Conservation of Moisture
The Moisture Equation
• Equation of State
• 1st Law of Thermodynamics (Conservation of
Energy)
• Moisture Equation (Conservation of
Moisture)
• Continuity Equation (Conservation of Mass)
• Equations of Motion (Conservation of
Momentum)
– Coming to an ATMS 251 lab near you on March 22
Hydrologic Cycle – What can
happen to moisture?
Moisture Equation
• Mathematical representation of what can
happen to water in a column of the atmosphere
Change of moisture
storage in the
column
Evapotranspiration
from ground
Precipitation
dS
 I  E O  P
dt
Moisture Inflow from
atmosphere
Moisture Outflow
from column
Precipitable Water
• The vertical integral of the specific
humidity for a column of atmosphere
• Represents the upper limit to the total
precipitation that may fall
• Units: m (mm)
Average Specific Humidity
for the layer
1 N
PW   qi pi
g i 1
Pressure Interval
Sum up the
number of levels
This will yield the precipitable water in units of kg/m2. To get PW in
units of meters, divide by the density of water (ρw=1000 kg/m3)
PW (m) 
PW (kg / m 2 )
w
http://www.osdpd.noaa.gov/PSB/IMAGES/images/amsua_tpw_des.gif
Moisture Advection
• Of course, moisture can be transported
horizontally and vertically in the atmosphere
– Moisture Advection

q
q
q
 V  q  u  v  w
x
y
z
http://ww2010.atmos.uiuc.edu/guides/mtr/af/adv/gifs/madv1.gif