Consistent assimilation of MERIS FAPAR and atmospheric CO 2 into a terrestrial vegetation model and interactive mission benefit analysis

Consistent assimilation of MERIS FAPAR and atmospheric CO2 into a terrestrial vegetation model and interactive mission benefit analysis T. Kaminski1, W. Knorr2,3,4, M. Scholze2,5, N. Gobron6, B. Pinty6, R. Giering1, and P.-P. Mathieu7 1FastOpt, Lerchenstraße 28a, 22767 Hamburg, Germany 2Dep. of Earth Sciences, University of Bristol, Bristol, BS8 1RJ, UK 3Dep. of Meteorology and Climatology, Aristotle University of Thessaloniki, Greece 4Dep. of Earth and Ecosystem Sciences, Sölvegatan 12, 223 62 Lund, Sweden 5University of Hamburg, Grindelberg 5, 20144 Hamburg, Germany 6European Commission, DG Joint Research Centre, Inst. for Environment and Sustainability, Global Environment Monitoring Unit, TP 272, via E. Fermi, 21020 Ispra (VA), Italy 7European Space Agency, Earth Observation Science & Applications, Via Galileo Galilei, Casella Postale 64, 00044 Frascati (Rm), Italy

tions provides parameter estimates and uncertainty ranges that are consistent with the observational information.In a subsequent step these parameter uncertainties are propagated through the model to uncertainty ranges for predicted carbon fluxes.
We demonstrate the consistent assimilation at global scale, where the global MERIS FAPAR product and atmospheric CO 2 are used simultaneously.The assimilation improves the match to independent observations.We quantify how MERIS data improve the accuracy of the current and future (net and gross) carbon flux estimates (within and beyond the assimilation period).
We further demonstrate the use of an interactive mission benefit analysis tool built around CCDAS to support the design of future space missions.We find that, for long-term averages, the benefit of FAPAR data is most pronounced for hydrological quantities, and moderate for quantities related to carbon fluxes from ecosystems.The benefit for hydrological quantities is highest for semi-arid tropical or sub-tropical regions.Length of mission or sensor resolution is of minor importance.

