Carbon dioxide retrieval from OCO-2 satellite observations using the nonlinear least squares four-dimensional variational method: observing system simulation experiments

In this study, we apply the nonlinear least squares four-dimensional variational (NLS-4DVar) method to the retrieval of the column-averaged dry air mole fraction of carbon dioxide (X_CO2 ) from the Orbiting Carbon Observatory-2 (OCO-2) satellite observations. The NLS-4DVar method avoids the computation of the tangent linear and adjoint models of the forward model, which reduces the computational and implementation complexity greatly. We use the forward model from the Atmospheric CO₂ Observations from Space (ACOS) X_CO2 retrieval algorithm. The inverse model is constructed of two parts, generating samples and minimizing the cost function. For the CO₂ profile, we apply an improved sampling algorithm based on ensemble singular value decomposition (SVD). For the other elements in the state vector, we apply a sampling algorithm based on normal distributions, and values of standard deviations of normal distributions are vital to the accuracy of retrieval. To minimize the cost function, the NLS-4Dvar method rewrite it into a nonlinear least squares problem, and solve it by a Gauss-Newton iterative method. We have tested our method in summer and winter at four sites through observing system simulation experiments, which are Lamont, Bremen, Wollongong and an ocean site in the North Pacific respectively. All the four sites show an improved X_CO2 and CO₂ profile after the retrieval.