Quantifying the constraint of biospheric process parameters by CO 2 concentration and ﬂux measurement networks through a carbon cycle data assimilation system

The sensitivity of the process parameters of the biosphere model BETHY (Biosphere Energy Transfer HYdrology) to choices of atmospheric concentration network, high frequency terrestrial ﬂuxes, and the choice of ﬂux measurement network is investigated by using a carbon cycle data assimilation system. Results show that monthly mean or low- 5 frequency observations of CO 2 concentration provide strong constraints on parameters relevant for net ﬂux (NEP) but only weak constraints for parameters controlling gross ﬂuxes. The use of high-frequency CO 2 concentration observations, which has allowed a great reﬁnement of spatial scales in direct inversions, adds little to the observing system in this case. This unexpected result is explained by the fact that the stations 10 of the CO 2 concentration network we are using are not well placed to measure such high frequency signals. Indeed, CO 2 concentration sensitivities relevant for such high frequency ﬂuxes are found to be largely conﬁned in the vicinity of the corresponding ﬂuxes, and are therefore not well observed by background monitoring stations. In contrast, our results clearly show the potential of ﬂux measurements to better constrain the model parameters relevant for gross primary productivity (GPP) and net primary productivity (NPP). Given uncertainties in the spatial description of ecosystem functions we recommend a combined observing strategy.


