Relative Humidity

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Introduction

Relative humidity is, perhaps, the most common measure of atmospheric moisture, especially among lay persons and on radio and television forecasts. The reason is probably because it seems easiest to understand at first glance. It describes how close the air is to being saturated. When the relative humidity is 100% the air is saturated. The lower the percentage is below 100%, the drier the air is.

In this activity you will practice computing the relative humidity and inspect a weather product that uses it.

Objectives

Be able to compute and interpret relative humidity.

References

Your text: pages 77-81 and page 406

Instruction

Symbols

To simplify our mathematics, we will use the following symbols for the remainder of this lab:

    e = actual vapor pressure in millibars
    es = saturation vapor pressure in millibars
    RH = relative humidity
    T = air temperature or dry-bulb temperature
    Tw = wet-bulb temperature
    Td = dew-point temperature

The Relative Humidity Formula

The relative humidity can be calculated from the formula

RH = ( e / es ) * 100%

where e is the value adjacent to the dew-point temperature and es is the value adjacent to the temperature in Table 1 below. For example,

if T = 60°F and Td = 50°F, then RH = ( 12.3 / 17.7 ) * 100% = 69% 

if T = 13°C and Td = 2°C, then RH = ( 6.9 / 14.8 ) * 100% = 47%

Table 1  Saturation Vapor Pressure over Water for Various Air Temperatures (Identical to TABLE B.1 in the appendix of your text)

Temperature
(°C)

Temperature
(°F)

Vapor Pressure
(mb)

-18

0

1.5

-15

5

1.9

-12

10

2.4

-9

15

3.0

-7

20

3.7

-4

25

4.6

-1

30

5.6

2

35

6.9

4

40

8.4

7

45

10.2

10

50

12.3

13

55

14.8

16

60

17.7

18

65

21.0

21

70

25.0

24

75

29.6

27

80

35.0

29

85

41.0

32

90

48.1

35

95

56.2

38

100

65.6

41

105

76.2

43

110

87.8

46

115

101.4

49

120

116.8

52

125

134.2

Interpolation in Tables

To obtain the vapor pressure corresponding to a temperature that is not given in the table, it is common to use a procedure referred to as linear interpolation (or just interpolation).

The basic mathematical concept behind interpolation is that of ratios or fractions. When the value of one parameter falls between those listed in the table, we calculate the ratio or fraction that represents the distance it is above the smaller of the table entries that it is between. For example, a temperature of 67°F falls between the table entries of 65°F and 70°F. In fact, it is  (67-65)/(70-65) = 2/5  of the distance from 65°F to 70°F. Now observe the vapor pressure entries in the table associated with 65°F and 70°F. They are 21.0 and 25.0 mb, respectively. We will now associate 67°F with a vapor pressure that is between 21.0 and 25.0 and 2/5 of the way above 21.0. The total distance from 21.0 to 25.0 is 4.0. Two-fifths of this distance is (2/5)*4.0 = 1.6 mb. So the vapor pressure we associate with 67°F is  21.0 + 1.6 = 22.6 mb. Here is one way to write the computation:

    e = 21.0 + (67 - 65) / (70 - 65) * (25.0 - 21.0)
       = 21.0 + (2/5)* 4.0
       = 21.0 + 1.6
       = 22.6

Be sure that you understand the computation above and then study the following examples.

1. Estimate the vapor pressure corresponding to a temperature of 21°F.

    e = 3.7 + (21-20)/(25-20)*(4.6-3.7) = 3.9 mb

2. Estimate the vapor pressure corresponding to a temperature of 12°C.

    e = 12.3 + (12-10)/(13-10)*(14.8-12.3) = 14.0 mb

Relative Humidity Calculations Using Interpolation

To complete the calculations of relative humidity given the temperatures and dew points in the following table, you will need to use interpolation to obtain some of the vapor pressures. Be sure that you understand the computations of e, es, and RH before continuing.

  T Td es mb e in mb RH = (e/es)*100%
1 9°F 0°F 2.3 1.5

65%
2 48°F 41°F 11.5 8.8 77%
3 39°F 39°F not required since T = Td not required since T = Td 100%
4 10°C -6°C 12.3 4.0 33%
5 30°C 20°C 43.4 23.7 55%
6 21°C 21°C not required since T = Td not required since T = Td 100%

Web Examples

Recall in the introduction to this activity, we stated that relative humidity is commonly used among lay folk because it seems easiest to understand at first glance. However, it is not the most commonly used by meteorologists, as it doesn't indicate how much moisture there actually is in the air. Among the moisture variables we will discuss, the dew point temperature is the best indicator of the actual amount of moisture in the air. We will return to this point in later activities.

