One effective data assimilation/inversion method is the four‐dimensional variational method (4D‐Var). However, it is a non‐trivial task for a conventional 4D‐Var to estimate a posterior error ...covariance matrix. This study proposes a method to estimate a posterior error covariance matrix applied to the linear inverse problem of an atmospheric constituent. The method was constructed within a 4D‐Var framework using a quasi‐Newton method with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. The proposed method was constructed such that conjugacy among the set of increment vector pairs was ensured. It is theoretically demonstrated that, when this conjugate property is coupled with preconditioning, an analytical solution of a posterior error covariance matrix could be obtained from the same number of vector pairs as observations. Furthermore, to accelerate the speed of convergence, the method can be coupled with an ensemble approach. By performing a simple advection test, it was confirmed that the proposed method could obtain an analytical matrix of the posterior error covariance within the same number of iterations as the observations. Furthermore, the method was also evaluated using an atmospheric CO2 inverse problem, which demonstrated its practical utility. The evaluation revealed that the proposed method could provide accurate estimates not only of the diagonal but also of the off‐diagonal elements of the posterior error covariance matrix. Although far more expensive than optimal state estimation, the computational efficiency was found to be reasonable for practical use, especially in conjunction with an ensemble approach. The accurate estimation of a posterior error covariance matrix resulting from the proposed method could provide valuable quantitative information regarding the uncertainties of estimated variables as well as the observational impacts, which would be beneficial for designing observation networks. Furthermore, error correlations derived from the estimated off‐diagonal elements could benefit the interpretation of optimised parameter variations.
This study proposes a new method for accurate and efficient estimation of a posterior error covariance matrix, in which conjugacy among the set of increment vector pairs is ensured. The accurate estimation of a posterior error covariance matrix resulting from the proposed method could provide valuable quantitative information regarding the uncertainties of estimated variables as well as the observational impacts. Furthermore, error correlations derived from the estimated off‐diagonal elements could benefit the interpretation of optimised parameter variations.
Abstract
The COVID-19 pandemic caused drastic reductions in carbon dioxide (CO
2
) emissions, but due to its large atmospheric reservoir and long lifetime, no detectable signal has been observed in ...the atmospheric CO
2
growth rate. Using the variabilities in CO
2
(ΔCO
2
) and methane (ΔCH
4
) observed at Hateruma Island, Japan during 1997–2020, we show a traceable CO
2
emission reduction in China during February–March 2020. The monitoring station at Hateruma Island observes the outflow of Chinese emissions during winter and spring. A systematic increase in the ΔCO
2
/ΔCH
4
ratio, governed by synoptic wind variability, well corroborated the increase in China’s fossil-fuel CO
2
(FFCO
2
) emissions during 1997–2019. However, the ΔCO
2
/ΔCH
4
ratios showed significant decreases of 29 ± 11 and 16 ± 11 mol mol
−1
in February and March 2020, respectively, relative to the 2011–2019 average of 131 ± 11 mol mol
−1
. By projecting these observed ΔCO
2
/ΔCH
4
ratios on transport model simulations, we estimated reductions of 32 ± 12% and 19 ± 15% in the FFCO
2
emissions in China for February and March 2020, respectively, compared to the expected emissions. Our data are consistent with the abrupt decrease in the economic activity in February, a slight recovery in March, and return to normal in April, which was calculated based on the COVID-19 lockdowns and mobility restriction datasets.
Cities are responsible for the largest anthropogenic CO2 emissions and are key to effective emission reduction strategies. Urban CO2 emissions estimated from vertical atmospheric measurements can ...contribute to an independent quantification of the reporting of national emissions and will thus have political implications. We analyzed vertical atmospheric CO2 mole fraction data obtained onboard commercial aircraft in proximity to 36 airports worldwide, as part of the Comprehensive Observation Network for Trace gases by Airliners (CONTRAIL) program. At many airports, we observed significant flight-to-flight variations of CO2 enhancements downwind of neighboring cities, providing advective fingerprints of city CO2 emissions. Observed CO2 variability increased with decreasing altitude, the magnitude of which varied from city to city. We found that the magnitude of CO2 variability near the ground (~1 km altitude) at an airport was correlated with the intensity of CO2 emissions from a nearby city. Our study has demonstrated the usefulness of commercial aircraft data for city-scale anthropogenic CO2 emission studies.
