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5..303W 1952AuSRA... A STUDY OF THE ANNUAL SOIL TEMPERATURE WAVE By E. S. WusT* LManuscript received November 26, 1951] Summary Soil temperatures recorded ut Griffith over sm 8 yeur period at a depth ranging from Yin. to 8 ft. have been examined and compazod with air temperatures. The observed fuctuations in the soil temperaturos fit closely the theoreticalequation for the propagation of a simple harmonio temperature wave into tho soil. The diffusivity of the soil has been deducod and compared with values found by other workers in other localities. . . “The annual wave of the daily mean temperature at the surfaco of tho soil has been deduced and compared with the annual wave of the daily mean air temperature and the differences in the means, amplitudes, and phaso displacoments have been discussed. T. INTEODUCTION The temperature of the soil and its variations are of interest to those studying plants and animals growing in or on the soil and to those interested in the weather and climate. Records of soil temperature down to a depth of-8 it. have been kept at the Irrigation Research Station, Griffith, and in this paper the summarized. data are presented -and discussed. Attention. is directed mainly to the annual temperature wave. 1. StIUATION, CLIMATE, AND Som, The following data on the location, climate, and soil are given as they are relevant to the soil temperature data. Griffith is situated at latitude 34º 17'8. and longitude 146º 03 E. Tt is 300 miles inland from the sea on an extensive plain. The climate is between a mediterranean and semi-continental type. Il is just outside the wheat belt for dry-land farming, but oranges, grapes, deciduous fruit, and rice grow well under irrigation. The average “annual rainfall is 15 in. | 'The soil belongs to the Grey and Brown soils of the major soil groups and is classified as a Hanwood Sandy Loam (Taylor and Hooper 1938). The A horizon 9in. deep is a sandy loam. The B1 horizon from 9-17 in. is clay. Below this is clay with limestone concretions. * CSIR.O. Irrigation Reseurch Station, Griffith, N.S.W. F & CSIRO Australia + Provided by the NASA Astrophysics Data System 1952AuSRA... 304 E. 8. WEST Hit. DesceIPIION OF RECORDING INSTRUMENTA Tbermograph records were taken at depths of 1 and 6 in., 1 and 2 ft., and records irom mercury-in-glass thermometers at 4, 6, and 8 ft, The recording instruments were placed in position as follows. ATectangular plot of land 5 by 4 yd. was kcpt untilled but free of scods and traffic. The recording * points” of the instruments were placed at the appropriate depths in tbe centre of this plot. The ground Jor some yards around this plot was also kept free of wecds. The records, therefore, refer to soil temperatures under bare, uncultivated land. . A conerete-lined pit was made on the south side of the plot. The pit was 6 tt. long, 3 ft. wide, and 10 ft. deep, the concrete walls being 4 in. thick. The 3 ft. side of the pit was centred on the south:side of the plot. Thê top of the pit was closed ith trap doors well insulated with cork dust. . Noon 149p— x E TEMPERATURE fr) nm = / -8 MONDAY TUESDAY WEDNESDAY THURSDAY FRIGAY SATURDAY SUNSAS O Fig. 1-Soil temperatures, January 16-22, 1939. This pit housed the recording instruments. The thermographs were Negretti and Zambra instrumenis. Their bulbs were placed at the appropriate depth 6 ft. to the nozth of the pit, that.is, in the centre of the plot. The leads came in horizontally from the bulb to the pit. The temperatures at the 4, 6, and 8 ft. depths were recorded by means of merenry-in-glass thermometers. with stems 2 metres long. The stems of these thermometers were encased in wood and the bulbs were protected by à pointed metal sheath. To instal these thermometers horizontal holes were bored: from the pit of just sufficient bore to take the wooden encasement of the stems, After pushing.thc thormomoters to the full length of the bores the instruments were lightly hammered to force the pointed steel sheaths into the soil at the-.end of the bore. These mercury-in-glass thermometers were very accurate, They were graduated in fifths of.a degree Fahrenheit. The objection may be raised that baxe soil is a rather unnatural condition. However, it is less unnatural than tilled soil, and the natural herbage is so varied in place and time in this locality that it would be difficult to decide on what is & “ typical ” cover, and it would be still more difficult to maintain it. “ Bare” soil at least. nas the virtue of being readily described and casily reproduced. & CSIRO Australia + Provided by the NASA Astrophysics Data System 1952AuSRA... 