694 ROSSiTER [chap. 16 



In consequence of the seasonal variations in total air pressure over the 

 oceans,! however, the statical law can only be satisfactorily examined on a 

 global scale. 



For empirical, statistical investigations where the individual effects of air 

 pressure and wind stress do not need to be separated, the method first used by 

 Witting (1918) in his study of Baltic storm-surges can be most effective. Instead 

 of using observed wind velocities and directions, atmospheric pressure gradients 

 in two mutually perpendicular directions can be used. This may be simplified 

 further by using observed air pressures at three stations chosen so as to form 

 roughly an equilateral triangle, and Doodson (1960) has used this technique to 

 study variations in annual mean sea-level in the English Channel, the North 

 Sea and the Cattegat. The data were made to give a best fit to the linear 

 expression 



Z-Z = ar{Br-Br), (1) 



where Z denotes annual mean sea-level, Br the annual mean air pressure at a 

 point r, and bars denote average values taken over a period of 27 years. The 

 maximum individual contributions to sea-level from pressure and wind in- 

 dicated by this type of formula during the years examined were found to be 

 35 mm for Newlyn, which is on the continental shelf, and 106 mm for Esbjerg, 

 which is situated in shallow water and hence responds more violently to meteoro- 

 logical influences. At Esbjerg the standard deviation of the annual means was 

 51 mm ; that of the residuals, after removing the computed contributions, was 

 21 mm. One noteworthy feature of Doodson's work is that, in the absence of 

 long series of records at some stations, he experimented with monthly instead 

 of annual means of his variables and found that the results from 36 monthly 

 means approximated very closely to the results from 27 annual means. 



The piling-up of water due to wind stress, most apparent in shallow water 

 and in the presence of land barriers, is generally accepted to be a quadratic 

 function of the relative velocities of surface wind and surface water, but also 

 subject to a roughness parameter ; it is essentially a phenomenon most ap- 

 propriately discussed theoretically elsewhere (see Section 2 and Chapters 3 

 and 15). In passing, it should be mentioned that although the linear expression 

 (1) can only be an approximation to the fundamental quadratic law of friction, 

 for long-term mean values it provides remarkably high correlation coefficients 

 (see Doodson, 1924, in respect of daily mean values). 



In the past, storm surges have been profitably studied by empirical, statistical 

 methods ; the advent of the electronic computer has made possible a more 

 theoretical approach by way of numerical integrations in time and space 

 involving viscosity and bottom friction. It may well be that such a treatment 

 could find a useful application to the study of seasonal variations in sea-level 

 due to winds and air pressure, for the problems are fundamentally the same, 

 differing only in their scales of time. 



1 "From 1012 mb in December to 1014 mb in July, due principally to a shift in air mass 

 towards Siberia in winter." (Pattullo et al., 1955, p. 101.) 



