RELATING MERIS FAPAR PRODUCTS TO RADIATION TRANSFER SCHEMES USED IN CLIMATE/NUMERICAL WEATHER PREDICTION AND CARBON MODELS

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1 RELATING MERIS FAPAR PRODUCTS TO RADIATION TRANSFER SCHEMES USED IN CLIMATE/NUMERICAL WEATHER PREDICTION AND CARBON MODELS Bernard Pinty 1, T. Lavergne 1, T. Kaminski 2, O. Aussedat 1, N. Gobron 1, and M. Taberner 1 1 European Commission, DG Joint Research Centre, Institute for Environment and Sustainability, Global Environment Monitoring Unit, TP 440, via E. Fermi, I Ispra (VA), Italy. 2 FastOpt, Schanzenstrasse 36, D Hamburg, Germany ABSTRACT The main goal of this study is to contribute bridging the gap between available remote sensing products and large-scale models. We present here results from the application of an inversion method designed to assimilate various remote sensing surface flux products, e.g. albedos from Terra and FAPAR from ENVISAT, into a a state of the art plane-parallel (2-stream) radiation transfer scheme. This method implements the adjoint and Hessian codes, generated using automatic differentiation techniques, of a cost function accounting for 1) the deviation from the prior knowledge on the model parameter values and, 2) the misfit between the remote sensing products and the 2-stream model calculations. Uncertainties associated with the products, models and priors are specified via relevant prior covariance matrices. The inversion method provides an estimate of the posterior covariance matrix on the model parameters which is further exploited to evaluate, in turn, the posterior probability density functions of the radiant fluxes simulated by the two stream model, including those that are not measured, e.g. the fraction of radiation absorbed in the ground. Applications presented here are performed using the operational MERIS FAPAR and MODIS-MISR broadband surface albedo products. Key words: 2-stream model; FAPAR; Adjoint and Hessian codes. 1. INTRODUCTION The accurate knowledge of the land processes controlling distribution and partition of solar radiant flux between the vegetation and the underneath soil layer is required to improve simulations of the soil-vegetation-atmosphere exchanges at various space and time scales of interest for climate, numerical weather prediction as well as carbon cycle models (e.g. Pitman, 2003). Global multi-annual time series of some of these radiant fluxes, such as broadband surface albedos and the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) have become available from various institutions. In the mean time, efforts have been made to improve the performance (notably with respect to their accuracy, capability, and software implementation as well) of the plane-parallel, so called 2-stream, radiation transfer schemes currently implemented in host models (e.g. Pinty et al., 2006a). This class of model is able to simulate accurately, that is within a few percent, the domain-averaged scattered, transmitted and absorbed fluxes related to most geophysical systems, irrespective of their intrinsic internal variability in the 3- D space, provided that effective instead of true model parameters are adopted. In the case of the Leaf Area Index (LAI), for instance, the effective value is associated with the interception of the direct radiation and is thus related to the direct transmission via the classical exponential decay as would occur in a turbid plane-parallel medium. In order to benefit from the available land flux measurements derived from remote sensing, it is first necessary to retrieve these effective values of the 2-stream model parameters. This step is mandatory for ensuring the physical consistency between the measured fluxes and the dimensionality of the model used to estimate the model parameters, i.e., the same class of model have to be used in inverse (to exploit remote sensing data) and forward (to simulate fluxes) mode. Pinty et al. (2007) have devised and documented the performance of such a retrieval procedure on the basis of a set of applications conducted over mid-latitude sites as well as using model-based series of inversion (Lavergne et al., 2006). This procedure delivers a Gaussian approximation of the Probability Density Functions (PDFs) of the retrieved model parameter values together with a posterior covariance matrix. This information enables us to estimate the radiant fluxes simulated by the 2-stream model, including those that are not part of the measurement set, e.g. the fraction of radiation absorbed in the ground. This contribution illustrates the potential of this inversion package in the complex case of tall spatially heterogeneous (3-D) forest canopies subject to significant changes in their background properties as due, for instance, to the occurrence of snow in the Winter and Spring seasons. Proc. Envisat Symposium 2007, Montreux, Switzerland April 2007 (ESA SP-636, July 2007)