Introduction
The terrestrial biosphere is a significant sink for atmospheric CO 2 and thus plays a key role in the radiative budget of the global climate system (Denman et al., 2007).Prognostic terrestrial vegetation models are used to simulate the strength and distribution of this sink and its response to climate change.These prognostic models solve the equations governing the evolution of the carbon, water, and energy balance.In their formulation, these equations rely on a set of constants, which we call process parameters.There is uncertainty in both the correct formulation of the equations and then the correct values of the process parameters.This uncertainty yields significant uncertainties in the simulated terrestrial carbon sinks on decadal and longer time scales (Denman et al., 2007).On shorter time scales parameter, uncertainty is reflected in large uncertainties in the hydrological cycle on all spatial scales.
The use of observational information is required to reduce this uncertainty.Systematic model calibration through inversion procedures can infer parameter ranges that are consistent with the observations and exclude parameter ranges that are inconsistent with observations (Tarantola, 1987).Remaining inconsistencies can be attributed to weaknesses in the formulation of the model equations or errors in the observational data.For such calibration procedures it is desirable to use multiple data streams and sample at multiple locations and points in time.To assure consistency, it is then essential to impose all observational constraints simultaneously, an approach we call consistent assimilation.In a non-linear model, any step-wise inclusion of the observational information typically yields a suboptimal estimate of final parameter values, i.e. consistency with the observational information used in early steps is not assured.
The first mathematically rigorous calibration of a prognostic terrestrial biosphere model was performed within the Carbon Cycle Data Assimilation System (CCDAS, http: //CCDAS.org)built around the Biosphere Energy Transfer HYdrology scheme (BETHY, Knorr, 2000;Knorr and Heimann, 2001).CCDAS estimates the values of BETHY's process parameters including their uncertainty ranges and maps them onto simulated carbon and water fluxes.The system was first used with 20 yr of atmospheric carbon dioxide observations provided by the GLOBALVIEW flask sampling network (GLOBALVIEW-CO 2 , 2008).The system evaluated the effect of this observational constraint on the net and gross fluxes of CO 2 over the assimilation period (Rayner et al., 2005), and also on their predictions from years (Scholze et al., 2007) to decades (Rayner et al., 2011).
The above studies showed that the flask sampling data can only constrain part of BETHY's parameter space.Fortunately there is an ever-increasing set of observational constraints on the terrestrial biosphere becoming available.One of the requirements for assimilation of a given data stream is the capability to simulate (by a so-called observation op-erator) its counterpart in the model.For the assimilation of atmospheric carbon dioxide, the role of the observation operator was taken by an atmospheric transport model (TM2, Heimann, 1995) that was coupled to BETHY.
A further observational constraint on the terrestrial biosphere is provided by "fraction of absorbed photosynthetically active radiation" (FAPAR) (Gobron et al., 2008) products.FAPAR is an indicator of healthy vegetation, which exhibits a strong contrast in reflectance between the visible and the near-infrared domains of the solar spectrum (Verstraete et al., 1996).FAPAR products can thus be derived from observations provided by space-borne instruments, e.g. by ESA's Medium Resolution Imaging Spectrometer (MERIS).The extensions of CCDAS for assimilation of FAPAR are detailed by Knorr et al. (2010), who also demonstrate the consistent assimilation of FAPAR at multiple sites.These extensions include modules for simulation of hydrology and leaf phenology and, as observational operator, a two flux scheme of the radiative balance within the canopy.
Here we report on the first consistent assimilation of flask samples of atmospheric CO 2 and FAPAR at global scale, i.e. the simultaneous assimilation of both data streams.To limit the computation time in development, testing, and debugging, this challenging exploration of uncharted territory was conducted in BETHY's fast, coarse spatial resolution.
A further application of advanced assimilation systems that can propagate uncertainties from the observations to target quantities of interest is quantitative network design (QND).QND is particularly appealing because it can evaluate the benefit of hypothetical data streams based on their assumed uncertainty.Kaminski and Rayner (2008) describe the methodological framework and present a set of examples related to the global carbon cycle.Within CCDAS, the QND concept was applied to support the design of an active LIDAR mission sampling atmospheric CO 2 from space (Kaminski et al., 2010).For FAPAR assimilation at sitescale, the concept was applied to evaluate the effect of modifications of sensor characteristics on uncertainties in current and future carbon fluxes (Knorr et al., 2008).In this paper we describe the development of an interactive mission benefit analysis (MBA) software tool based on the global version of CCDAS.The MBA tool quantifies the benefit of space missions in terms of their constraint on various carbon and water fluxes, and we demonstrate the effect of design aspects such as mission length and sensor resolution.
The remainder of the paper is organised as follows.Section 2 describes first CCDAS (Sect.2.1) and then the MBA tool (Sect.2.2).The observational data are presented in Sect.3. Next, Sect. 4 describes the consistent globalscale assimilation of MERIS FAPAR and atmospheric CO 2 (Sect.3.2), and Sect. 5 presents our simulations for mission design.Finally, we draw conclusions and give perspectives in Sect.6.
In brief, BETHY, simulates carbon uptake and plant and soil respiration embedded within a full energy and water balance and phenology scheme (Knorr, 2000).The model is fully prognostic and is thus able to predict the future evolution of the terrestrial carbon cycle under a prescribed climate scenario.The process formulation distinguishes 13 plant functional types (PFTs) based on the classification by Wilson and Henderson-Sellers (1985).Each model grid cell can be populated by up to three different PFTs.Driving data (precipitation, minimum and maximum temperatures, and incoming solar radiation) were derived from a combination of available monthly gridded and daily station data (R.Schnur, personal communication, 2008) using a method by Nijssen et al. (2001).
