Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
1/29
Error estimation: parameter error on base configuration and error
on output field
Table of content
1
Introduction ____________________________________________________________ 2
2
Principle of error calculation and error propagation ____________________________ 3
3
Analysis of model structural error for ORCHIDEE _____________________________ 4
4
3.1
Principle of the approach ___________________________________________________ 5
3.2
Results: Temporal structure of the errors on the NEE ___________________________ 6
3.3
Results: Spatial structure of the errors on the NEE ______________________________ 8
3.4
Results: overall model structural error ________________________________________ 9
Parameter errors estimated after MODIS-NDVI and FluxNEt data assimilation ____ 10
4.1 The error on the annual NEE obtained from the propagation of the parameter error onto
the flux error, for each site.Tropical broadleaf evergreen forests _______________________ 10
5
4.2
Temperate coniferous evergreen forests ______________________________________ 12
4.3
Temperate broadleaf evergreen forests _______________________________________ 14
4.4
Temperate broadleaf deciduous forests _______________________________________ 15
4.5
Boreal coniferous evergreen forests __________________________________________ 17
4.6
Boreal broadleaf deciduous forests ___________________________________________ 18
4.7
C3 grassland _____________________________________________________________ 20
Error on global carbon fluxes _____________________________________________ 22
5.1
Set up of the error propagation _____________________________________________ 22
5.2
Error maps on the NEE ____________________________________________________ 22
6
Conclusion and perspectives ______________________________________________ 26
7
References _____________________________________________________________ 27
8
Annexes: ______________________________________________________________ 28
8.1
Distribution of the PFT fractions ____________________________________________ 28
1
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
2/29
1 Introduction
This report includes two initial deliverables linked to the error assessment: D430.1 on parameter
errors on the base configuration and D430.2 on error on output field. Given the tight links between
estimated parameter errors and their impact on the output fields we grouped these two analyses in a
single document with error assessment.
The errors on the land surface model parameters were estimated through a step-wise (or sequential
approach) that is recalled in figure 1.1.
Figure 1.1: Sequential assimilation of the different data streams into 4 steps.
Given the delay in the finalization of step 4 with the correction of the ORCHIDEE land surface model
parameters (using atmospheric CO2 data), we present in this report a first analysis based on the
parameter uncertainties from step 2. These uncertainties account for MODIS-NDVI data (step 1) and
for FluxNet data (net carbon exchange and latent heat flux; step 2).
At the final meeting or for a revision of this deliverable, we will provide an uncertainty analysis based
on the results of step 4. Note, that step 4 adds new parameters linked to the initial soil carbon pool
sizes (compared to step 2) for an ensemble of 50 regions and includes only a small set of parameters
that were considered in step 2 (3 parameters per Plant Functional Type). Overall, the preliminary
analysis presented in this report should still capture the main feature of the parameter errors and
their impact on the outputs.
We present below:

brief description of the methodology used for parameter error estimations and their
propagation on the output variables,

a specific study that was performed to adjust the model error in the optimization with
FluxNet data (step 2) and that highlights the contribution of model structural error versus
parameter errors to the overall model error,
2
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
3/29

the results for step 2 with the parameter errors obtained for each PFT,

the impact of these parameter errors on the net carbon fluxes, at global scale.
2 Principle of error calculation and error propagation
The concept of the CARBONES project relies on the use of a Carbon Cycle Data Assimilation System
(CCDAS) to optimize internal parameters of a dynamical model of the global carbon cycle (Kaminski
et al., 2002; Rayner et al., 2005; Scholze et al., 2007).
The problem has been formulated following the Bayesian probability theory. In this framework,
several hypothesis were made to solve the inversion problem and further estimate the model
parameter uncertainties:

All errors (parameters, model, measurements) were assumed Gaussian,

The land ecosystem model was linearized at the minimum of the cost function in order to
compute the posterior uncertainties on the parameter following the linear assumption (see
for instance Tarantola 1987)
With the linear assumption, the posterior error variance-covariance matrix Pb' on the estimated
parameters is expressed as a function of the a priori error variance-covariance matrices on the
parameters Pb and on the observations R, as well as a function of the Jacobian matrix of the model H
describing the sensitivity of the different outputs to the parameters that are optimized. Note that R
includes both the measurement errors and the model errors (see detailed discussion in section 3).
The expression for Pb' is:

Pb '  H t .R 1 .H  Pb

1 1
(1)
Such formulation may involve a potentially very large matrix H that has the dimension: nobs x npar
with nobs being the number of observations and npar being the number of parameters. Depending
on the number of observations or parameters the size of H may become prohibitive.
For each step of the sequential approach we have:

