288
Air Pollution and Turbulence: Modeling and Applications
have prompted intensive study of the global carbon cycle. Direct observations of
the global increase in CO 2 provide important information about how the carbon
cycle responds to steadily growing inputs, but only limited information about how
the cycle would behave under other conditions (Enting, 2007). In order to obtain
additional information about the carbon cycle, extensive investigations of indirect
data have been undertaken.
One widely-applied indirect technique involves the deduction of surface CO 2
fl uxes from data on the spatial distribution of concentrations. This type of inverse
calculation goes back to Bolin and Keeling (1963), with little further study until
the late 1980s, and then widespread application since then. Important milestones
were the development of techniques including formal analysis of uncertainties arising from data error (Enting et al., 1993, 1995) and the establishment of the TransCom
working group to study the role of model error in CO 2 inversions.
The principle of trace gas inversions is that the observed spatial distribution of concentrations refl ects the combined effect of the spatial distribution of sources and sinks
and of atmospheric transport. Therefore, in principle, if the contribution of transport can be calculated, then the net result of sources and sinks can be estimated. In
practice, the ability to resolve details of sources is severely limited by the mathematical characteristics—technically termed ill-conditioning—of the estimation problem.
While much of the research effort in global-scale trace gas inversions has concentrated on CO 2 , inversion studies have been undertaken for other gases such as
methane (CH 4 ) and various halogenated compounds. There have been a number of
reviews of trace gas inversions (Enting, 2000a,b; Prinn, 2000). One of my books
(Enting, 2002) gives an extensive discussion of many aspects of trace gas inversion.
More recently, Heimann et al. (2004) have reviewed the contribution of space–time
inversions to our understanding of the carbon cycle.
This chapter reviews inversion techniques, places them in the context of statistical
estimation, and considers the limits to resolution imposed by the ill- conditioning of
the inverse problem. The results of inversions of CO 2 data are considered in some
detail, noting applications to other long-lived tracers. Many of these topics are
addressed in greater detail in my book (Enting, 2002), but the fi eld is undergoing
continuous rapid development. Consequently, in Section 11.5, the present chapter
tries to identify new emerging areas of development.
11.2 TECHNIQUES
11.2.1 ESTIMATION AND STATISTICS
For a quantitative uncertainty analysis, an inversion should be treated as a process
of statistical estimation. The statistical formulation of inverse problems is espoused
by Tarantola (1987) as a general principle, and forms the basis of the analysis of
meteorological data assimilation by Kalnay (2003). For trace gas inversions, the statistical formulation of inversions is the theme of my book (Enting, 2002). The statistical approach to inverse problems has recently been advocated by Evans and Stark
(2002). In particular, they suggest that nonparametric statistical approaches are most
appropriate.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
have prompted intensive study of the global carbon cycle. Direct observations of
the global increase in CO 2 provide important information about how the carbon
cycle responds to steadily growing inputs, but only limited information about how
the cycle would behave under other conditions (Enting, 2007). In order to obtain
additional information about the carbon cycle, extensive investigations of indirect
data have been undertaken.
One widely-applied indirect technique involves the deduction of surface CO 2
fl uxes from data on the spatial distribution of concentrations. This type of inverse
calculation goes back to Bolin and Keeling (1963), with little further study until
the late 1980s, and then widespread application since then. Important milestones
were the development of techniques including formal analysis of uncertainties arising from data error (Enting et al., 1993, 1995) and the establishment of the TransCom
working group to study the role of model error in CO 2 inversions.
The principle of trace gas inversions is that the observed spatial distribution of concentrations refl ects the combined effect of the spatial distribution of sources and sinks
and of atmospheric transport. Therefore, in principle, if the contribution of transport can be calculated, then the net result of sources and sinks can be estimated. In
practice, the ability to resolve details of sources is severely limited by the mathematical characteristics—technically termed ill-conditioning—of the estimation problem.
While much of the research effort in global-scale trace gas inversions has concentrated on CO 2 , inversion studies have been undertaken for other gases such as
methane (CH 4 ) and various halogenated compounds. There have been a number of
reviews of trace gas inversions (Enting, 2000a,b; Prinn, 2000). One of my books
(Enting, 2002) gives an extensive discussion of many aspects of trace gas inversion.
More recently, Heimann et al. (2004) have reviewed the contribution of space–time
inversions to our understanding of the carbon cycle.
This chapter reviews inversion techniques, places them in the context of statistical
estimation, and considers the limits to resolution imposed by the ill- conditioning of
the inverse problem. The results of inversions of CO 2 data are considered in some
detail, noting applications to other long-lived tracers. Many of these topics are
addressed in greater detail in my book (Enting, 2002), but the fi eld is undergoing
continuous rapid development. Consequently, in Section 11.5, the present chapter
tries to identify new emerging areas of development.
11.2 TECHNIQUES
11.2.1 ESTIMATION AND STATISTICS
For a quantitative uncertainty analysis, an inversion should be treated as a process
of statistical estimation. The statistical formulation of inverse problems is espoused
by Tarantola (1987) as a general principle, and forms the basis of the analysis of
meteorological data assimilation by Kalnay (2003). For trace gas inversions, the statistical formulation of inversions is the theme of my book (Enting, 2002). The statistical approach to inverse problems has recently been advocated by Evans and Stark
(2002). In particular, they suggest that nonparametric statistical approaches are most
appropriate.
© 2010 by Taylor and Francis Group, LLC