Overview:
The variation observed in temperature in the atmosphere with respect to elevation is known as the temperature lapse rate. It describes how temperature changes as we move upward through the atmosphere. The lapse rate can vary depending on various factors such as atmospheric conditions, location, time of day, and season.

Explanation:
The temperature variation in the atmosphere with respect to elevation follows a specific pattern. Let's understand the different stages of this variation.

1. Troposphere:
The troposphere is the lowest layer of the atmosphere, extending from the Earth's surface up to an average height of about 11 kilometers. In the troposphere, temperature generally decreases with increasing altitude. This is because the Earth's surface is warmed by the sun, and the warm air rises, causing a decrease in temperature as we move upward.

2. Tropopause:
The tropopause is the boundary between the troposphere and the layer above it, called the stratosphere. It is characterized by a stable temperature layer, where the temperature remains constant or slightly increases with height. This is due to the absorption of ultraviolet radiation by the ozone layer in the stratosphere.

3. Stratosphere:
In the stratosphere, the temperature generally increases with height. This is primarily caused by the absorption of solar radiation by the ozone layer, which releases heat and warms the surrounding air.

4. Stratopause and Mesosphere:
The stratopause is the boundary between the stratosphere and the mesosphere. At this level, the temperature stops increasing and remains constant for a short distance. Above the stratopause, the temperature begins to decrease again with increasing altitude in the mesosphere.

5. Thermosphere:
In the thermosphere, the temperature increases with height due to the absorption of high-energy solar radiation. However, the density of air in this region is extremely low, so the temperature increase does not have a significant impact on the overall atmospheric conditions.

Conclusion:
In conclusion, the variation in temperature in the atmosphere with respect to elevation follows a pattern where temperature decreases with height in the troposphere, remains relatively constant in the tropopause and lower stratosphere, increases in the upper stratosphere, remains constant in the stratopause and mesosphere, and increases again in the thermosphere. This pattern is known as the temperature lapse rate and is influenced by various factors such as the sun's radiation, ozone layer, and atmospheric composition.