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CCDAS evaluation : Error estimations
on parameters (D430.1) and output
fields (D430.2)
Authors
Company
Philippe PEYLIN
LSCE
Bacour Cédric
NOVELTIS
Abdou Khane
CLIMMOD
Approval
Company
Pascal PRUNET
NOVELTIS
Deliverable D430.1
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CHANGE RECORDS
ISSUE DATE
§ : CHANGE RECORD
1
Document Creation
05/02/2016
AUTHOR
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Table of contents
1.
INTRODUCTION.............................................................................................................................................. 4
2.
CARBONES CCDAS VERSION V0 AND ERROR ESTIMATION ............................................................................. 5
2.1
OVERALL CCDAS APPROACH ................................................................................................................5
2.2
PRINCIPLE OF ERROR ESTIMATION ..........................................................................................................6
2.3
CCDAS COMPONENTS AND ASSOCIATED ERROR ESTIMATION ..................................................................7
2.3.1
Land component (step 1 and 2) ........................................................................................................7
2.3.2
Ocean component (step 3) .............................................................................................................11
2.3.3
Atmospheric component (step 4) ...................................................................................................12
3.
PRIOR ERROR STATISTICS ON PARAMETERS AND OBSERVATIONS ............................................................... 13
3.1
3.1.1
Prior error statistics on the parameters .........................................................................................13
3.1.2
Error statistics on the observations and the model ........................................................................13
3.2
OCEAN COMPONENT (STEP 3) ............................................................................................................. 14
3.3
ATMOSPHERIC COMPONENT (STEP 4): ERROR ON CO2 CONCENTRATIONS ............................................. 16
4.
ESTIMATED ERROR STATISTICS FROM THE MODEL-DATA FUSION: PARAMETERS & STATE
VARIABLES ................................................................................................................................................... 16
4.1
ASSIMILATION OF SATELLITE NDVI (STEP 1) ......................................................................................... 16
4.2
ASSIMILATION OF IN SITU FLUX MEASUREMENTS (STEP 2) ...................................................................... 18
4.3
ASSIMILATION OF OCEAN PCO2 DATA (STEP 3) ..................................................................................... 25
4.4
ASSIMILATION OF ATMOSPHERIC CO2 DATA (STEP 4) ........................................................................... 25
5.
6.
LAND COMPONENT (STEP 1 & 2) .......................................................................................................... 13
SUMMARY AND PERSPECTIVES .................................................................................................................... 30
5.1
SUMMARY OF THE ERROR ESTIMATIONS ............................................................................................... 30
5.2
FUTURE ASSIMILATION OF BIOMASS DATA ............................................................................................. 30
REFERENCES ................................................................................................................................................. 33
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1. Introduction
The initial aim of the two reports (condensed into one, see justification below) was to present the
uncertainties associated to the 20-year CARBONES reanalysis products. However, several constraints
led us to revise the objectives of these deliverables as detailed in the following remarks:

First, we have chosen to merge the deliverables D430.1 and D430.2 on the error estimations
associated to the Carbon Cycle Data Assimilation System (CCDAS). Indeed the separation
between the errors on the parameters and the errors on the output fields is not
straightforward, at least given the set up of the first V0 version of the system (see below). A
more logical split is to discuss the a priori errors used as input to the CCDAS and then the
estimated errors both on the parameters and the associated output fields.

This report should be considered as a preliminary report describing part of the errors
associated to the CCDAS. Indeed, due to some technical problems, not initially anticipated
(i.e., the completion of the adjoint of ORCHIDEE, the compatibilities between the different
data streams to be assimilated in the CCDAS, …), the global system is only entering in the
“production phase”. We thus have not yet characterized the uncertainties associated to the
use of all input data streams, simultaneously.

Finally, we should recall the CCDAS approach for this first V0 version has been modified
compared to the initial proposition in the Document of Work (DoW). Although these changes
are detailed in a previous report (D410.1), we will briefly recall the new CCDAS approach and
slight modifications compared to the report D410.1.
Given these remarks, we are only able to provide a first hint on the uncertainties associated to the
different CARBONES products. In this context such report will be revised in 6 months in order to
incorporate the results from the “global optimization step” (see below).
In the following, we will thus describe:

In section 2, the various components of the CCDAS (models and data streams) together with
the principles of the error estimation on parameters and the propagation of errors in the
space of the state variables;

in section 3, the determination of the a priori error statistics on the model parameters and
observations;

in section 4, the determination of the posterior errors on model parameters and
observations;

