1. Measurements of CO 2 Molar Mixing Ratio by Infrared Absorption Spectroscopy C, mole fraction (μmole mole -1 = ppm) LI-COR analyzers measure absorbance at 4.26 μm V = kA (voltage proportional to absorbance) ρ c = P c /RT = CP/RT (molar density of absorber) ρ c L = CPL/RT (absorber amount in absorption cell)

3. LiCor internal schematic

4. 100 cc/min

5. Virial Equation of State (REAL not IDEAL) : PV = nRT(1 + nB(T)/V + nC(T)/V 2 + …) neglect higher order terms Solve for n: n = -(V/2B){1 – (1 + 4PB/RT) 1/2 } B (10 -6 m 3 mole -1 ) (in air at T = 300 K) air -7.7 CO 2 -42.3 Using this, we find the equivalence of (at 300 K and 1 Bar): volume mixing ratio370.0 x 10 -6 m 3 CO 2 / m 3 air molar mixing ratio370.5 x 10 -6 mole CO 2 / mole air

6. LiCor Analyzer Response Curve: C = [a 0 + a 1 (V P 0 /P) + a 2 (V P 0 /P) 2 ] T/T 0 C is CO 2 mole fraction P 0, T 0 are pressure and temperature during calibration

8. Pressure Broadening effective pressure:P e = P N 2 + Σb i P i GasCoef (b i )% of air N 2 1.00 78.084 O 2 0.81 20.946 Ar 0.78 0.934 H 2 O≈1.57 ≈1

9. Pressure Broadening Example calibration curve in air (P O2 = 20 kPA, P N2 = 80 kPA): P e = 80 kPa x 1.00 + 20 kPa x 0.81 = 96.2 kPa C = 326.61 + 0.1738 V + 4.5095 x 10 -5 V 2 A LiCor response of 300 mV implies CO 2 = 382.82 ppm What if you calibrated using pure N 2 ? (P N2 = P e = 100 kPa) C = 326.61 + 0.1807 V + 4.8723 x 10 -5 V 2 Now a response of 300 mV gives CO 2 = 385.21 ppm ! What error is made using synthetic (no Argon) vs. real air?

10. Water Vapor (1)Pressure broadening of CO 2 line b H2O ≈ 1.57 (2)Dilution of air – adding 1% H 2 O displaces 1% of CO 2 (≈ 3.7 ppm) Solution: DRY THE AIR! How dry is dry enough? 0.1 ppm / 370 ppm = 0.027% → H 2 O ≤ 0.00027 m 3 /m 3 air Error in CO 2 Dewpoint 0.1 ppm -36.5 o C 0.2 ppm -29.4 o C

11. What if we had 3 standard gases instead of 4 ???

12. The results differ for different LiCor CO 2 analyzers under the same conditions!!!