Prior Flux Errors Research Articles

Regional CO2 Inversion Through Ensemble‐Based Simultaneous State and Parameter Estimation: TRACE Framework and Controlled Experiments

AbstractAtmospheric inversions provide estimates of carbon dioxide (CO2) fluxes between the surface and atmosphere based on atmospheric CO2 concentration observations. The number of CO2 observations is projected to increase severalfold in the next decades from expanding in situ networks and next‐generation CO2‐observing satellites, providing both an opportunity and a challenge for inversions. This study introduces the TRACE Regional Atmosphere–Carbon Ensemble (TRACE) system, which employ an ensemble‐based simultaneous state and parameter estimation (ESSPE) approach to enable the assimilation of large volumes of observations for constraining CO2 flux parameters. TRACE uses an online full‐physics mesoscale atmospheric model and assimilates observations serially in a coupled atmosphere–carbon ensemble Kalman filter. The data assimilation system was tested in a series of observing system simulation experiments using in situ observations for a regional domain over North America in summer. Under ideal conditions with known prior flux parameter error covariances, TRACE reduced the error in domain‐integrated monthly CO2 fluxes by about 97% relative to the prior flux errors. In a more realistic scenario with unknown prior flux error statistics, the corresponding relative error reductions ranged from 80.6% to 88.5% depending on the specification of prior flux parameter error correlations. For regionally integrated fluxes on a spatial scale of 106 km2, the sum of absolute errors was reduced by 34.5%–50.9% relative to the prior flux errors. Moreover, TRACE produced posterior uncertainty estimates that were consistent with the true errors. These initial experiments show that the ESSPE approach in TRACE provides a promising method for advancing CO2 inversion techniques.

Development of a Mesoscale Inversion System for Estimating Continental‐Scale CO2 Fluxes

AbstractComputational requirements often impose limitations on the spatial and temporal resolutions of atmospheric CO2 inversions, increasing aggregation and representation errors. This study enables higher spatial and temporal resolution inversions with spatial and temporal error structures similar to those used in other published inversions by representing the prior flux error covariances as a Kronecker product of spatial and temporal covariances and by using spectral methods for the spatial correlations. Compared to existing inversion systems that are forced to degrade the resolution of the problem in order to bring the dimensionality down to computationally tractable levels, this inversion framework is able to take advantage of mesoscale transport simulations and more of the complexity of spatial and temporal covariances in the surface CO2 fluxes. This approach was successfully implemented over one month with an identical‐twin observing system simulation experiment (OSSE) using a set of assumptions about the prior flux uncertainties compatible both with continental‐scale uncertainty estimates and with comparisons of vegetation models to flux towers. The demonstration illustrates the potential of the newly developed inversion system to use high‐temporal‐resolution information from the North American tower network, to extract high‐resolution information about CO2 fluxes that is inaccessible to coarser resolution inversion systems, and to simultaneously optimize an ensemble of prior estimates. This demonstration sets the stage for regional flux inversions that can take full advantage of the high‐resolution data available in tower CO2 records and mesoscale atmospheric transport reanalyses, include more realistic prior error structures, and explore specifying prior fluxes with ensembles.

Technical Note: Atmospheric CO<sub>2</sub> inversions on the mesoscale using data-driven prior uncertainties: methodology and system evaluation

Abstract. Atmospheric inversions are widely used in the optimization of surface carbon fluxes on a regional scale using information from atmospheric CO2 dry mole fractions. In many studies the prior flux uncertainty applied to the inversion schemes does not directly reflect the true flux uncertainties but is used to regularize the inverse problem. Here, we aim to implement an inversion scheme using the Jena inversion system and applying a prior flux error structure derived from a model–data residual analysis using high spatial and temporal resolution over a full year period in the European domain. We analyzed the performance of the inversion system with a synthetic experiment, in which the flux constraint is derived following the same residual analysis but applied to the model–model mismatch. The synthetic study showed a quite good agreement between posterior and true fluxes on European, country, annual and monthly scales. Posterior monthly and country-aggregated fluxes improved their correlation coefficient with the known truth by 7 % compared to the prior estimates when compared to the reference, with a mean correlation of 0.92. The ratio of the SD between the posterior and reference and between the prior and reference was also reduced by 33 % with a mean value of 1.15. We identified temporal and spatial scales on which the inversion system maximizes the derived information; monthly temporal scales at around 200 km spatial resolution seem to maximize the information gain.

