Chapter 3 Thermodynamics

Daily Temperature Variations Diurnal temperature range = the difference between the daily maximum and minimum temperature.

Daily Temperature Variations Factors that control how warm it can get during the day include: Season – warmer in summer than winter Presence of clouds or haze will reduce warming Type of soil and soil moisture content – less warming with moist soil Presence or absence of vegetation – more warming without vegetation Snow cover – will reduce temperature

Daily Temperature Variations Coldest nighttime temperatures and strongest nocturnal inversions occur with: Winter – long night and long period of radiative cooling Clear skies – allows LW radiative loss from ground with little downwelling LW from the atmosphere Light winds – reduce depth of atmosphere that cools by turbulent heat fluxes so this thin layer can become very cold Snow cover – insulates the atmosphere from warmer ground below and is an effective emitter of LW radiation

The Earth’s Annual Energy Budget On an annual basis, the earth and atmosphere have a balance between energy gained and lost. Each part of the atmosphere (top, atmosphere, and ground) must be in energy balance.

Regional Temperature Variations Factors controlling temperature variability across Earth: Latitude – T decreases with increasing latitude Land/water distribution – larger temperature variation over continents than over oceans Ocean currents – warm currents like Gulf Stream or cold currents like along the west coast of North America Elevation – T decreases with elevation (removed from figures) Average January Temperature (℉) Average July Temperature (℉)

Regional Temperature Variations Temperature gradient is larger between the tropics and the pole in the winter hemisphere. The warmest air occurs in the sub-tropics of the summer hemisphere (NH in July, SH in January). The main reason ocean temperatures varies less than continental temperatures is that water has a larger heat capacity than land so oceans warm and cool less than land for the same radiative input. Ocean currents transport heat to reduce the amount of warming and cooling locally.

Apparent Temperature Indices How hot or cold we feel depends on more than just the air temperature. The human body transfers energy from/to its environment by: Radiation – LW loss by humans and LW & SW gain from environment Conduction and turbulent transfer Evaporation – latent heat The wind chill and heat indices attempt to account for how exposed skin “feels” under windy or humid conditions compared to reference conditions.

Apparent Temperature Indices Wind Chill Index Temperature and wind impact how cold we feel Water on the skin will evaporate and cool a person Frostbite = freezing of the skin Hypothermia = a lowering of the body’s core temperature below its normal range

Apparent Temperature Indices The heat index accounts for the role of humidity in making you feel warmer (or cooler) than the actual air temperature. In the summer, high humidity limits how much sweat can evaporate and thus limits how effectively the human body can cool itself.

Review + Exercices

Lapse Rate (Γ) Process (parcel) lapse rate = the lapse rate of an air parcel experiencing a specific process (such as moving vertically through the atmosphere): Theoretical lapse rate Can be determined using the First Law of Thermo! Environmental lapse rate = the lapse rate of the air surrounding an air parcel: Observational lapse rate Can be determined by launching a radiosonde!

Exercise 1 Calculate the environmental lapse of the troposphere for the standard atmosphere temperature profile shown here. -56.5℃ 11 km Γ=− 𝑇 2 − 𝑇 1 𝑧 2 − 𝑧 1 =− ∆𝑇 ∆𝑧 15℃

Exercise 1 11 km -56.5℃ 15℃ Troposphere: At z1 = 0 km, T1 = 15 ℃ At z2 = 11 km, T2 = -56.5 ℃ 𝑇 1 =15℃+273.15=288.15𝐾 𝑇 2 =−56.5℃+273.15=216.65𝐾 Γ=− ∆𝑇 ∆𝑧 =− 𝑇 2 − 𝑇 1 𝑧 2 − 𝑧 1 Γ=− 216.65𝐾−288.15𝐾 11𝑘𝑚−0𝑘𝑚 =6.5 𝐾 𝑘𝑚 → T decreases 6.5 K for every 1 km increase in altitude in the troposphere.

Dry Adiabatic Lapse Rate ( Γ 𝑑 ) DALR = an air parcel lapse rate when no heat (energy) enters or leaves the air parcel (∆𝑞=0). Γ 𝑑 =− ∆𝑇 ∆𝑧 = 𝑔 𝐶 𝑝 =9.8 𝐾 𝑘𝑚 −1 DALR is larger than the average lapse rate in the troposphere (6.5 𝐾 𝑘𝑚 −1 ) calculated before. The standard atmosphere is not completely dry (contains water). Water has a high heat capacity, which acts to decrease the lapse rate.

