660 
Schmidt succeeds in explaining quantitatively all facts 
of this atmospheric phenomenon in a satisfactory man- 
ner. Most certainly, his theory has greatly contributed 
to a better understanding of local winds. 
Schmidt’s assumption concerning temperature is 
characterized by the fact that the entire horizontal 
and vertical temperature distribution is given. He super- 
imposes on the normal vertical temperature decrease 
the daily radiation temperature wave which is assumed 
to reach its maximum amplitude near the coast at a 
distance inland amounting to half the wave length of the 
temperature oscillation. This amplitude is supposed to 
decrease exponentially with altitude. However, for 
reasons of simplicity, he neglects the fact that the 
maximum amplitude is a function of time which, after 
all, should be of some importance to the theory. The 
variation in air density caused by the radiation temper- 
ature wave can be calculated; its amplitude also de- 
creases exponentially with altitude. Part of the pressure 
variation is ascribed to the resulting density variation, 
and the remainder is caused by divergence and con- 
vergence of the compressible air. This influence of diver- 
gence is also assumed by Schmidt to decrease ex- 
ponentially with altitude. If the pressure gradient is 
known, the horizontal velocity component can be calcu- 
lated by application of the Guldberg-Mohn friction 
formula. Finally, the friction constant is assumed to be 
a quantity that decreases with altitude according to 
the expression e~”, where r is a constant representing the 
decrease of friction with height and z is the height. 
This is necessary in order to obtain sufficient variation 
with altitude of the sea breeze’s starting time. We shall 
not discuss here how far such assumptions are justi- 
fied; moreover, it would be preferable if the theory 
itself would yield the variations with altitude of all 
these quantities. Nevertheless, the theoretical deter- 
mination of the deviation of the wind direction from 
the perpendicular to the coast and of the shift of the 
wind in the course of a day gives a satisfactory result. 
The most recent work on the theory and observation 
of land and sea breezes has been published by Pierson 
[61]. In this work the theoretical considerations of 
F. H. Schmidt are considerably improved. Pierson 
makes assumptions regarding the temperature contrast 
between land and water that closely approximate reality 
and he takes into consideration not only the Coriolis 
force but also that type of friction which is used in the 
derivation of the Ekman spiral. A solution is given 
of the Navier-Stokes equations for laminar flow with 
consideration of the apparent eddy viscosity. Theoreti- 
cal hodographs illustrate the variations of land and sea 
breezes under the influence of this type of friction, the 
Coriolis force, and the variable pressure-gradient force 
at all altitudes. The temperature contrast between 
land and water and its periodic variation during the 
course of a day as well as its variation with altitude 
are assumed, with due consideration for eddy diffusion 
(W. Schmidt, see [61, p. 9]), in a manner similar to that 
employed by F. H. Schmidt. From this the density 
and pressure distribution can be computed, and the 
wind field can be obtained from the equations of motion; 
LOCAL CIRCULATIONS 
the equation of continuity is unnecessary here. A com- 
parison of the theoretical results with observations 
made at Boston (42°N), Madras (13.4°N), and Bata- 
via (6°S) shows good agreement. 
Recently, Haurwitz [37] made an interesting and im- 
portant contribution to the theory of the land- and 
sea-breeze circulation. In contrast to previous investi- 
gators, he chooses Bjerknes’ circulation theorem as his 
point of departure. With it he proves that the intensity 
increases, not only as long as the land-water temper- 
ature difference increases, but that it keeps growing ~ 
until this difference disappears. Thus, the phase shift 
between temperature difference and wind maximum 
would be a quarter of the period, that is, six hours. 
Haurwitz shows that the introduction of frictional in- 
fluences causes a considerable decrease of this phase 
shift which leads to a better agreement with obser- 
vation. The daily shifting of the sea breeze, which was 
clearly observed in several locations, can be explained 
without difficulty as an effect of the Coriolis force. 
Haurwitz’ work excels in its logical, all-mclusive con- 
sideration of all factors that are of importance for the 
development of land and sea breezes. However, as in 
the work by F. H. Schmidt, the theory of the land- 
and sea-breeze circulation is incomplete. In all these 
investigations the temperature contrast between land 
and water at the surface and at all levels above it is 
assumed. A complete theory should furnish the temper- 
ature distribution with altitude as well as the circu- 
lation from a given temperature contrast at the surface. 
The temperature distribution with altitude depends 
not only on the vertical turbulent heat exchange, but 
also on the circulation itself. For this reason, with a 
given boundary condition of temperature at the sur- 
face, the equation of heat conduction (as in the theory 
of the slope winds, see p. 666) must be incorporated in 
the theory. 
If we approach the land and sea breeze as a single 
circulation cell in the sense of Lord Rayleigh’s con- 
vection theory [64], we come considerably closer to 
the problem of these local winds. Furthermore, with 
this method we can take vertical as well as horizontal 
heat transfer and turbulent friction into account. The 
solution must yield not only the entire temporal de- 
velopment of the periodic current system, but also its 
dimensions as a function of heat supply or of the land- 
water temperature difference, respectively. I have re- 
cently attempted such a solution [18], which actually 
furnishes the required results in full conformity with 
observations. For the land-water temperature difference 
near the surface, which we have assumed as given, I 
used the simple harmonic function ? = Me*** sin Ia, 
where « is the normal to the coast, 3 the potential 
temperature, M the amplitude of the temperature vari- 
ation, Q = 27/(sidereal day) = 7.292 X 10~* sec™, 
and the length of the circulation cell is fixed as L/2 = 
1/1. This solution permits the utilization of any desired 
form of the land-water temperature difference, pro- 
vided it is expressed by a Fourier series; the solution 
given above then holds for every one of its terms. 
This solution, based on the assumption that & is 
