READ_DMX.TXT file 8-apr-1997 das/dgm The DMEX97 DEFLECTION OF THE VERTICAL MODELS -------------------------------------------- The DMEX97 model is a high resolution deflection of the vertical model covering the region 14-33N, 119-86W. It has been prepared in cooperation with the Instituto Nacional de Estadistica, Geografia e Informatica (INEGI). The DMEX97 deflection model has been designed specifically for Mexico. Due to data coverage and computational issues, one will find differences between DMEX97 and DEFLEC96 in regions of overlap. You have received these models on CD-ROM, or downloaded them from the National Geodetic Survey (NGS) web site, the NGS FTP site, the NGS bulletin board system, or have received the models on individual floppy disks. Among the files you have received are DEFLEC.EXE the deflection interpolation program (DEFLEC.FOR is source code) (version 3.1 -- Written specifically for distribution with DMEX97, but equally compatable with previous deflection models) DOSXMSF.EXE 32-bit DOS extender (needed for DEFLEC.EXE) AREA.PAR text file of the filenames of pairs of deflection grids DMEX97NW.XII (.ETA) the DMEX97 pair for Northwest Mexico 22-33N, 119-106W DMEX97NC.XII (.ETA) the DMEX97 pair for Northcent Mexico 22-33N, 109- 96W DMEX97NE.XII (.ETA) the DMEX97 pair for Northeast Mexico 22-33N, 99- 86W DMEX97SW.XII (.ETA) the DMEX97 pair for Southwest Mexico 14-25N, 119-106W DMEX97SC.XII (.ETA) the DMEX97 pair for Southcent Mexico 14-25N, 109- 96W DMEX97SE.XII (.ETA) the DMEX97 pair for Southeast Mexico 14-25N, 99- 86W DEFGRD.EXE utility program for sub-area extraction and format conversion (DEFGRD.FOR is the source code) To Install (after uncompressing the files) 1) Make a subdirectory on your hard disk (example: mkdir c:\dmex97). 2) Copy the various deflection files into that subdirectory. copy *.* c:\dmex97 /v (for example) 3) Repeat step 2) as required for your other sets of deflection files. (If you have installed from floppies, the files are put in the designated subdirectory.) 4) Check your AUTOEXEC.BAT and CONFIG.SYS files to insure compliance with the following notes: Note 1: DOSXMSF.EXE must either be present in the same directory as DEFLEC.EXE, or, it must be in a directory in your DOS PATH environment variable. (such as: c:\dos, for example) DOSXMSF.EXE may be freely reproduced and distributed, without royalty. Note 2: You must have a statement FILES=46 (or a number greater than 46) in your CONFIG.SYS file. Note 3: Do NOT put DMEX97 files in the same directory as other deflection models (such as DEFLEC96). To Execute Type DEFLEC , and follow the prompts. To Terminate You can stop the program at any time by the Control C key combination. BUT, PLEASE DON'T START YET. PLEASE KEEP READING THIS DOCUMENT. How Program DEFLEC Works ------------------------ The deflection grids are stored in the ".XII" and ".ETA" files. Program DEFLEC will assume that the files in your local directory with .XII or .ETA extensions are deflection files. You can operate with as few as one .XII/.ETA pair, or as many as 18. When the program interpolates a given point, it checks the AREA.PAR file for .XII/.ETA boundaries, and uses the earliest list entry whose boundaries contain that point. The order in which the .XII/.ETA pairsappear on the opening screen indicates the order in which the .XII/.ETA pairs are searched. When running program DEFLEC.EXE, the latitude and longitude of each point must be input. The DEFLEC96 models are relative to the NAD 83 ellipsoid, while all other recent deflection models (DMEX97 and DCAR97) are relative to a GRS-80 ellipsoid, centered at the ITRF94(1996.0) origin. However, latitudes and longitudes in the ITRF94/GRS-80 system are very close to those of the NAD 83 system (with only 1-2 meters of horizontal shift.) So either type of latitude and longitude (NAD 83 or ITRF94) may be input, without affecting the interpolated deflection values. This does *not* imply that the deflections are relative to a different ellipsoid. Using NAD 83 latitudes and longitudes interchangably with ITRF94/GRS-80 latitudes and longitudes is merely an acceptable horizontal approximation. Each deflection model will always contain deflections relative to a specific ellipsoid, stated above. Do *NOT* use NAD 27 latitudes and longitudes. The horizontal shifts between NAD 83 and NAD 27 can exceed 100 meters, causing a noticable