August 1965 Arnold Court and David Wac0 51 7
MEANS AND MIDRANGES OF RELATIVEHUMIDITY
ARNOLD COURT AND DAVID WAC0 *
San Fernando Valley State College, Northridge, Calif.
ABSTRACT
Daily midranges (average of highest and lowest) of relative humidity overestimate the true 24-hr. mean by about 3 percent at humidities of less than 15 percent and underestimate by it an equal amount athumidities over 85 percent. Daily readings at five United States stations in January and July, 1961-63: and at Burbank for all months, 1961-63, were studied.
1. INTRODUCTION rections to be applied to the average monthly values of the relative humidities at 8” and 8P (75th meridian time). to Relative humidity, despite its many limitations, is the . . reduce the latter values totrue %-hour means.” For measure of atmospheric moisture content most used by eight of the stations, all “corrections” were negative, up the general public. Temperatureand relative humidity to as much as 5 percent in early autumn. In one month are reported incessantly by radioannouncers, and pub- each at Boise (Feb.) and San Francisco (Dec.), the correc- lished inmost newspapers. Often a day’s highest and tions were positive, while a.11 ohher corrections were zero or lowest values of relativehumidity are presented, along with the maximum and minimum temperatures. negative.Fresno had three positive corrections (in win- ter), the rest zero or negative, while at Sacramento winter Although Blanc [l] reported “no known plans to com- pute daily means based on daily maximum and minimum corrections were positive, summer corrections zero. Day’s data are given in table 1. values” of relative humidity, such midranges have been Similarly, Cox and Armington [2] declared that published in the Local Climatological Datu for at least one “average values for meanrelative humidity . . based WeatherBureau station (Burbank). This practice is an . . . upon observationstaken at 7a.m. and 7 p.m. obvious extension of thestandard procedure of calling . are somewhat higher than the mean of observations taken the temperature midrange the “average” temperature of tat each of the twenty-four hours of the daywould give, and theday. The validity of such an approximation for also slightly higher thanthe mean obtained from the humidity is the subjectof this paper, begun by studentsin maximum and minimumrelative humidity of tshe suc- .a climatology class and continued by the junior author cessive days.” The average of bi-hourlyvalues was under supervision of the senior author. higher than the 7 a.m. and 7 p.m. average each month Despite its widespread popular use, relative humidity in at Chicago, May 1911 to April 1912. hasnot been studied extensively inthe United States. These times are Central Standard Time, corresponding Because it depends on airtemperature as much as on to the 8 a.m.and 8 p.m. EST times cited by Day. But moisture content, relative humidity is less used in meteor- theyactually refer to synopticobservations madehalf- ology than other more stable measures, suchas dzw point an-hour earlier, so that in some tabulations they are listed and mixing ratio. as 7 a.m. and p.m., as in the Climatological Record Books 2. HISTORICAL (Hagarty [4]) for each of thethree periods covered by lhose bound volumes, 1871-1910,1911-30, and 1931-50; Half-a-century ago, Day [3] with the help of Marvin and in the third volume a page was added for the local noon Kincer analyzed five series of psychrometric observations: observation, begun in 1918 and abolished in 1938. a. at 2 p.m. local time at 64 stations, 1876-1880; Blanc 111 compared the 24-hr. means of relative humid- b. every 4 hr. from 7a.m. to 11 p.m., EST, at 11 ity with those based on the four synoptic observations, stations, 1881-1886; but did not investigate midranges of humidity, although c. at 8 a.m. and 8 p.m., EST, at 173 stations, 1889- he did so for temperature and dew point.Five years 1913; (1955-59) of data for mid-season months showed thal d. every 2 hr. at 11 stations, 1911-1915. the synoptic-hour means were within 1.3 percent of the From the fourth set, he computed the monthly means 24-hr. means at nine stations,the greatest departures of the bi-hourly observations, and offered a table of (‘cor- being +1.2 at Miami and -1.3 at Salt Lake City, both ’ Dr. Court is Professor of Climatology, Mr. Waco a graduate student. in October.
