That the undisturbed surface of a body of water, large or small, constitutes a level surface is almost axiomatic. As a matter of course, we reckon heights on land and depths in the sea from the level of the sea, expressing these as so many feet or miles above or below sea level. To be sure, the surface of the sea is at all times disturbed by wind and wave and tide. But we feel instinctively that if by one means or another the effects of these disturbing agencies are eliminated, we arrive at the true level of the sea, a level surface.
In connection with a number of problems relating to the sea, of both practical and scientific character, it becomes necessary to determine accurately this level of the sea or mean sea level as it is frequently called. When this is attempted the fact develops that it is far from a simple matter, for sea level determined at one time is found to differ from that determined at the same place at another time. After eliminating the disturbing effects of tides and waves, sea level is found to vary from day to day, from month to month, and from year to year.
The disturbing effects of waves may be eliminated in various ways. By connecting a well with the sea by means of a pipe, the inlet of which is placed some distance below the surface of the sea, the water in the well will at all times be at the same level as that of the sea, but it will at the same time be free from waves. A simpler method, which may be used at some places, is to ' choose some sheltered spot in a harbor which is free from waves. As regards the effects of the rise and fall of the tide, it is evident that since this rise and fall has a period of about twelve and a half hours, the disturbing effect of the tide on sea level may be largely eliminated by measuring the height of the surface of the sea at frequent intervals during a half day and averaging these heights. A better elimination will be effected if the height of the sea is measured at regular intervals during an entire day and these heights averaged.
Now suppose that in some harbor or at some point along the coast we fix in a vertical position, against the face of a wharf, a board on which a scale of feet and tenths of feet has been painted. Then if during the whole day at regular intervals, say every ten minutes, we read the height of the water on this scale, the level of the sea for that day will be derived by averaging our ten- minute readings of the height of the water. However, instead of making our readings of the height of the water “by hand,” it will be more advantageous to get this done by some instrument. Various instruments, tide gauges for example, may be used which will automatically record the height of the water at regular intervals; or better yet, we may use an instrument which draws a continuous curve of the height of the water throughout the day. From such a curve it is a simple matter to get the height of the water at frequent intervals. Averaging these heights for a day gives the height of sea level for that day.
If we derive sea level for a number of consecutive days it becomes immediately evident that sea level varies from day to day. For example, in New York harbor during a typical winter month, sea level may vary from one day to the next by as much as a foot or more; and within any one month sea level for two different days may differ by more than two feet. And this, it is to be emphasized, is after the disturbing effects of waves and tides have been eliminated. Such changes obviously are to be ascribed to variations in wind and weather. It is a matter of common knowledge that a wind blowing towards the shore tends to raise the level of the sea along the shore, while a wind blowing from the shore tends to lower it.
Not only in winter but in summer also sea level varies from day to day, though obviously to a lesser degree. During a typical summer month sea level in New York harbor from one day to the next may differ by as much as half a foot and within a month sea level for two different days may differ by a foot or more. This arises from the fact that the wind is not the only agency which may cause differences in the level of the sea from day to day. Variations in barometric pressure likewise bring about fluctuations in sea level. Indeed, we may regard any arm of the sea as constituting a huge inverted water barometer. When the atmospheric pressure over this arm of the sea rises the level of the water will be lowered, and when the pressure decreases the level of the water will rise.
The relation between changes in barometric pressure and the resultant changes in sea level may be easily derived as follows. The barometric pressure is measured in inches (or millimeters) of mercury. And since mercury is thirteen times as heavy as sea water, it follows that a change in barometric pressure of one inch should be reflected by an inverse change of thirteen inches in the level of the sea. Or approximately we may put it that the change in sea level in feet should be inversely as the change in barometric pressure in inches.
From day to day wind and weather may vary widely and thus give rise to relatively wide variations in sea level from day to day. But within a month such variations obviously tend to balance out. If the varying heights of the sea over periods of a month are averaged, the results show that sea level changes also from month to month by amounts varying from less than a tenth of a foot to as much as three-quarters of a foot. And within a single year sea level for two different months may differ by more than a foot.
In one feature the variation of monthly sea level is strikingly different from that of daily sea level. The latter, it is clear, varies as the weather does. From one day to the next sea level may be higher or lower depending on the weather. But in the change in sea level from month to month there is a large element of periodicity. For any one year this seasonal variation may be masked by accidental or non-periodic variations. But if at any one place we average the corresponding monthly heights of sea level for a number of years, haphazard or nonperiodic variations will be eliminated and the seasonal variation will appear in its true form. The seasonal variations in wind and weather being different at different places it is to be expected that the seasonal variation in sea level will likewise vary from place to place. This is borne out by observations, and is illustrated in Figure 1 for the harbors of Boston, New York, and Charleston, South Carolina.
