Calculate everything with `CO2SYS`¶

Syntax¶

The simplest way to use PyCO2SYS is to follow the approach of previous versions of CO2SYS and calculate every possible variable of interest at once. We can do this using the top-level CO2SYS function:

# Import the function
from PyCO2SYS import CO2SYS

# Run CO2SYS
CO2dict = CO2SYS(PAR1, PAR2, PAR1TYPE, PAR2TYPE, SAL, TEMPIN, TEMPOUT,
    PRESIN, PRESOUT, SI, PO4, pHSCALEIN, K1K2CONSTANTS, KSO4CONSTANTS,
    NH3=0.0, H2S=0.0, KFCONSTANT=1, buffers_mode="auto")

# Get (e.g.) aragonite saturation state, output conditions
OmegaARout = CO2dict["OmegaARout"]

Each input can either be a single scalar value or a NumPy array containing a series of values. The output is a dict containing a series of NumPy arrays with all the calculated variables. These are described in detail in the following sections.

Using the Pythonic API¶

Alternatively, a more Pythonic API can be used to interface with CO2SYS. This returns a Pandas DataFrame in place of the dict, with the same names for the various outputs. The function uses keyword arguments, meaning that only the specified marine carbonate system parameters have to be entered.

from PyCO2SYS.api import CO2SYS_wrap as co2sys

# Call with defaults
df1 = co2sys(dic=2103, alk=2360)

# The above is equivalent to:
df1 = co2sys(
    dic=2103, alk=2360, pco2=None, fco2=None, pH=None,
    carb=None, bicarb=None, co2aq=None,
    temp_in=25, temp_out=25, pres_in=0, pres_out=0,
    sal=35, si=0, po4=0, nh3=0, h2s=0,
    K1K2_constants=4, KSO4_constants=1, KF_constant=1, pHscale_in=1,
    buffers_mode="auto", verbose=True)

CO2SYS_wrap: incomplete functionality

In the main PyCO2SYS.CO2SYS function, each input row of PAR1 and PAR2 can contain a different combination of parameter types. This is not currently possible with PyCO2SYS.api.CO2SYS_wrap: each call to the function may only have a single input pair combination, with the others all set to None.

This wrapper function will also accept NumPy arrays, pandas.Series or xarray.DataArrays as inputs. Scalar or default values will be broadcast to match any vector inputs.

Inputs¶

Most of the inputs should be familiar to previous users of CO2SYS for MATLAB, and they work exactly the same here. Each input can either be a single scalar value, or a NumPy array containing a series of values. If arrays are used then they must all be the same size as each other, but a combination of same-size arrays and single scalar values is allowed.

PyCO2SYS.CO2SYS inputs

Carbonate system parameters¶

PAR1 and PAR2: values of two different carbonate system parameters.
PAR1TYPE and PAR2TYPE: which types of parameter PAR1 and PAR2 are.

These can be any pair of:

Total alkalinity (type 1) in μmol·kg⁻¹.
Dissolved inorganic carbon (type 2) in μmol·kg⁻¹.
pH (type 3) on the Total, Seawater, Free or NBS scale¹. Which scale is given by the input pHSCALEIN.
Partial pressure (type 4) or fugacity (type 5) of CO₂ in μatm or aqueous CO₂ (type 8) in μmol·kg⁻¹.
Carbonate ion (type 6) in μmol·kg⁻¹.
Bicarbonate ion (type 7) in μmol·kg⁻¹.

For all inputs in μmol·kg⁻¹, the "kg" refers to the total solution, not H₂O. These are therefore most accurately termed molinity values (as opposed to concentration or molality).

Hydrographic conditions¶

SAL: practical salinity (dimensionless).
TEMPIN: temperature at which PAR1 and PAR2 inputs are provided in °C.
TEMPOUT: temperature at which output results will be calculated in °C.
PRESIN: pressure at which PAR1 and PAR2 inputs are provided in dbar.
PRESOUT: pressure at which output results will be calculated in dbar.

For example, if a sample was collected at 1000 dbar pressure (~1 km depth) at an in situ water temperature of 2.5 °C and subsequently measured in a lab at 25 °C, then the correct values would be TEMPIN = 25, TEMPOUT = 2.5, PRESIN = 0, and PRESIN = 1000.

Nutrients and other solutes¶

Required:

SI: total silicate in μmol·kg⁻¹.
PO4: total phosphate in μmol·kg⁻¹.