306 E. 8. WEST by summihg under-the continuous curve. Using readings at 4-hourly or 2-bourly intervals did not appreciabiy improve the estimate. - These four readings were therefore used. The figures for the weekly means for this depth are, therefore, derived from 224 observations (4 readings for 7 days of 8 years). The recording instruments were checked before instailing and were found to record accurately. over the whole range recorded. However, no provision was made to check the instrument after installation. A further difficulty arose from the fact that the recording pen arm for the 1 in. depth had to be lowered 30 ºF, during summer to keep it on the scale. The precantion was taken of marking the position of the pen before and after these adjustments so that the amount of adjustment was recorded. Nevertheless, the possibility exista that am error in setting may have accumulated over the ycars. As the amplitude of the diurnal wave-at this depth is so large, thé observations as read from the charts are subject to rather large errors compared with those for the other depthe, but owing to the large number of óbserrations that go into one weekly mean as recorded, the mcan measured by: the method adopted woulã be quite good. However, there are likely to be large systematic errors (relative to the readings for the other depths). “Lhese would affect the annual mcans but probably not the amplitudes or phases of the periodie curves. (ii) Six In. Depth —The daily thermograph for the 6 in. depth is smoother than that for the:1 in. depth and is msrkedly damped but still departs markedly from the sine curve. However, half the sum of the minimum and maximum gives a close approximation to the mean and this was used. (ii) One Ft. Depth-—The daily thermograph at this depth closely approxi- mátes » sine curve and half the sum of the minimum and maximum was used to determine the mean. (iv) Two Ft. Depth-—The daily wave at this depth is almost damped out. The-reading at 9 am. was taken for this depth. (v) Four, Sia, and Pight Fi. Depths.-—These thermometers were read at 9 am. each morning. Ovwing to a rise in the water-table the 8 ft. thermometer was flooded for a period of about 1 year, and records are not available for this period. Rather than restrict the whole analysis to à 7 year period the 8 ft. temperatures were estimated for this period. For each week the mean temper- ature for the 8 ft. depth was plotted against that for the 6 ft. depth for the 7 years that the complete data are available. The plots fell close to straight ines and the missing 8 ft. depth figure was read off using the figure for the 6 ft. depth-for that year. The error involved in this estimation would be quite small. (vi) AWw Temperature—Temperatures were taken in a standard Stevenson screen situated close to where the soil temperatures were taken. Maximam and minimum and 9 am. readings were available. A- preliminary examination & CSIRO Australia + Provided by the NASA Astrophysics Data System 1952AuSRA... ANNUAL SOIL TEMPERATURE WAVE 307 based on 48 sample days in January and 48 in July gave the following. com- parisons of estimates oi the mean compared with the mean as calculated. by summing under the curve. January | . July Readings — — | Mesm Difforenco | Standard | Mean Difference! Standard CE) Deviation | CF) Deviation tmax.famin)j2 | -0-36 1861 —0-19 : 0-889 9 am. 10-02 4-021 +3:53 t 577 Half the sum of the minimum and maximum readings gives a more precise estimate of the means than the 9 a.m. reading and this estimate was therefore used. V. ANALYSIS OF DATA Harmonic analyses were made of the summarized temperature data for each depth of the soil and for the air. The following are the equations for the fundamental and first harmonies for the soil temperature at the 1 in. depth and the air temperature. Zrt 7 01;n,==66 44421-483 sim ( est) 41-54 sin (7+0-000), [98] =11,990 557 [0,04] =209-201 [404] =149-661, 6,=61-38-/14-075 sin (qe1eses) 41:21 sin (T+0-108), [80]=-5,285 777 [wm]=143:828 [9,0,]=105-734, where 0,m. and 0,=the mean daily soil temperature at 1 in. depth and the mean daily air temperature respectively, t=the time in days measured from 9 p.m. December 