scholarly journals Importance of fossil fuel emission uncertainties over Europe for CO<sub>2</sub> modeling: model intercomparison

2009 ◽  
Vol 9 (2) ◽  
pp. 7457-7503 ◽  
Author(s):  
P. Peylin ◽  
S. Houweling ◽  
M. C. Krol ◽  
U. Karstens ◽  
C. Rödenbeck ◽  
...  
Keyword(s):  
Inverse Modeling ◽  
Fossil Fuel ◽  
Transport Model ◽  
Carbon Sink ◽  
Temporal Distribution ◽  
Co2 Concentration ◽  
Transport Models ◽  
Annual Variations ◽  
Diurnal Cycles ◽  
Fossil Fuel Emission

Abstract. Inverse modeling techniques used to quantify surface carbon fluxes commonly assume that the uncertainty of fossil fuel CO2 (FFCO2) emissions is negligible and that intra-annual variations can be neglected. To investigate these assumptions, we analyzed the differences between four fossil fuel emission maps with spatial and temporal differences over Europe and their impact on the model simulated CO2 concentration. Large temporal flux variations characterize the hourly fields (~40% and ~80% for the seasonal and diurnal cycles, peak-to-peak) and annual country totals differ by 10% on average and up to 40% for some countries (i.e., The Netherlands). These emissions have been prescribed to seven different transport models, resulting in 28 different FFCO2 concentrations fields. The modeled FFCO2 concentration time series at surface sites using time-varying emissions show larger seasonal cycles (+2 ppm at the Hungarian tall tower (HUN)) and smaller diurnal cycles in summer (−1 ppm at HUN) than when using constant emissions. The concentration range spanned by all simulations varies between stations, and is generally larger in winter (up to ~10 ppm peak-to-peak at HUN) than in summer (~5 ppm). The contribution of transport model differences to the simulated concentration std-dev is 2–3 times larger than the contribution of emission differences only, at typical European sites used in global inversions. These contributions to the hourly (monthly) std-dev's amount to ~1.2 (0.8) ppm and ~0.4 (0.3) ppm for transport and emissions, respectively. First comparisons of the modeled concentrations with 14C-based fossil fuel CO2 observations show that the large transport differences still hamper a quantitative evaluation/validation of the emission inventories. Changes in the estimated monthly biosphere flux (Fbio) over Europe, using two inverse modeling approaches, are relatively small (less that 5%) while changes in annual Fbio (up to ~0.15 Gt C/yr) are only slightly smaller than the differences in annual emission totals and around 30% of the mean European ecosystem carbon sink. These results point to an urgent need to improve not only the transport models but also the assumed spatial and temporal distribution of fossil fuel emission maps.

scholarly journals Importance of fossil fuel emission uncertainties over Europe for CO<sub>2</sub> modeling: model intercomparison

2011 ◽  
Vol 11 (13) ◽  
pp. 6607-6622 ◽  
Author(s):  
P. Peylin ◽  
S. Houweling ◽  
M. C. Krol ◽  
U. Karstens ◽  
C. Rödenbeck ◽  
...  
Keyword(s):  
Inverse Modeling ◽  
Fossil Fuel ◽  
Transport Model ◽  
Carbon Sink ◽  
Temporal Distribution ◽  
Co2 Concentration ◽  
Emission Inventories ◽  
Transport Models ◽  
Diurnal Cycles ◽  
Fossil Fuel Emission

