These examples are displayed with (in white) and without the snow mask from MODIS as appropriate. In the latter case, the maps exhibit the JRC-TIP retrievals under snow conditions, that is after switching the background prior values to the snow scenario, as explained in section 3.2. The overall performance of the inversion package is such that it delivers physically valid solutions for about 99.5% of the 1 km resolution MODIS albedo pixels [Clerici et al., 2010]. The remaining 0.5% are flagged as non physically valid (or dubious) solutions and the majority of such cases occur over very bright and dry surfaces, e.g., over the Sahara. In these rare instances, the mean values of the retrieved PDFs can take slightly negative (thus physically unrealistic) values, e.g., LAI ≈−0.02, but the retrieved albedos match very closely the observed values.
 The radiation fluxes simulated by the two-stream model (which are analyzed in the companion paper) include the surface albedo products as observed (see section 3). The comparison between the observed and posterior albedo values provides an overall estimate of the quality of the fits, that is a measure of the ability of the two-stream model to represent the measurements using the optimized model parameter values.
Figure 3 (bottom) (near-infrared domain) and Figure 4 (bottom) (visible domain) illustrate the quality of the fits obtained from inversion of the two-stream model against the albedo products mapped on Figures 3 (top) and 4 (top), respectively, for the 13–28 August 2005 16 day period. The relative differences remain well below the measurement uncertainty levels specified in the covariance matrix Cd, i.e., 5% (7%) for high-quality (good quality) flag conditions. The confrontation of the bottom and top panels in Figures 3 and 4 indicates that the reconstructed albedos tend to be slightly biased low (high) by approximately 1 to 2% (3 to 4%) over dark (bright) regions. The same conclusion generally holds true for the other 16 day periods including under the occurrence of snow. This limited bias is mainly induced by the use of relative uncertainties on the input albedo products. The JRC-TIP thus delivers optimized model process parameters that are capable of generating albedo values as observed well within the uncertainty range of the measurements.
Sections 4.1–4.3 present examples of results obtained from the JRC-TIP for two 16 day periods representative of typical situations during the North Hemisphere summer (13–28 August) and winter (18 February to 5 March) 2005.
4.1. Effective Leaf Area Index
Figure 5 shows the maps of the mean values of the retrieved PDFs for the effective LAI. Figure 5 (top) and Figure 5 (bottom) refer to the 13–28 August and 18 February to 5 March 2005 16 day periods, respectively. On these and other maps displayed in this paper, the grid cells lacking an albedo value in the MODIS product are shown in black, while the grid cells with a majority of snow occurrence during each 16 day periods are displayed in white. The green tone associated with the mean value of the prior PDF (see Figure 1) is also shown on top of the color scale that ranges from light yellow (low LAI) to dark green (high LAI). Under high effective LAI conditions, a further increase in LAI will not translate into a change in the observed albedos since vegetation approaches or matches the limit of radiatively semi-infinite conditions [Gobron et al., 1997]. In such cases, the effective LAI cannot be resolved accurately; the LAI = 3.0 limit reported here is close to this saturation level but actual effective LAI values can be larger.
 Both maps exhibit broad patterns related to well-known vegetation features. High effective LAI values occurring in the Northern Hemisphere during summer relate mainly to agricultural activities and broadleaf forests, for example, over United States, Europe and China, or are associated with dense evergreen forests over equatorial regions, e.g., Amazonia and Africa. Effective LAI values are equal (or very close) to zero over well-known hot and cold deserts, and take on intermediate values over boreal forests, e.g., over Russia and Canada. The seasonal change is also correctly accounted for by the effective LAI maps, with a general decline of LAI values in the Northern Hemisphere between August and February periods that contrasts with the expected increase in the Southern Hemisphere including over savannah regions, e.g., in South America and Africa. All these well-established spatiotemporal patterns illustrate the performance of the JRC-TIP that operates on a pixel by pixel basis without any prior information on the land cover type. This nicely complements earlier results showing the temporal consistency of 1 km resolution time series (see, for instance, Figure 2) that were obtained without prior correlation in the time domain; that is, no time-dependent relationship is specified in the cost function [Pinty et al., 2008].
