VERTICAL DISTRIBUTION

The vertical distribution of atmospheric pressure refers to how pressure changes with altitude in the Earth’s atmosphere. This distribution is essential for understanding various meteorological and environmental phenomena.

Vertical Distribution of Atmospheric Pressure

1. Basic Principle:
   • Atmospheric pressure decreases with increasing altitude. This is because the density and weight of the air decrease as you move higher from the Earth’s surface.
2. Exponential Decrease:
   • The rate at which pressure decreases with height is not linear but exponential. This means that pressure drops more rapidly at lower altitudes and more gradually at higher altitudes.

Components Influencing Vertical Distribution

1. Altitude:
   • Effect: As altitude increases, the number of air molecules above a surface decreases, leading to lower pressure.
   • Example: At sea level, the atmospheric pressure is about 1013.25 mb. At an altitude of 5,000 meters (approximately the height of Mount Kilimanjaro), the pressure drops to about 540 mb, which is roughly half of the sea-level pressure.
2. Temperature:
   • Effect: Temperature variations can affect the rate of pressure decrease with altitude. Warm air expands and rises, causing a more gradual decrease in pressure, while cold air contracts and sinks, leading to a steeper pressure gradient.
   • Example: During the day, the atmosphere near the ground is heated by the sun, causing a slower pressure decrease with height. At night, cooling causes a more rapid pressure decrease near the surface.
3. Humidity:
   • Effect: Moist air is less dense than dry air, which can affect pressure gradients. Higher humidity can cause a slightly slower decrease in pressure with altitude compared to dry conditions.
   • Example: In tropical regions with high humidity, the decrease in pressure with altitude can be less steep compared to arid regions like deserts.
4. Latitude:
   • Effect: The distribution of atmospheric pressure can vary with latitude due to the Earth’s rotation and the distribution of solar heating. Polar regions typically have a different pressure gradient compared to equatorial regions.
   • Example: The polar regions experience lower temperatures, which lead to a steeper pressure gradient with altitude compared to the tropics, where the warmer temperatures result in a more gradual pressure decrease.

Standard Atmosphere Model

1. International Standard Atmosphere (ISA):
   • The ISA provides a reference for atmospheric pressure at various altitudes. It assumes a standard temperature lapse rate and a specific composition of the atmosphere.
   • Temperature Lapse Rate: The ISA assumes a temperature decrease of 6.5°C per kilometer in the lower atmosphere (troposphere).
2. Pressure Calculation:
   • The barometric formula is used to calculate pressure at different altitudes in the standard atmosphere.
   • Formula: P=P0(1−L⋅hT0)g⋅MR⋅LP = P_0 \left(1 – \frac{L \cdot h}{T_0} \right)^{\frac{g \cdot M}{R \cdot L}}P=P0​(1−T0​L⋅h​)R⋅Lg⋅M​
     • PPP = pressure at height hhh
     • P0P_0P0​ = sea-level standard atmospheric pressure (1013.25 mb)
     • LLL = temperature lapse rate (0.0065 K/m)
     • hhh = height above sea level in meters
     • T0T_0T0​ = sea-level standard temperature (288.15 K)
     • ggg = acceleration due to gravity (9.80665 m/s²)
     • MMM = molar mass of Earth’s air (0.0289644 kg/mol)
     • RRR = universal gas constant (8.31432 N·m/(mol·K))

Atmospheric Layers and Pressure Distribution

1. Troposphere:
   • Characteristics: Extends from the Earth’s surface up to about 8-15 km (5-9 miles). It contains approximately 75% of the atmosphere’s mass.
   • Pressure Decrease: The pressure decreases rapidly in the troposphere. For example, at 10 km (the typical cruising altitude of commercial airplanes), the pressure is about 250 mb.
2. Stratosphere:
   • Characteristics: Extends from the top of the troposphere to about 50 km (31 miles) above the Earth’s surface.
   • Pressure Decrease: The pressure continues to decrease but at a slower rate compared to the troposphere. At 50 km, the pressure is about 1 mb.
3. Mesosphere:
   • Characteristics: Extends from the stratosphere up to about 85 km (53 miles).
   • Pressure Decrease: The pressure decreases further. At 85 km, the pressure is about 0.01 mb.
4. Thermosphere and Exosphere:
   • Characteristics: Extends from the mesosphere to outer space. The thermosphere extends up to about 600 km (373 miles), and the exosphere is beyond that.
   • Pressure Decrease: In the thermosphere, pressure is extremely low, approaching the vacuum of space.

Example of Vertical Pressure Distribution in Weather Systems

1. Mountain Weather:
   • Example: On a mountain like Mount Everest, the base camp at around 5,300 meters has a pressure of approximately 540 mb, while the summit at 8,848 meters has a pressure of about 330 mb. This drastic pressure decrease affects both weather conditions and human physiology.
2. Aircraft Flight:
   • Example: Commercial aircraft flying at an altitude of 10 km experience pressures of about 250 mb, requiring pressurized cabins to maintain a habitable environment for passengers and crew.