As mentioned above, assimilation of atmospheric CO 2 requires, as an observation operator, an atmospheric transport model (TM2, Heimann, 1995) coupled to BETHY.CO 2 fluxes from processes not represented in BETHY, i.e. fossil fuel emissions, exchange fluxes with the ocean and emissions from land use change, were prescribed as in Scholze et al. (2007).The observation operator for FAPAR calculates the vertical integral of the absorbed photosynthetically active radiation (PAR) by healthy green leaves between the canopy top and the canopy bottom, divided by the incoming radiation.FAPAR thus equals the net PAR flux entering the canopy at the top (incoming minus outgoing) minus the net PAR flux leaving the canopy at the bottom (outgoing minus incoming, i.e. reflected from soil background), divided by the incoming PAR flux at the top of the canopy.The PAR flux is calculated by a two-flux scheme (Sellers, 1985), which takes into account soil reflectance, solar angle and incoming amount of diffuse radiation.
Equating satellite and model FAPAR means that, given the same illumination conditions, the same number of photons enter the photosynthetic mechanism of the vegetation, even if some of the assumptions differ between BETHY and the model used to derive FAPAR (Gobron et al., 2000).It also means that FAPAR in the model is defined based on the assumption that the canopy consists only of photosynthesising plant parts (Pinty et al., 2009), which is consistent with the definition used for deriving the MERIS FAPAR product.The resultant LAI is one that ensures measured and modelled absorbed PAR are consistent.BETHY also assumes that the conductance of the leave pores, or "stomata", for both CO 2 and water vapour adapts to the available PAR across the canopy.This means that shaded sections of the canopy do not only absorb less PAR, they also have a lower leaf conductance.This assumption is well supported by the fact both whole-canopy conductance and FAPAR show a similar saturating behaviour for increasing leaf area index (Schulze et al., 2001).We therefore assume that adjusting the leaf area index to match measured FAPAR will also improve the consistency between modelled and actual canopy conductance to water vapour.
Assimilation of FAPAR required the extension of CCDAS by components included in BETHY for simulating hydrology and leaf phenology.In the previous CCDAS setup, these components were used in a preliminary assimilation step that provided input to CCDAS.This extension was necessary to allow consistent assimilation of FAPAR and atmospheric CO 2 .
CCDAS implements a probabilistic inversion concept (see Tarantola, 1987) that describes the state of information on a specific physical quantity by a probability density function (PDF).The prior information on the process parameters is quantified by a PDF in parameter space and the observational information by a PDF in the space of observations.Their respective means are denoted by x 0 and d and their respective covariance matrices by C 0 and C d , where C d accounts for uncertainties in the observations as well as uncertainties from errors in simulating their counterpart (model error).If the prior and observational PDFs were Gaussian and the model linear, the posterior PDF would be Gaussian, too, and completely characterised by its mean x post and covariance matrix C post .Further, x post would be the minimum of the following cost function: where M(x) denotes the model operated as a mapping of the parameters onto simulated counterparts of the observations.Further, C post would be given by: where J (x post ) denotes the Hessian matrix of J , i.e. the matrix composed of its second partial derivatives ∂ 2 J ∂x i ∂x j .Our model is non-linear, and we approximate the posterior PDF by a Gaussian with x post as the minimum of Eq. ( 1) and C post from Eq. ( 2).The inverse step is followed by a second step, the estimation of a diagnostic or prognostic target quantity y.The corresponding PDF is approximated by a Gaussian with mean y = N (x post ) (3) and covariance where N (x) is the model operated as a mapping of the parameters onto the target quantity.In other words, the model www.biogeosciences.net/9/3173/2012/Biogeosciences, 9, 3173-3184, 2012 is expressed as a function of the vector of its parameters x and returns a vector of quantities of interest, for example the uptake of carbon integrated over a region and time interval.The linearisation (derivative) of N around x post is denoted by N (x post ) and also called Jacobian matrix.C y,mod denotes the uncertainty in the simulation of y resulting from errors in N.
If the model was perfect (a hypothetical case), C y,mod would be zero, and only the first term would contribute to C y .Conversely, if all parameters were known to perfect accuracy (an equally hypothetical case), C post would be zero and only the second term would contribute to C y .The minimisation of Eq. ( 1) and the propagation of uncertainties are implemented in a normalised parameter space with Gaussian priors.The normalisation is such that parameter values are specified in multiples of their standard deviation, i.e.C 0 is the identity matrix (for details see Kaminski et al., 1999;Rayner et al., 2005).In addition, for some bounded parameters a suitable variable transformation is included.Through comparison with a Monte Carlo approach, Ziehn et al. (2012) demonstrate that the Gaussian assumption is a good approximation for the posterior parameter PDF.
The authors of that study therefore recommend use of Gaussian prior PDFs in a gradient method, which was found to be greatly more efficient computationally.They used CCDAS with assimilation of CO 2 data similar to this study, but had to restrict the investigation to a subset of the full parameter space due to the very high computational costs of the Monte Carlo algorithm.
Technically, the minimisation of J is performed by a powerful iterative gradient algorithm, where, in each iteration, the gradient of J is used to define a new search direction.The gradient (plus J itself) are efficiently evaluated by a single run of the so-called adjoint code of J .The associated computational cost is independent of the number of parameters and is in the current case comparable to 3-4 evaluations of J .Likewise, J (x post ) is evaluated by a single run of the derivative code of the adjoint code (Hessian code).Here the associated computational cost grows roughly linearly with the number of parameters (more precisely an affine function of the number of parameters).In the present case of 71 parameters, the cost is comparable to about 60 evaluations of J .These numbers are only a rough indication of performance as they vary with platform, compiler, and even compiler flags.For performance numbers of the previous CCDAS implementation, we refer to Kaminski et al. (2003).All CC-DAS derivative code (adjoint, Hessian, Jacobian) is generated from the model code by the automatic differentiation tool Transformation of Algorithms in Fortran (TAF, Giering and Kaminski, 1998).The Hessian code is generated by reapplying TAF to the adjoint code.