2 2. OUTLINE OF THE INVERSION METHODOL- OGY Our formulation of the inverse problem follows Tarantola (1987) and Enting et al. (1995). It is such that the solutions are combining all the available information, i.e., prior knowledge on the PDFs of the model parameters X with mean values X prior and a covariance matrix C Xprior, the measurements d, and the constraint provided by the 2-steam model M(X). The posterior probability distribution P (X) can be approximated by a Gaussian PDF with mean value and covariance matrix denoted X post and C Xpost, respectively (where T represents the transpose operator and C 1 the inverse matrix of C): [ P (X) exp 1 ] 2 (X X post) T C 1 X post (X X post ) (1) X post represents the mean of P (X) and minimises the cost function J(X) expressed as follows : Table 1. Mean values X prior and associated standard deviations σ Xprior used to set the diagonal of the prior covariance matrix C Xprior. λ 1 and λ 2 correspond to the broadband visible and near-infrared spectral domains, respectively. ω l (λ 1,2 ), d l (λ 1,2 ) and r g (λ 1,2 ) refer to the single scattering albedo, asymmetry factor and background albedo, respectively. Variable X prior σ Xprior LAI ω l (λ 1 ) d l (λ 1 ) r g (λ 1 ) and and ω l (λ 2 ) d l (λ 2 ) r g (λ 2 ) and and (2) Values adopted for the bare soil (snow) case with a correlation factor of (0.8670) set in C Xprior. + [( M(X) d ) T C 1 ( ) M(X) d J(X) = 1 d 2 ( ) T ( )] X X prior C 1 X prior X X prior The posterior uncertainties on the model parameters are estimated from an analysis of the curvature of J(X), and the covariance matrix C Xpost is further exploited to estimate the PDFs of the radiant flux quantities that the model M(X), (the two-stream model in present application) is able to simulate. For all practical purposes, the compiler tool Transformation of Algorithms in C++ (TAC++) (Giering and Kaminski, 1998) available from FastOpt ( has been used to generate the adjoint, tangent linear and Hessian codes of the cost function J(X). 3. INVERSION SET-UP (2) Table 1 indicates the mean values X prior and associated standard deviations σ Xprior used to set the diagonal of the prior covariance matrix C Xprior at wavelengths λ 1 and λ 2 corresponding to the broadband visible and nearinfrared spectral domains, respectively. The retrievals discussed in this paper relate to the contribution from the green elements of the canopy, as can be noticed from the prior values specified on the single scattering albedo values, i.e., very small uncertainty values associated with the mean of the PDFs. Note that some level of correlation (given as footnotes of table 1) is imposed on the uncertainties of the background albedos, including the case of snow as well. The inversion procedure is operated by switching the set of priors on the background albedos from bare soil to snow-like conditions whenever a snow event occurs. These events are detected using the 8-day composite MODIS snow product, identified as MOD10A2 (version 4). In the context of the present application, we selected time series of remote sensing surface albedo products estimated during year 2005 over one of the BOREAS sites located in Canada identified as NSA-OBS ( N; W). The dominant vegetation type at this particular location corresponds to an evergreen needle forest mainly composed of black spruce trees (see for instance These albedo products that are used here are the visible and near-infrared broadband 16-day composite MODIS (products associated with high QA values only were considered) and daily MISR (following the procedure described in Pinty et al. (2004)) white sky albedos or Bi- Hemispherical Reflectances (BHRs). All retrievals discussed here are based on the specification, in the covariance matrix C d, of an uncertainty of 5% (relative) of the albedo products and no correlation among uncertainties is assumed. 4. RESULTS The variability observed in the MODIS and MISR BHR values over the selected site (see left panel in Figure 1) is dominated by the occurrence of snow events at the end and beginning of the year. These events are marked by triangles on the top axis of the figure. Under most of such conditions and as expected, the BHR values in the visible domain increase dramatically and reach a higher level than those estimated in the near-infrared domain. The