Joint inverse estimation of fossil fuel and biogenic CO2 fluxes in an urban environment: An observing system simulation experiment to assess the impact of multiple uncertainties

The Indianapolis Flux Experiment aims to utilize a variety of atmospheric measurements and a high-resolution inversion system to estimate the temporal and spatial variation of anthropogenic greenhouse gas emissions from an urban environment. We present a Bayesian inversion system solving for fossil fuel and biogenic CO2 fluxes over the city of Indianapolis, IN. Both components were described at 1 km resolution to represent point sources and fine-scale structures such as highways in the a priori fluxes. With a series of Observing System Simulation Experiments, we evaluate the sensitivity of inverse flux estimates to various measurement deployment strategies and errors. We also test the impacts of flux error structures, biogenic CO2 fluxes and atmospheric transport errors on estimating fossil fuel CO2 emissions and their uncertainties. The results indicate that high-accuracy and high-precision measurements produce significant improvement in fossil fuel CO2 flux estimates. Systematic measurement errors of 1 ppm produce significantly biased inverse solutions, degrading the accuracy of retrieved emissions by about 1 µmol m–2 s–1 compared to the spatially averaged anthropogenic CO2 emissions of 5 µmol m–2 s–1. The presence of biogenic CO2 fluxes (similar magnitude to the anthropogenic fluxes) limits our ability to correct for random and systematic emission errors. However, assimilating continuous fossil fuel CO2 measurements with 1 ppm random error in addition to total CO2 measurements can partially compensate for the interference from biogenic CO2 fluxes. Moreover, systematic and random flux errors can be further reduced by reducing model-data mismatch errors caused by atmospheric transport uncertainty. Finally, the precision of the inverse flux estimate is highly sensitive to the correlation length scale in the prior emission errors. This work suggests that improved fossil fuel CO2 measurement technology, and better understanding of both prior flux and atmospheric transport errors are essential to improve the accuracy and precision of high-resolution urban CO2 flux estimates.

A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 2: Optimization scheme and identical twin experiment of atmospheric CO<sub>2</sub> inversion

Abstract. A four-dimensional variational method (4D-Var) is a popular technique for source/sink inversions of atmospheric constituents, but it is not without problems. Using an icosahedral grid transport model and the 4D-Var method, a new atmospheric greenhouse gas (GHG) inversion system has been developed. The system combines offline forward and adjoint models with a quasi-Newton optimization scheme. The new approach is then used to conduct identical twin experiments to investigate optimal system settings for an atmospheric CO2 inversion problem, and to demonstrate the validity of the new inversion system. In this paper, the inversion problem is simplified by assuming the prior flux errors to be reasonably well known and by designing the prior error correlations with a simple function as a first step. It is found that a system of forward and adjoint models with smaller model errors but with nonlinearity has comparable optimization performance to that of another system that conserves linearity with an exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is demonstrated, as the global error is reduced by about 15 % by adding prior error correlations that are simply designed when 65 weekly flask sampling observations at ground-based stations are used. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to global scales. The optimization algorithm introduced in the new system does not require decomposition of a matrix that establishes the correlation among the prior flux errors. This enables us to design the prior error covariance matrix more freely.

