## 3 Results  
Original, daily time series of surface EC tower measurements and mid-tropospheric AIRS observations of CO\({}_{2}\) concentration from 2007 to 2010 over KFS, KZU, and K4B are shown in Figure 1. [PERSON] _et al_. [42] have shown that, neglecting CO\({}_{2}\) released during burning regimes when towers are turned off, all three EC sites are net carbon sinks. AIRS time series exhibit less amplitude and seasonal variation in CO\({}_{2}\) concentrations than EC tower time series. Despite high missing daily values in the original AIRS time series, a linear regression of weekly averages of the AIRS time series follows the increasing global trend in atmospheric CO\({}_{2}\) concentrations from approximately 384 ppmv in 2007 to approximately 394 ppmv in 2010. Figure 1: Time series of surface EC tower and mid-tropospheric AIRS observations of CO\({}_{2}\) concentration from 2007 to 2010 over (**a**) KFS; (**b**) KZU; and (**c**) K4B. In all panels, the black line indicates the weekly mean of the EC time series and the dark gray line indicates the weekly mean of the AIRS tower time series. Root mean square error (RMSE) values between the original AIRS and EC time series show a difference of 12.9 ppmv at KFS, 18.9 ppmv at KZU, and 13.9 ppmv at K4B. Once the missing values in the time series have been replaced with the mean of each time series, the RMSE values increase to 13.9 ppmv at KFS, decrease slightly to 18.8 ppmv at KZU, and increase to 14.2 ppmv at K4B. Bias calculations show that AIRS mid-tropospheric observations exhibit a difference from surface measurements of \(-2.1\) ppmv at KFS, \(-3.0\) ppmv at KZU, and \(-3.2\) ppmv at K4B before replacing missing daily values. After replacing the missing values with the mean of each time series, these biases increase to \(-7.6\) ppmv at KFS, \(-8.8\) ppmv at KZU, and \(-8.3\) ppmv at K4B. The RMSE values and bias calculations indicate that site KFS and the corresponding AIRS pixel have the least difference in CO\({}_{2}\) concentration values. Filling missing data values increases the RMSE the most at KFS and bias calculations show an additional difference of at least 5 ppmv at all sites. Correlations of the original time series and wavelet decompositions of the fields at each temporal scale (Figure 2) indicate that the greatest positive correlations between surface CO\({}_{2}\) and mid-tropospheric measurements occurs at the 512-day timescale. At correlation coefficients of 0.2 and above, wavelet decomposed versions of EC time series compared with the original AIRS time series of the corresponding pixels (Figure 1(a)) show that the KZU site best reflects AIRS mid-tropospheric CO\({}_{2}\) concentrations on a 512-day scale compared with sites KFS and K4B. The reverse relationship, where wavelet decomposed versions of AIRS are compared with the original EC time series, also highlights the 512-day scale at which mid-tropospheric CO\({}_{2}\) may be exchanged with the land surface at the KZU site (Figure 1(b)). Comparing wavelet decomposed versions of both EC and AIRS time series (Figure 1(c)) reveals scales of greater contribution between surface and mid-tropospheric CO\({}_{2}\) exchanges. Stronger positive correlations exist at the 128-day (0.25), 256-day (0.44), and 512-day (0.61) scales for site KFS; at the 16-day (0.25) and 64-day (0.25) scales for site KZU; and at the 512-day (0.28) scale for K4B. Stronger negative correlations are seen at KFS at the 64-day (\(-0.43\)) scale, and at K4B at the 64-day  
Figure 1: Cont. time series, and wavelet decomposed versions of both AIRS and EC time series are shown in Figure 3. Lower relative entropy values correspond to greater similarity between the pdfs of the time series, _i.e._, less additional information is needed to capture the observed pdf. The timescale for which surface CO\({}_{2}\) concentrations are closest to the corresponding mid-tropospheric AIRS pixel varies between sites (Figure 3a).