LAB #5
MIXING RATIO, SATURATION MIXING RATIO AND RELATIVE HUMIDITY
METR 101
NAME: __________________________________
DUE DATE: Tuesday, October 13, 2009
-
80 POINTS
Task 1 - CREATING A GRAPH OF TEMPERATURE AND SATURATION
MIXING RATIO (30 Points)
Using the data in the chart below, construct a graph with temperature on the x-axis and
saturation mixing ratio on the y-axis. Make sure that your axes have consistently valued
intervals.
Use the following chart to assist you in constructing your graph:
At a pressure of 1000mb
Saturation
Mixing
0.1
Ratio (g/kg)
Temperature
(degrees C)
-42
At a pressure of 1000mb
Saturation
Mixing
10.0
Ratio (g/kg)
Temperature
(degrees C)
14
0.6
1.0
2.0
5.0
-22
-18
-9
4
20.0
40.0
25
37
The saturation mixing ratio (ws) represents an air parcel’s maximum capacity for water
vapor. At constant pressure, this value is dependent on the temperature of the air parcel.
For instance, a saturation mixing ratio of 20 g/kg means that for every kilogram of dry
air, the air can hold at most 20 grams of water vapor.
Task 2 - Using the graph you constructed, answer the following questions:
(20 Points)
1) What is the difference in saturation mixing ratio between an air parcel at -15 degrees
C and an air parcel at 0 degrees C? (Answer in units of g/kg pronounced “grams per
kilogram”)
2) What is the difference in saturation mixing ratio between an air parcel at 0 degrees C
and an air parcel at 15 degrees C?
3) What is the difference in saturation mixing ratio between an air parcel at 15 degrees C
and an air parcel at 30 degrees C?
4) As temperature increases, saturation mixing ratio increases (under constant pressure
conditions). Using your answers to #1-3 above, over what interval (-15 to 0, 0 to 15,
15 to 30) does the saturation mixing ratio increase the most?
5)
Given the saturation mixing ratio value you obtained for #2 above, what is the
maximum number of grams of water vapor that 5 kilograms of dry air at 0 deg C can
hold?
MIXING RATIO
The mixing ratio (w) of an air parcel (also measured in grams of water vapor per
kilogram of dry air) represents the actual amount of water vapor contained in an air
parcel, as opposed to the saturation mixing ratio which tells the maximum amount of
water vapor that an air parcel can hold.
For instance, an air parcel could have a saturation mixing ratio of 10 g/kg while having a
mixing ratio of 5 g/kg. This means that while the maximum capacity for water vapor is
10 grams of water vapor for each kilogram of dry air, the actual amount of water vapor
contained is 5 grams for each kilogram of dry air.
We can use the mixing ratio and the saturation mixing ratio values to calculate a well
known measure of atmospheric water vapor content, relative humidity.
Relative Humidity can be calculated by using the following equation:
Relative Humidity (in %)
=
Mixing ratio(g/kg)……
Saturation Mixing Ratio (g/kg)
x
100%
In the given example, an air parcel with a mixing ratio of 5 g/kg and a saturation mixing
ratio of 10 g/kg would have a relative humidity of:
RH
= 5/10 x 100%
=
0.5 x 100%
=
50%
Meaning that the air is at
half-capacity with
respect to water vapor.
Task 3 – (30 Points)
For the following questions, assume that the air parcel is at a pressure level of 1000 mb.
Use the table on the first page to determine the saturated mixing ratio.
Show your work:
1. An air parcel has a mixing ratio of 5 g/kg and a saturation mixing ratio of 20 g/kg.
What is the relative humidity of this air parcel?
2. An air parcel at a temperature of 14 deg C has a mixing ratio of 5 g/kg.
What is the relative humidity of this air parcel?
3. An air parcel at a temperature of 20 deg C has a mixing ratio of 5 g/kg.
What is the relative humidity of this air parcel?
4. The air parcels in questions #2 and #3 above have equal mixing ratios (5 g/kg) and yet
they have different relative humidity’s. Given a constant mixing ratio, how does the
relative humidity of an air parcel change as temperature increases?
5. An air parcel at 25 deg C is at 100% relative humidity. What is the mixing ratio of
this air parcel?
If this parcel cools to a temperature of 14 deg C, how many grams of water must
condense inside the parcel?