Download Fall 2007

Winter 2010
Geography 2P04
Professor Tony B. Shaw
Lab # 3
Atmospheric Stability and Atmospheric Humidity
Purpose of the Tephigram: A tephigram is a graph showing the vertical distribution of temperature and
water vapor content of the air above a point of the earth’s surface.
It is used to indicate:
(a)
how relative humidity changes at any level if the air is heated or cooled, or if water vapor is
added or taken away
(b)
how air temperature and relative humidity change if the air rises or sinks
(c)
how stable an air mass is, i.e. whether upcurrents will develop if the air mass is heated from the
ground
(d)
whether clouds will form if upcurrents develop or the air mass is lifted
(e)
the likelihood of precipitation
(f)
the difference between air masses
Composition:
(a)
Height: the horizontal lines. Values are given in millibars and meters.
(b)
Temperature (T): solid lines sloping upwards to the right, every 5°C.
(c)
Moisture content (rs): these are dashed lines, also sloping upwards to the right. They are
marked in g kg-1 (i.e. grams of water vapor per kilogram of dry air or mixing ratio). Spacing
of these lines is not linear and values therefore have to be interpolated carefully.
(d)
Dry adiabatic lapse rate (DALR): the rate at which dry (i.e. unsaturated) air cools if lifted in
the atmosphere or alternatively, the rate at which it warms if it sinks. This is a constant rate of
1°C per 100 metres. The dry adiabats are the straight, parallel lines sloping upwards to the left
and are given in K. If the air at any point in the atmosphere rises or falls, its temperature
changes at a rate given by a line, through the temperature parallel to one of these lines
(providing the air does not become saturated).
(e)
Saturated adiabatic lapse rate (SALR): the saturated adiabats are lines curving upwards to
the left. They represent the rate at which saturated air (i.e. air having an RH of 100%) changes
in temperature if it rises or falls. This rate becomes almost the same as the dry adibatic lapse
rate at very low temperatures when even saturated air contains only very small quantities of
water vapor.
Procedure
Plot the following radiosonde measurements for Wilmington, Ohio for October 11, 2006.
(a)
the dry bulb temperature (Temp)
(b)
the dew point temperature (DewP)
2
1. The forecasted maximum temperature at mid-day was 25°C with a surface dew point of 20°C.
Follow the dry adiabatic lapse rate curve and the mixing ratio line and indicate the following:
(a)
(i)
The lifting condensation level (L.C.L. - the height where the RH reaches 100%). The
point at which a line along a dry adiabat through the surface air temperature (T) intersects
a line of the saturation mixing ratio through the surface dew point temperature (T d). Give
the height and corresponding temperature.
(ii)
H
m and mb
(iii)
T
C°
(iv) The height of the lifted condensation level can also be estimated using the following
formula:
Where:
H =
125 (T - Td)
H =
Height of cloud base (in metres)
T
Surface air temperature
=
Td =
Surface dew point temperature
Answer:
(b)
The lifted index is a measure of atmospheric stability that is used in severe storm and tornado
forecasting. Using a forecasted maximum temperature for the day, assume an air parcel is
lifted adiabatically to 500 mb (5.5 km). It will rise at first at the dry adiabatic lapse rate until
saturation occurs at the lifted condensation level. Above this level the air will cool at the
