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Version history


Version numbering aims to follow semantic versioning. Therefore:

  • New patch versions (e.g. 1.1.0 to 1.1.1) make minor changes that do not alter fuctionality or calculated results.
  • New minor versions (e.g. 1.0.1 to 1.1.0) add new functionality, but will not break your code. They will not alter the results of calculations with default settings (except for in the hopefully rare case of correcting a bug or typo).
  • New major versions (e.g. 1.1.1 to 2.0.0) may break your code and require you to rewrite things. They may significantly alter the results of calculations with default settings.

We will always add aliases for existing functions if their API is updated, to avoid unforseen breaking changes wherever possible.


Will (not) break your code refers only to the functions covered in this documentation.

For the main CO2SYS functions as imported with

import PyCO2SYS as pyco2
results = pyco2.sys(*args, **kwargs)  # new Pythonic syntax
results = pyco2.CO2SYS(*args, **kwargs)  # old MATLAB syntax

the only things that may change, in at least a minor version release, are:

  1. Additional inputs may be added to the kwargs, but always with default values such that the results do not change if they are not explicitly set.
  2. Additional calculated variables may be returned in the output results.

The structure of the underlying modules and their functions is not yet totally stable and, for now, may change in any version increment. Such changes will be described in the release notes below.


Adds atmospheric pressure input for pCO2-fCO2-xCO2 interconversions and (from v1.8.2) optional hydrostatic pressure effect on CO2 solubility and fugacity. Uncertainty analysis updated for more reproducible results. Rigorously validated and fully documented in peer-reviewed journal article (Humphreys et al., 2022).

1.8.3 (16 February 2024)

Changes in v1.8.3

New features

  • Added "dlnfCO2_dT" and "dlnpCO2_dT" results, the theoretical effect of temperature on the natural log of ƒCO2 and pCO2.
  • Added the PLR18 parameterisation of the carbonic acid constants for sea-ice brines.

Default options

  • Reverted default opt_k_carbonic to 10 (i.e., LDK00) for consistency with the best practice guide.

Bug fixes

  • Updated pyco2.equilibria.p1atm.kH2CO3_NBS_MCHP73 (used for opt_k_carbonic options 6 and 7) to update any salinity values less than 10–16 to be 10–16, because zero salinities give a NaN for K2, which causes problems for Autograd. This should not make any practical difference, because the parameterisation is only valid for salinities above 19.
  • Added opt_pressured_kCO2 to results dict and incorporated it correctly into the uncertainty propagation functions.


  • Updated from building with to pyproject.toml.
  • PyCO2SYS can now be installed with conda/mamba (via conda-forge).

1.8.2 (19 January 2023)

Changes in v1.8.2

New features

  • Added opt_pressured_kCO2 to enable pressure corrections for the fugacity factor and CO2 solubility constant following W74. These have been added to CO2SYS-MATLAB by Jon Sharp at the same time with consistent results (differences less than 10−4 %). These pressure corrections are not enabled by default, for consistency with previous versions.

Bug fixes

  • Fixed logicals in solve.core() that had meant no results were returned for parameter type combinations 7, 10, 7, 11, 8, 10 and 8, 11.
  • Updated Autograd version for compatibility with Python 3.11.

1.8.1 (18 May 2022)

Changes in v1.8.1

Breaking changes

  • For consistency with other settings, buffers_mode kwarg key changed to opt_buffers_mode and its values are now integers rather than strings.

New features

  • Adds new par1_type / par2_type options 10 and 11 for saturation states with respect to calcite and aragonite.
  • Adds KSK18 parameterisation for estimating total borate from salinity.


  • Switched to Autograd v1.4.

1.8.0 (27 October 2021)

Changes in v1.8.0

New features

  • Adds pressure_atmosphere and pressure_atmosphere_out arguments, rather than assuming 1 atm total barometric pressure.

Behind-the-scenes improvements

  • Adds additional constraint to the initial pH estimate for more robust results for the alkalinity-CO2 fugacity parameter pair.
  • Difference derivatives for uncertainties now have a fixed step size for each argument, instead of scaling depending on arguments, for more reproducible results.


Adds new syntax to return equilibrium constants and total salts without needing to solve the full carbonate system. Fully documented in manuscript in review (Humphreys et al., 2021, Geosci. Model Dev. Discuss.).

1.7.1 (10 August 2021)

Changes in v1.7.1

Bug fixes

  • Improved handling of zero-valued inputs.
  • Adjusted CO2SYS_wrap to work with latest pandas release.