Mission benefit analysis
Our mission benefit analysis is based on the Quantitative Network Design (QND) methodology presented by Kamin-ski and Rayner (2008).The approach exploits the fact that the uncertainty propagation from the observations to the parameters (via Eq. 2) and then further to the target quantities (Eq.4) can be performed independently from the parameter estimation.The requirements for the evaluation of J in Eq. ( 2) are the data uncertainty (C d ), the capability to simulate (expressed by M(x)) a counterpart of the data stream via an appropriate observational operator, and a reasonable parameter vector.We can then evaluate the benefit of hypothetical or planned observational data streams on the uncertainty reduction in relevant target quantities.
A QND system for mission benefit analysis (MBA tool) was built around the extended CCDAS framework for global scale assimilation described in Sect. 4. The tool can combine prior information, flask samples of atmospheric carbon dioxide, and global coverage FAPAR within a single cost function (see Fig. 1).For the tool, the sensitivity of each data item (each observation of FAPAR or atmospheric CO 2 ) with respect to the process parameters was precomputed and stored for a run of 14 yr.These sensitivities are the derivatives of M(x) (see Eq. 1), which are evaluated for the optimal parameter vector x determined by the assimilation run (see Sect. 4).To approximate the posterior parameter uncertainty (Eq.2) resulting from a user-defined data uncertainty (C d of Eq. 1) requires just matrix multiplications and a matrix inversion.In this inversion step, the user can choose the length of the mission.This will determine how many of the 14 yr of data for which sensitivities were precomputed are actually used in the assessment.Further, the user can choose to include or exclude the information from the atmospheric CO 2 observations.Evaluation of Eq. ( 4) yields posterior uncertainties for any target quantity that can be simulated by the model.The target quantities offered by the MBA tool are annual mean values of net ecosystem production (NEP), net primary production (NPP), evapotranspiration, and plant available soil moisture averaged over five years.Each of these quantities is available for six regions of the globe.The Jacobian matrix N (of Eq. 4) representing the derivative of the target quantities with respect to the model parameters was also precomputed and stored.For this step, just as for the previous step, the tool only requires matrix multiplications.
In summary, all steps to assess a mission configuration from the precomputed CCDAS output only involve matrix algebra.On a standard notebook these operations take only a few seconds, which enables the tool to run in interactive mode.The options for the configuration comprise the uncertainty in the FAPAR product, the length of the mission, and whether atmospheric CO 2 observations are included or excluded.Based on the same methodology, a similar tool (including a web interface, see http://imecc.ccdas.org)was set up for the design of networks composed of in situ measurements (direct measurements of the biosphere-atmosphere exchange flux as well as flask and continuous samples of the