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TABLE1.-Difference between mean relative humidities from bi-hourly observations and from averages of observations at 0800 and 9000 EST (From Day [SI,table 5)
Station and Period JAN.FER. MAR. APR. MAY JUNEJULY AUG. SEPT. OCT. NOV. DEC. I Burlington, Vt., July1911 to Apr. 1916 ...... -2 -2 -2 -1 0 -1 -1 -2 -3 -3 -3 “2 Ithaca, N.Y., Nov. 1911 to Dee. 1915...... -2 -2 -3 -3 -2 -1 -2 -4 -5 -4 -3 -2 Columbus, Ohio, May 1911 to Mar. 1916...... -2 -2 -2 -2 -1 -1 -2 -2 -2 -2 -2 -1 Grand Rapids, Mich., July 1912 to Apr. 1916...... -1 -2 -2 -2 -2 -1 -1 -3 -4 -5 -4 -2 Chicago, Ill.. May 1911 to Apr. 1916...... -1 0 -2 -2 -2 -1 -1 -1 -2 -2 -2 -1 Springfield, Ill., Feb. 1912 to Apr. 1916_...... -1 -2 -2 -2 -2 -2 -2 -3 -2 -2 -3 -1 St. Louis, Ma., May 1911 to Nov. 1914 ...... -2 -1 -2 -2 -1 -2 -1 -2 -2 -2 -2 -1 Sheridau Wyo., July 1913 to Apr. 1916 ...... -2 -2 -1 -2 -1 -2 -2 -4 -4 -3 -4 -2 Boise, Idaho, May 1911 to May 1915- ...... 0 f2 -2 0 -2 -1 -2 -2 0 0 0 0 Sacramento, Calif., July 1913 t,o Apr. 1916 ...... +1 +2 0 0 0 0 0 +3 Fresno. Calif., May 1912 to Apr. 1916 ...... +E 2; -2 -2 0 0 0 2: +; +1 San Fralwisco, Calif., May 1911 to Apr. 1915...... +; +; -1 -1 -2 -2 -1 -1 -2 -3 -1 +1 - - -
3. SUMMARIES fist three years of these publications (1961-63) [7] were used for the present study. Average relative humidity in each month at 8 a.m. and 8 p.m., and at local noon, at Weather Bureau first order 4. DATA stations was given in the 1930 “ClimaticSummary of the UnitedStates” (called Bulktin W),but not in its Six stations were used for this study: Burbank, Calif.; 1952 Supplement.Similar values were presentedregu- Las Vegas, Nev. ; GreatFalls, Mont.; Wichita, Kans. ; larly(through 1949) in the Monthly Weather Review, Jacksonville, Fla.;and Nantucket, Mass. These were in the Bureau’s monthly and annual summaries for indi- chosen because of their diversity in climate, ranging from the desert situation at Las Vegas to the maritimeclimates vidualweather stations (Local Climatological Data), and in special tabulations suchas “Fifty Years’ Weather in of Jacksonville andNantucket. Lyingsomewhere in between these extreme examplesof dry andwet conditions Kansas City, Mo., 1889-1938” (Hamrick and Martin [5]). arethe continental-type stations of GreatFalls ‘ and Maps of mean relative humidity at 8 a.m., noon, and 8 p.m. in January and Julywere published in “Climate and Wichita and the modified maritime station at Burbank. Typical of mostinland locations, Great. Falls and Man” [6], and widely reprinted (e.g., Visher [SI). Wichita undergo fluctuations in humidity with changing The increasein thenumber of synoptic observations to fourper day was reflected intabulations of mean wind directionsduring all seasons. Inthe winterboth stationsare subject to outbursts of dry polarair with monthly relative humidity, at each observation time, in accompanying falls in humidity. Whereas Great Falls is the Local Climatological Data for individualstations, in supplementary tables in the monthly state Climatologic,al often influenced by the flow of modified Pacific air onto Data, and in the “Climatesof the States”,issued in 1959 as the continent, Wichita is commonly under the dominance Climatography of the United States No. 60-xx. Monthly of astrong anticyclonic flow which produces southerly of varying moisture content. averages of thesefour daily values are given in the winds Bureau’s Climatological Data,National Summary. They Burbank, like many stations near the Pacific Coast, is also appear on monthly maps of average relative humidity exposed to direct inflow of moist ocean air which has been slightly altered by its path across land. In addition, its (on a 1961 sheet of the National Atlas), based on readings climate is affected to a variable degree by the dry Santa at 1:30 and 7:30 a.m. and p.m., EST, at 236 stations with Ana winds, especially in autumn and winter, which may at least 20 years of data up to 1959. Supplements to theLocal Climatological Data for stations alter the average relative humidity of a given month by taking 24 observations per daybegan as “Special Meteoro- as much as 20 percent. logical Data’’ in1949, listing hourly values for all elements, The effect of location on humidityis readily apparent in including relative humidity, in chronological order, with table 2. At maritimestations (Burbank and Nantucket no totals or averages.Summaries gave frequencies of andto some extentJacksonville) average humidity in- occurrence of relative humidity, by 10-percent (or other) creases from January to July, while at inland stations it classes, for eachhour of the day,and also of various TABLE2.