Abstract. Inverse modeling techniques used to quantify surface carbon fluxes commonly assume that the uncertainty of fossil fuel CO2 (FFCO2) emissions is negligible and that intra-annual variations can be neglected. To investigate these assumptions, we analyzed the differences between four fossil fuel emission inventories with spatial and temporal differences over Europe and their impact on the model simulated CO2 concentration. Large temporal flux variations characterize the hourly fields (~40 % and ~80 % for the seasonal and diurnal cycles, peak-to-peak) and annual country totals differ by 10 % on average and up to 40 % for some countries (i.e., the Netherlands). These emissions have been prescribed to seven different transport models, resulting in 28 different FFCO2 concentrations fields. The modeled FFCO2 concentration time series at surface sites using time-varying emissions show larger seasonal cycles (+2 ppm at the Hungarian tall tower (HUN)) and smaller diurnal cycles in summer (−1 ppm at HUN) than when using constant emissions. The concentration range spanned by all simulations varies between stations, and is generally larger in winter (up to ~10 ppm peak-to-peak at HUN) than in summer (~5 ppm). The contribution of transport model differences to the simulated concentration std-dev is 2–3 times larger than the contribution of emission differences only, at typical European sites used in global inversions. These contributions to the hourly (monthly) std-dev's amount to ~1.2 (0.8) ppm and ~0.4 (0.3) ppm for transport and emissions, respectively. First comparisons of the modeled concentrations with 14C-based fossil fuel CO2 observations show that the large transport differences still hamper a quantitative evaluation/validation of the emission inventories. Changes in the estimated monthly biosphere flux (Fbio) over Europe, using two inverse modeling approaches, are relatively small (less that 5 %) while changes in annual Fbio (up to ~0.15 % GtC yr−1) are only slightly smaller than the differences in annual emission totals and around 30 % of the mean European ecosystem carbon sink. These results point to an urgent need to improve not only the transport models but also the assumed spatial and temporal distribution of fossil fuel emission inventories.

scholarly journals Global to local impacts on atmospheric CO2 caused by COVID-19 lockdown

2021 ◽  
Author(s):  
Ning Zeng
Keyword(s):  
Fossil Fuel ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Carbon Sink ◽  
Co2 Concentration ◽  
Atmospheric Co2 ◽  
Monitoring Systems ◽  
Carbon Cycle Model ◽  
Safe Level ◽  
Small Change

&lt;p&gt;&lt;span&gt;The world-wide lockdown in response to the COVID-19 pandemic in year 2020 led to economic slowdown and large reduction of fossil fuel CO2 emissions 1,2, but it is unclear how much it would reduce atmospheric CO2 concentration, the main driver of climate change, and whether it can be observed. We estimated that a 7.9% reduction in emissions for 4 months would result in a 0.25 ppm decrease in the Northern Hemisphere CO2, an increment that is within the capability of current CO2 analyzers, but is a few times smaller than natural CO2 variabilities caused by weather and the biosphere such as El Nino. We used a state-of-the-art atmospheric transport model to simulate CO2, driven by a new daily fossil fuel emissions dataset and hourly biospheric fluxes from a carbon cycle model forced with observed climate variability. Our results show a 0.13 ppm decrease in atmospheric column CO2 anomaly averaged over 50S-50N for the period February-April 2020 relative to a 10-year climatology. A similar decrease was observed by the carbon satellite GOSAT3. Using model sensitivity experiments, we further found that COVID, the biosphere and weather contributed 54%, 23%, and 23% respectively. In May 2020, the CO2 anomaly continued to decrease and was 0.36 ppm below climatology, mostly due to the COVID reduction and a biosphere that turned from a relative carbon source to carbon sink, while weather impact fluctuated. This seemingly small change stands out as the largest sub-annual anomaly in the last 10 years. Measurements from global ground stations were analyzed. At city scale, on-road CO2 enhancement measured in Beijing shows reduction of 20-30 ppm, consistent with drastically reduced traffic during the lockdown, while station data suggest that the expected COVID signal of 5-10 ppm was swamped by weather-driven variability on multi-day time scales. The ability of our current carbon monitoring systems in detecting the small and short-lasting COVID signal on the background of fossil fuel CO2 accumulated over the last two centuries is encouraging. The COVID-19 pandemic is an unintended experiment whose impact suggests that to keep atmospheric CO2 at a climate-safe level will require sustained effort of similar magnitude and improved accuracy and expanded spatiotemporal coverage of our monitoring systems.&lt;/span&gt;&lt;/p&gt;

scholarly journals Characterizing uncertainties in atmospheric inversions of fossil fuel CO<sub>2</sub> emissions in California

2019 ◽  
Vol 19 (5) ◽  
pp. 2991-3006 ◽  
Author(s):  
Kieran Brophy ◽  
Heather Graven ◽  
Alistair J. Manning ◽  
Emily White ◽  
Tim Arnold ◽  
...  
Keyword(s):  
Fossil Fuel ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Temporal Distribution ◽  
Potential Effect ◽  
Spatial And Temporal Distribution ◽  
Transport Models ◽  
Total State ◽  
Pseudo Data ◽  
Atmospheric Inversions

