There must be a relationship between ppm in the water, and ppm in the air trapped above the water. I assume the partial pressures of the CO2 would be equal, but what would the relationship be between the two ppm's?
Given this diagram, I would imagine the CO2 levels would be the same as in the water.
For example, in the case of CO2 injection, the levels of CO2 in the water are higher. CO2 will off gas from the water into the atmosphere and into the bell shaped jar. When the levels of CO2 in the jar reaches the same level as the water, then it will not increase anymore.
Of course, CO2 will be diffusing from the water into the atmosphere as well as into the jar.