Elevations are the least understood of all coordinate components. Most surveyors have a basic knowledge of northings (y) and eastings (x), even if they have many complaints regarding their manipulation and use, but few understand elevations (z). Surveyors know it is based on some form of sea level, but what is sea level and how does it relate to the elevations surveyors utilize?

THE 1857 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 35, REPORT OF SUB-ASSISTANT H. MITCHELL ON OBSERVATIONS OF TIDES AND CURRENTS IN NANTUCKET AND MARTHA’S VINEYARD SOUNDS AND IN THE EAST RIVER AT HELL GATE, WITH REMARKS ON THE REVISION OF LEVELLINGS ON HUDSON RIVER, marks the first mention of leveling of more than just a local nature. Mr. G. B. Vose carried out the double series of leveling from New York City to Albany connecting the tide stations. Assistant Mitchell writes, "In order to place our results beyond all possible doubt, I directed Mr. Vose, to whom the leveling was assigned, to proceed slowly and with great care from station to station between New York and Albany. As you directed, a double series of levelings was made throughout the whole route and every doubtful step was retraced." Mr. Vose states, "From a hasty computation which I made, it appears that the probable error for the entire distance from New York to Greenbush does not exceed two-tenths of a foot. In some parts of the route—as, for instance, across the long bridge near Tivoli—it was necessary to run over the work five times." In Greenbush bench mark "Gristmill" was established at an elevation of 14.73 feet (which much later was determined to be about one foot too high, although this may be a result of differing tidal datums). No details as to the instruments, methods or results have been published and no record of the datum or origin has been found. The benchmark "Gristmill" was used by the United States Lake Survey as the basis of elevations in the great lake area as per a letter from the Superintendent of the United States Coast Survey dated July 9, 1880.

THE 1871 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 12, REPORT ON THE LEVELING OPERATIONS BETWEEN KEYPORT, ON THE RARITAN BAY, AND GLOUCESTER, ON THE DELAWARE RIVER, TO DETERMINE THE HEIGHT ABOVE MEAN TIDE OF THE PRIMARY STATIONS BEACON HILL, DISBOROUGH, STONY HILL, MOUNT HOLLY, AND PINE HILL, BY RICHARD D. CUTTS, ASSISTANT, COAST SURVEY, IN CHARGE OF SECONDARY TRIANGULATION. Written by Charles Ferguson, sub-assistant, published the results of the run from Keyport to Gloucester, a total length of 71 miles with 13 miles of offsets. As well as establishing elevations on the primary triangulation stations it established bench marks along its route and established the elevation of a mark, described as "Tuttle’s gate, Matteawan" and later known as "VI" in the report of 1882, as 16.780 meters. This mark was established as a "triangle upon a flagstone walk" and is one of a few ever recovered and releveled. In later reports the elevation for 1871 is listed as 16.7885 meters, although this may be a result of corrections applied to the levels. The elevations used in this report were established by tide observations consisting of ½ lunation at each end of the run. The leveling appeared to reveal that the ½ tides at Gloucester were 1.04 meters above those at Keyport. The leveling of 1871 is interesting in that it connects to a series of "barometer cisterns" used in 1870 to establish elevations at the listed primary stations and finds the cisterns to average 0.75 meter higher than the leveling with a range of +2.26 meters to -1.14 meters.

The single most important document relating to sea level is THE 1882 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 11, RESULTS OF THE TRANS-CONTINENTAL LINE OF GEODETIC SPIRIT-LEVELING NEAR THE PARALLEL OF 398. FIRST PART FROM SANDY HOOK, N.J., TO SAINT LOUIS, MO., EXECUTED BY ASSISTANT ANDREW BRAID. Written by Charles A. Schott, assistant, established the level of half-tide at Sandy Hook, N.J. The value this report established for sea level defined sea level in the northeast, Great Lakes region, and across the Trans-continental arc of Triangulation until the Pacific Ocean was reached around Seattle in 1907. For many decades, records of elevations throughout the nation referred to "Half-Tide Level at Sandy Hook, New Jersey."

