Statistical methods are used to combine available information to estimate CO2 fluxes in an optimal way. In particular the following information is exploited in an inverse procedure (see figure 1 ):
- observations of atmospheric trace gas concentrations
- a priori knowledge of sources and sinks, and
- atmospheric transport model to link sources and sinks to atmospheric observations.
A review article describing and comparing the CO2 inversions fluxes can be downloaded here. The CO2 flux inversion process follows the general scheme shown on figure 1.
The inversion products presented in this website are results from different laboratories. Details on the sepecifics of each product are available on the website of the data provider.
Figure 1 : General scheme of atmospheric inversion
figure 2 : Measurement Network
In inverse procedures, atmospheric observations can be used as means (yearly, monthly, weekly or daily) or as raw data for recent procedures. Uncertainties attached to these data should account for both observational error (generally small) and for representativeness error (possibly large). The latter is due to inabilities of atmospheric models to properly represent measurements mainly because of smoothed topography, transport error, and chemistry errors. Practically, representativeness error is difficult to calculate precisely and is often estimated by proxy approaches.
Figure 3 : Prior Fluxes
In most inverse procedures, a prior knowledge of the spatio-temporal distribution of the fluxes to estimate is necessary, directly or indirectly. This knowledge is given either by gridded inventories or by models . Inventories are generally used for anthropogenic emissions and are based on economic and trade data (e.g. fossil fuel emissions of CO2 from combustions). Natural sources and sinks often come from more or less sophisticated models representing involved processes (e.g. wetland emissions of CH4 calculated by a vegetation model). Uncertainties attached to prior fluxes can be a side-product of the methodologies employed to build the fluxes (inventories, models). However, this is not always available and prior flux uncertainties are often chosen (more or less arbitrarily) in order to be large enough not to nudge the flux estimate towards the prior knowledge. The relative weight of observations uncertainties and of prior flux uncertainties is a critical point of inverse procedures. Prior fluxes are optimize by the inverse procedure with a time resolution varying from one day to one year, most of the inversions performed so far being monthly inversions.
An inverse procedure combines mathematically atmospheric observations, prior fluxes and a chemistry-transport model to produce an optimal estimate of fluxes together with their uncertainties. This is done through the minimization of a cost function J :
y is the vector of observations
H(x) is the matrix of response functions (jacobian matrix)
x is the vector of fluxes (to be optimized)
xb is the vector of prior fluxes
R is the variance-covariance matrix representing observation errors
B is the variance-covariance matrix representing flux errors
J is a quadratical form built as the sum of two terms, the first one figuring model versus observations differences weighted by R , and the second one figuring a distance between prior fluxes and optimized fluxes weighted by B (Bayesian term). As the inverse problem is ill-posed, the second term helps regularising the solution of the problem. This approach is based on the Bayes paradigm. J is minimized either analytically (for small problems) or numerically using, for instance, conjugate gradient formulations.