Storm surge is caused by two main factors-wind, which drags the water along and
ID: 114892 • Letter: S
Question
Storm surge is caused by two main factors-wind, which drags the water along and piles it up along the coastline, and the inverse barometer (IB) effect. The IB effect occurs because at some datum far below the surface of the ocean, the sum of the hydrostatic pressure from air and from water must be equal, i.e., Pair+ Pwater constant. If not,a horizontal pressure gradient (force imbalance) occurs, causing water to move until a balance is restored. 5. Look up the lowest minimum atmospheric pressure (at sea-level) for hurricane Maria, and compare to standard atmospheric conditions. What is the pressure difference, in Pascals? Now, consider a datum that is below the water surface, for example, -100m below the mean sea level datum. What is the total pressure Ptotal (water pressure + atmospheric pressure) under standard atmospheric conditions at this datum? Assume a water depth of 100m and a density of 1020 kg/m3. Assuming that Ptotal at -100m (sea level datum) is constant, how high must the water level rise above the sea level datum in order that Pir+Pwater- constant underneath the eyewall of hurricane Maria? Ignore dynamic effects such as the effect of wind or the time for the system to reach an equilibrium. a. b. c. d. Why is this called the "inverse barometer" effect?Explanation / Answer
a. The lowest minimum atmospheric pressure for hurricane Maria was 983 mbar (hPa). The average atmospheric pressure is 1013 mbar (hPa). The pressure difference is 30 hPa or 3000 Pascals.
b. Water pressure can be calculated using the equation:
Pw = g h
where, Pw = water pressure (Pa); = density of sea water (1020 kg/m3); g = acceleration of gravity (9.81 m/s2); h = depth of water at which the pressure is measured (100m)
Therefore, Pw = 1020 * 9.81 * 100 = 1000620 Pa
Total pressure Ptotal = water pressure + atmospheric pressure = 1000620 + 101325 = 1101945 Pa
c. The sum of hydrostatic pressure from air and water at the sea level datum must be constant and till that happens the water level will rise:
(Pair + Pwater)maria = (Pair + Pwater)atm = Ptotal
(Pair + Pwater)maria = 1101945 Pa
We know the lowest minimum atmospheric pressure for hurricane Maria, (Pair)maria = 98300 Pa.
Therefore, (Pwater)maria = 1101945 - 98300 = 1003645 Pa
Using the density value 1020 kg/m3 and acceleration of gravity, g as 9.81 m/s2 , the depth of water to achieve the pressure of 1003645 Pa is;
h = P / g = 1003645 / (1020 * 9.81) = 100.3023 m
Therefore, the water level must rise 100.3023 m above sea level datum
d.
In a typical barometer, there exists a tube submerged in a fluid, with a vacuum at the top. The "inverted barometer" is, when, over the oceans, high-pressure systems push down on the water, lowering sea surface heights a bit. Here, sea surface height goes down as air pressure goes up. It is rather a static (isostatic) response of the oceans to atmospheric pressure. The basic equation as employed earlier here, is IB = -(change in pressure) / [(seawater density)*(acceleration due to gravity)]. Its an inverse relation i.e. with the increase in pressure the sea level decreases and vice versa. So the whole system essentially acts like an inverted barometer and hence the name.