60 MONTHLY WEATHER REVIEW FEBRUABY, 1932
The third section of the work deals with wind distribu- tion in the Mediterranean district. Data are included in the tables of this section for a number of countries, includ- '
Italy, the Balkans, Palestine, Turkey, and Algiers. T h e region of the Tropics is next taken up and discussed under two headings, viz, temperature and wind. A table of mean temperatures and lapse rates is given for Batavia, and also a table of the average height and temperature of the tropopause for the various months. A table of mean relative humidities for the wet and dry seasons for Batavia shows large differences between these two se&8ons. Monthly means of air displacement are given for Batavia for he' hts up to 24 kilometers, and are based
regions include central Africa, Honolulu, Samoa, and Mauritius. Mention is also made of Guam, San Juan, and Barranquills. The section relating to the Atlantic Ocean is compara- tively short, especially that dealing with temperature, little actual data of which are given. However, the important features are mentioned and a few references given. No tables of wind values are given for the Atlantic Ocean, but mean stream lines are shown for winter and summer for the 1-1.5 kilometer and 4-5 kilo- meter levels. A good discussion is given of the temperature and wind distribution over India. Mean monthly and annual temperatures a t Agra are shown for heights up to 20 kilometers. The temperature gradients, and the mean heights and teniperatures of the tropo ause for the various months have also been coni- pute if and are given for this station. Wind data are given for eight stations for three charac- teristic months, viz, April, Au ust, and December.
balloon observations are given for the region of Spitz- bergen and for the base of the British htarctic expedtion of 1911. The part dealing with winds in the polar regions in- cludes discussions and tables of data for the east and west coast of Greenland, Iceland, the Arctic Ocean, and the Weddell Sea.
on several hun T red observations. Wind data for other
Various temperature tables % ased on kite and sounding
The next section of the work deals with iaolated seta of observations in the following countries: Egypt, Australia, New Zealand, Japan, Uruguay, and Russian Turkestan. The part dealing with Egypt contains a table giving free-air pressures, temperatures, and humiditiee for Helwan. Upper-air wind directions are given for six stations. The means of a large number of wind observations are given for Australia and New Zealand, and also mean temperatures based on 13 sounding balloon observations. The means of several hundred wind observations are given for Tateno, Japan, and the means of a lesser number for Montevideo and for Tashkent, in Russian Turkestan. In the last section the author discusses the free-air temperature and pressure in a meridional section of the Northern Hemsphere. A @e has been drawn to rep- resent the temperature and height of the tropopause along a meridian and with the aid of these temperatures the pressures in a meridional section have been cpmputed. From the pressures a table of pressure grahents was computed and the general circulation discussed with reference to this table. In this connection it was found that equatorially di- rected pressure gradients4 e., lower pressure toward the EquatoI-occur in the following areas: In summer (1)
a t the surface between 30' and 10' and again between 90' and 70' latitude; (2) from 6 kilometers up to the greatest heights between 10' and 0'; (3) above 16 kilo- meters from the Pole to 50' to 40'. In winter (1) in the low levels between the horse latitudes and Equator; (2) above 18 kilometers between 10' and 30' lahtude, (3) in the region of the Pole. Relatively large poleward directed pressure radients
between 0' and 10' latitude. Thus a t these heights in winter, west winds theoretically can occur near the Equator. Such winds have been observed in the pilot balloon flights of Batavia. The maxima pressure gradients were found, a t the surface, to be between 50' and 60 ' latitude in summer and between 70' and 80' latitude in winter. In both seasons the maxima are displaced equatorially with increasing height.
were found in winter at heights of 12 to 18 kl? ometers,
THE COLDER THE AIR THE THINNER THE ICE
By W. J. HUMPHRBYS
It is a saying among certain Great Lakes fishermen that ice grows faster in zero (Fahrenheit) weather than it does when the temperature is considerably subzero. This, if true, is one of nature's many pleasing puzzles which it always is a delight to solve. But is it true? Evidently the rate of thickening of the ice (at the under surface, of course) is proportional to the rate of loss of
heat by the water up through the ice cover. Under steady conditions this rate in turn is proportional di- rectly to the thermal conductivity of the ice and the difEerence in temperature between its upper and under surfaces, and indirectly to the thickness of the ice sheet. In other words, it is proportional to the conductivity of the ice and the temperature gradient throu h it. Now the conductivity of ice is a constant, nearly, i f we neglect, or take into account and average, the effect of air bubbles and other irregularities. Also the temperature at the under surface of the ice is a constant, namely, 32' F., in the case of fresh water. We, therefore, can say that for any given thickness of the ice, the rate of its further
growth, under stead conditions, ie directly proportional to the extent to whic 3: the temperature of ita outer surface is below the freezing point. That is, it is pro ortional to
Fahrenheit thermometer, of the upper surface. If, then, this upper surface always had the temperature of the air above it, there would be no occasion to explain the para- dox in question, for there would be no paradox. But this relation does not always hold, and in that fact we have the solution of our fisherman's puzzle. At temperatures around zero Fahrenheit there is nut likely to be much fog drifting over the ice from the open water ferther out in the lake, and often too at such times there is wind enough to keep the surface of the ice swept clean of snow. On the other hand, when the temperature of the air is considerably lower the "frost smoke," pro-
" of the open, deep water and duced by the remaining unevaporate a t the low temperature, well may spread out slowly over the ice and thereby not only decrease the net loss of heat by radiation, as fogs and
32 -t8, in which t8 is the temperature, as in I f icated by a
"Stearmndi
hBkUARY, 1932 MONTHLY WEATHER REVIEW 61
clouds always do b the return radiation they themselves
over the ice an insulating sheet of finely Any substance, even a metal, when g e l y divided, is a poor conductor of heat, and snow is one of the poorest. Hence ice covered with a layer of h e snow, even though that layer be very thin, loses heat
to colder air above much more slowly than it would if bare. Obviously, therefore, under otherwise like con- ditions ice increases in thickness much faster when bare than it does when snow covered. Ice of any given thickness grows fastest when its sur- face is coldest; but this temperature depends in part on the condition of the air abov-lear, cloudy, or foggy- and on the condition of its surface, clean or snow covered. And the fog blanket and the h e snow cover are most likely to form in relatively calm and very cold weather, drifted by the entle movement of the air that commonly
the leeward of the remaining open water. It well may be, therefore, as fishermen tell us, that at certain places, a t least, along the shores of the Great Lakes more ice is formed occasionally, perhaps also on the average, when the temperature of the air is around zero Fahrenheit than there is when that temperature is even 20' to 30' lower, owing, as explained, to the greater prevalence of clear air and clean ice in the first case and fo gy air and snowy ice in the second. %ut here also, as everywhere and always, a few appro- priate figures afford a very necessary check on one's general or qualitative reasoning. Let the conditions be:
a. Temperature of the air -1 8 O C., 0' F., approxi- mately. Thickness of ice, 5, 10, 25, 50 centimeters, respectively. Snow covering, none. b. Tem erature of the air - 29' C., - 20' F., roughly. 4iickness of ice, as in cases a. Snow covering,
1 millimeter.
