Download Understanding the Dew Point - NCCTM 2014

NCCTM 2014
Angela Teachey
NC School of Science and Mathematics
[email protected]
• Refers to the amount of water vapor in the air.
• In much of the eastern US, summers are usually
hot & humid, suggesting very uncomfortable
conditions outdoors.
BUT… hot, “dry” desert heat usually
has MORE water vapor than cold,
“damp” polar air.
Does that mean that “dry” desert air is
more humid than “damp” polar air?
• Answer: YES and NO.
• It depends on the TYPE of humidity in
question!
1. 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑟 (𝑔)
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎𝑖𝑟 (𝑚3 )
Absolute humidity is, thus, the density of water vapor
in the air parcel and is normally measured as grams
of water vapor per cubic meter of air.
2.
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑟(𝑔)
𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑎𝑖𝑟 (𝑘𝑔)
• Specific humidity is not affected by
changes in the volume of air.
• Specific humidity remains constant as long
as water vapor is not added to or
removed from the air.
• Important note: Warm air has a greater capacity for
water vapor than does cold air.
• The temperature of air is the measure of average kinetic energy of
its molecules. Higher temperatures Higher average speed
• At higher temperatures, condensation is less likely because most of
the molecules have sufficient speed (and energy) to remain a
vapor.
• As temperatures decrease, the average speed of molecules
decreases, and fewer molecules have sufficient speed (and energy)
to remain in the air as a vapor.
• SO… Because “damp” polar air cannot hold as much water vapor
in the first place as warm desert heat, the desert heat most likely
has a HIGHER SPECIFIC HUMIDITY than polar air.
• Another way to describe air’s moisture content is
by measuring the pressure exerted by the water
vapor in the air.
• The total pressure inside an air parcel is due to
the collision of all of the molecules against the
inside surface of the parcel.
• The total pressure inside the parcel is equal to
the sum of the pressures of the individual gases.
• Ex. If the air pressure for a parcel is
1000 mb and the gases include 78%
nitrogen, 21% oxygen, and 1% water
vapor, then what would be the partial
pressures of each component?
• The partial pressure of the water vapor (10 mb in this
case) is called the ACTUAL VAPOR PRESSURE.
• Actual vapor pressure is a good measure of the total
amount of water vapor in the air because high actual
vapor pressure indicates the presence of relatively
large numbers of water vapor molecules while low
actual vapor indicates the presence of relative low
numbers of water vapor molecules
• SATURATION VAPOR PRESSURE is the pressure that
water vapor molecules would exert if the air were
saturated with vapor at a given temperature.
3. 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦 =
𝑎𝑐𝑡𝑢𝑎𝑙 𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
∗ 100%
• So, which has the higher relative humidity?
• “Damp” polar air at 20 degrees Fahrenheit with actual vapor
pressure 3.4 mb and saturation vapor pressure 3.7 mb.
• OR “Dry” desert heat at 110 degrees Fahrenheit with actual
vapor pressure 40.2 mb and saturation vapor pressure 87.8
mb?
• Why, then, is the relative humidity reported by your
TV meteorologist not particularly helpful in revealing
how humid it will feel outside?
• Why do we suffer with such horribly dry skin and
chapped lips during the winter months?
• The dew point is the temperature when relative humidity is
100%, or 𝑎𝑐𝑡𝑢𝑎𝑙 𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
• Why do you think it’s called the dew point?
• What could be another name if the dew point is below
freezing?
• Why, then, is dew point a more useful statistic for TV
meteorologists to report if viewers understand what it is?
• In the fall, we often have temperatures of 78o with dew points in the 30s
or 40s.
• In the summer, we see dew points in the low 70s with highs in the 80s and
90s.
• Why does it not usually feel “humid” when the weather is cold (even if the
relative humidity is high)?
• Temperatures cannot fall below the dew point!
• So… dew point temperatures can be a good guess of
the minimum possible overnight low temperature
UNLESS…
• the air mass changes overnight, sometimes the dew point will
drop in tandem with the temperature.