 The one-sigma PDF global patterns of the effective LAI values are shown in Figure 6 for the 13–28 August (Figure 6, top) and 18 February to 5 March (Figure 6, bottom) 2005 16 day periods. The distribution of points in Figure 6 (and subsequent similar graphs), which exhibits regular patterns and seemingly more random dispersion, results from the particular discretization of the TIP tables. The overall reduction of the prior uncertainty set at 5.0 (see Table 1) is quite notable and reaches a factor close to 10.0 over regions with low LAI values; that is, the (LAI) is even less than 10−2 over desertic regions. Its spatial and temporal variability is largely correlated with the mean LAI values; that is, the uncertainty increases with LAI for reasons discussed previously. It must be recalled that bright background conditions, as found under snowy conditions, favor the retrieval of LAI and yield a reduction in the uncertainty over boreal forest regions during the winter [Pinty et al. 2008, Figures 2 and 3].
Figure 7 (top) represents a subsampling of the TIP LUT tables driven by the observed albedos and suggests that three domains can be identified when analyzing the correlation between the mean and one-sigma PDF values in effective LAI (at the resolution of the retrievals). Specifically, for LAI lower than 0.5, the LAI uncertainty mainly mirrors the observational uncertainties that limit the increase in accuracy of the retrieval to a minimum saturation level around 0.3–0.4. At intermediate LAI values [0.5–2.0], the uncertainty increases quasi linearly with LAI such that (LAI) ≈ 1.6 × LAIpost − 0.4. By contrast, for LAI values beyond 2.0, the uncertainty can be rather large and saturates at a value close to 3.0. The large scatter of points is partly caused by the mixing of two different uncertainty levels in the observations, i.e., 5 and 7%. The widening of the PDF with increasing LAI values is inherent to the physics of the radiation transfer problem and retrieving accurate LAI values from dense canopies remains an extremely challenging task. The saturation in the LAI uncertainty is to some extent also driven by the priors [Pinty et al., 2007, section 3.1]. Using larger (LAI) would, however, yield extremely large (LAI) such that the knowledge gained from ingesting albedo data sets will be very limited anyway.
 The retrieved LAI uncertainty is considerably reduced for intermediate LAI values when increasing the prior constraints on the effective single scattering albedo of the vegetation, i.e., when operating the ‘green leaf’ scenario specified in Table 1, as can be seen in Figure 7 (bottom). This ‘green leaf’ scenario indeed specifies low uncertainty values, i.e., a strong inversion constraint, on the single scattering albedo of the vegetation that straightforwardly decreases the retrieval uncertainties by contrast to the standard scenario. It must be recalled that the ‘green leaf’ scenario constrains the observed albedos to be interpreted by the two-stream model as if all vegetation scattering elements were behaving like healthy green leaves that is, exhibiting a high scattering efficiency in the near-infrared domain. This is one of the fundamental but hidden assumptions in simple algorithms such as vegetation indices that are widely used to estimate vegetation state [Pinty et al., 2009].
4.2. Background Albedo
 The mean values of the background albedo in the near-infrared domain are displayed, without the snow mask, in Figure 8 (top) for the 13–28 August and (Figure 8, bottom) 18 February to 5 March 2005 16 day periods. Figure 8 thus shows the brightness of the Earth land surfaces in the absence of any contribution from the vegetation. Some well-organized patterns are easily discernible, especially over regions with low vegetation density.