saturated adiabatic lapse rate to the 500 mb (5.5 km). The lifted index is then equal to the
measured temperature (ELR) at 500 mb (5.5 km) minus the temperature of the saturated parcel
of air. It is negative if the temperature of the lifted parcel is greater than the temperature of the
environment. A negative lifted index indicates an unstable atmosphere and a positive lifted
index a stable atmosphere. Tornado activity is usually associated with indices less than -2°C.
0 or greater = Stable Conditions
-1 to -4
= Marginal Conditions
-5 to -7
= Large Instability
-8 or less = Extreme Instability
Estimate the lifted index at the (5.5 km) level.
2
3
(c)
KI - The K-Index is a simple index using data from discreet pressure levels, instead of a lifted
parcel. It is based on vertical temperature changes, moisture content of the lower atmosphere, and the
vertical extent of the moist layer. Where KIs are greater than 35, air mass thunderstorms are likely, the
higher the number, the higher the probability. Values <15 indicate areas of stable weather where skies
are generally clear. The formula for KI is:
KI = (T850-T500) + (TD850-(T700-TD700)) where:
T850 = Temperature at 850mb
T500 = Temperature at 500mb
TD850 = Dewpoint temperature at 850mb
T700 = Temperature at 700mb
TD700 = Dewpoint temperature at 700mb
Calculate the K-Index
(d)
TTI - The Total Totals Index, like the K-Index, is computed using discreet pressure
level information, but is more indicative of severe weather potential. Values of TTI of
around 40-45 indicate the potential for thunderstorms.
Around 50, severe
thunderstorms are possible. Around 55, storms producing tornados are possible. It’s
formula is:
TTI = (T850 + TD850) - 2(T500)
Calculate TTI - Total - Totals Index
(e)
The Severe Weather Threat (SWEAT) Index provides a measure of several parameters,
including instability, low level moisture, wind speed, and wind shear. It serves as an
important tool for determining both severe thunderstorm potential and tornado
potential.
(f)
SWEAT = 12 x TD850 + 20 x (TT -49) + 2 x f850 + f500 + 125 x (s + 0.2)
3
4
(g)
Follow the saturated lapse rate curve to the point where the temperature is the same as
that of the environment. This will indicate the height of the cloud top. What type of
clouds will develop? Give the height of its top and temperature.
(f)
Above the L.C.L. (lifting condensation level) the air, now saturated, follows in the temperature
along a saturated adiabat. It will continue to rise whilst its temperature remains warmer than
its surrounding and clouds will continue to develop as it traces out its ascent path. The area
between ascent path (along a saturated adiabat) and the environment curve represents the
energy available for lift. It is termed the “heating convective energy”. This energy is produced
by the release of latent heat. The greater the area the more intense the ascent of air. Shade in
this area on the tephigram.
(g)
Describe and explain the vertical variation in the moisture content (W) of the air from the
surface to the 250 mb level. What is the relationship to the air temperature?
(h) Calculate the precipitable water between the 1000 - 300 mb levels. If all the vapor, liquid and
solid water within a column of air in the atmosphere were to precipitate out, the resulting depth
of water on the earth’s surface is called the precipitable water, d w . It is given by
d
where
r
w

