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In many parts of the world there are dry lands below sea level, such as parts of the Netherlands. Since we know that temperature decreases with increasing altitude, does it mean that temperature will increase as we go lower below sea level?

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Yes. The height of the ground or ocean surface is of no consequence to the lapse rate as long as we remain above it -- in the atmosphere. E.g. the dry adiabatic lapse rate is a conservation of entropy as a parcel of air rises or descends. This means the temperature change is related only to the expansion of contraction of the parcel as it responds to changes in pressure. When you move down below sea level there is nothing fundementally different than starting at 500 m height and moving down from there. Both are moving down into higher pressure and the parcel will contract and warm as a result.

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The wet and dry adiabatic lapse rates apply regardless of whether or not the altitude in question is below sea level. The Dead Sea is 413 meters below sea level. The dry adiabatic lapse rate is 1°C/100m, so a parcel of air moving from sea level into the Dead Sea area would be expected to heat by just over 4°C, ignoring any possible heating from the change from the dry adiabatic lapse rate to the wet adiabatic lapse rate, which is 0.5°C/100m.

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