We present a method for assimilating total column CH

In the past century, the concentrations of many potent greenhouse gases
(GHGs) have increased in the atmosphere due to anthropogenic activities. The
atmospheric dry air mole fraction of the greenhouse gas methane
(

The top-down approach uses inverse modeling techniques to reduce the
uncertainty in the bottom-up-derived emission estimates on the basis of
atmospheric measurements of

Total column measurements of

High-quality

In some regions, the sparse network of surface measurement sites does not
provide sufficient constraints on

Our motivation for implementing the ratio method is to find a representation
of

We perform observing system simulation experiments (OSSEs) to test the
performance of the ratio method for reproducing the assumed true fluxes of

We use the TM5-4DVAR inversion system in this study. It is comprised of the
Tracer Transport Model version 5

Our inversion setup for the proxy approach is linear. However, for the new
ratio method the operator

To compare the difference in convergence between M1QN3 and CONGRAD, we performed additional proxy inversions using both optimization methods (see Appendix A). We find that M1QN3 has a slower convergence rate in comparison to CONGRAD, and therefore the number of iterations needed to find the inversion solution is generally higher. Another drawback of the M1QN3 algorithm available to us is that, unlike CONGRAD, it provides no information about the posterior flux uncertainties in a straightforward way.

The dynamic symbols (blue–green crosses) show the location of the
NOAA measurements sites included in inversions using surface measurements
(see Table

The assumed true

Covariance parameters of the a priori flux uncertainties per grid box per month used in the inversions. The uncertainty
is expressed as a fraction of the a priori flux. Error correlations are defined by exponential (“e”) and Gaussian (“g”)
correlation functions using the specified length scales

Time series of the true and prior fluxes (per month) integrated
over Tropical South America, Temperate South America, Boreal Eurasia and
Temperate Eurasia. For

Fit of the RATIO inversion to the annually averaged “true”

Pseudo-surface observations are generated from a forward run of TM5 using the
“true” fluxes as boundary conditions, and they are sampled at coordinates
and times of samples collected by cooperative flask-sampling network run by
NOAA/ESRL

The observational part of the cost function is calculated by weighing the
mismatch between the model simulations and measurements (

Formally, we should perturb the pseudo-measurements with noise according to
the data covariance matrix

In the ratio inversion, the GOSAT measurements are in terms of

Summary of the inversions performed in this study.

In this study, we perform OSSEs comparing different global inversion setups
using the same truth and a priori fluxes. The inversions system is run at
a

The TRU-DAT represents an inversion which assumes that we have perfect
knowledge of

In Sect.

Taylor plots

Annual prior and posterior

Figure

As Fig.

As explained in Sect.

Next we analyze the difference between the proxy inversion (PROXY), using
optimized

Figure

As Fig.

As Fig.

We find that with the additional information provided by the satellite
measurements RATIO and PROXY are able to reproduce the true fluxes better
than SURFCH4. However, it is difficult to conclude if RATIO or PROXY performs
better, as their relative performances vary across the regions. As can be
seen in Figs.

As Fig.

As explained in Sect.

Figure

In principle, the performance of PROXY should improve with the performance of
SURFCO2. If SURFCO2 reproduces the true

The upper panel of Fig.

We have developed the “ratio” method for TM5-4DVAR inversions system. It is
an inversion system for assimilating the ratio of satellite-retrieved total
columns of

Top:

The performance of the ratio method is tested in comparison with the
traditional proxy method and surface-only inversions in an OSSE using the
TM5-4DVAR atmospheric inversion system. Overall, we observe that the ratio
method is capable of reproducing the true

The ratio method is a more complicated inversion to solve than a proxy
inversion as it is a nonlinear inversion problem, and therefore the widely
used CONGRAD optimizer cannot be used. In our setup, we use the M1QN3
optimizer, which is capable of handling the nonlinearity. However, inter-comparing inversions using different optimizers requires great attention as
their mode of operation is mathematically different. For example, CONGRAD
solves for the largest spatial and temporal scales in the first few
iterations, gradually adjusting to finer scales in subsequent iterations. M1QN3
works in similar manner, however, it has a much slower convergence rate for
the finer scales than CONGRAD. Hence, the overall convergence rate of M1QN3 is
slower than CONGRAD, and to achieve the same gradient norm reduction takes
more iterations

Another drawback of M1QN3 compared to CONGRAD is that no information is
obtained about posterior flux uncertainties. They are essential for inverse
modeling applications using real data to quantify the constraints on the
fluxes imposed by measurements. This is true, despite the fact that several
important sources of uncertainty, such as transport model uncertainties, are
difficult to account for. Furthermore, the accuracy of CONGRAD's uncertainty
approximation may be rather poor for large optimization problems, limiting
its use. An alternative method for calculating posterior uncertainties is to
use a Monte Carlo approach

We focus on a comparison between the proxy and ratio approach and also
perform a

The ratio inversion system is weakly nonlinear. The

Now that we have demonstrated that the ratio method works in a synthetic
environment, the next step is the application of the method to real satellite
data. A first step in this direction is to validate GOSAT-observed

We developed a new inverse modeling method within the TM5-4DVAR inverse
modeling framework for direct assimilation of satellite-observed ratios of
total column

We performed additional inversions in our OSSE setup to compare the
performance of inversions using proxy and ratio retrievals from GOSAT. In
addition, we compare the performances of these inversions, which also use
surface measurements, with inversions that only use surface measurements.
Additional inversions are performed to test the sensitivity of proxy
inversions to the quality of the model-derived

We conclude that for most Transcom regions the ratio method is capable of
reproducing the true seasonality and annually integrated

We tested the convergence rate of CONGRAD and M1QN3 using the setup of PROXY
described in Sect.

Absolute annual

This work is supported by the Netherlands Organization for Scientific Research (NWO), project number ALW-GO-AO/11-24. The
computations were carried out on the Dutch national supercomputer Cartesius, and we thank SURFSara (