Is there a relationship between pressure drop and sea level rise?

Question

Climate Fresk is a NGO which publishes a card game aimed at educating people about climate change. Card 33 (page 16 of this pdf file) reads (emphasis mine):

Cyclones and atmospheric waves bring wind, waves and low pressure conditions. A 1 hectopascal pressure drop causes a 0.4 inches sea level rise. Therefore cyclones can cause marine submersions (or coastal flooding), amplified by the sea level rise already caused by sea level rise.

Is there really a relationship between pressure drop and sea level rise? And if so, which relationship and what is the mechanism behind it? I find it hard to believe, because water has a very low compressibility, so I don't see how a drop, even big, in atmospheric pressure, could cause such a rise in sea level. The Climate Fresk project claims that all its facts come from the IPCC reports, but I don't know where to start digging...

_{(PS: I'm not questioning the need to educate people about climate change, nor the integrity of the Climate Fresk project; I just want to get the facts straight.)}

Answer 1

Is there really a relationship between pressure drop and sea level rise?

The author of the card was writing about storms at sea. By way of analogy, think of what happens when a person with a significant other flops onto a waterbed. Suppose the significant other, who weighs half as much as the flopper, is already in bed. The significant other may get a bit of a lift from the flop. Another analogy: Think of how you start siphoning gasoline from a gas tank: You reduce the pressure in the siphon. It is the low compressibility of a liquid that makes those responses possible.

When there is a storm at sea, it is the waves that are responsible for the bulk of the storm surge. Reduced atmospheric pressure plays a lesser role, but that role does exist. A cyclone whose central pressure is 50 mb less than surrounding areas can cause a huge storm surge. Most of that is wind driven, but about half a meter is pressure driven.

Answer 2

Not an expert but a quick google search gave me this answer: Inverted barometer contributions to recent sea level changes along the northeast coast of North America

"Sweet and Zervas [2011] interpret anomalously high sea levels along the northeast coast of the United States during the 2009/2010 cool season without reference to the inverted barometer effect; they reconcile this event in terms of anomalous northeasterly winds over the Gulf of Maine connected to sea level pressure changes over the southeastern United States and eastern Canada linked to El Niño. Similarly, Goddard et al. [2015] reason that extreme sea level rise along Atlantic Canada and New England between 2008 and 2010 was largely connected to changes in the overturning circulation and wind stress anomalies related to exceptional values of the North Atlantic Oscillation; these authors posit that the inverted barometer contributed only ∼15% to the extreme rise. Our findings, based on four different pressure data sets, give inverted barometer contributions around 50% (Figure 3), or roughly 3 times larger than those found by Goddard et al. [2015], and indicate that isostatic effects were of central importance to this unique sea level rise event."