Greenhouse gas network design using backward Lagrangian particle dispersion modelling – Part 2: Sensitivity analyses and South African test case

Abstract. This is the second part of a two-part paper considering a measurement network design based on a stochastic Lagrangian particle dispersion model (LPDM) developed by Marek Uliasz, in this case for South Africa. A sensitivity analysis was performed for different specifications of the network design parameters which were applied to this South African test case. The LPDM, which can be used to derive the sensitivity matrix used in an atmospheric inversion, was run for each candidate station for the months of July (representative of the Southern Hemisphere winter) and January (summer). The network optimisation procedure was carried out under a standard set of conditions, similar to those applied to the Australian test case in Part 1, for both months and for the combined 2 months, using the incremental optimisation (IO) routine. The optimal network design setup was subtly changed, one parameter at a time, and the optimisation routine was re-run under each set of modified conditions and compared to the original optimal network design. The assessment of the similarity between network solutions showed that changing the height of the surface grid cells, including an uncertainty estimate for the ocean fluxes, or increasing the night-time observation error uncertainty did not result in any significant changes in the positioning of the stations relative to the standard design. However, changing the prior flux error covariance matrix, or increasing the spatial resolution, did. Large aggregation errors were calculated for a number of candidate measurement sites using the resolution of the standard network design. Spatial resolution of the prior fluxes should be kept as close to the resolution of the transport model as the computing system can manage, to mitigate the exclusion of sites which could potentially be beneficial to the network. Including a generic correlation structure in the prior flux error covariance matrix led to pronounced changes in the network solution. The genetic algorithm (GA) was able to find a marginally better solution than the IO procedure, increasing uncertainty reduction by 0.3 %, but still included the most influential stations from the standard network design. In addition, the computational cost of the GA compared to IO was much higher. Overall the results suggest that a good improvement in knowledge of South African fluxes is available from a feasible atmospheric network, and that the general features of this network are invariable under several reasonable choices in a network design study.

U.S. emissions of HFC‐134a derived for 2008–2012 from an extensive flask‐air sampling network

AbstractU.S. national and regional emissions of HFC‐134a are derived for 2008–2012 based on atmospheric observations from ground and aircraft sites across the U.S. and a newly developed regional inverse model. Synthetic data experiments were first conducted to optimize the model assimilation design and to assess model‐data mismatch errors and prior flux error covariances computed using a maximum likelihood estimation technique. The synthetic data experiments also tested the sensitivity of derived national and regional emissions to a range of assumed prior emissions, with the goal of designing a system that was minimally reliant on the prior. We then explored the influence of additional sources of error in inversions with actual observations, such as those associated with background mole fractions and transport uncertainties. Estimated emissions of HFC‐134a range from 52 to 61 Gg yr−1 for the contiguous U.S. during 2008–2012 for inversions using air transport from Hybrid Single‐Particle Lagrangian Integrated Trajectory (HYSPLIT) model driven by the 12 km resolution meteorogical data from North American Mesoscale Forecast System (NAM12) and all tested combinations of prior emissions and background mole fractions. Estimated emissions for 2008–2010 were 20% lower when specifying alternative transport from Stochastic Time‐Inverted Lagrangian Transport (STILT) model driven by the Weather Research and Forecasting (WRF) meteorology. Our estimates (for HYSPLIT‐NAM12) are consistent with annual emissions reported by U.S. Environmental Protection Agency for the full study interval. The results suggest a 10–20% drop in U.S. national HFC‐134a emission in 2009 coincident with a reduction in transportation‐related fossil fuel CO2 emissions, perhaps related to the economic recession. All inversions show seasonal variation in national HFC‐134a emissions in all years, with summer emissions greater than winter emissions by 20–50%.

Carbon monitoring system flux estimation and attribution: impact of ACOS-GOSAT XCO2 sampling on the inference of terrestrial biospheric sources and sinks