Step 1 and step 2: in these cases the number of parameters and the number of observations
were relatively small (few hundreds) so that we could easily estimate Pb' with equation (1)

Step 4 (with atmospheric CO2 data): In this case H becomes the product of a Jacobian matrix
for the ORCHIDEE land surface model with the Jacobian matrix from the transport model.
Given the size of these intermediate matrices we were only able to derive the uncertainty
for a restricted period. The calculation for one year of atmospheric observation is underway
and results should be presented at the final meeting.
3
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
4/29
After the computation of the error variance covariance matrix on the parameters, we can directly
derive the errors on the output variables due to parameter errors (error propagation) and especially
characterize the errors on the net CO2 fluxes. Such standard error propagation follows the matrix
product:
R'  H .Pb '.H t
with R’ being the error variance covariance matrix on the outputs. Note that in this case H will only
correspond to the Jacobian of the ORCHIDEE land surface model, as the targeted quantities are the
net ecosystem fluxes.
In the following sections, we compare the estimation of R' accounting for either 1) the a priori
estimate of B (hence Rprior') or 2) the posteriori error variance-covariance matrix on the parameters
after optimisation (Rpost'). The square root of the diagonal elements of R' corresponds to the standard
deviation  on the output quantity. In order to appraise the knowledge improvement brought by the
assimilation, the error reduction is determined as 1   posterior  prior .


