1. Dampening the effect of those damn damp * mixing ratios in TM5 * slightly wet

2. Dampening the effect of those damn damp * mixing ratios in TM5 * slightly wet Thank you John! Thank you Arjo! Thank you Andy! Thank you Sander! Thank you Maarten! Thank you Sourish! Thank you Wouter! Thank you Martin H! Thank you Peter B! Thank you Christian!

3. New observation methods force us to think about the way we sample the TM5 model typemethodreported flasks dry sample, then GC, detect molecules burned (FID) CO2/dry air mole fraction in-situ (Licor) dry air flow then detect CO2 absorption of radiation (NDIR), scale to standards CO2/dry air mole fraction in-situ (Cavity Ring Down) air flow, detect CO2, H2O, air volume CO2/dry air mole fraction FTS no sample, measure radiances of CO2 and O2 CO2/O2 mole fraction SCIA-CO2 no sample measure radiances of CO2 and O2 CO2/O2 mole fraction GoSat (SRON) measure radiance of CO2 and surface pressure from ECMWF minus H2O(g) CO2/simulated dry air mole fraction Thank you Sourish!

4. This raises several questions How do we deal with measurements of mole fractions in TM5? Could or should we do better? What error do we accept, how far do we want to go?

5. Current sampling strategy in TM5 Where the column integral of m adds up to the (wet) surface pressure M air represent the dry air mole fraction

6. Does this make the TM5 mole fraction a strange beast? This seems all wrong! But... This mole fraction is based on two conserved quantities in the model (and thus conserved itself) It results in a well mixed atmosphere after ~3 years of mixing It only shows variations due to sources and sinks and not due to water vapor This is just like the dry air mole fraction that is measured...! Message: don’t panic, we didn’t do anything stupid... ;)

7. But what is wrong with it? 1. The total air mass in TM5 is (made) consistent with observed surface pressure changes, and part of the mass is thus from water vapor which we do not correct m for 2. It thus also has a slightly lower mole mass M air 3. We enforce in TM5 that the total mass of the atmosphere is conserved at each time step: this is not true, only the dry air mass is conserved (...)

8. Issue 1: part of the mass we divide by comes from H2O

9. Snapshot water vapor Thank you Arjo!

10. Issue 1: part of the mass we divide by comes from H 2 O 1.0% of the pressure caused by H 2 O = 1.0% of the volume is H 2 O => A 390 ppm dry air mixing ratio could be represented as: X dry = 390 umol CO 2 /1.00 mol dry Air = 390.00 ppm X wet =390 umol CO2/ 1.01 mol wet Air = 386.14 ppm X wet =390 umol CO2/ 1.01 mol wet Air = 386.14 ppm So using wet instead of dry mole masses leads to a ~1% error But this is not quite right, when we go through mass... Thank you John!

11. Issue I+1I: We also use the wrong molar mass of air M = 592.5e-6 kg CO 2 X dry = 592.5e-6 kgCO 2 / 1 kg Air / (44g/mol)/(28.96 g/mol) = 390 ppm MM wet = 592.5e-6 kg CO2/(1 kg dry air + 18/28.96*0.01) = 588.84e-6 kg CO 2 /kg air Issue II: Now we can go back to mole fraction in two ways: (1) using TM5 dry molar mass: X TM5 = 588.84e-6*28.96/44.=387.56 ppm (0.6% error) (2) using true wet molar mass: X wet =588.84e-6*28.85/44.=386.11 ppm (1% error) Thank you John!

12. Issue 1+II together: So in principal, the error is proportional to the mole fraction of water vapor in the column (1%), BUT: (1) in TM5, we compensate a fraction of this 1% by also using the “wrong” molar mass of dry air, and we only incur 0.6% of the error (2) The error we make is only on the variations of the total tracer mass (sources and sinks) since we made the same error on initialization of the initial mixing ratio (~370 ppm). Thank you John! Thank you Martin H!

13. Global water vapor pressure Seasonal cycle! Thank you Arjo!

14. Mass conservation forced by rescaling global mean surface pressure to 985 hPa at each step but only dry air mass should be globally constant Net mass flux into / out of the column is forced to match the surface pressure tendency The pressure tendency includes net condensation / evaporation and therefore this balance is not supposed to hold exactly Issue III: TM5 mass conservation

15. Global mean air pressure Actual surface pressure Constant surface pressure Variations = water vapor Thank you Arjo!

16. Global mean air pressure Variations = constant dry + varying water vapor Thank you Arjo!

17. but only dry air mass should be globally mean constant We could easily enforce the dry air mass to be conserved in the global mean, and allow surface pressure variations through the water column We would then balance the mass fluxes of dry air, given the ECMWF “flow fields” (u,v) When making mole fractions in TM5, we then divide rm only by m dry, the dry fraction of the column, and divide by M dry = 28.96. This is a conserved dry mole fraction! For convenience, we could also keep a total air mass (m tot ) which has the mass of dry+wet components, to be used in pressure/mass conversions and height/geopotential calculations Issue III: TM5 mass conservation

18. Local transitions of water vapor are now aliased into mass fluxes This is automatically solved if we no longer balance mass fluxes based on total pressure, but only on dry air pressure (two flies with one stone)...the size of this error was likely small given other transport errors that we alias into the conserved mass fluxes (advection scheme of ECMWF, phase transitions/precipitation amounts in ECMWF, regridding to lat/lon,...) Issue III: TM5 mass conservation Thank you Maarten!

19. So... We had TM5 mole fractions that were pretty good errors of 0.6%, seasonal, latitudinal ~0.2 ppm for 30 ppm gradients of CO 2 ~0.6 ppb for 100 ppb gradients in CH 4 (Sander, check) conserved, constant over long time But we can maybe do a bit better, improving the comparison to remote sensing data The new framework is not that hard to build But requires some careful recoding in a new version (not backward compatible in code, no changes to produced meteo though)