scholarly journals Towards better error statistics for atmospheric inversions of methane surface fluxes

2013 ◽  
Vol 13 (2) ◽  
pp. 3735-3782
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
S. Conil ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Transport Model ◽  
Real Data ◽  
Surface Fluxes ◽  
Mass Composition ◽  
Error Statistics ◽  
The North ◽  
Error Covariance ◽  
Data Framework ◽  
General Statistical

Abstract. In this study, we adapt general statistical methods to compute the optimal error covariance matrices in a regional inversion system inferring methane surface emissions from atmospheric concentrations. We optimally estimate the error statistics with a minimal set of physical hypotheses on the patterns of errors. With this very general approach applied within a real-data framework, we recover sources of errors in the observations and in the prior state of the system that are consistent with expert knowledge. By not assuming any specific error patterns, our results show the variability and the inter-dependency of errors induced by complex factors such as the mis-representation of the observations in the transport model or the inability of the model to reproduce well the situations of steep gradients of air mass composition in the atmosphere. By analyzing the sensitivity of the inversion to each observation, ways to improve data selection in regional inversions are also proposed. We applied our method to a recent significant accidental methane release from an offshore platform in the North Sea.

scholarly journals Towards better error statistics for atmospheric inversions of methane surface fluxes

2013 ◽  
Vol 13 (14) ◽  
pp. 7115-7132 ◽  
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
S. Conil ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Transport Model ◽  
Vertical Mixing ◽  
Real Data ◽  
Surface Fluxes ◽  
Error Statistics ◽  
The North ◽  
Error Covariance ◽  
Methane Fluxes ◽  
General Statistical

Abstract. We adapt general statistical methods to estimate the optimal error covariance matrices in a regional inversion system inferring methane surface emissions from atmospheric concentrations. Using a minimal set of physical hypotheses on the patterns of errors, we compute a guess of the error statistics that is optimal in regard to objective statistical criteria for the specific inversion system. With this very general approach applied to a real-data case, we recover sources of errors in the observations and in the prior state of the system that are consistent with expert knowledge while inferred from objective criteria and with affordable computation costs. By not assuming any specific error patterns, our results depict the variability and the inter-dependency of errors induced by complex factors such as the misrepresentation of the observations in the transport model or the inability of the model to reproduce well the situations of steep gradients of concentrations. Situations with probable significant biases (e.g., during the night when vertical mixing is ill-represented by the transport model) can also be diagnosed by our methods in order to point at necessary improvement in a model. By additionally analysing the sensitivity of the inversion to each observation, guidelines to enhance data selection in regional inversions are also proposed. We applied our method to a recent significant accidental methane release from an offshore platform in the North Sea and found methane fluxes of the same magnitude than what was officially declared.

scholarly journals 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

2017 ◽  
Vol 10 (6) ◽  
pp. 2201-2219 ◽  
Author(s):  
Yosuke Niwa ◽  
Yosuke Fujii ◽  
Yousuke Sawa ◽  
Yosuke Iida ◽  
Akihiko Ito ◽  
...  
Keyword(s):  
Transport Model ◽  
Surface Fluxes ◽  
Identical Twin ◽  
Inversion Problem ◽  
Model Errors ◽  
Optimization Scheme ◽  
Error Covariance ◽  
Optimal Setting ◽  
Source Sink ◽  
Quasi Newton

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.

scholarly journals The potential of Orbiting Carbon Observatory-2 data to reduce the uncertainties in CO<sub>2</sub> surface fluxes over Australia using a variational assimilation scheme

2020 ◽  
Vol 20 (14) ◽  
pp. 8473-8500
Author(s):  
Yohanna Villalobos ◽  
Peter Rayner ◽  
Steven Thomas ◽  
Jeremy Silver
Keyword(s):  
Boundary Conditions ◽  
Dispersion Model ◽  
Grid Point ◽  
Surface Fluxes ◽  
Co2 Fluxes ◽  
Error Statistics ◽  
Error Covariance ◽  
Horizontal Grid ◽  
Assimilation Scheme ◽  
Total Column

