Does cold air or warm air need more water to become saturated and relationship between temperature and the amount of water vapor required for saturation?
Cold air actually requires less water vapor to become saturated compared to warm air. The relationship between temperature and the amount of water vapor required for saturation is governed by the concept of saturation vapor pressure.
Saturation vapor pressure is the pressure exerted by the water vapor molecules in the air when the air is saturated with moisture at a given temperature. It is the maximum vapor pressure possible at that temperature and corresponds to the point at which the air is holding as much water vapor as it can without condensation occurring.
The colder the air, the lower its saturation vapor pressure. This means that at lower temperatures, the air can hold less water vapor before it becomes saturated. Conversely, warm air has a higher saturation vapor pressure, allowing it to hold more water vapor before reaching saturation.
To put it simply:
Cold air has a lower saturation vapor pressure, so it requires less water vapor to become saturated.
Warm air has a higher saturation vapor pressure, so it requires more water vapor to become saturated.
This relationship between temperature and the amount of water vapor required for saturation is a fundamental aspect of meteorology and plays a significant role in processes such as condensation, cloud formation, and precipitation.
Hot air expands, and rises; cooled air contracts – gets denser – and sinks; and the ability of the air to hold water depends on its temperature. A given volume of air at 20°C (68°F) can hold twice the amount of water vapor than at 10°C (50°F). The saturation mixing ratio is a property of air and depends on the air temperature - there can be a lot more water vapor in warm air than in cold air. Cold air can be saturated more quickly than warm air since it does not take much water vapor to saturate cold air. Limiting this is the fact that the rate of evaporation is less in cold air. It is often explained that warm air holds more water because warmer water is less likely to condense. This and other explanations just seem to be circular arguments. If the warmer air picks up enough moisture it will saturate and then water will still condense at 100% humidity. If the air is moist enough, the cooling causes it to reach saturation and visible water droplets form. We often call this type of fog ground fog because it lies so close to the surface. Advection fog forms when warm moist air moves over a colder surface. Another physical process that affects DO concentrations is the relationship between water temperature and gas saturation. Cold water can hold more of any gas, in this case oxygen, than warmer water. Warmer water becomes "saturated" more easily with oxygen. As water becomes warmer it can hold less and less DO.The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. The boiling point of water is the temperature at which the saturated vapour pressure equals the ambient pressure. The saturated vapor pressure of any substance depends on its temperature. At higher temperatures, more molecules have sufficient kinetic energy to break from the liquid surface into the vapor phase. Under these conditions, equilibrium is reached at a higher pressure. The saturated vapor pressure of any substance depends on its temperature. At higher temperatures, more molecules have sufficient kinetic energy to break from the liquid surface into the vapor phase. Under these conditions, equilibrium is reached at a higher pressure.The higher the temperature, the more water vapor a volume of air is capable of holding. Therefore, any change in temperature alters the volume's water vapor capacity. As air warms, its capacity for holding water vapor increases; as it cools, the capacity decreases.