☁️Atmospheric Physics Unit 2 – Atmospheric Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, energy, work, and temperature and how they affect the behavior of systems
• Atmospheric thermodynamics focuses on the application of thermodynamic principles to the Earth's atmosphere and its processes
• Temperature measures the average kinetic energy of molecules in a substance and is a key variable in atmospheric thermodynamics
• Pressure is the force exerted by the weight of the atmosphere on a unit area and decreases with altitude
• Density refers to the mass per unit volume of a substance and varies with temperature and pressure in the atmosphere
• Specific heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius per unit mass
• Latent heat is the energy absorbed or released during a phase change without a change in temperature (melting, freezing, vaporization, condensation)

Fundamental Laws of Thermodynamics

• The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • In the atmosphere, this law governs the exchange of energy between the Earth's surface, the atmosphere, and space
• The second law of thermodynamics states that the entropy of an isolated system always increases over time
  • Entropy is a measure of the disorder or randomness of a system
  • In the atmosphere, this law explains why heat flows from warmer to cooler regions and why weather systems tend to dissipate over time
• The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other
  • This law provides the basis for the concept of temperature and its measurement
• The ideal gas law relates pressure, volume, temperature, and the amount of gas in a system: $PV = nRT$
  • $P$ is pressure, $V$ is volume, $n$ is the number of moles of gas, $R$ is the universal gas constant, and $T$ is temperature in Kelvin
• The Clausius-Clapeyron equation describes the relationship between the saturation vapor pressure and temperature of a substance
  • This equation is crucial for understanding the formation of clouds and precipitation in the atmosphere

Atmospheric Composition and Structure

• The atmosphere is composed primarily of nitrogen (78%) and oxygen (21%), with the remaining 1% consisting of trace gases such as argon, carbon dioxide, and water vapor
• The atmosphere is divided into layers based on temperature changes with altitude: troposphere, stratosphere, mesosphere, thermosphere, and exosphere
• The troposphere is the lowest layer of the atmosphere, extending from the Earth's surface to an average height of 12 km
  • Most weather phenomena occur in the troposphere, and temperature generally decreases with altitude in this layer
• The stratosphere extends from the top of the troposphere to about 50 km above the Earth's surface
  • Temperature increases with altitude in the stratosphere due to the absorption of ultraviolet radiation by ozone
• The tropopause is the boundary between the troposphere and stratosphere, characterized by a sharp change in the temperature lapse rate
• The mesosphere extends from the top of the stratosphere to about 85 km, with temperature decreasing with altitude
• The thermosphere extends from the top of the mesosphere to about 500 km, with temperature increasing with altitude due to the absorption of solar radiation by oxygen and nitrogen molecules

Temperature and Pressure Relationships

• Temperature and pressure are closely related in the atmosphere, with pressure decreasing exponentially with altitude
• The hydrostatic equation describes the relationship between pressure and altitude in the atmosphere: $dP = -\rho g dz$
  • $dP$ is the change in pressure, $\rho$ is the density of air, $g$ is the acceleration due to gravity, and $dz$ is the change in altitude
• The ideal gas law relates temperature, pressure, and density in the atmosphere: $P = \rho R_d T$
  • $P$ is pressure, $\rho$ is density, $R_d$ is the specific gas constant for dry air, and $T$ is temperature in Kelvin
• The geopotential height is a vertical coordinate that accounts for the variation of gravity with altitude and is used in atmospheric models and weather maps
• The hypsometric equation relates the thickness of an atmospheric layer to the mean temperature and mean pressure of the layer
  • This equation is used to calculate the height of pressure surfaces in the atmosphere
• The virtual temperature is the temperature that dry air would need to have the same density as moist air at the same pressure
  • Virtual temperature is used to account for the effects of moisture on atmospheric processes

Moisture and Phase Changes in the Atmosphere

• Water vapor is the gaseous form of water and is a crucial component of the atmosphere, influencing weather and climate
• Relative humidity is the ratio of the actual water vapor pressure to the saturation vapor pressure at a given temperature, expressed as a percentage
  • High relative humidity indicates that the air is close to saturation, while low relative humidity indicates dry air
• Dew point temperature is the temperature at which air becomes saturated with water vapor, and condensation begins
  • The dew point depression is the difference between the air temperature and the dew point temperature, with smaller differences indicating more humid air
• Latent heat is the energy absorbed or released during phase changes of water in the atmosphere, such as evaporation, condensation, freezing, and melting
  • Latent heat of vaporization is the energy required to convert liquid water to water vapor, while latent heat of fusion is the energy required to convert ice to liquid water
• Saturation vapor pressure is the maximum water vapor pressure that air can hold at a given temperature
  • The Clausius-Clapeyron equation describes the relationship between saturation vapor pressure and temperature
• Condensation occurs when water vapor changes to liquid water, typically forming clouds or fog
  • Condensation nuclei, such as dust particles or ice crystals, provide surfaces for water vapor to condense upon
• Evaporation is the process by which liquid water changes to water vapor, requiring an input of energy
  • Evaporation rates depend on factors such as temperature, humidity, and wind speed

