METR215 – Advanced Physical Meteorology
Lecture 4: Mixing and Convection
Texts:
Rogers, R.R., and M. K. Yau, A Short Course in Cloud Physics, Pergamon Press, 1989.
Modified from
Steve Platnick
Notes
Cold Cloud Processes
Warm Cloud
Processes
PHYS 622 - Clouds, spring ‘04, lect. 1, Platnick
Water Cloud Formation
Water clouds form when RH slightly greater than 100% (e.g., 0.3%
supersaturation). This is a result of a subset of the atmospheric aerosol
serving as nucleation sites (to be discussed later). Common ways for
exceed saturation:
1.
Mixing of air masses (warm moist with cool air)
2.
Cooling via parcel expansion (adiabatic)
3.
Radiative cooling (e.g. ground fog, can lead to process 2)
Platnick
Video: cloud formation in Tucson
• http://www.youtube.com/watch?v=NiCSk1z
xMEs
Timelapse of Tucson cloud formations
Q: How and why do clouds form on some
days and not on others?
Q: Why does the atmosphere sometimes produce
stratus clouds (thin layered) while other times we get cumulus,
or cumulonimbus clouds to form?
The answer is largely related to the concept of
atmospheric stability.....
Assessing Atmospheric Stability
to assess stability, what two pieces
of information do we need ?
We need to know
• the vertical temperature profile
•The temperature of parcel of the air
Absolute Stability
Absolute Stability
• The condition for absolute stability is:
– Gd>Gm>Ge
• Gd is the dry adiabatic lapse rate (10°C
km-1)
• Gm is the moist adiabatic lapse rate (6°C
km-1)
• Ge is the environmental lapse rate (variable
- 0°C km-1 in this case)
Stability of Inversion Layers
How would you characterize the stability of an inversion layer?
They are absolutely stable
see diagram to the right -->>
note that the absolute stability criteria:
Ge<Gm<Gd
Formation of Subsidence
Inversions
• How does the stability change for a descending layer of
air?
Formation of Subsidence
Inversions
• How does the stability change for a descending layer of
air?
Absolute Instability
• consider the diagram to the right, notice that at 2 km (or anywhere for
that matter):
Tsp > Tup > Te
• Hence, an unsaturated
or saturated parcel will
always be warmer than
the environment and will
continue to ascend
• This is an example of absolute instability
• The condition for absolute instability is:
– Ge>Gd>Gm
•
•
•
Ge is the environmental lapse rate (30°C km-1)
Gd is the dry adiabatic lapse rate (10°C km-1)
Gm is the moist adiabatic lapse rate (6°C km-1)
Conditional Instability
• consider the diagram to the right, notice that at 2 km (or anywhere for
that matter):
• Tup < Te < Tsp
• The unsaturated parcel will be cooler than then environment and will
sink back to the ground
• The saturated parcel will be warmer than the environment and will
continue to ascend
• This is an example of conditional instability
• The condition for conditional instability is:
– Gd>Ge>Gm
• Gd is the dry adiabatic lapse rate (10°C km-1)
• Ge is the environmental lapse rate (7.8°C km-1)
• Gm is the moist adiabatic lapse rate (6°C km-1)
Conditional Instability - example
• consider a parcel with a surface temperature and dew point of 30 °C
and =14°C, respectively -->>
•
•
the parcel is initially forced to rise in an environment where the environmental
lapse rate (Ge) is 8°C km-1 up to 8 km.
let's follow the parcel upward......
Conditional Instability - 1km
the parcel is rising dry adiabitically (10°C km-1)
as it is unsaturated
note Tp < Te so something is forcing
the parcel upward...
onward to 2km ....
Conditional Instability - 2km
• the parcel has just become saturated
• note Tp < Te so something is still forcing
the parcel upward...
• onward to 3km ...
Conditional Instability - 3km
the parcel is now rising moist adiabatically (6°C km-1)
note Tp < Te so, something is still forcing it upward....
onward to 4km .....
Conditional Instability - 4km
• the parcel is still rising moist adiabatically (6°C km-1)
• note that now Tp = Te
• what happens if the parcel is pushed upward just a little???
Conditional Instability - 5km and
above
Conditional Instability - 5km and
above
• note Tp > Te
• A: it will rise on its own since now it is less dense than the surrounding
environmental air
• The height where Tp becomes equal to and then larger than Te is called
the level of free convection
• the parcel is still rising moist adiabatically (6°C km-1)
• the parcel will continue to rise until:
– Tp = Te
• above that point, Tp < Te , so the parcel will rise no further
• so, below 4 km where Tp < Te , the atmosphere is stable to parcel
movement
• above 4 km where Tp > Te , the atmosphere is unstable to parcel
movement
• this is an example of a conditionally unstable atmosphere... the
condition is lifting the parcel above 4 km where it can then rise on its
own
Stability of the environment
• To determine the environmental stability, one must
calculate the lapse rate for a sounding
• lapse rate = DT/DZ = T2-T1/Z2-Z1
• Since the environment is often composed of layers
with different stabilities, it is useful to first
identify these layers and then calculate their
respective lapse rates
• recall the stability criteria:
• Ge < Gm - Absolutely stable
• Gm < Ge < Gd - Conditional Instability
• Gm < Gd < Ge - Absolutely unstable
Stability of the environment
• Characterize the stability of the layers in the
sounding to the right -->
• layer 1
• layer 2
• layer 3
• layer 4
• layer 5
• layer 6
Atmospheric Instability and Cloud
Development
What determines the base (bottom) of a cloud??
Q: What determines the height to which the cloud will grow??
let's use the previous example of a rising air parcel -->>
Q: On this diagram, where is cloud base?
