When the climate is warming, how the cycle of water between the atmosphere, ocean and land will change? Here is an example of what a scientist can say with relatively simple considerations.
[[I place this page just temporarily. It will be revised and moved to another place in the future.]]
The first simple thinking goes as follows.
As temperature rises, the saturation specific humidity, or the capacity of air to hold water vapor, becomes larger. Physically speaking, this is actually not the capacity of air, but rather the capacity of space. It is determined by the equilibrium between the liquid phase and the gas (vapor) phase of water, and expressed by the formula of Clapeyron and Clausius. The dependence of the saturation specific humidity to temperature is like an exponential function. As temperature becomes higher, the increase of moisture capacity becomes stronger.
The actual content of water vapor in the atmosphere will probably change in proportion to the change of the capacity. In other words, "relative humidity" (which many people colloquially refers to as "humidity") will be held constant. This is not a relationship proved theoretically, but considered to be approximately valid based on experience in observation-based and numerical modeling studies.
Thus, if the mean residence time of water vapor in the atmosphere would not change, both precipitation and evaporation would increase with exponential dependence on temperature. And, if the increase occur uniformly, the flow of water resources for agricultural, industrial and urban activities would increase in proportion.
But the two if's are probably not fulfilled. Before entering the discussion, let us make sure that what "precipitation" and "evaporation" mean in the quantitative context.
"Precipitation" and "evaporation" are evaluated as mass fluxes (of water) per unit area per unit time. Alternatively, assuming the standard density of liquid water (1 g/cm3), they can be expressed as volume fluxes of liquid water per unit area per unit time. And note that "volume per unit area" is depth, whose unit may be millimetres. There are various choices for the unit of time: second, hour, day, year, etc. Anyway, it is important that they are flow quantities.
Water vapor has more internal energy than liquid water has at the same temperature. Therefore, evaporation from the surface (of the land or the ocean) is accompanied by energy flow (usually called "latent heat flux") from the land or the ocean to the atmosphere. In order for the land or the ocean to be nearly in steady state, the energy needs to be returned from the atmosphere in some forms (radiation or sensible heat flux).
Warming of climate accompanies increase of available energy at the surface. But the increase is not like an exponential function of temperature. It is more like linear than exponential. (Note that I do not mean that it is exactly linear.) Thus, evaporation will increase as climate warms, but the increase is not as fast as that of water vapor content in the atmosphere. The mean residence time of water vapor in the atmosphere will decrease. In terms of mass per unit time, water cycle will "accelerate", but in terms of rate of recycling (reciprocal of mean residence time), it will "decelerate".
The amount of water vapor in the atmosphere is small as a reservoir of mass of water: The mean residence time is 9 days currently. Therefore, precipitation and evaporation should be almost balanced in the global mean sense. Thus, global mean precipitation will increase as climate warms, but the increase is not as fast as that of water vapor content in the atmosphere.
But, at some places and at some times, horizontal convergence of air flow in the lower atmosphere can concentrate water vapor evaporated from surface in a broad area. At such places, exponential increase of water vapor capacity may enable exponential increase of precipitation rate. Thus, it is very likely that global warming results in increase of heavy rain events. It means that the risk of floods will increase.
At other places and other times, evaporation will increase almost linearly as discussed in section (2) (unless the supply of water exhausts because of drying-up soils). The manner of change of precipitation will be very uneven. But, as it should match evaporation in the global average, it will be generally smaller than the change of evaporation except at the places and times of heavy rain events. It probably means that the risk of droughts will increase, too.
The view expressed in this section may be a little too pessimistic. But it is sure that we cannot be contented with the optimistic view expressed in the section (1) alone.
I am indebted to the popular article by KITOH (2005) for a simple explanation of likely increase of heavy rain events. I am also grateful to my colleague Hiromichi IGARASHI (FRCGC) for making a demonstration of changes of recycling rate in simulations of global warming, and to climate modeling teams of MRI/JMA and CCSR+NIES for providing their results of experiments.