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Error estimation: parameter error on base configuration and error
on output field
Table of content
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Introduction ____________________________________________________________ 2
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Description of the approach _________________________ Error! Bookmark not defined.
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Result of the forward simulations ____________________ Error! Bookmark not defined.
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Conclusions______________________________________ Error! Bookmark not defined.
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References _____________________________________________________________ 23
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1 Introduction
2 Principle of error calculation and error propagation
The posterior error variance-covariance matrix Pb' on the estimated parameters expresses as a
function of the a priori error variance-covariance matrices on the parameters Pb and on the
observations R, as well as the Jacobian matrix of the model H (a preciser comme tu veux):

Pb '  H t .R 1 .H  Pb

1 1
The error on the model parameters can be propagated into the space of the net CO2 fluxes using the
following matrix product:
R'  H .Pb '.H t
In this study, we compare the estimation of R' accounting either 1) for 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' correspond to the standard
deviation  on NEE of each pixel. In order to appraise the knowledge improvement brought by the
assimilation the assimilation, the error reduction is determined as 1   posterior  prior . We also


evaluate the benefit of the assimilation by investigation two temporal scales, the yearly error and the
monthly error (with a focus on January and July) on NEE.
3 Parameter errors estimated after MODIS-NDVI and
FluxNEt data assimilation
The errors discussed in this section correspond to those obtained after the step 2…
3.1
Tropical broadleaf evergreen forests
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Figure 3.1: Values and uncertainties of optimized parameters for tropical evergreen forest: The a priori is in grey (with
several value 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).
Figure 3.1 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.
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Temperate coniferous evergreen forests
Figure 3.1: Same as figure 3.1 but for Temperate coniferous evergreen forests
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Figure 3.2 Left: Same as figure 3.2 but for temperate coniferous evergreen forest
3.3
Temperate broadleaf evergreen forests
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Figure 3.1: Same as figure 3.1 but for Temperate broadleaf evergreen forests.
Figure 3.3 Left: Same as figure 3.2 but for temperate broadleaf evergreen forests.
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Temperate broadleaf deciduous forests
Figure 3.1: Same as figure 3.1 but for Temperate broadleaf deciduous forests.
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Figure 3.4 Left: Same as figure 3.2 but for temperate broadleaf evergreen forests.
3.5
Boreal coniferous evergreen forests
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Figure 3.1: Same as figure 3.1 but for Boreal coniferous evergreen forests.
Figure 3.5 Left: Same as figure 3.2 but for Boreal coniferous evergreen forests.
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Boreal broadleaf deciduous forests
Figure 3.1: Same as figure 3.1 but for Boreal Broadleaf deciduous forests.
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Figure 3.2: Same as figure 3.2 but for Boreal Broadleaf deciduous forests.
3.7
C3 grassland
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Figure 3.2: Same as figure 3.1 but for C3 grassland.
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Figure 3.2: Same as figure 3.2 but for C3 grassland.
4 Analysis of ORCHIDEE model structural error
5 Error on global carbon fluxes
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Figure 1 presents the map of the optimised annual NEE fluxes after assimilation of atmospheric CO2
concentrations, to which we can compare the prior and posterior error on NEE.
Figure 6: Global map of the optimised NEE fluxes after assimilation of atmospheric CO2 concetrations (kgC/m2/year).
In the following, we consider two cases depending on the number of parameters let free during the
assimilation of flux tower data. As a consequence, we have accounted for two Jacobian of the
ORCHIDEE model in the determination of the R' matrices. They have 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 broad-leaved raingreen, Temperate needleleaf evergreen,
Temperate broad-leaved summergreen, Boreal needleleaf evergreen, Boreal broad-leaved
summergreen and C3 grass.
As expected (from the analytical expression of R'), the case with the higher of free parameters lead to
higher errors on the NEE fluxes.
On the yearly error maps, we see that the prior errors are higher in the tropics (in particular over
Amazonia) and at high latitudes. The spatial structure is tightly linked to the PFT distribution as seen
in Figure…: the high errors over the tropics correspond to Tropical Broad-leaved Evergreen
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vegetation; at high latitudes, they are associated to mixed ecosystems of Boreal Broad-leaved
Summergreen and C3 grass species.
The analysis of the monthly error maps allows understanding to which processes are related the
error given that the heterotrophic respiration dominates over photosynthesis at mid and high
latitudes in January, while the respective proportion of these two processes on the NEE balance has
little temporal variation. Hence, the high errors seen over Europe in January is attributed to
heterotrophic respiration. The spread of the error pattern from East to West is strongly correlated to
the vegetation map of C3 agriculture ecosystems, that have not been accounted for here for the
determination of H.
CAS PEU DE PARAMETRES (configuration assimilation 20 ans)
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CAS PLEIN DE PARAMETRES
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Tropical broad-leaved evergreen
Tropical broad-leaved raingreen
Temperate needleleaf evergreen
Temperate broad-leaved summergreen
Boreal needleleaf evergreen
Boreal broad-leaved summergreen
C3 grass
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6 Conclusion and perspectives
Maybe mention the expected climate change from the optimize parameter run compared to the
standard run using the beta factor …
7 References
8 Annexes
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