1.7.0 (13 May 2021)

Changes in v1.7.0

New features

  • Can now run pyco2.sys with no carbonate system parameter arguments provided, to just return all the equilibrium constants etc. under the specified conditions.
  • Can also run pyco2.sys with only one carbonate system parameter argument. This does not solve the carbonate system, but does calculate all that can be calculated with that parameter.
  • Added carbonic acid constants parameterisation of SB21.
  • Added bisulfate dissociation constant parameterisation of WM13/WMW14.
  • Added spreadsheet-to-spreadsheet function pyco2.ezio (with thanks to Daniel Sandborn).
  • Integrated uncertainty propagation into the main pyco2.sys function and expanded its capabilities.

Internal updates

  • Switched default first-guess pH for solving from the alkalinity-carbonate ion parameter pair at low alkalinity from 10 to 3.
  • Renamed various internal functions and variables for better consistency with the Pythonic pyco2.sys i/o syntax.
  • Removed the PyCO2SYS.test module, instead defining the round-robin test functions it contained directly in the test suite.
  • Added various internal settings for testing and validation against older CO2SYS-MATLAB versions.
  • Adjust aqueous CO2 calculation for better consistency with CO2SYS-MATLAB (but negligible changes in the results).
  • Can now use PyCO2SYS.hello() to find version number and credits (alias for PyCO2SYS.say_hello()).
  • The final component of DIC (or DIC itself) to be calculated is now always computed by difference from the known components.
  • Various functions in convert module renamed.


  • Rigorous validation against various CO2SYS-MATLAB versions performed, as described in forthcoming PyCO2SYS manuscript (Humphreys et al., in prep.).

Bug fixes

  • par1, par2, par1_type and par2_type arguments now always get broadcasted to the maximum size, even if they are scalar.
  • Erroneous "k_phosphate_*" keys corrected to "k_phosphoric_".
  • Override values for equilibrium constants under output conditions now assigned correctly.
  • Fixed minor errors in initial pH estimates when solving from alkalinity and either DIC or [CO_2(aq)].


Adds extra alkalinity components with arbitrary pK values.

1.6.0 (26 October 2020)

Changes in v1.6.0

Bug fixes

  • Updates the total alkalinity equation to fix minor error in pH scale conversions inherited from CO2SYS-MATLAB (see related note in v1.5.0 release notes).

New inputs and outputs

  • Enables inputting total molalities and equilibrium constants for up to two additional contributors to total alkalinity.
  • Full chemical speciation returned in the output dict of pyco2.sys, not just the alkalinity components as before.

New syntax

  • Adds sys as an alias for CO2SYS_nd at the top level. Recommended Python-style syntax is thus now pyco2.sys.


Introduces a more Pythonic top-level function that accepts multidimensional arguments and that only returns results at "output" conditions if explicitly specified.

1.5.1 (30 July 2020)

Changes in v1.5.1

Bug fixes

  • Switched dx-scaling function in PyCO2SYS.uncertainties to use numpy.nanmedian instead of numpy.median.
  • Fixed PyCO2SYS.uncertainties.propagate_nd bug that prevented calculations on non-scalar arguments.

1.5.0 (29 July 2020)

Changes in v1.5.0

New top-level functions

  • Adds PyCO2SYS.CO2SYS_nd top-level function with a more Pythonic interface and with NumPy broadcasting of n-dimensional inputs.
  • In PyCO2SYS.CO2SYS_nd, results at "output" conditions are only calculated if output temperature or pressure is provided.
  • Adds corresponding PyCO2SYS.uncertainty.forward_nd and PyCO2SYS.uncertainty.propagate_nd functions for uncertainty propagation.

Alternative calculations

  • New alkalinity equation fixing pH scale conversion bug inherited from CO2SYS-MATLAB is available, but not yet implemented by default.

Extra arguments and results

  • Solubility constants for aragonite and calcite available directly as outputs from PyCO2SYS.CO2SYS and PyCO2SYS.CO2SYS_nd
  • Explicit values for the solubility constants can be given as arguments to override the default internal calculation.

Internal reorganisation

  • All 2-to-3 functions in PyCO2SYS.solve.get now have a more consistent set of inputs.
  • Revised pH scale conversion functions for consistency and added tests for their internal accuracy.
  • Switched preallocations to use np.shape not np.size in preparation for working with n-dimensional inputs.
  • Updated style to import the whole NumPy module as np instead of individual functions separately.
  • Converted PyCO2SYS.engine to a sub-module.