Introduction
Uncertainties in the distribution of the carbon flux to the atmosphere limit both the skill 20 of predictive models and the application of evidence-based carbon accounting. Given the importance of this problem a large suite of measurements (including dedicated satellite missions) is gathered and quite sophisticated systems have been built to use them. There are two main approaches: the simplest are direct inversion systems in which atmospheric transport models and Bayesian estimation methods are used to 25 infer surface fluxes from atmospheric CO 2 concentrations. These have been broadly 24132 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | used but their estimates vary widely due to differences in set-up, observational data, prior estimates of the fluxes and transport models (e.g. Gurney et al., 2002Gurney et al., , 2004Law et al., 2003;Baker et al., 2006;Rayner et al., 2008;Chevallier et al., 2010). A second approach uses a range of observations to constrain the possible trajectories of dynamical models of the carbon cycle. The process parameters of the dynamic model are 5 first constrained and then the optimized model is used to predict the various quantities of interest. The uncertainties in the parameters of the dynamic model are projected forward to output of the constrained model by the observations. Because of the use of an explicit dynamical model this approach is often termed carbon-cycle data assimilation (by analogy with data assimilation in numerical weather prediction). The trade-offs 10 between these two approaches are discussed in Kaminski et al. (2002).
The Carbon Cycle Data Assimilation System (CCDAS) can ingest many types of observations, e.g. atmospheric CO 2 Scholze et al., 2007;Koffi et al., 2012), vegetation activity and atmospheric CO 2 (Kaminski et al., 2011), vegetation activity at site level alone (Knorr et al., 2010) and its combination with eddy-correlation Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | continuous observations to the constraint of model parameters (the CCDAS approach). On the positive side is the obvious analogy between the methods which both rely on information about fluxes. Furthermore the time variations in fluxes themselves (such as the response to changes in photosynthetically active radiation forced by changing cloudiness) may probe the roles of particular parameters, even though model errors 5 are strongly correlated in time (Chevallier et al., 2012). The major dampener on our optimism is the inherent difference in scales implicit in the two approaches. Assimilation systems such as Rayner et al. (2005) constrain a small number of parameters (57 in that case). These modulate, via the model dynamics, structures in flux and hence concentration. For the majority of parameters their impact extends to the coverage of 10 a particular plant functional type (PFT). Other parameters have a global impact since they apply to plants or soils everywhere. The main impact of continuous observations in direct inversions has been a refinement of scale, an advantage that may not apply in an assimilation system. However, as noted by Rayner et al. (2005) and Koffi et al. (2012) there are still many unconstrained parameters in an assimilation system so it is worth 15 asking the question whether this readily available data fills the need.
There is another major dataset available on the terrestrial carbon cycle in the form of continuous measurements of fluxes at very small scales (e.g. Foken and Wichura, 1996;Aubinet et al., 2000;Baldocchi, 2003;Rebmann et al., 2005;Reichstein et al., 2005;Papale et al., 2006;Lasslop et al., 2010, and references therein). These have af- 20 forded much information on processes affecting the terrestrial carbon-cycle (e.g. Piao et al., 2008). They have been used in various assimilation efforts (e.g. Wang et al., 2001;Knorr and Kattge 2005;Medvigy et al., 2009). They have also been tested in a simplified assimilation system (Kaminski et al., 2002) where they showed a large impact. Knorr et al. (2010) used remotely sensed vegetation activity at site level 25 alone and Kato et al. (2012) combined it with eddy-correlation flux measurements of latent heat in a full CCDAS. Kaminski et al. (2012) also used the full CCDAS to assess and analyze the constraint of observational networks composed of continuous flux measurements, daily and monthly atmospheric concentration measurements. In 24134 to radiation and temperature. These variations are likely to reveal different sensitivities of fluxes and concentrations that can provide additional constraints on parameters. Thus our task here is to use daily forcing data to assess, in a theoretical framework, the power of continuous concentration and flux observations to constrain model parameters and, if the constraint is useful, to understand the sources of the information in the 10 measurements and make recommendations for their use.
To achieve the above mentioned objective, we use the CCDAS  built around the biosphere model BETHY (Biosphere Energy Transfer HYdrology) and some functionalities of the general Bayesian optimisation system PYVAR (PYthon VARiationnal) (Chevallier et al., 2005). The outline of the paper is as follows: 15 We describe in Sect. 2 the main pieces that compose both CCDAS and the PYVAR assimilation system. The formalism used to compute the uncertainty in parameters of the biosphere model is defined in Sect. 3. The data are described in Sect. 4. The different model/data configurations used to achieve the objectives of the paper are detailed in Sect. 5. The constraint of the parameters available from (i) high frequency Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Overall methodology
Our task is to quantify the information content of various sources of measurement that can be retrieved by an assimilation system. We quantify the information by the reduction in the uncertainty of model parameters, operationally defined as the ratio of prior and posterior standard deviations. Under the linear Gaussian assumption the posterior 5 uncertainty is dependent only on the prior uncertainty, the assumed uncertainty for the measurements and the sensitivity of the simulated observations to changes in the parameter (usually called the Jacobian). Thus the main technical task described below is the calculation of these Jacobians for various classes of observations. 10 CCDAS combines the biosphere model BETHY (Knorr, 2000) and an atmospheric transport model. We use the version of Koffi et al. (2012) which includes the atmospheric model TM3 (Heimann and Körner, 2003). The process parameters of BETHY (Table 1) we are using are those optimised by Koffi et al. (2012). Note that Kaminski et al. (2012) used the same process parameters but different values, taken from an 15 optimisation by Scholze et al. (2007) against a different observational network and with a different transport model.

CDAS
BETHY is a process-based model of the terrestrial biosphere which simulates carbon assimilation and plant and soil respiration, embedded within a full energy and water balance (Knorr, 2000). BETHY uses 13 plant functional types (PFTs; see Fig. 1). A grid 20 cell can contain up to three different PFTs, with the amount specified by their fractional coverage. A complete description of BETHY for the assimilation of CO 2 concentrations is given in Rayner et al. (2005) and the version used in this study is detailed in Koffi et al. (2012). Therefore, we briefly define the BETHY fluxes together with their relevant parameters which we use later. BETHY computes the gross primary productivity (GPP)

The PYVAR system
The PYVAR system (Chevallier et al., 2005) is a generic Bayesian optimisation system used for global and regional inversions of tracer fluxes. It can be interfaced to several atmospheric transport models. In this case we use the global atmospheric transport model LMDz (Hourdin et al., 2006). PYVAR can ingest various sources of measure-15 ments such as surface flask samples and continuous CO 2 concentrations (e.g. Chevallier et al., 2010) and satellite CO 2 data (Chevallier at al., 2007). The PYVAR system also allows interpolating simulated concentrations to the locations of the stations of the observing network. 20 In our case we do not use the optimization capabilities of PYVAR. For our error analysis we require the sensitivity of observations to parameters. For concentration observations we obtain these by first calculating the sensitivity of NEP with respect to parameters then transporting these sensitivities with LMDz via the PYVAR system (see the next Sect. 3.1 for details on the formalism).

