Environmental Modelling > Week Three: Parcel Models > Flashcards

Week Three: Parcel Models Flashcards

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1
Q

What is a parcel model?

A

A simulation of air properties along a path using simplified assumptions—often treated as a closed system.

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2
Q

What governs the rate of change of properties in a parcel model?

A

First-order Ordinary Differential Equations (ODEs)

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3
Q

What does “adiabatic” mean in this context?

A

No heat exchange occurs between the parcel and its environment.

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4
Q

What assumption is made about atmospheric properties in parcel models?

A

Properties at a given height in the parcel match those of the surrounding atmosphere.

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5
Q

How does kinetic energy relate to temperature?

A

Temperature is proportional to the average kinetic energy of molecules—faster molecules mean higher temperature.

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6
Q

What law links energy and work in thermodynamics?

A

The First Law of Thermodynamics:
Delta U = Q - W
Where Delta U is internal energy, Q is heat added, and W is work done by the system.

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7
Q

What does the Clausius-Clapeyron equation describe?

A

The relationship between temperature and the equilibrium vapour pressure of water.

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8
Q

Why can warm air hold more water vapour than cold air?

A

Because equilibrium vapour pressure increases exponentially with temperature.

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9
Q

What does an equilibrium vapour pressure curve show?

A
  • Above the curve: water exists as liquid + vapour
  • Below the curve: water exists only as vapour
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10
Q

What is the equation for temperature change in a parcel?

A

{dT}/{dt} = {R_a T}{c_p P} {dP}/{dt} + {L_v}/{c_p} {dw_l}/{dt}
Where:
- R_a: gas constant for dry air
- c_p: specific heat at constant pressure
- P: pressure
- L_v: latent heat of vaporisation
- w_l: liquid water mixing ratio

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11
Q

What are Cloud Condensation Nuclei (CCN)?

A

Aerosol particles that provide surfaces for water vapour to condense and form cloud droplets.

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12
Q

What happens as air cools during expansion?

A

Water vapour condenses onto CCN, forming clouds.

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13
Q

What is the Twomey effect?

A

Increasing aerosol concentration leads to more but smaller cloud droplets, increasing cloud albedo (reflectivity)

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14
Q

Why does cloud reflectivity increase with more CCN?

A

More droplets mean more surface area to scatter sunlight—clouds appear whiter and reflect more solar radiation

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15
Q

What does the bird’s-eye view of cloud droplets show?

A
  • Same total water volume
  • Fewer droplets → larger size → less reflective
  • More droplets → smaller size → more reflective
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16
Q

What is Marine Cloud Brightening?

A

A geoengineering technique to increase cloud reflectivity by adding sea salt aerosols to the marine boundary layer.

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17
Q

How does the Marine Cloud Brightening technique work?

A
  • Spray seawater droplets at ocean surface
  • Droplets evaporate, leaving NaCl aerosols
  • Aerosols ascend via thermals and act as CCN
  • Clouds become more reflective
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18
Q

What happens when MCB sprayers are turned off?

A

The system returns to baseline within about a week.

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19
Q

Why is NaCl effective for this method?

A

It’s naturally occurring, hygroscopic, and forms efficient CCN.

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20
Q

Why does aerosol size matter?

A
  • Smaller particles → more numerous droplets → higher albedo
  • Larger particles → fewer droplets → lower reflectivity
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21
Q

Why is Aerosol Size Importnat for Climate?

A

Reflecting more sunlight can cool the Earth’s surface—potential mitigation for global warming.

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22
Q

What happens in a wetting tube?

A

Water adheres to the surface, forming a concave meniscus—lower vapour pressure.

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23
Q

What happens in a non-wetting (hydrophobic) tube?

A

Water repels the surface, forming a convex meniscus—higher vapour pressure.

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24
Q

Why is this aerosol size important for cloud formation?

A

Cloud droplets are curved; their positive curvature affects vapour pressure and condensation dynamics.