 Background albedo rises to values close to unity, especially in the visible domain, due to the contribution from regions that are densely covered by fresh snow, e.g., in the polar zones. The largest discernible seasonal changes occur at northern latitudes in the boreal regions that are subject to snow fall and snow melting events on short time scales. The changes in background albedo values can be evaluated by comparing differences in Figure 8 (top) and Figure 8 (bottom) and the regions where snow occurrence has been observed (in white color in Figure 5 (bottom)). Compared to higher latitudes, changes in background albedo at regional and seasonal scales, especially around 50°N or under snowy conditions, are quite noticeable, as can be seen from the bottom panel of Figure 5. It is noteworthy that the occurrence of snowy backgrounds over short vegetation (as can be seen for example close to the Canada–United States border) translates into higher background albedo values than over tree-covered regions. These regional-scale features illustrate the capability of the two-stream model to discern, from the observed surface albedos and within the uncertainty range delivered by the inverse method, between various levels of snow reflectance in presence of moderately dense vegetation that basically darkens the bright background [Pinty et al., 2011c]. The presence of snow in winter leads to radiatively complex geophysical situations due the coupled effects of relatively dark (highly absorbing) forest and the bright background floor underneath. The surface radiation balance with snow-covered background becomes difficult to establish accurately but such bright backgrounds have a strong incidence on the quality of the temperature forecast [e.g., Viterbo and Betts, 1999], for instance.
Figure 9 illustrates the spectral relationships between the mean values of the vegetation background albedos retrieved in the visible and the near-infrared spectral domains for the 18 February to 5 March 2005 16 day period, with (blue points) and without snow (black points). As expected, the two large ensembles of values, i.e., with and without snow, are distributed along the relationships specified in the prior with the appropriate correlation factors (see Table 1). The regions of this parameter space that are not accessible to the solutions are clearly delineated by a sharp edge on the left part of each distribution. Although these regions may fall within the domain covered by the 1.5 sigma PDF of the prior background albedo values they correspond to background solutions that are not favored by the inversion procedure; that is, comparatively lower cost function values are always reached with at least one of the [rg(VIS), rg(NIR)] combinations shown in black (snow-free) and blue (snow). The occurrence of very bright surfaces in both spectral bands leads to relatively high cost function values (shown in red) that is, larger than 3.0, due to the significant departure from the prior values, e.g., the second term on right-hand side of equation (1)) while providing the optimal solutions to interpret the observations.
 The uncertainties, (rg), associated with the snow-free mean background albedo values mainly mirror those from LAI and the retrieved values remain close to the prior under high LAI conditions for reasons discussed earlier in this section. Figure 10 illustrates the relationships between the one-sigma PDF in background albedo and the mean effective LAI in the visible (Figure 10, top) and near-infrared (Figure 10, bottom) domains. This relationship is indeed largely modulated by LAI values, especially when reaching the saturation domain, i.e., close to semi-infinite canopy conditions, where the uncertainties are analogous to their prior values. The strong nonlinearity of the radiation transfer processes in some regions of the space parameters also translates into uncertainty values that may exceed those specified in the priors. As discussed in detail by Lavergne et al. , section 3.1, these unusual cases are caused by a slightly negative curvature in the term representing the contribution from the deviations to the observations to the cost function (first term on the right-hand side of equation (1)).
 While the (rg) values are rather small with bright background conditions, they increase notably when low-density canopies overlying dark backgrounds are analyzed. One can notice that the occurrence of snow (blue points) leads to rather uncertain estimates of the visible background albedo in the case of intermediate LAI conditions over medium bright snowy backgrounds. This region of the parameter space is indeed poorly constrained by the prior information. By contrast, stronger constraints on the background snow brightness in the near-infrared domain lead to more accurate estimates of that parameter (see Figure 10, bottom).
 One can finally notice a few occurrences of high LAI values under snow conditions also associated with high cost function values. The rise in the cost function is caused by extremely large (between 0.95 and 1.0) single scattering albedo values in both the visible and near-infrared domains that cannot be related to snow-free vegetation properties. These unrealistic but rare situations are probably induced by the presence of unscreened clouds that the two-stream model attempts to interpret in terms of surface properties; the inversion procedure thus returns parameter values corresponding to a dense layer (LAI is forced to take large values for masking the effect of the background darkening effect) composed of highly scattering elements in order to fit the observations. Similar situations may also occur due to the assignment of false prior background values, e.g., snow-free versus snowy conditions, that forces the two-stream model to adopt unrealistic scenarios to interpret the observations as highlighted by Pinty et al. [2008, section 3.1 and Figure 3]. Although these observations are not properly interpreted, the inversion returns values that can be used further to flag these conditions and eventually improve the albedo and snow flag products.
