Dynamic Meteorology 1: Exam 3 Study Guide

Moist Air

Combination of dry air and water

Mixing Ratio

(w) mass vapor/mass dry air

Total Water Mixing Ratio

(w_T) (mass vapor + liquid + ice)/mass dry air

Liquid Water Mixing Ratio

(w_L) mass liquid/mass dry air

Ice Mixing Ratio

(w_I) mass ice/mass dry air

Specific Humidity

(q) mass vapor/mass total (air)

Relationship between specific humidity and mixing ratio

q ≈ w

Relative Humidity

Proximity to saturation

RH = e/e_s

Bergeron Process

• e_si < e_sl

• Atmosphere can be saturated for ice but not for liquid

• Snow grows at the expense of liquid water

• e_si < –40°C

• e_sl > 0°C

Pseudoadiabatic

Heat stays in parcel but condensed water precipitates out; irreversible and entropy not conserved

Adiabatic

Heat and water mass remain in parcel; reversible and entropy conserved

Why use T_v

Adjust parcels to be dry so they follow dry adiabatic processes

The Temperature Framework

T_LCL < T_d < T_wp < T_w < T < T_v < T_ei < T_ep

LCL Temperature

(T_LCL) temperature of a parcel, lifted adiabatically, at the LCL

• Dry adiabatic expansion

• Coolest temperature

Dew Point

(T_d) temperature at which air is saturated

• Isobaric cooling

Pseudoadiabatic Wet Bulb Temperature

(T_wp) temperature of parcel lowered to any level pseudoadiabatically 

• Pseudoadiabatic descent

Wet Bulb Temperature

(T_w) temperature of parcel after evaporative cooling until reaching saturation

• Isobaric, adiabatic evaporative cooling

Temperature

dry-bulb temperature

Virtual Temperature

(T_v) equivalent temperature of air if it was dry (at same pressure and density)

• “adjusted temperature” to compensate for moisture

Isobaric Equivalent Temperature

(T_ei) equivalent temperature if all vapor condensed out of parcel

• Isobaric, adiabatic heat release 

• Opposite of wet bulb

Pseudoadiabatic Equivalent Temperature

(T_ep) temperature after all vapor condensed and removed from parcel (precipitated)

• Isobaric pseudoadiabatic latent heat release

Potential Temperature Framework

θ_wp < θ ≈ θ_m < θ_v < θ_ei < θ_ep

Pseudoadiabatic Wet Bulb Potential Temperature

(θ_wp) temperature if parcel lowered to 1000mb following moist adiabat

Potential Temperature

(θ) temperature if parcel lowered to 1000mb following dry adiabat

Moist Air Potential Temperature

(θ_m) potential temperature adjusted for moist air

Virtual Potential Temperature

(θ_v) potential temperature calculated using virtual temp

• accounts for moisture already in parcel

Equivalent Isobaric Potential Temperature

(θ_ei) temperature after water condensed from parcel, then isobarically lowered to 1000mb

Equivalent Potential Temperature

(θ_e) temperature after water condensed from parcel adiabatically, then adiabatically lowered to 1000mb

• reversible process

Pseudoadiabatic Potential Temperature

(θ_ep) temperature after water condensed from parcel psuedoadiabatically, then lowered to 1000mb

• plotted on skew-T diagrams

Isobaric Adiabatic Cooling

Liquid water will evaporate until saturation or no more liquid left

Saturation via Adiabatic Ascent

• mass of vapor conserved (follow line of constant mixing ratio)

  • for atmospheric temps T < 1550K, e↓ slower than e_s↓, so saturation possible

Γ_dew

Dew point lapse rate ≈ 1.8 K/km

Assumptions of Vertical Motion

1. Hydrostatic equilibrium (background)

2. Parcel doesn’t mix with surroundings

3. Parcel doesn’t disturb surroundings

4. Parcel follows adiabatic process 

5. Pressure of parcel = pressure of environment (at a given level)

Static Stability DEs: Stable

• parcel cooling faster than environment (Γ_v’ _> Γ_v)

  • parcel will oscillate with nudge—sin function (Brunt-Vaisala Frequency)

Static Stability DEs: Unstable

• parcel cooling slower than environment (Γ_v’ _< Γ_v)

• parcel will exponentially accelerate with nudge—exponential function

Static Stability DEs: Neutral

• parcel cooling equal to environment (Γ_v’ ₌ Γ_v)

• parcel will not accelerate—linear function

Stability of Unsaturated Parcels

• Use T_v to be able to follow DALR

• Stable: Γ_v < Γ_d

• Neutral: Γ_v = Γ_d

• Unstable: Γ_v > Γ_d

Stability of Saturated Parcels

• Stable: Γ_v < Γ_s

• Neutral: Γ_{v =} Γ_s

• Unstable: Γ_{v >} Γ_s

Conditional and Absolute Stability

• Absolutely Stable: Γ_v < Γ_s

• Conditionally Unstable: Γ_{s <} Γ_{v <} Γ_d

  • more humid places, more unstable

Stability using θ_v with height

Stable: θ_v ↑

Neutral: θ_v —

Unstable: θ_v ↓

Stability Using θ_ep with Height

Stable: θ_ep ↑

Neutral: θ_ep—

Unstable: θ_ep ↓