Q: On this diagram, where is cloud top?
Atmospheric Instability and Cloud
Development
•
•
•
•
•
Q: On this diagram, where is cloud base?
A: Where the parcel reaches saturation - 2 km
Q: On this diagram, where is cloud top?
A: Where the parcel will no longer be able to rise - 9 km
Here, Tp = Te - this is often referred to as the
equilibrium level
Concepts of Mixing
es(T)
(T1,e1)
e
saturated
Radiative
Cooling
Mixing
(T2,e2)
unsaturated
T
Hygrometric Chart - Isobaric mixing of two air samples
Platnick
q, w, e, T of the mixed air
• See textbook and notes
M2
• q= M1
q +
M1+M2
W=
e=
T=
1
M1+M2
q2
Saturation Vapor Pressure (Clausius-Clapeyron equation)
At equilibrium, evaporation and condensation have the
same rate, and the air above the liquid is saturated
with water vapor; the partial pressure of water vapor, or
the Saturation Vapor Pressure (es) is:

es (T)  es Ttr  e
Air and
water vapor
T
T Water
L 1 1
( 
)
R v T Ttr
Where Ts=triple point temperature (273.16K), L is the latent heat of
vaporization (2.5106 J/kg), es(Ttr) = 611Pa (or 6.11 mb). Rv is the
gas constant for water vapor (461.5 J-kg1-K1).
specific
Platnick
Saturation Vapor Pressure
An approximation for the saturation vapor pressure
(Rogers & Yau):

e s (T )  Ae
Over liquid water:
L = latent heat of vaporization/condensation,
A=2.53 x 108 kPa, B = 5.42 x 103 K.
Over ice:
L = latent heat of sublimation,
A=3.41 x 109 kPa, B = 6.13 x
103 K.
Platnick
B
T
p R/Cp
Pseudoadiabatic Chart (Stuve diagram)
dry adiabat
saturation
adiabat
saturation
mixing ratio
PHYS 622 - Clouds, spring ‘04, lect.2, Platnick
p R/Cp
Pseudoadiabatic Chart (Stuve diagram)
ex. Parcel at T=30C, 1000mb, w=5 g/kg
dry adiabat
saturation
adiabat
saturation
mixing ratio
PHYS 622 - Clouds, spring ‘04, lect.2, Platnick
p R/Cp
Pseudoadiabatic Chart (Stuve diagram)
ex. Parcel at T=30C, 1000mb, w=5 g/kg
dry adiabat
LCL ≈ 670mb
saturation
adiabat
saturation
mixing ratio
PHYS 622 - Clouds, spring ‘04, lect.2, Platnick
p R/Cp
Pseudoadiabatic Chart (Stuve diagram)
ex. Parcel at T=30C, 1000mb, w=5 g/kg
2 g/kg
dry adiabat
saturation
adiabat
saturation
mixing ratio
Platnick
p R/Cp
Pseudoadiabatic Chart (Stuve diagram)
ex. Parcel at T=30C, 1000mb, w=5 g/kg
2 g/kg => parcel water content at 500mb = 3 g/kg
dry adiabat
saturation
adiabat
saturation
mixing ratio
Platnick
p R/Cp
Pseudoadiabatic Chart (Stuve diagram)
ex. Parcel at T=30C, 1000mb, w=5 g/kg
LWC = 3 g/kg * rd(T,p) = 3 g/kg * (p/RdT)
= 3 g/kg * 0.68 kg/m3 ≈ 2 g/m3
dry adiabat
saturation
adiabat
saturation
mixing ratio
Platnick
Convective development
(mesoscale, local)
Synoptic development
Cold front - steep frontal slopes
Warm front - shallow frontal slopes
PHYS 622 - Clouds, spring ‘04, lect. 1, Platnick
Clouds are difficult, in part, by the nature
of the relevant spatial scales and interdisciplinary fields
Scale
Relevant Physics
synoptic
~1000s km
(large scale dynamics/thermodynamics, vapor fields)
mesoscale
~100s km
local (cloud scale)
<1-10 km
(dynamics/thermodynamics, turbulence, mixing)
particle
µm - mm
(nucleation, surface effects, coagulation,
turbulence, stat-mech)
molecular
PHYS 622 - Clouds, spring ‘04, lect. 1, Platnick
Convective condensation level
(CCL)
• Text book P47
• The convective condensation level (CCL)
represents the height where an air parcel
becomes saturated when lifted adiabatically
to achieve buoyant ascent. It marks where
cloud base begins when air is heated from
below to the convective temperature,
without mechanical lift.
CCL vs LCL
• The convective temperature (CT or Tc) is the
approximate temperature that air near the surface
must reach for cloud formation without
mechanical lift. In such case, cloud base begins at
the convective condensation level (CCL), whilst
with mechanical lifting, condensation begins at the
lifted condensation level (LCL). Convective
temperature is important to forecasting
thunderstorm development.
• LCL and CCL often agree closely with one
another (R&Y, p48)
Convection: elementary parcel
theory
• See Text book p48-50
• Convection can be induced by buoyant or
mechanical forces
• Buoyant convection represents a conversion
of potential energy to kinetic energy.
• Velocity can be determined from eq. of
motion (4.14)
METR215 Clouds
Emphasis on cloud microphysics: cloud particle nucleation, growth
•
Water Clouds
– Formation concepts
– Water path for adiabatic cloud parcel
– Nucleation theory for water droplets (In October)
•
Ice Clouds
•
Aerosol-cloud interaction (Martin Leach + Guest Lecture)
•
Precipitation mechanisms
•
Cloud Modeling (Guest lecture)
PHYS 622 - Clouds, spring ‘04, lect. 1, Platnick