r
T

g. liq
P
B

P
T
T is average total-water mixing ration, PB and PT are ambient air pressures at
the bottom and top of the column segment,
and Plig  1000 kg  m
3
g  9 .8 m  s 2 is gravitational acceleration,
is density of liquid water.
Solved Example: If an average of 5 g/kg of water existed in the troposphere, between 100 kPa
and 30 kPa, what is the precipitable water depth?
Solution:
Given:
Find:
r
T  0.005 kg / kg , PB  100 kPa , PT  30 kPa
dw  ?m
Use equation and recall
d

w
1kPa  1000 kg air  m  s 2
0.005kg / kg   100  30kPa
9.8m  s   1000kg  m 
liq
air
2
3
liq
= 0.036 m = 3.6 cm
 1.4 inches
4
5
(i)
Describe the relationship between the dew point spread (DD) and the relative humidity (RH)?
(j)
Vertical motion (thermal updraft) is also strengthened by the Polar Front Jet Stream which
pulls up warm moist air from below. The position of the Jet is usually found where wind
speeds are the highest just below the tropopause. Identify the position of the Jet and give its
approximate height.
(k)
Estimate the ventilation coefficient (VC). This is given as the product of the mixing height
(lifted condensation level) and average wind speed below condensation level.
Where:
=
MH x
VC
=
Ventilation coefficient in m2 s-1
MH =
Mixing height in meters (m)
U=
(l)
U
VC
Mean wind speed in m s-1
Describe the general direction from which the winds blow: what type of advection is this?
(i) Below the 850 mb level.
(ii) Between the 850 mb and 250 mb levels - what type of advection is this?
5
6
Table 1
Date:1200Z 11 OCT 06
Station: Wilmingtom, Ohio
WMO ident: 72426
Latitude:
39.42
Longitude: -83.82
Elevation: 317.00
----------------------------------------------------------------LEV PRES HGHT TEMP DEWP RH DD
WETB DIR SPD
mb
m
C
C
%
C
C deg knt g/kg
-----------------------------------------------------------------0 1000
38 18.4 16.2 97 2.2
192
8 11.82
1 970
317 16.2 15.5 96 0.7 15.8 190
9 11.52
2 950
481 16.4 14.2 87 2.2 15.0 201 26 10.78
3 930
705 15.6 11.7 78 3.9 13.2 210 40
9.37
4 900
928 15.8
7.8 59 8.0 11.2 215 41
7.38
5 850 1420 12.0
5.0 62 7.0
8.1 215 45
6.44
6 810 1801
8.4
3.4 71 5.0
5.7 215 47
6.02
7 760 2312
4.0
3.5 97 0.5
3.7 220 47
6.46
8 700 3009
0.0 -0.3 98 0.3 -0.2 220 49
5.35
9 660 3480 -1.7 -1.7 100 0.0 -1.7 224 40
5.12
10 560 4693 -7.1 -9.1 86 2.0 -7.9 232 32
3.39
11 500 5650 -13.7 -14.4 94 0.7 -13.9 245 33
2.51
12 470 6101 -17.3 -18.3 92 1.0 -17.6 250 38
1.92
13 420 6883 -21.7 -31.7 40 10.0 -23.5 247 42
0.63
14 400 7310 -25.1 -37.1 32 12.0 -26.8 245 44
0.40
15 300 9330 -40.7 -52.7 26 12.0 -41.3 215 66
0.10
16 270 10085 -47.3 -50.1 73 2.8 -47.4 210 77
0.15
17 250 10540 -51.1 -57.1 49 6.0 -51.3 210 58
0.07
18 240 10804 -53.5 -59.5 48 6.0 -53.7 211 60
0.05
19 200 11960 -60.3 -65.3 52 5.0 -60.4 220 84
0.03
20 190 12412 -62.7 -68.7 44 6.0 -62.8 225 84
0.02
21 170 12897 -61.8 -68.5 40 6.7 -61.9 230 95
0.02
22 150 13750 -60.1 -68.1 34 8.0 -60.2 230 60
0.03
23 140 14182 -59.7 -67.7 35 8.0 -59.9 235 70
0.03
24 130 14740 -62.9 -70.9 33 8.0 -63.0 241 79
0.02
25 100 16280 -58.3 -67.3 31 9.0 -58.6 250 5
0.04
26
98 16407 -58.1 -67.1 31 9.0 -58.4 247 48
0.05
27
80 17667 -62.7 -71.7 29 9.0 -62.9 245 32
0.03
28
70 18490 -61.3 -69.3 34 8.0 -61.6 260 34
0.05
29
65 18952 -58.9 -66.9 35 8.0 -59.2 270 35
0.07
30
55 19990 -62.9 -70.9 33 8.0 -63.1 256 29
0.05
31
50 20580 -60.1 -69.1 30 9.0 -60.5 250 27
0.07
32
45 21242 -57.5 -66.5 31 9.0 -58.1 259 29
0.11
33
37 22476 -58.1 -68.1 27 10.0 -58.8 260 26
0.11
TRP 186 12412 -62.7 -68.7 44 6.0 -62.8 225 84
0.02
WND 172 12897 -61.8 -68.5 40 6.7 -61.9 230 95
0.02
6