Computation of uncertainty
The formalism used to calculate the uncertainties in the parameters is first defined. Then, the methods used to quantify the sensitivity of the parameters to observations from both CO 2 concentrations and flux measurement networks are described. 5 We apply the network design approach described by Kaminski and Rayner (2008) and demonstrated by Kaminski et al. (2010Kaminski et al. ( , 2012: in brief, the parameters we are using were optimized by using a Bayesian inference scheme (Enting, 2002;Tarantola, 2005). This inference scheme minimizes a cost function J(x) representing the negative log likelihood. J(x) includes contributions from the model-observation mismatch and the 10 departure of parameter values from their prior estimates and is defined as follows:

CO 2 concentration network
Where x is the parameter vector to be optimized with prior value x 0 with uncertainty covariance C(x 0 ). d i is the observed CO 2 concentrations and m i the corresponding 15 value simulated by the transport model. The standard deviation σ(d i ) represents the summed uncertainty in the terrestrial model (here BETHY), the transport model, and concentration observations. The parameter errors (or uncertainties) as well as the observation errors are uncorrelated in our formulation. We calculate the second derivative or Hessian (H) of the cost function with respect to the parameters (e.g. Kaminski and 20 Rayner, 2008;Kaminski et al., 2010). The contribution of observations to H can be written as follows: Where dm/dx is the first derivative (Jacobian) of the simulated CO 2 concentration with respect to the parameters x. n is the number of observations. If m is linear, its second derivative is 0 and we have a simple expression for H in terms of the Jacobian. Under these circumstances the covariance (i.e. (dx/dm) 2 ) is the inverse of the Hessian and we see that (as noted by Hardt and Scherbaum, 1994) neither the values of the prior 5 parameters nor the observations appear directly in the Hessian (Eq. 2). For a nonlinear model such as BETHY, the sensitivities are, of course, dependent on the value of the optimised parameters. The total derivative dm/dx can be written as a function of partial derivatives as follows: Where f stands for NEP. M represents the derivative of CO 2 concentration m with respect to f (i.e. ∂m/∂f ). ∂f /∂x stands for the sensitivity of f with respect to the parameter x. The Jacobian matrix dm/dx is computed by chaining the tangent linear (TL) code 15 of BETHY and the TL code of LMDz. The TL code of BETHY is generated by the automatic differentiation tool Transformation of Algorithms in Fortran (TAF; Giering and Kaminski, 1998;Kaminski et al., 2003) while the TL code of LMDz has been coded manually by Chevallier et al. (2005). We first compute the quantities ∂f /∂x using the TL code of CCDAS and map them onto the LMDz grid. Then, the TL code of LMDz is 20 used to transport these sensitivities to derive dm/dx, as given in Eq. (3).

The flux measurement network
We note again that this is a synthetic data study where, following our assumption of linearity, we can calculate the constraint on the parameters without the use of actual data. We use the same linearity assumptions as for concentrations so that the critical quantity becomes the Jacobian of the fluxes with respect to parameters (i.e. ∂f /∂x). These are also calculated by the tangent linear mode of TAF and here we have no need of an atmospheric transport model.

Uncertainty reduction 5
The second derivative (Hessian H) is used to approximate the inverse of the covariance matrix that quantifies the uncertainty ranges on the parameters. We use the standard deviation obtained from the inverse of the Hessian (Eq. 2) to characterize the uncertainty in the parameters. Following, e.g. Kaminski et al. (1999), we quantify the reduction of the uncertainty (hereafter U R ) in a selected parameter from its prior as 10 follows: Where σ x (derived from Eqs. 2-3) and σ x0 (Table 1) are the posterior and prior uncertainties in the parameter x, respectively. The unit of U R is %.

