A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

摘要

Atmospheric inversions are frequently used to estimate fluxes of atmosphericgreenhouse gases (e.g., biospheric CO₂ flux fields) at Earth's surface.These inversions typically assume that flux departures from a prior model arespatially smoothly varying, which are then modeled using a multi-variateGaussian. When the field being estimated is spatially rough, multi-variateGaussian models are difficult to construct and a wavelet-based field modelmay be more suitable. Unfortunately, such models are very high dimensionaland are most conveniently used when the estimation method can simultaneouslyperform data-driven model simplification (removal of model parameters thatcannot be reliably estimated) and fitting. Such sparse reconstruction methodsare typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for theestimation of fossil fuel CO₂ (ffCO₂) emissions in the lower 48 statesof the USA.Our new method is based on stagewise orthogonal matching pursuit (StOMP), amethod used to reconstruct compressively sensed images. Our adaptationsbestow three properties to the sparse reconstruction procedure which areuseful in atmospheric inversions. We have modified StOMP to incorporate priorinformation on the emission field being estimated and to enforcenon-negativity on the estimated field. Finally, though based on wavelets, ourmethod allows for the estimation of fields in non-rectangular geometries, e.g.,emission fields inside geographical and political boundaries.Our idealized inversions use a recently developed multi-resolution (i.e.,wavelet-based) random field model developed for ffCO₂ emissions andsynthetic observations of ffCO₂ concentrations from a limited set ofmeasurement sites. We find that our method for limiting the estimated fieldwithin an irregularly shaped region is about a factor of 10 faster thanconventional approaches. It also reduces the overall computational cost bya factor of 2. Further, the sparse reconstruction scheme imposesnon-negativity without introducing strong nonlinearities, such as thoseintroduced by employing log-transformed fields, and thus reaps the benefitsof simplicity and computational speed that are characteristic of linearinverse problems.