[Figure 1: Seasonal variation in sea level, Atlantic coast]
The horizontal line associated with each curve in Figure 1 represents the mean level of the sea at each of the stations as determined from a number of years of observation. The open circles give the heights of monthly sea level relative to mean sea level. Each curve shows distinctive features as regards both the range of the seasonal variation and also its phase. This means in other words that at each place the seasonal variation in sea level has definite local characteristics. It will be noted however that along the Atlantic coast of the United States the range in the seasonal variation of sea level shows wider differences than does the phase. Indeed, from Boston to Charleston, the phase may be said to be very much the same. All along this coast the level of the sea is, on the average, below its mean height in the winter and early spring, and above its mean height in the autumn. Characteristic, too, is the slight fall during July which becomes more accentuated in going from north to south.
For comparison with the seasonal variation of sea level in the harbors on the Atlantic coast of the United States illustrated in Figure I, there are shown the curves of seasonal variation at several ports on the Gulf and Pacific coasts in Figure 2. For the Gulf of Mexico the curves for Key West, Florida, and Galveston, Texas, show that the seasonal variation of sea level is somewhat similar to that along the Atlantic coast. On the Pacific coast, however, the variation is totally different. Moreover, the curve for San Francisco, California, is radically different from that for Seattle, Washington.
[Figure 2: Seasonal variation in sea level, Gulf and Pacific coasts]
Now if we average the height of sea level at any one place over the period of a year it is obvious that the periodic seasonal variation will be eliminated. Within a year, too, the non-periodic fluctuations in sea level tend to balance out. We might therefore be led to conclude that sea level derived from a year of observations will so closely approximate mean sea level that from one year to the next there will be no variation. Let us test this conclusion by examining the results of observations.
[Figure 3: Yearly sea level, New York and San Francisco]
In Figure 3 are plotted the yearly values of the height of sea level in New York harbor and in San Francisco Bay for the twenty-eight year period from 1898 to 1925. For each year sea level was determined by averaging the height of the surface of the sea as measured at the beginning of every hour. In other words each of the heights shown in Figure 3 is the average of more than eight thousand hourly heights of the level of the sea. The horizontal line drawn trough each of the two curves represents the mean sea level at each of the places, as derived from the twenty-eight years of observations.
That sea level varies from year to year is evident at once from Figure 3. But that this variation is relatively small is likewise evident from the fact that the scale giving the heights in the figure must make use of divisions as small as tenths of a foot. From one year to the next the change in sea level is generally less than a tenth of a foot, though at times it may be as much as a quarter of a foot or even more, as exemplified by the variation between the years 1900 and 1901 in New York harbor and between 1913 and 1914 in San Francisco Bay. Figure 3 also brings out the fact that the variation from year to year is not progressive. That is, the sea level of one year is not always lower than the preceding year, nor is it always higher. For several years it may go down and then for the following period of several years it will rise.
A comparison of the two curves of Figure 3 shows that no simple relation exists between the variation in yearly sea level at New York and that at San Francisco. But if we compare New York with some other port on the North Atlantic coast of America or San Francisco with some other port on the North Pacific coast, we find that as regards yearly sea level they behave very much alike. In fact a detailed study of this phase of the question on the Atlantic coast of the United States brings out clearly that if for any one year sea level is high at one point on the coast, it is high all along the coast; and similarly for a year of low sea level. For the whole of the Pacific coast of the United States a similar state of affairs has likewise been found to obtain. This feature, we shall see later, is of considerable importance in the determination of mean sea level.
A number of problems arise from the fact that sea level varies from year to year, To begin with we are confronted by the questions of what constitutes mean sea level and how long a period of observations is necessary to determine it? Since the change in sea level from year to year is not progressive, it is obvious that the longer the period of observations the closer the approximation to mean sea level. From considerations based on the theory of the tides a period of nineteen years is taken as constituting a full tidal cycle, for during this period the more important of the tidal variations will have gone through complete cycles. Hence sea level derived from nineteen years of observations may be taken as giving accurately the mean sea level at any place.
Nineteen years is a relatively long period of time. Cannot the period of observations necessary for securing an accurate determination of mean sea level be shortened? Examining the curves of Figure 3, rough periodicities become apparent. Thus, in the change of sea level in New York harbor there appears a period of approximately nine years, as the peaks for the years 1902, 1910, and 1919 bring out. A like period is also evidenced to some degree by the curve for San Francisco. There appears, furthermore, a variation with a period of something like four or five years —clearly shown in the curve for New York harbor and somewhat less clearly for San Francisco Bay.