A bench mark consisting of a horizontal pencil line with five tacks was established on the wharf of the New Jersey Southern Railroad on the bay side of Sandy Hook and designated "Tidehouse" or "T.H." It was referenced to a self-registering tide gauge, the length of which was 18 feet, set at an arbitrary height. Readings began on Oct. 21, 1875 and continued to the end of 1881. The average of the annual high and low waters was analyzed by Mr. Avery, of the Tidal Division, and tabulated on a yearly basis from 1876 to 1881, and a half-tide of 8.548 feet, +/- 0.031 foot was determined. This probable error being rather large according to Assistant Schott, the Tidal Division constructed several other tables. A Mr. Ferrel produced a table for the years 1876 to 1881 based on lunar tides and solar tides. This table was then analyzed by lunar components and combined in another table giving a mean, based on harmonic analysis of 8.5610 feet +/- 0.0289 foot. The values of ½ low and high were then compared to those produced by harmonic analysis and were found to deviate annually from as little as 0.003 foot to 0.037 foot. The value of 8.5610 feet +/- 0.0289 foot was then adopted as mean sea level, thereby establishing "T.H." as 3.4881 meters +/- 0.0091 meter. Essentially this value is a snapshot of an event in motion, for sea level is never the same at any two points or at any one point at different times.

This first line of geodetic spirit leveling established a series of primary bench marks (lettered), secondary bench marks (roman numerals) and temporary marks (arabic numerals). This line touched upon a bench mark established in "Matteawan" or Mattawan, N.J. (spelling errors or alternate spellings are common in the reports of this era) established in 1871 by Charles Furgeson. The elevation of this mark in 1881 was found to be 16.8599 meters, and the mark was reported as disturbed.

THE 1887 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 14, REPORT ON THE RESULTS OF SPIRIT-LEVELING OF PRECISION ABOUT NEW YORK BAY AND VICINITY 1886 AND 1887. Written by Charles A. Schott, assistant, continued the tide observations at Sandy Hook. Observations from Jan. 1, 1882 to Aug. 31, 1884 yielded a result of 8.719 feet +/- 0.030 foot and from Dec. 1, 1886 to March 31, 1888 a result of 8.634 feet +/- 0.023 foot, for a combined result of 8.590 feet +/- 0.025 foot. The bench mark "T.H." was held as 3.4881 meters as previously fixed and a line of levels was run from Red Bank, N.J., where it taps the line of 1881, to Dobbs’ Ferry, N.Y. The main line was 72 miles long and offset lines added another 49 miles. As stated in the report, "The leveling of 1881 was carried out under instructions, which demanded the running of two simultaneous parallel lines, but also obliged the observer to run for a limited distance an independent third line in a direction opposite of the two parallel lines, in order that the efficiency of the method of running parallel lines might be tested." The leveling of 1886 was accidentally carried out under these instructions but was changed in 1887 to run the lines forward and backward separately. At this time a great deal of discussion was taking place regarding the question of coastal subsidence. Around 1857, George H. Cook, a professor at Rutgers College in New Jersey, published an article in the American Journal of Science, s.s., vol. xxiv, pp. 341-354, in which he discussed his belief in subsidence along the New Jersey and Long Island coastline. As evidence, he sites the occurrence of recently deceased timber in marshlands and in water below tide level, remains of logs, roots and stumps in these areas, and the rapid loss of land based on old survey lines ending at the sea. At this time Professor Cook believed the rate of subsidence to be about two-foot per century. Later, as the State Geologist, Professor Cook published in the Annual Report of the State Geologist, 1881 chapter III, Geologic Notes, another discussion of coastal subsidence. He sites the same evidence as in his previous article and expounds upon his theory. He describes in great detail the loss of coastline along New Jersey, utilizing United States Coast Survey charts from 1839 and 1867, which show loss as great as 525 feet at one point and an average loss of 310 feet at ten locations. He also discusses the remains of trees in marshland from Newark to Cape May, the great storm of 1821, the loss of formerly upland islands in the Delaware Bay, and the discovery of ancient buried logs at great depths. Professor Cook revised his subsidence rate to one foot per century. In 1896, the Geological Survey of New Jersey, published a map, entitled, A map of New Jersey Showing approximately the area which would be submerged were the land to sink 100 feet. The map shows that two islands would be left in southern New Jersey, centered on Glassboro and New Egypt, with a new coastline running from north of Trenton, northeast to Passaic. In 1911, Professor Douglas Johnson, Ph.D., of Columbia University, published an article in the Annales de Geographie, vol. XXI, pp. 193-212, in which he refuted Professor Cooks’ conclusions. Having examined great stretches of shoreline from Florida to Maine, Professor Johnson felt satisfied that there was no evidence of subsidence. Instead he offers a point by point explanation of the "apparent evidence of coastal subsidence." He explains the loss of land along the coast is due to erosion rather than subsidence and that cliffs created in remote history by the sea and isolated by intervening beaches are exactly where they would be should the beaches be removed. In 1911, C.C. Vermeule, a consulting engineer and former State Geologist, re-ran a series of level lines in southern New Jersey, at the suggestion of Professor Johnson, which were originally run in 1886 by Professor Cook. The results, as reported by Mr. Vermeule," show that the agreement between the levels…is extremely close and entirely within the probable error of the observation." In Precise Leveling in New York City from 1909 to 1914, by Frederick W. Koop of the New York Board of Estimate and Apportionment, coastal subsidence is discussed in the vicinity of New York City. Mr. Koop, having run level lines from Perth Amboy, N.J., to Dobbs Ferry, N.Y., was able to re-level 12 primary and six secondary bench marks established in 1886-87 by the Coast and Geodetic Survey. And although he discovered several bench marks had not moved in elevation, he found that 13 had lower elevations than previously published. He was, however, able to prove that those bench marks, which were lower in elevation, had settled due to poor placement or intervening circumstances.