Optional (these default to zero if not specified):

NH3: total ammonia in μmol·kg⁻¹.
H2S: total hydrogen sulfide in μmol·kg⁻¹.

Again, the "kg" in μmol·kg⁻¹ refers to the total solution, not H₂O. These are therefore most accurately termed molinity values (as opposed to concentration or molality).

Settings¶

Required:

pHSCALEIN: which pH scale was used for any pH entries in PAR1 or PAR2, as defined by ZW01:
- 1: Total, i.e. $\mathrm{pH} = -\log_{10} ([\mathrm{H}^+] + [\mathrm{HSO}_4^-])$ .
- 2: Seawater, i.e. $\mathrm{pH} = -\log_{10} ([\mathrm{H}^+] + [\mathrm{HSO}_4^-] + [\mathrm{HF}])$ .
- 3: Free, i.e. $\mathrm{pH} = -\log_{10} [\mathrm{H}^+]$ .
- 4: NBS, i.e. relative to NBS/NIST reference standards.
K1K2CONSTANTS: which set of equilibrium constants to use to model carbonic acid dissociation:
- 1: RRV93 (0 < T < 45 °C, 5 < S < 45, Total scale, artificial seawater).
- 2: GP89 (-1 < T < 40 °C, 10 < S < 50, Seawater scale, artificial seawater).
- 3: H73a and H73b refit by DM87 (2 < T < 35 °C, 20 < S < 40, Seawater scale, artificial seawater).
- 4: MCHP73 refit by DM87 (2 < T < 35 °C, 20 < S < 40, Seawater scale, artificial seawater).
- 5: H73a, H73b and MCHP73 refit by DM87 (2 < T < 35 °C, 20 < S < 40, Seawater scale, artificial seawater).
- 6: MCHP73 aka "GEOSECS" (2 < T < 35 °C, 19 < S < 43, NBS scale, real seawater).
- 7: MCHP73 without certain species aka "Peng" (2 < T < 35 °C, 19 < S < 43, NBS scale, real seawater).
- 8: M79 (0 < T < 50 °C, S = 0, freshwater only).
- 9: CW98 (2 < T < 35 °C, 0 < S < 49, NBS scale, real and artificial seawater).
- 10: LDK00 (2 < T < 35 °C, 19 < S < 43, Total scale, real seawater).
- 11: MM02 (0 < T < 45 °C, 5 < S < 42, Seawater scale, real seawater).
- 12: MPL02 (-1.6 < T < 35 °C, 34 < S < 37, Seawater scale, field measurements).
- 13: MGH06 (0 < T < 50 °C, 1 < S < 50, Seawater scale, real seawater).
- 14: M10 (0 < T < 50 °C, 1 < S < 50, Seawater scale, real seawater).
- 15: WMW14 (0 < T < 50 °C, 1 < S < 50, Seawater scale, real seawater).

The brackets above show the valid temperature (T) and salinity (S) ranges, original pH scale, and type of material measured to derive each set of constants.

KSO4CONSTANTS: (1) which equilibrium constant to use to model bisulfate ion dissociation and (2) which boron:salinity relationship to use to estimate total borate:
- 1: D90a for bisulfate dissociation and U74 for borate:salinity.
- 2: KRCB77 for bisulfate dissociation and U74 for borate:salinity.
- 3: D90a for bisulfate dissociation and LKB10 for borate:salinity.
- 4: KRCB77 for bisulfate dissociation and LKB10 for borate:salinity.

The somewhat inelegant approach for combining these into a single option is inherited from CO2SYS for MATLAB and retained here for consistency.

Optional:

KFCONSTANT: which equilibrium constant to use for hydrogen fluoride dissociation:
- 1: DR79 (default, consistent with CO2SYS for MATLAB).
- 2: PF87.
buffers_mode: how to calculate the various buffer factors (or not).
- 'auto': using automatic differentiation, which accounts for the effects of all equilibrating solutes (default).
- 'explicit': using explicit equations reported in the literature, which only account for carbonate, borate and water alkalinity.
- 'none': not at all.

For buffers_mode, 'auto' is the recommended and most accurate calculation, and it is a little faster to compute than 'explicit'. If 'none' is selected, then the corresponding outputs have the value nan.

Outputs¶

The results of CO2SYS calculations are stored in a dict of NumPy arrays. The keys to the dict are the same as the entries in the output HEADERS in CO2SYS for MATLAB and are listed in the section below.

