BOX 4.1

Tracer-Transport Inversion

A forward model of the atmospheric and/or oceanic abundance of a trace gas is based on solution of the continuity equation:


The tendency in local abundance of species X at time t (∂X/∂t), written on the left as a finite difference over the time interval Δ, is equal to the local emission rate E into the volume being sampled plus in situ chemical production P minus loss rates L minus the divergence of the transport flux . These models are often designated chemistry-transport models or tracer-transport models. In a tracer-transport inversion, the measurements of X(t), along with a model for the chemistry and transport (P – L, ), are used to derive emissions (E) by subtracting P – L and from both sides of equation (1).

With current chemistry-transport models, this continuity equation is solved on a three-dimensional grid of more than a million points, using a meteorology (including winds, convection, diffusive mixing, clouds, and precipitation) that varies hourly. Most analyses today employ the Bayesian synthesis method (Enting, 2002; Gurney et al., 2003) that includes a priori estimates of emissions (the best estimate of the emission patterns, including uncertainties, obtained from independent data and modeling). In regions where the atmospheric measurements clearly constrain the emissions, the resulting a posteriori emissions are independent of the a priori; but in regions where the available measurements are inadequate for constraining the emissions, the method just returns what was assumed, the a priori. Thus, Bayesian methods result in more stable estimates of emissions, but sometimes add no new information.

dently verifying self-reported emissions by countries. This chapter reviews studies that used tracer-transport inversion methods to estimate CO2 emissions and to check self-reported emissions of other greenhouse gases. The chapter also identifies four ways to reduce uncertainties associated with atmospheric monitoring of national CO2 emissions.


Tracer-transport inversion methods have been used to estimate emissions of CO2, CH4, N2O, and hydrofluorocarbons (HFCs). This section summarizes the results of inverse modeling studies for estimating greenhouse gas emissions (especially CO2) and for checking self-reported emissions (especially chlorofluorocarbons [CFCs] and HFCs) at national to global scales.

Inversions of CH4, N2O, and HFCs

Top-down, atmospheric inverse model derivations of greenhouse gas emissions have been applied extensively to CO2, CH4, N2O, and the fluorinated gases. In general, these approaches use the patterns of variability in the trace gases to infer the geographic pattern of emissions, but they require some prior knowledge of the spatial and temporal patterns. For N2O, the Bouwman et al. (1995) work on uncertainties in the global distribution of emissions forms the core a priori data that are tested with atmospheric observations and models (Hirsch et al., 2006; Huang et al., 2008). Thus far, these studies, as well as similar ones for HFCs (e.g., Stohl et al., 2009), have been successful at testing the assumed emissions only at the scale of broad latitudinal bands. Some studies suggest that current observations and modeling are capable of providing information on individual country emissions (e.g., Manning et al., 2003), but these claims remain untested. Many such studies assume that the atmospheric transport model represents tracer transport perfectly and do not consider the large, uncharacterized errors in the models (e.g., Patra et al., 2003; Rayner, 2004; Prather et al., 2008).

A number of studies have derived top-down emission patterns for CH4 (e.g., Fung et al., 1991; Hein et al., 1997; Houweling et al., 1999), sometimes taking advantage of additional information contained in the relative isotopic abundances (e.g., 13CH4 versus 12CH4; Fletcher et al., 2004). These studies were able, for example, to verify the European Commission’s Emission Database for Global Atmospheric Research (EDGAR) inventory of CH4 emissions on a scale of North America to within an uncertainty of 20 percent, but they rely strongly on assumed patterns of emissions within the continent. Assimilation of satellite observations of CH4 (Bergamaschi et al., 2007; Meirink et al., 2008) may be able to constrain large emissions at a subnational level (e.g., rice paddies in India and Southeast Asia), but this has not yet been verified using a multimodel approach with realistic errors on the satellite data or by comparing predictions with regional inventories and surface observations. On the other hand, intense scientific campaigns involving regional measurements

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