Each 1x1 degree pixel of our domain was assigned one of the categories above bases on the Olson category that was most prevalent in the 0.5x0.5 degree underlying area.

2.2   Ensemble Size and Localization
The ensemble system used to solve for the scalar multiplication factors is similar to that in Peters et al. [2005] and based on the square root ensemble Kalman filter of Whitaker and Hamill, [2002]. We have restricted the length of the smoother window to only five weeks as we found the derived flux patterns within Europe and North America to be robustly resolved well within that time. We caution the CarbonTracker users that although the North American and European flux results were found to be robust after five weeks, regions of the world with less dense observational coverage (the tropics, Southern Hemisphere, and parts of Asia) are likely to be poorly observable even after more than a month of transport and therefore less robustly resolved. Although longer assimilation windows, or long prior covariance length-scales, could potentially help to constrain larger scale emission totals from such areas, we focus our analysis here on a region more directly constrained by real atmospheric observations.

Ensemble statistics are created from 150 ensemble members, each with its own background CO2 concentration field to represent the time history (and thus covariances) of the filter. In contrast to our earlier system design, we currently do not apply any localization to the statevector.

2.3   Dynamical Model
In CarbonTracker, the dynamical model is applied to the mean parameter values λ as:

λ tb = (λ  t-2a + λ  t-1 a + λ  p  )   ⁄   3.0

Where "a" refers to analyzed quantities from previous steps, "b" refers to the background values for the new step, and "p" refers to real a-priori determined values that are fixed in time and chosen as part of the inversion set-up. Physically, this model describes that parameter values λ for a new time step are chosen as a combination between optimized values from the two previous time steps, and a fixed prior value. This operation is similar to the simple persistence forecast used in Peters et al. [2005], but represents a smoothing over three time steps thus dampening variations in the forecast of λ b in time. The inclusion of the prior term λ p acts as a regularization [Baker et al., 2006] and ensures that the parameters in our system will eventually revert back to predetermined prior values when there is no information coming from the observations. Note that our dynamical model equation does not include an error term on the dynamical model, for the simple reason that we don't know the error of this model. This is reflected in the treatment of covariance, which is always set to a prior covariance structure and not forecast with our dynamical model.

2.4   Covariance Structure
Prior values for λ p are all 1.0 to yield fluxes that are unchanged from their values predicted in our modules. The prior covariance structure Pp describes the magnitude of the uncertainty on each parameter, plus their correlation in space.

In each of these regions on the northern hemisphere, individual λ(x,y) parameters are coupled through an isentropic covariance structure which makes two boxes i and j at a distance d of each other have a covariance C of

C = 0.64• exp(-d/L).

In this formula the covariance length scale L varies across the globe. Over Boral and Temperate North America where the observation network is relatively dense, L=300km, but in Boreal and Temperate Asia the number of observations constrains a much smaller number of parameters individually and we chose L=1000km. In Europe, with its strongly heterogeneous land-use and land management and large volume of observations available we took L=200km. In the rest of the world, the length scale is taken infiniely large, coupling fully all grid boxes and associated λ's in the tropics and southern hemisphere.