PyCO2SYS.CO2SYS outputs

The only output is a dict of NumPy arrays. Its keys are as follows:

Dissolved inorganic carbon¶

'TCO2': dissolved inorganic carbon in μmol·kg⁻¹.
'CO3in'/'CO3out': carbonate ion at input/output conditions in μmol·kg⁻¹.
'HCO3in'/'HCO3out': bicarbonate ion at input/output conditions in μmol·kg⁻¹.
'CO2in'/'CO2out': aqueous CO₂ at input/output conditions in μmol·kg⁻¹.
'pCO2in'/'pCO2out': seawater partial pressure of CO₂ at input/output conditions in μatm.
'fCO2in'/'fCO2out': seawater fugacity of CO₂ at input/output conditions in μatm.
'xCO2in'/'xCO2out': seawater mole fraction of CO₂ at input/output conditions in ppm.

Alkalinity and its components¶

'TAlk': total alkalinity in μmol·kg⁻¹.
'BAlkin'/'BAlkout': borate alkalinity at input/output conditions in μmol·kg⁻¹.
'PAlkin'/'PAlkout': phosphate alkalinity at input/output conditions in μmol·kg⁻¹.
'SiAlkin'/'SiAlkout': silicate alkalinity at input/output conditions in μmol·kg⁻¹.
'NH3Alkin'/'NH3Alkout': ammonia alkalinity at input/output conditions in μmol·kg⁻¹.
'H2SAlkin'/'H2SAlkout': hydrogen sulfide alkalinity at input/output conditions in μmol·kg⁻¹.

pH and water¶

'pHin'/'pHout': pH at input/output conditions on the scale specified by input pHSCALEIN.
'pHinTOTAL'/'pHoutTOTAL': pH at input/output conditions on the Total scale.
'pHinSWS'/'pHoutSWS': pH at input/output conditions on the Seawater scale.
'pHinFREE'/'pHoutFREE': pH at input/output conditions on the Free scale.
'pHinNBS'/'pHoutNBS': pH at input/output conditions on the NBS scale.
'HFreein'/'HFreeout': "free" proton at input/output conditions in μmol·kg⁻¹.
'OHin'/'OHout': hydroxide ion at input/output conditions in μmol·kg⁻¹.

Carbonate mineral saturation¶

'OmegaCAin'/'OmegaCAout': saturation state of calcite at input/output conditions.
'OmegaARin'/'OmegaARout': saturation state of aragonite at input/output conditions.

Buffer factors¶

Whether these are evaluated using automatic differentiation, with explicit equations, or not at all is controlled by the input buffers_mode.

'RFin'/'RFout': Revelle factor at input/output conditions².
'psi_in'/'psi_out': ψ of FCG94 at input/output conditions.
'gammaTCin'/'gammaTCout': buffer factor γ_DIC of ESM10 at input/output conditions³.
'betaTCin'/'betaTCout': buffer factor β_DIC of ESM10 at input/output conditions.
'omegaTCin'/'omegaTCout': buffer factor ω_DIC of ESM10 at input/output conditions.
'gammaTAin'/'gammaTAout': buffer factor γ_TA of ESM10 at input/output conditions.
'betaTAin'/'betaTAout': buffer factor β_TA of ESM10 at input/output conditions.
'omegaTAin'/'omegaTAout': buffer factor ω_TA of ESM10 at input/output conditions.
'isoQin'/'isoQout': isocapnic quotient of HDW18 at input/output conditions.
'isoQapprox_in'/'isoQapprox_out': approximate isocapnic quotient of HDW18 at input/output conditions.

Totals estimated from salinity¶

'TB': total borate in μmol·kg⁻¹.
'TF': total fluoride μmol·kg⁻¹.
'TS': total sulfate in μmol·kg⁻¹.
'TCa': total calcium in μmol·kg⁻¹.

Equilibrium constants¶

All equilibrium constants are returned on the pH scale of input pHSCALEIN except for 'KFinput'/'KFoutput' and 'KSinput'/'KSoutput', which are always on the Free scale.