CCDAS
The system needs both forcing data to drive BETHY and atmospheric CO 2 concentration data for the assimilation. BETHY is driven by observed monthly climate and radiation data over the period 1979-2001(Nijssen et al., 2001 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the two above mentioned periods. We use monthly CO 2 concentration data from the 68 stations used in Koffi et al. (2012).

BETHY fluxes
In the standard set-up of CCDAS, BETHY is run such that it simulates hourly GPP and NPP for one representative day in a month. To quantify the contribution of hourly 5 flux measurements to the reduction of uncertainties in parameters, the hourly NPPs are used. The storage efficiency scheme is not appropriate for calculating hourly heterotrophic respiration. We assume that the magnitude of the diurnal cycle (noted by Knorr and Kattge (2005) as the key observable from hourly flux measurements) is driven by NPP not heterotrophic respiration. Hence, when considering the flux measurement network, only the thirty-eight parameters relevant for NPP are first analyzed (Table 1). There is no clear algorithm for assigning uncertainties to flux data in CCDAS since it varies widely with conditions (Hagen et al., 2006) and depends on the capability of the model itself (Chevallier et al., 2012). We therefore choose a conservative value of 25 % on the hourly measurements. Note that this will translate into much larger percent-15 age errors on diurnal and annual sums (where fluxes partially cancel but errors do not). Thus, the uncertainties in BETHY hourly NPP observations are assumed to be equal to 25 % of the corresponding NPP values. To test the sensitivity of flux measurements to the parameters strongly related to NEP, we use a "pseudo" hourly NEP computed by dividing the daily heterotrophic respiration into 24 equal-sized hourly fluxes and subtract 20 these fluxes from the hourly NPP as performed in Kaminski et al. (2012). As for the NPP observations, we assume that the uncertainties in these NEP are equal to 25 % of the corresponding NPP values. For NPP zero, we consider larger uncertainties to be 25 % of the maximum of the NPP, which is obtained from all the grid cells of BETHY and over the selected period. Introduction

Prior values of the parameters and uncertainties
The uncertainties in prior parameters of BETHY are those of Koffi et al. (2012). For biophysical parameters (e.g. the carboxylation capacity of the leaf, V max ), the prior values are taken from literature summarized in Knorr (2000). For other parameters such as the beta storage efficiency (β) relevant for carbon balance NEP, the uncertainties are 5 assumed to be large since there is little knowledge of these parameters (Table 1). Finally, prior information not only includes results of previous studies but also knowledge of the physical limits of the parameters. For example many parameters are physically limited to positive values. A log-normal PDF was considered for these bounded parameters while a Gaussian PDF was applied to those parameters that have not such 10 critical threshold values (marked by an asterix in Table 1; Koffi et al., 2012).

Transport model and CO 2 concentrations
For the tracer transport, we use the pre-computed transport Jacobians of the TM3 model (Heimann and Körner, 2003 and some additional CO 2 measurement sites for which the TM3 Jacobians are available. The uncertainties in these data include those from models (BETHY and transport) and measurement errors and range from 0.51 ppm to 4.9 ppm, as described in Koffi et al. (2012). To represent the CO 2 concentration measurement network, we use the same data as Chevallier et al. (2010). These data come from three large data bases: the NOAA Earth System Laboratory (ESRL) archive, the CarboEurope IP project, and the World Data Centre for Greenhouse Gases (WDCGG) of the World Meteorological Organization (WMO) Global Atmospheric Watch Programme. The three databases include both

Combination of CCDAS and PYVAR data
CCDAS provides monthly or daily NEP and their sensitivities with respect to BETHY parameters to the PYVAR system. To use high frequency observations of CO 2 con-5 centrations, PYVAR divides the day into 8 three-hour time windows in which the flux is constant. When using monthly fluxes from CCDAS within PYVAR, the value of the flux for a month is considered representative for the days of the month and for each of the 8 time windows of a day. For daily NEP, the value of the flux for a day is considered representative for each of the 8 time windows of PYVAR. 10

Experimental set up
The different configurations of model/data used to study the sensitivity of the parameters to (i) high frequency observations of CO 2 concentrations and (ii) temporal resolution of meteorological and phenological data used to force BETHY are first defined. Then, the configurations relevant for flux measurements are given.

