Statistical properties of atmospheric greenhouse gas measurements: Looking down from space and looking up from the ground

Abstract

Remote sensing platforms can collect measurements on a global scale within a few days, which provides an unprecedented opportunity to characterize and understand the spatio-temporal variability of environmental variables. Because of the additional challenges of making precise and accurate measurements from space, it is essential to validate satellite remote sensing datasets with highly precise and accurate ground-based measurements. The focus of this article is on two sets of measurements: Atmospheric column-averaged carbon dioxide (CO 2) collected by the Orbiting Carbon Observatory-2 (OCO-2) mission in its target mode of operation; and ground-based data used for validation from the Total Carbon Column Observing Network (TCCON). The current statistical modeling of the relationship between the OCO-2 data and the TCCON data assumes a linear regression and different measurement errors that reside in both the TCCON data and the OCO-2 data. To obtain consistent estimates of the regression coefficients, it is critical to determine the error variance of each datum in the regression. In this article, a rigorous statistical procedure is presented for obtaining the error variances through modeling the spatial and/or temporal dependence structure in the OCO-2 and TCCON datasets. Numerical results for analyzing a pair of datasets at the Lamont TCCON station and OCO-2 orbit number 3590 illustrate our procedure. AbstractRemote sensing platforms can collect measurements on a global scale within a few days, which provides an unprecedented opportunity to characterize and understand the spatio-temporal variability of environmental variables. Because of the additional challenges of making precise and accurate measurements from space, it is essential to validate satellite remote sensing datasets with highly precise and accurate groundbased measurements. The focus of this article is on two sets of measurements: Atmospheric column-averaged carbon dioxide (CO 2 ) collected by the Orbiting Carbon Observatory-2 (OCO-2) mission in its target mode of operation; and ground-based data used for validation from the Total Carbon Column Observing Network (TC-CON). The current statistical modeling of the relationship between the OCO-2 data and the TCCON data assumes a linear regression and different measurement errors that reside in both the TCCON data and the OCO-2 data. To obtain consistent estimates of the regression coefficients, it is critical to determine the error variance of each datum in the regression. In this article, a rigorous statistical procedure is presented for obtaining the error variances through modeling the spatial and/or temporal dependence structure in the OCO-2 and TCCON datasets. Numerical results for analyzing a pair of datasets at the Lamont TCCON station and OCO-2 orbit number 3590 illustrate our procedure.

Comparisons of the Orbiting Carbon Observatory-2 (OCO-2) <i>X</i><sub>CO<sub>2</sub></sub> measurements with TCCON

“…The residual footprint correction does not impact the slope or R 2 value of the relationship. Zhang et al (2017) have shown that the uncertainties computed on this slope are likely to be significantly overestimated.…”

Inference for Errors-in-Variables Models in the Presence of Systematic Errors with an Application to a Satellite Remote Sensing Campaign

“…To ensure consistent estimation of regression coefficients a and b, the weights {w x,i } and {w y,i } should be chosen as the reciprocals of the variances of { x,i } and { y,i }, respectively (e.g., Carroll and Ruppert, 1996;Zhang et al, 2017). It can be shown that each summation term in S(a, b) is the weighted perpendicular distance from (X i , Y i ) to the regression line.…”

“…. , N (e.g., Zhang et al, 2017). Unbiasedness of estimating equations is a desirable property, since unbiased estimating equations lead to consistent parameter estimators under regularity conditions (Godambe, 1960;Yi and Reid, 2010).…”

“…, N . Since {X i } and {Y i } are typically aggregated data obtained from datasets of individual observations (in Section 5, they are from the TCCON time series and the OCO-2 spatial observations, respectively), Zhang et al (2017) proposed to estimate error variances of the aggregated TCCON ({X i }) and OCO-2 ({Y i }) regression data from the corresponding datasets of individual observations. Importantly, account was taken of the temporal dependence between the individual TCCON observations and of the spatial dependence between the individual OCO-2 observations.…”

“…When correlation between individual observations is present, the square of the sample standard error is a biased estimator of the random-error variances. To account for spatial/temporal correlations between individual OCO-2/TCCON observations in this first stage of the calibration, we propose (asymptotically) unbiased estimates based on local spatial/temporal covariance functions; see Zhang et al (2017).…”