3 Analysis of model structural error for ORCHIDEE
The use of a Carbon Cycle Data Assimilation System (CCDAS) to optimize internal parameters of a
dynamical model of the global carbon cycle offers the advantage to potentially use a much larger
diversity of observations than the standard flux correction using atmospheric data (atmospheric
inversion). The downside of this strategy is the interference from the errors of the model equations
in the data assimilation process. Indeed the choice of a process-based approach imposes these
equations as a strong constraint to the inversion, even though they are an imperfect representation
of the biophysical and ecophysiological mechanisms that drive terrestrial ecosystems.
Using the Bayes’ theorem to build the CCDASs, implies characterizing the uncertainties of each
CCDAS component:
1. the measurement error;
2. the model error, which stems from inappropriate equation forms or from missing processes
in the carbon- cycle model structure;
3. the error brought by the meteorological and vegetation forcing data, here considered as a
part of the model error;
4. the parameter error, arising from inadequate knowledge about a series of parameters.
Following the usual convention, what we call the observation error is the sum of the measurement
error and the model error (i.e., the first three items in the above list). The overall objective of
CARBONES was to optimize the model parameters, so that “type 4” errors would be reduced as much
as possible. However, “type 2 and 3” errors are usually considered as large and they are poorly
4
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
5/29
quantified. If the model structural errors dominate, this would somehow reduce the potential of the
CCDAS and could critically hamper the predictability of the optimized ecosystem model.
In this section, we try to assess the ORCHIDEE model structural error using the FluxNet observations
(Net carbon ecosystem exchange) from several sites of a given Plant Functional Type: temperate
deciduous broadleaf forests.
3.1
Principle of the approach
Denoting as “prior” the state of the carbon-cycle model before any observational constraint, we
analyze the statistics of the prior residuals (observations minus prior simulations) with the help of the
assigned prior parameter uncertainties projected in the observation space. Within the Bayesian
framework, these two pieces of information and the observation error, which is the summed
contribution of model and measurement errors, are linked together. We then take advantage from
previous studies that have characterized the uncertainties of the measurements (e.g., Richardson et
al., 2008) to isolate the model structural error.
Defining the prior state xprior as the vector of prior parameters, the prior model output (the daily NEE)
is given by H (xprior ), where H is the observation operator. Assuming the linearity of the model in the
vicinity of the prior state, we introduce the Jacobian matrix H that corresponds to the linearised
version of H. With normally distributed and uncorrelated prior-parameter and observation errors, we
can write (e.g., Desroziers et al., 2005):
H.B.HT + R = D
(1)
where, H.B.HT is the projection of the prior parameter error covariance matrix B in the observation
space, R is the covariance matrix of the observations errors (i.e., model errors + measurement
errors), and D is the covariance matrix for the distribution of the residuals from the prior model doprior (i.e., the observation-minus-model mismatch), defined as :
do-prior = yo − H(xprior)
(2)
where yo is the observation vector (daily NEE in our case). R is composed of two terms: Rmeas the
covariance matrix of the measurement error and Rmod the covariance matrix of the model error. Their
respective contribution to the total observation error budget will be discussed.
An additional diagnosis makes use of the optimised model state, i.e., the NEE fluxes after the
optimisation of the model parameters x (following the results of step 2 of our sequential CCDAS) to
directly derive an estimate of R:
Rpost = F
(3)
where F is the covariance between the prior residuals do-prior (see above) and the posterior residuals
do-post. The latter is defined as (Deroziers et al., 2005):
do-post = yo− H(xpost)
(4)
5
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
6/29
The prior and posterior diagnoses proposed in these two approaches are respectively the starting
points toward a prior estimation of the covariance matrix of observation errors (i.e., model errors +
measurement errors) Rprior and a posterior estimation Rpost. With an independent knowledge of Rmeas
we can thus derive in this particular case Rmod, the quantity that is being sought.
3.2
Results: Temporal structure of the errors on the NEE
Figure 3.1 shows the temporal autocorrelation structure of the prior residual (observation minus
simulation) and of the prior parameter error projected in the observation space (first term of Eq. 1),
for the different FluxNet sites. The two curves represent the all-site median values, using 1-day bins.
The correlation structure reveals a similar seasonal pattern in both cases, with ever positives values,
larger at short lags and at lags close to one year. For the parameter error, the moderately high
correlation at the one-year lag (0.44) indicates that inappropriate parameter values controlling
seasonal processes (e.g., the maximum photosynthetic capacity) affect the seasonal pattern of NEE in
the same direction each year.
The autocorrelation of the prior-parameter error (projected in the flux space) is generally larger than
that of the prior residual. The all-site correlation of the prior residual falls below 0.5 after 7 days and
reaches a nearly stable value around 0.12 for lags between 50 and 330 days. The more persistent
autocorrelation of the prior parameter error can be linked to the small size of the state vector. In our
case, as in most optimisation studies (Williams et al., 2009), the number of tuned parameters is
rather small, which keeps the number of degrees of freedom low.
The correlation of the prior residual error is above that of the prior-parameter error for lags between
120 and 230 days correlation, with in particular a bump around the 150-day lag. This last feature
comes from an overestimation of the growing season length in ORCHIDEE: the NEE residual
(observation minus simulation) tends to be negative both at the beginning and at the end of the
