Background: Henry's law states that:
At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.
And mathematically:
$$S=k\times p_{\text{gas}}$$ where $S$ is solubility, $k$ is Henry's constant and $p$ is the partial pressure of the gas.
Question: I want to calculate the oxygen solubility down the sea. Is partial pressure the atmospheric one? If it is so, we have same solubility on all sea deepness, which is contradictory. What am I missing?
Edit
I know this law can be thought as depending on this equilibrium:
$$\ce{A {(g)} <=> A {(s)}}$$