4.3. Vegetation Scattering Properties
Figure 11 provides an example of the ωl maps generated over the Americas in the visible (Figure 11, top) and near-infrared (Figure 11, bottom) spectral domains, for the 13–28 August (Figure 11, left) and 18 February to 5 March (Figure 11, right) 2005 16 day periods. The vegetation scattering properties (controlled by leaf greenness and occasionally the presence of woody material) can be resolved by the JRC-TIP under favorable conditions associated with high LAI values. The patterns and gradients thus follow from those in LAI discussed earlier. One can notice that mean of the PDF ωl values lower than the priors in both spectral domains dominate over the Amazon basin in South America as well as over boreal systems in the summer season that exhibit a range of values especially in the visible domain. Some of these patterns in ωl are, to some extent, related to vegetation phenological cycles that correlate with land use categories; the broadleaf forests and agricultural activities prevailing in United States in summer are associated with an increase in vegetation scattering properties in the near-infrared domain as would be the case with green and healthy leaves. The ωl parameter is, however, not accurately resolved by the inversion and values then remain very close to their priors over rather large regions, e.g., over North America in winter.
 The dependency of the accuracy in the ωl parameter retrievals with respect to LAI is illustrated in Figure 12. While low LAI conditions lead to high uncertainty in the single scattering albedo, the occurrence of high LAI values significantly decreases the retrieval uncertainties by a factor of two to three with respect to the priors. The most uncertain situations, i.e., enhanced widening of the PDFs, happen with intermediate LAI conditions where the background brightness also contributes significantly to the observations. Such conditions are especially noted in the presence of relatively dark backgrounds below the vegetation canopy.
 The spectral distribution of the ωl (VIS), ωl (NIR) values reveals the presence of high-density sectors in the spectral space as exhibited in Figure 13, generated from the values retrieved over the globe for the 13–28 August 2005 16 day period. On can indeed discern a sector coupling ωl (VIS) values in the [0.10–0.18] range with largely stable ωl (NIR) values in the [0.68–0.72] range and another sector where the ωl (VIS) values are restricted in the [0.15–0.20] range but paired with relatively large ωl (NIR) values in the [0.70–0.78] range. Explaining the occurrence of regions exhibiting, in the spectral space, a higher probability of finding solutions, i.e., correlations between the two spectral domains, requires further investigation. It is, however, noticeable that the majority of single scattering albedo spectral values do not correspond to those of typical green leaves and appear to be biased high in the visible and low in the near-infrared domain with respect to such typical leaf state. The relative increase in the visible regions where single scattering regime dominates due to strong chlorophyll absorption can be straightforwardly explained by the presence of less absorbing material such as stems and trunks or leaves that are less green than anticipated. The latter components generally induce a reduction in the multiple scattering efficiency of the canopy elements. In addition, Pinty et al. [2008, section 3.3.3] demonstrated that, in the case of structurally heterogeneous scenario, the reduction in ωl (NIR) is required to correctly balance the absorption process due to multiple scattering in the actual vegetation layer when represented by a 1-D model.
 The use of effective parameters to express the properties of vegetation systems of arbitrary complexity (due to the spatially unresolved spectral and structural heterogeneities prevailing inside the domain observed by individual remote sensing measurements) guarantees the accurate simulations of the scattered, transmitted and absorbed fluxes in the vegetation and background layers at the scales and resolutions appropriate for climate models. The retrieval of these effective parameter values constitutes a necessary step toward the generation of the radiation fluxes discussed in a companion paper [Pinty et al., 2011a].
