Global and regional carbon budget 2015–2020 inferred from OCO-2 based on an ensemble Kalman filter coupled with GEOS-Chem
- 1Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 100084, China
- 2Institute of Environment and Ecology, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
- 3State Environmental Protection Key Laboratory of Sources and Control of Air Pollution Complex, Beijing 100084, China
- 4State Key Joint Laboratory of Environment Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing 100084, China
- 1Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 100084, China
- 2Institute of Environment and Ecology, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
- 3State Environmental Protection Key Laboratory of Sources and Control of Air Pollution Complex, Beijing 100084, China
- 4State Key Joint Laboratory of Environment Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing 100084, China
Abstract. Understanding carbon sources and sinks across the Earth’s surface is fundamental in climate science and policy; thus, these topics have been extensively studied but have yet to be fully resolved and are associated with massive debate regarding the sign and magnitude of the carbon budget from global to regional scales. Developing new models and estimates based on state-of-the-art algorithms and data constraints can provide valuable knowledge and contribute to a final ensemble model in which various optimal carbon budget estimates are integrated, such as the annual Global Carbon Budget paper. Here, we develop a new atmospheric inversion system based on the four-dimensional local ensemble transform Kalman filter (4D-LETKF) coupled with the GEOS-Chem global transport model to infer surface-to-atmosphere net carbon fluxes from Orbiting Carbon Observatory-2 (OCO-2) V10r XCO2 retrievals. The 4D-LETKF algorithm is adapted to an OCO-2-based global carbon inversion system for the first time in this work. On average, the mean annual terrestrial and oceanic fluxes between 2015 and 2020 are estimated as −2.02 GtC yr−1 and −2.34 GtC yr−1, respectively, compensating for 21 % and 24 %, respectively, of global fossil CO2 emissions (9.80 GtC yr−1). Our inversion results agree with the CO2 atmospheric growth rates reported by the National Oceanic and Atmospheric Administration (NOAA) and reduce the modelled CO2 concentration biases relative to the prior fluxes against surface and aircraft measurements. Our inversion-based carbon fluxes are broadly consistent with those provided by other global atmospheric inversion models, although discrepancies still occur in the land-ocean flux partitioning schemes and seasonal flux amplitudes over boreal and tropical regions, possibly due to the sparse observational constraints of the OCO-2 satellite and the divergent prior fluxes used in different inversion models. Four sensitivity experiments are performed herein to vary the prior fluxes and uncertainties in our inversion system, suggesting that regions that lack OCO-2 coverage are sensitive to the priors, especially over the tropics and high latitudes. In the further development of our inversion system, we will optimize the data-assimilation configuration to fully utilize current observations and increase the spatial and seasonal representativeness of the prior fluxes over regions that lack observations.
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Yawen Kong et al.
Status: final response (author comments only)
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RC1: 'Comment on acp-2022-183', Anonymous Referee #1, 18 May 2022
The authors present a new framework for performing atmospheric flux invesions. This framework is based on a four-dimensional local ensemble transform Kalman filter (4D-LETKF), with GEOS-Chem used as the transport model. The method is applied to version 10r column-averaged CO2 retrievals from the OCO-2 satellite over the five year period from 2015 to 2020. The estimated fluxes were found to be broadly consistent with those from other flux inversion systems. This represents the first application of a 4D-LETKF algorithm to perform an atmospheric inversion using OCO-2 data.
I find the paper to be well written and clear in general. The method is novel because it combines a high-dimensional grid-based parameterisation with an ensemble Kalman filtering approach. I appreciate that the authors performed sensitivity experiments to better understand what is driving the results. My main critique is that I find the mathematical description of the method lacking. My secondary critique relates to the lack of a discussion of the advantages or disadvantages of the method in comparison to other inversion systems.
Major comments
- I found it difficult to understand the method based on Section 2.1. Here are my specific questions:
- How are the ensemble members initialised?
- The matrix B appears in equation (1) but not in equations (2)-(5). Is B the error structure for x^b that is mentioned in line 115? How does B affect the posterior state if it does not appear in the calculations?
- What is contained within the vector x^b (and x^a, and so on)? Is it the control variables (scaling factors) for the whole assimilation period (7 days), or is it just for the first day? If it's just the first day, what are the implied values for the next 6 days, which will affect the modelled concentrations y^{b(i)}? Are these assumed to be equal to the prior mean? I looked at Figure~1 but I still could not understand what was happening.
- Related to the last point, the calculation of \bar{x}^b is described as "the average optimized result from the two previous time steps and a fixed value of one". Does this calculation apply to the new day entering the assimilation period, or to all the days?
- The modelled concentrations y^{b(i)} must also depend on state values from before the assimilation period. Are these set to the posterior mean, or are they different from each ensemble member? What is assumed exactly?