finally, in section 5, we summarize the results and describe the anticipated impact on error
estimation from the assimilation of biomass data in the future version (V1) of the CCDAS.
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2. CARBONES CCDAS version V0 and error estimation
The description of version V0 of the system has been detailed in a previous report (D410.1).
However, we briefly recall below the different steps that are performed (section 2.3) in order to
define the context of the error estimations associated to each step.
2.1 Overall CCDAS approach
Results obtained during the consolidation phase of the system led us to propose a sequential
assimilation of the different data streams (satellite products measuring vegetation activity (e.g.
NDVI), ecosystem fluxes measured at several sites, ocean pCO2 measurements, and atmospheric CO2
measurements). The reasons of this new approach (compared to what has been proposed in the
DoW) are detailed in the report D410.1.
The different steps of this sequential approach are described in Figure 1 and are as follows:
Step 1: Assimilation of the remotely sensed products of vegetation greenness (NDVI)
derived from MODIS into ORCHIDEE; the prior parameters including values and error
covariance (X0 and P0) are optimized to produce a first set of optimized parameters X1
with error covariance P1.
Step 2: Assimilation of in situ flux measurements ; the parameters X1 and P1 are used as
input to the optimization system (adding new parameters) and further optimized to
produce the second set of optimized parameters (X2 and their error covariance P2).
Step 3: Assimilation of ocean pCO2 measurements into a statistical model (neural
network) to produce a priori air-sea fluxes
Step 4: Final assimilation step using the atmospheric CO2 measurements as a global
constraint; the parameters X2 and their error covariance P2 are used as prior for the
ORCHIDEE model and the air-sea fluxes from step 3 are used as prior ocean fluxes. The
result of this last optimization step will consist of i) final parameters for ORCHIDEE with
the associated optimized land fluxes and ii) the optimized ocean fluxes.
In the remaining part of the document we will make reference to the above four sequential
assimilation steps.
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Figure 1: Sequential assimilation of the different data stream into 4 steps.
2.2 Principle of error estimation
For each step described above (except for the computation of the prior ocean-atmosphere CO2 flux,
step 3), the model parameters are optimized using a 4D-var assimilation method. The approach relies
on the minimization of a misfit function J(x) that measures the mismatch between 1) a set of
observations Y and corresponding model outputs M(x), and 2) the values x of the parameters (to
optimize) and some prior information on them xp, weighted by the prior error covariance matrices
on observations R and parameters Pb (Tarantola, 1987):
1
J ( x)  (Y  M ( x)) t R 1 (Y  M ( x))  ( x  x p ) t Pb ( x  x p )
Eq. 1
Within this Bayesian inversion framework, we then account for uncertainties regarding the model
and the observations (through R), and the prior parameters (through Pb), assuming that the errors on
prior parameters and observations follow Gaussian distributions.
The optimal set of parameters is the one that minimize the misfit function. The posterior estimation
uncertainties associated to these optimized parameter values are characterized by the matrix Pb':

Pb '  H t .R 1 .H  Pb

1 1
Eq. 2
Pb' is the posterior error covariance matrix on the parameters. Its determination follows Gaussian
assumptions on the distribution of the parameter values and errors, and assumes that the model is
linear in the vicinity of the solution. The matrix H is the Jacobian matrix of the model M at the
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minimum of J: it quantifies the sensitivity of the model outputs with respect to each parameter
(∂M(x)/∂x).
Finally, we need to asses the impact of the data assimilation on the uncertainties associated to the
state variables, i.e. the carbon fluxes and stocks. Such step involves the propagation of the parameter
error variance-covariance matrix (Pb’) to the state variables. This step is usually performed assuming
linearity of the model around the optimal parameter set. Following the standard rule of error
propagation, the corresponding posterior error covariance matrix on the state variable R'sv can be
expressed as:
R'sv  H sv .Pb '.H sv
t
Eq. 3
Where, Hsv represents the jacobian matrix of the model relating the parameters to the state variables
of interest (fluxes and stocks). Note that this matrix may be different than the H matrix as this later
matrix represents the sensitivity of the observations (which are not necessarily the state variables) to
the parameters.
In the following section we recall briefly for each inversion step, the associated parameters and how
the above uncertainty calculation has been implemented.
2.3 CCDAS components and associated error estimation
2.3.1 Land component (step 1 and 2)
The assimilation system component is based on the ORCHIS tool (described in D410.1) to estimate
the set of ORCHIDEE parameters x that provide the best fit between model outputs and observations.
Its functional description is recalled in Figure 2.
Figure 2: Functional description of the ORCHIS assimilation system for the ORCHIDEE model.
The ORCHIS system can combine several streams of data together. At the end of the iterative process
minimizing the cost function J(X), a routine computes the posterior uncertainties on model
parameters from Eq. 2 (written in FORTRAN-90). The system has been designed in such a way that
any assimilation run requires only simple modification of a configuration file, with various possible
options.
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The user can tune:

the number of parameters to optimize, as well as their respective uncertainty and range of
variation;

the number of observations to assimilate, their temporal resolution, as well as their
respective uncertainty;

the main optimization parameters such as maximum number of loops, termination criteria,
etc.
In the first V0 version of CARBONES CCDAS, we use the multisite version of ORCHIS that allows
optimizing a mean set of parameters using simultaneously information from several measurement
sites. Consequently, the observations state vector is the concatenation of the observations vectors
from all the sites, whereas for the parameters the size of the control variable vector x depends on
the assumptions of “genericity” that are made. The following types of parameters can be considered:

site-specific parameters. These parameters are not considered as generic and therefore vary
for each site considered (ex: the multiplicative factor of soil carbon pools, that is strongly tied
to the site history);

region-generic parameters. They are involved in PFT-independent processes, such as
heterotrophic respiration or energy balance. The control vector x have as many components
as there are regions considered in the optimization;