Whether these are true periodicities, and if so, what they are due to, are matters about which little is at the present time known. But taken in connection with the fact that the change in sea level from year to year is not progressive, these periodicities make possible a determination of mean sea level over periods much less than nineteen years. If we average the height of sea level over periods of nine years we get a very close determination of mean sea level, and even four years give a result sufficient for most purposes.
Advantage may also be taken of the fact that all along any coast the change in sea level during a given period is much the same. Thus, if it is required to determine mean sea level at any point on the Atlantic coast, a year of observations at the point is compared with simultaneous observations at some place like New York where a long series of observations has already been secured. By means of this comparison the mean sea level at the point desired may be derived with a good real of precision. Indeed, by this method of comparison we can from a month of observations determine mean sea level within a tenth of a foot, whereas the result of the observations uncorrected by means of such comparison might be in error as much as half a foot or more.
In connection with the question of the stability of the coast the accurate determination of mean sea level assumes great importance. For such determinations furnish perhaps the only data of a quantitative nature in studying whether a given coast is rising, sinking, or remaining stationary. If it be assumed, as is sometimes done, that sea level determined from one year of observations gives a close approximation to mean sea level, erroneous conclusions with regard to the coast are bound to result.
As an example, suppose the alleged gradual subsidence of the coast of New Jersey were being studied and that the coast of Atlantic City were chosen, the study beginning in 1912. Throughout that year the height of the sea was recorded automatically, and sea level was determined by averaging the heights at the beginning of each hour. This average height of sea level was then very carefully related to some fixed point on the shore.
Seven years later, in 1919, the observations were repeated with the same care as before. Now, however, the point on the coast which in 1912 was exactly at sea level, in 1919 was found to be 0.36 foot below sea level. In other words, in the seven years from 1912 to 1919 there was an apparent sinking of the coast of more than a third of a foot or at the rate of five feet a century.
But this sinking is only apparent; for as we have seen, sea level varies from year to year, and as determined from one year of observations may differ several tenths of a foot from mean sea level. Turning back to Figure 3 it is seen that 1912 was a year of low sea level on the Atlantic coast of the United States while 1919 was a year of high sea level—being in the former year at New York, 0.17 foot below its mean value, and in the latter year, 0.20 foot above its mean value. If now we correct our yearly values of sea level at Atlantic City to a mean value we find that instead of a difference of 0.36 foot during the seven years, the difference is only one hundredth of a foot. In other words no change in the relation of land to sea took place during this period, for a difference of a hundreth of a foot is altogether too small to be of significance in this connection.
Long series of sea level observations furnish the data for determining the relative elevations of land to sea. If these observations give, superimposed on the fluctuations from year to year, a continually rising sea level, then obviously either the coast is sinking or the level of the sea is rising. But to determine this with any degree of precision long series of observations are necessary in order that the fluctuations of sea level from year to year may be eliminated. Furthermore, long series are necessary to eliminate any periodic cycles such as the four and nine year cycles of which some evidence was found. It is possible, too, that variations of still longer period exist in the change of sea level—perhaps one with a period of something like thirty-five years corresponding to the so-called Bruckner cycle in the weather.
The question of what brings about the fluctuations in sea level we have been discussing opens up a subject with many ramifications. Undoubtedly these fluctuations are due to the variations in a large number of factors, among which may be mentioned barometric pressure, direction and velocity of wind, rainfall and evaporation, temperature and density of sea water, and the velocity and direction of non-tidal currents. The larger fluctuations in sea level that occur from day to day show a very close correlation with the variations in wind and in barometric pressure, and it appears reasonable to assume that the variations of longer period likewise are to be ascribed to changes in wind and weather.
It is to be observed, however, that in ascribing the variations in sea level to effects of wind and weather it is tacitly assumed that the mean level of the sea remains fixed. But may not this mean level itself be changing? In answer to this question it may be noted that such a change in the absolute level of the sea may arise from a change in the volume of the ocean basins or from a change in the volume of the ocean waters. As to the causes that are adequate to bring about such changes a number may be mentioned: earth movements which bring about changes in the dimensions of the ocean basins; addition of water through volcanic action or subtraction of water through chemical binding during the alteration of rocks; decrease of water through increased glaciation on land, or increase of water through decreased glaciation.
That changes in the absolute height of sea level have taken place during geologic time by reason of the operation of the causes enumerated above is unquestioned. If it is asked whether such changes are taking place at the present time the answer is that in view of the enormous volume of the ocean waters, changes in the absolute height of sea level must be extremely small—so small in fact as to escape detection except by careful observations over periods of time measured in centuries. If at any point we find a change taking place in the relative elevation of land to sea, it is a reasonable assumption that it is the land which is changing in height.