Enables uncertainty propagation with forward finite-difference derivatives.

1.4.3 (16 July 2020)

Changes in v1.4.3

Bug fixes

  • Corrected missing a pH scale conversion in SLH20 option for carbonic acid dissociation. Any calculations with this option in PyCO2SYS v1.4.1 or v1.4.2 should be updated!


  • Results validated against new release candidate version of CO2SYS-MATLAB v3.


  • New wrapper function with the same input order and default gas constant option as the new CO2SYS-MATLAB v3 available in PyCO2SYS.api.CO2SYS_MATLABv3.

Internal reorganisation

  • _approx function inputs in updated to match the exact Autograd functions for easier switching.

1.4.2 (9 July 2020)

Changes in v1.4.2

Bug fixes

  • Swapped order of totals and Ks arguments for all functions in for consistency with other modules.
  • Inverted the alkalinity-pH residual equations in


  • Broke out some parts of PyCO2SYS.equilibria.assemble into separate functions.

1.4.1 (1 July 2020)

Changes in v1.4.1

Extra calculation options

  • Added the 2018 CODATA value for the universal gas constant R as an option for consistency with forthcoming CO2SYS-MATLAB v3. The original DOEv2 version remains default.
  • Added the SLH20 equations as option 16 for the carbonic acid dissociation constants.

1.4.0 (9 June 2020)

Changes in v1.4.0

New features

  • Added uncertainty module with functions to evaluate derivatives of PyCO2SYS outputs with respect to inputs, along with corresponding documentation.
  • Specific input values can optionally be provided for all total concentrations and equilibrium constants that are estimated internally from salinity, temperature and pressure.

General improvements

  • Added basic sanity checking to prevent some invalid marine carbonate system parameter input values.
  • Nutrient concentrations have always been set to zero internally for K1K2CONSTANTS options 6 and 8, and salinity too for 8, regardless of the input values. This is now reflected in the output values of these variables in the CO2dict.

New outputs

  • Substrate:inhibitor ratio (SIR) of B15, calculated with SIratio in new module bio.
  • Inputs PAR1 and PAR2.
  • The "Peng correction" factor.
  • The fugacity factor for converting between CO2 partial pressure and fugacity.
  • The activity coefficient of the H+ ion for NBS pH scale conversions.



Adds bicarbonate ion and aqueous CO2 as inputs from which the carbonate system can be solved. Continues to reorganise code behind the scenes. Makes almost everything Autograd-able and uses this approach to calculate buffer constants. Validates results against CO2SYS for MATLAB.

1.3.0 (1 May 2020)

Changes in v1.3.0

New features

  • Added bicarbonate ion (type 7) and aqueous CO2 (type 8) as options for known input marine carbonate system variables.
  • Added module test with functions to perform internal consistency checks on PyCO2SYS.CO2SYS calculations and compare results with those from other sources.
  • Added module api with a wrapper for PyCO2SYS.CO2SYS to allow inputs as Pandas Series and/or Xarray DataArrays.

Improved calculations

  • The Revelle factor and all other buffer factors added in v1.2 are now evaluated using automatic differentiation, which means that the effects of all equilibrating species are taken into account.
    • The original, non-automatic functions that do not account for nutrient effects are still available in buffers.explicit.
    • Can switch between calculation methods using new optional input opt_buffers_mode.
  • Corrected Revelle factor calculations:
    • Added missing "Peng correction" to Revelle factor calculation at output conditions. Note that this correction is currently also missing from CO2SYS for MATLAB!
    • Decreased DIC perturbation size for more accurate finite-difference "explicit" evaluation.
    • Finite-difference calculation now references the correct DIC value.
  • Implemented better initial guesses for pH in all iterative solvers in solve.get following M13 and OE15.
  • Switched to using exact slopes in iterative solvers in solve.get, evaluated using Autograd in new submodule
  • Updated entire package to be Autograd-able.
  • Return NaN instead of negative DIC if an impossible pH-alkalinity combination is given as input (i.e. pH is too high).
  • Return NaN where DIC and one of its components is given if the component is impossibly large.

