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

POEIdt

dS

Moisture Inflow fromatmosphere

Evapotranspirationfrom ground

Moisture Outflow from column

PrecipitationChange of moisturestorage in the 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)

N

iii pq

gPW

1

1

Sum up the number of levels

Average Specific Humidityfor the layer

Pressure Interval

This will yield the precipitable water in units of kg/m2. To get PW inunits of meters, divide by the density of water (ρw=1000 kg/m3)

w

mkgPWmPW

)/(

)(2

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

z

qw

y

qv

x

quqV

http://ww2010.atmos.uiuc.edu/guides/mtr/af/adv/gifs/madv1.gif