SECT. 5] SURGES 613 



does not exceed that of the atmospheric system causing the surge, T^ is simply 

 the period of a free seiche of the water in the direction in which the atmospheric 

 action (wind stress, pressure difference) works. If, however, the extent of water 

 affected does exceed the atmospheric system horizontally, Tt may be defined by 



n = AjCb, (2) 



Cb being the velocity of propagation of long (or "tidal") waves in the sea area 

 under consideration and A having the same meaning as before. 



The above scheme of extreme cases (i) and (ii) is more or less ideal. Reality 

 will, in general, lie somewhere in between. In particular, the two periods Ta 

 and Tb may even be nearly equal, Ta ~ Tb, in which case a sort of resonance 

 occurs. In the case of Ta and Tb being given by formulas (1) and (2), the condi- 

 tion for resonance becomes Ca ~ Cb. 



A less sophisticated classification of surges may be established by dis- 

 tinguishing between (1) surges occurring in an at least partly enclosed sea 

 area (or a lake) and affecting it at any moment more or less as a whole, and (2) 

 surges of the running-wave type, travelling over a sea area which is large in 

 comparison with the atmospheric disturbance involved. The former type is the 

 simpler one for mathematical treatment, especially if at the boundaries where 

 the sea area under consideration meets the ocean outside, simple boundary 

 conditions may be supposed to hold. Moreover, surges of this type have more 

 extensively been studied, since damaging storm surges have especially been 

 frequent in such partly enclosed sea areas, e.g. like the North Sea. Damaging 

 storm surges of the running-wave type are mainly confined to those caused by 

 tropical cyclones. 



D. Treatment 



A treatment of the dynamics and forecasting of surges of atmospheric origin 

 will be given which follows the last mentioned classification. Besides, a more 

 statistical treatment of surges, as "long" period variations of sea-level, is 

 presented, including results of work on spectral analyses and correlations with 

 weather. 



2. Description 



The mechanism of surges varies considerably between the high- and the low- 

 frequency portion of the spectrum we are considering. At the low-frequency 

 end, sea-level is often in equilibrium with the disturbing forces and the principles 

 of statics apply. At the other end, surges with periods of only a few hours are 

 almost always governed by dynamical considerations; i.e., the inertial forces 

 are important. For example, let us consider a typical continental shelf of 

 constant slope whose edge is 100 m deep and 100 km from shore. The gravest 

 mode of a standing barotropic wave has a period of about 7 h (four times the 

 \/{gh) travel time across the shelf). Thus we might expect that the day-to-day 

 variation would be in equilibrium with the disturbing forces, while surges of 