growing season, with the temporal distance between these two events being about 150 days.
6
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
7/29
Figure 3.1: All-site median of the autocorrelation of the residuals from the prior ORCHIDEE model (black, corresponding
to D in Eq. 1) and of the prior-parameter error projected in the flux space (purple, corresponding to HBHT in Eq. 1), as
functions of the time lag, for daily NEE.
Figure 3.2, shows the autocorrelation of the observation errors (model + measurement errors)
computed at each site (median of all sites), for different approaches (prior diagnostic with linear
assumption or ensemble approach and posterior diagnostic). One can notice a very rapid decrease,
since after one day the correlation falls to a ten-day long plateau at 0.4, and then decreases to reach
0.1 after one month. For larger lags, the correlation is mostly negligible although there is a bump
reaching almost 0.4 around the 150-day lag and a weaker one around the 220-day lag. These last two
features originate from the prior residual error and are not significant in the posterior diagnostic. The
seasonality of the observation error correlation is also significant, although similar to both the prior
residual and the prior-parameter error for large time lags.
In figure 3.2, the grey curve shows autocorrelations corresponding to the posterior diagnosis. For lags
shorter than 100 days or longer than 250 days, there is a remarkable consistency with the
observation error statistics diagnosed a priori (orange curve). Elsewhere, it is nearly uncorrelated and
only weakly reproduces the two bumps (around the 150-day and 220-day lags) mentioned above. It
indicates that these features are most probably only partially related to the model error. Instead, this
particular correlation structure may be present in the structure of the prior parameter error, but is
currently ignored due to the prior parameter diagonal assumption made in the inversions.
7
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
8/29
Figure 3.2: All-site median of the autocorrelation of the observation error (i.e., model error + measurement error) R,
estimated at each site with three methods: prior diagnostics with the linear assumption (orange, Rprior, from Eq. 1), prior
diagnostics with ensemble simulations (blue, Rprior, from Eq. 1), and posterior diagnostics (grey, Rpost, Eq. 3).
3.3
Results: Spatial structure of the errors on the NEE
The spatial footprint of the observation error without time lag is shown by the distance correlogram
in Fig. 3.3, using the posterior diagnosis (Eq. 3), which provides a better numerical stability than the
prior diagnosis of Eq. (1). Each point in Fig. 3 represents a pair of sites that have at least one year of
data in common. The all-site median is calculated using 400-km bins. It shows a declining spatial
structure of the correlation within the first 500 km, where it remains larger than 0.4, while it
converges toward zero for larger lag distances. Since all sites present the same dominant PFT and
since the spatial correlations of the measurement error is considered as negligible, we suggest that
the inferred spatial structure of the observation error derives from the model error and that the
correlation decline originates from the meteorology. This spatial structure can be approximated by
an exponential decay, with an e-folding length of 500 km in the flux space (black dotted line in Fig. 3).
8
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
9/29
Figure 3.3: Distance correlogram of the observation (model+measurement) error Rprior estimated from Eq. (1), using pairs
of distant sites for a same time. The value represented by each blue diamond includes all the common years of one site
pair. The thick black line represents the overall median using 400-km bins, and the dotted line an exponential decay with
an e-folding length of 500 km.
3.4
Results: overall model structural error
Overall, the median standard deviation of the prior residual is equal to 2.1 gC m−2 d−1 when
combining the sites altogether, while the median prior-parameter error contributes to an uncertainty
of 1.3 gC m−2 d−1 in the observation space. This latter value is not negligible, which indicates that the
current uncertainty on the main model parameters induces a significant uncertainty on the simulated
NEE.
The median standard deviation of the observation error is estimated to be 1.7 gC m−2 d−1 (using eq.
1). This number combines measurement and model contributions. Using measurements across
different types of forest ecosystems, Richardson et al. (2008) found that the random measurement
errors range approximately from 0.2 to 0.8 gC m−2 d−1, being somewhat proportional to the absolute
flux magnitude, which means that the variance due to the measurement errors accounts for 1 to 25
% of the total observation variance. Additionally, Lasslop et al. (2008) showed that no significant
measurement error correlation remains at the daily time scale. From these elements, we conclude
that the seasonal structure of the model structural error in ORCHIDEE is very similar to that of the
observation error described above (the orange curve in Fig. 3.2), with a standard deviation ranging
from 1.5 to 1.7 gC m−2 d−1. The estimated structure notably indicates that the model error is
somewhat correlated across seasons: for instance, any underestimation /overestimation of the NEE
in summer or winter remains the following year. Finally, the posterior diagnostic lead to a standard
deviation of the observation error equal to 1.9 gC m−2 d−1 (equation 3 and 4), somewhat higher than
that brought by the prior diagnosis.
Overall the model structural error is not negligible with a typical standard deviation of 1.6 gC m-2 d-1
and temporal correlations with seasonal patterns (following the graphs shown above). We should
thus always keep in mind this type of error when applying a CCDAS with a terrestrial model similar to
ORCHIDEE. These results are detailed in a recent article, Kuppel et al. 2012.
9
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
10/29
4 Parameter errors estimated after MODIS-NDVI and
FluxNEt data assimilation
The errors discussed in this section correspond to those obtained after step 2 of the sequential
approach. Note that we have tested several cases with different numbers of parameters in the
optimization. We present below the results with the highest number of parameters. For each PFT we
will briefly discuss:
4.1