region-and-PFT-generic parameters. These parameters allow describing the behavior of the
sites located in the same region and sharing the same PFT (ex: the maximum leaf area index,
the maximum rate of carboxylation, etc.).
We have chosen to use ORCHIDEE default parameter values as the a priori information xp on the
parameters (Bayesian term in the misfit function). Furthermore, each parameter has been assigned a
range of variation (minimum and maximum values) in order to constrain the searched solution into
physically acceptable ones. The range of variation depends on the type of vegetation for PFT specific
parameters. The broad ranges of variation (across all PFTs) for each parameter are given in Table 1.
parameter name
lower bound upper bound
Vcmax_opt
17
140
Fstressh
0.8
10
Humcste
0.2
10
Gsslope
0
15
Tphoto_opt_c
5
57
Tphoto_min_c
-10
18
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lower bound upper bound
Tphoto_max_c
18
75
Kpheno_crit
0.5
2
Senescence_temp_c
-5
22
LAI_MAX
1.5
10
SLA
0.004
0.05
Leafagecrit
30
1110
Klaihappy
0.35
0.7
Tau_leafinit
5
30
LAI_init
0.1
10
Z0_over_height
0.02
0.1
Kalbedo_soil
0.8
1.2
Kalbedo_veg
0.8
1.2
So_capa_dry
0.9*1e6
2.7*1e6
So_capa_wet
1.5*1e6
4.5*1e6
Q10
1
3
Moistcont_a
-2
0
Moistcont_b
1.8
6
Moistcont_c
0.1
0.6
Moistcont_min
0.1
0.6
KsoilC
0.25
4
Maint_resp_c
0.1
2
Maint_resp_slope_c
0.04
0.48
Frac_growthresp
0.1
0.5
Dpu_cste
0.1
6
Z_decomp
0.05
5
Hcrit_litter
0.01
5
Table 1: Broad range of variations (across all PFTs) of the ORCHIDEE parameters.
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Assimilation of satellite NDVI products (step 1):
In the first step we assimilate NDVI products derived from MODIS observations over the 2000-2008
period. In V0 version of the CCDAS, ORCHIDEE does not embed any radiative transfer model, so that
we use a simple observation operator to compare ORCHIDEE Leaf Area Index outputs (LAI) to satellite
observations.
The Fraction of Absorbed Photosynthetically Active Radiation (fAPAR) is derived by ORCHIDEE as a
function of the LAI, the latter being computed prognostically by the model at a daily time step:
fAPAR = 1-exp(-0.5 x LAI)
Eq. 4
NDVI and fAPAR are linearly related. As we are more confident in the seasonal behaviour of fAPAR
than in its absolute value, we only account in the misfit function for the normalized values of both
NDVI and fAPAR. To avoid the influence of spurious outliers, we reject values below / above the 5% /
95% thresholds, respectively. As described in the D410.1 report, the satellite data are used to
constrain only few phenological parameters whose respective role on the seasonal cycle is recalled in
Figure 3. Compared to the initial description of the system in the D410.1 report, the LAI_MAX
(maximum leaf area) parameter has been replaced in the optimization by the parameter Klaihappy,
that controls the value of LAI at which plants stop using the carbohydrate reserves. The reason for
discarding LAI_MAX from the optimization is because the assimilation is conducted on normalized
data thus loosing the information from the maximum LAI (or fAPAR) values. As LAI_MAX impacts the
amplitude of the seasonal cycle, we would have changed it value during the optimization process for
any marginal improvement in the phase of the model phenology but no real direct constraint.
Figure 3: Optimized ORCHIDEE phenological parameters
Finally, as explained in the report describing the CCDAS (D410.1), we have chosen to use only a
subset of all possible MODIS measurements for each PFT. Instead of using all grid points with
significant PFT fractional cover, we selected those that have the maximum PFT coverage and that
present enough clear sky measurements to accurately characterize the seasonal evolution of the
vegetation activity. Typically we selected around 10-20 pixel for each PFT.
Deliverable D430.1
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Assimilation of flux measurements (step 2):
Compared to the initial description of the CCDAS in the D410.1 report, we slightly increased the
complexity of this step in order to increase the efficiency of the overall system and in particular of
the last global optimization (step 4). Step 2 now combines two types of observations:

The standard net ecosystem carbon exchange (NEE) and latent Heat flux (LE) measured in situ
for a collection of flux tower sites. The data are described in the report D300.1. We will
assimilate only daily means rather using the high frequency measurements.

Additional NEE derived from a previous 4D-var atmospheric assimilation of atmospheric CO2
concentration (such as described in section 4.4, following Chevallier et al. 2010). The
estimated fluxes are used as pseudo-observations, at a daily time step, and at the spatial
resolution of the atmospheric transport model (LMDz) grid: 3.75°x2.5°. Only a subset of
“pseudo observations” for each plant functional types (on the order of 10) has been selected.
We selected the grid cells that are dominated by the considered PFT (following ORCHIDEE
land cover map).
The use of these additional “pseudo-observations” allows pre-optimizing the ORCHIDEE model. The
objective is to find a set of parameters that already produces net carbon fluxes that are partly
compatible with the seasonal cycle of the atmospheric CO2 concentrations. This approach will help to
reduce the number of iterations in the final global optimization (step 4).
Note that for both types of observation, the daily data are further smoothed using a moving average
window of ±15 days (for the model and the observations) in order to remove high frequency
variations in the data that can not yet be properly captured by ORCHIDEE. Finally, there is on the
order of 50 parameters to be optimized, depending on the set-up.
2.3.2 Ocean component (step 3)
The ocean fluxes are computed as:
aq
atm
Fco2 = Kex * ( PCO2
– PCO2
)
Eq. 5
Where PCO2 is the partial pressure respectively in the sea surface water (aq) and the atmosphere at
the interface to the water (atm), Kex (piston velocity times the solubility) the exchange coefficient