-Means and standard deviations of daily midrangeof relative temperature-humidity combinations for three wind speed humidity, January and July, 1961-65 (in percent) intervals. January July In 1961, a summary (denoted Table G) was added to Station - these Supplements, giving ‘L24-H~urAverages” of various Mean S.D. 1 Mean S.D. of 1 elements, including relative humidity, for each day the Burbank, Calif ...... 47.420.0 8.0 64.9 month. These averages afford ready comparison, for the LasVegas, Nev...... 13.0 38.3 17.6 11.1 Great Falls, Mont ...... 60.0 15.8 11.3 48.9 first time, of the 24-hr. mean relative humidity with that Wichita, Kaus.” ...... 70.6 12.4 10.3 64.6 Jacksonville, Fla ...... 11.0 71.6 5.7 72.7 based on two or four synoptic observations, and on the Nantucket, Mass ...... 14.0 73.5 83.0 15.7 midrange of the hourlyhumidities. Daily data for the
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+I0 I I. I JAN...... P=-1.78+4.I3x .. rs0.985 .. r. 0.968 ...... +: ...... : ... ‘ - -.-.-: ! -...... =====i-. :...... I -5
FEE. \=-3.09+8.57): n=-4.92+11.56 r=0.988 r. 0.952 ...... - ...- . Ot- ”----- .. -5 F
I 1
MAR. n--~80+10.57) r.0.973 ... A
A PR. 0=-7.59+11.7on r=0.972
M AY a=-3.74+7.56x r= 0 972
..
I I I. II I I
FIGURE1.-Mean-midrange difference of daily relative humidity vs. midrange at Burbank, Calif., by months, 1961-63.
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520 MONTHLYWEATHER REVIEW Vol. 93, No. 8
JANUARY ?
A"0.75 + 0.8IX 1r- 0.981 i
&- -1.75 + 2.10X r= 0.969 t ......
FIGURE2.-Mean-midrange difference of daily relative humidity vs. midrange for 5 stations, January and July, 1961-63.
decreases. The seasonal increase at Burbank during these months for the five stations severely curtails the validity three years is larger than the long-term mean, in which the of conclusions concerning seasonal trends of the mean- relativehumidity is close to 60 percentin January. midrange relations. To reducethe complexity of thestudy, data for only Figures 1 to 3 show themean-midrange difference January and July were used at five stations. For Burbank, plotted against midrange, with the respective regression however, each month was investigated in an attempt to lines. Figure 1 is for the 12 months at Burbank, figure 2 depict overall seasonal trends. The limitation to only two for January and July at the other five stations, and figure.
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A LAS VEGAS (Jan.+July 1 A=-1.76 + 2.84X r = 0.991 t lo ...... L ... - .___.__.& - 0 - : ...... - - .. "5 .. -
"-10 -
5 I5 B I STATIONS ( Jon+July 5 1 - 10 A = -3.40+ 6.79): :... ..: r = 0.988 . .: : :: j: ...... _.: .: ...... :.. .. - . ....,...... /j:::) / ...... :. - .: . : : . i:: . : .::: .i. . . :.:.. ... :. ::.;.;;*, ... : ...... :...... L.:: :::.. . - _..:.: :.. -:.::.-:-::.:::. : ... . ._: 0 :: .7 ...: ::...... :...... ;...... A ...... I . : ..... :...... : ...:. .. :.::...... :...... : ...: ..: .. : - .. ..:: . : ., "5 . :. . . ::. ,. - .....:I: :, : .... - - "IO - C I BURBANK ( 12 Mos.) A =-4.21 + 9.15X r = 0.979
. .;...... :. ::. .: .:-
FIGURE3.-Mean midrange differ- !.-II ence of daily relative humidity vs. midrange, 1961-63, (A) for Las Vegas, Nev., in January and July, ..I combined; (B) for 5 stationsin January and July, combined; and I (C) for Burbank, Calif., in all months. 1'2 I '* 100
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3 consists of various combinations of the data in figures 1 TABLE3.-Corrections formidrange of relativehumidity io $t the mean and 2. In the linear regression I Midrange (%) _____...... _..-..0-15 16-30 3145 46-55- 56-70 71-85 86-100 A=a+bx, Correction to mean (%) ._._._..._...._-3 -2 -1 +1 +2 +3