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25
Why is vapour pressure higher over a curved surface?
- Fewer intermolecular forces pull molecules inward - Net downward force is weaker - Molecules escape more easily → higher vapour pressure needed to maintain equilibrium
26
What happens to vapour pressure on a flat surface? What does this imply about aersol size?
- Molecules experience balanced inward forces - Lower vapour pressure is sufficient to prevent escape - Larger aerosols resemble flat surfaces → easier for condensation → better CCN
27
What does Kelvin’s equation calculate?
The equilibrium vapour pressure over a curved droplet surface: e_v = e_0 (2 \sigma_w}{R_v T \rho_l r_i})
28
What does the ratio e_v/e_0 represent?
How much higher vapour pressure is over a curved surface compared to flat
29
What is the atmospheric limit for e_v/e_0?
Rarely exceeds 1.02 (i.e. 102%)
30
What does the atmospheric limit mean for CCN size?
Aerosols <50 nm radius are generally ineffective CCN due to high required vapour pressure.
31
What condition must be met for condensation onto aerosols?
Actual vapour pressure must exceed equilibrium vapour pressure.
32
What governs the rate of condensation?
- Diffusion of vapour to the droplet - Release of latent heat during condensation
33
Why don’t we solve a differential equation for each aerosol particle?
It’s computationally expensive—millions of particles would require millions of equations.
34
What is the bin or sectional approach?
Aerosols are grouped into size/mass categories (bins), and growth is calculated for the centre of each bin.
35
Can bin widths change?
Yes—individual bins can grow or shrink depending on the distribution
36
How do aerosol sizes tend to distribute?
They clump into modes and follow a log-normal distribution.
37
What defines a log-normal distribution for Aerosol Size/Distribution?
- Total number or area - Mode diameter - Standard deviation (spread)
38
What are the typical aerosol modes?
- Nucleation - Accumulation - Coarse - Sea salt (geoengineering)
39
What types of aerosols act as CCN?
Organics, salts, sulphates, and sea salt aerosols.
40
Why add sea salt aerosols to the atmosphere?
To increase CCN concentration and enhance cloud droplet formation—part of marine cloud brightening strategies.
41
What makes sea salt aerosols effective CCN?
Their size and hygroscopic nature—larger particles resemble flat surfaces, making condensation easier
42
How many bins are typically used in cloud microphysics models?
~60 bins for aerosol/cloud droplet size distribution
43
What does each bin require?
A first-order differential equation to track mass growth—totaling ~64 ODEs including pressure and temperature.
44
What language is used for solving these equations efficiently?
Fortran—a compiled language ideal for high-performance scientific computing
45
What is the ideal gas law?
PV = n R_{{gas}} T Where: - P: pressure (Pa) - V: volume (m³) - n: number of moles - R_{{gas}}: universal gas constant - T: temperature (K)
46
How is the specific gas constant for air (R_a) defined?
R_a = {R_{gas}{M_a} Where M_a = 29 g/mol is the molecular weight of air.
47
How does the Specifc Gas Constant for Air modify the ideal gas law?
PV = n M_a R_a T
48
How is air density (rho_a) defined?
rho_a = {M_{air}/{V}
49
What is the final form of the ideal gas law for air?
P = rho_a R_a T
50
What is temperature in terms of molecular motion?
It’s a measure of the average kinetic energy of gas molecules—the faster they move, the higher the temperature.
51
How does molecular motion relate to pressure?
Molecules collide with container walls, exerting force—this creates pressure. More motion = higher pressure.
52
What are the main processes that change air temperature in the atmosphere?
- Conduction from land to air - Convection transporting heat and mass - Radiation absorbed by gases and particulates - Chemical reactions releasing heat - Expansion/compression due to pressure changes