 The effective vegetation parameter values discussed here are specific to the two-stream version of the model implemented in the TIP and can be validated or compared only indirectly against in situ measurements. Indeed, they all relate to radiation fluxes which can themselves be, in principle, measured by ground-based devices. For instance, the spectrally invariant effective LAI expresses the capability of the vegetation layer to intercept the direct radiation (it thus encapsulates the interception probability due to any element composing the vegetation canopy) and results from a simple logarithmic transformation of the direct transmission reaching the background. This transmitted fraction of the direct incoming irradiance at the top of the vegetation layer can be measured by an upward looking radiometer placed on the background under the canopy layer. One advantage of this biome-independent definition is that it corresponds to the default methodology applied to interpret data from instruments commonly used for estimating LAI such as the LAI-2000 plant canopy analyzer [Breda, 2003; Morisette et al., 2006]. In fact, these instruments actually retrieve an effective LAI from an analysis of the transmission of direct radiation through the canopy gaps, assuming random distribution of scatterers with no distinction between the foliage and other elements composing the canopy [Stenberg et al., 1994]. Preliminary comparisons of retrieved effective LAI with ground-based estimations yielded quite satisfactory agreement over four different sites exhibiting limited structural complexity [Pinty et al., 2007, Figures 13 and 14].
 The retrieved values of the effective LAI are associated with somewhat large uncertainties. The latter are inherent to the radiation transfer processes represented accurately by the two-stream model, but also to the uncertainties prescribed on the input surface albedo data sets and specified in the prior PDFs of the model parameters. One approach to limit the uncertainties on the effective LAI with the same observations and prior set of information consists in adding constraints as a function of time using a simple but generic time-dependent model to represent the dominant phenological patterns (e.g., P. G. Lewis et al., An Earth Observation Land Data Assimilation System (EO-LDAS), submitted to Remote Sensing of Environment, 2011). The benefits from adopting such an approach will be explored in the near future.
 The effective single scattering albedo is related to the radiation scattered upward and downward by the vegetation canopy layer and can thus be inferred from diffuse transmission as discussed by Pinty et al. [2004a, section 3.3.2]. Accordingly, one can validate model parameter values indirectly through the measurable radiation fluxes generated by this model from the retrieved parameter values. It is however worth noting that the background reflectance is directly estimated rather than as an effective quantity when using the two-stream model in inverse mode and, consequently, this two-stream model parameter can actually be estimated from in situ measurements to further assess the quality of the retrieved model parameter values.
 The retrieval of effective vegetation parameters, in particular due to three-dimensional vegetation structure, contrasts with the estimate of true values of the background albedo. The latter are considered as true with respect to the role of this lower boundary condition in the two-stream model. This offers the possibility to validate directly this information using in situ albedometer measurements to sample at best the spatial variability of the background conditions. The retrieval of accurate background albedo values may prove of value and relevance for regional climate studies, in particular those addressing the importance of soil moisture and snow cover at high latitudes [e.g., Knorr et al., 2001; Jin et al., 2002; Pitman, 2003; Rechid et al., 2009; Pongratz et al., 2009; Fletcher et al., 2009; Loew and Govaerts, 2010]. The relative darkening and brightening processes of land surfaces associated with the presence of water in the soil and the occurrence of snow, respectively, are indeed well resolved by the TIP thanks to the strong signatures of such events in the near-infrared domain.
 Land surface systems exhibit considerable spatial variability at subpixel scale that translates into large uncertainties in ground-based estimates at 1 km pixel resolution, especially over biomes characterized by the presence of significant clumping and vertical structures. It is also noteworthy to recall that the two-stream model implements a plane-parallel approach and that the input albedo products have no explicit correction for topography effects for instance, and the local-scale impact on the derived products remain to be established. Although the estimate of pixel-averaged quantities is rather challenging from local scale in situ measurements [Chen and Cihlar, 1995], the differences between effective and true parameter values mainly concern the magnitude of the values by contrast to their phase or temporal variations. For instance, the retrieved fields in effective LAI values must reflect the temporal changes that are expected to occur due to vegetation phenological cycles. Similarly, the spatial gradients depicted by these effective values must, as shown here, follow the well-known patterns related to different biomes.