MERIS FAPAR
We use FAPAR products derived from the Medium Resolution Imaging Spectrometer (MERIS) of the European Space Agency (ESA).We use the Level 3 product for the period June 2002 to September 2003.The data were processed at ESA's Grid Processing on Demand (GPoD, http://gpod.eo.esa.int) facility on a global 0.5 degree grid in the form of monthly composites and then interpolated to the model's coarse resolution 10 by 8 degree grid.
We use an uncorrelated data uncertainty of 0.1 for the definition of C d in Eq. (1) irrespective of how many observations where used in the spatial averaging of the FAPAR pixels (Gobron et al., 2008).

Atmospheric CO 2
We use monthly mean values of atmospheric CO 2 concentrations provided by the GLOBALVIEW flask sampling network (GLOBALVIEW-CO 2 , 2008).We use data for the period from 1999 to 2004 at two sites, Mauna Loa (MLO) and South Pole (SPO).We use the time series of residual standard deviations (RSD) from the compilation to assign a data uncertainty to the observations.We only use data from years when sufficient measurements are made to assign values without the gap-filling procedures in the GLOBALVIEW compilation.

Assimilation experiments
The consistent assimilation uses both data streams, the MERIS FAPAR product and the atmospheric CO 2 observations, as simultaneous constraints.Figure 1 displays the flow of information in the forward sense, i.e. from process parameters to the cost (or misfit) function.As mentioned, we use the computationally fast, 8 by 10 degree resolution with about 170 land grid cells.Our assimilation interval is the five year period from 1999 to 2004.
Several approaches to address the problem of bias in the FAPAR data product have been investigated.For the globalscale assimilation, we resolved to the following solution: we computed the average FAPAR over three years for each model grid cell and compared this value to the average observed value.We then multiplied the cover fraction of each PFT within the grid cell concerned by the ratio averaged observed FAPAR divided by average model FAPAR.If this ratio was above 1, which only occurred in very few grid cells, no correction was applied.
In order to investigate the occurrence of multiple minima, we started five minimisations of the cost function from different starting points, including the prior parameter value.Out of these five minimisations, four find the same minimum.The minimisation starting from the prior parameter value takes 153 iterations to reduce the cost function J from from 4574 to 2829, and the norm of its gradient by more than eight orders of magnitude from 4×10 3 to 2×10 −5 .At the minimum, the respective contributions (see Eq. 1) of the prior term, the CO 2 observations, and the MERIS observations to the total cost function J are 124, 61, and 2644.
At both stations, MLO (left hand panel of Fig. 2) and SPO (right hand panel of Fig. 2), the fit to atmospheric CO 2 has  improved considerably.The trend and both the amplitude and the phase of the seasonal cycle have improved.Figure 3 displays the change in simulated FAPAR through the assimilation (posterior-prior) for four months of 2003.FAPAR is reduced over the Amazon Forest, increased over Australia, and exhibits an increased seasonal cycle over East Asia and the North American high latitudes.
For validation of the calibrated model, i.e. the model with the posterior parameter values, we need independent information.This information is provided by flask samples of the atmospheric CO 2 concentration at extra sites withheld from our assimilation procedure.Figure 4 displays observed concentration (black) together with concentrations simulated with prior (blue) and posterior (red) parameter values for Point Barrow, a marine site in Alaska (left hand panel), and Izaña, a mountain site on the Canary Islands (right hand panel).We note that the posterior provides a considerably better fit than the prior, i.e. the validation confirms that the calibrated model performs better than the uncalibrated model.
The uncertainty reduction for the parameters is displayed in  Of more general interest are uncertainty reductions in target quantities such as predicted fluxes, because they are less specific to the model used than the process parameters.Here, we select net ecosystem production and net primary production (NEP and NPP) integrated over the period from 1999 to 2003 and six regions (Fig. 6).For all regions and both target quantities, we find a considerable degree of uncertainty reduction, where fluxes in Australia are somewhat less constrained by the data than it is the case for the other con-tinents.It is interesting to note that, even though the observed atmospheric CO 2 is more closely related to the net atmosphere-biosphere flux (NEP) than to only one component of it (NPP), the impact of the two data sets is to constrain NPP more than NEP compared to the prior case.

