On the windward side of the mountain, should the relative humidity of the parcel change as it rises from 2000 m to 4000 m?

None

No, it should not.

On the windward side of a mountain, the relative humidity of an air parcel generally decreases as it rises in elevation. This is because as the air parcel moves upward, it expands due to decreasing atmospheric pressure. As the parcel expands, its temperature decreases, and if the parcel is initially saturated (100% relative humidity) at the lower elevation, the lower temperature at higher elevations causes the relative humidity to decrease.

Therefore, in the given scenario, as the air parcel rises from 2000 m to 4000 m on the windward side of the mountain, its relative humidity is expected to decrease.

To determine whether the relative humidity of a parcel of air changes as it rises on the windward side of a mountain from 2000 m to 4000 m, we need to consider the processes affecting the parcel of air.

When air rises over a mountain, it cools adiabatically due to the decrease in atmospheric pressure with higher altitude. As the air cools, its capacity to hold moisture decreases, which can lead to condensation and the formation of clouds.

In the case of the windward side of a mountain, as the air rises, it undergoes upward motion. As the air moves upward, its temperature decreases, and if it contains enough moisture, it can reach its dew point temperature, causing condensation and cloud formation.

Therefore, on the windward side of the mountain, as the parcel of air rises from 2000 m to 4000 m, it is possible that the relative humidity of the parcel will change if condensation occurs. If the air reaches its dew point temperature and condensation occurs, the relative humidity will increase because the air will be holding a higher fraction of the maximum moisture it can hold at that temperature. On the other hand, if the air remains dry and does not reach its dew point, the relative humidity will not change significantly.

The specific conditions and overall moisture content of the air will determine whether condensation occurs and thus whether the relative humidity changes during the ascent. Monitoring the temperature, dew point, and moisture content of the air at different altitudes will provide a clearer understanding of how the relative humidity changes on the windward side of the mountain.