Abstract. Atmospheric inverse modelling has become an increasingly useful tool for evaluating emissions of greenhouse gases including methane, nitrous oxide, and synthetic gases such as hydrofluorocarbons (HFCs). Atmospheric inversions for emissions of CO2 from fossil fuel combustion (ffCO2) are currently being developed. The aim of this paper is to investigate potential errors and uncertainties related to the spatial and temporal prior representation of emissions and modelled atmospheric transport for the inversion of ffCO2 emissions in the US state of California. We perform simulation experiments based on a network of ground-based observations of CO2 concentration and radiocarbon in CO2 (a tracer of ffCO2), combining prior (bottom-up) emission models and transport models currently used in many atmospheric studies. The potential effect of errors in the spatial and temporal distribution of prior emission estimates is investigated in experiments by using perturbed versions of the emission estimates used to create the pseudo-data. The potential effect of transport error was investigated by using three different atmospheric transport models for the prior and pseudo-data simulations. We find that the magnitude of biases in posterior total state emissions arising from errors in the spatial and temporal distribution in prior emissions in these experiments are 1 %–15 % of posterior total state emissions and are generally smaller than the 2σ uncertainty in posterior emissions. Transport error in these experiments introduces biases of −10 % to +6 % into posterior total state emissions. Our results indicate that uncertainties in posterior total state ffCO2 estimates arising from the choice of prior emissions or atmospheric transport model are on the order of 15 % or less for the ground-based network in California we consider. We highlight the need for temporal variations to be included in prior emissions and for continuing efforts to evaluate and improve the representation of atmospheric transport for regional ffCO2 inversions.

scholarly journals Characterizing Uncertainties in Atmospheric Inversions of Fossil Fuel CO<sub>2</sub> Emissions in California

2018 ◽  
Author(s):  
Kieran Brophy ◽  
Heather Graven ◽  
Alistair J. Manning ◽  
Emily White ◽  
Tim Arnold ◽  
...  
Keyword(s):  
Fossil Fuel ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Temporal Distribution ◽  
Temporal Variations ◽  
Potential Effect ◽  
Spatial And Temporal Distribution ◽  
Transport Models ◽  
Pseudo Data ◽  
Atmospheric Inversions

Abstract. Atmospheric inverse modelling has become an increasingly useful tool for evaluating emissions of greenhouse gases including methane, nitrous oxide and synthetic gases such as hydrofluorocarbons (HFCs). Atmospheric inversions for emissions of CO2 from fossil fuel combustion (ffCO2) are currently being developed. The aim of this paper is to investigate potential errors and uncertainties related to the spatial and temporal prior representation of emissions and modelled atmospheric transport for the inversion of ffCO2 emissions in the U.S. state of California. We perform simulation experiments based on a network of ground-based observations of CO2 concentration and radiocarbon in CO2 (a tracer of ffCO2), combining prior (bottom-up) emission models and transport models currently used in many atmospheric studies. The potential effect of errors in the spatial and temporal distribution of prior emission estimates is investigated in experiments by using perturbed versions of the emissions estimates used to create the pseudo data. The potential effect of transport error was investigated by using three different atmospheric transport models for the prior and pseudo data simulations. We find that the magnitude of biases in posterior state-total emissions arising from errors in the spatial and temporal distribution in prior emissions in these experiments are 1–15 % of posterior state-total emissions, and generally smaller than the 2-σ uncertainty in posterior emissions. Transport error in these experiments introduces biases of −10 % to +6 % in posterior state-total emissions. Our results indicate that uncertainties in posterior state-total ffCO2 estimates arising from the choice of prior emissions or atmospheric transport model are on the order of 15 % or less for the ground-based network in California we consider. We highlight the need for temporal variations to be included in prior emissions, and for continuing efforts to evaluate and improve the representation of atmospheric transport for regional ffCO2 inversions.

scholarly journals Sensitivity of simulated CO<sub>2</sub> concentration to sub-annual variations in fossil fuel CO<sub>2</sub> emissions

2016 ◽  
Vol 16 (4) ◽  
pp. 1907-1918 ◽  
Author(s):  
Xia Zhang ◽  
Kevin R. Gurney ◽  
Peter Rayner ◽  
David Baker ◽  
Yu-ping Liu
Keyword(s):  
Fossil Fuel ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Vertical Mixing ◽  
Grid Cell ◽  
Co2 Concentration ◽  
Tracer Transport ◽  
Annual Variations ◽  
Atmospheric Co2 Concentrations ◽  
The Impact

