Description of the CCDAS

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Oct 20, 2013 (4 years and 2 months ago)

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Description of the CCDAS




This section describes the evolution of the sequential approach from the first description in
the deliverable D410 and the different implementations of such approach that have been / will be
applied to versions V1 and V1.5.

General scheme and evolution from the first description

We first recall the different steps of the sequential approach and highlight the changes that
were made compared to the initial description in D410. Figure 2.2 describes these steps:

Step 1
: Assimila
tion of the remotely sensed products of vegetation greenness (NDVI) derived from
MODIS into ORCHIDEE; the prior parameters including values and error covariance (
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and
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) are optimized to
produce a first set of optimized parameters
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with error covariance
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, as well as the corresponding global
optimized net CO2 flux
es
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and their associated uncertainty
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.

Step 2
: Assimilation of
in situ

flux measurements; the parameters
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and
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are used as input to the optimization
system together with new parameters controlling the major processes in ORCHIDEE. These
parameters are further optimized to produce both

i)

a second set of optimized
parameters (
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and their error covariance
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)

ii)

ii) a set of optimized NEE fluxes and their uncertainties to be also used as prior input in
step 4 (
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and their error covariance
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).

The second option was not described initially in D410 and has been added as a complementary
approach. Indeed it allows more flexibility in t
he system and prevents from relying too strongly on
ORCHIDEE’s equations and parameters with the possibility to correct independently the land fluxes
for all pixels. This approach will be used in version V1 of the CARBONES products (see
0
).

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. It
uses as input the results of step 2 for the land part and step 3 for the ocean part. We will consider
two complementary approaches for the land component. The optimized parameter (and attached
uncertainty) will
either consist in:

-

approach a: the parameters
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of ORCHIDEE and their error covariance
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from step 1 or 2.
The approach then consists in readjusting the parameters that have been previously pre
-
optimized using FluxNet data and satellite observations;

-

approach b: the net CO2 fluxes over

land
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and their errors
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from

step 1 or 2.
They will then be further optimized pixel by pixel.

The result of this last optimization step will consist of i) either final parameters for ORCHIDEE and
errors or directly the net land carbon fluxes and ii) the optimized ocean fluxes. For t
he land, in the
case of the flux optimization, some inconsistencies will still remain between the land carbon stocks
and the land fluxes, although a final adjustment (post
-
processing) will be performed to adjust the
gross fluxes (i.e. respiration and photo
synthesis) so it matches the estimated net flux.


Figure 2.2: Sequential assimilation of the different data streams into 4 steps.


Details of the different versions

We briefly precise below the specific implementations for the two versions based on the
sequential
approach.



Version V1:




In this version we have not implemented step 2, given that the information content of the
flux tower measurements was not fully quantified for all Plant Functional Types (PFTs). We
have thus directly used the output of step 1 and step 3 to feed the final s
tep 4. In this
version, we optimize directly the NEE fluxes for each grid cell: we have thus directly used in
step 4 the land fluxes
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and their

errors
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calculated with the parameter
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forme.
, and their
errors
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en forme.
. That way the assimilation relies more heavily on the atmospheric information and
less on the ORCHIDEE model str
ucture. The version also uses the first estimates of the ocean
air
-
sea fluxes from the Neural Network approach (see section 3).



Version V1.5:


In this version, we will implement step 2, as compared to version V1, and thus account for all
four data streams
in the carbon re
-
analysis. The choice for the land component between the
optimization of the ORCHIDEE parameter
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,
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or directly the optimization of the net
land fluxes (
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mise en forme.
,
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) is not finalized. The objective is to implement both approaches (a and b)
in order to see how the fluxes are changed when the system has more
degrees of freedom
with the flux correction.


Simultaneous CCDAS approach


This approach defines the ultimate goal of the CCDAS system; to

combine all four
observational data streams in order to estimate the land component process
-
based ecosystem
parameters. This will ensure a complete consistency between the optimized land carbon stocks and
the gross/net CO2 fluxes. Over ocean, the approach
will be first based on a flux correction and
ultimately on parameter corrections (to be described in the next version of this report).
This report
should be considered as a first overview of the simultaneous CCDAS and a more in depth
description will be pr
ovided in the next and final release of delivery D420
.

We detail below the main principles that are similar to the sequential approach, although performed
in one step. The different data streams are combined within a 4D variational data assimilation
syste
m (4D
-
var) relying on:

i)

The ORCHIDEE Global Vegetation Model, to relate the process
-
based parameters to be
optimized to measured eddy
-
covariance fluxes and to satellite observations;

ii)

The statistical ocean model (see report D410);

iii)

The LMDz

tracer transport model “coupled” to ORCHIDEE (i.e. using ORCHIDE flux
estimates) to relate the land parameters to atmospheric CO2 concentrations and also
using the ocean fluxes from the statistical model.

2.3.1. System description

The coupled CCDAS is bui
lt on the merging of two pre
-
existing inversion schemes used for the
sequential approach described above and both relying on a Bayesian framework:

1.