Let's inspect three common meteorological products and notice that the two that meteorologists are more likely to use (Meteograms and Surface Plots) include only the dew point, whereas the Weather Roundups have both dew point and relative humidity. Locate the appropriate product to compare Portland, Maine in all three of the products. Are all three reporting the same T and Td for Portland? Is the Weather Roundup the only one reporting RH?

Meteogram (select KPWM)

Regional Surface Plots (select Current Weather)

Current Weather Reports for Maine

Practice Questions

1. Estimate the vapor pressure corresponding to a temperature of 51°F.

2. Estimate the vapor pressure corresponding to a temperature of 26°C.

3. Calculate the relative humidity for a temperature of 31°F and a dew point of  21°F.

4. Calculate the relative humidity for a temperature of 23°C and a dew point of  12°C.

5. Calculate the relative humidity for locations a, b, and c below.

    a.  ne_plots.gif (62750 bytes)      b.  sp_plots.gif (65703 bytes)     c.  sw_plots.gif (54700 bytes)

6. In the Florida State Weather Roundup below, check the RH calculations for the the underlined locations. Differences of 1-2% may be attributed to rounding in the vapor pressure table and in the calculations.

FLORIDA STATE WEATHER ROUNDUP
NATIONAL WEATHER SERVICE MIAMI FL
1000 AM EST SAT JAN 23 1999  
NOTE: FAIR INDICATES FEW OR NO CLOUDS BELOW 12,000 FEET WITH NO
SIGNIFICANT WEATHER AND/OR OBSTRUCTIONS TO VISIBILITY.  
CITY           SKY/WX   TEMP DEWPT RH  WIND    PRES    REMARKS  
FLORIDA
CRESTVIEW      TSTM      65   63   93  S8      29.85R  
CROSS CITY      N/A      75   67   76  S16G21  30.01F  
DESTIN         CLOUDY    66   63   90  S12G20  29.84S  FOG     
GAINESVILLE    CLOUDY    74   67   79  S14     30.06S  
JACKSONVILLE   CLOUDY    76   69   79  S16G21  30.06F  
MARIANNA       RAIN      63   62   97  SE9     29.91S  
ST AUGUSTINE   MOSUNNY   75   64   69  S20G25  30.08S  
TALLAHASSEE    LGT RAIN  70   68   93  S13G23  29.96R  
VALPARAISO     SHOWER    66   64   93  S29     29.86R  
BARTOW         CLOUDY    75   70   84  SE17    30.13R  
BROOKSVILLE    CLOUDY    75   70   84  SE14G21 30.07S  
DAYTONA BEACH  PTSUNNY   78   70   76  SE10G17 30.12S  
OCALA          CLOUDY    75   66   74  S10G17  30.07S  
ORLANDO        PTSUNNY   76   70   82  S15     30.10S  
WINTER HAVEN   CLOUDY    75   69   82  SE18G22 30.10R  
LEESBURG       CLOUDY    74   69   84  SE14G21 30.08F  
ST PETERSBURG  MOSUNNY   76   69   79  SE17    30.04F  
TAMPA          CLOUDY    75   69   82  SE14G20 30.06S  
NAPLES         PTSUNNY   77   70   79  SE9     30.08R  
FT MYERS       MOSUNNY   77   71   82  SE17    30.06S  
SW RGNL ARPT   PTSUNNY   77   70   79  SE15G22 30.07R

Answers

1. e = 12.8 mb

2. e = 33.2 mb

3. RH = (3.9/5.9)100% = 66%

4. RH = (14.0/28.1)100% = 50%

5.   a. 100%      b. 33%      c. 38%  

Some details of the calculations for 5 b and c

b. T=35°F so es = 6.9 mb, Td=9°F so e = 1.9 + 0.8*0.5 = 2.3 mb, RH = (2.3/6.9)*100% = 33%

c. T=44°F so es = 8.4 + 0.8*1.8 = 9.84 mb, Td=20°F so e = 3.7 mb, RH = (3.7/9.8)*100% = 38%

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Revised 06/16/04