difference in the interpolated deflection values. To convert from NAD 27 to NAD 83 latitudes and longitudes you may use programs NADCON or CORPSCON, available from NGS. The AREA.PAR File ---------------- AREA.PAR is a plain, ASCII text file. It specifies the order in which .XII/.ETA files are to be used. If you have a favorite .XII/.ETA pair, put the basename at the top of the AREA.PAR list. There is no problem in having overlapping .XII/.ETA files, nor is there any problem in having nested .XII/.ETA files. The AREA.PAR file specifies which .XII/.ETA pairs are available and their priority of use. PLEASE NOTE: The AREA.PAR file we distribute with DMEX97 contains the names of all the DMEX97 grid pairs. You may not have recieved them all; you may not want them all. This is not a problem. If a .XII/.ETA basename is in the AREA.PAR file, but not in the local directory, then a warning message is issued, and program DEFLEC proceeds with the files that are available and listed. You must have an entry in AREA.PAR for each .XII/.ETA pair to be searched. An Example: You just wish to work with the DMEX97 - Southwest file. So, load AREA.PAR into your favorite line editor, and delete the lines in AREA.PAR referring to the other deflection files. You may now delete those .XII/.ETA files (assuming you ever had them) without receiving any irritating warning messages on the opening screen of program DEFLEC. Data Input ---------- You can key data by hand, point by point, or you can create an input file using a text editor. Several file formats are supported, including the NGS "Blue Book" format. These formats are detailed in a "Help" menu option which appears if you specify an input file name. That file doesn't need to exist if you are only going to look at the supported formats in the "Help". Data Output ----------- Results are collected into an output file. The default name of these files is DEFLEC.OUT, but you can use any legal file name you choose. (A word of advice: Don't use misleading extensions such as .EXE, .XII .ETA, .BAT, etc.) The format of the output file is linked to the format of the input file to maintain consistency. ===================> THE SENSE OF THE SIGNS <====================== A positive meridian component of deflection of the vertical (Xi) indicates that the astronomic latitude will fall to the north of the corresponding geodetic latitude of the point. A positive prime-vertical component of deflection of the vertical (Eta) indicates that the astronomic longitude will fall to the east of the corresponding geodetic longitude of the point. The computed Laplace correction (Hor.Laplace) should be ADDED to a clockwise astronomic azimuth, to obtain a "near-geodetic" Laplace azimuth. Note: the deflection correction is usually negligible, yielding a geodetic azimuth. Note: in many textbooks, the Laplace correction is shown with the opposite sign and is subtracted from astronomic azimuth. The DMEX97 Model ------------------ The DMEX97 model was computed on April 3, 1997 using over one million terrestrial and marine gravity values originally used in the computation of the MEXICO97 geoid height model. The deflections are derived from spline models of the curvatures of MEXICO97. The result is a pair of deflection grids with a 2' X 2' spacing in latitude and longitude, referred to the Geodetic Reference System 1980 (GRS 80) normal ellipsoid. In order to have the deflections refer to the surface of the Earth (and not to sea level), a correction for the curvature of the plumbline was included. One may expect to see larger tilts in the DMEX97 model south of 20 degrees North latitude, due to a lack of adequate gravity coverage. To further exemplify this point, an ASCII map of the data coverage in DMEX97 is included below. Data gaps show up as a blank (a 30' cell with less than 13 gravity measurement points). This is an ASCII map of file: mex97.ns8.released.b It is bounded in latitude by: 14.0 to 33.0 N(degrees) and in longitude by: 241.0 to 274.0 E(degrees) Cell sizes mapped are 30.0 minutes in lat and 30.0 minutes in lon For a cell to have an X, instead of a space, it must contain a minimum of 13.0 points and a maximum of 999999.0 points. There are a total of 38 cells in latitude and 66 cells in longitude. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXX XXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXX XXXXXXX XX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXX XXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXX XX XXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXX X XXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X XXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XX XX X XXXXXX XXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XX XXXXXXXXXXX XXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXX XXXXX XX XXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXX XXXX X XXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X XXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XX XXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX (As an example on reading the above map, the cell which is bounded on the north by 17.0 degrees, on the south by 16.5 degrees, on the west by 269.5 and on the east by 270.0 degrees has an "X", but all 8 surrounding cells do not. This cell is in central Guatamala.) The Instituto Nacional de Estadistica, Geografia e Informatica (INEGI) ---------------------------------------------------------------------- Mexico's Instituto Nacional de Estadistica, Geografia e Informatica (INEGI) was very helpful in providing the observed Mexican gravity data used in the development of this geoid. Most of this information is also contained in the global gravity data base managed by NIMA (see later). INEGI also assisted in various aspects related to quality control when observed gravity values had anomalous behavior relative to surrounding points. It is expected that INEGI's participation in these areas will continue if future revisions of MEXICO97 and DMEX97 models are prepared. The National Imagery and Mapping Agency -------------------------------------- The National Imagery and Mapping Agency (NIMA), which incorporates the former Defense Mapping Agency (DMA), has been of immense help in this endeavor. NIMA has provided a major portion of the NGS land gravity data set. NIMA has also been instrumental in the creation of the various 30" and 3" elevation grids in existence. And, NIMA was a partner in the joint project to compute the new global geopotential model, EGM96. Although the work of the NIMA generally precludes public recognition, their cooperation is gratefully acknowledged. GSFC/NIMA Geopotential Model, EGM96 ----------------------------------- The Goddard Space Flight Center (GSFC) and the National Imagery and Mapping Agency (NIMA) have been engaged in a joint project to compute an improved global spherical harmonic model of the Earth's geopotential. This model incorporates the latest satellite tracking data, as well as altimeter data from TOPEX/Poseidon, ERS-1, and the Geosat Geodetic Mission. EGM96 also incorporates new surface and marine gravity data covering the globe, including the former Soviet Union. EGM96 is a global geopotential model expressed as spherical harmonic coefficients complete to degree and order 360. Therefore, the shortest wavelength this model can exhibit is one degree, and its resolution is one-half degree (about 50 km). Although this model does not reproduce geoid structure at very fine resolution, it is global. We thank the many members of the project team for making this model available. The Laplace Correction ---------------------- An azimuth measured with a theodolite is an astronomic azimuth. It refers to an azimuth expressed in a local horizon coordinate system aligned along the local gravity vector (line of the plumb bob). A geodetic azimuth, on the other hand, is expressed about a local normal to the ellipsoid. An astronomic azimuth is converted into a geodetic azimuth by applying the Laplace correction. The Laplace correction typically takes one of two forms: The Simplified Laplace Correction (Hor. Laplace) : - Eta x Tangent(Geodetic Latitude) The Complete (Extended) Laplace Correction: - Eta x Tangent(Geodetic Latitude) - [Xi x Sine(Azimuth) - Eta x Cosine(Azimuth)] x Cotangent(Zenith Dist.) The second term is known as the deflection correction, and it is negligible for horizontal lines of sight. The output from DEFLEC provides not only the Xi and Eta components of deflection of the vertical, but also provides the horizontal (simplified) Laplace correction. The sense of the sign is such that one should ADD the correction from program DEFLEC (Hor. Laplace) to an astronomic azimuth that is measured clockwise, thereby obtaining a "Laplace Azimuth." Such an azimuth does not contain the deflection correction, and is suitable for encoding into a *60* "Horizontal Blue-Book" record. The MEXICO97 and DMEX97 Models ------------------------------- The geoid is only one of an infinite number of equipotential surfaces of the Earth -- each one is at a different height. The geoid, by definition, corresponds to sea level. Slopes of the geoid surface provide the components of deflection of the vertical at sea level. However, deflections of the vertical at high altitudes will not be the same as sea level deflections. This difference is called "curvature of the plumb line", and can reach several arc-seconds in areas of high altitude and rugged terrain. DMEX97 contains a correction to provide surface deflections of the vertical. For this reason, MEXICO97 slopes will not exactly correspond to DMEX97 deflection components. In short, MEXICO97 and DMEX97 are completely compatible in the sense that they were computed by the same technique (FFT) from a common grid of gravity data. MEXICO97 and DMEX97 are not compatible in the sense that MEXICO97 refers to sea level (geoid height), whereas DMEX97 models deflections of the vertical at the surface of the Earth. The DEFGRD Utility Program -------------------------- DEFGRD -- This converts to and from ".XII/.ETA" pairs of binary files and ASCII text file pairs. It can also be used to extract subgrids in the process of conversion. For example: one can make a .XII/.ETA pair for the state of Quintana Roo by using D96NWU.XII (.ETA), and "converting" from binary (.XII/.ETA) into binary (.XII/.ETA) and specifying the appropriate area boundaries. Remember two things: 1) If you do create new deflection grids, you must update your AREA.PAR file. And, 2) a total of only 18 pairs of deflection grids can be open at once with the PC version of DEFLEC. If you construct many different grid pairs, consider creating different sub- directories with different combinations of grid pairs in them. A Technical Note on Program DEFLEC ---------------------------------- Some users prefer to write their own interpolation software. If you do, please be aware that there is a loss of precision in the grid file headers for grid spacings of 2'. This is accomodated in program DEFLEC 3.00 (and later versions, including the 3.10 version supplied with DMEX97) by internally re-computing the grid spacing in subroutine GRIDS. You might need to place similar code in your interpolation software, depending upon how it was written. ------------------ (Example Fortran 77 code) ----------------------------- *** patch for inexact headers (due to 2' spacing) idx1=idnint(DX1*3600.d0) DX(NAREA) = dble(idx1)/3600.d0 idy1=idnint(DY1*3600.d0) DY(NAREA) = dble(idy1)/3600.d0 ***** DX(NAREA) = DX1 **** old code ***** DY(NAREA) = DY1 **** old code ---------------------------------------------------------------------------- Future Plans ------------ A research effort is underway to improve deflection estimates in the future, in conjunction with an improved geoid height model. One important direction is integrating gravity data with GPS and geodetic leveling measurements, and the study of error in GPS ellipsoid heights and in the NAVD88 vertical datum. It is likely that this research, in conjunction with the completion of the state upgrade GPS surveys, will yield a significant improvement to our geoid and deflection models in 1999. Acknowledgements ---------------- We would like to thank all of the agencies that have contributed to the NGS databases. We thank the United Nations Environment Programme (UNEP) for their GTOPO30 global 30 arcsecond digital terrain data, which was used south of latitude 24N. We also thank the National Geophysical Data Center (NGDC) for their TOPO30 digital terrain data (TOPO30) which was used north of latitude 24N. For More Information -------------------- For Products Available From the National Geodetic Survey: Information Services Branch National Geodetic Survey, NOAA, N/NGS12 301-713-3242 fax: 301-713-4172 For Information on DMEX97 and Future Research: Dr. Dru A. Smith National Geodetic Survey, NOAA, N/NGS5 301-713-3202 Internet: dru@ngs.noaa.gov Dr. Dennis G. Milbert National Geodetic Survey, NOAA, N/NGS5 301-713-3202 Internet: dennis@ngs.noaa.gov Visit our web site: http://www.ngs.noaa.gov/GEOID/geoid.html Best Wishes! README file 8-apr-1997 das/dgm