Abstract. Recent advances in fossil fuel CO2 (FFCO2) emission inventories enable sensitivity tests of simulated atmospheric CO2 concentrations to sub-annual variations in FFCO2 emissions and what this implies for the interpretation of observed CO2. Six experiments are conducted to investigate the potential impact of three cycles of FFCO2 emission variability (diurnal, weekly and monthly) using a global tracer transport model. Results show an annual FFCO2 rectification varying from −1.35 to +0.13 ppm from the combination of all three cycles. This rectification is driven by a large negative diurnal FFCO2 rectification due to the covariation of diurnal FFCO2 emissions and diurnal vertical mixing, as well as a smaller positive seasonal FFCO2 rectification driven by the covariation of monthly FFCO2 emissions and monthly atmospheric transport. The diurnal FFCO2 emissions are responsible for a diurnal FFCO2 concentration amplitude of up to 9.12 ppm at the grid cell scale. Similarly, the monthly FFCO2 emissions are responsible for a simulated seasonal CO2 amplitude of up to 6.11 ppm at the grid cell scale. The impact of the diurnal FFCO2 emissions, when only sampled in the local afternoon, is also important, causing an increase of +1.13 ppmv at the grid cell scale. The simulated CO2 concentration impacts from the diurnally and seasonally varying FFCO2 emissions are centered over large source regions in the Northern Hemisphere, extending to downwind regions. This study demonstrates the influence of sub-annual variations in FFCO2 emissions on simulated CO2 concentration and suggests that inversion studies must take account of these variations in the affected regions.

scholarly journals Sensitivity of simulated CO2 concentration to sub-annual variations in fossil fuel CO2 emissions

2015 ◽  
Vol 15 (14) ◽  
pp. 20679-20708 ◽  
Author(s):  
X. Zhang ◽  
K. R. Gurney ◽  
P. Rayner ◽  
D. Baker ◽  
Y.-P. Liu
Keyword(s):  
Fossil Fuel ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Vertical Mixing ◽  
Grid Cell ◽  
Co2 Concentration ◽  
Tracer Transport ◽  
Annual Variations ◽  
Atmospheric Co2 Concentrations ◽  
The Impact

Abstract. Recent advances in fossil fuel CO2 (FFCO2) emission inventories enable sensitivity tests of simulated atmospheric CO2 concentrations to sub-annual variations in FFCO2 emissions and what this implies for the interpretation of observed CO2. Six experiments are conducted to investigate the potential impact of three cycles of FFCO2 emission variability (diurnal, weekly and monthly) using a global tracer transport model. Results show an annual FFCO2 rectification varying from −1.35 to +0.13 ppm from the combination of all three cycles. This rectification is driven by a large negative diurnal FFCO2 rectification due to the covariation of diurnal FFCO2 emissions and diurnal vertical mixing, and a smaller positive seasonal FFCO2 rectification driven by the covariation of monthly FFCO2 emissions and monthly atmospheric transport. The diurnal FFCO2 emissions are responsible for a diurnal FFCO2 concentration amplitude of up to 9.12 ppm at the grid cell scale. Similarly, the monthly FFCO2 emissions are responsible for a simulated seasonal CO2 amplitude of up to 6.11 ppm at the grid cell scale. The impact of the diurnal FFCO2 emissions, when only sampled in the local afternoon is also important, causing an increase of +1.13 ppmv at the grid cell scale. The simulated CO2 concentration impacts from the diurnally and seasonally-varying FFCO2 emissions are centered over large source regions in the Northern Hemisphere, extending to downwind regions. This study demonstrates the influence of sub-annual variations in FFCO2 emissions on simulated CO2 concentration and suggests that inversion studies must take account of these variations in the affected regions.

scholarly journals Carbon balance of China constrained by CONTRAIL aircraft CO<sub>2</sub> measurements

2014 ◽  
Vol 14 (6) ◽  
pp. 7683-7709
Author(s):  
F. Jiang ◽  
H. M. Wang ◽  
J. M. Chen ◽  
T. Machida ◽  
L. X. Zhou ◽  
...  
Keyword(s):  
Transport Model ◽  
Carbon Sink ◽  
Terrestrial Ecosystem ◽  
Co2 Flux ◽  
Co2 Concentration ◽  
Atmospheric Co2 ◽  
Inversion Method ◽  
Climate Factors ◽  
Mean Climate ◽  
Atmospheric Co2 Concentrations

