We have developed a novel framework (“Tan-Tracker”) for assimilating
observations of atmospheric CO

Carbon cycle data assimilation systems offer a promising new tool for
CO

The four-dimensional variational data assimilation (4D-Var) method has also been introduced in this field (e.g., Baker et al., 2006a; Engelen et al., 2009). Compared with EnKF, 4D-Var has its own attractive features: for example, it has the ability to simultaneously assimilate the observations at multiple times to the analysis fields (Tian and Xie, 2012). Nevertheless, the needs of the adjoint model and the linearization of the forecast model limit the wider applications of 4D-Var. Tian et al. (2008b, 2011) proposed the POD-based (proper orthogonal decomposition) ensemble four-dimensional variational data assimilation method (PODEn4DVar) based on the POD and ensemble forecasting techniques, which aims to exploit the strengths of the two forms (i.e., EnKF and 4D-Var) of data assimilation while simultaneously offsetting their respective weaknesses. In PODEn4DVar, the control (state) variables in the 4D-Var cost function appear explicitly so that the adjoint model is no longer needed and the data assimilation process is significantly simplified (Tian et al., 2008). Furthermore, PODEn4DVar largely retains the basic advantages of the traditional 4D-Var. Its feasibility and effectiveness are demonstrated in an idealized model with simulated observations (Tian et al., 2011; Tian and Xie, 2012). It is found that the PODEn4DVar performs better than both 4D-Var and EnKF, and with lower computational costs than the EnKF (Tian et al., 2011). This method has been successfully applied to land data assimilation (Tian et al., 2009, 2010). Furthermore, we have built a PODEn3DVar (the three-dimensional version of PODEn4DVar)-based radar assimilation system on the atmospheric transport WRF model platform (Pan et al., 2012). This WRF-based data assimilation system indicates its (PODEn4DVar) potential in the atmospheric transport data assimilation.

In this study, we report on a new development of a CF data assimilation
system based on the PODEn4DVar approach, named Tan-Tracker (in Chinese,
“Tan” means carbon). This system is developed by incorporating a joint
PODEn4DVar assimilation framework into the GEOS-Chem model (V9-01-03,

In Sect. 2, we describe our Tan-Tracker data assimilation system,
including the Tan-Tracker joint assimilation framework, a simple review of
the PODEn4DVar assimilation approach and its coupling with the joint
assimilation framework, and its covariance localization scheme. The following section (Sect. 3) shows observing system simulation experiments (OSSEs) for the
evaluations of the Tan-Tracker system in comparison to its simplified
version only taking CFs as the prognostic variables.
Furthermore, another assimilation experiment for assimilation of real
spaceborne CO

Joint or dual-pass assimilation schemes have been utilized to optimize model
states and parameters simultaneously from noisy measurements through
classical filters (e.g., the dual UKF or EnKF) (Tian et al., 2008; Tian and
Xie, 2008). Tian et al. (2009) expanded the dual-pass assimilation strategy
to the PODEn4DVar approach and built a PODEn4DVar-based dual-pass microwave
land data assimilation system (Tian et al., 2010). Similar to the usual
joint assimilation schemes, the augmented vector used in LETKF-CDAS is also
a state-parameter-augmented one and the CFs are treated as the model
parameters. However it should be noted that the prognostic variable used in
Tan-Tracker is the large-scale vector made up of CFs and CO

Flowchart of the Tan-Tracker joint data assimilation system.

An ordinary ensemble-based assimilation system (for example, CarbonTracker)
usually begins with the preparation of an ensemble of

The 4-D moving sampling strategy.

Figure 2 shows the makeup of the assimilation window (i.e., the optimized
window

Correspondingly, in the sampling run, we run the CTM from the background
CO

In conclusion, Tan-Tracker works as follows: two CTM runs forced by the
background CFs' series are firstly achieved over the assimilation window and
the sampling window, respectively: the background run is used to prepare the
background joint vector, and the sampling run is used to produce the joint
vector ensemble by applying a 4-D moving strategy (Wang et al., 2010) to the
sampling simulations throughout the sampling window. The background joint
vector and the joint vector ensemble are then input into the PODEn4DVar
processor, in which the usual observation operator (e.g., the interpolation
function to interpolate the model gridded variables to the in situ
observations) compares the simulated CO

The PODEn4DVar approach is born out of the incremental format of the 4D-Var
cost function

With the prepared background field

In particular, in Tan-Tracker,

We have realized the coupling between the joint assimilation framework with the PODEn4DVar assimilation processor through Eqs. (18–22) (see the green part of Fig. 1).

