This paper addresses the question of how much uncertainties in

The future of climate change depends mainly on the trajectory of greenhouse gas concentrations in the Earth's atmosphere, in particular carbon dioxide (

Several studies over Europe

Satellite-based retrievals of total-column

The SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY

The Orbiting Carbon Observatory-2 (OCO-2, launched on 2 July 2014) was also designed to be sensitive to

Since 2013, several studies have used GOSAT retrievals to estimate

In this study, we present a regional-scale four-dimensional variational flux-inversion system to assimilate OCO-2 retrievals. The study area here is Australia, chosen for the following three reasons. First, the current estimate of Australian

This paper aims to assess the likely uncertainty reduction for

The methodology to perform our OSSEs follows

Diagram representing an overview of the observing system simulation experiments (OSSEs) and how the inversion is performed using the L-BFGS-B minimization algorithm.

In this study the OSSEs were performed only for the months of March, June, September and December 2015. We ran an ensemble of five inversions for each month using different perturbations, generating five samples of the posterior probability density function (PDF). In the following subsections we describe the main ingredients of this procedure.

The inversion scheme for optimizing

The first term in Eq. (

The gradient of the cost function in Eq. (

Our underlying physical variables are the monthly averaged fluxes at the spatial resolution of CMAQ (

Number of eigenvectors included in our control vector (

We used OCO-2 level 2 satellite data (Lite File Version 9) distributed by the National Aeronautics and Space Administration (NASA) (available for download from

However, and because the average shown in Eq.

Third, we also considered a baseline uncertainty (

The second step was to take these 1 s averages and average them within the CMAQ vertical columns using Eq.

After averaging the OCO-2 sounding over the CMAQ domain, we generated a set of pseudo-observations as described in step 1 of Fig.

The first term of Eq. (

As is stated in Sect.

The post-processing of 3-hourly NEE data involved four steps. First, we calculated daily GPP. Then we used daily GPP to estimate the daily ecosystem respiration (ER); in terms of carbon balance, the ER can be calculated as

Fossil-fuel

Fire emissions were taken from the Global Fire Emission Database, version 4 (GFEDv4). This version of GFEDv4 provides gridded monthly fire emissions at 0.25

Ocean

After defining the emission profiles and their uncertainties, we incorporated spatial correlations into our prior error covariance matrix

After defining

We solve the minimization with a change of variable

This step (often called pre-conditioning) accelerates convergence. It also simplifies the system since, all target variables have unit standard deviation. In our case, where we solve for perturbations around a background state, they also have a true value of zero. Generating our prior flux for the inversion is achieved by defining a vector of normally distributed random numbers with unit standard deviation and zero mean. The process to generate the pseudo prior is represented in Eq. (

We used the CMAQ modelling system and its adjoint

We treat

Physics parameterizations used in the Weather Research and Forecasting (WRF) model setup.

The CMAQ model is an offline model, and thus requires three-dimensional meteorological fields as inputs for the transport calculations. We simulated meteorological data using the
Weather Research and Forecasting model (WRF) Advance Research Dynamical Core WRF-ARW (henceforth, WRF) version 3.7.1

The meteorological initial conditions were based on the ERA-Interim global atmospheric reanalysis

The WRF modelled meteorology was nudged towards the global analysis fields above the boundary layer. The default grid-nudging configuration was used; that is, nudging coefficients were assumed to be

The WRF model output was post-processed by the Meteorology-Chemistry Interface Processor (MCIP) version 4.2

As is seen in Eq. (

In this section, we present an assessment of the uncertainty reduction resulting from the flux-inversion process. First, we present an analysis of the convergence of our minimization and evaluate the information content (degrees of freedom for signal) of our OSSE simulation experiments. This is followed by an analysis of the uncertainty reduction categorized by MODIS land coverage. Finally, we present seven sensitivity experiments to determine the robustness and consistency of our inversions.