Using an Observing System Simulation Experiment (OSSE), we investigate the impact of JAXA Greenhouse gases Observing SATellite ‘IBUKI’ (GOSAT) sampling on the estimation of terrestrial biospheric flux with the NASA Carbon Monitoring System Flux (CMS-Flux) estimation and attribution strategy. The simulated observations in the OSSE use the actual column carbon dioxide (XCO2) b2.9 retrieval sensitivity and quality control for the year 2010 processed through the Atmospheric CO2 Observations from Space algorithm. CMS-Flux is a variational inversion system that uses the GEOS-Chem forward and adjoint model forced by a suite of observationally constrained fluxes from ocean, land and anthropogenic models. We investigate the impact of GOSAT sampling on flux estimation in two aspects: 1) random error uncertainty reduction and 2) the global and regional bias in posterior flux resulted from the spatiotemporally biased GOSAT sampling. Based on Monte Carlo calculations, we find that global average flux uncertainty reduction ranges from 25% in September to 60% in July. When aggregated to the 11 land regions designated by the phase 3 of the Atmospheric Tracer Transport Model Intercomparison Project, the annual mean uncertainty reduction ranges from 10% over North American boreal to 38% over South American temperate, which is driven by observational coverage and the magnitude of prior flux uncertainty. The uncertainty reduction over the South American tropical region is 30%, even with sparse observation coverage. We show that this reduction results from the large prior flux uncertainty and the impact of non-local observations. Given the assumed prior error statistics, the degree of freedom for signal is ~1132 for 1-yr of the 74 055 GOSAT XCO2 observations, which indicates that GOSAT provides ~1132 independent pieces of information about surface fluxes. We quantify the impact of GOSAT's spatiotemporally sampling on the posterior flux, and find that a 0.7 gigatons of carbon bias in the global annual posterior flux resulted from the seasonally and diurnally biased sampling when using a diagonal prior flux error covariance.

Hyperparameter estimation for uncertainty quantification in mesoscale carbon dioxide inversions

Uncertainty quantification is critical in the inversion of CO2 surface fluxes from atmospheric concentration measurements. Here, we estimate the main hyperparameters of the error covariance matrices for a priori fluxes and CO2 concentrations, that is, the variances and the correlation lengths, using real, continuous hourly CO2 concentration data in the context of the Ring 2 experiment of the North American Carbon Program Mid Continent Intensive. Several criteria, namely maximum likelihood (ML), general cross-validation (GCV) and χ2 test are compared for the first time under a realistic setting in a mesoscale CO2 inversion. It is shown that the optimal hyperparameters under the ML criterion assure perfect χ2 consistency of the inverted fluxes. Inversions using the ML error variances estimates rather than the prescribed default values are less weighted by the observations, because the default values underestimate the model-data mismatch error, which is assumed to be dominated by the atmospheric transport error. As for the spatial correlation length in prior flux errors, the Ring 2 network is sparse for GCV, and this method fails to reach an optimum. In contrast, the ML estimate (e.g. an optimum of 20 km for the first week of June 2007) does not support long spatial correlations that are usually assumed in the default values.

What eddy‐covariance measurements tell us about prior land flux errors in CO2‐flux inversion schemes

To guide the future development of CO2‐atmospheric inversion modeling systems, we analyzed the errors arising from prior information about terrestrial ecosystem fluxes. We compared the surface fluxes calculated by a process‐based terrestrial ecosystem model with daily averages of CO2flux measurements at 156 sites across the world in the FLUXNET network. At the daily scale, the standard deviation of the model‐data fit was 2.5 gC·m−2·d−1; temporal autocorrelations were significant at the weekly scale (>0.3 for lags less than four weeks), while spatial correlations were confined to within the first few hundred kilometers (<0.2 after 200 km). Separating out the plant functional types did not increase the spatial correlations, except for the deciduous broad‐leaved forests. Using the statistics of the flux measurements as a proxy for the statistics of the prior flux errors was shown not to be a viable approach. A statistical model allowed us to upscale the site‐level flux error statistics to the coarser spatial and temporal resolutions used in regional or global models. This approach allowed us to quantify how aggregation reduces error variances, while increasing correlations. As an example, for a typical inversion of grid point (300 km × 300 km) monthly fluxes, we found that the prior flux error follows an approximate e‐folding correlation length of 500 km only, with correlations from one month to the next as large as 0.6.