Synoptic-scale variabilities of atmospheric CO2 and CH4 observed at Yonagunijima (Yonaguni Island, YON, 24.47°N, 123.01°E) during winter (from January to March) in 1998–2020 were examined. The ...monthly mean variability ratios (ΔCO2/ΔCH4) based on correlation slopes within 24 h time windows showed a clear increasing trend, which is mainly attributed to the unprecedented increase in the fossil fuel-derived CO2 (FFCO2) emissions from China. A similar increasing trend of the ΔCO2/ΔCH4 ratio had been reported for the observation at Hateruma Island (HAT, 24.06°N, 123.81°E), located at approximately 100 km east of YON. Nevertheless, the absolute values for YON were 34 % larger than those for HAT. Additionally, the monthly average in February 2020 for YON showed no marked change, whereas that for HAT showed an abrupt considerable decrease associated with the FFCO2 emission decrease in China presumably caused by the COVID-19 lockdown. Investigating the diurnal variations, we found that the local influences were larger at YON, especially during daytime, than at HAT. Using nighttime data (20-6 LST) and a longer time window (84 h), we succeeded in reducing the local influences and the resulting monthly mean ΔCO2/ΔCH4 ratio showed considerable similarity to that observed at HAT including the abrupt decrease in February 2020. These results convinced us that the ΔCO2/ΔCH4 ratio could be successfully used to investigate the relative emission strength in the upwind region.
Accurate estimates of the carbon dioxide (CO
2
) fluxes at the earth’s surface are imperative for comprehending the carbon cycle mechanisms and providing reliable global warming predictions. ...Furthermore, they can also provide valuable science-based information that will be helpful in reducing human-induced CO
2
emissions. Inverse analysis is a prominent method of quantitatively estimating spatiotemporal variations in CO
2
fluxes; however, it involves a certain level of uncertainty and requires technical refinement, specifically to improve the horizontal resolution so that local fluxes can be compared with other estimates made at the regional or national level. In this study, a novel set of inversion schemes was incorporated into a state-of-the-art inverse analysis system named NISMON-CO
2
. The introduced schemes include a grid conversion, observational weighting, and anisotropic prior error covariance, the details of which are described. Moreover, pseudo-observation experiments were performed to examine the effect of the new schemes and to assess the reliability of NISMON-CO
2
for long-term analysis with practical inhomogeneous observations. The experiment results evidently demonstrate the advantages of the grid conversion scheme for high-resolution flux estimates (1° × 1°), with notable improvements being achieved through the observational weighting and anisotropic prior error covariance. Furthermore, the estimated seasonal and interannual variations in regional CO
2
fluxes were confirmed to be reliable, although some potential bias in terms of global land–ocean partitioning was observed. Thus, these results are useful for interpreting the flux variations that result from real-observation inverse analysis by NISMON-CO
2
ver. 2021.1.
The Greenhouse Gases Observing Satellite (GOSAT) was successfully launched in January 2009, with the aim of providing global observations of greenhouse gases. We developed an algorithm to retrieve ...CO2 vertical profiles from the terrestrial radiation spectra at 700–800 cm−1 and assessed its validity. For this purpose, we first computed GOSAT pseudomeasurement spectra and then performed CO2 retrieval simulations using the maximum a posteriori (MAP) method, with analytical data for temperature information. Our simulations with no uncertainty in the estimates of atmospheric conditions such as surface temperature, surface emissivity, and profiles of temperature, water vapor, and ozone showed that the retrieved CO2 profiles had an accuracy of 1% above 800 hPa, with little dependence on the a priori profiles. Introducing correlations between layers in an a priori error covariance matrix was important for CO2 retrieval especially above 200 hPa. Enhancing the correlations below 800 hPa was important for CO2 retrieval there. Selecting 100 channels based on CO2 information content for all layers, 10 channels for the region above 55 hPa, and 50 channels for the region below 800 hPa was sufficient to achieve CO2 retrieval with 1% accuracy from the troposphere through the stratosphere. Our simulations with possible errors in the atmospheric conditions showed that 1% accuracy was also achieved at 600–100 hPa in every latitude region, although the retrieved CO2 concentrations probably included up to 4% positive and negative biases at 30°S–30°N above 100 hPa and at mid‐ and high latitudes below 600 hPa, respectively.
Inverse analysis was used to estimate fire carbon
emissions in Equatorial Asia induced by the big El Niño event in 2015.
This inverse analysis is unique because it extensively used high-precision
...atmospheric mole fraction data of carbon dioxide (CO2) from the
commercial aircraft observation project CONTRAIL. Through comparisons with
independent shipboard observations, especially carbon monoxide (CO) data,
the validity of the estimated fire-induced carbon emissions was demonstrated.
The best estimate, which used both aircraft and shipboard CO2
observations, indicated 273 Tg C for fire emissions from
September–October 2015. This 2-month period accounts for 75 % of the annual total fire emissions and 45 % of the annual total net carbon flux within the region, indicating that fire emissions are a dominant driving force of interannual variations of carbon fluxes in Equatorial Asia.