31, T=the period, that is, taken as 364 days. The angles are given in radians, and , [86] =the sum of squares of the departure of the “ observed ”* temper- atures from the mean. By “observed ” temperatures is meant the. 8 years” means of the weekly periods, [v,my]=the sum of the squares of the residuals after fitting the funda- menta! term, [vavo]=the sum of squares of the residuals after fitting the first hermonie term. Tt is seen that; tho observed data for hoth the soil and air temperatures fit closely a simple sine curve. The coefficients of the fiest harmonie terms are quite small. Most of the total variance is aceounted for by the fundamental term the first harmonic not reducing the residual váriance by an appreciable & CSIRO Australia + Provided by the NASA Astrophysics Data System 1952AuSRA... ANNUAL SOIL TEMPERATURE WAVE 309 temperature trend leading to waves of temperature with periods varying from about 5 to 10 days. Averaging this effect over a period of 8 years reduces the amplitudes but longthens the periods of these waves, but 8 years is probably not a sufficiently long period to remove them entirely. Though it might be expected that a sufficiently long period would cause thesc fluctuations to disappear, the possibility must not be overlooked that they may, in fact, be genuine cycles superimposed on the annual trend, similar in nature to the well-known Buchan cycle. Tt will be seen that for the 8 ft. depth the observed points fall almost exactly on the sine curve. The departnres from the smooth curve seen in the plot for the 1 in. depth decrease more or less logarithmically with depth as one might expect. If the sole source of these departures was duc to the fluctuations in +20 4 õ DEPARTURE FROM MEAN o & 6 20 E do o 52 WEEKS Fig. 3—Carves fittod for the Lin. (X) and'8 ft. (D) annual temperature wave. the weather onc would expect [vv] to be an inverse logarithmic function of the depth. 'This relation holds fairly well for the lower depths but the curve log [v0]=5 —ex curves up for the top three depths. This is what was expected as the mean temperatures for the 1 ft. and 6 in, depths were less accurately estimated than those for the lower depths and the means for the 1 in. depth were subject to still greater errors of estimate. he coefficient of the sine term gives the amplitudes of the curves, and the constant in the sine term gives the phase. As explained, one can expect these to be more accurately determined than the means for the surface depths as the instrument errors and errors of estimating the means would probably not affect these statistics. These equations can now be considered in terms of the theoretical equation for the propagation of a simple harmonic temperature wave in a uniform medium. Tí the soil has a uniform heat diffusivity, and a varying temperature in the form of à simple harmonie heat wave is applied to the surface, the propagation of the heat wave downwards is given by 0=A,e-mafá ain Pr ( > RD (2) & CSIRO Australia + Provided by the NASA Astrophysics Data System 303W ã E g É ã 8 310 E. 8. WESI where 6=tbe temperature in “F. measured from the mean, Oo=the amplitude at the surface, e=depth in ft., A=-wavelength, that is, the distance between two depths in the soil at which the maximum or minimum occurs simultaneously, t=the time in days (measured from 9 p.m. December 31), T=the period (taken as 364 days), the phase displacement in days at the suriace. The amplitude at any depth is given by the exponential term and the phase at any depth is given by the second term in the brackets of the sine term. N á AMPLITUDE Ed PHASE ANGLE, j (RADIANS) $ 4 E O E AMPLITUDE (Fa Dera Fig. 4.—Relation botween phase angle and depth, and amplitude end depth. The diffusivity is given by KO MR = where K is the heat conductivity and c is the thermal capacity per unit volume, This gives à method for determining k. From the sine term in (2) wê have = E, where q =the phase displacement cast, that is, the constants in the sine terms Figure 4 shows the values of q! in (1) Plotted against &. equation is p= —1-89213 40 184227 o. The regression & CSIRO Australia + Provided by the NASA Astrophysics Data System 5..303W 1952AuSRA... 312 E. 8. WEST (a) Evaluation of Diffusivity Using the value of à given in (6) in equation (3) we have the diftusivity k=:0-3850 ft.?/day or in c.g.s. units 0-004319 em.?