and F the flux directed to the atmosphere.
In this first V0 version we have developed a statistical model based on a neural network technique to
reconstruct the relationship between the Pco2 at the surface water and some variables which are
supposed to control its variations at the first order (see report D410.1 for more details). These
variables are the Seas Surface Temperature (SST), the Sea Surface Salinity (SSS), the Mixed Layer
Depth (MLD), and the CHLorophyll content (CHL).
The atmosphere Pco2 input to the system is taken from an atmosphere inversion model (Chevallier et
al. 2010). Many formulation of the exchange coefficient exists in the literature. They all depend on
the wind speed and the maximum dispersion is obtained for high wind speed.
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For this particular step, we will not use the classical Bayesian error estimation/propagation. The sea
surface water Pco2 calculated from the neural network will be compared to independent Pco2
measurements in order to evaluate the characteristic of the errors: i.e. the shape of the distribution
and an associated standard deviation. The neural network will also be used to derive spatial
correlation between these errors.
2.3.3 Atmospheric component (step 4)
The final step consists in the assimilation of atmospheric CO2 measurements to optimize
simultaneously the ocean and land fluxes, using prior air-sea fluxes for each grid cell from step 3 and
the pre-optimized ORCHIDEE model for the land fluxes (steps 2 & 3). The approach relies on the
iterative minimization of a cost function, following the principles of the four dimensional variational
(4D-Var) systems developed for numerical weather prediction [e.g., Courtier et al., 1994] A single
inversion is performed that covers the 20 years at once. The operator that links the variables to be
optimized (i.e., the surface fluxes) and the observations (i.e., the atmospheric measurements) in the
inversion scheme is version 4 of the LMDZ transport model [Hourdin et al., 2006], nudged to
European Centre for Medium‐Range Weather Forecasts (ECMWF).The scheme is described in more
details in the report D410.1.
Following Chevallier et al. (2007) we rely here on a Monte Carlo approach to estimate the error
statistics of the inverted ocean fluxes (each pixel fluxes): these are reconstructed from an ensemble
of inversions using synthetic data as input. The ensemble is defined in such a way that it rigorously
explores the statistics of the prior errors and of the observation errors. In other words, if the
ensemble of inversions grows, the corresponding ensemble of observations converges toward the
assigned observation error statistics. The same feature applies to the ensemble of the prior fluxes
that converge toward the assigned prior error statistics. By construction, the ensemble of the
inverted fluxes then follows the theoretical error statistics of the posterior fluxes. This feature will be
exploited here with a synthetic 20 year inversion over the same period.
For the errors on ORCHIDEE parameters, we will use the standard approach described in 2.2, with the
linear approximation for the ORCHIDEE model. The computation of Pb’ will be performed with Eq. 2.
The H term will combine i) the adjoint model of the transport model LMDz that provides the
sensitivity of the cost function to all surface fluxes with ii) the tangent linear model of ORCHIDEE (first
version of CARBONES) that provides the sensitivity of these fluxes to the main parameters. In the
future version of the system, we will use the adjoint model of ORCHIDEE (under completion) to
derive more efficiently these sensitivities.
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3. Prior error statistics on parameters and observations
3.1 Land component (step 1 & 2)
3.1.1 Prior error statistics on the parameters
For the determination of the prior error variance-covariance matrix on parameters Pb, only diagonal
elements (variances) are accounted for, because the error correlations between these various
parameters are rather difficult to estimate. Thus, the a priori errors on the parameters are assumed
uncorrelated.
Rather large uncertainties have been assigned to each parameter in order to let the observations
mainly drive the inversion. The Bayesian term has thus a smaller influence on the retrieved values of
the parameters, but it still ensures the stability of the algorithm towards a proper determination of a
unique minimum of the misfit function. The a priori errors on ORCHIDEE parameters are determined
with a generic approach: for a given parameter, the prior standard deviation is set to 40% of its
prescribed definition interval. For the parameters depending on PFT, this implies that the prior errors
have distinct values with respect to the PFT considered
3.1.2 Error statistics on the observations and the model
Only the diagonal elements of the prior variance-covariance matrix on observations R are considered.
Whether the assimilation is performed on satellite NDVI products or on in situ flux measurements,
we have chosen a rather general approach to define the corresponding priori uncertainties: the a
priori estimate of the observation error is set equal to the Root Mean Square Error (RMSE) between
the various measurements (site dependent) and the corresponding ORCHIDEE outputs using the a
priori (standard) parameterization.
Note that the assimilation system let the possibility to further scale these a priori uncertainties,
considering that our ability to make the model and the various observations match should be
consistent with the error statistics we use in assimilation (Gaussian hypothesis).
Assimilation of flux data
The computation of daily means for NEE should, in an ideal case, either put lower weight to data
measured during the night, or keep only daytime values. Indeed, the error associated to night-time
measurements is usually higher than that of daytime observations for several reasons:

atmospheric stratification resulting from low turbulence (calm nights) may result in an
accumulation of CO2 within the canopy which lead to an underestimation of the night-time
net CO2 flux ;
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
the CO2 accumulated can be released suddenly at dawn, turbulence increasing at the nightday transition, which lead to an overestimation of the net CO2 flux ;

these error sources for the CO2 flux at night also concern the other fluxes.
However, the informational content of night-time data on ecosystem heterotrophic respiration is
highly valuable, because this signal then impacts most of the observations in the absence of plant
photosynthetic activity. Given that we choose not to use the information content from the full
diurnal cycle (in order to focus on seasonal time scale), we therefore kept night-time measurements
for the computation of flux daily means.
3.2 Ocean component (step 3)
We describe in this section how are characterized the errors affecting the sea-air fluxes estimated by
the ocean component of the CCDAS CARBONES.
To estimate the error of the flux, we use the formula for flux in Eq. 5 and estimate the error coming
from each term:
dFco2
aq
atm
aq
atm
dKex * ( PCO2
– PCO2
) + Kex * (d PCO2
– d PCO2
)
=
Eq. 6
Eq. 6 can be seen as a formula to propagate the errors coming from the terms of Eq. 5 for each time
step.




aq
atm
aq
atm
Err_Fco2 = Err_Kex * ( PCO2
– PCO2
) + Kex * (Err_ PCO2
– Err_ PCO2
)
Eq. 7
The error from Err_Kex will be expressed from the spread between some different formulations
depending on the wind speed (Figure 4). We notice with this figure that the larger the wind speed,
 between

the larger the difference
the different 
formulation 
of the exchange coefficient. We are thus
currently deriving a formulation to express the error on Kex proportional to the wind speed.
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Figure 4: Spread of the piston velocity depending on the wind speed within different formulations in the literature.
atm
The errors Err_ PCO2
are provided by the atmosphere inversion system and taken in a first
aq
approximation to be negligible. The Errors Err_ PCO2
are estimated from the residual errors measured
on the statistical neural network model. Figure 5 presents below the histogram of the differences
aq
aq
between
 the results of the Neural Network PCO2 and the raw PCO2 data from the Takahashi database
(see more details on these input data in the report D300.1). The histogram indicates that are

statistical model produces non biased estimates with a distribution centred on zero. The spread of
the histogram is also relatively small with 95 % of the data below 10 % errors.

