Abstract
Abstract. The scheme to propagate correlations between on-line and off-line state variables in atmospheric inversions using the fixed-lag Kalman smoother proposed in Bruhwiler et al. (2005) is explained as a process to impose a balanced constraint on the on-line state variables. It is then extended to the fixed-lag ensemble square root Kalman smoother and fixed-lag square root sigma-point Kalman smoother, allowing us to treat nonlinear observation operators easily. Further, to constrain the posterior fluxes within their feasible ranges, the constrained fixed-lag Kalman smoother is presented and the variable transform technique is proposed for the other two smoothers. Comparisons between various methods and observational data are conducted using a synthetic inversion of atmospheric CH4 fluxes. The results indicate that our developed methods are good alternatives to existing methods for conducting sequential inversion of atmospheric trace gases. It is also shown that the benefit to include the correlations between on-line and off-line state variables is case dependent.
Highlights
Closing the budget of various greenhouse gases, such as CO2, CH4 and N2O, has been an important task in our understanding of the human-induced climate change
Tang important role in quantifying the sources and sinks of various trace gases (Enting, 2002). It involves the comparison of forward model simulations from atmospheric transport models using prior sources and sinks with the spatiotemporally discrete observations
We extend the fixed-lag KS in Bruhwiler et al (2005) to two ensemble-based methods, the fixedlag ensemble square root Kalman smoother (ESRKS) and the fixed-lag square root central difference Kalman smoother (SRCDKS)
Summary
Closing the budget of various greenhouse gases, such as CO2, CH4 and N2O, has been an important task in our understanding of the human-induced climate change. Atmospheric inversion modeling plays an important role in quantifying the sources and sinks of various trace gases (Enting, 2002). It involves the comparison of forward model simulations from atmospheric transport models using prior sources and sinks with the spatiotemporally discrete observations. The prior sources and sinks are optimized by minimizing a cost function defined by the distances between the forward model simulation and observations (e.g., Gurney et al, 2002). In the Bayesian theorem, the fluxes and their associated error characteristics that are known as the prior (Pr(s)) and the observations and their error characteristics that define the likelihood function (Pr(o | s)) are used to obtain the posterior fluxes (Pr(s | o)) as
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