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The effect of air pressure on tidal height is substantial and all too easy to be forgotten. The invisible medium in which we live has a not inconsiderable weight causing an effect which can be embarrassing at times!
The weight of the atmosphere creates a force pushing down on the sea. Perhaps surprisingly, one cubic metre of air at sea level weighs about one kilogram. A rough guide is that a change in pressure of one hectoPascal (one millibar in days gone by) will change the sea level by one centimetre. Tide tables assume a standard pressure of 1013 hPa. This means that a pressure of 1040 hPa, pretty high but not abnormally so, could give a sea level lower by nearly 30 cm than expected. That could make the difference between crossing the sill and ignominiously hitting it.
The lowest pressure recorded around the British Isles is about 925 hPa which would give sea levels nearly a metre above tide table predictions. This can be an important factor in storm surge conditions when the East Coast is threatened. Unless air clearance is critical, a skipper is unlikely to worry overmuch about too much rise of tide. The highest pressure around the UK is about 1050 hPa which would give sea levels about 40 cm lower.
In a nutshell, worry about the pressure effect if the pressure is higher than 1020 hPa and your depth is getting critical. I speak as one who just touched the sill at St Peter Port and had to be helped off!.