A shared-window mean-shape ensemble for CO2 profile retrieval from differential absorption lidar

Retrieving vertical CO2 profiles from differential absorption lidar requires separating absorption from scattering, gain, and background effects while preserving sensitivity to concentration changes. We introduce a shared-window mean-shape ensemble (SHMS) that fits paired raw online and offline returns over a 120-profile window and separately combines component profile means and centred shapes. Each component estimates a mean offset and a scaling of reference vertical structure under different signal and prior constraints. Under approximately stable absorption and relative gain, temporally centred channel fluctuations retain differential-attenuation information while removing constant additive backgrounds. Their covariance constrains a component whose vertical structure can contribute independently of its concentration level. In four semi-synthetic scenarios constructed with measured dual-channel fluctuations, SHMS achieved lower root-mean-square error than four single-profile comparators: local-slope, Tikhonov-regularized, optimal-estimation, and raw-signal maximum-a-posteriori retrievals. SHMS recovered 66.2% of the imposed change in bottom-to-top concentration difference and 17.8% of the layer-mean change; optimal-estimation and maximum-a-posteriori estimates remained nearly unchanged. In a measured application from the same day's record, the temporal-fluctuation-constrained component contributed 41.19 ppm to the retrieved vertical contrast of 47.06 ppm while receiving zero mean weight. SHMS thus integrates signal levels and temporal covariability through distinct contributions to concentration level and vertical contrast, providing a framework for designing profile retrieval algorithms that combine complementary constraints according to the concentration features they inform.