Figure 5: Performances of the statistical model

aq
PCO2
estimator on an independent set of climatological observations.
The x-axis corresponds to the relative error ; the y-axis to the number of observations.
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3.3 Atmospheric component (step 4): error on CO2 concentrations
In this section, we describe the error statistics that will be applied to the atmospheric CO2
concentrations used in the CCDAS. The location of the different stations is described in the report on
the “Input data stream of the CCDAS” (D300.1).
The uncertainty assigned to each observation within the inversion system includes the error of the
measurement, the error of the forward model that simulates it from the parameters to be optimized,
and the representativeness error (i.e. the mismatch between the scale of the measurement and the
scale of the transport model). It is here time-independent: its variance is set to half the variance of
the high-frequency variability of the de-seasonalized and de-trended CO2 time series of the
measurement at a given station (even for two stations - CSJ and KOT -where the data are provided as
daily averages). The high-frequency variability is calculated following Masarie and Tans (1995). The
resulting error varies between a few tenths of a ppm for marine stations and several ppm for
continental ones, reaching 6 ppm at CBW0200 station, in the Netherlands, which means that they are
more than one order of magnitude larger than the measurement errors at all stations. Because of the
large temporal error correlations of the transport models that simulate the measurements in the flux
inversion systems, the continuous measurements have been further de-weighted by multiplying the
observation error by the square root of the number of local data each day. Error correlations are
therefore neglected. This reference set-up is well adapted for flux inversion (Chevallier et al. 2010). It
will be adapted to account for the errors of the ORCHIDEE model that should further lessen the
weight of the observations in the inversion system (increasing their errors).
4. Estimated error statistics from the model-data fusion: parameters
& state variables
As explain in the introduction, the different steps of our model-data fusion approach have not been
all completed yet. Steps 1, 2, and 3 are partially completed while the final step is still in a “test
phase”. We thus describe below, for each step, only preliminary error estimates.
4.1 Assimilation of satellite NDVI (step 1)
In order to illustrate the estimation of posterior errors on model parameters and model state
variables when assimilating NDVI products, we present the results of the multisite inversion focusing
on the Boreal Needleleaf Summergreen PFT. Note that because we choose to optimize only
ORCHIDEE parameters that are dependant on the PFT, we can conduct separate optimization for
each PFT. The results for all PFT is only partially analysed yet and we discuss briefly discuss the typical
result we will obtain.
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The assimilation has been conducted on daily MODIS NDVI products aggregated at 0.7°x0.7° and
available for the 2000-2008 period, for 15 pixels. These pixels have been chosen because of their
thematic homogeneity with respect to this type of vegetation (fraction of Boreal Needleleaf
Summergreen > 50%).
Figure 6 illustrates the error correlation matrix on the optimized phenological parameters (the
correlation matrix is directly estimated from the posterior error covariance matrix on parameters P'b
presented in §2.2, Eq. 2). The analysis of the posterior correlation matrix on parameters indicates the
level of constraint associated to each parameter from the observations that are used. For the
combination of satellite observations over several different pixels considered through the multisite
optimization, the optimized parameters are only slightly correlated. The maximum correlations
between the different parameters are lower than 0.3 in absolute values. The results thus indicate
that there is enough information in the remote sensing signal to resolve the different phenological
stages these parameters are controlling.
Figure 6: Posterior correlations between the estimated phenological parameters for the assimilation conducted on
satellite NDVI data for the 15 sites located inthe Northern Hemisphere.
The propagation of errors in the space of the state variables (fAPAR is chosen as a first example) is
illustrated in Figure 7 for two of the pixels that are used in the optimization. We present the
temporal variation over the 2000-2008 period of the posterior standard deviation (square root of the
diagonal elements of the matrix R'sv, see §2.2, Eq. 3). We can see that the posterior uncertainty on
simulated fAPAR is rather small (usually below 0.015), as compared to the prior observation error
that was set to about 0.4 for all pixels considered. This strong error reduction is directly proportional
to the high number of observations that are used. The posterior error is close to zero in winter, due
to the model insensitivity to variations of the phenological parameters in this season. The variation of
the error during the growing season are mainly associated to the parameter Leafagecrit (controlling
the age of leaves), and to a smaller extent to the parameter Klaihappy (controlling the value of the
leaf area index after which vegetation stops using carbohydrate reserves). The strong error peaks at
the beginning and end of the growing season are attributed to the parameters Kpheno_crit and
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Senescence_temp_c driving respectively the date of leaf onset and the threshold temperature at
which leaves enter in senescence.
The implication in terms of error reduction on the estimated carbon fluxes from the error reduction
on the phenology parameters after the assimilation of MODIS data is only under investigation. These
results will be presented and discussed in a revised version of this report.
Figure 7: Posterior uncertainties on simulated fAPAR time series for two pixels located in the Northern Hemisphere. The
first tree digits of the pixel name relate to the latitude coordinate, the two last digits refer to longitude.
4.2 Assimilation of in situ flux measurements (step 2)
We illustrate in this section the determination of the posterior error on the ORCHIDEE model
parameters for one particular case (one PFT), knowing that the optimization for the other PFTs using
as many sites as possible is only under completion. As noticed above for the first step of satellite data
assimilation the optimization for the different PFTs can be conducted separately given that we
choose to optimize PFT specific parameters. The delay in the different optimizations is partly due to
difficulties in the completion of the optimization system and in the collection of the FluxNet
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observations. The results presented below also do not yet account for the additional “pseudoobservations” from a previous atmospheric inversion, as described in section 2.3.1. They are