Configurations using observing network of CO 2 concentration
To test the sensitivity of the parameters to high frequency CO 2 concentration data, we first use BETHY monthly NEP over the period 1989-2001 to compute various versions of the Jacobian relating parameters to atmospheric concentrations (see Eq. 3). The following configurations, which are summarized in Table 2, are considered: -PYV all : as for PYV configuration, but for all the stations used in Chevallier et al. (2010). In total, we consider 104 stations over the period 1989-2001.
The differences between M TM3 and M PYV configurations give information on the sensitivity of parameters to the transport models while M PYV , PYV, and PYV all give the sensitivity of the parameters to the number and type of observations. The observing networks of CO 2 concentrations for the configurations defined above are shown in Fig. 1.

Configurations using daily fluxes
To test the sensitivity of the parameters to the temporal resolution of the meteorological 15 and phenological data used to force BETHY and hence to the temporal resolution of BETHY fluxes, we use the following configurations that are also summarized in Table 2: -MM PYV : both monthly meteorological and phenological data are used to force BETHY. The simulated monthly fluxes by BETHY are considered.
-DM PYV : both daily meteorological and phenological data are used to force BETHY. 20 Daily fluxes are calculated from BETHY, but monthly mean values from these daily fluxes are considered. Comparison with MM PYV tests the sensitivity to the assumption of a single representative day made in BETHY.
-DD PYV : both daily meteorological and phenological data are used to force BETHY. Daily fluxes computed by BETHY are considered.
The differences between MM PYV and DM PYV give information on the sensitivity of the parameters to the temporal resolution of the meteorological and phenological data. The configurations MM PYV and DD PYV probe the sensitivity of the parameters to the temporal resolution of BETHY fluxes. For these three configurations, all the available stations of the observing network of CO 2 concentrations that can be handled by the 5 PYVAR system are used. Results of MM PYV , DM PYV , and DD PYV are derived for several single years drawn from the period 1996-2006.

Configurations using the flux measurement network
In our model, a flux measurement samples the flux over a particular grid cell. We design two configurations for two potential networks of flux measurements 10 -BETHY-PFT: we use 13 sites that cover the 13 PFTs of the BETHY model. The stations are selected on the basis of the dominant PFTs of BETHY. Table 3 gives the percentages of coverage of the 13 PFTs over their corresponding BETHY grid cell (Fig. 2). Note that this network is constructed similarly to the 9 PFT network over Europe -BETHY-FLUXNET: we consider a network based on both the international FLUXNET network (Baldocchi, 2003;Papale et al., 2006 in the BETHY-FLUXNET network (Table 3). For example, the C4 grass PFT is represented by 28 grid cells of BETHY (or stations), while only 1 grid cell is used for swamp vegetation (Wetl). Also, for some PFTs, the percentages of coverage over their relevant BETHY pixels are low (Table 3). The networks relevant to BETHY-PFT and BETHY-FLUXNET configurations are shown in Fig. 2. 5 6 Results Figure 3 shows the reduction of the uncertainties (U R ) for the 56 studied parameters of BETHY (see Table 1 for the definition of the parameters) when considering M TM3 , 10 M PYV , and PYV, and PYV all configurations (see Sect. 5.1). Overall, the uncertainty reductions in the parameters are not significantly sensitive to the transport models. Similar U R values are found between M TM3 (TM3 model) and M PYV (LMDz model).