Internal reorganisation

  • Major internal reorganisation that is probably not fully captured in these notes.
  • Renamed modules:
    • assemble is now engine.
    • concentrations is now salts.
    • extra is now buffers.explicit.
  • Module equilibria now contains sub-modules:
    • p1atm for calculating constants at atmospheric pressure.
    • pcx for determining pressure correction factors.
    • pressured for calculating constants at given pressure.
  • Module solve now contains sub-modules:
    • initialise to generate first-guess estimates of pH for the TA-pH solvers.
    • get to calculate a new system variable from various input pairs.
  • Added module solubility for mineral solubility calculations.
  • Relocated _CaSolubility function from root to solubility.CaCO3.
    • Separated out its internal calculations into a set of subfunctions also in the solubility module.
    • Added calcium molinity TCa as an input, instead of being evaluated internally.
  • Added calcium molininty TCa (estimated from salinity) into the main CO2dict output from PyCO2SYS.CO2SYS.
  • Relocated _RevelleFactor function from root to buffers.RevelleFactor.
  • Relocated _FindpHOnAllScales function from root to convert.pH2allscales.
  • Added module constants for storing values of universal physical constants.
  • Lists of equilibrium constants and total concentrations now passed around internally as dicts, for safety.
  • Total sulfate and bisulfate dissociation constant renamed from TS and KS to TSO4 and KSO4 internally to avoid confusion with sulfide species.
  • The as-close-as-possible MATLAB clone in PyCO2SYS.original no longer produces a dict but just the original DATA, HEADERS and NICEHEADERS outputs.


  • Documentation substantially expanded and switched to using Material for MkDocs.
    • Validation section added with internal consistency checks and an external comparison of PyCO2SYS calculations with CO2SYS for MATLAB.
  • All code now formatted with Black (except for module original).
  • Version number now reported with PyCO2SYS.say_hello() in homage to the original MS-DOS program.


Calculates a wider variety of chemical buffer factors.

1.2.1 (9 April 2020)

Changes in v1.2.1

  • Fixed typo in ESM10 equations that had been carried through into extra.buffers_ESM10 function (thanks Jim Orr!).

1.2.0 (8 April 2020)

Changes in v1.2.0

  • Added module extra containing functions to calculate variables not included in CO2SYS for MATLAB:
  • buffers_ESM10 calculates the buffer factors of ESM10, corrected for the typos noted by RAH18.
  • bgc_isocap calculates the "exact" isocapnic quotient of HDW18, Eq. 8.
  • bgc_isocap_approx calculates the approximate isocapnic quotient of HDW18, Eq. 7.
  • psi calculates the \psi factor of FCG94.
  • Added all functions in extra to the CO2dict output of the main CO2SYS function, and documented in the Github repo README.


Adds optional inputs of total ammonium, hydrogen sulfide, and carbonate ion molinities for consistency with forthcoming MATLAB "v1.21".

1.1.1 (20 March 2020)

Changes in v1.1.1

  • Removed unnecessary WhoseTB input to assemble.equilibria.

1.1.0 (19 March 2020)

Changes in v1.1.0

  • Updated pH-solving iterative functions so that iteration stops separately for each row once it reaches the tolerance threshold.
  • Extracted all functions for solving the CO2 system into a separate module (solve).
  • Extracted other key subfunctions into module assemble.
  • Added total ammonium (NH3) and hydrogen sulfide (H2S) concentrations as optional inputs to be included in the alkalinity model.
  • Added optional input to choose between different equations for hydrogen fluoride dissociation constant (KFCONSTANT).
  • Added functions to enable carbonate ion as an input carbonate system variable.
  • Output is now only the CO2dict dict, not the original DATA, HEADERS and NICEHEADERS.
  • Eliminated all global variables throughout the entire program.


1.0.1 (28 February 2020)

Starts to make things more Pythonic.

Changes in v1.0.1

  • Extracted all equations for concentrations and equilibrium constants into functions in separate modules (concentrations and equilibria).
  • Eliminated all global variables from the _Constants function.
  • Moved the as-close-as-possible version into module original. The default from PyCO2SYS import CO2SYS now imports the more Pythonic implementation.

1.0.0 (3 February 2020)

An as-close-as-possible clone of MATLAB CO2SYS v2.0.5.

Release notes for v1.0.0

  • The first output DICT is new: a dict containing a separate entry for each variable in the original output DATA, with the keys named following the original output HEADERS.
  • The output DATA is transposed relative to the MATLAB version because Numpy is row-major while MATLAB is column-major.
  • Every combination of input options was tested against the MATLAB version with no significant differences (i.e. all differences can be attributed to floating point errors).