One could have a greenhouse to evaporate seawater near the sea and have a long greenhouse (or "greenhouse pipe") running upwards to where the dam areas are. Because the air will be kept warm during the day in the greenhouse pipe and moist air is less dense than drier air, the air will rush up through the greenhouse pipe and heat the dry air region and increase relative humidity there. Now it might seem that this would have little effect, but this system could be kept running day and night throughout the year. From my "stack effect" calculations quite a few cubic kilometres of warm moist air could be delivered every week to higher regions. The slight increase in relative humidity could just tip the balance enough to help it rain significantly more.
More humid air is less dense than drier air, enabling it to rise when it is at the same temperature as surrounding drier air:
Example:
1) At sea level the air pressure is 101.325 kPa. The air has a temperature of 30 deg C and the relative humidity (RH) is 95%. Then the density of the air is 1147 g per cubic metre.
2) At sea level the air pressure is 101.325 kPa. The air has a temperature of 32 deg C and the relative humidity (RH) is 50%. Then the density of the air is 1147 g per cubic metre.
So humidifying the 30 deg C air by increasing RH from 50% to 95% has about the same affect on air density as heating the RH=50% and T=30 deg C air to T=32 deg C.
Note: RH drops slightly on heating from 30 to 32 deg C, but it does not affect calculations much.
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