c. Same as b in respect to temperature of air and thickness of ice. Snow covering, 5 millimeters.
Now since the radiations of snow and ice at these low temperatures are small; the reflection of sunlight and sky- light by snow roughly 90 per cent; the amount of such radiation absorbed by ice also small, especially since there is not likely to be much of it to absorb in midwinter at latitude 47' N., say; and the heat conductivity of ice very low; therefore, as a first approximation, we may assume the temperature of the top surface of the snow or bare ice
've out, but ale0 B ecrease it, sometimes very greatly, by
snow.
obtains on suc E occasions over and onto the ice sheet to
to be that of the adjacent air. The temperature of the under surface of the ice is, of course, 0' C. Furthermore, as experiment has shown, the conductivity of very loose snow may be as low as one three-hundredths that of ice. Assume it, in the present, case, to be one one-hundredth that value, so that as a heat insulator, a layer of our h e snow
1 millimeter deep is the equivalent of a sheet of ice 100 times as thick, 10 centimeters; a 5-millimeter covering of snow t,he equivalent of a 50-centimeter sheet of ice; and
so on for other depths and thicknesses. In case a the difference in temperature between the under and upper surfaces of the ice is 18' C., and in cases b and c the difference between the temperature of the un- der surface of the ice and top surfnce of the snow 29' C. Therefore our various temperature gradients, in terms of
centigrade degrees and thicknesses, or equivalent thick- nesses, in centimeters, of ice are as given m the following table :
Temperature gradients
From these gradients it is clear that often bare ice can grow faster when the temperature of the air is 0' E". than can snow-covered ice of the same thickness when the air is much colder, even -20' F. "ken the thickness of the ice is 16.3 centimeters (6.4 inches) it grows just as fast in 0' F. weather, if bare, as it would with a l-milli- meter covering of loose snow (conductivity of snow one one-hundredth that of ice) in weather a t -20' F. If thinner, the bare ice would grow faster than the snow covered at the given temperatures, and if thicker it would grow slower. If the depth of the snow were 5 millimeters the thickness of the ice would need to be 81.8 centimeters (32.2. inches) for the rates of growth under the given conditions to be the same. In the fist of these cases the rate of increase of thick- ness is about 1 centimeter in four hours, the conductivity of ice being 0.005 (transmitting 0.005 calory per second per square centimeter cross section when the temperature gradient is 1' C. per centimeter), and in the second case 1
centimeter in 20 hours. Thus the fisherman's interesting paradox, the colder the air the thinner the ice, has become orthodox and lost its fascination.
BIBLIOGRAPHY
C. FITZHUQH TALYAN, in charge of library
RECENT ADDITIONS Barney. Maginel (Wright.)
Weather signs and rhymes. New York. 1931. [lo31 p. The following have been selected from among the titles of books recently received as representing those most
likely to be useful to Weather Bureau officials in their meteorological work and studies :
Abbot. C. G. Constantin.
col. illus. 19% cm.
Clute, Willard N.
Frost flowers. 12 p. illus. 23 cm. (Amer. botanist, v. 38, no. 1. Jan. 1932.)
Observatoire de Saint-Louis du SBnBgal (6cole secondaire.) Observations mBt6orologiques. Moyennes conclues de 23 ann6ea d'observatiom. p. 437-474. 25% cm. (Bull. du com. d'6tudea hist. et sci. de 1'Afrique Ocoid. franc. t. 13.1108. 3-4. Juil.-dBc. 1930.)
Periodometer: an instrument for finding and evaluating periodicitiee in long series of observatiom. Washington. 1932. 6 p. figs. pl. 2436 cm. (Smith. misc. coll., v. 87, no. 4.) (Pub. 3138.)
Febris. Cesare. Aldrich, L. B.
Clupplementary notes on body radiation. Washington. Teorie moderne BU l'origine e su la struttura dei cicloni. 1932. 12 figs. 24% cm. (Smith. mkc. coll., v. 85, Pisa. 1931. 106 p. figs. 24% cm. (Pubb. com. naa. no. 11.) (h b . 3131.) ital. geod. e la geof. (Consig. naa. delle ricer.) (N. 2.)