Mission benefit analysis
As a first example we analyse the individual information content in our two data streams (Fig. 7).We assume a long mission of 14 yr.For simulation of regional NEP (left hand panel), we note that the FAPAR constraint is marginal, and that most of the uncertainty reduction can be attributed to the atmospheric CO 2 observations.The same holds for NPP (right hand panel).
Interestingly, the picture is reversed for hydrological target quantities (Fig. 8), i.e. evapotranspiration (left hand panel) and plant available soil moisture (right hand panel).It appears that FAPAR is a powerful constraint for those parameters with a strong effect on hydrological fluxes, while atmospheric CO 2 is powerful in constraining parameters with a strong effect on the carbon fluxes for the case of long-term averages.
Next we investigate why the constraint of FAPAR on carbon fluxes is weak.Mathematically, this weak constraint is reflected by a sub-space within the overall parameter space that is at the same time crucial to simulate long-term carbon fluxes and either not at all or only weakly constrained by the MERIS FAPAR data (Fig. 7).In the first case the model simulated FAPAR data would have zero sensitivity to this part of the parameter space, while in the second case the sensitivity would be only small.There is an important difference between both cases: unlike the zero sensitivity, the weak sensitivity can be compensated for by a reduced data uncertainty.
Such a reduced data uncertainty would correspond to a new hypothetical mission concept.We investigate two  hypothetical sensor concepts: the first sensor has higher spatial resolution than the MERIS sensor and the second is a hypothetical sensor with ideal resolution.We reproduce the characteristics of the sensor with higher resolution by reducing the data uncertainty for FAPAR from 0.1 (corresponding to our data uncertainty for the MERIS sensor, see Sect.3.1) to 0.05.For the sensor with ideal resolution, we use a data uncertainty of 0.001.We stress that this low value is selected to explore an extreme case, not a case we can hope to achieve in reality.Even if future instruments might allow considerably higher precision, the theoretical limitations imposed by radiative transfer through heterogeneous canopy would prevent data uncertainties as low as this.
Figure 9 shows the reduction in parameter uncertainty for the MERIS sensor and both hypothetical mission concepts.
We see that while for some parameters the uncertainty reduction improves with sensor resolution, a large fraction of the parameters remains unobserved.Figure 10 shows the corresponding uncertainty reductions in annual NEP and NEP averaged over the mission period of 14 yr (note change of scale on y-axis).Indeed, the uncertainty reduction improves only marginally with sensor resolution, i.e. the unobserved parameters are important for constraining these carbon fluxes.
We further studied the effect of mission length.Figure 11 indicates that for the hydrological target quantities, the gain in uncertainty reduction through a mission length extension from 3 to 14 yr is hardly larger than 10 percentage points.Underlying this result is a similar mechanism as in the enhanced resolution experiment.Extending the mission length does improve the constraint on those parameters that influence    FAPAR but it cannot reduce uncertainties of parameters that do not influence FAPAR.The residual uncertainty in the hydrological target quantities can be attributed to uncertainty in these unobserved parameters.