A is the difference between mean and midrange, and x is most revealing results of thestudy. In all themonths the observeddaily midrange. Alinear relation was except Junethe midrange underestimates the mean at assumed,after trials tended to point in this direction. high values andoverestimates it at low values. The Correlationcoefficients (r,~),telling how closely the combination of the 12 monthsadheres closely to this variables A and x are related to each otheron the regression principle, which can easily beseen inthe scattering of line, are presented with each figure. points about the regression line in figure 3. In addition, The original regression lines were computed to estimate the steepness of the slope shows a definite seasonal trend mean from observed midrange. For convenience the lines with maxima in both spring and fall and minima in sum- were adjusted so that corrections could be read directly merand winter (fig. 1). This doublemaximum is from the graphs. Algebraic addition of these corrections unique: none of the parameters-yearly average humidity, (A) tothe observedmidrange (x) gives thepredicted standarddeviation of themidrange and correction, or value of the mean relative humidity. correlation-shows a similar seasonal trend. 5. ANALYSIS 6. CONCLUSION The moststriking similarities between the regression Theresults of thisstudy, presented graphically for lines in figures 1 to 3 are their slopes and intercepts. In five stationsin figure 3B, indicatethat the midrange the 25 examples, 24 lines have positive slopes, 22 have A overestimates the meanfor low values of relative humidity, intercepts below the x axis, and 21 lines cross the x axis. and underestimatesthe meanfor high values. Unless In most cases the midrange underestimates the mean at computation for individual stations shows otherwise, the high values of relative humidity and overestimates it at corrections in table 3 may be used to adjust daily mid- low values. rangevalues to the mean. The few exceptions tothese trends usually occur in samples confined withinsmall ranges. At Nantucket in REFERENCES July, the only example in which the regression line slopes 1. M. L.Blanc, “A Comparison of Methods for Computing Daily downward,only one-tenth of themidrange values are Mean Values of Dry Bulb Temperatures, Dew Point,and below 70 percentrelative humidity and none below 60 Relative Humidity,” Monthly Weather Review, vol. 89, No. 10, percent. The other two cases with positive intercepts are Oct. 1961, pp. 401-410. atBurbank in June (averagemidrange 67.5 percent, 2. H. J. Cox and J. H. Armington, “The Weather and Climate of Chicago,”Geographic Society of Chicago, Bulletin No. 4, standarddeviation only 9.5) and at Jacksonville in University of Chicago Press, 1914, 375 pp. (ref. on page 242). January (midrange 71.6 percent, standard deviation 11.5). 3. P. C. Day, “Relative Humidities and Vapor Pressures over the In these two cases, only about one day per month has a United States, including a Discussion of Data from Recording humiditymidrange below 50 percent.At the other end Hair Hygrometers for a Period of About Five Years,” Monthlg of the scale, Las Vegas in July has the only case of a line Weather Review Supplement No. 6, U.S. Weather Bureau, 1917, 61 pp. 4-34 plates. withpositive slope andnegative intercept but which 4. J. H.Hagarty, “History of WeatherBureau Climatological fails to cross the x axis. Here only one-twentieth of the Record Forms for Surface Synoptic and Airway Observations,” humidities are greater than 30 percent. Key to MeteorologicalRecords Documentation NO. 2.211,U.S. Thatthese apparent anomalies may be theresult of Weather Bureau, 1964, 62 pp. fitting regression lines toa limited scatter of points is 5. A. M. Hamrickand H. H.Martin, “Fifty Years’ Weatherin Kansas City, Mo.,” MonthlyWeather Review Supplement No. borneout by the results of the combined January and 44, U.S. Weather Bureau, 1941, 53 pp July regression for Las Vegas(fig. 3A). For this wider 6. U.S. Department of Agriculture, “Climate and Man,” Yearbook range of observations,the regression line crosses the x of Agriculture, 1941, 1248 pp. axis near 60 percent, which fits the general rule of low 7. U.S. WeatherBureau, LocalClimatological Data,Supplement, midrangereadings at highhumidities. Combining the Burbank, Calif., Las Vegns, Ncv., Great Falls, Mont., Wichita, Kans.,Jacksonville, Fla., and Nantucket, Mass., monthly January and July readingsfor all stations except Burbank 1961-1963. (fig. 3B)smooths out the anomalies: the line fits very 8. S. S. Visher, Climatic Atlas of the United States, Harvard Univer- neatly, having a relatively steep slope and crossing ‘the sity Press, Cambridge, Mass., 1954, 403 pp. x axis near 50 percent. The graphsfor Burbank (figs. 1 and 3C) are perhaps the [Received April 8, 1965; revised June 3, 19651
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