The standard deviation of the errors on the retrieved parameters, together with the
parameter values. The errors obtained from the multi-site optimization (all sites for a given
PFT at once, MS) are also compared with the errors from optimization where each site was
considered independently (SS)

The error correlation between the different parameters.
The error on the annual NEE obtained from the propagation of the parameter error onto the
flux error, for each site.Tropical broadleaf evergreen forests
Figure 4.1 compares the prior parameter mean and standard deviation with the posterior single- and
multi-site values. For most of the parameters, the parameter uncertainty does not decrease postoptimization, with the exception of Vcmax,opt and Gsslope, and SLA, LAI_init and leafagecrit for
some sites. Vcmax,opt and Gsslope are negatively correlated (figure 4.2 left), suggesting that a
unique parameter set has not been found by the optimization and therefore the lower posterior
uncertainty may represent over-fitting to the observations.
The posterior value in the multi-site (MS) optimization does not often correspond to the average of
the single-site (SS) optimizations, and can be outside the range of the SS optimizations (e.g. Vcmax,
opt, leafagecrit, Z_decomp). This suggests that taking the posterior parameters from SS optimizations
and averaging to get a global parameter value is not an appropriate method to follow. The fact that
the posterior fluxes resulting from the MS optimization mostly correspond to that of the SS is
encouraging however, in that it suggests a global optimized parameter set can be found.
Other than the parameters involved in photosynthesis (Vcmax,opt, Gsslope, cTopt, cTmin, cTmax), which
show both negative and positive correlations, parameters involved in the determination of LAI (SLA
and leafagecrit, and in some cases LAIinit) are also strongly negatively correlated. So are parameters
that are involved in the computation of the different respiration terms, as MRa and MRb, HRH,b and
HRH,c, and fstressh and Humcste, which is to be expected. It is unclear why the Ksoilc parameters, which
are optimized on a site-by-site basis, show such a strong correlation. This is being investigated
further.
10
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
11/29
Figure 4.1: Values and uncertainties of optimized parameters for tropical evergreen forest: The a priori is in grey (with
several values when the parameter is not generic across sites), the multi-site optimization (MS) is in black, and the monosite optimizations are in colors (see the legend).
11
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
12/29
Figure 4.2: Left: Error correlation matrix for the optimized parameters; Top Right: annual mean fluxes for each site for the
observations, the prior model (in grey) and the optimized model (in blue); Bottom Right: Error on the annual fluxes
estimated from the parameters error covariance matrix for prior (in grey) and posterior (in blue) error matrix.
The right hand panel of Figure 4.2 shows the parameter uncertainty projected to the annual NEE
fluxes, compared to the annual NEE balance. There is a 80 – 90% reduction in the uncertainty,
however the posterior uncertainty is likely underestimated as this does not account for model
structural errors as discussed in the previous section.
4.2
Temperate coniferous evergreen forests
In general the parameters that have a lower range in the posterior mean value for the SS
optimizations (e.g. cTmax and MRb in figure 4.3) are the same as for tropical broadleaved evergreen
forests, and vice versa for those that do not. This gives insights into which parameters are more
global, and which may require optimization on smaller regions. Still, again the MS posterior value is
often not the value that would be obtained from averaging the SS mean values. Also as per the
tropical broadleaved evergreen forests, the uncertainty on the SS posterior values is not significantly
reduced when compared to the prior, except for Vcmax,opt and Gsslope. However, the MS
uncertainty is markedly reduced, which is probably the result of including more sites in the
optimization, thus providing a stronger constraint.
In addition the same correlation structures are evident, with the exception of leafagecrit, which is
strongly negatively correlated to the photosynthesis-related parameters (figure 4.4 left panel), and a
similar magnitude of reduction in uncertainty is seen (figure 4.4 right panel), which again is likely to
be an underestimate of the true posterior uncertainty.
12
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
13/29
Figure 4.3: Same as figure 4.1 but for Temperate coniferous evergreen forests
Figure 4.4 Left: Same as figure 4.2 but for temperate coniferous evergreen forest
13
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
4.3
14/29
Temperate broadleaf evergreen forests
Figure 4.5: Same as figure 4.1 but for Temperate broadleaf evergreen forests.
For temperate broadleaf evergreen forests many of the posterior mean value of the parameters are
close to that of the prior, except for those related to photosynthesis (figure 4.5). As there is not
considerable variation in the SS optimizations with so few sites, the MS mean value is often closer to
that of the SS. There is again a reduction in uncertainty in only a few of the parameters, including
Vcmax,opt and Gsslope, as seen previously, but also SLA, leafagecrit, Q10 and Zdecomp.
The same correlation structures are evident as seen for tropical broadleaf evergreen and temperate
coniferous evergreen forests, with the exception that the Q10 parameter is correlated with the Ksoilc
(figure 4.6). This suggests there is not enough information in the observations to uniquely identify
parameters related respiration processes in the model.
14
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
15/29
Figure 4.6 Left: Same as figure 4.2 but for temperate broadleaf evergreen forests.
4.4
Temperate broadleaf deciduous forests
A higher number of parameters are included in the optimizations for deciduous PFTs, mostly relating
to the leaf phenology models (i.e. the timing of leaf onset and senescence). Interestingly these
parameters (Kphenocrit, senescence temp. (csenescence), leafagecrit) all show a marked reduction in the
posterior uncertainty for temperate broadleaf deciduous forests (figure 4.7), corresponding to a
strong observational constraint on the reduction of the growing season length first through step 1 of
the optimization process (with MODIS-NDVI data) and then step 2.
As per the evergreen forest PFTs, most other parameters do not show a reduction in the SS
uncertainty post-optimization; although with the inclusion of more sites the MS posterior uncertainty
is markedly reduced for most parameters, as can be expected. However the same behavior is seen in
the correspondence, or lack thereof, between the MS posterior mean and the average of SS posterior
mean values.
The same correlation structures are seen in the parameter posterior values (figure 4.8), with a strong
negative correlation also seen between the Klaihappy and LAImax parameters. It is clear therefore that
more information is needed to uniquely determine parameters related to the magnitude of the LAI
(rather than the timing of onset and senescence), or that there are too many inter-related
parameters in the simulation of LAI, which may call for a simplification of the processes in the model.
15
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
16/29