Conclusions and perspectives
The study demonstrates the potential of consistent assimilation of multiple data streams, i.e. as a simultaneous constraint on the process parameters of a terrestrial biosphere model.This is the first study to combine, in a mathematically rigorous framework, observed FAPAR and atmospheric CO 2 .
The most important result of this study is that the MERISderived FAPAR product can be used to constrain quantities of the global water cycle.In more general terms, FAPAR can be highly valuable and beneficial for local to global scale ecosystem, hydrology and carbon cycle modelling when applied within a data assimilation framework.This includes prognostic studies where data from climate simulations are used and predictions are made beyond the period of observations.Validation of the calibrated model resulting from the assimilation against independent observations shows a clear performance improvement.
The systematic application of the mathematically rigorous uncertainty propagation capability implemented by CC-DAS allows to support the design of space missions with maximised benefit expressed in terms of uncertainties of inferred carbon or water fluxes.The study has developed an interactive mission benefit analysis (MBA) tool that allows instantaneous evaluation of a range of potential mission designs.Applying the MBA tool, the study showed that the benefit of FAPAR data is most pronounced for hydrological quantities, and moderate for quantities related to carbon fluxes from ecosystems.In semi-arid regions, where vegetation is strongly water limited, the constraint delivered by FA-PAR for hydrological quantities was especially large, as documented by the results for Africa and Australia.Sensor resolution is less critical for successful model calibration, and with even relatively short time series of only a few years, significant uncertainty reduction can be achieved.The enhanced constraint through a higher resolution or an extended mission length can only achieve an extra uncertainty reduction in the part of the parameter space that impacts FAPAR.The residual uncertainty in the hydrological or carbon fluxes reflects uncertainty in the unobserved parameters.The unobserved part of the parameter space can only be illuminated by a complementary type of observation.Obviously, the parameter space will differ between models and even between setups of the same model.Also, the link between the parameters and a specific data stream obviously depends on details of the process formulation.The mechanism that creates residual uncertainty from parameters not observed by a given observational network is, however, general.
For computational efficiency this pilot study uses a coarse spatial resolution.We find that CCDAS at this resolution reproduces the main features of the observed global FAPAR distribution, which gives us confidence that the results are representative of a simulations at higher spatial resolution.One would certainly expect that the constraint of FAPAR will be stronger on finer scales as more observations enter the data assimilation procedure with the number of parameters kept constant.However, the above-described residual uncertainty through parameters not observable through the combination of FAPAR and atmospheric CO 2 will remain.
We note that the approach used here to constrain process parameters of a global model can be considered an automated procedure for scientific investigation of the processes the parameters represent.We further note that the approach of multi-data stream assimilation presented here could easily be extended to include more than one data stream from remotely sensed products.Obvious candidates are land surface temperature from the Advanced Along-Track Scanning Radiometer (AATSR), surface soil moisture from the Soil Moisture and Ocean Salinity (SMOS) mission, and possibly column-integrated CO 2 observations.This would allow a rigorous assessment of the consistency of multiple data streams (as done here for FAPAR and atmospheric CO 2 ).Use of SMOS is particularly interesting, as it would allow comparing the benefits of SMOS soil moisture data to the already considerable benefit of FAPAR for hydrological quantities.
The complementary nature of existing and potential future data streams could be explored by an extension of the MBA tool.A prominent candidate observation would be a column-integrated CO 2 product.The MBA tool could be extended such that observational data uncertainty and sampling strategy for the mission are assessed in terms of the uncertainty reduction in the tool's target quantities, i.e. terrestrial carbon fluxes but also hydrological quantities.The tool's concept is, however, general and thus also applicable to other sensor types, such as RADAR (e.g.BIOMASS, SMOS, or the Advanced Orbiting Satellite, ALOS) or LIDAR (e.g. the Geoscience Laser Altimeter System, GLAS, on ICEsat), individually or combined.
While the study emphasises improvement of process parameters, the highly flexible structure of the variational approach allows, as a slight modification of the existing CC-DAS framework, to devise a soil moisture monitoring system that adjusts state variables through time such as soil moisture instead of static parameters.If input data for the ecosystem model can be derived from near-real time sources such as weather forecasting analyses or satellite data, this could result in an effective operational monitoring system for soil moisture.
Underlying the CCDAS-approach is the assumption of fundamental equations that govern the processes controlling the terrestrial biosphere and that rely on process parameters in their formulation.Following this assumption of universal mechanisms, the specification of parameter values that depend on the type of plant/ecosystem but not on its location is reasonable.The distinction between these types can be based on a map of PFTs, as done in BETHY and the majority of the state-of-the-art global terrestrial biosphere models.The number PFTs required for an accurate representation of the variation in plant function is a matter of debate and depends on the question asked (see, e.g.Groenendijk et al., 2011).The selection of PFTs chosen in this study is motivated mainly by the large functional differences between the major life forms of trees.While the number of PFTs and the associated size of the parameter space will certainly impact our results in a quantitative way, the mechanisms we describe are general.

Fig. 1 .
Fig. 1.Flow of information for evaluation of the cost function.J is the sum of the cost function contributions from the individual information items.Ovals denote data and rectangular boxes denote processing (i.e.code modules).

T.
Fig. 6.Uncertainty reduction in simulated NEP (left hand panel) and NPP (right hand panel) over six regions.

Fig. 7 .
Fig. 7. Reduction in uncertainty in NEP (left hand panel) and NPP (right hand panel) over six regions from MERIS sensor for a 14-yr mission.For assimilation of CO 2 (red) and FAPAR (brown) separately and jointly (green).

Fig. 8 .
Fig. 8. Reduction in uncertainty in evapotranspiration (left hand panel) and plant available soil moisture (right hand panel) over six regions from MERIS sensor for a 14-yr mission.For assimilation of CO 2 (red) and FAPAR (brown) separately and jointly (green).

Fig. 9 .
Fig. 9. Reduction in parameter uncertainty for a 14-yr mission for FAPAR data from the MERIS sensor (top left hand panel) a hypothetical higher resolution sensor (top right hand panel) and from a hypothetical ideal resolution sensor (bottom panel).

Fig. 10 .
Fig. 10.Reduction in uncertainty in NEP (left hand panel) and NPP (right hand panel) over six regions from three sensor concepts: the MERIS sensor (green), the higher resolution sensor (brown), and the ideal resolution sensor (red).

Fig. 11 .
Fig. 11.Reduction in uncertainty in evapotranspiration (left hand panel) and plant available soil moisture (right hand panel) over six regions from MERIS sensor for a mission length of 3 yr (green), 5 yr (brown) and 14 yr (red).