ICOS Science Conference, Session 3

1. Tobias Steinhoff1,2, Ingunn Skjelvan1, Siv Lauvset1 and Matthew Humphreys3
Uncertainty analysis for calculations of
the marine carbonate system
1NORCE Norwegian Research Centre AS, Bjerknes Centre for Climate Research, Bergen, Norway
2GEOMAR, Helmholtz Centre for Ocean Research Kiel, Kiel, Germany
3NIOZ Royal Netherlands Institute for Sea Research and Utrecht University, Texel, the Netherlands
Contact: Tobias Steinhoff, tost@norceresearch.no

2. Overall ICOS goal:
“ICOS shall provide harmonised and high-precision scientific data on carbon cycle and
greenhouse gas budget and perturbations”
Goal of ICOS-Oceans stations
This translates to ICOS-Oceans as
1. Quantifying air-sea CO₂ Fluxes
2. Assessing Variability and Drivers

3. The marine carbonate system
H2CO3 ⇋ HCO3
−
+ H+ ⇋ CO3
2−
+ 2H+
Atmosphere
Ocean
fCO2
DIC (Dissolved Inorganic Carbon)
TA (Total Alkalinity)
pH
CO2 aq + H2O ⇋ H2CO3
↓↑
CO2 g

4. Orr
The marine carbonate system
pCO2
DIC (Dissolved Inorganic Carbon)
TA (Total Alkalinity)
pHBy knowing two variables, the
other two can be calculated
Package Language Reference
CO2SYSa QBasic Lewis and Wallace (1998)
CO2SYSb Excel Pelletier et al. (2007)
CO2SYSa Excel Pierrot et al. (2006)
CO2SYSa MATLAB van Heuven et al. (2011)
CO2calcc Visual Basic Robbins et al. (2010)
csysd MATLAB Zeebe and Wolf-Gladrow (2001)
ODVe CCC Schlitzer (2002)
mocsyf Fortran 95 Orr and Epitalon (2015)
seacarbg R Gattuso et al. (2015)
swco2h Excel Hunter (2007); Mosley et al. (2010)
swco2h Visual Basic Hunter (2007)
PyCO2SYS Python Humphrey et al. (2020)

5. SOOP: Ship of Opportunity
• Commercial vessels or research vessels
• Measurement of carbon variables in the surface ocean: fCO2 (alkalinity,
pH)
ICOS-Oceans stations - SOOP
This translates to ICOS-Oceans as
1. Quantifying air-sea CO₂ Fluxes
2. Assessing Variability and Drivers
But what is with the drivers ?

6. FOS: Fixed Ocean Station
• Surface buoy with attached instruments
• Subsurface mooring with instruments at different depths
• Regular ship sampling programm
ICOS-Oceans stations - FOS
VLIZ
This translates to ICOS-Oceans as
1. Quantifying air-sea CO₂ Fluxes
2. Assessing Variability and Drivers

7. SOOP lines (class 2):
SOOP lines (class 1):
ICOS-Oceans labelling criteria
Variable uncertainty
fCO2 2 µatm
Variable uncertainty
fCO2 2 µatm
Dissolved oxygen 2 %
TA or
DIC
10 µmol kg-1
5 µmol kg-1
FOS (class 2):
FOS (class 1)
Variable Uncertainty
fCO2 10 µatm
TA or
DIC
4 µmol kg-1
2 µmol kg-1
Variable Uncertainty
fCO2 10 µatm
TA or
DIC
4 µmol kg-1
2 µmol kg-1
Two out of
[NO3, PO4, Si(OH)4]
1-3 %

8. The basis for the defined uncertainties is the definition of the Global Ocean
Observing System (GOOS) essential ocean variables (EOV’s) and the Global
Ocean Acidification Observing network (GOA-ON) approach of “weather” and
“climate goals (Newton et al. , 2014):
• Weather goal:
• relative spatial patterns and short-term variations
• supporting mechanistic responses to and impact on local, immediate ocean acidification
dynamics
• Climate goal:
• assess long-term trends with a defined level of confidence
• support detection of the long-term anthropogenically driven changes in hydrographic
conditions and carbon chemistry over multi-decadal time scales
ICOS-Oceans labelling criteria
Weather goal Climate goal
pH 0.02 0.003
TA, DIC 10 µmol kg-1 2 µmol kg-1
fCO2 2.5% (=10 µatm @ 400 µatm) 0.5% (=2 µatm @ 400 µatm)