3 good agreement between both MODIS and MISR derived product data sets is noticeable given the large variations depicted by the surface albedos, although some slight differences exist (see for instance Pinty et al. (2006b)). The FAPAR values estimated from the posterior modelparameter values are shown (open circles) in the right panel of Figure 1, together with their associated uncertainties inferred from the posterior covariance matrix (vertical lines). This figure reveals that 1) time-series in the retrieved FAPAR exhibit smooth variability as can be expected from the dominant vegetation type and cover and, consequently it shows that our inversion procedure is able to properly account for drastic changes in the measurement sets, i.e., the surface albedos, due to snow occurrence, 2) the amplitude in the seasonal trend over the evergreen needleaf site is quite limited and the FA- PAR values (considering green material only) remain within approximately 0.10 and, 3) the FAPAR values retrieved from the MODIS and MISR albedos are in remarkable agreement with those delivered by the MERIS (violet crosses) operational processor (Gobron et al., 1999, 2007) as well as those generated from Sea- WiFS (green crosses) using the JRC-FAPAR algorithm (Gobron et al., 2006), 4) the FAPAR values generated by the operational MODIS (red crosses) (Myneni et al., 2002) processor exhibit a rather large and probably unrealistic intra-annual variability with 8-day composite values ranging from about 0.1 to 0.9, and finally 5) the values delivered by MISR (blue crosses) (Knyazikhin et al., 1998) operational processor do not exibit any significant bias as is the case for MODIS but, in some instances, they show a large temporal variability and suddenly raise to high values, e.g. in the Spring time season. The performance of our inversion procedure to account properly from the temporal changes in the radiative properties of the forest background while maintaining smooth or no variation in LAI can be evaluated on Figure 2. The background albedo values (left panel) are capturing most of the variations observed in the surface albedo at the top of the canopy but with a larger spectral contrast under occurrence of snow, i.e., the visible values get much larger than those retrieved in the broadband near-infrared domain. By contrast, in absence of snow, the leaf absorption (scattering) process in the visible (near-infrared) domain yields a much more limited, and even reversed, spectrally contrasted situation. These results have to be evaluated together with the retrieved LAI and associated uncertainties (right panel) which, as pointed out before with the FAPAR product, shows a very smooth temporal profile. This ensemble of results illustrates our current ability to separate the radiation transfer processes controlling the relative contribution due to the vegetation layer from its background. 5. CONCLUSION We have shown that our inversion procedure is able to reconcile remote sensing flux products from different sources, i.e., surface albedos from MODIS and MISR with the MERIS FAPAR product in this application. Such a level of consistency between these fluxes is promising for future applications and promotes the design of integrated systems capable of assimilating a variety of sources of information. A first step in this direction has been already taken and discussed in Pinty et al. (2007) where both surface albedos from MODIS-MISR and FA- PAR products from SeaWiFS are used jointly to reduce the uncertainties on the retrieved 2-stream model parameters and notably on the LAI. Here we have shown that, in addition, the availability of a snow indicator, is beneficial to the analysis of products generated under Winter and early Spring seasons, especially at high latitudes. It is worthwhile emphasizing that our inversion package fullfils the stringent requirements imposed by operational processing such as, reliability, robustness and computer efficiency. ACKNOWLEDGMENTS The authors gratefully acknowledge the contribution from M. Robustelli and F. Mélin. The authors would like to thank all the providers of the remote sensing datasets needed to perform this research. The MERIS products are available at from the European Space Agency (ESA). The MISR products were obtained from the NASA Langley Research Center Atmospheric Sciences Data Center. The MODIS data used in this study were acquired as part of the NASA s Earth- Sun System Division and archived and distributed by the Goddard Earth Sciences (GES) Data and Information Services Center (DISC) Distributed Active Archive Center (DAAC) and the National Snow and Ice Data Center and the NASA Land Processes DAACs. The authors are grateful to the SeaWiFS Project (Code 970.2) and the Distributed Active Archive Center (Code 902) at the Goddard Space Flight Center, Greenbelt, MD 20771, for the production and distribution of the SeaWiFS data, respectively. The authors are also grateful to Brockman Consult (Geesthacht, Germany), ACRI (Sophia Antipolis, France) and ESA. This research has been suppported by the Global Environment Monitoring unit of the Institute for Environment and Sustainability at the DG Joint Research Centre, an institution of the European Commission. REFERENCES Enting, I. G., Trudinger, C. M., and Francey, R. J. (1995). A synthesis inversion of the concentration and δ 13 C of atmospheric CO 2. Tellus, Serie B, 47: Giering, R. and Kaminski, T. (1998). Recipes for adjoint code construction. ACM Transactions on Mathematical Software, 24: Gobron, N., Pinty, B., Aussedat, O., Chen, J. M., Cohen, W. B., Fensholt, R., Gond, V., Huemmrich, K. F., Lavergne, T., Mélin, F., Privette, J. L., Sandholt, I.,

4 VIS (MODIS, MISR) NIR VIS (MODIS, MISR) Input Broadband White-Sky Albedo Fraction Absorbed in Vegetation [VIS] Figure 1. Left panel: time series of the surface albedo products over NSA-OBS. MODIS (MISR) derived values are featured in red (blue) color. Products estimated in the broadband visible (near-infrared) domain are depicted with full circles (squares). Triangles on the top axis mark snow events. Right panel: time series of the fraction of absorbed radiation in vegetation by green material only in the visible domain. The red, blue, green and violet crosses are for the MODIS 8-day composite, the daily MISR, the daily JRC-SeaWiFS and MERIS operational products, respectively. The open circles identify the values retrieved by our inversion procedure using MODIS (red color) and MISR (blue color) broadband white sky albedos. The standard deviations associated with the PDF of the retrieved values are reported with vertical bars. VIS (MODIS, MISR) NIR 7.00 LAI (MODIS, MISR) Ground Albedo Effective LAI Figure 2. Left panel: time series of the retrieved background surface albedo values over NSA-OBS. MODIS (MISR) derived values are featured in red (blue) color. Products estimated in the broadband visible (near-infrared) domain are depicted with full circles (squares). Right panel: time series of the effective LAI due to the green elements of the vegetation canopy. The standard deviations associated with the PDF of the retrieved values are reported with vertical bars. Triangles on the top axis mark snow events.

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