Uncertainty reduction with high frequency and continuous CO 2 concentrations
The differences in U R between M TM3 and M PYV are less than 25 % for 55 of the 56 parameters (Fig. 3). The largest difference (44 %) is obtained for NEP parameter β 15 for the temperate evergreen forest (TmpEv). To investigate the differences between M TM3 and M PYV , we have run the M PYV setup with the uncertainty from the M TM3 setup, which is on average a factor of 1.8 lower. Compared to the default M PYV setup this increases the uncertainty reduction for all parameters. As expected, the uncertainties in the parameters are more strongly reduced as the number of observations increases 20 but the reduction becomes relatively small between two large sets of observations. As an example, for V max of the tropical evergreen forest, U R values are 59 % and 81 % when using 4326 (M PYV ) and 198 335 (PYV) observations, respectively. It is only 88 % from 441 873 observations. When considering the PYV all configuration (which represents the largest number of observations used), the largest uncertainty reductions (> 90 %) 25 are obtained for almost all the parameters related to carbon balance NEP (i.e. β) and 24147 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | to soil respiration (i.e. Q 10f , Q 10s , τ f , κ, f s ). The smallest reduction (75 %) is found for the β parameter relevant for swamp vegetation (Wetl PFT). These results agree with those reported in Ziehn et al. (2011) who also found large uncertainty reductions in the β parameters.
For the PYV all configuration, the uncertainties in E Rd and f R,leaf parameters relevant 5 for NPP are reduced by 60 % and 90 % from their prior values, respectively (Fig. 3).
Only a weak reduction is obtained for the parameter f R,growth relevant for the growth respiration of the plant (about 40 %). Significant reductions (between 60 % and 90 %) are found for the V max parameters, with the largest reduction being for V max for temperate deciduous (TmpDec) forest. The smallest reduction is again obtained for swamp vegetation (i.e. Wetl PFT). We obtain relatively small uncertainty reductions for the parameters a J,V (< 15 %). The uncertainties are also weakly reduced (< 40 %) for almost all the global parameters relevant for the photosynthesis (i.e. E K 0 , E K , σ i 25 , K 0 ). Among these global parameters, only the uncertainties in both E V max and α q parameters are significantly reduced (about 60 %). 15 We find that uncertainty reduction saturates for large numbers of observations (not shown). As discussed in Kaminski et al. (2011Kaminski et al. ( , 2012, we can understand the saturation of the information provided by observations by considering the Eigen-values of the Hessian. These describe particular directions in parameter space and the eigen-value is a measure of the information content in that direction. Increasing the number of ob- 20 servations may well improve the information content in a particular direction but not necessarily constrain new directions in parameter space. Eventually the uncertainty in a particular direction approaches zero and the uncertainty in a parameter is determined by its projection onto the subspace spanned by the well-constrained directions. With 56 parameters we have 56 available directions in parameter space. An analysis 25 of the eigen-values for our different cases shows the observations constrain at most 40 of these directions. Observing these directions better will not provide much more information, only new types of observations will constrain the remaining directions. Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Uncertainty reduction with daily fluxes
Our initial hypothesis was that the response of daily fluxes to variations in forcing would contain information about the model parameters and would, in turn, be visible in daily measurements of CO 2 concentration. We investigate this using the MM PYV , DM PYV , and DD PYV configurations. Figure 4 shows U R for the year 2000. Overall, U R for all 5 three cases are roughly comparable. This surprising result comes despite the welldocumented capability of high-frequency observations to resolve details of flux distributions (Law et al., 2003). It raises the question whether this is a fundamental limit or a function of the placement of current stations. Following Koffi et al. (2012) we investigate this by calculating global fields of the sensitivity of concentration to parame-10 ters rather than the Jacobians at stations. We simulate the sensitivity of surface CO 2 concentrations to parameters by using the LMDz model. We use the sensitivities of NEP with respect to V max for tropical evergreen and temperate deciduous forests respectively. Sensitivities from the cases MM PYV and DD PYV are considered. We run the transport model LMDz for 3 yr using the two NEP sensitivities obtained for year 2000 15 as inputs. We then analyse the surface fields of the last year of LMDz simulations. The differences between the two simulations are quantified by the root mean square difference (rmsd) computed both in space and time (Fig. 5). For both cases, the differences between the daily and monthly cases are restricted to the regions of the relevant PFTs. Thus the impact of considering the daily flux responses to these two parameters does 20 not travel far enough to be observed by the sparse network. Figure 6 shows U R for the years 1998, 2000, 2001, 2003 and 2005. These years were chosen to represent the inter-annual variability in the forcing. We do not find large differences in uncertainty reductions (less than 19 %) between the different years. The 25 relatively small differences between the selected years occur despite large differences in the density of observations. As an example, the year 1998 exhibits similar uncertainty Introduction  . 6) with mean uncertainty 1.4 time as large. Figure 7 shows U R values obtained when using NPP flux measurements for the year 5 2000 and for the two cases BETHY-PFT and BETHY-FLUXNET. There are dramatic uncertainty reductions for all the GPP V max parameters and the parameters f R,leaf and f R,growth relevant to NPP. Except for the tundra PFT, BETHY-PFT produces uncertainty reductions in V max of more than 80 %. This is more effective than the DD PYV case (i.e. CO 2 concentration network with daily BETHY fluxes) despite BETHY-PFT using only 10 12 % as many observations as DD PYV . This confirms the result of Kaminski et al. (2012) who found uncertainty reductions of over 99 % in simulated NEP and NPP over Europe with only 9 flux sites. Consequently, these results demonstrate the potential of high frequency flux measurements in reducing the uncertainties in V max parameters. When using a larger number of flux measurements allowed by the BETHY-FLUXNET config-15 uration, very large uncertainty reductions are obtained for all the parameters V max of GPP and the three parameters of NPP (between 85 % and 98 %), as shown in Fig. 7. In contrast to observations of CO 2 concentrations, flux data significantly constrains other parameters such as the a J,V (PFT dependent) and global parameters related to photosynthesis (i.e. to GPP). As expected, the constraint increases with the num-20 ber of measurements, hence U R for BETHY-FLUXNET is highly variable. For the C4 plant, a J,V is not sensitive to flux measurements (Fig. 7). Indeed, we do not find any difference between BETHY-PFT and BETHY-FLUXNET configurations, but BETHY-FLUXNET uses 28 times the number of observations of BETHY-PFT. This is due to the fact that the Jacobians are close to zero for this parameter. E V max , which appears 25 in the descriptions of both C3 and C4 photosynthesis, shows U R of 91 % while most parameters which affect C3 photosynthesis only yield 48-85 %. For C4 vegetation, the parameter E k does not show any U R , suggesting that V max limitation is not active. As expected, NEP measurements allow us to greatly reduce the uncertainties in the parameters related to the carbon balance NEP (i.e. β) (Fig. 8). Moreover, with NEP measurements, uncertainty reductions for some a J,V parameters related to the photosynthesis become larger (e.g. C4 grass and Wetl) (Figs. 7 and 8).