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THE 1898-99 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 8, PRECISE LEVELING IN THE UNITED STATES. Written by John F. Hayford, assistant, examined all leveling of precision performed to that date. A committee consisting of John Hayford, Isaac Winston, J.J Gilbert and A.L. Baldwin was formed to examine all leveling of precision to date. Direct results of the observations, instruments and methods of the various agencies, the relative elevation of the Atlantic ocean and the Gulf of Mexico, systematic errors, preliminary adjustments and suggestions for future methods and instruments are all discussed. As well as C&G lines, level lines from other sources were included, such as the United States Lake Survey, the United States Engineers, the United States Geological Survey, the Deep Waterways Commission and the Pennsylvania Railroad. For this first adjustment of the "level net," 25 circuits comprising 54 links and 4,200 benchmarks were adjusted. In this report the lines of 1881 and 1886-7 from Sandy Hook northward were compared. As the lines closely agreed up to bench mark VIII in South Amboy they were combined and averaged, however less than 1 kilometer away a discrepancy of 32.3 millimeters developed at bench mark F. Examining and averaging 19 tidal stations north of bench mark F an apparent correction to the leveling of +44.8 millimeters resulted. Therefore, all the elevations of the 1886-7 line from bench mark F to Dobbs Ferry were raised 32.3 millimeters to agree with the line of 1881. In the adjustment sea level on the Atlantic Ocean, Chesapeake Bay, and the Gulf of Mexico were considered the same height, although a series of four lines across Florida seemed to indicate the Gulf was nearly 0.462 meters above the Atlantic. Again, benchmark "T.H." was held fixed at 3.4881 meters.

In examining the systematic errors in Coast Survey lines prior to 1898, it seemed that a horizontal plane as defined by leveling, was tipped upward to the northeast and downward to the southwest, regardless of the direction of leveling. This error reached its maximum at about 208 north of west or south of east, and corrections were computed for a line running due north at +1.144 millimeter per kilometer and due south at –0.393 millimeter per kilometer. Having established the effect, a cause was then sought. Although radial heating from the sun (direct heating being blocked by a shade) was suspected, proof was sought through examination of the relative direction of lines and azimuth of the sun. The average effective azimuth of the sun is a little west of south, both because the afternoon observation period is larger and because the heat reflected will be greater in the afternoon. A total of 2,400 kilometers of level lines were examined, "57 percent showed the discrepancy … in agreement with the theory ... and about three times as large as for those lines which disagreed." Furthermore, "whenever the direction of the line changes in such a way to approach the direction 128 west of south, the minus rate of divergence … should increase, and if the change of direction is such as to make it approach 128 east of north, the plus divergence should increase. The examination showed that out of 2,300 kilometers examined 82 percent agreed with the theory and 18 percent disagreed."

It was also in this report that the orthometric correction was first discussed. This correction is a function of the shape of the Earth. "The mean surface of the sea is approximately an ellipsoid of the revolution which may be considered to be generated by the rotation of an ellipse about its shorter axis which is in coincidence with the axis of the Earth. Any other equipotential surface above mean sea level is a similar ellipsoid of revolution. The distance between the sea surface considered produced under the land, and a given equipotential surface above it, necessarily increases as the equator is approached. If, then, a line of levels run along a meridian indicates that a series of bench marks are all at the same level, said bench marks all lie, except for errors of observation, in the same equipotential surface, but the bench marks at the southern end are further from sea level than those on the northern end." This correction is obviously zero in an east-west direction but tends to be greatest in north-south lines near the 45th parallel. At this time it was decided to ignore this correction because it was not well known outside the geodetic community and was liable to be misunderstood, and because the corrections, which required a great deal of computation, would result in corrections smaller than the probable error of the lines involved.