/sec. Table 1 shows how this compares. with values found by other workers. Tasig 1 . DIFFUSIVITE VALUES COMPARED WITH THOSE OF OTHER WORKERS | : Author | Soil Typo Locality Mensurement (em.*/s06.) Present work -- | Clay Grifith i Annual wave 0-00432 Rambaut (1916) «. | Gravel Oxford Annual wave 0:00758 Kelvin* “ +. | Trap tock Calton Hill Annual wavo 0-00786 Sand Calton Hill Annual wave 000877 Sandstone Craigleith Annual wave 0-02310 : Quarry “ Everettt .. «. | Gravel | Greenwick Annual wave 0-01249 Wright (1981) “. | Light loam Kow Annual and di- 0-0044 j umai waves Wright (1931) - | Light losm | Kow Annual and di- 0-0066 | urmal waves Wright (1931) -- |! Sand Potsdam Annual wave 00109 Patten (1909) : .. | Sands Washington, Laboratory | 0-0026-0-008 . - D.O. | measurement Paiten (1909) .. | Loems | Washington, | Laboratory | 0-003-0:007 DO. meagurement Patten (1909) + | Clay Washington, | Laboratory | O"0025-0-0045 ! D.C. ! measurement | I À ! * Reported by Preston (1919). 1 Reported by Rembant (1916). Patten's results were for a variety of soils at a range of moisture content. “The lower limits of his values were for dry soils and the highest limits were for soils at the moisture content of maximum diftusivity. The values of the diffusivity at Griffith are similar tó those reported for loams and clays by other workers. Sands and rocks tend to have a higher diffusivity. (b) Relation of Air Temperature to Surface Soil Temperatures Putting «=0 in equation (7) and introducing the mean temperature as à constant we have the temperature at the surface in degrees Fahrenheit as follows : r For comparizon the equation for the air temperature expressed in the same form is 6,=69-6421-34 sin ae(, 6,=61:4-14-08 sin a(o, & CSIRO Australia + Provided by the NASA Astrophysics Data System 5..303W 1952AuSRA... ANNUAL SOIL TEMPERATURE WAVE sis The surface of the soil receives short-wave radiation from the Sun and some long-wave radiation from the atmosphere. Tt loses heat by long-wave radiation into. space and by conduetion to tbe air. There is also a downward diffusion of heat into the soil in summer and autumn and an upward diffusion of heat to the surface during winter and spring. The conduction of heat to the air is not true conduction but is due mainly to the mass movement of warm air upwards due to turbulence caused by wind. The surface of the soil is thus the centre from. which heat is received and lost, and controls the temperature of the air above and soil beneath. Conduction is the only important process in the vistribution of heat within the soil. The transfer of heat by movement of water and air within the soil is of minor importance. The transfer of heat to and from, the air is more complex: Water evaporating from foliage would cool the air ; but it is probable that the difference between tie average air temperature and the average temperature of the surface of the soil is due to tho moving in of cold air from cooler regions. This moving in wf cold air may be from a distant or a local source. For example, if the wind blows more frequentiy from a cooler region say from the south, than from a warmer region say from the north-west, one would expect the air to have a lower mean temperature than the soil. Again, the observation plot which was on bare soil may be expected to have a higher mean surface temperature than adjacent grass- or tree-covered surface, as found by Johnson and Davies (1927), which latter would then be a source of cold air. Comparisons between the mean air temperatire and the mean soil temper- ature for different localities are shown in Table 2. At the first thrée localities TABLE 2 COMPARISON OF ATE AND SOIL TEMPERATURES AT DIFFERENT LOCALTEMS Mean Soil Mean Air Localiby Temperaturo | Temperature CE) CE) Anburn, Alabama (Fitton and Brooks 1931) . 84.9 63-6 Oxford, England (Rambaus 1916) a 50:7 49.2 Urbana, Illinois (Fitton and Brooks 1981) | (580 51.0 East Lensing, Miohigen (Fitton end Bros 1981) .. 50-6 47:8 Anaheim, California (Bliss 1944) .. to 84.6 58.7 Griith, NS.W. a 09.6 "* 61:4 Indio, Califomia (Bliss, Moore, and Bream 1942) .. eta, 1.9 the soil and-air temperature are approximately the same. The small differences could possibly be explained by the methods adopted.in measuring the temper- atures. For the next three localítios the mean air temperature is appreciably below the mean soil temperature, The cool air temperature at Anaheim is & CSIRO Australia + Provided by the NASA Astrophysics Data System 