One interesting diagnostic of the convergence is to compare the cost function at the end of the optimization to its expected theoretical value. In a consistent system, the theoretical value of the cost function at its minimum should be close to half the number of assimilated observations, assuming all error statistics are correctly specified

Convergence diagnostics of the inversion system using an ensemble of five independent OSSEs for March, June, September and December 2015. Date format is YYYY-MM.

The number of degrees of freedom for signal (DFS) in our OSSEs is another useful diagnostic of the inversion

The uncertainty reduction between the posterior and prior fluxes is a useful way to evaluate the potential of satellite data to constrain

Spatial distribution of OCO-2 soundings (land nadir and glint data) over the CMAQ domain for March, June, September and December 2015.

Monthly mean of

The cumulative percentage variance explained

The percentage error reduction of the monthly-mean

In March, the largest uncertainty reductions (Fig.

To get a better understanding of the constraint on

Aggregation of land cover classes over CMAQ domain using MODIS Land Cover Type Product (MCD12C1) Version 6 data product. Colour bars represent each category: (0) ocean, (1) grasses and cereal, (2) shrubs, (3) evergreen needleleaf forest, (4) savannah, (5) evergreen broadleaf forest, and (6) unvegetated land.

Prior and posterior uncertainties (in Pg C yr

The bar chart in Fig.

The largest uncertainty reduction in March is over SH (81 %). The large uncertainty reduction is likely due to the large number of OCO-2 soundings in this region (464 observations). The next largest uncertainty reductions are over GC (78 %) and ENF forest (68 %) likely due to the relatively large NPP in these regions (Fig.

June shows less uncertainty reduction for GC (51 %) compared to March, likely due to the smaller number (one third as many) of OCO-2 soundings (Fig.

In September the most significant uncertainty reduction was found over EBF (74 %) and GC (68 %) compared with all other months, associated with the peak of the growing season in much of Australia. Uncertainty reductions in these categories are much larger due to the increase of OCO-2 soundings in south-eastern Australia (see Fig.

Similar to September, in December we found the largest uncertainty reductions over EBF (72 %) in line with the structure of the uncertainties seen in south-eastern of Australia in (Fig.

Table

Prior and posterior uncertainties (in Pg C yr

Differences in the uncertainty reduction between months not only depend on the number of soundings and the structure of the uncertainty but also other variables (e.g. wind direction). Coastal grid points present a problem for our inversion when the wind direction comes from the ocean because our system only assimilates data over land). Prevailing winds in this coastal zone restrict the ability of OCO-2 to constrain surface fluxes (Figs. S1–S3 in the Supplement).

To assess the robustness and consistency of the previous results, we performed seven different sensitivity experiments (S1, S2, S3, S4, S5, S6-A, S6-B), which are summarized in Table

A brief description of the sensitivity OSSEs performed for March 2015.

Land nadir data is defined as LN, and land nadir and glint data as LNG.

Table

Number of degrees of freedom for signal (DFS) in the prior flux uncertainty and the number the principal eigenvector in the prior error covariance matrix for sensitivity experiments S1, S2 and S3.

Figure

Maps of the percentage of error reduction for the three sensitivity cases.

Experiment S2 (Fig.

Experiment S3 (Fig.

Figure

Sensitivity experiments for the prior and posterior uncertainties (in Pg C yr

Similarly, case S2 (Fig.

Uncertainty reduction of the total Australian

Prior and posterior uncertainties (in Pg C yr

Experiment S2 shows an uncertainty reduction over Australia from 73 % compared to 76 % (control case). This small shift in the percentage of reduction is related to the number of soundings found in the northern region of Australia. By removing glint land data from our observations, we are reducing the coverage of surface flux footprints.

Experiment S3 demonstrates the same artefact as S1, though the generally higher prior uncertainties in S3 result in a higher uncertainty reduction for the total Australian flux. In this case, the assimilation reduces the total uncertainty to 34 %.

We mentioned in Sect.

Posterior bias of monthly

Results of experiment S5 are illustrated in Fig.