9. SOOP lines (class 2):
SOOP lines (class 1):
ICOS-Oceans labelling criteria
Variable uncertainty
fCO2 2 µatm
Variable uncertainty
fCO2 2 µatm
Dissolved oxygen 2 %
TA or
DIC
10 µmol kg-1
5 µmol kg-1
FOS (class 2):
FOS (class 1)
Variable Uncertainty
fCO2 10 µatm
TA or
DIC
4 µmol kg-1
2 µmol kg-1
Variable Uncertainty
fCO2 10 µatm
TA or
DIC
4 µmol kg-1
2 µmol kg-1
Two out of
[NO3, PO4, Si(OH)4]
1-3 %
a. How accurately should the second
carbon variable be measured on SOOP
lines and at FOS?
b. Can fCO2 be calculated with a sufficient
uncertainty by two other carbon
parameters?

10. Uncertainty of the calculated parameter depends on
1. Uncertainty of input variables (measurement uncertainty)
Uncertainty of calculated values
Measurement
uncertainty DIC
fCO2
TA
fCO2
TA
DIC
pH
TA
pH
DIC
pH
fCO2
pH ± 0.004 ± 0.0025 ± 0,0026 ± 0.0062
TA
[µmol kg-1]
± 1 ± 3.4 ± 2.7 ± 21
DIC
[µmol kg-1]
± 1 ± 3.2 ± 3.8 ± 18
fCO2
[µatm]
± 0.5 ± 5.7 ± 2.1 ± 1.8
Millero, 2007

11. Uncertainty of calculated values
Uncertainty of the calculated parameter depends on
1. Uncertainty of input parameters (measurement uncertainty)
2. Error propagation including equilibrium constants
a. Temperature dependent
b. fCO2 dependent

12. Extension for CO2sys :
Calculates the uncertainty propagation taking into account uncertainties in
constants, temperature, salinity, ...
Uncertainty of calculated values
The following calculations were performed using the Matlab versions of CO2sys
(van Heuven et al. 2009; Lewis and Wallace 1998; Orr et al. 2018) and the
accompanied error calculations provided by Orr et al. (2018). The uncertainty of a
variable is noted as u(variable name).
Please note: When using the Matlab version of the error propagation (errors.mat),
be sure to update the file co2sys.mat provided by Orr et al. (2018), as there are
minor changes compared to the version of van Heuven et al. (2009).
Detailed results can be found in Steinhoff (2020), doi: 10.18160/vb7c-z758
https://otc.icos-cp.eu/  documents

13. f(fCO2, DIC)
u(measurements):
u(TA) = ± 3.4 µmol kg-1
u(pH) = ± 0.0025

14. f(fCO2, TA)
u(measurements):
u(DIC) = ± 3.2 µmol kg-1
u(pH) = ± 0.0026

15. f(fCO2, pH)

16. Resulting uncertainties
fCO2 & … Input
uncertainty
DIC
[µmo/kg]
pH TA
[µmol/kg]
DIC [µmol/kg] 5 <<0.02 <10
pH 0.001 >25 >27
TA [µmol/kg] 10 <10 <<0.02
SOOPlines
fCO2 & … Input
uncertainty
DIC
[µmo/kg]
pH TA
[µmol/kg]
DIC [µmol/kg] 5 <<0.02 <10*
pH 0.001 >30 >30
TA [µmol/kg] 10 <10* <<0.02
FOS

17. • Limitations of ocean fCO2 measurement capabilities at FOS mean that fluxes cannot be
determined to the accuracy desired for large scale carbon budgets. – As of today!
• When aiming for data with uncertainties fulfilling the “climate goal” these data need to be
measured. There is no combination of fCO2 and a second carbon variable that allow the
calculation of the other two variables with sufficient uncertainty. – As of today!
• Using fCO2 and pH will result in uncertainties that are above the thresholds for the
“weather goal”.
• Using two variables of the marine carbonate system to calculate fCO2 is only suitable for
FOS. There is no combination that results in an uncertainty for calculated fCO2 better
than 3.5 μatm.
Conclusion

18. Questions
welcome!