A new exponentially-decaying error correlation model for assimilating OCO-2 column-average CO2 data, using a length scale computed from airborne lidar measurements.

To check the accuracy of column-average dry air CO₂ mole fractions ("X_CO2 ") retrieved from Orbiting Carbon Overvatory (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 of 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-second-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-second averages and their uncertainties, including the constant-correlation-with-distance error model currently being used to summarize the OCO-2 version 9 X_CO2 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-second spans, to collapse the cross-track distribution of the real data onto the 1-D path assumed by the new model. A small percentage of the data that cause non-physical negative averaging weights in the model are thrown out. 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-second X_CO2 averages that are only a few tenths of a 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 those inversion methods that choose to assimilate each X_??푂2 retrieval individually, and to account for correlations between separate 10-second averages when these are assimilated instead. [ABSTRACT FROM AUTHOR]