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Changes in Rising and Sinking Air: Adiabatic Processes
Process Lapse Rates
When air rises it is depressurized and expands. As a result its temperature falls.
When unsaturated air rises, its rate of cooling or lapse rate is called the Dry
Adiabatic Lapse Rate (DALR). It is a constant equal to,
DALR  10C/km.
Expansion also causes Td of unsaturated air to decrease by about 2C/km.
If air rises and cools enough it eventually becomes saturated. When saturated
air rises, T and Td cool together at the Saturated Adiabatic Lapse Rate
(SALR). The SALR is always less than the DALR because vapor condenses
and releases heat to the surroundings as saturated air cools. This offsets the
cooling due to expansion. The warmer the saturated air more vapor it holds and
the more rapid the condensation and heating rates. As a result,
SALR < 5C/km
in very warm air
SALR > 9C/km
in very cold air.
Exact values of SALR and condensation rates can be found by using the SkewT diagram. The next slide shows how rapidly cooling and condensation occur
for two samples of air. The second slide gives a good approximation to use
when you do not have a Skew-T diagram handy (i. e., the rest of your lives).
The warmer air has a larger
mixing ratio that decreases
more rapidly while its T
decreases more slowly.
Even though SALR varies, it is useful to approximate it with a typical value,
SALR  6C per km. Therefore, use the rules below (illustrated in the diagram
to the right) when calculating changes of T and Td when air rises or sinks.
Rising Unsaturated Air (T > Td)
T cools 10C per km
(upward)
Td cools 2C per km
Rising Saturated Air (T = Td)
T and Td both cool 6C per km
Sinking Air*
T warms 10C per km (downward)
Td warms 2C per km (downward)
These rules are valid whether air rises
vertically in a thunderstorm, or obliquely
over a front.
*Because most rain and snow fall out of the
clouds, little is left to evaporate once air
begins to sink. The sinking air then quickly
becomes unsaturated. both T and Td then
increase at the rates for unsaturated air.
On the next two slides we use these rules to find how T and Td
change as air passes over a 1: mountain and, 2: a dome of cold air.
3 km
2 km
1 km
0.5 km
Here it is necessary to move upwards at ½ km steps
The Chinook is a warm, dry downslope wind. It occurs in many mountainous regions but
has different local names (Foehn in Germany, Zonda in Argentina, Santa Ana in Los
Angeles, etc.). The air on the right ends up warmer and drier than it started on the left
because vapor condensed (adding latent heat to the air) and precipitated out of the air
when the air rose on the windward side of the mountains.
Height
(km)
3.0
Cross Sections and Precipitation Form
T=-2 Td=-2
2.5
T=01 Td=01
2.0
T=04 Td=04
1.5
T=07 Td=07
1.0
T=12 Td=08
0.5
0.0
T=17 Td=09
T=09
Precipitation Form
Reasons
T=06
T=03
T=-1
None
R?
R
ZR, IP
S
Air aloft
unsaturated
Air aloft
just at
LCL.
Any ppt
is rain
because
T > 0 at
ground
T > 0 at
ground
so ppt
melts
T > 0 aloft
so ppt
melts; T <
0 at ground
so ppt
refreezes
T < 0 at
all levels
so snow
never
melts
As warm and cold air masses converge in low pressure,
a front forms at the boundary and the warm air slides
over the dome of cold air like a conveyer belt. As we
have seen, the form of precipitation depends on T both
aloft and at the surface. T aloft is determined by the
DALR and SALR as the warm air rises.
T=-2
When will
air rise freely?
When it is heated and buoyant and the atmosphere is unstable.
Stability
Thunderstorms form when a rising bubble or parcel of air, which is indicated by the
process lapse rate, is warmer and hence lighter than the sounding of the surrounding
atmosphere. This condition is unstable. On the other hand, vertical motions are
suppressed when the rising parcel is colder and denser than the surrounding
atmosphere. This condition is stable and leads to polluted air when winds are light and
there is a source of pollution. Therefore,
Unstable Atmosphere
Stable Atmosphere
Sounding T decreases faster with height than rising parcel.
Sounding T decreases slower with height than rising parcel.
Atmospheric stability is determined by the following steps:
1. Draw the sounding.
2. Lift a parcel of air from ground level using the process cooling rate for unsaturated air
to the point of saturation and the process cooling rate for saturated air thereafter.
3. Compare temperatures of sounding and lifted parcel. The atmosphere is unstable if
the lifted parcel is warmer then the sounding and stable if the lifted parcel is cooler.
Sometimes, the lifted parcel will be cooler than the sounding for the first few hundred
meters of lifting but warmer at some greater heights. This means that the atmosphere
will need a push to get it going. Such an atmosphere is potentially unstable, and the
instability will be realized only if the air near the ground is heated further, or if some
atmospheric process forces the entire atmosphere to rise. Examples of forced rising
include upslope flow against mountains or over frontal surfaces.
When rising air crosses the tropopause it
becomes colder than the surroundings, and
sinks back to its equilibrium level
TROPOPAUSE
Thunderstorms form when T of the
surrounding atmosphere falls more
rapidly with height than T of the rising
air from near ground level. This is an
atmosphere with an unstable lapse
rate.
Slightly Hotter Ground
15
20
15
1 km
22
20
22
Stability Exercises
If a person is disturbed – given a push – and is
not fazed by it, that person is stable. Similarly,
if a balloon or parcel of air is given a push
upwards and sinks back to the original level it
is stable. But if the parcel accelerates up after
the initial upward push it is unstable.
The procedure to determine stability is:
1. Lift the air parcel 1 km, changing its T by
the DALR if it is unsaturated and by the SALR
if it is saturated.
2. Compare T of the parcel to T of the
environment at the same height (1 km).
