A review on the use of the adjoint method in four‐dimensional atmospheric‐chemistry data assimilation

Abstract

In this paper we review a theoretical formulation of the adjoint method to be used in four-dimensional (4D) chemistry data assimilation. The goal of the chemistry data assimilation is to combine an atmospheric-chemistry model and actual observations to produce the best estimate of the chemistry of the atmosphere. The observational dataset collected during the past decades is an unprecedented expansion of our knowledge of the atmosphere. The exploitation of these data is the best way to advance our understanding of atmospheric chemistry, and to develop chemistry models for chemistry-climate prediction. The assimilation focuses on estimating the state of the chemistry in a chemically and dynamically consistent manner (if the model allows online interactions between chemistry and dynamics). In so doing, we can: produce simultaneous and chemically consistent estimates of all species (including model parameters), observed and unobserved; fill in data voids; test the photochemical theories used in the chemistry models. In this paper, the Hilbert space is first formulated from the geometric structure of the Banach space, followed by the development of the adjoint operator in Hilbert space. The principle of the adjoint method is described, followed by two examples which show the relationship of the gradient of the cost function with respect to the output vector and the gradient of the cost function with respect to the input vector. Applications to chemistry data assimilation are presented for both continuous and discrete cases. The 4D data variational adjoint method is then tested in the assimilation of stratospheric chemistry using a simple catalytic ozone-destruction mechanism, and the test results indicate that the performance of the assimilation method is good.

Structure of forecast error covariance in coupled atmosphere–chemistry data assimilation

“…In prediction of air quality, the coupled physical and chemical processes are essential, which include transport, deposition, emission, chemical transformation, aerosol interactions, photolysis, and radiation (Grell et al, 2005). Optimized initial conditions for a numerical model, including such coupled processes, can be obtained by data assimilation (DA; e.g., Houtekamer and Mitchell, 1998;Eibern and Schmidt, 1999;Wang et al, 2001;Evensen, 2003;Park and Zupanski, 2003;Navon, 2009;Zupanski, 2009). Data assimilation has also been applied to the atmospheric chemical transport models (CTMs) (e.g., Constantinescu et al, 2007;Singh et al, 2011).…”

Ensemble data assimilation of total column ozone using a coupled meteorology–chemistry model and its impact on the structure of Typhoon Nabi (2005)

“…Therefore, the coupled meteorology-chemistry model is essential for the air quality and weather forecasting (e.g., Carmichael et al, 2008). The coupled system forecast is improved through coupled meteorology-chemistry data assimilation (DA), which estimates the best initial conditions by combining the information from the model and observations in a mathematically consistent manner (e.g., Houtekamer and Mitchell, 1998;Elbern and Schmidt, 1999;Wang et al, 2001;Evensen, 2003;Park and Zupanski, 2003;Navon, 2009;Zupanski, 2009;Park et al, 2015).…”

Multiscale ensemble filtering for reservoir engineering applications

“…In the past few years, successful applications of Kalman filter theory were reported in many areas of research: the meteorological applications [2,9], nonlinear shallow-water storm-surge models [25], and atmospheric chemistry and transport modeling (e.g., [12,23,26]). …”