As an ensemble-based assimilation system, Tan-Tracker also utilizes the
covariance localization techniques to ameliorate the contaminations
resulting from the spurious long-range correlations (Houtekamer and
Mitchell, 2001). It uses the following exponential decay of the covariance
structure with distance between state and observational variables (Gaspari
and Cohn, 1999),

Consequently, the covariance localization in Tan-Tracker can be implemented
by calculating the Schur product

In this section, Tan-Tracker will be comprehensively evaluated through a group of well-designed global observing system simulation experiments (OSSEs) over a given assimilation period.

We simulate atmospheric CO

The observational sites used in this study.

The performance of our Tan-Tracker system is examined by comparison with the
simplified version (referred to as TT-S), taking only CFs as the prognostic
variables. TT-S is somewhat similar to CarbonTracker except that
the ensemble square root filter (EnSRF) has been replaced by the PODEn4DVar approach and the GEOS-Chem model is used instead of the TM5 model. Similar to CarbonTracker,
the GEOS-Chem model in TT-S is actually the observation operator linking the
CFs with CO

Time series of the global mean

Time series of the posterior uncertainties (shaded areas) of the analyzed surface fluxes (TT) from 1 January to 31 December 2010.

Time series of the averaged scaling factors from 1 January to 31 December 2010.

To evaluate Tan-Tracker's performance in a general view, time series of
the daily global mean fluxes and CO

Time series of the daily mean CO

Same as Fig. 8 but for CO

Similar to Peters et al. (2005), we also aggregated the daily, gridded
(2

Root-mean-square errors (RMSEs) (units are

To evaluate the performance of our Tan-Tracker data assimilations system
comprehensively, we show the root-mean-square errors (RMSEs) for the daily,
gridded (2

Another group of experiments using the Tan-Tracker system with different
horizontal localization radii (

Finally, to investigate the impacts of sample sizes on Tan-Tracker's
assimilation results, we also conduct another group of Tan-Tracker
assimilation experiments with the ensemble numbers

Same as Fig. 10 but for CO

Time series of the daily global mean

Time series of the daily global mean

Comparisons between the observed

In this section, a preliminary real assimilation experiment is conducted by
using spaceborne CO

The basic experimental designs (such as the GEOS-Chem model, ensemble size,
assimilation window, localization radius, etc.) are exactly the same as
those adopted in Sect. 3. Nevertheless, in this real-data experiment, we
took the default surface CO

In order to assimilate the spaceborne

The lack of reliable independent CF estimates derived from GOSAT

In this study, a new carbon cycle data assimilation system (i.e.,
Tan-Tracker) is developed based on an advanced hybrid assimilation approach
(PODEn4DVar), as a part of the preparation for the launch of the Chinese
carbon dioxide observation satellite (TanSat) (Liu et al., 2012; Cai et al.,
2014). Tan-Tracker adopts a joint data assimilation framework: a simple
persistence model is chosen to describe the CFs' evolution, which acts as
the CF dynamical sub-model and constitutes an augmented dynamical model
together with the GEOS-Chem atmospheric transport model. In such an
augmented dynamical model, the large-scale state vector made up of CFs and
CO

Our future work will focus on the realization of

We would like to acknowledge Annemarie Fraser, Wouter Peters and Ross Bannister for constructive comments on the manuscript. The two anonymous reviewers are thanked for their critical comments and suggestions, which helped to improve the manuscript. This work was supported by the National High Technology Research and Development Program of China (grant no. 2013AA122002), the Knowledge Innovation Program of the Chinese Academy of Sciences (grant no. KZCX2-EW-QN207), the Special Fund for Meteorological Scientific Research in Public Interest (GYHY201306045) and the National Natural Science Foundation of China (grant no. 91437220). Edited by: M. Heimann