If the lifted air parcel is warmer (colder) than
its new environment at 1 km it will be lighter
(denser) and will accelerate up (down). This
situation is unstable (stable).
T = 30 30 Td = 10
0 km
T = 30
30 Td = 10
The atmosphere to the left (right) is unstable (stable) because the lifted parcel is warmer (colder) than the
surroundings. In both cases the rising, unsaturated air cooled at the same rate (the DALR) because it is
governed by a PROCESS while the surroundings differed because they represent changeable SITUATIONS.
Stability and Inversions
3000
2500
2000
1500
1000
Subsidence
Inversion
500
Fog or Low Stratus
0
-5
0
5
10
15
20
25
30
Inversions indicate extremely stable
situations. Cold air below is much too
dense to rise, while warm air above
is much too light to sink. Inversions
are associated with air pollution
outbreaks (especially when winds
are light or calm) precisely because
pollutants cannot be dispersed aloft
unless the wind is very strong.
Inversions can be destroyed by
heating the air below. This happens
almost every clear day near the
ground. Overnight the ground cools
and an inversion forms in the lowest
few hundred
meters
of
the
atmosphere. The rising sun heats the
ground, which heats the air near the
ground until it becomes warmer than
the air above and rises. This
destroys the inversion, disperses
pollutants upward and may even
sprout cumulus or thunderstorms.
The Skew_T Log_ p Diagram
Thermodynamic diagrams are graphical computers for calculating adiabatic
processes and resulting changes of temperature and humidity. (The first such
diagram was created by James Watt, to calculate changes of pressure and
temperature in the steam engine as water boiled and as steam condensed!)
The Skew-T is the standard thermodynamic diagram used by meteorologists.
It was designed to depict most soundings as more or less vertical lines.
In the typical sounding diagram the x axis represents temperature and the y
axis represents height or some function of decreasing pressure. Therefore,
isotherms or lines of constant T are vertical lines while isobars or lines of
constant pressure are horizontal lines.
But T decreases so drastically with height in the troposphere, that the only
way to depict atmospheric soundings as more or less vertical lines is to make
isotherms slope up to the right. This is what makes the Skew-T so useful to
meteorologists but so difficult to learn to read.
The following slides show how the Skew-T is designed and how it acts as a
process calculator.
Skew_T: Key to Lines
Isobar p
Skew-T Diagram of Sounding of a Snowstorm at Upton, NY
Td
T
Inversion
Now let us use the SKEW-T as a calculator
Isobar p
For air starting at p = 1000 hPa,
T = 25C, Td = 0C, find the
1. Mixing Ratio, w
2. Saturated Mixing Ratio, ws
3. Relative Humidity, RH
4. Lifting Condensation Level, LCL
LCL
For air starting at p = 1000 hPa, T = 25ºC,
Td = 0ºC and rising to p = 300 hPa, find
1. T
2. Mixing Ratio, w
3. Amount of Condensed Vapor
4. Wet Bulb Temperature, Tw
Isobar p
LCL
Td
T
Solutions
1. Lifting Condensation Level (LCL) = 690 hPa
2. w = 3.8 ppt
ws = 22 ppt
3. RH = w/ws = 3.8/22 = 17 %
4. Tw = 11oC
5. At 300 hPa, T = -50.5oC, w = 0.12 ppt, Dw = 3.68 ppt
Isobar p
Run SKEW_T
LCL
Td
Tw
T
The Lifted Index (LI) gives a
simple measure of the degree
of instability. Lift air from the
surface to 500 hPa. Subtract
Tpar of the lifted parcel from
Tenv of the environment or
sounding (LI = Tenv-Tpar). The
warmer the parcel compared
to the environment the
greater the instability and the
more negative LI.
A parcel accelerates upward
so long as it is warmer than
the environment (indicated by
the green area). Once the
rising parcel is colder than the
surroundings, it will slow.
Cloud top occurs where the
negatively buoyant purple
area is about half the buoyant
green area.
Example of the Lifted Index
Lift air from p = 1000 hPa, T = 25oC, Td = 0oC to 500 hPa. Find the LI.
Lifted Index  T500 - TLP = -16 - (-22) = 6
Sounding T
The Lifted Parcel is colder than the
surroundings or sounding (thick black
line). LI is positive and the air is
stable. No convective showers or
thunderstorms will occur.
Sounding Td
TLP
T500
Td
T
Sparking Convection
Thunderstorms are children of the afternoon. The air near the ground cools at night,
stabilizing the morning sounding. But since the air more than 50 or 100 hPa above
ground level changes little from day to night (aside from changes due to wind) the
sounding provides crucial information about the probability, timing, and intensity of
thunderstorms later in the day. The Convective Temperature (TC) is the minimum
surface temperature to start convection and the Convective Condensation Level
(CCL) is the level of the cloud base once the surface air warms to TC. The pink area
is proportional to the heat that must be added to reach TC.
CCL
TC
Convective Available Potential Energy
Convective Inhibition
CAPE or Convective Available Potential Energy is the maximum energy
available to a rising air parcel in an unstable atmosphere. It is proportional to
the green area between the Temperature of the Lifted Parcel and the
Temperature of the Sounding of the next slide. Values of CAPE greater than
1500 indicate strong thunderstorms are possible.
CIN or Convective Inhibition is the energy an air parcel near ground level
needs to reach the Level of Free Convection (or level above which a rising
parcel becomes warmer than the surrounding air – indicated by the red
circle). Often in the morning the air near the ground is stable and restricts
convection. Only when the Sun heats the air enough or when large scale
motions lift the air enough is CIN eliminated. Then convection starts.
CAPE
Isobar p
Level of Free Convection
CIN
Td
T
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