Abstract. Terrestrial CO2 flux estimates in China using atmospheric inversion method are beset with considerable uncertainties because very few atmospheric CO2 concentration measurements are available. In order to improve these estimates, nested atmospheric CO2 inversion during 2002–2008 is performed in this study using passenger aircraft-based CO2 measurements over Eurasia from the Comprehensive Observation Network for Trace gases by Airliner (CONTRAIL) project. The inversion system includes 43 regions with a focus on China, and is based on the Bayesian synthesis approach and the TM5 transport model. The terrestrial ecosystem carbon flux modeled by the BEPS model and the ocean exchange simulated by the OPA-PISCES-T model are considered as the prior fluxes. The impacts of CONTRAIL CO2 data on inverted China terrestrial carbon fluxes are quantified, the improvement of the inverted fluxes after adding CONTRAIL CO2 data are rationed against climate factors and evaluated by comparing the simulated atmospheric CO2 concentrations with three independent surface CO2 measurements in China. Results show that with the addition of CONTRAIL CO2 data, the inverted carbon sink in China increases while those in South and Southeast Asia decrease. Meanwhile, the posterior uncertainties over these regions are all reduced. CONTRAIL CO2 data also have a large effect on the inter-annual variation of carbon sinks in China, leading to a better correlation between the carbon sink and the annual mean climate factors. Evaluations against the CO2 measurements at three sites in China also show that the CONTRAIL CO2 measurements have improved the inversion results.

scholarly journals Radiocarbon method in monitoring of fossil fuel emission

2011 ◽  
Vol 38 (4) ◽  
pp. 314-324 ◽  
Author(s):  
Andrzej Rakowski
Keyword(s):  
Isotopic Composition ◽  
Fossil Fuels ◽  
Fossil Fuel ◽  
Isotope Composition ◽  
Carbon Isotopic Composition ◽  
Co2 Concentration ◽  
Atmospheric Co2 ◽  
Fossil Carbon ◽  
Fossil Fuel Emission ◽  
Urbanized Areas

AbstractThe traditional radiocarbon method widely used in archaeology and geology for chronological purposes can also be used in environmental studies. Combustion of fossil fuels like coal, natural gas, petroleum, etc., in industrial and/or heavily urbanized areas, has increased the concentration of carbon dioxide in the atmosphere. The addition of fossil carbon caused changes of carbon isotopic composition, in particular, a definite decrease of 14C concentration in atmospheric CO2 and other carbon reservoirs (ocean and terrestrial biosphere), known as the Suess effect. Tree rings, leaves, as well as other annual growing plants reflected the changes of radiocarbon concentration in the atmosphere due to processes of photosynthesis and assimilation of carbon from the air. By measuring radiocarbon concentration directly in atmospheric CO2 samples and/or biospheric material growing in industrial and/or highly urbanized areas where high emission of dead carbon is expected, it is possible to estimate the total emission of dead CO2. Based on equations of mass balance for CO2 concentration, stable isotopic composition of carbon and radiocarbon concentration it is possible to calculate CO2 con-centration associated with fossil fuel emission into the atmosphere. The procedure use differences between the radiocarbon concentration and stable isotope composition of carbon observed in clean areas and industrial or/and highly urbanized areas.

scholarly journals Carbon balance of China constrained by CONTRAIL aircraft CO<sub>2</sub> measurements

2014 ◽  
Vol 14 (18) ◽  
pp. 10133-10144 ◽  
Author(s):  
F. Jiang ◽  
H. M. Wang ◽  
J. M. Chen ◽  
T. Machida ◽  
L. X. Zhou ◽  
...  
Keyword(s):  
Transport Model ◽  
Carbon Sink ◽  
Terrestrial Ecosystem ◽  
Co2 Flux ◽  
Co2 Concentration ◽  
Atmospheric Co2 ◽  
Inversion Method ◽  
Climate Factors ◽  
Terrestrial Carbon ◽  
Atmospheric Co2 Concentrations