Prior (blue) and posterior (red) monthly-mean

Unlike global flux inversions, regional flux inversions are sensitive to lateral boundary conditions (BCs). To explore how sensitive our system is to biased BCs, we ran two further sensitivity experiments (collectively termed “S6”). In sensitivity experiment S6-A we increased the BCs by adding 0.5

Posterior bias of monthly

Experiment S6-B was designed to see if the inversion could correct for biases in the boundary conditions given additional parameters to optimize. After solving for BCs in the inversion, the biases introduced to BCs in S6-A were corrected. We analysed the corrections by looking at the bias of the posterior flux for each land-use category. Figure

One key uncertainty in any OSSE is the realism of the observational uncertainties. One simple test involves performing a limited inversion of data and assessing whether the cost function (Eq.

Figure

The distribution of the difference between simulated and observed

In this paper, we quantified the potential uncertainty reduction in monthly

Our results must be interpreted with caution, because, like all OSSEs, they depend strongly on assumed inputs (such as

Sensitivity experiments S1 and S3 show that the uncertainty reduction in

Sensitivity experiment S4 shows that the existence of biases in the observations has a significant impact on our posterior flux estimate. Adding biases to our simulated OCO-2 observation prevents our inversion from converging on optimal fluxes. We saw in Sect.

Results in sensitivity case S5 shows that biased prior fluxes satisfy the theoretical assumption in the variational optimization similar to using an unbiased prior case. We demonstrated that our system is able to handle the impact of possible biases in the CMAQ model that might contaminate the resulting posterior fluxes.

Another direction for future work would be to explore the impact of a finer temporal and horizontal resolution on the resulting fluxes. Model simulations at higher spatio-temporal resolutions have been shown to have better agreement with observations, partly on account of allowing for a better representation of the measurements.

We emphasize again that our study quantifies the uncertainty but not the realism of our posterior flux estimates. The assessment of posterior fluxes from assimilation of real data will be the subject of an upcoming paper. This requires comparison with independent concentration data or, if available, flux estimates at comparable scales.

We have performed an observing system simulation experiment for the retrieval of

Convergence diagnostic of the inversion system using an ensemble of five independent OSSEs for March 2015 (

Convergence diagnostic of the inversion system using an ensemble of five independent OSSEs for June 2015 (

Convergence diagnostic of the inversion system using an ensemble of five independent OSSEs for September 2015 (

Convergence diagnostic of the inversion system using an ensemble of five independent OSSEs for December 2015 (

Uncertainty reduction of total

Uncertainty reduction of total

Uncertainty reduction of total

Uncertainty reduction of total

Convergence diagnostic of sensitivity case (1) after the inversion using an ensemble of five independent OSSEs for March 2015 (

Convergence diagnostic of sensitivity case (2) after the inversion using an ensemble of five independent OSSEs for March 2015 (

Convergence diagnostic of sensitivity case (3) after the inversion using an ensemble of five independent OSSEs for March 2015 (

Sensitivity case (1): uncertainty reduction of total

Sensitivity case (2): uncertainty reduction of total

Sensitivity case (3): uncertainty reduction of total

The inversion system for this work was performed in py4dvar code, which was written by Steven Thomas, available at

The supplement related to this article is available online at:

YV performed all the OSSEs, including pre- and post-processing of data, and was responsible for developing the paper. ST was the principal developer of the py4dvar code with overall scientific guidance with additional analysis code from PR and JS. PR and JS also contributed to the writing of the article.

The authors declare that they have no conflict of interest.

This project was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government, and the resources of the High-performance Computing Centre of the University of Melbourne, SPARTAN

This research has been supported by the National Commission for Scientific and Technological Research (CONICYT) scholarship, Becas Chile (grant no. 72170210), the Education Infrastructure Fund of the Australian Government, and the Australian Research Council (ARC) of the Centre of Excellence for Climate Extreme (CLEX, grant no. CE170100023).

This paper was edited by Yugo Kanaya and reviewed by three anonymous referees.