• other atmospheric conditions like cloud cover or wind prevent
the temperature from falling as much as it might on a clear
night.
• Generally, dew points in the 50s and below feel
pretty comfortable to humans. Dew points in the 70s
mean oppressive humidity.
• When temperatures are high and dew points are close to
high temperature (high relative humidity), sweat cannot
evaporate easily from human skin. Since the evaporation
of sweat is an essential cooling mechanism for the body,
hot and humid summer days feel very uncomfortable.
• The National Weather Service combines air temperature
with relative humidity to calculate a heat index that is
reported to inform people of the temperature that it “feels
like” outside. This is an effort to inform citizens when their
body could experience adverse effects from the weather
conditions.
Given an air temperature (T) in degrees Fahrenheit and a
relative humidity (rh), which requires knowing the dew
point, we can calculate the heat index with this formula:
Source: http://www.srh.noaa.gov/
OR…
Source: weather.com
The data:
Source: Meteorology Today, 4th Edition, C.D. Ahrens, 1991
.
• Original data (𝑎𝑖𝑟𝑡𝑒𝑚𝑝, 𝑆𝑉𝑃) where
𝑆𝑉𝑃 = 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
• After educated guess and check, linearize by
(𝑎𝑖𝑟𝑡𝑒𝑚𝑝, ln(𝑆𝑉𝑃 + 2.5))
• Linear Model: ln 𝑆𝑉𝑃 + 2.5 = 0.03057 ∗ 𝑎𝑖𝑟𝑡𝑒𝑚𝑝 + 1.171
ln 𝑆𝑉𝑃 + 2.5 = 0.03057 ∗ 𝑎𝑖𝑟𝑡𝑒𝑚𝑝 + 1.171
𝑆𝑉𝑃 + 2.5 = 𝑒 0.03057∗𝑎𝑖𝑟𝑡𝑒𝑚𝑝+1.171
𝑆𝑉𝑃 + 2.5 = 𝑒 1.171 ∗ 𝑒 0.03057∗𝑎𝑖𝑟𝑡𝑒𝑚𝑝
𝑆𝑉𝑃 = 3.225 ∗ 𝑒 0.03057∗𝑎𝑖𝑟𝑡𝑒𝑚𝑝 − 2.5
𝑆𝑉𝑃 = 3.225 ∗ 𝑒 0.03056∗𝑎𝑖𝑟𝑡𝑒𝑚𝑝 − 2.5
Thinking about 𝑆𝑉𝑃 = 3.225 ∗ 𝑒 0.03057∗𝑎𝑖𝑟𝑡𝑒𝑚𝑝 − 2.5
• What does the model tell us about
humidity?
• Domain and the horizontal asymptote
• For what change in air temperature does
saturation vapor pressure double or
triple?
• Built-in Regression Function on TI is 𝑦 = 𝑎 ∗ 𝑏 𝑥 . Not
preferred by physicists because there is no way to
eliminate units in the exponent. 𝑏 𝑥 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝐹𝑎ℎ𝑟𝑒𝑛ℎ𝑒𝑖𝑡 has
no real world meaning.
• Better to use a manually defined model on TI or use other
graphing utility that has a model of the form 𝑦 = 𝑎 ∗
𝑏 𝑐𝑥 + 𝑑 where the c can include a factor where the units
are divided (ex. 1/32 could be a factor of c in the case
of temperature) and where a vertical shift can be included.
• When using built-in functions on technology, you are
making assumptions about the nature of the data. Reexpression allows us to see if data are actually
exponential, quadratic, cubic, etc.
Practice Problems
𝑆𝑉𝑃 = 3.225 ∗ 𝑒 0.03057∗𝑎𝑖𝑟𝑡𝑒𝑚𝑝 − 2.5
Discussion/Questions
Thank you for coming and…
Angela Teachey
NCSSM
[email protected]