Uncertainty reduction with flux measurements
As might be expected with the stronger constraint afforded by flux measurements, 5 combining flux and concentration measurements does not improve much on the fluxonly case (Figs. 7 and 8).
The data uncertainty in fluxes is dominated by model error. We have carried out a sensitivity study (not shown) in which we used a 75 % error. In this case, the smaller flux network BETHY-PFT still yielded reductions in parameter uncertainties larger than 10 with concentration measurements alone but here the differences were not so clear.

Sensitivities of observations to parameters
Finally, we have investigated the sensitivities of both the CO 2 concentration (Eq. 3) and flux with respect to each of the 56 studied parameters (not shown). For CO 2 concentrations, as expected the largest sensitivities are found for parameters related to soil 15 respiration and carbon balance NEP. The largest sensitivity is found for the parameter f s which describes the fraction of decomposition from the short-lived litter pool that goes to the long-lived soil carbon pool. The weakest sensitivity is found for the parameter E k relevant for the PEP case (i.e. the initial CO 2 fixating enzyme in C4 plants). Concerning the flux measurements (here NPP), the largest sensitivities are found for parameters 20 relevant for NPP and some parameters V max of GPP. The largest sensitivity is obtained for the parameter f R,leaf , the fraction of GPP used for the maintenance respiration of the plant. Again, the weakest sensitivity is for E k . See Rayner et al. (2005) and Koffi et al. (2012) for details of the parameters and the physical quantities they affect.