Abstract. Terrestrial carbon dioxide (CO2) flux estimates in China using atmospheric inversion method are beset with considerable uncertainties because very few atmospheric CO2 concentration measurements are available. In order to improve these estimates, nested atmospheric CO2 inversion during 2002–2008 is performed in this study using passenger aircraft-based CO2 measurements over Eurasia from the Comprehensive Observation Network for Trace gases by Airliner (CONTRAIL) project. The inversion system includes 43 regions with a focus on China, and is based on the Bayesian synthesis approach and the TM5 transport model. The terrestrial ecosystem carbon flux modeled by the Boreal Ecosystems Productivity Simulator (BEPS) model and the ocean exchange simulated by the OPA-PISCES-T model are considered as the prior fluxes. The impacts of CONTRAIL CO2 data on inverted China terrestrial carbon fluxes are quantified, the improvement of the inverted fluxes after adding CONTRAIL CO2 data are rationed against climate factors and evaluated by comparing the simulated atmospheric CO2 concentrations with three independent surface CO2 measurements in China. Results show that with the addition of CONTRAIL CO2 data, the inverted carbon sink in China increases while those in South and Southeast Asia decrease. Meanwhile, the posterior uncertainties over these regions are all reduced (2–12%). CONTRAIL CO2 data also have a large effect on the inter-annual variation of carbon sinks in China, leading to a better correlation between the carbon sink and the annual mean climate factors. Evaluations against the CO2 measurements at three sites in China also show that the CONTRAIL CO2 measurements may have improved the inversion results.

Time-series of GhG emissions estimation for the learning of inverse modeling

2021 ◽  
Author(s):  
Carlos Gómez-Ortiz ◽  
Guillaume Monteil ◽  
Marko Scholze
Keyword(s):  
Time Series ◽  
Inverse Modeling ◽  
Fossil Fuel ◽  
Transport Model ◽  
A Priori ◽  
Ghg Emissions ◽  
Atmospheric Concentration ◽  
Training Tool ◽  
Sources And Sinks ◽  
Atmospheric Inversions

&lt;p&gt;Inverse modeling is a commonly used method to infer greenhouse gases (GhGs) sources and sinks based on their observed concentrations in the atmosphere. It is a Bayesian framework and requires a priori fluxes of all the evaluated sources and sinks, atmospheric observations, an atmospheric transport model that relates the observations to the a priori fluxes and the uncertainties of both fluxes and observations. Various techniques exist to solve the inversion.&lt;/p&gt;&lt;p&gt;Atmospheric inverse modeling is and will become even more important in the future quantification of GhGs to monitor the compliance of the Nationally Determined Contributions (NDCs) under the Paris Agreement. Therefore, the scientific and educational communities are becoming more interested in using atmospheric inversions and this has risen a necessity of creating tools that facilitate understanding as well as training in these techniques.&lt;/p&gt;&lt;p&gt;Quantifying anthropogenic GhG emissions, such as CO&lt;sub&gt;2&lt;/sub&gt; from fossil fuel burning or CH&lt;sub&gt;4 &lt;/sub&gt;from human activities, from atmospheric concentration observations is difficult since the carbon from all sources, both natural and anthropogenic, is mixed in the atmosphere, making it necessary to use other signals or tracers to separate anthropogenic emissions from natural sources. For fossil fuel CO&lt;sub&gt;2&lt;/sub&gt; emissions radiocarbon (&lt;sup&gt;14&lt;/sup&gt;CO&lt;sub&gt;2&lt;/sub&gt;) is an excellent emission tracer because, due to its radioactive decay (~ 5000 years), it cannot be found in fossil fuels, which have been deposited millions of years ago as organic material. We have developed a Jupyter Notebook based on Python for the quantification of multi-tracer GhGs fossil fuel emissions and its isotopes. The notebook solves for the emissions by applying atmospheric inversions within a practical two-box model. The inverse modeling notebook is based on the analytical maximum a posteriori (MAP) solution of the Bayes&amp;#8217; theorem and allows to assess the error in the state vector and its uncertainty.&lt;/p&gt;&lt;p&gt;This basic but powerful notebook is meant to be an educational and training tool for university students and new researchers in the field as well as for researchers interested in the estimation of long-term (&gt;centennial) time-series of GhG emissions since it is built as a modular algorithm to be easily modified, coupled or expanded to other approaches or models depending on the application. The notebook was initially developed for the inverse modeling of CO&lt;sub&gt;2&lt;/sub&gt; and &lt;sup&gt;14&lt;/sup&gt;CO&lt;sub&gt;2&lt;/sub&gt; simultaneously and it is being expanded for additional GHG such as CH&lt;sub&gt;4&lt;/sub&gt; and &lt;sup&gt;13&lt;/sup&gt;CH&lt;sub&gt;4&lt;/sub&gt;.&lt;/p&gt;

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