Atmospheric Stability and Instability

• Atmospheric stability refers to the resistance of an air parcel to vertical motion when displaced from its original position
• Stable atmosphere occurs when an air parcel, if displaced vertically, tends to return to its original position
  • In a stable atmosphere, vertical motion is suppressed, leading to less turbulence and smoother air
• Unstable atmosphere occurs when an air parcel, if displaced vertically, tends to continue moving away from its original position
  • In an unstable atmosphere, vertical motion is enhanced, leading to more turbulence and the development of convective clouds
• Conditionally unstable atmosphere occurs when the stability of an air parcel depends on its saturation state
  • If the air parcel is unsaturated, it is stable, but if it becomes saturated, it becomes unstable
• The environmental lapse rate is the rate at which temperature decreases with altitude in the surrounding atmosphere
  • The dry adiabatic lapse rate (DALR) is the rate at which the temperature of an unsaturated air parcel decreases with altitude as it rises adiabatically (about 9.8°C/km)
  • The moist adiabatic lapse rate (MALR) is the rate at which the temperature of a saturated air parcel decreases with altitude as it rises adiabatically (varies with temperature and pressure, but is typically around 5-7°C/km)
• Atmospheric stability can be assessed by comparing the environmental lapse rate to the dry and moist adiabatic lapse rates
  • If the environmental lapse rate is less than the MALR, the atmosphere is absolutely stable
  • If the environmental lapse rate is between the MALR and DALR, the atmosphere is conditionally unstable
  • If the environmental lapse rate is greater than the DALR, the atmosphere is absolutely unstable

Adiabatic Processes and Lapse Rates

• Adiabatic processes occur when an air parcel exchanges no heat with its surroundings, and any temperature changes are due to the expansion or compression of the air parcel
• The dry adiabatic lapse rate (DALR) is the rate at which the temperature of an unsaturated air parcel decreases with altitude as it rises adiabatically (about 9.8°C/km)
  • The DALR is a constant value and is derived from the first law of thermodynamics and the ideal gas law
• The moist adiabatic lapse rate (MALR) is the rate at which the temperature of a saturated air parcel decreases with altitude as it rises adiabatically
  • The MALR varies with temperature and pressure, but is typically around 5-7°C/km
  • The MALR is less than the DALR because the latent heat released during condensation partially offsets the cooling due to expansion
• The potential temperature is the temperature that an air parcel would have if it were brought adiabatically to a reference pressure level (typically 1000 hPa)
  • Potential temperature is conserved during adiabatic processes and is useful for comparing air parcels at different altitudes
• The equivalent potential temperature is the potential temperature that an air parcel would have if all its moisture were condensed out, and the latent heat released were used to warm the air parcel
  • Equivalent potential temperature is conserved during both adiabatic and pseudoadiabatic processes, making it a useful tracer of air masses
• The wet-bulb potential temperature is the potential temperature that an air parcel would have if it were brought adiabatically to saturation and then brought to a reference pressure level
  • Wet-bulb potential temperature is conserved during pseudoadiabatic processes and is useful for assessing atmospheric stability

Applications in Weather Forecasting

• Atmospheric thermodynamics plays a crucial role in weather forecasting by providing the foundation for understanding and predicting various weather phenomena
• Stability analysis is used to forecast the development of convective storms, such as thunderstorms and tornadoes
  • Unstable atmospheric conditions favor the development of convective storms, while stable conditions suppress vertical motion and storm development
• Thermodynamic diagrams, such as Skew-T log-P diagrams and Stüve diagrams, are used to analyze the vertical structure of the atmosphere and assess stability
  • These diagrams plot temperature, dew point, and wind data from radiosondes and help forecasters identify potential for severe weather
• Moisture analysis is essential for forecasting cloud formation, precipitation, and fog
  • The relative humidity, dew point temperature, and saturation vapor pressure are used to determine the likelihood and type of precipitation
• Adiabatic processes and lapse rates are used to predict the formation and dissipation of inversions, which can trap pollutants and affect air quality
  • Temperature inversions occur when the environmental lapse rate is negative (i.e., temperature increases with altitude) and can lead to the accumulation of pollutants near the surface
• Numerical weather prediction models incorporate atmospheric thermodynamics to simulate the evolution of weather systems
  • These models solve complex equations that describe the motion, temperature, pressure, and moisture of the atmosphere, using thermodynamic principles to ensure physically consistent results
• Climate models also rely on atmospheric thermodynamics to simulate the long-term behavior of the Earth's climate system
  • Thermodynamic processes, such as the greenhouse effect, radiative transfer, and energy balance, are crucial for understanding and predicting climate change