Several sensitivity experiments demonstrated that aircraft observations
could measure fire signals, though they showed a certain degree of
sensitivity to prior fire-emission data. The inversions coherently estimated
smaller fire emissions than the prior data, partially because of the small
contribution of peatland fires indicated by enhancement ratios of CO and
CO2 observed by the ship. In future warmer climate conditions,
Equatorial Asia may experience more severe droughts, which risks releasing a
large amount of carbon into the atmosphere. Therefore, the continuation of
aircraft and shipboard observations is fruitful for reliable monitoring of
carbon fluxes in Equatorial Asia.
Emissions from biomass burning (BB) are a key source of atmospheric tracer gases that affect the atmospheric carbon cycle.
We developed four sets of global BB emissions estimates (named GlcGlob, ...GlcGeoc, McdGlob, and McdGeoc) using a bottom-up approach and by combining the remote sensing products related to fire distribution with two aboveground biomass (AGB) and two land cover classification (LCC) distributions.
The sensitivity of the estimates of BB emissions to the AGB and LCC data was evaluated using the carbon monoxide (CO) emissions associated with each BB estimate.
Using the AGB and/or LCC data led to substantially different spatial estimates of CO emissions, with a large (factor of approximately 3) spread of estimates for the mean annual CO emissions: 526±53, 219±35, 624±57, and 293±44 Tg CO yr−1 for GlcGlob, GlcGeoc, McdGlob, and McdGeoc, respectively, and 415±47 Tg CO yr−1 for their ensemble average (EsmAve).
We simulated atmospheric CO variability at an approximately 2.5∘ grid using an atmospheric tracer transport model and the BB emissions estimates and compared it with ground-based and satellite observations.
At ground-based observation sites during fire seasons, the impact of intermittent fire events was poorly defined in our simulations due to the coarse resolution, which obscured temporal and spatial variability in the simulated atmospheric CO concentration.
However, when compared at the regional and global scales, the distribution of atmospheric CO concentrations in the simulations shows substantial differences among the estimates of BB emissions.
These results indicate that the estimates of BB emissions are highly sensitive to the AGB and LCC data.
Systematic measurements of the atmospheric Ar∕N2
ratio have been made at ground-based stations in Japan and Antarctica since
2012. Clear seasonal cycles of the Ar∕N2 ratio with summertime maxima
were ...found at middle- to high-latitude stations, with seasonal amplitudes
increasing with increasing latitude. Eight years of the observed Ar∕N2
ratio at Tsukuba (TKB) and Hateruma (HAT), Japan, showed interannual
variations in phase with the observed variations in the global ocean heat
content (OHC). We calculated secularly increasing trends of 0.75 ± 0.30
and 0.89 ± 0.60 per meg per year from the Ar∕N2 ratio observed at
TKB and HAT, respectively, although these trend values are influenced by
large interannual variations. In order to examine the possibility of the
secular trend in the surface Ar∕N2 ratio being modified significantly
by the gravitational separation in the stratosphere, two-dimensional model
simulations were carried out by arbitrarily modifying the mass stream
function in the model to simulate either a weakening or an enhancement of
the Brewer–Dobson circulation (BDC). The secular trend of the Ar∕N2
ratio at TKB, corrected for gravitational separation under the assumption of
weakening (enhancement) of BDC simulated by the 2-D model, was 0.60 ± 0.30 (0.88 ± 0.30) per meg per year. By using a conversion factor of
3.5 × 10−23 per meg per joule by assuming a one-box ocean with a temperature
of 3.5 ∘C, average OHC increase rates of 17.1 ± 8.6 ZJ yr−1 and 25.1 ± 8.6 ZJ yr−1 for the period 2012–2019 were
estimated from the corrected secular trends of the Ar∕N2 ratio for the
weakened- and enhanced-BDC conditions, respectively. Both OHC increase
rates from the uncorrected- and weakened-BDC secular trends of the Ar∕N2
ratio are consistent with 12.2 ± 1.2 ZJ yr−1 reported by ocean
temperature measurements, while that from the enhanced-BDC is outside of the
range of the uncertainties. Although the effect of the actual atmospheric
circulation on the Ar∕N2 ratio is still unclear and longer-term
observations are needed to reduce uncertainty of the secular trend of the
surface Ar∕N2 ratio, the analytical results obtained in the present
study imply that the surface Ar∕N2 ratio is an important tracer for
detecting spatiotemporally integrated changes in OHC and BDC.
This article reviews the development of a global non-hydrostatic model, focusing on the pioneering research of the Non-hydrostatic Icosahedral Atmospheric Model (NICAM). Very high resolution global ...atmospheric circulation simulations with horizontal mesh spacing of approximately O (km) were conducted using recently developed supercomputers. These types of simulations were conducted with a specifically designed atmospheric global model based on a quasi-uniform grid mesh structure and a non-hydrostatic equation system. This review describes the development of each dynamical and physical component of NICAM, the assimilation strategy and its related models, and provides a scientific overview of NICAM studies conducted to date.
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