🌦️Atmospheric Science Unit 4 – Atmospheric Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, energy, and work in a system
• Atmosphere is a complex system composed of gases, water vapor, and other particles surrounding Earth
• Temperature measures the average kinetic energy of molecules in a substance
• Pressure is the force exerted by the weight of the atmosphere on a unit area
  • Measured using barometers (mercury or aneroid)
• Humidity quantifies the amount of water vapor present in the atmosphere
  • Relative humidity expresses the amount of water vapor in the air compared to the maximum amount possible at a given temperature
• Adiabatic processes occur without heat exchange between a system and its surroundings
• Lapse rate describes the rate at which temperature changes with altitude in the atmosphere
  • Environmental lapse rate (ELR) refers to the actual temperature change with height in the atmosphere

Fundamental Laws of Thermodynamics

• First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • Expressed as: ΔU = Q - W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done by the system
• Second Law of Thermodynamics introduces the concept of entropy, stating that the entropy of an isolated system always increases over time
  • Entropy measures the degree of disorder or randomness in a system
• Zeroth Law of Thermodynamics defines thermal equilibrium: if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other
• Ideal Gas Law relates pressure, volume, temperature, and 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
• Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas

Atmospheric Composition and Structure

• Atmosphere is primarily composed of nitrogen (78%) and oxygen (21%), with trace amounts of other gases (argon, carbon dioxide, water vapor)
• Atmospheric layers are defined by temperature changes with altitude
  • Troposphere is the lowest layer, extending from Earth's surface to an average height of 12 km
    • Most weather phenomena occur in the troposphere
  • Stratosphere extends from the tropopause to approximately 50 km, characterized by increasing temperature with height due to ozone absorption of UV radiation
  • Mesosphere extends from the stratopause to about 85 km, with temperature decreasing with height
  • Thermosphere extends from the mesopause upwards, characterized by increasing temperature with height due to absorption of high-energy radiation
• Ozone layer in the stratosphere absorbs harmful UV radiation, protecting life on Earth
• Atmospheric pressure decreases exponentially with height, as described by the barometric formula

Temperature and Pressure Relationships

• Temperature and pressure are fundamentally linked in the atmosphere
• Ideal Gas Law ($PV = nRT$) demonstrates the direct relationship between temperature and pressure, assuming constant volume and amount of gas
• Hydrostatic equation describes the balance between the vertical pressure gradient force and gravity in the atmosphere
  • $dP = -ρgdz$, where $dP$ is the change in pressure, $ρ$ is air density, $g$ is gravitational acceleration, and $dz$ is the change in height
• Pressure decreases with altitude because the weight of the overlying atmosphere decreases
• Temperature generally decreases with altitude in the troposphere due to adiabatic cooling as air parcels expand and rise
  • Dry adiabatic lapse rate (DALR) is approximately -9.8°C/km
  • Saturated adiabatic lapse rate (SALR) varies with temperature and pressure but is typically around -6°C/km

Moisture and Phase Changes

• Water vapor is the gaseous form of water in the atmosphere
• Evaporation is the process by which liquid water transforms into water vapor
  • Requires energy input (latent heat of vaporization)
• Condensation is the process by which water vapor transforms into liquid water
  • Releases energy (latent heat of condensation)
• Sublimation is the direct transition from solid (ice) to gas (water vapor) or vice versa
• Relative humidity is the ratio of the actual water vapor pressure to the saturation vapor pressure at a given temperature
  • Saturation occurs when relative humidity reaches 100%
• Dew point temperature is the temperature at which air becomes saturated (100% relative humidity) when cooled at constant pressure
• Latent heat is the energy absorbed or released during phase changes without a change in temperature
  • Latent heat of vaporization (evaporation/condensation): ~2.5 × 10^6 J/kg
  • Latent heat of fusion (melting/freezing): ~3.3 × 10^5 J/kg
  • Latent heat of sublimation: ~2.8 × 10^6 J/kg

Atmospheric Stability and Instability

• Atmospheric stability refers to the atmosphere's resistance to vertical motion
• Stable atmosphere suppresses vertical motion, leading to limited convection and generally fair weather
  • Occurs when the environmental lapse rate (ELR) is less than the saturated adiabatic lapse rate (SALR)
• Unstable atmosphere promotes vertical motion, leading to enhanced convection and potentially severe weather
  • Occurs when the ELR is greater than the dry adiabatic lapse rate (DALR)
• Conditionally unstable atmosphere is stable for unsaturated air parcels but unstable for saturated air parcels
  • Occurs when the ELR is between the SALR and DALR
• Inversion layers, where temperature increases with height, strongly suppress vertical motion and indicate a highly stable atmosphere
• Stability can be assessed using various indices and parameters
  • Lifted Index (LI) compares the temperature of a lifted parcel to the ambient temperature at a given pressure level (usually 500 hPa)
  • Convective Available Potential Energy (CAPE) measures the amount of energy available for convection

Energy Transfer in the Atmosphere

• Radiation is the transfer of energy through electromagnetic waves
  • Solar radiation is the primary energy source for Earth's atmosphere
  • Earth's surface and atmosphere emit longwave (infrared) radiation
• Conduction is the transfer of energy through direct contact between molecules
  • Important for heat transfer between Earth's surface and the lower atmosphere
• Convection is the transfer of energy through the bulk motion of fluids (air in the atmosphere)
  • Convection currents are driven by buoyancy differences due to temperature and density variations
• Latent heat transfer occurs during phase changes of water (evaporation, condensation, sublimation)
  • Evaporation from Earth's surface absorbs energy, while condensation in the atmosphere releases energy
• Greenhouse effect is the process by which atmospheric gases (primarily water vapor and carbon dioxide) absorb and re-emit longwave radiation, warming Earth's surface
• Earth's energy balance is maintained by the equilibrium between incoming solar radiation and outgoing longwave radiation

Applications in Weather Forecasting

• Thermodynamic principles are crucial for understanding and predicting weather phenomena
• Atmospheric stability assessment helps predict the likelihood of convection, thunderstorm development, and severe weather
• Skew-T log-P diagrams are used to analyze vertical profiles of temperature, dew point, and wind, aiding in stability assessment and convection forecasting
• Numerical weather prediction (NWP) models incorporate thermodynamic equations to simulate atmospheric processes and predict future weather conditions
• Moisture and heat budgets are analyzed to understand energy transfer and phase changes in the atmosphere, influencing precipitation forecasts
• Thermodynamic indices (e.g., CAPE, LI) are used to assess the potential for severe weather, such as thunderstorms and tornadoes
• Understanding of adiabatic processes and lapse rates helps predict cloud formation, precipitation type, and the evolution of air masses
• Knowledge of atmospheric composition and structure is essential for modeling radiative transfer and the greenhouse effect, which impact long-term climate forecasts