THE 1903 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 3, PRECISE LEVELING IN THE UNITED STATES, 1900-03, WITH A READJUSTMENT OF THE LEVEL NET AND RESULTING ELEVATIONS. Written by John F. Hayford, assistant, again examined the fast growing level net. This report adjusted 48 circuits comprising 106 links and established elevations on 6,900 bench marks. As an example of changing elevations due to the various adjustments, bench mark "Gristmill," established by the C&G and used by the Lake Survey as the basis of their elevations around the Great Lakes, was considered as 4.4897 meters above sea level in 1880, 4.1389 meters from a preliminary engineers line adjustment in 1899, 4.1270 meters in a preliminary general adjustment in 1899, 4.1384 meters in the final adjustment of 1899, 4.2292 meters in 1902, and finally 4.2255 meters in the final adjustment of 1903. The bench mark at Sandy Hook, N.J., was held at 3.4881 meters.

THE 1905 ANNUAL REPORT OF THE COAST AND GEODETIC SURVEY, APPENDIX 4, PRECISE LEVELING FROM RED DESERT, WYOMING, TO SEATTLE, WASHINGTON, 1903-1904, completed the leveling to the Pacific ocean. Mr. Hayford, after 22 years, finally had his line of Transcontinental leveling. A Mr. F. H. Sewall ran the levels westward to Hunts Junction, Wash., where he met Mr. G. Clyde Baldwin, who carried the levels eastward from the Tide Gauge at Seattle. Mr. Sewall’s elevation for bench mark P3 was 127.5028 meters, while Mr. Baldwin found 127.3153 meters, for a discrepancy of 187.5 millimeters (0.615 foot). As Mr. Hayford wrote, "Two questions at once arise in connection with this discrepancy: Is it probably due simply to the errors of observations concerned in fixing the elevation of bench mark P3? How shall this discrepancy be distributed in fixing the elevations hereafter to be used as standard for the bench marks along the line from Seattle eastward?" The computed probable error from the line of levels commencing at Sandy Hook, N.J., was ±76 millimeters. However, the actual discrepancy was two and one half times as large as this.

The shortest line of levels connecting the Atlantic and Pacific commenced at Sandy Hook, N.J., then proceeded north to Oswego, N.Y., continued through the Great Lakes by way of water leveling to Chicago and then through St. Louis, for a length of 4,800 miles, which would result in a calculated rate of accumulation of 0.025 millimeter per kilometer. The distance to the other "principal" connection with sea level at Biloxi, Miss., was 3,500 miles, with a calculated rate of accumulation of 0.033 millimeters per kilometer. The tide readings at Seattle commenced in 1899 and continued to 1903. The mean was 4.2320 meters ±0.008 millimeter. Mean sea level was fixed at Sandy Hook by six years of readings and five years at Biloxi. The total range in the annual means at Sandy Hook was 0.098 millimeters and 0.030 millimeters at Biloxi. Evidently tide readings could contribute only a small part of the discrepancy. Mr. Hayford then believed the discrepancy was due to the leveling, as he wrote, "According to the doctrine of chances, such a discrepancy, two and one half times the probable error, should occur about once in ten times. An observation is not ordinarily rejected unless the discrepancy is from three and one half to five times the probable error of the observation. From this point of view of the method of least squares no reason exists, therefore, for believing that this discrepancy is not due simply to the errors of observation."

Proceeding next to the distribution of the error, Mr. Hayford decided "after careful consideration" to hold the elevations running from Sandy Hook to Red Desert, Wyo., and adjust the discrepancy into the line from Seattle to Red Desert.

In 1907 another general adjustment was made. In PRECISE LEVELING IN THE UNITED STATES, 1903 – 1907, WITH A READJUSTMENT OF THE LEVEL NET AND RESULTING ELEVATIONS, a special publication by Hayford and Pike, did not adjust all 9,100 bench marks, due to the fact that such small adjustments were found in the eastern United States, and thus was not strictly a general adjustment.

In 1912 another tide gauge at San Diego, Calif., was reached and a north-south line run. In FOURTH GENERAL ADJUSTMENT OF THE PRECISE LEVEL NET IN THE UNITED STATES AND THE RESULTING STANDARD ELEVATIONS, a special publication by Bowie and Avers, 11,100 bench marks were adjusted based on five tide stations on the Atlantic, two on the Gulf, and two on the Pacific. Again it found that only slight adjustments would arise in the eastern United States, and these were thus held as fixed.