Exercise 2 Suppose you hike down in the Grand Canyon on a dry day ( Γ 𝑑 ). On the rim, the temperature is 95℉ (35℃). In the canyon, 1500m below, how hot is it? Γ 𝑑 =− ∆𝑇 ∆𝑧 Γ 𝑑 =9.8 𝐾 𝑘𝑚 −1 Don’t forget to convert T in K!!

Exercise 2 What do we know? What are we looking for? 𝑇 1 ∆𝑧=1.5 𝑘𝑚 𝑇 2 =35℃+273.15=308.15𝐾 Γ 𝑑 =9.8 𝐾 𝑘𝑚 What are we looking for? 𝑇 1 Γ 𝑑 =− ∆𝑇 ∆𝑧 =− 𝑇 2 − 𝑇 1 ∆𝑧 −Γ 𝑑 ∙∆𝑧= 𝑇 2 − 𝑇 1 𝑇 1 = 𝑇 2 + Γ 𝑑 ∙∆𝑧 𝑇 1 =308.15𝐾+9.8 𝐾 𝑘𝑚 ∙1.5𝑘𝑚 𝑇 1 =322.85𝐾=49.7℃=121.5℉

Potential Temperature (𝜃) The potential temperature can be calculated using: 𝜃=𝑇 𝑧 + Γ 𝑑 ∙𝑧 𝑜𝑟 𝜃=𝑇 𝑃 0 𝑝 𝑅 𝑑 𝐶 𝑝 Potential temperature will not change as the parcel rises or sinks for a dry adiabatic process because no heat is added or removed from the air parcel. Potential temperature is conserved (constant) for a dry adiabatic process but the temperature of the air parcel will change. Poisson’s Equation Always use SI units!! (temperature in K and pressure in Pa)

Exercise 3 What is the potential temperature 𝜃 at NCAR’s Mesa Lab? (you can assume dry air)

Exercise 3 1st method: 𝜃=𝑇 𝑧 + Γ 𝑑 ∙𝑧 𝜃= 12.6℃+273.15 +9.8 𝐾 𝑘𝑚 ∙1.885𝑘𝑚 𝜃=304.2𝐾=31.07℃ 2nd method: 𝜃=𝑇 𝑃 0 𝑝 𝑅 𝑑 𝐶 𝑝 𝜃=(12.6℃+273.15) 100,000𝑃𝑎 81,200𝑃𝑎 287 𝐽 𝐾∙𝑘𝑔 1005 𝐽 𝐾∙𝑘𝑔 𝜃=303.26𝐾=30.11℃ Need to know T and z! Need to know T and p!

Exercise 4 If a parcel is lifted dry adiabatically, what happens to pressure, temperature, and potential temperature q? Pressure increases, temperature decreases, q increases Pressure increases, temperature increases, q decreases Pressure decreases, temperature stays the same, q decreases Pressure decreases, temperature decreases, q stays the same Pressure decreases, temperature increases, q stays the same

Exercise 4 If a parcel is lifted dry adiabatically, what happens to pressure, temperature, and potential temperature q? Pressure increases, temperature decreases, q increases Pressure increases, temperature increases, q decreases Pressure decreases, temperature stays the same, q decreases Pressure decreases, temperature decreases, q stays the same Pressure decreases, temperature increases, q stays the same

Thermodynamic Diagram isotherms = lines of constant temperature isobars = lines of constant pressure Pressure A basic thermodynamic diagram shows pressure (on the vertical axis) and temperature (on the horizontal axis). dry adiabats = lines of constant potential temperature Temperature

Thermodynamic Diagram Dry adiabats: Relate temperature and pressure at different levels in the atmosphere for a dry adiabatic process on a thermodynamic diagram. Represent the process lapse rate for a dry adiabatic process (a process in which no heat is exchanged with the parcel and no phase change of water occur).

Exercise 5 Air parcel: p = 750 mb T = 15 ℃ What happens when the air parcel is: brought down isothermally to p = 1000 mb? cooled isobarically to T = -10 ℃? raised adiabatically to p = 500 mb?