Atmospheric Humidity

Objectives:

To measure atmospheric humidity and understand how to express it in a variety of ways.

Background:

Atmospheric humidity or the moisture status of the air is determined in different ways for different purposes. One of the most basic ways of representing it is absolute humidity ($\rho_{{v}}^{}$ ), with units of density, (kg m^-3 or g m^-3 ). This is the mass of water vapour contained in a volume of air, and is also known as the water vapour density. As this measure of humidity varies with pressure and temperature and is difficult to determine, a commonly used alternative and the one used in this lab, is water vapour pressure (e ) with units of pressure (hPa or Pa). e is the partial pressure exerted by vapour molecules in the air. Remember that vapour molecules are just one of the component gases in the atmosphere and represent a small part of the total atmospheric pressure. These two humidity measures are linked through the Gas Law:

e = $$\rho_{{v}}^{}$$R_vT

where:
R_v is the gas constant for water vapour = 462 Pa m³ kg^-1 K^-1 , and T is the absolute temperature (K).

Another very useful humidity measure, is the mixing ratio, r . This is defined as the number of grams of moisture per kilogram of dry air (i.e. air with all the moisture removed). It has units of g kg^-1 and is a useful way to determine humidity as it only depends on the amount of water in the air. Unlike some other humidity measures, it does not vary with air pressure or temperature.
The mixing ratio can be defined as follows:

r = $${\frac{{0.622 \times e}}{{P - e}}}$$ x 1000

where: r is the mixing ratio in g kg^-1 , e is the vapour pressure and P is the air pressure (e and P must have the same units, e.g. hPa).

If a sample of air contains the maximum possible amount of water vapour when it is in equilibrium with liquid water, it is said to be at saturation. This value is dependent on the temperature of the sample, as shown in Table , and Figure , and is called the saturation vapour pressure ( e^*_(T) )^5.1 Similarly, saturation can be defined in terms of the mixing ratio, and is called the saturation mixing ratio (r_s ). A given amount of moisture in a sample can be brought to saturation by cooling it to its dew-point temperature (T_d ). Therefore it follows that the actual vapour pressure (e) of a sample is equal to the saturation value at its dew-point temperature, i.e. e = e^*_(Td) .

Table: Psychrometric table.

Tw (o C)	T - Tw (o C)
	0.0	0.5	1.0	1.5	2.0	2.5	3.0	4.0	5.0	6.0	8.0	10.0
0	100	92	83	75	67	61	54	42	31	22	7	0
2	100	92	84	77	70	64	58	47	37	28	14	2
4	100	93	86	79	73	67	61	51	42	33	20	9
6	100	93	87	81	75	69	64	54	46	38	25	15
8	100	94	88	82	76	71	66	57	49	42	29	19
10	100	94	88	83	78	73	69	60	52	45	33	24
12	100	95	89	84	79	75	70	62	55	48	37	28
14	100	95	90	85	81	76	72	64	57	51	40	31
16	100	96	90	86	82	77	74	66	60	54	43	34
18	100	96	91	86	83	78	75	68	62	56	45	37
20	100	97	91	87	83	79	76	69	63	58	48	39
22	100	97	92	87	84	80	77	71	65	59	50	41
24	100	97	92	88	85	81	78	72	66	61	51	43
26	100	98	92	88	85	82	79	73	67	62	53	45
28	100	98	93	89	86	83	80	74	68	63	55	47
30	100	98	93	89	86	84	80	75	69	65	56	48
32	100	98	93	90	87	84	81	76	70	66	57	50
34	100	98	93	90	87	85	82	76	71	67	58	51
36	100	98	94	91	88	85	82	77	72	68	59	52
38	100	98	94	91	88	86	83	78	73	68	60	53

Figure 5.1: Graph of saturation vapour pressure as a function of temperature. Note this graph also represents vapour pressure as a function of dewpoint temperature.

The degree of saturation is commonly given in terms of the relative humidity (RH):

RH = $${\frac{{e}}{{e^{*}_{(T)}}}}$$ x 100%

or the vapour pressure deficit (vpd ):

vpd = (e^*_(T) - e)

One of the simplest and still most useful techniques for measuring atmospheric humidity is psychrometry. A psychrometer is an instrument that consists of two thermometers one of which has a wetted wick around its bulb (a wet-bulb). The wet-bulb is cooled by evaporation to a temperature that depends on the ambient humidity. From measurements of wet- and dry-bulb temperatures on a properly exposed psychrometer, (T_w and T respectively) humidity can be calculated as follows:

e = e^*_(Tw) - $$\lambda$$(T - T_w)

where $\lambda$ is the psychrometric constant = 66 Pa ^o C^-1 . In this lab you will use this technique to determine and compare the humidity in different areas.

Equipment:

1. several sling psychrometers
2. Väisällä Temperature / RH probe connected to a Campbell Scientific CR10 data logger on lab building roof
3. Canadian Tire ``el cheapo'' hygrometer
4. Assmann-type aspirated psychrometer

Method:

In the classroom, and outside:

1. Record the time of observation, and the ambient weather conditions.
2. To make measurements of water vapour content of the air, you will use a sling psychrometer. Examine the psychrometer and notice the wick on the wet-bulb thermometer. Use distilled water to wet the wick thoroughly. Take the instruments outdoors, and measure the wet- and dry-bulb temperatures. Ventilate the thermometers by spinning them. You will need to wait 3 or 4 min. for the thermometers to reach equilibrium.
3. Record the Väisällä temperature and RH, the Assmann psychrometer temperature and wet-bulb temperature, as well as the ``el-cheapo'' temperature and RH values.

Questions:

1. Calculate the water vapour in the air in the classroom and outdoors.
   1. Using your sling psychrometer measurements calculate the following values for both indoors and outdoors: e, r, vpd, RH, T_d,$\rho_{{v}}^{}$ .

   2. Compare the temperature and relative humidity measurements obtained from the instruments. Which is most accurate and why?

   3. Which of the above measures of humidity ( e, r, vpd, RH, T_d,$\rho_{{v}}^{}$ ) are of use in comparing the actual amount of moisture outside and inside? [HINT: think about which measures of humidity depend only upon the amount of water vapour, and not upon other quantities as well]

   4. Explain any humidity differences between the locations.

   5. If the heating system indoors jammed and temperatures rose considerably what would happen to the values of e, RH, T_d, r ?

2. A cool winter Canadian air mass with a temperature of -4$\mbox{$^{\circ}$}$C and a relative humidity of 91% meets a warm air mass sweeping northward from Texas with a temperature of 17 ^o C and a relative humidity of 28%. In the mixing process will the southern border of the Canadian air gain or lose water vapour content? Explain.