Figure 4.7: Same as figure 4.1 but for Temperate broadleaf deciduous forests.
Figure 4.8 Left: Same as figure 4.2 but for temperate broadleaf evergreen forests.
16
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
4.5
17/29
Boreal coniferous evergreen forests
Figure 4.9: Same as figure 4.1 but for Boreal coniferous evergreen forests.
In the boreal coniferous evergreen forests, the posterior SS and MS mean values are very close to
that of the prior, with the exception of Q10 (figure 4.9). The posterior uncertainty is also not reduced,
with the exception of leafagecrit and Q10. This shows that despite the high number of observations,
the information they contain is not enough of a constraint to move away from the prior, or that the
prior values in the model are mostly correct. As a result, the posterior uncertainty on the annual NEE
flux is not significantly reduced from that of the prior (figure 4.10 right panel).
The fact that leafagecrit is strongly negatively correlated with the photosynthesis parameters (figure
4.10 left panel), as was the case for temperate coniferous evergreen forests, is to be expected for
evergreen species; due to the absence of specific leaf onset and senescence it is the leaf age which
controls the phenology of the trees. However this correlation is not seen for tropical and temperate
broadleaf evergreen forests, and not as strongly in boreal regions. This may point to the influence of
different drivers/limitations on photosynthesis based on the larger surface area of the leaves.
17
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
18/29
Figure 4.10 Left: Same as figure 4.2 but for Boreal coniferous evergreen forests.
4.6
Boreal broadleaf deciduous forests
As for boreal coniferous evergreen forests, many of the parameters for the boreal broadleaf
deciduous forest do not show a marked deviation from the prior value in both the SS and MS
optimizations (figure 4.11), with the exception of Vcmax,opt, Q10, and cTopt. There is also little
reduction in the posterior uncertainty, at least for the SS optimizations. As was seen in temperate
regions, optimizing the parameters relating to the timing of leaf phenology results in lower posterior
uncertainty on the parameters.
The correlation structures are again similar to other forest types (figure 4.12 left panel). Most
parameters are uncorrelated, however there are some negative correlations between
photosynthesis-related parameters, and parameters relating to water availability and its affect on
stomatal conductance (Dpucste, Humcste and fstressh). Note that we the projected error on the NEE
shows close to zero values for one site, a problem that will be investigated (likely an error).
18
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
19/29
Figure 4.11: Same as figure 4.1 but for Boreal Broadleaf deciduous forests.
Figure 4.12: Same as figure 4.2 but for Boreal Broadleaf deciduous forests.
19
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
4.7
20/29
C3 grassland
For C3 grassland sites, unlike most forest sites there is a wide range of variability in the SS posterior
values for all the parameters with the exception of the SLA (figure 4.13). C3 grasses are found in most
biomes and regions of the world, unlike all the forest PFTs, which may explain this variation. It is
hypothesised that SLA would be globally representative as there is likely to be a lower range of
variation in the SLA of grasses compared to trees.
However like the forest PFTs where the SS posterior values vary from the prior, the MS posterior
value is often not similar to the average SS value, as discussed in more depth for tropical broadleaf
deciduous forests. With the high number of sites, the MS values tends to be well-constrained, giving
confidence that this value can be used as a global parameter for C3 grasses.
There are similar correlations between parameters as for forest PFTs, but there is not a correlation
between the site-based Ksoilc and LAIinit parameters. As discussed earlier the reason for this is still
being investigated.
Figure 4.13: Same as figure 4.1 but for C3 grassland.
20
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
21/29
Figure 4.14: Same as figure 4.2 but for C3 grassland.
21
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
22/29
5 Error on global carbon fluxes
5.1
Set up of the error propagation
As explained in the introduction, we only present here a first attempt to characterize the spatial
distribution of the errors on the Net Ecosystem Exchange (NEE) obtained from the propagation of the
errors on the parameters. Given that we could not use yet the parameter error covariance matrix
from step 4 to account for all data-streams, we have used instead the parameter error covariance
matrix from step 2 (as a preliminary assessment). This error propagation thus only accounts for the
MODIS-NDVI and the FluxNet data.
We have propagated the parameter error covariance matrix on the NEE for two temporal scales, the
yearly mean flux error and the monthly mean flux error (with a focus on January and July). We also
restricted the error propagation (from the parameters to the fluxes) to only one year (2002) to
illustrate the typical spatial patterns that we obtain. Indeed the year-to-year variations of the annual
or monthly NEE errors are likely to vary little, given that the model sensitivities (Jacobian) are rather
similar for each years.
The NEE errors should in fine be compared to the fluxes themselves in order to estimate whether the
estimated sources and sinks are robust or nor. The maps of the optimised annual NEE fluxes after
step 4 (assimilation of atmospheric CO2 concentrations) will thus be compared to the prior and
posterior errors on NEE.
Note that the jacobian has been determined for the same vegetation types than the ones considered
in the flux tower assimilation (that is 7 among 12): Tropical broad-leaved evergreen, Tropical broadleaved raingreen, Temperate needleleaf evergreen, Temperate broad-leaved summergreen, Boreal
needleleaf evergreen, Boreal broad-leaved summergreen and C3 grass. The other PFTs were indeed
not optimized given that we either lack FluxNet data or that we choose not to optimize the crop PFTs.
5.2
Error maps on the NEE
Annual mean NEE errors:
Figure 5.1 displays the prior and posterior annual NEE errors as well as the error reduction and the
mean annual NEE. We obtain large prior errors at high latitudes, in china, and the tropical regions
(especially the Amazon basin). The spatial structure of the prior error is tightly linked to the PFT
distribution (see the maps of PFTs fraction per grid cell in Figure 8.1 in the Appendix). The large errors
at high latitude correspond mainly to the boreal broadleaf summer green forests and C3 grassland.
Over China there is a mix of PFTs that contribute to the overall large NEE prior error, while over the
Amazon it is the tropical evergreen forests that dominate the error budget. Note that these errors
range from 60 gC/m2/year to 300 gC/m2/year and that they are similar to the values discussed in
section 4 at the site level.
22
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
23/29
After the optimization the error are significantly reduced everywhere to values around 50
gC/m2/year. The largest error reduction occurs at high northern latitudes, over the Amazone and
over the central part of Asia. These error reductions reach 80% in these regions but they remain
around 50% in other regions.
Overall, the posterior errors are still on the same order of magnitude than the mean annual NEE flux
over most regions indicating that:

The use of MODI-NDVI and FluxNet data allows to decrease the parameter errors to a
sufficiently low level to estimate with high confidence the sign of the annual land carbon
fluxes for a given year except for regions with small carbon uptake.

We expect that the use of the atmospheric concentration in step 4 will additionally reduce
the parameter errors and/or induce strong correlations between parameter errors that will
after propagation lead to even smaller annual NEE errors.
If we now compute the global total NEE error over land, we obtain for the prior a value of 14
GtC/year, which is unrealistically high. This potentially indicates that our prior error variance
covariance matrix has too large variances for the considered parameters and most likely that we are
missing some negative error covariances (off diagonal elements are neglected in the prior matrix).
After optimization the global error budget falls down to 3.1 GtC/year for a particular year, which is
still relatively high. More in depth analysis of the aggregated error budget will be provided at the
final meeting.
Finally, we also tested a case with a larger set of parameters in step 2 of the sequential optimization.
The figures are not shown. In general we observe, as expected, that with a larger number of
parameters we obtain larger errors and smaller error reductions. The differences are significant and
reveal that the choice of parameter to optimize and their prior error is crucial.
23
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
24/29
Figure 5.1: Error on the annual NEE fluxes for 2002 estimated from the parameter error variance-covariance matrix (case
of a large set of parameters). Top right: NEE errors from the prior parameter errors. Top left: NEE errors from the
posterior parameter errors. Lower right: error reduction expressed in percentage.
January and July mean NEE errors:
The analysis of the monthly error maps allows understanding the seasonal evolution of the errors
and their link to some respiration only processes in winter for extra-tropical ecosystems. Figure 5.2
displays the error estimates for January together with the mean January NEE. We obtain large errors
over Europe attributed to errors in the heterotrophic respiration, and large errors over the tropics
combining both photosynthesis and respiration. The spread of the error pattern from East to West
over Europe is strongly correlated to the sensitivity of the heterotrophic respiration flux to
temperature (Q10) that vary with the mean temperature. The error reductions for January are
slightly smaller than for the annual mean, with values around 50%.
In July the error patterns are slightly different with the high northern latitudes having much larger
errors than in January. The error reductions become lager with values around 70% to 85%. A more
complete analysis with the temporal evolution of these errors, aggregated at continental scale, is in
progress.
24
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
Figure 5.2: Same as 5.1 but for the January mean flux errors.
Figure 5.3: Same as 5.1 but for the July mean flux errors.
25
25/29
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
26/29
6 Conclusion and perspectives
The report describes the error estimation for the CARBONES CCDAS. We first discussed the
estimation of the parameter errors for step 2 of our sequential CCDAS approach, i.e. after having
assimilated MODIS-NDVI and FluxNet data. The final estimates from step 4 are still in progress and
will be used to update the content of the report. From the above analysis we could derive important
features linked to error estimation and error propagation:

First, the estimated error covariance matrix on the optimized parameters of ORCHIDEE
provides few significant error correlations across parameters, especially those controlling the
different respiration terms; this illustrate the need to further improve the optimization by
including additional observations that would better constraint the respiration. Potential
directions are the use of “night time” versus “day time” NEE average and/or specific soil flux
chamber measurements.

