Fig. 1 CO2 band at 1.6 m observed on June 17, 2008 by TCCON at Park Falls (Wisconsin) with solar zenith angle of 22.5. Fig. 2. Calibration curve of CO2. Red points for using H2O as dry air standard (0.73±1.49 ppm); Black points for using O2 as dry air standard (-5.02±0.49 ppm). Dots for Parkfalls site and diamonds for Lamont site. Fig. 3. (a) Original CO2 profile in black line and perturbed CO2 profile in blue line. (b) Changes of CO2 (∆𝑥) are mostly in boundary layer. (c) Calculated differences of the radiances. Black is the difference of two forward model simulations. The red is the estimates of the difference using linear equation (9). Their residuals plotted in (d) are three orders of magnitude smaller than the noise level (dotted line in c). Fig. 4 (a) The square root of the diagonal in CO2 covariance matrix. (b) The 2-D plot of the CO2 covariance matrix. Figure 5 CO2 profiles measured by aircraft (black) and TES Geos-chem assimilation (red) at SGP on the same day in 2009. Their best agreements are mostly above 600 hPa in free troposphere. Figure 6 The comparison of TCCON total column CO2 with smoothed aircraft CO2 (black, with cloud filter) and the comparison of PBL CO2 by TCCON/TES with smoothed aircraft PBL CO2 (red). Similar comparison of PBL CO2 by TCCON a priori is also plotted in blue dots to provide a view of improvement by combining TCCON and TES data. Fig. 7 (a) Monthly mean column averages and PBL CO2 in 2009 at Lamont. Flight column-averaged estimates in black solid line. TCCON column averages in black dots. Flight PBL estimates in red solid line and TCCON/TES PBL estimates in red dots. (b) The difference of PBL CO2 and column-averaged CO2 by flight (solid line) and by TCCON/TES (dots). The agreements to the flight estimated differences are better. Unit (ppm) Day (yymmdd) 090108 090116 090129 090204 090211 090219 090221 090304 090308 090314 090316 090318 090329 090407 090408 090420 090421 090423 090517 090518 090520 090526 090528 090530 090604 090607 090610 090612 090616 090621 090623 090629 090701 090706 090715 Without cloud filter Actual Sample Bias (1 × 𝜎) # -5.05 0.31 167 -5.20 0.30 171 -5.31 0.30 170 -5.08 0.26 169 -4.85 0.52 132 -5.41 1.08 102 -5.01 0.41 131 -4.42 3.49 24 -5.39 0.52 163 -4.84 0.99 108 -5.64 0.37 157 -5.47 1.44 163 -5.65 0.88 104 -5.54 0.26 98 -5.67 0.42 129 -6.36 1.45 93 -5.98 0.29 131 -5.88 0.33 131 -5.86 0.32 130 -4.86 0.32 131 -4.98 0.58 90 -5.79 0.62 96 -5.56 0.30 130 -5.37 0.34 130 -5.66 0.38 128 -6.69 1.16 3 -6.06 1.63 47 -6.49 1.26 102 -6.99 0.34 129 -6.52 0.28 97 -6.22 0.34 131 -5.52 0.36 123 -5.8 0.86 126 -4.66 1.56 53 -7.94 1.49 4 With cloud filter Expected Actual Sample 𝜎(𝐒̂𝐦 Bias (1 × 𝜎) # 𝜎(𝐒̂𝐦 ) + 𝐒̂𝐬 ) -5.03 0.30 161 0.27 0.79 -5.20 0.30 171 0.33 0.81 -5.32 0.30 169 0.34 0.84 -5.08 0.26 169 0.33 0.81 -5.00 0.49 90 0.33 0.82 -5.28 0.38 96 0.33 0.83 -5.00 0.42 130 0.34 0.84 -4.27 N/A 1 0.32 0.75 -5.42 0.39 132 0.32 0.78 -4.69 0.42 102 0.33 0.80 -5.67 0.27 154 0.32 0.76 -5.38 0.44 112 0.32 0.76 -5.75 0.28 76 0.33 0.79 -5.54 0.26 98 0.33 0.79 -5.70 0.40 121 0.32 0.76 -6.27 0.44 69 0.32 0.78 -5.99 0.29 130 0.32 0.77 -5.89 0.30 122 0.32 0.74 -5.86 0.32 130 0.32 0.77 -4.86 0.32 131 0.32 0.75 -5.08 0.50 75 0.32 0.74 -5.79 0.36 86 0.32 0.75 -5.56 0.30 130 0.32 0.75 -5.37 0.34 130 0.32 0.73 -5.66 0.38 128 0.32 0.75 -6.12 N/A 1 0.31 0.71 -6.44 1.27 27 0.32 0.73 -6.62 0.35 72 0.32 0.73 -6.99 0.34 128 0.31 0.71 -6.52 0.28 95 0.31 0.71 -6.23 0.32 129 0.31 0.70 -5.5 0.32 118 0.31 0.71 -5.9 0.46 119 0.31 0.72 -4.76 0.33 43 0.32 0.73 -6.63 N/A 1 0.31 0.70 090731 090802 090803 090822 090823 090901 091019 091101 091102 091103 091111 091122 091218 091220 091227 Mean 1×𝜎 -5.33 -5.39 -7.82 -5.56 -6.37 -4.65 -7.80 -6.11 -6.33 -6.60 -6.47 -6.05 -5.86 -5.30 -5.61 -5.78 0.78 0.36 0.29 0.31 1.24 0.38 0.70 N/A 0.36 0.33 0.35 1.25 0.52 0.47 0.38 0.66 0.67 127 131 130 7 130 103 1 130 131 131 89 82 127 101 10 108 -5.34 -5.39 -6.06 -5.65 -6.37 -4.67 -7.78 -6.11 -6.33 -6.60 -6.40 -6.01 -5.86 -5.30 -5.29 -5.71 0.67 0.34 0.29 0.33 1.05 0.38 0.66 N/A 0.36 0.33 0.35 0.63 0.39 0.47 0.38 1.18 0.39 125 131 130 3 130 102 1 130 131 131 67 68 127 101 3 100 0.32 0.31 0.31 0.32 0.31 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.33 0.33 0.34 0.32 0.73 0.72 0.70 0.73 0.72 0.73 0.74 0.75 0.76 0.77 0.77 0.78 0.82 0.79 0.84 0.78