Auxiliary information required to compare TCCON data to other data or model output are embedded in the netCDF files for GGG2014. For (now obsolete) GGG2012, they are posted on the TCCON database auxiliary data page, and at the bottom of this page for the (obsolete) GGG2009 data.
Note: this is a work-in-progress!
In order to compare our data with, say, model or high-resolution aircraft profile data, you need to use our column averaging kernels and a prioris. This information is also covered in Wunch et al. (2010) and is based on Rodgers and Connor (2003). The main equation is:
where is the quantity of interest: the smoothed column DMF (a scalar), is the TCCON a priori column (a scalar), describes the vertical summation (a vector), is the TCCON absorber-weighted column averaging kernel (a vector), is the DMF "truth" (either the model profile or the aircraft profile) and is the TCCON a priori profile (vector). There is one a priori profile per local day of measurements (many TCCON sites measure over two UTC days per local day because of their time zones). In order to compute the smoothed columns, you need to know the pressure weighting function, which is the ratio of the vertical column of the gas in each layer () to the vertical column of dry air ( in molecules/cm^2):
where is the dry mole fraction of the gas of interest ( or from the first equation)
where is defined by convention:
and the and are in kg/molecule, requiring Avogadro's constant to convert the molar weights. g is the gravitational acceleration and i is the atmospheric layer.
This makes the first equation become:
The current version of our .map files contain g and all the constants necessary to compute the equations above, but you can also find relationships for g as a function of altitude and latitude from, e.g., http://en.wikipedia.org/wiki/Gravity_of_Earth.
IMPORTANT!
In order to test the effect of neglecting some of the aspects mentioned above, and highlight there importance, a number of sensitivity studies have been undertaken. These are done using CT2011 simulations, provided as "special output" at 90 minute intervals at TCCON locations. In these studies, we generate one CT "smoothed" point for each FTS measurement, thereby temporally interpolating between the spanning CT model outputs. This has a couple of advantages:
1. We can then use the solar zenith angle of the measurement to interpolate from the generic averaging kernels to provide the averaging kernel for smoothing, along with the daily TCCON apriori profile.
2. Because the TCCON data are not temporally uniform, this ensures that there are no biases between the model and data introduced by non-uniform sampling, even when averaging to daily/weekly/less-frequent periods.
Here we use 3 sites to illustrate the sensitivities - Darwin (wet, tropical), Lamont (mid-lat) and Spitsbergen (dry, polar).
As the figure below shows, this induces significant differences (on the order of the TCCON precision and accuracy), and could thereby compromise any comparison between TCCON measurements and models. The differences are noticeably smaller at the dry site, Spitsbergen.
By the formulation above, when integrating it is strictly necessary to consider the H2O correction as being the dry-air mole fraction of H2O (by definition, by considering it as a mixing ratio rather than a mole fraction). This makes a small difference (<< 0.1ppm) to the smoothed xCO2.
TCCON averaging kernels, aprioris and other values are provided at exact levels, not averaged across an altitude range. Here we have compared the formulation integrating across every layer using the mean of the level boundaries of the layer with assuming that the value at the lower altitude (i.e. higher pressure) is representative of the entire layer above. The differences are bordering on significant, at approximately 0.1 ppm.
This is a common mistake, and critical. The effect of convolving the profile with the averaging kernel can be large, however it is mostly cancelled out by the effect of also convolving the apriori profile with the kernel. Ignoring the apriori therefore leads to large errors, sometimes larger than 1% depending on the zenith angle of the measurement (because of the zenith angle dependence of the averaging kernels).
Because the integration deals with dry-air mole fractions, but an integration over pressure is effectively with respect to wet-air (i.e. the pressure includes the contribution of H2O), this dilution due to H2O must be taken into account. This differences from ignoring this are generally small because of cancellation between the VC(gas) and the VC(air), but can exceed 0.1 ppm.
Note: These things are to be added:
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