A new exponentially decaying error correlation model for assimilating OCO-2 column-average CO<sub>2</sub> data using a length scale computed from airborne lidar measurements

Abstract

Abstract. To check the accuracy of column-average dry air CO2 mole fractions (XCO2) retrieved from Orbiting Carbon Observatory (OCO-2) data, a similar quantity has been measured from the Multi-functional Fiber Laser Lidar (MFLL) aboard aircraft flying underneath OCO-2 as part of the Atmospheric Carbon and Transport (ACT) – America flight campaigns. Here we do a lagged correlation analysis of these MFLL–OCO-2 column CO2 differences and find that their correlation spectrum falls off rapidly at along-track separation distances under 10 km, with a correlation length scale of about 10 km, and less rapidly at longer separation distances, with a correlation length scale of about 20 km. The OCO-2 satellite takes many CO2 measurements with small (∼3 km2) fields of view (FOVs) in a thin (<10 km wide) swath running parallel to its orbit: up to 24 separate FOVs may be obtained per second (across a ∼6.75 km distance on the ground), though clouds, aerosols, and other factors cause considerable data dropout. Errors in the CO2 retrieval method have long been thought to be correlated at these fine scales, and methods to account for these when assimilating these data into top-down atmospheric CO2 flux inversions have been developed. A common approach has been to average the data at coarser scales (e.g., in 10 s long bins) along-track, then assign an uncertainty to the averaged value that accounts for the error correlations. Here we outline the methods used up to now for computing these 10 s averages and their uncertainties, including the constant-correlation-with-distance error model that was used to summarize the OCO-2 version 9 XCO2 retrievals as part of the OCO-2 flux inversion model intercomparison project. We then derive a new one-dimensional error model using correlations that decay exponentially with separation distance, apply this model to the OCO-2 data using the correlation length scales derived from the MFLL–OCO-2 differences, and compare the results (for both the average and its uncertainty) to those given by the current constant correlation error model. To implement this new model, the data are averaged first across 2 s spans to collapse the cross-track distribution of the real data onto the 1-D path assumed by the new model. Considering correlated errors can cause the average value to fall outside the range of the values averaged; two strategies for preventing this are presented. The correlation lengths over the ocean, which the land-based MFLL data do not clarify, are assumed to be twice those over the land. The new correlation model gives 10 s XCO2 averages that are only a few tenths of 1 ppm different from the constant correlation model. Over land, the uncertainties in the mean are also similar, suggesting that the +0.3 constant correlation coefficient currently used in the model there is accurate. Over the oceans, the twice-the-land correlation lengths that we assume here result in a significantly lower uncertainty on the mean than the +0.6 constant correlation currently gives – measurements similar to the MFLL ones are needed over the oceans to do better. Finally, we show how our 1-D exponential error correlation model may be used to account for correlations in inversion methods that choose to assimilate each XCO2 retrieval individually and also to account for correlations between separate 10 s averages when these are assimilated instead.

OCO‐2 Satellite‐Imposed Constraints on Terrestrial Biospheric CO2 Fluxes Over South Asia

“…Because high spatiotemporal resolution OCO‐2 soundings do not offer independent pieces of information to global flux inversion systems with coarse spatial resolutions, 10‐s OCO‐2 XCO 2 averages of individual soundings were calculated. OCO‐2 data retrieval error and model representation error were also calculated, and reported along with each 10‐s data (Baker et al., 2021; Basu et al., 2018; Crowell et al., 2019).…”

“…The observational error covariance matrix ( O ) was specified corresponding to the assimilated in situ CO 2 concentrations and OCO‐2 XCO 2 column retrievals following OCO‐2 v9 MIP protocols. No observation error correlations between individual IS or 10‐s‐averaged OCO‐2 data were applied in this study, although error correlations were accounted for in calculating the uncertainties placed on the 10‐s OCO‐2 data (Baker et al., 2021). The MDM values estimated for each IS observation were used in the observational error covariance for IS data.…”

National CO2 budgets (2015–2020) inferred from atmospheric CO2 observations in support of the Global Stocktake

“…Specifically, individual scenes within the 10 s span are weighted according to the inverse of the square of the X CO2 uncertainty (standard deviations) produced by the retrieval, and correlations of +0.3 for land scenes and +0.6 for ocean scenes are assumed when calculating the uncertainty on the 10-second averages (see Sect. 3.2.1 of Baker et al, 2022); transport model errors are also considered (based on Schuh et al, 2019). Only 10 s spans with 10 or more good quality retrievals were used (sparser data being thought to be more prone to cloud-related biases).…”

Improving the joint estimation of CO2 and surface carbon fluxes using a constrained ensemble Kalman filter in COLA (v1.0)

“…In addition, the retrieval error needs to be estimated. We used postprocessed OCO-2 level 2 data based on a new exponentially decaying error correlation model with a length scale computed from airborne lidar measurements (Baker et al, 2022). Since ocean glint observations have system bias compared with land observations (Crowell et al, 2019), only the land nadir and land glint data are assimilated (Fig.…”