Articles | Volume 11, issue 8
Atmos. Meas. Tech., 11, 4909–4928, 2018
Atmos. Meas. Tech., 11, 4909–4928, 2018

Research article 27 Aug 2018

Research article | 27 Aug 2018

A singular value decomposition framework for retrievals with vertical distribution information from greenhouse gas column absorption spectroscopy measurements

Anand K. Ramanathan1,2, Hai M. Nguyen3, Xiaoli Sun2, Jianping Mao1,2, James B. Abshire2, Jonathan M. Hobbs3, and Amy J. Braverman3 Anand K. Ramanathan et al.
  • 1Earth System Science Interdisciplinary Center, University of Maryland, College Park, MD 20740, USA
  • 2NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA
  • 3NASA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

Abstract. We review the singular value decomposition (SVD) framework and use it for quantifying and discerning vertical information in greenhouse gas retrievals from column integrated absorption measurements. While the commonly used traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We review the SVD method, explicitly recognize the use of an uninformative prior and show it to incur no bias from the choice of the prior. We also make the connection between the SVD method and the pseudo-inverse, which makes it more intuitive and easy to understand. We illustrate the use of the SVD method on an integrated path differential absorption CO2 lidar measurement model and verify our derivations and bias-free properties versus optimal estimation using numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. Hence, the SVD method is particularly useful for situations in which knowledge of the prior mean and prior covariance of the true state (e.g., greenhouse gas profiles) is inadequate.

Short summary
Remote sensing of greenhouse gases (GHG) such as CO2 and CH4 in the atmosphere from space is important for studying emissions and the carbon cycle. Present-day techniques measure the absorption of light passing through the atmosphere and determine the column-averaged gas concentration in the atmosphere. Here, we draw from a well-known singular value decomposition (SVD) framework to develop a technique of extracting information about the GHG concentration profile from the column absorption.