Network design for mesoscale inversions of CO2 sources and sinks

ABSTRACTRecent instrumental deployments of regional observation networks of atmospheric CO2 mixing ratios have been used to constrain carbon sources and sinks using inversion methodologies. In this study, we performed sensitivity experiments using observation sites from the Mid Continent Intensive experiment to evaluate the required spatial density and locations of CO2 concentration towers based on flux corrections and error reduction analysis. In addition, we investigated the impact of prior flux error structures with different correlation lengths and biome information. We show here that, while the regional carbon balance converged to similar annual estimates using only two concentration towers over the region, additional sites were necessary to retrieve the spatial flux distribution of our reference case (using the entire network of eight towers). Local flux corrections required the presence of observation sites in their vicinity, suggesting that each tower was only able to retrieve major corrections within a hundred of kilometres around, despite the introduction of spatial correlation lengths (~100 to 300 km) in the prior flux errors. We then quantified and evaluated the impact of the spatial correlations in the prior flux errors by estimating the improvement in the CO2 model-data mismatch of the towers not included in the inversion. The overall gain across the domain increased with the correlation length, up to 300 km, including both biome-related and non-biome-related structures. However, the spatial variability at smaller scales was not improved. We conclude that the placement of observation towers around major sources and sinks is critical for regional-scale inversions in order to obtain reliable flux distributions in space. Sparser networks seem sufficient to assess the overall regional carbon budget with the support of flux error correlations, indicating that regional signals can be recovered using hourly mixing ratios. However, the smaller spatial structures in the posterior fluxes are highly constrained by assumed prior flux error correlation lengths, with no significant improvement at only a few hundreds of kilometres away from the observation sites.

Inverse modeling of Asian 222Rn flux using surface air 222Rn concentration

When used with an atmospheric transport model, the 222Rn flux distribution estimated in our previous study using soil transport theory caused underestimation of atmospheric 222Rn concentrations as compared with measurements in East Asia. In this study, we applied a Bayesian synthesis inverse method to produce revised estimates of the annual 222Rn flux density in Asia by using atmospheric 222Rn concentrations measured at seven sites in East Asia. The Bayesian synthesis inverse method requires a prior estimate of the flux distribution and its uncertainties. The atmospheric transport model MM5/HIRAT and our previous estimate of the 222Rn flux distribution as the prior value were used to generate new flux estimates for the eastern half of the Eurasian continent dividing into 10 regions. The 222Rn flux densities estimated using the Bayesian inversion technique were generally higher than the prior flux densities. The area-weighted average 222Rn flux density for Asia was estimated to be 33.0 mBq m −2 s −1, which is substantially higher than the prior value (16.7 mBq m −2 s −1). The estimated 222Rn flux densities decrease with increasing latitude as follows: Southeast Asia (36.7 mBq m −2 s −1); East Asia (28.6 mBq m −2 s −1) including China, Korean Peninsula and Japan; and Siberia (14.1 mBq m −2 s −1). Increase of the newly estimated fluxes in Southeast Asia, China, Japan, and the southern part of Eastern Siberia from the prior ones contributed most significantly to improved agreement of the model-calculated concentrations with the atmospheric measurements. The sensitivity analysis of prior flux errors and effects of locally exhaled 222Rn showed that the estimated fluxes in Northern and Central China, Korea, Japan, and the southern part of Eastern Siberia were robust, but that in Central Asia had a large uncertainty.

What can we learn from European continuous atmospheric CO<sub>2</sub> measurements to quantify regional fluxes – Part 2: Sensitivity of flux accuracy to inverse setup

Abstract. An inverse model using atmospheric CO2 observations from a European network of stations to reconstruct daily CO2 fluxes and their uncertainties over Europe at 50 km resolution has been developed within a Bayesian framework. We use the pseudo-data approach in which we try to recover known fluxes using a range of perturbations to the input. In this study, the focus is put on the sensitivity of flux accuracy to the inverse setup, varying the prior flux errors, the pseudo-data errors and the network of stations. We show that, under a range of assumptions about prior error and data error we can recover fluxes reliably at the scale of 1000 km and 10 days. At smaller scales the performance is highly sensitive to details of the inverse set-up. The use of temporal correlations in the flux domain appears to be of the same importance as the spatial correlations. We also note that the use of simple, isotropic correlations on the prior flux errors is more reliable than the use of apparently physically-based errors. Finally, increasing the European atmospheric network density improves the area with significant error reduction in the flux retrieval.