OK so you need to have either a pressure sensor with absolute reference or the back side of you sensor (i.e. pressure reference) must be open to the surface.
If you go the absolute route, you need to know the temperature and maybe atmospheric pressure. Likely not on the atmospheric pressure but it should be considered before being ignored.
phone can process and store the data for further analysis once the phone is retrieved.
Might an SD card work here? Or possibly an EEPROM.