26 



BJ0RN HELLAND-HANSEN 



[REP. OF THE "MICHAEL SARS" NORTH 



downwards, from 10 to 50 metres say. From about 50 

 metres to 200 or 300 metres below the surface the tem- 

 perature decreases at a slower rate, but further downwards 

 to some 500 metres the temperature gradient is again 

 very great. We have here two such "steps" as were men- 

 tioned above (section 20). 



The temporal variations of r, 5 or a, now dealt with, 

 whether periodic or not, may a priori be expected to be 

 greatest at those depths where the vertical gradients of 

 these elements are greatest. The differance / — i . 



c» max mm 



between the highest and the lowest temperatures observed 

 is given in column 7 of the table on p. 27. We find 

 upon the whole that this difference is greater with a great 

 vertical temperature-gradient than with a small, but no 

 direct proportionality exists. We have, for instance, much 

 the same vertical temperature-gradient at 300 metres as 

 at 400 metres at Stat. 115, but the values of r — r . 



max mm 



are very different. 



23 Harmonic Analysis. Tidal Variations. 



The oscillations found by earlier investigations seemed 

 to be connected partly with the tidal phenomena, and 

 later observations have given further support to this con- 

 clusion, as mentioned above. The temporal variations 

 observed at our Stat. 115 seem also at first sight, at any 

 rate at some levels, to exhibit a periodicity in accordance 

 with the tidal periods. As the influence of the moon 

 generally is predominant in the tides it is reasonable to 

 use lunar hours as the unit of time (1-035 solar hours, 

 reckoned from the upper passage of the moon). 



Values have been interpolated for every lunar hour, 

 Greenwich time. We have selected this division of the time 

 also for the analysis of the Scottish observations, so that 

 we get the interpolated records of temperature for both 

 stations referred to the same moments of time. 



The upper passage of the moon occurred at Green- 

 wich on August 12th at 17'' SI"" G. M. T. and on August 

 13th at 18'" 15"" (civil time, the day reckoned from midnight 

 to midnight). At Stat. 115 the observations commenced 

 early in the morning on August 13th, so that data may 

 be obtained for 24 lunar hours beginning with the r2th 

 lunar hour. At the Scottish station the observations com- 

 menced about 5 hours later. 



The temperature-values interpolated for every lunar 

 hour have been subjected to harmonic analysis. Calcu- 

 lations have been made according to the formula 



^ = ^m + 2 '^"^ ^^° i^-f^i) + y <:os SOP {t - k^) 

 where r is the temperature at the lunar hour t, t^ the 



mean temperature, A the total variation (the double am- 

 plitude) due to a diurnal, fi to a semi-diurnal harmonic 

 oscillation, k^ the time (expressed in lunar hours) when 

 the maximum occurs at the diurnal, k, at the semi-diurnal 

 variations. 



The first cosine-term in the formula above corresponds 

 to the small elliptic moon-tide, Mj, which is generally of 

 but quite secondary importance. It has a period of 

 24-84 (ordinary) hours -= 24 lunar hours. A much greater 

 weight is in most cases ascribed to the partial tides O 

 with a period of 25-82 hours and K, with a period of 

 23-93 hours. As our observations embrace 24 lunar hours 

 only, it is impossible to separate the different partial tides 

 of the diurnal type, and it is much the same which of 

 the periods is selected for the analysis. As Mj has a 

 period just between O and K,, and it is most convenient 

 to use the horary angle of 15° (referred to lunar hours) 

 for the calculations, the harmonic constants have been 

 computed for Alj as representing the total diurnal variation. 

 The result gives at any rate a rough approximation only 

 and is very uncertain on account of the shortness of the 

 series of observations. 



The second cosine-term in the formula above corre- 

 sponds to the chief moon-tide TM,-,, which in our case can 

 not be kept distinct from the semi-diurnal solar tide S2. 

 From the Danish observations which extended over as 

 much as 67 hours, Knudsen [1911] has made an attempt 

 to separate the two periods with regard to the tempera- 

 tures at 400 metres. His computations indicate an unex- 

 pectedly great amplitude due to the solar period. The 

 short series of observations at our Stat. 115 and the Scot- 

 tish station do not permit an attempt to separate the M^ 

 and S., periods. Both of them will be included in our 

 computations. 



The harmonic analysis has been carried through with 

 regard to the temperatures observed at the surface and at 

 every hundred metres of depth below the surface at Stat. 

 115 and the Scottish station.') The results are combined 

 in the following table, where also are included the data 

 published by Knudsen for the Danish station in May. 



The amplitudes found by the harmonic analysis are 

 upon the whole comparatively great, indicating that the 

 temperature variations have been to a considerable e.xtent 

 diurnal and semi-diurnal. For the sake of brevity we shall 

 in the following name these partial variations the tidal 

 variations. The term is not exhaustive and may be mis- 

 leading, because some of the tidal periods possible are 



') The Scottish observations are publislied in Bulletin Hydro- 

 graphique pour I'AnnOe Juillet 1910 — Juin 1911 [Copenhagen 1912|. 

 The present author is indebted to Dr. A. Bowman, Superintendent of 

 the Fishery Board for Scotland, for detailed records of the exact time 

 when the observations were taken. 