ORCHIS

(ORCHIDEE Inversion System), specifically designed to optimize ORCHIDEE
parameters with respect to
in
situ

flux measurements and/or remotely sensed products of
vegetation activity (NDVI, fAPAR or LAI). This scheme was used for step 1 and step 2 of the
sequential approach described in section 2.2.

2.

PYVAR
, designed to optimize surface fluxes over land and oce
an with the global transport
model LMDz and some pre
-
existing information about the fluxes, and their error covariance
matrix. This scheme is the central part of step 4 for the sequential approach. It has been
described extensively in Chevallier
et al.

201
0.

The approach relies on the minimization of a misfit function
J(x)

that measures the mismatch
between 1) all observation datasets
y

and corresponding model outputs
H.x
, and 2) the values
x

of
the parameters (to optimize) and some prior information on the
m
x
b
, weighted by the prior error
covariance matrices on observations
R

and parameters
B

(Tarantola, 1987):

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Eq.
1

We explicitly account for uncertainties regarding the model and the observations (through
R
), and the prior parameters (through
B
), assuming that the errors on prior parameters and
observations follow Gaussian distributions. Compared to the sequential approach, the vector
x

comprises the parameters for the land and fluxes for the ocean (at least for version V2).

The minimization of

the misfit function is performed iteratively using one of the following
optimizers: i) CONGRAD, ii) M1QN3 (Gilbert and Lemarechal, 1989) or iii) L
-
BFGS
-
B (Zhu
et al.
, 1995).
The final choice of the method is still under investigation and will follow from
the respective
performances of each algorithm; i.e. its efficiency to minimize
J
. Note however that regarding some
non
-
linearities in the ORCHIDEE vegetation model with respect to the parameters to optimize (in
particular phenological parameters), we will

rather favour the use of the two latter algorithms as
compare to CONGRAD that is more efficient is case of linear problems.

At each iteration, the optimizer requires the value of the misfit function and its gradient with respect
to the ORCHIDEE parameters

or with respect to the ocean fluxes.

As we do not account for cross
-
correlation between data streams, the misfit function for the
observations is a linear combination of the cost functions corresponding to each data stream:

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Eq.2

where
R
i

are diagonal matrices (see section 3 for more information).



For the CO2 atmospheric concentrations and the land component,
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actually corresponds
to
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forme.

computed

at a 3.5°x2.5° spatial resolution every 3 hours, based on ECMWF
meteorological forcing spatially aggregated at the resolution. Note that we are also currently
implementing a version with
H
orch

calculated at a higher resolution, i.e. the resolution of the
ECMWF forcing (0.7 degree), and then an intermediate step averaging the fluxes ant the
H
LMDz

resolution.



For the CO2 atmospheric concentrations and the ocean component,
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champs de mise en forme.

corresponds to
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forme.

computed at a 3.5°x2.5° spatial resolution every 3 hours with
x

being the fluxes from
the Neural
network averaged from the original 1° x 1° resolution to a 3.5°x2.5°.



For the assimilation of
in situ

flux measurements or satellite products,
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is
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where the model
is applied at point scale. In this case, the meteorological forcing corresponds to the measured
forcing at each eddy
-
covar
iance site. For MODIS satellite products, as explained in section 3,
we have selected a set of points representative of the different Plant Functional Types to
perform the assimilation of NDVI. These points are thus run individually with the
meteorological

forcing extracted from IERA at (forcing at 0.7°).

The gradient of the misfit function expresses as:

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Eq.2

where
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forme.

stands for the adjoint of the model:



in the case of the CO2 atmospheric concentrations and the land component,
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is
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,
computed at a monthly temporal resolution in order to reduce the computational

cost of the
adjoint model;



In the case of he CO2 atmospheric concentrations and the ocean component,
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simply
represent the LMDz

sensitivities to surface fluxes computed at a monthly time step;



for
in situ

flux measurements or satellite products,
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is simply
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; the same temporal
resolution than for the determination of
J(
x
)
is considered.

In the current version of the CCDAS,
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for ORCHIDEE is determined thanks to the vectorized version of
the tangent linear model of ORCHIDEE for most parameters but few phenological parameters
(
Kpheno_crit

and
Senescence_temp_c
, see Appendix 5.3) for which the sensitivity of the model
outputs is computed with a finite difference approach.
The reason is that these particular parameters
are involved in threshold conditions, for which the tangent linear model may p
rovide too little
sensitivity (even null sensitivity in some cases) depending on the value of the parameter.
For the
atmospheric transport model
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is determined with the adjoint model of LMDz as described in Chevallier
et al.
, 2005.


Finally, for an improved optimization efficiency,
x

is preconditioned which means that the
optimizer is fed with the control variable
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rather than
x

(Chevallier
et al.
, 2005).

A more detailed description of the various components, especially the observations
y

and
their error
R
, can be found in the two
reports D410 (description of the first version of the CCDAS) and
D300 (input parameters of the CCDAS). In section 3, we resume them and provide some insight on
the information content of each data stream. Below, we also provide few insights on the specific

case
of the initial conditions for the carbon pools and their optimization.