'K0input'/'K0output': Henry's constant for CO₂ at input/output conditions.
'K1input'/'K1output': first carbonic acid dissociation constant at input/output conditions.
'K2input'/'K2output': second carbonic acid dissociation constant at input/output conditions.
'pK1input'/'pK1output': -log₁₀(K1input)/-log₁₀(K1output).
'pK2input'/'pK2output': -log₁₀(K2input)/-log₁₀(K2output).
'KWinput'/'KWoutput': water dissociation constant at input/output conditions.
'KBinput'/'KBoutput': boric acid dissociation constant at input/output conditions.
'KFinput'/'KFoutput': hydrogen fluoride dissociation constant at input/output conditions.
'KSinput'/'KSoutput': bisulfate dissociation constant at input/output conditions.
'KP1input'/'KP1output': first phosphoric acid dissociation constant at input/output conditions.
'KP2input'/'KP2output': second phosphoric acid dissociation constant at input/output conditions.
'KP3input'/'KP3output': third phosphoric acid dissociation constant at input/output conditions.
'KSiinput'/'KSioutput': silicic acid dissociation constant at input/output conditions.
'KNH3input'/'KNH3output': ammonium equilibrium constant at input/output conditions.
'KH2Sinput'/'KH2Soutput': hydrogen sulfide equilibrium constant at input/output conditions.

Function inputs¶

'TEMPIN'/'TEMPOUT': inputs TEMPIN/TEMPOUT.
'PRESIN'/'PRESOUT': inputs PRESIN/PRESOUT.
'PAR1TYPE'/'PAR2TYPE': inputs PAR1TYPE/PAR2TYPE.
'K1K2CONSTANTS': input K1K2CONSTANTS.
'KSO4CONSTANTS': input KSO4CONSTANTS.
'KFCONSTANT': input KFCONSTANT.
'pHSCALEIN': input pHSCALEIN.
'SAL': input SAL.
'PO4': input PO4.
'SI': input SI.
'NH3': input NH3.
'H2S': input H2S.

Finally, CO2SYS splits up the input KSO4CONSTANTS into two separate settings variables internally, which are also returned in the CO2dict output:

'KSO4CONSTANT':
- 1 for KSO4CONSTANTS in [1, 3] (i.e. bisulfate dissociation from D90a).
- 2 for KSO4CONSTANTS in [2, 4] (i.e. bisulfate dissociation from KRCB77).
'BORON':
- 1 for KSO4CONSTANTS in [1, 2] (i.e. borate:salinity from U74).
- 2 for KSO4CONSTANTS in [3, 4] (i.e. borate:salinity from LKB10).

The original CO2SYS clone¶

Originally, the main CO2SYS function in PyCO2SYS was an as-close-as-possible clone of CO2SYS v2.0.5 for MATLAB (from here). Since then the code has been substantially reorganised and made more Pythonic behind the scenes and it is this Pythonised version that is now called up by from PyCO2SYS import CO2SYS.

Warning

We strongly recommend that you use the Pythonised version described above!

If you do need to use the as-close-as-possible clone instead, this is still available via:

# Import the original CO2SYS clone
from PyCO2SYS.original import CO2SYS

# Run CO2SYS
DATA, HEADERS, NICEHEADERS = CO2SYS(PAR1, PAR2, PAR1TYPE, PAR2TYPE,
    SAL, TEMPIN, TEMPOUT, PRESIN, PRESOUT, SI, PO4,
    pHSCALEIN, K1K2CONSTANTS, KSO4CONSTANTS)

The inputs are the same as described above except:

PAR1TYPE and PAR2TYPE can only take values from 1 to 5 inclusive.
The optional extra inputs (NH3, H2S and KFCONSTANT) are not allowed. This is equivalent to using NH3 = 0, H2S = 0 and KFCONSTANT = 1 in the Pythonic version.

The outputs are also the same as described above, except:

There are no buffer factors other than the Revelle factor.
The Revelle factor at output conditions does not include the "Peng correction" (applicable only for K1K2CONSTANTS = 7).
The KSO4CONSTANTS input is not split into KSO4CONSTANT and BORON.
There are none of the outputs associated with the NH3 and H2S equilibria.
TCa is not provided.
They are reported in the original MATLAB style:
- DATA contains a matrix of all calculated values.
- HEADERS indicate the variable in each column of DATA.
- NICEHEADERS is an alternative to HEADERS containing a little more information about each variable.

To convert these MATLAB-style outputs into a dict comparable to CO2dict:

CO2dict = {header: DATA[:, h] for h, header in enumerate(HEADERS)}

See ZW01 for definitions of the different pH scales. ↩
In buffers_mode='explicit', the Revelle factor is calculated using a simple finite difference scheme, just like the MATLAB version of CO2SYS. ↩
Equations for the buffer factors of ESM10 in buffers_mode='explicit' have all been corrected for typos following RAH18 and OEDG18. ↩

Calculate everything with CO2SYS¶