conducted with daily variations of Net Ecosystem CO2 Exchange (NEE) and Latent Heat (Qle) fluxes
measured on the sites.
Figure 8: Locations of the measurements sites used for the optimization. The yellow and green latitude bands are the
regions used to group the parameters.
The results are presented for assimilations performed with twelve sites representative of the
Temperate Broadleaved Summergreen ecosystem, and distributed in two predefined regions
corresponding to the Northern and Southern hemispheres (Figure 8). All sites have more than 70% of
their vegetation represented by temperate deciduous broadleaved forests, the rest of the biomass
being C3 grasslands. We illustrate below only the results for the multi-sites assimilation conducted on
the sites located in the Northern Hemisphere region (green region of Figure 8).
The performances of the multi-site assimilation approach, in terms of optimized parameter values
and corresponding posterior uncertainties, is presented in Figure 9. The results are compared to
results of the assimilations conducted on each site separately (single site optimization versus multisite optimization).
The notion of "parameter genericity" varies with the parameters considered. For some, the
estimated values following the multisite optimization is an average (within the estimation
uncertainty) of the individual values obtained with the single-site assimilation approach: Vcmax_opt,
Fstressh, Tphoto_opt_c, SLA, Tau_leafinit, etc., for instance. Considering that the model fit to the
data after the optimization is very similar in the single-site and multisite approaches (though slightly
better in the case of the single-site assimilation), this points out that a common set of parameter
values may be derived for the various sites considered.
On the other hand, other parameters show very strong site dependencies, that the multisite
assimilation fails to resolve: Gsslope (slope of the stomatal conductance), Kpheno_crit, Leafagecrit,
Q10, etc. For the parameters depending on PFT, this can indicate that the type of vegetation is
actually different between the sites considered (i.e. different species with different behaviours), due
to a strong influence of the local climatic drivers, soil characteristics, physiological properties,
management histories, contrary to our prior assumptions that they all share the same generic PFT
concept with the same parameters. Note that this feature can also be related to the numerical
assimilation procedure, that can fail to capture the global minimum of the misfit function due to non-
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linearities and/or numerical accuracy. For instance, the sensitivity of the model to the phenological
parameters Kpheno_crit and Senescence_temp_c, is computed with a finite difference approach that
is less accurate than the use of the tangent linear model of ORCHIDEE (used for the other
parameters).
Figure 9 (see next page): Optimized values of the parameters for the assimilation conducted on the sites of the
Northern Hemisphere region. Prior values and uncertainties are in thin black, multisite optimized values and
uncertainties in thick black, and each local values and uncertainties in thick color.
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Figure 10 presents the posterior correlation matrix on some of the optimized parameters. It generally
exhibits rather low correlations between the various parameters. One can note strong error
correlations between the different site dependant KsoilC parameters controlling the amount of soil
carbon pools. From a general point of view, the highest correlations are obtained for the parameter
involved in the same processes. This is for instance the case for Fstressh and Humcste, both
governing plant hydric stress, or for the parameters tightly driving photosynthesis (Vcmax_opt the
maximal rate of carboxylation, Gsslope the slope of stomatal conductance, and Tphoto_opt_c
determining the temperature at which photosynthesis is optimal). The correlation gauges the level of
interaction between the parameters. High correlation values indicate that the corresponding
parameters cannot be resolved with the observations that are currently used.
Such matrix is important to analyse in order to assess the potential of the overall assimilation process
and especially not to over-interpret the results. The correlations also highlight the parameters and
thus the processes that are not well constrained by the chosen set of observations. For this particular
case, it points to the need of specific measurements to optimize separately the parameters
controlling the above ground respiration (growth and maintenance) versus the below ground
heterotrophic respiration. These could be soil chamber measurements.
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Figure 10: Posterior correlations between the estimated parameters for the assimilation conducted on the sites of the
Northern Hemisphere region.
The propagation of the estimated error on the parameters onto the space of the state variables is
showed in Figure 11. It presents the temporal variation of the posterior uncertainty (standard
deviation) on the Net Ecosystem CO2 Exchange (NEE) and Latent Heat (Qle) fluxes for four sites (on
the specific period where observations are available at each site).
Once again one can observed a strong reduction of the error, considering that the prior error on NEE
and Qle is respectively on the order of 2 gC/m2/day and 20 w/m2. Except for the Willow Creek site
(US-WCr), the temporal variation of the posterior uncertainty mimics the seasonal cycle for NEE
whereas this feature is less pronounced for Qle. For the latent heat flux, the error exhibit stronger
synoptic variations. For NEE, the higher errors are obtained during the peak of the growing season,
where photosynthesis is maximum. This is link in particular to the error on the parameters that
control the maximum photosynthetic capacity and its dependency to temperature and soil moisture.
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These results still need further investigations. In particular we need to derive the errors associated to
the annual and seasonal carbon fluxes for individual sites like in Figure 11, but also for the total
carbon flux of a given region. This is the particular objective of step 4 of the current V0 version of the
system and it will only be fully achieved in the coming months.
Figure 11: Posterior uncertainties on simulated NEE and latent heat fluxes for four sites located in the Northern
Hemisphere region: Hainich (Germany), Soroe (Danemark), Hesse (France), and Willow Creek (USA)
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4.3 Assimilation of ocean Pco2 data (step 3)
Step 3 of the sequential CCDAS approach consists in the provision of net air-sea carbon fluxes from
aq
an ensemble of observations including in particular PCO2
data. Section 3.2 described the principle of
the approach and the errors associated to the input fields: errors on the exchange coefficient Err_Kex