53
What is a lapse rate?
The rate at which temperature decreases with height in the atmosphere.
54
What is the environmental lapse rate?
The actual rate at which the surrounding atmosphere cools with altitude.
55
What is the parcel lapse rate?
The rate at which a rising air parcel cools with altitude.
56
When is the atmosphere considered unstable?
When the parcel cools more slowly than the environment—making it warmer and more buoyant.
57
When is the atmosphere considered stable?
When the parcel cools faster than the environment—making it cooler and less buoyant
58
What is the dry adiabatic lapse rate?
~10 K/km—applies to unsaturated (dry) air parcels.
59
What is the moist adiabatic lapse rate?
~6 K/km—applies when condensation occurs in moist air parcels.
60
Why is the moist lapse rate lower than the dry lapse rate?
Because condensation releases latent heat, which offsets some cooling.
61
What triggers condensation in a rising parcel?
Cooling to the dew point—water vapour condenses onto aerosols.
62
What is the latent heat of vaporisation?
L_v = 2.5 times 10^6 { J/kg} Energy released when water vapour condenses.
63
What forms when condensation begins?
- Haze: affects visibility and air quality - Fog or clouds: with further cooling
64
What is partial pressure?
The pressure exerted by a single gas component in a mixture.
65
What is the ideal gas law for water vapour?
e = rho_v R_v T Where: - \rho_v: water vapour density - R_v: specific gas constant for water vapour - T: temperature
66
What is saturation vapour pressure e_s(T)?
The maximum partial pressure of water vapour air can hold at a given temperature.
67
What is the Clausius-Clapeyron equation?
e_s(T) = 610.7 e[{L_v}{R_v} ({1}/{273.15} - \frac{1}{T}\right)\right] Where L_v = 2.5 \times 10^6 J/kg is the latent heat of vaporisation.
68
What happens when air reaches saturation and cools further?
Water vapour condenses—forming dew, fog, or clouds.
69
What is relative humidity?
RH = {e}/{e_s(T)} It’s the ratio of actual water vapour pressure to saturation vapour pressure.
70
What does RH = 1 (or 100%) indicate?
Air is saturated—cloud formation is imminent or occurring.
71
What is the mass-mixing ratio r_w?
Mass of water vapour per unit mass of air.
72
How is r_w derived? What does this ratio tell us?
r_w = {\rho_v}/{\rho_a} = {R_a e}/{R_v P} Where: - \rho_v = {e}/{R_v T} - \rho_a = {P}/{R_a T} - How much water vapour is present relative to the total air mass—important for cloud and precipitation modelling.
73
What does Köhler theory describe?
How aerosol particles grow by condensation of water vapour as relative humidity increases.
74
What causes aerosol particles to swell?
Increasing partial pressure of water vapour pushes molecules toward aerosols, which condense onto them.
75
What is the Köhler equation for RH over a particle?
RH = {n_w}/{n_w + nu n_s} e({4 M_w \sigma}{R_{{gas}} T \rho_w D}) Where \nu: dissociation factor, D: particle diameter, n_w: moles of water, n_s: moles of solute.
76
What relates particle size to moles of water and solute?
{pi}/{6} D^3 \rho_{{sol}} = n_w M_w + n_s M_s
77
How is solution density calculated?
\rho_{sol}} = {n_w M_w + n_s M_s}/{{n_w M_w}/{\rho_w} + \frac{n_s M_s}{\rho_s}}
78
What reduces visibility in the atmosphere?
Aerosol particles scatter and absorb light—this is called extinction.
79
What is the extinction coefficient \beta?
\beta = {2 \pi D^2}{4} x N_p Where D: particle diameter, N_p: number density.
80
How is visual range calculated?
{Visual Range} = {K}/{beta} Where K \approx 1.9 (Koschmieder constant)
81
What is particulate matter (PM)?
Solid or liquid particles suspended in air—harmful to human health.
82
How is PM quantified?
In micrograms per cubic metre (µg/m³)
83
What are PM categories?
- PM10: particles <10 µm - PM2.5: particles <2.5 µm - PM1.0: particles <1 µm
Environmental Modelling
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