V. MEAN SEA LEVEL 
Definition 
Mean sea level at any point may be defined simply as the mean level of the sea 
at that point. It is the primary tidal datum plane, all the other tidal datum planes 
being generally derived with reference to mean sea level. 
Strictly, mean sea level should be determined by integrating the tide curve. It is 
much more convenient, however, to derive mean sea level as the average of the tabulated 
hourly heights of the tide. For a very.short period of observations the difference 
between the two determinations may be relatively large, but for a series covering a 
month or more the difference, if any, would be insignificant. The hourly heights of 
the tide are generally tabulated to the nearest tenth of a foot, and the mean sea level 
derived therefrom is taken to the nearest hundredth of a foot for series up to a year 
in length. 
Mean sea level is generally assumed to constitute an equipotential surface; but as 
derived from tide observations at different places, mean sea level must be expected to 
deviate somewhat from a theoretical equipotential surface in consequence of the net 
or resultant effects of such agencies as winds or variations in. barometric pressure. 
As a first approximation, however, mean sea level as derived from tide observations 
along open coasts may, for most purposes, be regarded as constituting an equipotential 
surface. 
Within coastal bodies of water draining large areas subject to considerable fresh- 
water run-off the mean level of the sea obviously tends to stand somewhat higher than 
along an open coast. In tidal rivers in which variations in the fresh-water run-off cause 
relatively large fluctuations in level it is sometimes preferable to speak of mean river 
level rather than mean sea level, though this mean river level is determined in precisely 
the same manner as mean sea level, namely, by averaging the hourly heights of the tide. 
It is convenient at times to use the expressions daily, weekly, monthly, and yearly 
sea level. These terms denote, respectively, the sea level derived by averaging the 
hourly heights of the tide for the period of a day, week, month, and year. With respect 
to weekly, monthly, or yearly sea level no ambiguity arises, but with respect to daily 
sea level it is necessary to define precisely how it is determined from the hourly heights 
of the day, for this determination is possible in three different ways. 
If the hourly heights of the tide for any given day are denoted by ho, hi, ho, . . - hes, 
hos, in which hy is the height at midnight beginning the day and hz, the height at midnight 
ending the day, then, strictly, sea level for the day is given by }1 (ho thi thethst+ ... 
+ hyo +he3 thos). It is much simpler, however, to sum the hourly heights as tabulated; 
furthermore, no useful purpose is served by the refinement of the first and last terms of 
the formula. Hence daily sea level is frequently taken as 45 (to thAit . . . -+Mo3thea). 
’ But, as shown in Figure 15, the hourly heights of the tide are tabulated with the 23d 
hour of the day as the last hour. It is therefore more convenient to derive daily sea 
level as 4 (hothithe+ . . . +Aee+ho3). Throughout this publication, unless other- 
wise specifically stated, daily sea level will be derived in accordance with the last formula. 
45 