aq
and on the partial pressure of CO2 at the surface of the ocean Err_ PCO2
.
From the different terms of Eq. 7 (see §3.2),
 we can derive a covariance matrix on the flux V_Fco2 by
doing a temporal mean from the respective error estimate at each time step:
V_Fco2 = E ( Err_Fco2 - E(Err_Fco2) )T ( Err_Fco2 -
E(Err_Fco2) )
Eq. 8
With this approach, we take the assumption of a temporal constant error covariance matrix. This
matrix will characterize only the spatial covariance of the error on the fluxes.
Given that the error estimation on the fluxes is only under completion, we will describe them in a
more comprehensive way in a next version of this report.
4.4 Assimilation of atmospheric CO2 data (step 4)
The final step of the overall model-data fusion, i.e. the assimilation of the atmospheric CO2
observations to adjust simultaneously land and ocean fluxes, is not completed yet. Indeed we faced
some technical problems and the system is currently only in the test phase (see report D410.1 for
more details on the reason of the delay).
Thus, we only provide below some typical uncertainties that would arise from this last step. For that
purpose, we used the set up of Chevallier et al. (2010), and performed a classical atmospheric
inversion with the same atmospheric CO2 data as constraint, the same transport model (LMDz), but
solving for the weekly land and ocean surface fluxes at the resolution of the transport model (3.75 x
2.5 degrees). The first V0 version of CARBONES will only replace the land component by the
ORCHIDEE model, solving for model parameters rather than the fluxes themselves. We first describe
the uncertainties obtained in this configuration and then discuss the expected modification with our
CCDAS set up.
Figure 12 illustrates the uncertainties obtained by the system for a 20 year inversion. As explained by
Chevallier et al. (2007), the Monte Carlo approach yields an estimate of the degree of freedom for
signal (DOFS) of the observation system. The DOFS quantifies the number of independent quantities
about the fluxes that the inversion system exploits. In this case it is about 400 per year. The
distribution of the fractional uncertainty reduction over the globe (Figure 12b and Figure 12c) shows
where in space the 400 information pieces lie. Further, these maps quantify the knowledge brought
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by the surface measurements on the CO2 weekly surface fluxes for the first (1988–1997) and second
(1998–2008) decades of the study. The fractional uncertainty reduction is defined as 1 minus the
ratio of the posterior error standard deviation to the prior error standard deviation. A value of 0
indicates that the observations have not provided any information to the prior. A value of 1 would be
reached if the observations gave a perfect knowledge about the fluxes. The impact of the
measurements results from the combination of assigned prior errors, assigned observation errors,
observation density, and transport characteristics. It is mostly located in the vicinity of the stations,
with values larger than 30% at continuous stations like in eastern Canada, in South Africa, and in
Finland. The difference between Figure 12b and Figure 12c mainly reflects the evolution of the
network between the two decades, with several stations added to the network.
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Figure 12: (a) Quadratic mean of the standard deviation of the errors of the prior weekly fluxes (gC m −2) per day)
throughout the 20 years. Expected uncertainty reduction in each grid point provided by surface stations for estimation of
8-day-mean CO2 surface fluxes for the periods (b) 1988–1997 and (c) 1998– 2008. The reduction is defined as [1 − (sa
/sb)], with sa the quadratic mean of the posterior error standard deviation and sb the prior error standard deviation.
The impact appears to be larger when the fluxes solved in each grid point and 8 day period are
aggregated in space and time. Figure 13 presents it at the scale of the widely used 22 TransCom3
regions of Gurney et al. (2002) and for weekly, monthly, and yearly averages for the second decade.
In the mid‐ and high latitudes of the Northern Hemisphere lands, where most stations are located, all
regional flux estimates are improved by more than 20% and by up to 60% (North American Boreal,
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North American Temperate, and Eurasian Boreal regions with annual fluxes). As an example, for the
TransCom3 “Europe” region the inversion theoretically reduces the flux uncertainty from 1.0 to 0.6
GtC.yr−1. The figures for the lands in the tropics and in the Southern Hemisphere are between 10 and
30%. Over ocean basins the reduction lies between 0 and 25%.
Figure 13: Expected uncertainty reduction provided by surface stations for estimation of CO 2 surface fluxes in the 22
TransCom3 regions for the period 1988–2008. As in Figure 13 the error reduction is defined as [1 − (sa /sb)], with sa the
posterior error standard deviation and sb the prior error standard deviation. Results for weekly (blue bars), monthly (red
bars), and annual (green bars) fluxes are shown. Note that for annual fluxes, sa and sb are computed on an ensemble of
21 realizations of the yearly errors only.
The inversion spreads a sink of a few GtC.yr−1 over the lands to yield the CO2 growth rate seen by the
measurements. This large negative increment varies in space and in time. For instance, in the North
American Boreal region, the mean budget remains around 0 throughout the years before and after
the inversion, while the inversion reduces the North American Temperate budget by a few tenths of
a GtC.yr-1 without a noticeable trend and increases a positive trend in the Eurasian Temperate region.
However, even at the regional/continental scale the carbon fluxes are still uncertain with few
significant error correlations between adjacent regions. Figure 14 illustrates the monthly error
correlations between the “classical Transcom3 regions”. For example, the location of the European
flux increment could well be placed in Eurasia instead of Europe, given the strong negative
correlation between these two regions. A larger observation network toward Eastern Europe and
Siberia would be needed to resolve this ambiguity. Note that the correlations computed for yearly
fluxes were found to be hardly reliable because the size of the ensemble in this case (21 members) is
too small, but we expect that they behave similarly to the monthly flux correlations shown here. For
more details see Chevallier et al. 2010.
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Figure 14: Correlations between the posterior uncertainties of the monthly regional fluxes aggregated at the scale of the
11 Transcom3 land regions. Names are abbreviated.
Expected changes of the error statistics with our CCDAS set-up:
The optimization of ORCHIDEE parameters instead of the biospheric fluxes themselves is expected to
have significant impacts both on the land fluxes and on their uncertainty. We summarize below the
expected outcomes:

First the use of model will avoid the problem of changing the observation network size. In the
case of an atmospheric inversion, the appearance of a new station usually induces abrupt
changes in the spatial distribution of the surface fluxes. Such artefact will disappear when
solving for parameter that control the fluxes for the entire period, because the optimization
of parameters associated to Plant Functional Types (13 different PFTs) induce strong
correlations between all fluxes of a given PFT.

As a consequence, the spatial distribution of the error reduction, illustrated in Figure 12 for
the standard atmospheric inversion, will be much smoother spatially.

The magnitude of the error reduction is likely to be also much larger than illustrated above.
Indeed with only around 50 parameters, the number of degrees of freedom of the inversion
is much smaller than with the optimization of all grid-cell fluxes (even with spatial prior error
correlations).

Finally, the error correlations between the flux errors of regions sharing similar PFT will be
much larger than those depicted in Figure 14 with the classical flux inversion.
All these changes will be presented and discussed in a revised version of this report.
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5. Summary and perspectives
5.1 Summary of the error estimations
This report should be considered as preliminary, given that the different steps are still under
completions. More specifically, the final step (system under verification) will only be launched after
finalization of the previous steps. We will thus update the current report within the next 6 months.
However the above results/analysis already highlights the potential of the CCDAS version 1, in terms
of error estimates on the parameters that are optimized and on the targeted state variables (mainly
the carbon fluxes).
For the land component, the error associated to the different ORCHIDEE parameters will likely be
rather small given the large number of observational constraints, compared to the number of
unknown parameters. The large error reduction will induce a large error reduction in the state
variables simulated by ORCHIDEE, i.e. the carbon fluxes and stocks of large regions.
For the ocean fluxes, our first two steps approach, with the computation of prior fluxes from a large
set of Pco2 data and the final optimization of each model grid-cell air-sea fluxes (using the
atmospheric CO2 data) is likely to bring smaller constraint than for the land fluxes (much more
unknowns) and thus larger errors. However, the next version of the CCDAS (V1) will move towards
the optimization of few parameters controlling the air-sea fluxes, rather than the fluxes themselves.
This will reduce the number of unknowns and thus enhance the ratio of observations versus
parameters.
However, the posterior errors on the estimated parameters are directly linked to the assigned prior
errors and to the errors assigned to each data stream. Given that these errors are difficult to
estimate, the errors returned by the CCDAS should also be interpreted with some caution. As
discussed in Santaren et al. 2007, the ratios between the uncertainties of the different parameters
are likely to be more robust than the absolute values. As a consequence, the spatial and temporal
variations of the errors associated to the fluxes (state variable) are also more robust that the flux
uncertainties themselves.
5.2 Future assimilation of biomass data
We now provide an example of the future use of biomass data to constrain more directly the
modelled carbon stocks. In this example, we describe a preliminary study with ORCHIDEE, based on
the assimilation of above ground biomass at one site (Le Bray).
Le Bray is a maritime pine forest located close to Bordeaux. It has been planted in 1970 and some
thinning has been done during the past 40 years. Note that it also suffered severe storm damages in
1999. Aboveground biomass data was available for all years between 2004 and 2007. The ORCHIDEE
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model was first run into equilibrium using the classical spin-up approach (recycling the meteorology
for 1000 years to equilibrate the soil carbon pools), after which the tree biomass was clearcut. The
forest was then grown to the realistic age of the forest (40 years).
With this simulation we clearly see that the model overestimates the aboveground biomass (Figure
16). In a next step, three model parameters related to the allocation of NPP to aboveground biomass,
leaf biomass and root biomass were optimized using the same method than described above. These
parameters are the residence time that describes the turnover rate of woody biomass and two
allocation parameters. The allocation parameter r0_opt affects the amount of biomass transferred to
fine roots, and the allocation parameter s0_opt the amount of biomass allocated to sapwood.
Uncertainties on those three parameters were greatly reduced after the optimization (Figure 15).
Estimation of the aboveground biomass by the model is significantly improved after the assimilation
(Figure 16).
The associated errors on both parameters and carbon stock (Figure 15 and Figure 16) are largely
reduced by the optimization. Such error reduction illustrates the potential of the biomass data given
the small number of observations (one estimate each year) in terms of additional model constraint
given that the eddy-covariance measurements and the satellite data will carry smaller information on
partition between above ground and below ground biomass. These data will thus be considered as
the next data stream to assimilate in the future version of the CCDAS.
Figure 15: A priori and a posteriori allocation parameter values and their uncertainties.
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Figure 16: Measured and modeled aboveground biomass before and after the optimization. The uncertainties on the
biomass state variable is indicated: 2 sigma values are plotted for the prior and posterior model outputs and for the
observations.
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6. References
Courtier, P., J.‐N. Thépaut, and A. Hollingworth (1994), A strategy for operational implementation
of 4D‐Var, using an incremental approach, Q. J. R. Meteorol. Soc., 120, 1367–1387,
doi:10.1002/qj.49712051912.
Chevallier, F., P. Ciais, T. J. Conway, T. Aalto, B. E. Anderson, P. Bousquet, E. G. Brunke, L. Ciattaglia, Y.
Esaki, M. Fröhlich, A.J. Gomez, A.J. Gomez-Pelaez, L. Haszpra, P. Krummel, R. Langenfelds, M.
Leuenberger, T. Machida, F. Maignan, H. Matsueda, J. A. Morguí, H. Mukai, T. Nakazawa, P. Peylin, M.
Ramonet, L. Rivier, Y. Sawa, M. Schmidt, P. Steele, S. A. Vay, A. T. Vermeulen, S. Wofsy, D. Worthy,
2010: CO2 surface fluxes at grid point scale estimated from a global 21-year reanalysis of
atmospheric measurements. J. Geophys. Res., 115, D21307, doi:10.1029/2010JD013887
Chevallier, F., F.‐M. Bréon, and P. J. Rayner (2007), The contribution of the Orbiting Carbon
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