Abstract. This paper addresses the question of how much uncertainties in CO2 fluxes over Australia can be reduced by assimilation of total-column carbon dioxide retrievals from the Orbiting Carbon Observatory-2 (OCO-2) satellite instrument. We apply a four-dimensional variational data assimilation system, based around the Community Multiscale Air Quality (CMAQ) transport-dispersion model. We ran a series of observing system simulation experiments to estimate posterior error statistics of optimized monthly-mean CO2 fluxes in Australia. Our assimilations were run with a horizontal grid resolution of 81 km using OCO-2 data for 2015. Based on four representative months, we find that the integrated flux uncertainty for Australia is reduced from 0.52 to 0.13 Pg C yr−1. Uncertainty reductions of up to 90 % were found at grid-point resolution over productive ecosystems. Our sensitivity experiments show that the choice of the correlation structure in the prior error covariance plays a large role in distributing information from the observations. We also found that biases in the observations would significantly impact the inverted fluxes and could contaminate the final results of the inversion. Biases in prior fluxes are generally removed by the inversion system. Biases in the boundary conditions have a significant impact on retrieved fluxes, but this can be mitigated by including boundary conditions in our retrieved parameters. In general, results from our idealized experiments suggest that flux inversions at this unusually fine scale will yield useful information on the carbon cycle at continental and finer scales.

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

2016 ◽  
Author(s):  
Yosuke Niwa ◽  
Yosuke Fujii ◽  
Yousuke Sawa ◽  
Yosuke Iida ◽  
Akihiko Ito ◽  
...  
Keyword(s):  
Transport Model ◽  
Global Scale ◽  
Surface Fluxes ◽  
Identical Twin ◽  
Model Errors ◽  
Optimization Scheme ◽  
New Approach ◽  
Error Covariance ◽  
Optimal Setting ◽  
Quasi Newton

Abstract. A 4-dimensional variational method (4D-Var) is a popular technique for inverse modeling 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 off-line 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. It is found that a system of forward and adjoint models that has less model errors but with non-linearity performs better than another system that conserves linearity with exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is confirmed; the global error is reduced by about 15 % by adding prior error correlations that are simply designed. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to a global scale. The optimization algorithm introduced in the new system does not require difficult 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.

scholarly journals Objectified quantification of uncertainties in Bayesian atmospheric inversions

2015 ◽  
Vol 8 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
J.-L. Bonne ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Spatial Scales ◽  
Surface Fluxes ◽  
Large Set ◽  
Error Statistics ◽  
Observation Operator ◽  
Probability Of Occurrence ◽  
Error Distributions ◽  
The Impact ◽  
Atmospheric Inversions

Abstract. Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system simulation experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted methane. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionally, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission aggregates reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyse. These scales are consistent with the chosen aggregation patterns.

scholarly journals Three-dimensional variations of atmospheric CO<sub>2</sub>: aircraft measurements and multi-transport model simulations

2011 ◽  
Vol 11 (4) ◽  
pp. 12805-12848 ◽  
Author(s):  
Y. Niwa ◽  
P. K. Patra ◽  
Y. Sawa ◽  
T. Machida ◽  
H. Matsueda ◽  
...  
Keyword(s):  
Marine Boundary Layer ◽  
Transport Model ◽  
Three Dimensional ◽  
Co2 Flux ◽  
Surface Fluxes ◽  
Dimensional Structure ◽  
Boreal Summer ◽  
Free Troposphere ◽  
Model Simulations ◽  
The North

Abstract. Numerical simulation and validation of three-dimensional structure of atmospheric carbon dioxide (CO2) is necessary for quantification of transport model uncertainty and its role on surface flux estimation by inverse modeling. Simulations of atmospheric CO2 were performed using four transport models and two sets of surface fluxes compared with an aircraft measurement dataset of Comprehensive Observation Network for Trace gases by AIrLiner (CONTRAIL), covering various latitudes, longitudes, and heights. Under this transport model intercomparison project, spatiotemporal variations of CO2 concentration for 2006–2007 were analyzed with a three-dimensional perspective. Results show that the models reasonably simulated vertical profiles and seasonal variations not only over northern latitude areas but also over the tropics and southern latitudes. From CONTRAIL measurements and model simulations, intrusion of northern CO2 in to the Southern Hemisphere, through the upper troposphere, was confirmed. Furthermore, models well simulated the vertical propagation of seasonal variation in the northern free-troposphere. However, significant model–observation discrepancies were found in Asian regions, which are attributable to uncertainty of the surface CO2 flux data. The models consistently underestimated the north-tropics mean gradient of CO2 both in the free-troposphere and marine boundary layer during boreal summer. This result suggests that the north-tropics contrast of annual mean net non-fossil CO2 flux should be greater than 2.7 Pg C yr−1 for 2007.

scholarly journals The potential of OCO-2 data to reduce the uncertainties in CO<sub>2</sub> surface fluxes over Australia using a variational assimilation scheme

