05/15/96

LVL_DH
National Geodetic Survey
Leveled Difference in Height Computation Program

The LVL_DH program computes the expected leveled difference in height between two North American Vertical Datum of 1988 (NAVD 88) bench marks.

Bench marks of NAVD 88 constitute the official national vertical datum for mapping and charting, and provide a vertical reference for the national infra- structure. Thus, surveyors frequently use these bench marks for reference points and to check their measurements.

Leveled height differences do not strictly correspond to differences of published NAVD 88 orthometric heights between bench marks, because the non- parallelism of level surfaces is not reflected in the leveling measurements collected in the field. In contrast to leveled heights, adjusted NAVD 88 heights published by the National Geodetic Survey (NGS) are defined in the same Helmert orthometric vertical system as the orthometric heights obtained through the Global Positioning System (GPS) measurements and the proper geoid height value (apart from occasional small system shifts), such as the values provided by GEOID99 (or the latest geoid model).

The difference between leveled height and orthometric height between two bench marks of the NAVD 88 network represents the "orthometric correction." When this correction is added to a leveled height, it becomes an orthometric height. Orthometric corrections can be as large as several centimeters in mountainous regions where the level surfaces exhibit steeper slopes than in lowlands.

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Published NAVD 88 orthometric heights were derived primarily from first- and second-order leveling (see Special Report by Zilkoski, Richards, and Young, "Results of the General Adjustment of the North American Vertical Datum of 1988" in Surveying and Land Information System, Vol. 52, No.3, 1992). The highest degree of accuracy in the measurement of height differences was achieved by using the most effective methods of observation. Instrumental and environmental systematic errors which cannot be sufficiently controlled by high quality observation techniques are minimized by applying the following corrections to observed data (see NOAA Technical Memorandum NOS NGS 34 by Balazs and Young, "Corrections Applied by the National Geodetic Survey to Precise Leveling Observations," 1982):

Magnetic corrections were also applied to some measurements which were obtained with leveling instruments with automatic compensators that were influenced by local magnetic fields (see NOAA Technical Memorandum NOS NGS 45 by Holdahl, Strange, and Harris, "Empirical Calibration of Zeiss Ni1 Level Instruments to Account for Magnetic Errors," 1986).

The expected leveled difference in height computed by the LVL_DH program includes the corrections documented in NOAA Technical Memorandums NOS NGS 34 and 45, except for the orthometric correction, and should be very close to the actual leveled (observed) height difference obtained in the field.

The slopes of level surfaces are influenced by the attracting forces of the Sun and Moon and by the Earth's gravitational force at a large scale, and by gravity at the local level. Astronomic corrections remove the temporal warpage of level surfaces caused by the Sun and Moon. Measured or interpolated gravity in conjuction with leveling measurements aid in computing the large scale and local slopes of level surfaces which in turn determine the magnitude of ortho- metric correction.

Program LVL_DH converts the published orthometric height difference between two NAVD 88 bench marks into a leveled height difference by removing the orthometric correction from the published relative height. This process requires the exact gravity values at the two bench marks used in the NAVD 88 adjustment. These gravity values are maintained by NGS in its data base. The program can be used either interactively by keying in the needed data or in the batch mode by attaching DSX software, also available from NGS, for the extraction of bench mark data from the data sheets stored on NGS CD-ROMs. The contents of sample file FL125.dat on the diskette were extracted from CD-ROM by the DSX software and include data sheet records; it can be used for testing LVL_DH as an excercise. File LVL_DH.OUT contains sample output from such test.

The expected error in estimating the orthometric correction is about one millimeter or less between two consecutive bench marks of a NAVD 88 level line. This error (in millimeters) will increase in proportion to 1.5 times the square- root of distance (in kilometers) between non-consecutive bench marks. The above estimated error could be slightly more in mountainous regions for bench mark distances of 10 to 30 kilometers. These estimates have been derived empirically and provide general guidelines.

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