- I find the notation regarding \bar{x} a little confusing. Is this the unweighted average of the ensemble members? I ask because \bar{x}^a and \bar{x}^b are not unweighted averages, so the notation is a little bit inconsistent.
- How does the localisation length work? It is stated that "y^o contains the assimilated OCO-2 XCO2 within the assimilation window and localization length". Since the state vector contains every grid cell for a day, how can any observations be excluded by the localization length?
- I think it would help for the authors to discuss how their method compares to other methods. For example, a convention al 4D-Var system has a similar state space and a similar cost function. What, in the authors view, are the advantages of their method? I think just a short discussion of the most common methods and how they compare qualitatively to the authors method would be enough.
Minor comments
Line 151, what does the word ``integrated'' mean here? Does it mean that the flux field was shifted to have annual mean zero? How was this done?
- I found it difficult to understand the method based on Section 2.1. Here are my specific questions:
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RC2: 'comment on acp-2022-183', Anonymous Referee #2, 19 May 2022
General comments.
The authors applied a flux inversion system based on LETKF algorithm to estimating the global and regional CO2 fluxes based on OCO-2 satellite observations. They obtained useful results indicating ability to reconstruct the regional surface fluxes fitting within a spread of the recent global inverse modelling results by other modelling systems. On the other hand, there are deficiencies of the method that authors could not overcome and hope to improve in further developments. Paper is well written and illustrated and can be accepted after minor revisions.
Detailed comments.
- The length of optimization window of 1 week limits the power of the remote observations to constrain the fluxes. One can see a difference between fluxes retrieved with Kalman smoother when applying 1-month and 3-month assimilation window (Bruhwiler et al, 2005). The deficiency has been noted in the abstract as ‘Four sensitivity experiments are performed herein to vary the prior fluxes and uncertainties in our inversion system, suggesting that regions that lack OCO-2 coverage are sensitive to the priors, especially over the tropics and high latitudes’, which authors hope to address in future.
- There are visible problems with posterior fluxes, as shown on Fig. 4, the range of annual mean grid fluxes occasionally goes out of reasonable range, exceeding 100 gC/m2/year, pointing to a poor balance between large scale and grid scale uncertainties, lack of a spatial correlation constraint on flux correction gradients. The results with the presumably similar algorithm in Liu et al (2019) do not show such noise, which pint to having some important differences that must be documented. Similar flux noise problem was encountered by Miyazaki et al, (2011) and later studies. Can authors isolate the cause of the problem? Could it be a result of using random grid fields as ensemble flux perturbations, while there is an alternative of using smoother random fields?
- Another issue related to the grid flux noise is the ensemble size. As shown by Chatterjee et al (2012), Chatterjee and Michalak, (2013) the inversion results are sensitive to ensemble size, and useful improvement are archived by increasing the ensemble size beyond 100. Miyazaki et al (2011) also obtained visible improvement of flux constraint by increasing the ensemble size from 48 to 96. Compared to those designs a system presented in this study relies on rather small ensemble size.
Despite of the visible success in weather forecast applications, LETKF use in carbon flux inversion has been tried in several studies but did not become widely used due to limitations, presumably not providing a better computational efficiency over adjoint-based variational or low rank inversion algorithms. In a revised manuscript it is advisable to mention the deficiencies of the LETKF system: limitations of small ensemble size and short window length (which may be reasonable for coupled weather-carbon cycle assimilation) and provide better arguments in support of this direction in comparison to other settings, for example Kalman filter approaches formulated by Feng et al, (2009).
Detailed comments
Line 72 In addition to Liu et al 2019, it is useful to mention the results by Miyazaki et al 2011 who also studied adding GOSAT satellite observations.
References
Bruhwiler, L. M. P., Michalak, A. M., Peters, W., Baker, D. F., and Tans, P.: An improved Kalman Smoother for atmospheric inversions, Atmos. Chem. Phys., 5, 2691–2702, https://doi.org/10.5194/acp-5-2691-2005, 2005
Chatterjee, A., A. M. Michalak, J. L. Anderson, K. L. Mueller, and V. Yadav (2012), Toward reliable ensemble Kalman filter estimates of CO2 fluxes, J. Geophys. Res., 117, D22306, doi:10.1029/2012JD018176
Chatterjee A., A. M. Michalak, Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO2 data assimilation, Atmospheric Chemistry and Physics, 10.5194/acp-13-11643-2013, 13, 23, 11643-11660, 2013.
Miyazaki, K., Maki, T., Patra, P., and Nakazawa, T. (2011), Assessing the impact of satellite, aircraft, and surface observations on CO2 flux estimation using an ensemble-based 4-D data assimilation system, J. Geophys. Res., 116, D16306, doi:10.1029/2010JD015366.
Yawen Kong et al.
Yawen Kong et al.
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