why is the parcel now warmer than it was at sea level on the windward side (what is the source of the heat energy

The parcel can become warmer on the windward side due to a process called adiabatic heating. The source of heat energy in this case is the adiabatic compression of the air parcel as it is forced to rise over mountains or other topographic barriers.

When moist air encounters a mountain range, it is forced to ascend on the windward side. As it rises, the air parcel experiences a decrease in pressure. According to the ideal gas law, decreasing the pressure of a gas while keeping the volume constant will cause the temperature to decrease as well. This process is known as adiabatic cooling.

However, as the air parcel is forced to rise, it also moves away from the surface and the atmospheric pressure decreases. The rate at which the air parcel cools due to adiabatic cooling progressively slows down until the temperature stops decreasing and starts to stabilize.

At this point, the air parcel reaches its lifting condensation level (LCL), and the water vapor in the air begins to condense into liquid water droplets. This release of latent heat, which is the energy released when water changes from vapor to liquid, partially offsets the cooling caused by adiabatic expansion.

As the air parcel continues to rise over the mountain range, it is subjected to more adiabatic heating. The combination of the latent heat released from condensation and the adiabatic heating causes the air parcel to become warmer than it was at sea level.

So, the source of the heat energy that warms the parcel on the windward side is the combination of adiabatic compression and the release of latent heat from condensation.

The parcel of air is warmer on the windward side due to a process called adiabatic heating, which is directly related to changes in atmospheric pressure and altitude.

When air approaches a mountain or any elevated terrain, it is forced to rise due to the barrier it encounters. As the air rises, it experiences a decrease in atmospheric pressure. According to the ideal gas law, when the pressure of a gas decreases, its temperature also decreases. Therefore, as the air rises, it cools down.

However, as the parcel of air rises and cools, it continues to hold the same amount of heat energy. This means that the heat energy is distributed over a larger volume of air, causing the temperature to drop. But since the total amount of heat in the parcel remains the same, the temperature reduction is not due to the loss of heat energy from the parcel.

On the windward side of the mountain, the rising air encounters even higher altitudes. As the air moves up the mountain slope, it continues to cool due to adiabatic expansion caused by decreasing pressure. The cooling process makes the air even colder than it was at sea level.

However, when the air reaches the summit and starts descending on the leeward side of the mountain, the opposite happens. The descending air experiences increasing atmospheric pressure, and according to the ideal gas law, its temperature increases. This process is known as adiabatic heating.

Therefore, the source of the heat energy that warms the parcel on the windward side is the adiabatic heating caused by the compression of air at higher atmospheric pressures as it descends on the leeward side of the mountain.