The aquatic inorganic carbon system is composed of the various ionic, dissolved, solid, and/or gaseous forms of carbon dioxide in water.  These species include dissolved carbon dioxide, carbonic acid, bicarbonate anion, carbonate anion, calcium carbonate, magnesium carbonate, and others.  The relative amounts of each species in a body of water depends on physical variables including temperature and salinity, as well as chemical variables like pH and gas partial pressure.  Variables like alkalinity and dissolved (or total) inorganic carbon further define a mass and charge balance that constrains the total state of the system.
Given any two of the four central inorganic carbon system parameters (pH, alkalinity, dissolved inorganic carbon, partial pressure of carbon dioxide) the remainder may be derived by solving a system of equations that adhere to the principles of chemical thermodynamics.
For most of the 20th century, chemical equilibria in marine and freshwater systems was calculated according to various conventions, which led to discrepancies among laboratories' calculations and limited scientific reproducibility. Since 1998, a family of software programs called CO2SYS has been widely used. This software calculate chemical equilibria for aquatic inorganic carbon species and parameters.  Their core function is to use any two of the four central inorganic carbon system parameters (pH, alkalinity, dissolved inorganic carbon, and partial pressure of carbon dioxide) to calculate various chemical properties of the system.  The programs are widely used by oceanographers and limnologists to understand and predict chemical equilibria in natural waters.