Discussion
The above results raise two questions. Firstly, why are the flux measurements so much more effective as a constraint in the CCDAS? Atmospheric concentrations, in the inverse method we use here, are themselves an observation of integrated flux. Yet they are far less effective as a constraint on process parameters than the fluxes themselves.

5
There are two likely reasons for this, both to do with the integrating action of atmospheric transport. Firstly each concentration observation integrates information from many flux pixels. This means they average out local variations in forcing which would otherwise provide information on the response of processes. This effect is reduced for seasonal and interannual forcing where climate anomalies are usually spatially coherent but we still lose much small-scale information. The other reason has already been mentioned, the spatial confinement of signals from high-frequency flux responses. Some of this problem may be addressed by spatially dense satellite measurements of concentration (Kaminski et al., 2010).
The other point to be drawn from the study is the relative value of flux and concen-15 tration measurements within a CCDAS. If our aim is limited to constraining parameters of biosphere process models, our results alone would argue for a substantial shift of resources from concentration to flux measurements. Of course this is not the only purpose of atmospheric measurements but it is an important one, contributing to the intensification of continental networks in the last decade. A counterpoint to this conclu-20 sion is provided by the recent study of Kaminski et al. (2012). Using different metrics but similar techniques, they also showed a much greater power of flux observations in reducing uncertainty of parameters in CCDAS and resultant calculated fluxes. Their results were, however, highly sensitive to the assumed heterogeneity of the biosphere. As soon as a PFT was left unsampled by the flux network it dominated the uncertainty in area-integrated flux. Since we can never be sure of the true process-level heterogeneity a combined observing strategy is clearly required.

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | The study showed large reductions of uncertainty for most BETHY parameters. We have noted throughout the dependence of this result on the magnitudes of data uncertainties we use and have conducted sensitivity studies where possible to quantify this dependence. It is likely that (unknown) correlations in the model errors significantly dampen the real observation impact. However, model error in BETHY is a contributor to 5 uncertainties in both types of observations so an underestimate of this contribution will affect both networks. It should therefore have less impact on our conclusion that flux observations are a strong constraint compared to concentration observations. More important here, is the conclusion from Ziehn et al. (2011) andKaminski et al. (2012) who noted that increased complexity (i.e. regionalization of the PFTs) of the biosphere 10 description both reduced the impact of observations on parameter uncertainty but particularly reduced the impact of flux observations. This analysis is restricted to only two types of measurement. Other data such as the fluorescence data from the GOSAT satellite (Frankenberg et al., 2011), remotely sensed vegetation activity (Knorr et al., 2010;Kaminski et al., 2011), and leaf level 15 observations (Ziehn et al., 2011) can be used as additional data to constrain the parameters related to GPP and NPP.

Conclusions
We have studied the sensitivity of BETHY process parameters using a carbon-cycle data assimilation system to choices of atmospheric concentration network, high fre-  Masarie, K., Prather, M., Pak, B., Taguchi, S., and Zhu, Z.: TransCom 3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO 2 fluxes, 1988, Global Biogeochem. Cy., 20, GB1002, doi:10.1029/2004GB002439, 2006: What can we learn from European continuous atmospheric CO 2 measurements to quantify regional fluxes -Part 1:
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 51 Fig. 8: As Fig. 7, but considering NEP flux measurements and then for all the 56 studied parameters of BETHY. See Fig. 1 for the definition of the acronyms of the PFTs and Table 1 for the prior values of the parameters. Fig. 8. As Fig. 7, but considering NEP flux measurements and then for all the 56 studied parameters of BETHY. See Fig. 1 for the definition of the acronyms of the PFTs and Table 1 for the prior values of the parameters.