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NYC Subway flooding 2nd September 2021

The incidents of severe flooding in the United States, Germany, Belgium and several other places in the world during the summer of 2021 were traumatizing and ruinous to the many people affected and a shock to weather forecasters and local authorities. A wake-up call has been served and much meteorological research and analysis has been set in motion.

But we all know that making deductions about the influence of climate change is fraught with difficulty. We accept that no one can claim 100% certainty, and this gives space for sceptics and cynics to challenge and reject assertions made, and to put forward alternative explanations.

This is the nature of debates with many voices, many strongly held beliefs and many interests to serve. No doubt it will continue this way. But at the same time it is useful to remind ourselves that atmospheric thermodynamics can furnish us with facts upon which we can all agree.

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Temperature and vapor pressure

It is a fundamental fact of nature that chemical substances in the solid and liquid states exert a vapor pressure, which means that some of the molecules escape into the vapor phase. And physical chemistry teaches us that vapor pressure varies solely with temperature.

Water exerts a vapor pressure, commonly seen in the phenomenon of evaporation. Molecules of water escape from the liquid surface to become molecules of water vapor in the air. Note that water vapor is not wet – it is a gas just like nitrogen, oxygen or carbon dioxide. What makes it different to other atmospheric gases is that it can change back from the gas phase to the liquid or solid phase as water or ice depending on how the thermodynamic conditions change.

The relationship between water vapor pressure and temperature deserves close attention. There are two distinct effects of temperature: one is that water vapor pressure increases linearly with temperature if the vapor density is constant. The other is that the saturation vapor pressure – the maximum pressure for a given temperature – increases logarithmically with temperature in accordance with the thermodynamically exact Clapeyron equation.

This dual effect is expressed in the following formula (see Appendix for derivation)

Since temperature is expressed in Kelvin, the T2/T1 term tends to be small – a 10 degree increase from 298K (25C) to 308K (35C) has a value of only 1.03. But the corresponding change in saturation vapor pressure is much larger – from 31.67 hPa at 25C to 56.31 hPa at 35C. The net effect of a modest temperature rise at constant vapor density is a significant (42%) drop in relative humidity and a substantial increase in water vapor capacity. A volume of 1 cubic meter can contain

The atmosphere is an open thermodynamic system which means that a unit volume of air can contain variable amounts of water vapor. It is instructive to examine the effect of a modest rise in temperature on water vapor density (absolute humidity AH) if the relative humidity is unchanged. The formula below expresses this relation

This is simply an inversion of the linear-logarithmic relation given above. The net effect of a modest temperature rise is a significant increase in absolute humidity which mirrors the increase in saturation vapor pressure.

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Wildfires and atmospheric water vapor capacity

The summer of 2021 showed how easily extreme heat can lead to wildfires. For the already heated atmosphere lying above such fires, the combustion of biomass not only produces intense additional heat but also substantial quantities of water vapor from combustion, which can be represented as

Wildfires therefore have a double effect on atmospheric water vapor, increasing the unit volume capacity as well as pushing water vapor into that volume, which serves to offset the reduction in relative humidity. The effect of maintained relative humidity on the water vapor capacity of increasingly warm air is shown in the graphic below

The foregoing, while not attempting to establish a predictive link between heatwaves and flooding events, does demonstrate the fact that increases in air temperature that are seen to occur in heatwaves are associated with significant increases in atmospheric water vapor capacity, and that wildfires undoubtedly produce substantial amounts of water vapor. Taking into account the ancient wisdom that what goes up must come down, it does not take too much imagination to see the potential for heavy rainfall and associated flooding that heatwaves and wildfires represent.

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Relative humidity (RH) is defined by the relation
RH(T) = pvap(T)/psat(T)
where pvap is the actual vapor pressure and psat is the saturation vapor pressure at temperature T. The behavior of water vapor in the atmosphere approximates that of an ideal gas due to its very low partial pressure. By the ideal gas law pV = nRT at constant vapor density (n/V = constant)
pvap(T2)/T2 = pvap(T1)/T1
At temperature T2
RH(T2) = pvap(T2)/psat(T2)
Substituting for pvap(T2)
RH(T2) = T2/T1 x pvap(T1)/psat(T2)
At temperature T1
RH(T1) = pvap(T1)/psat(T1)
Substituting for pvap(T1)
RH(T2)/RH(T1) = T2/T1 x psat(T1)/psat(T2) [constant vapor density]

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P Mander September 2021

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