Towards better error statistics for atmospheric inversions of methane surface fluxes

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

Natural and anthropogenic methane fluxes in Eurasia: a mesoscale quantification by generalized atmospheric inversion

“…We then sample the observations during the afternoon when the PBL is higher than 500 m as suggested by prior studies (e.g. Berchet et al, 2013b) and we pick the observed and simulated mixing ratios at the time when the observations are minimum.…”

“…Recent studies inquired into objectified ways of specifying these matrices (e.g. Michalak and Kitanidis, 2005;Winiarek et al, 2012;Berchet et al, 2013b). The approach in these papers was to find optimal uncertainty matrices R and B along an objective statistical criterion: the maximum likelihood.…”

“…in order to evaluate their impact on the inversion results (Lauvaux et al, 2009;Winiarek et al, 2012;Berchet et al, 2013b;Ganesan et al, 2014). In Berchet et al (2015), we proposed a general method in order to objectively quantify most of the critical sources of errors in the inversion.…”

Diagnostic methods for atmospheric inversions of long-lived greenhouse gases

“…For example, the impact of assumptions about the statistical representation of prior errors and model-data-mismatch errors can be examined by performing multiple inversions, as can the impact of approaches aimed at optimizing these error statistics (e.g., Bousquet et al, 2011;Cressot et al, 2014;Wu et al, 2013;Ganesan et al, 2014;Berchet et al, 2013). Sensitivity tests may also be run on other statistical parameters such as the assumed correlation length of fluxes (Corazza et al, 2011).…”

“…In the simplest case, spatially aggregated posterior fluxes can be assessed based on expert knowledge of the system. For example, methane emissions in regions dominated by natural gas extraction, urbanization, wetlands, or cattle feedlots are expected to substantially outweigh soil methane uptake, and negative estimated emissions in such regions would point to errors in the inversion (e.g., Berchet et al, 2013). Similarly, global decadal atmospheric growth rates and latitudinal gradients of greenhouse gases are well constrained by long-term baseline observations (e.g., Conway et al, 1994), and posterior flux estimates can be evaluated against such large-scale constraints (e.g., Cressot et al, 2014).…”