A characterisation of the error budget associated to the NEE fluxes, using FluxNet data,
indicates that: the parameter errors are still only about half of the total model error, the
other half arising from model structural errors. The magnitude of the model structural error
for the Temperate Deciduous broadleaf forests is around 1.6 gC/m2/day. Such large value
reinforce the need to improve our current land surface model and to include for instance the
impact of forest management, specific crop phenology, nitrogen limitation, …

The spatial distribution of the NEE annual or monthly mean errors provides interesting
features. They highlight regions where the FluxNEt and MODIS-NDVI data bring significant
information through the constraint on specific ecosystem model parameters. However the
NEE errors obtained from the parameter errors are still significant and sometime around the
mean value of the NEE (especially at the annual scale).

The error characterization presented in this report only deals with random errors. However
as seen in the report on the evaluation of CARBONES products (D610) that the systematic
errors (i.e. all biases) may be as large or larger than the random error. A full comprehensive
analysis of the uncertainties should thus include “random error” estimation but also
comparison to other estimates/proxies for the more systematic errors.
This work is only a preliminary investigation that will be completed with:

The results from step 4 of our sequential approach.

An in depth analysis of the continental/regional error budget for the NEE and their temporal
evolution (seasonal and for few different years across the 20 year period of the reanalysis).

The computation of the errors for the other quantities simulated by CARBONES, i.e. the gross
photosynthesis and respiration fluxes as well as the biomass carbon stocks.
This report will be thus slightly updated before the final submission.
26
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
27/29
7 References
G. Desroziers, L. Berre, B. Chapnik, and P. Poli. Diagnosis of observation, background and analysiserror statistics in observation space. Quarterly Journal of the Royal Me- teorological Society, 131(613)
:3385–3396, 2006.
T. Kaminski, W. Knorr, PJ Rayner, and M. Heimann. Assimilating atmospheric data into a terrestrial
biosphere model : A case study of the seasonal cycle. Global Biogeoche- mical Cycles, 16(4) :1066,
2002.
S. Kuppel, F. Chevallier, and P. Peylin. Quantifying the model structural error in carbon cycle data
assimilation systems. Geoscientific Model Development, 6 :45–55, 2013. doi : doi:10.5194/gmd-6-452013.
G. Lasslop, M. Reichstein, J. Kattge, and D. Papale. Influences of observation errors in eddy flux data
on inverse model parameter estimation. Biogeosciences, 5(5) :1311– 1324, 2008.
PJ Rayner, M. Scholze, W. Knorr, T. Kaminski, R. Giering, and H. Widmann. Two de- cades of
terrestrial carbon fluxes from a carbon cycle data assimilation system (CC- DAS). Global
Biogeochemical Cycles, 19(2) :GB2026, 2005.
A.D. Richardson, M.D. Mahecha, E. Falge, J. Kattge, A.M. Moffat, D. Papale, M. Reich- stein, V.J.
Stauch, B.H. Braswell, G. Churkina, et al. Statistical properties of random CO2 flux measurement
uncertainty inferred from model residuals. Agricultural and Forest Meteorology, 148(1) :38–50, 2008.
M. Scholze, T. Kaminski, P. Rayner, W. Knorr, and R. Giering. Propagating uncertainty through
prognostic carbon cycle data assimilation system simulations. J. Geophys. Res, 112 :D17305, 2007.
A. Tarantola. Inverse problem theory : methods for data fitting and model parameter estimation.
Elsevier ; Distributors for the United States and Canada, Elsevier Science Pub. Co., Amsterdam ; New
York New York, NY, U.S.A., 1987.
M. Williams, A. D. Richardson, M. Reichstein, P. C. Stoy, P. Peylin, H. Verbeeck, N. Car- valhais, M.
Jung, D. Y. Hollinger, J. Kattge, R. Leuning, Y. Luo, E. Tomelleri, C. M. Trudinger, and Y. P. Wang.
Improving land surface models with FLUXNET data. Bio- geosciences, 6(7) :1341–1359, 2009.
27
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
28/29
8 Annexes:
8.1
Distribution of the PFT fractions
The figure below presents the fraction coverage for the different PFTs of ORCHIDEE.
Tropical broad-leaved evergreen
Tropical broad-leaved raingreen
Temperate needleleaf evergreen
Temperate broad-leaved evergreen
Temperate brad-leaved summergreen
Boreal needleleaf evergreen
Boreal broadleaf summergreen
Boreal needleleaf summergreen
28
Deliverable D430.1-2
Ref
CARBONES-D430.1-REP-LSCE-012-02-00
CARBONES-D430.2-REP-LSCE-013-02-00
Date
25/03/2013
Page
C3 grass
C4 grass
C3 crops
C4 crops
Figure 8.1: fraction of PFTs per grid cell.
29
29/29