High Pressure Systems?

"A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain. Depending on its location and strength, a tropical cyclone is referred to by different names, including hurricane, typhoon, tropical storm, cyclonic storm, tropical depression, and simply cyclone. A hurricane is a tropical cyclone that occurs in the Atlantic Ocean and northeastern Pacific Ocean, a typhoon occurs in the northwestern Pacific Ocean, and a cyclone occurs in the south Pacific or Indian Ocean."

Anti-cyclones are storms caused by High Pressure Systems and are restricted to the bands of latitude North and South of the Equator known as "The Horse Latitudes" (Between 30 and 38 degrees North and South of the Equator).

"An anticyclone (that is, opposite to a cyclone) is a weather phenomenon defined by the United States National Weather Service's glossary as "a large-scale circulation of winds around a central region of high atmospheric pressure, clockwise in the Northern Hemisphere, counterclockwise in the Southern Hemisphere". Effects of surface-based anticyclones include clearing skies as well as cooler, drier air. Fog can also form overnight within a region of higher pressure."

Only time I have had to deal with water under pressure has been connected with the hydrostatic testing of pipelines and pressure vessels. All water contains minute quantities of air in solution. In conducting a hydrostatic test of a pressure vessel or a pipeline pressure is built up gradually to the point at which this included gas is forced out of solution. At this point a hold is made, and an air inclusion test is performed. The pressure drops slightly during this hold and the extent of the drop is noted along with the temperature both at the surface and on the seabed if you are testing a pipeline. Having acquired the pressure drop due to included air the vessel or pipeline is then cycled up to full test pressure - On achieving that everything apart from the instrumentation lines are locked off and sealed and pen recorders graphically measure temperature, pressure and time. The Test is conducted over a 24 hour period. The pressure in the vessel or pipeline is allowed to fluctuate within given parameters that can be fully explained due to included air, and temperature variations - atmospheric pressure is not considered as the system under test is isolated. A steady pressure hold within those explainable parameters indicates a successful test, an unaccountable steady drop indicates a leak.

The influence of atmospheric pressure on the density of sea water and on the seabed would I think be so miniscule to be completely insignificant.