It was at this time that the “orthometric correction” was first applied to leveling computations. The need for this correction was hinted at in the 1899 adjustment, under a section titled, “Systematic error in old Coast and Geodetic Survey leveling." It was discovered that a line run in a north-south direction required a greater adjustment than a line run in an east-west direction. The cause being the oblate spheroid shape of the Earth. Level surfaces converge toward the poles of the Earth, thus in 1912 the correction was applied to leveling west of the Mississippi.

In 1927 a special adjustment of the level net was performed for theoretical purposes. Only closed circuits were adjusted and when the net was “consistent within itself," the elevation of the Houston, Texas, junction point, whose elevation was determined from sea level at Galveston, was carried through the net to other tide stations. As published in SPECIAL PUBLICATION NO. 134, GEODETIC OPERATIONS IN THE UNITED STATES, JANUARY 1, 1924, TO DECEMBER 31, 1926, by Bowie, the results showed the Pacific sea level to be higher than Atlantic sea level, and that sea level rose in both towards the north, and west along the Gulf of Mexico.

In 1929 a special adjustment was performed, which verified the 1927 special adjustment and extended its results into the Canadian level net. Unfortunately, these special adjustments were based on differing tidal epochs at these tide stations. In 1963, a theoretical study using the same tidal epoch at all these tide stations produced a more uniform slope than the earlier results.

In 1929, the last general adjustment of the net was performed and published by Bowie in SPECIAL PUBLICATION NO. 166, GEODETIC OPERATIONS IN THE UNITED STATES, JANUARY 1, 1927 TO DECEMBER 31, 1929,. Twenty-one tide stations in the United States and for the first time, five in Canada, were assigned an elevation of zero. This datum was known as the "Sea Level Datum of 1929" until 1973, when it became the "National Geodetic Vertical Datum of 1929." The problem with this datum is the fact that by holding different tidal epochs at so many widely spaced tidal stations it tended to warp the surface to meet these zero elevations at the tide stations.

The latest adjustment of elevations is the North American Vertical Datum of 1988. The recomputation began in 1977 and was completed in 1991. It is not described as a sea level datum, although it is based on a local mean sea level determination at bench mark "Point-au-Pere," or Father Point/Rimouski, Quebec, Canada. A minimum constraint adjustment of leveling data in the United States, Mexico and Canada was performed holding fixed the height of this primary tidal bench mark. This bench mark is the reference station used for the International Great Lakes Datum of 1985, and is located on the Saint Lawrence River north of Maine. The resulting determination of elevations in NAVD ’88 differ from nearly –40 centimeters in the East to +150 centimeters in the West, when compared with NGVD ’29 elevations. Although considered the same, in IGLD ’85, bench mark values are given in dynamic heights, while in NAVD ’88, heights are in Helmert orthometric units.

Before the recomputation, 51,000 miles of releveling was performed in areas identified as subject to crustal motion associated with earthquakes, postglacial rebound, and subsidence from subsurface fluid extraction. As a test of the distortions introduced into NGVD ’29 by holding fixed the 26 tide stations, the adjustment of 1929 was re-examined using newer, more accurate data and large residuals were discovered. Several exceed 50 centimeters and there is one that exists between St. Augustine, Fla., and Fort Stevens, Wash., of nearly 90 centimeters. Upon examining the differences generated between NAVD ’88 and Local Mean Sea Level, it was found that generally the Eastern Seaboard of the United States is below LMSL, as expressed in NAVD ’88 values, by 10 centimeters in the north and 37 centimeters in the south, while on the Western Seaboard it was between 70 centimeters higher in the south and 125 centimeters higher in the north. Some investigation of Sea Surface Topography took place during the adjustment, but the results determined that a great deal of additional work would be necessary and not cost-effective in estimating these corrections.

The benefits of the new adjustment include the removal of the warping introduced due to holding as fixed the 26 tide stations, the removal of systematic errors associated with older leveling, the recomputation of 625,000 kilometers of leveling performed since NGVD ’29, the inclusion of 81,500 kilometers of leveling never adjusted to NGVD ’29, remonumentation caused by loss associated with development, the introduction of a single new datum to replace NGVD ’29 and IGLD ’85, and orthometric heights compatible with GPS geoid models.