SO345: Atmospheric Thermodynamics

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SO345 Atmospheric Thermodynamics

• CHAPTER 9
• INTRODUCTION TO MOISTURE MOISTURE VARIABLES

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INTRODUCTION TO MOISTURE MOISTURE VARIABLES

• Up to this point we have been pretty much
  talking about ideal situations like ideal gases,
  reversible processes, and adiabatic processes.
  We have been primarily dealing with dry air,
  which we consider to act as an ideal gas. But
  as we know, the air that we are breathing right
  now is not the perfectly dry air (the ideal gas),
  but moist air which is a mixture of dry air and
  water vapor.

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INTRODUCTION TO MOISTURE MOISTURE VARIABLES

• Water vapor is simply water in gaseous form --
  we can say that water vapor itself also acts as
  an ideal gas (as long as we restrict ourselves to
  conditions far enough away from any potential
  phase changes). Unfortunately when we mix these
  two gtideal gases together, the resultant mixture
  will not act as close to an ideal gas as the
  individual components did. This makes some of
  our moist air calculations a little more involved.

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ATMOSPHERIC MOISTURE VARIABLES

• Scientists and meteorologists have various
  ways of expressing the amount of water vapor or
  moisture in the air. The following are
  definitions of some of the moisture variables
•  
• rv, e, w, q, r, Td, Tw, T ?

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ABSOLUTE HUMIDITY (?v)

• ?v is the density of the water vapor. Since
  density (?) is mass/volume (the inverse of a),
  the mass is the mass of the water vapor (Mv) and
  the volume (V)is the volume of the total air
  sample.
• (Eq 9.1)

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VAPOR PRESSURE (e)

• e is the partial pressure exerted by only the
  water vapor in the sample. The atmospheric
  pressure (p) is equal to e plus the partial
  pressure of dry air.
• - saturation vapor pressure (es)
• es is the upper limit of pressure that can be
  exerted by the water vapor. This upper limit
  (saturation) represents the maximum amount of
  vapor that can remain gaseous (for a particular
  temperature). It should be emphasized that es is
  a very strong function of temperature, and this
  will be highlighted in the Clausius-Clapeyron
  equation section.

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MIXING RATIO (w)

• w is the ratio of the water vapor mass (Mv)
  to the dry air mass (Md).
• (Eq 9.2)
• - saturation mixing ratio (ws)
• ws is the maximum limit of Mv which can
  remain gaseous with a particular Md at some
  temperature and pressure.

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SPECIFIC HUMIDITY (q)

• q is the ratio of Mv to the total moist air
  mass (MvMd). Since the maximum value of Mv is
  always small compared to Md, the values of w and
  q end up being nearly equal.
• (Eq 9.3)
• - saturation specific humidity (qs)
• qs, like ws, is the saturation value
  for q

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RELATIVE HUMIDITY (r)

• r is the percent of the amount of water vapor
  present in the moist air to its saturation limit.
  Since the saturation limit varies with
  temperature and pressure, r is also a function of
  pressure and temperature. r may be expressed in
  equation form by the following ratios of
  variables and their corresponding saturation
  limits
• (Eq 9.4)

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DEW-POINT TEMPERATURE (Td)

• Td is the temperature to which moist air must
  be cooled to at constant pressure and water vapor
  content (example w stays constant) so that the
  air just becomes saturated.

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WET-BULB TEMPERATURE (Tw)

• Tw is the temperature to which moist air must
  be cooled by evaporating water into it at
  constant pressure until the air just becomes
  saturated.
• Note that the difference between Tw and Td is
  that the water vapor content does not stay
  constant for Tw. The air samples vapor content
  must actually increase due to the forced
  evaporation of water into the sample.

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LIFTING CONDENSATION LEVEL (LCL)

• LCL is the level to which moist air must be
  dry adiabatically lifted to reach saturation and
  therefore produce condensation.

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VIRTUAL TEMPERATURE (T)

• T is the temperature at which dry air would
  have to be in order to have the same density as a
  moist air sample, both at the same pressure. The
  practicality of this T definition at this point
  is probably not apparent. The reason for
  devising this fictitious temperature will become
  clear in the discussion of the moist air equation
  of state.
• (Eq 9.5)
• where e (mv/md) 0.622

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BEHAVIOR OF MOISTURE VARIABLES DURING A DRY
ADIABATIC ASCENT

• Now that we have provided the basic
  definitions of many of the moisture variables,
  one good follow up to further understanding these
  variables and how they act, is to take an air
  parcel and lift (or lower) it dry adiabatically.
  It may become clear why some moisture variables
  are better suited to scientific and mathematical
  calculations than others.

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BEHAVIOR OF MOISTURE VARIABLES DURING A DRY
ADIABATIC ASCENT

• During a dry adiabatic ascent, recall that an
  air parcels volume will increase and its
  temperature will decrease. You should be able to
  explain why each of the following moisture
  variables behaves as it does during a dry
  adiabatic ascent.

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BEHAVIOR OF MOISTURE VARIABLES DURING A DRY
ADIABATIC ASCENT

• - absolute humidity (?v) decreases
• - vapor pressure (e) decreases
• - mixing ratio (w) stays constant
• - specific humidity (q) stays constant
• - relative humidity (r) increases
• - virtual temperature (T) decreases
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• (The behavior of the variables not mentioned in
  this adiabatic ascent example es, ws, qs, Td,
  Tw, LCL may not yet be easily explained based on
  the knowledge presented so far).
•  
• (The development of additional moisture variable
  relationships and formulas can be found in
  Appendix F).