2019 ◽  
Author(s):  
Yohanna Villalobos ◽  
Peter Rayner ◽  
Steven Thomas ◽  
Jeremy Silver
Keyword(s):  
Dispersion Model ◽  
Surface Fluxes ◽  
Co2 Fluxes ◽  
Error Statistics ◽  
Satellite Measurements ◽  
Error Covariance ◽  
Horizontal Grid ◽  
Assimilation Scheme ◽  
Data Assimilation System ◽  
Total Column

Abstract. This paper addresses the question of how much uncertainties in CO2 fluxes over Australia can be reduced by assimilation of total-column carbon dioxide retrievals from the Orbiting Carbon Observatory-2 (OCO-2) satellite instrument. We apply a four-dimensional variational data assimilation system, based around the Community Multiscale Air Quality (CMAQ) transport-dispersion model. We ran a series of observing system simulation experiments to estimate posterior error statistics of optimized monthly mean CO2 fluxes in Australia. Our assimilations were run with a horizontal grid resolution of 81 km using OCO-2 data for 2015. We found that on average, the total Australia flux uncertainty was reduced by up to 40 % using only OCO-2 nadir measurements. Using both nadir and glint satellite measurements produces uncertainty reductions up to 80 %, which represents 0.55 PgC y−1 for the whole continent. Uncertainty reductions were found to be greatest in the more productive regions of Australia. The choice of the correlation structure in the prior error covariance was found to play a large role in distributing information from the observations. Overall the results suggest that flux inversions at this unusually fine scale will yield useful information on the Australian carbon cycle.

scholarly journals Objectified quantification of uncertainties in Bayesian atmospheric inversions

2014 ◽  
Vol 7 (4) ◽  
pp. 4777-4827 ◽  
Author(s):  
A. Berchet ◽  
I. Pison ◽  
F. Chevallier ◽  
P. Bousquet ◽  
J.-L. Bonne ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Spatial Scales ◽  
Surface Fluxes ◽  
Error Statistics ◽  
Observation Operator ◽  
Aggregation Pattern ◽  
Error Distributions ◽  
The Impact ◽  
Meso Scale ◽  
Atmospheric Inversions

Abstract. Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. At the meso-scale, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results and enhance the classical Bayesian inversion framework through a marginalization on all the plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is complicated and not explicitly describable. We then carry out a Monte-Carlo sampling relying on an approximation of the probability of occurence of the error distributions. This approximation is deduced from the well-tested algorithm of the Maximum of Likelihood. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly includes the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of emission aggregation pattern and sampling protocol in order to reduce the computation costs of the method. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the meso-scale with real observation sites in Eurasia. Observing System Simulation Experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted gas. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionnaly, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission regions reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyze. These scales proved to be consistent with the chosen aggregation patterns.

scholarly journals Influence of the North Atlantic oscillation on the atmospheric levels of benzo[a]pyrene over Europe

2021 ◽  
Author(s):  
Pedro Jiménez-Guerrero ◽  
Nuno Ratola
Keyword(s):  
Spatial Pattern ◽  
North Atlantic Oscillation ◽  
North Atlantic ◽  
Transport Model ◽  
Regional Scale ◽  
The South ◽  
Climatic Fluctuations ◽  
The North ◽  
The North Atlantic ◽  
The North Atlantic Oscillation

AbstractThe atmospheric concentration of persistent organic pollutants (and of polycyclic aromatic hydrocarbons, PAHs, in particular) is closely related to climate change and climatic fluctuations, which are likely to influence contaminant’s transport pathways and transfer processes. Predicting how climate variability alters PAHs concentrations in the atmosphere still poses an exceptional challenge. In this sense, the main objective of this contribution is to assess the relationship between the North Atlantic Oscillation (NAO) index and the mean concentration of benzo[a]pyrene (BaP, the most studied PAH congener) in a domain covering Europe, with an emphasis on the effect of regional-scale processes. A numerical simulation for a present climate period of 30 years was performed using a regional chemistry transport model with a 25 km spatial resolution (horizontal), higher than those commonly applied. The results show an important seasonal behaviour, with a remarkable spatial pattern of difference between the north and the south of the domain. In winter, higher BaP ground levels are found during the NAO+ phase for the Mediterranean basin, while the spatial pattern of this feature (higher BaP levels during NAO+ phases) moves northwards in summer. These results show deviations up to and sometimes over 100% in the BaP mean concentrations, but statistically significant signals (p<0.1) of lower changes (20–40% variations in the signal) are found for the north of the domain in winter and for the south in summer.

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

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