 Through a series of examples, the present paper illustrates the definite benefits in adopting inversion techniques based on optimal control theory for the interpretation of advanced remote sensing products such as surface albedos. These benefits include the generation of physically consistent information about the density and absorbing properties of the vegetation layer together with the brightness of the background underneath. The basic setup of the inversion procedure accounts for the relative roles of the uncertainties associated with the products, the radiation transfer processes implemented in a model able to simulate these products and some prior knowledge about the model parameters. The integration of these elements in a well-defined mathematical framework that ensures the internal physical consistency between the input products and their associated uncertainties and the solutions, derived in the space of model parameters, approximated by a multidimensional Gaussian PDF.
 The results presented in this paper exploit year 2005 MODIS Collection 5 white sky surface albedo products available at 1 km spatial and 16 day temporal resolutions. The current analysis acknowledges the role of the effective LAI as the main variable driving the radiation transfer processes to exploit surface albedo products. Our analysis confirms that the JRC-TIP delivers optimized two-stream model process parameters that are capable of simulating the observed albedo values, i.e., under snow-free and snowy conditions, well within the uncertainty ranges of the visible and near-infrared products. The small number of cases where the remote sensing products cannot be reliably interpreted by the JRC-TIP procedure are flagged as nonphysically valid (or dubious), and these cases are so infrequent (less than 0.5% of all pixels processed) that a backup algorithm is unnecessary.
 The mean values of the derived effective LAI follow geographical patterns related to the dominant vegetation type and phenological cycles. Given that the specified priors are not space dependent, these patterns thus result directly from the input products, i.e., the remote sensing albedos. The estimated uncertainties on LAI are strongly correlated with the LAI itself and to a lesser extent to the brightness of the underlying background. Background spectral albedo products that are physically consistent with the effective LAI and observed albedos can be generated which, to our knowledge, represents new and original information. This information should prove valuable for a series of applications, especially those where snow related events play an important role. The uncertainties associated with these spectral products strongly depend on the effective LAI and the background brightness itself, green canopies with low LAIs over a bright background being a rather favorable situation.
 The dominant role of the effective LAI, which acts as an optical thickness with respect to the radiation transfer processes controlling the observed albedos, justifies the use of loose, space and time invariant priors for this quantity when exploiting global-scale products. The transition from effective to true values is possible only if additional information, notably about the (unresolved) vegetation structure is available for each 1 km processed pixel, e.g., leaf clumping, subpixel horizontal heterogeneities [see, e.g., Chen et al., 1997, 2005]. This constitutes a somewhat challenging task given the complex and strong dependency of domain-averaged LAI with respect to local canopy properties in spatially heterogeneous systems. This step, that implies prescribing space- and time-dependent priors, must thus be achieved with great care and its impact on the uncertainty of the final true LAI product also requires propagating the uncertainties associated with this additional prior knowledge.
 The JRC-TIP also delivers information on the scattering/absorption efficiency of the elements composing the vegetation canopy. This is done using the concept of spectral single scattering albedo that is in fine, strongly related to the ‘color’ of the scattering elements. This new information is retrieved rather accurately for dense canopies and exhibits discernible spectral correlations. Finally, The PDFs of the model parameters Xpost discussed in the present paper can be used in forward simulations of the two-stream model to generate radiation fluxes that are absorbed in the vegetation layer and the background underneath, transmitted through the vegetation layer and finally scattered at the top of the vegetation canopy. Results from this step are discussed in a companion paper [Pinty et al., 2011a].
 This research was performed jointly in the Global Environment Monitoring unit of the Institute for Environment and Sustainability at the Joint Research Centre, an institution of the European Commission and at the Earth Observation Directorate of the European Space Agency. Bernard Pinty acknowledges the support of the Science, Applications and Future Technologies Department of the European Space Agency. The MODIS products were obtained from the National Snow and Ice Data Center and the NASA Land Processes Distributed Active Archive Centers. The maps shown in this paper use color tables kindly made available at http://colorbrewer2.org/by Cynthia Brewer, Pennsylvania State University. The output generated by the JRC-TIP from the 2005 MODIS white sky surface albedos is available upon request to the first author.