README file 26-jul-94 dgm/dgs You have probably received one to nine floppies, depending upon your request. Among the files on the floppies are: DEFLEC.EXE the deflection interpolation program (DEFLEC.FOR is source code) AREA.PAR text file of the filenames of pairs of deflection grids D93NE.XII (.ETA) the DEFLEC93 pair for Northeastern U.S. 36-50N, 87- 66W D93NC.XII (.ETA) the DEFLEC93 pair for Northcentral U.S. 36-50N, 106- 85W D93NW.XII (.ETA) the DEFLEC93 pair for Northwestern U.S. 36-50N, 125-104W D93SE.XII (.ETA) the DEFLEC93 pair for Southeastern U.S. 24-38N, 87- 66W D93SC.XII (.ETA) the DEFLEC93 pair for Southcentral U.S. 24-38N, 106- 85W D93SW.XII (.ETA) the DEFLEC93 pair for Southwestern U.S. 24-38N, 125-104W D93HW.XII (.ETA) the DEFLEC93 pair for Hawaii 18-24N, 154-161W D93PR.XII (.ETA) the DEFLEC93 pair for Puerto Rico/V.I. 15-21N, 70- 63W AL94N.XII (.ETA) the ALASKA94 pair for northern Alaska 61-72N, 179-128W AL94S.XII (.ETA) the ALASKA94 pair for southern Alaska 51-62N, 179-128W To Install 1) Make sure your original floppies are write protected! 2) Make a subdirectory on your hard disk (DEFLEC will also run on floppies) md deflec93 (for example) 3) Go into the new subdirectory . cd deflec93 (for example) 4) Copy the first floppy disk into your subdirectory. copy A:*.* /v 5) Repeat step 4) as required for your other floppies. 6) Put the original floppies in a safe place! 7) How many files can be open at the same time? a) Go to the main directory and list CONFIG.SYS > c: > cd \ > type config.sys b) Look for a "FILES=..." entry. eg: FILES=20 c) DEFLEC can open up to 20 files at one time (with 6 pairs of grids). If you do not have a "FILES=..." command, then you need to add one to CONFIG.SYS using a text editor. Add the line: FILES=20 If you do have a "FILES=..." command, but the number of files is less than 20, then you need to edit that line using a text editor. Edit the line to read: FILES=20 You can read more about CONFIG.SYS and FILES in your DOS manual. 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 six. When the program interpolates a given point, it checks an internal list of boundaries, and uses the earliest list entry whose boundaries contain that point. The order in which the .XII/.ETA pairs appear on the opening screen indicate the order in which the .XII/.ETA pairs are searched. 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 on your floppies contains the basenames of six DEFLEC93 grid pairs. You may not have gotten all six; you may not want all six. 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. There are NO default names for .XII and .ETA files. You must have have an entry in AREA.PAR for each .XII/.ETA pair to be searched. An Example: You just wish to work with the DEFLEC93 - Southwest file. So, load AREA.PAR into your favorite line editor, and delete the lines referring to D93SC, D93SE, D93NW, D93NC, and D93NE. 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. 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 DEFLEC93 Model The DEFLEC93 model was computed on February 3, 1993 using the over 1.8 million terrestrial and ship gravity values originally used in the computation of the GEOID93 geoid height model (Therefore, we retain the "93" designation). The deflections are derived from spline models of the curvatures of GEOID93. The result is a pair of deflection grids with a 3' X 3' spacing in latitude and longitude, referred to the Geodetic Reference System 1980 (GRS 80) normal ellipsoid. In our study, we assessed the accuracy levels of the earlier (May, 1991) DEFLEC90 model with observed astronomic latitude and longitudes at 3421 control points (NAD83) throughout the United States. It was demonstrated that DEFLEC90 has a 1 arc-second RMS accuracy. However, it is likely that the typical user will obtain even better results, particularly at lower elevations and in less rugged terrain at high elevations. One study indicates that one may achieve 0.5 arc-second (one sigma) accuracy in the Eastern part of the United States. The ALASKA94 Model Deflections of the vertical in Alaska were computed from the ALASKA94 geoid model similar to the manner that was used for the DEFLEC93 model. Because of the convergence of the meridians in high latitudes, a 3' by 6' (latitude and longitude, resp.) was used. A correction for the curvature of the plumbline was included using Helmert's projection. This more elaborate correction was not applied in the DEFLEC93 model. At the time of this issue an accuracy assessment has not been made. Generally, the results are expected to be similar to those for DEFELC93, although in regions with poor data coverage the accuracy may degrade. Work in this area is continuing and will be available in the near future. The Defense Mapping Agency The Defense Mapping Agency (DMA) has been of immense help in this endeavor. DMA has provided a major portion of the NGS land gravity data set. DMA has also been instrumental in the creation of the various 30" elevation grids in existence. Although the work of the DMA generally precludes public recognition, their cooperation in this work is gratefully acknowledged. Other Programs Depending on which disks you requested, you may have received some other programs which are nice to have. 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 Wyoming by using D93NW.XII (.ETA), and "converting" from binary, .XII/.ETA into binary, .XII/.ETA, and specifying the Wyoming state 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 6 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. 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 GEOID93 and DEFLEC93 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, is at 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. DEFLEC93 contains a "normal curvature of the plumb line" model to provide approximate surface deflections of the vertical. For this reason a meridional (N-S) GEOID93 slope will not exactly correspond to a DEFLEC93 Xi component. (For ALASKA94 a normal correction model was not employed, but rather a Helmert projection to account for the plumbline curvature between the geoid and the earth's surface. A constant density was assumed of 2670 kg/m**3. ) In short, GEOID93 and DEFLEC93 are completely compatible in the sense that they were computed by the same technique (FFT) from a common grid of gravity data. GEOID93 and DEFLEC93 are not compatible in the sense that GEOID93 refers to sea level (geoid height), whereas DEFLEC93 models deflections of the vertical at the surface of the Earth. The same is true for ALASKA94 and its deflections. 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 measurments. It is likely that this research, in conjunction with greater availability of high precision GPS surveys, will yield a significant upgrade to our deflection and geoid height models in the next several years. For More Information For Products Available From the National Geodetic Survey: National Geodetic Information Center 301-713-3242 For Information on DEFLEC93, GEOID93, or ALASKA94 and Future Research: Dr. Dennis G. Milbert Donald G. Schultz Internet: Dennis.Milbert@noaa.gov Internet: donald@charybdis.ngs.noaa.gov National Geodetic Survey, NOAA 301-713-3202 Best Wishes! README file 26-jul-94 dgm/dgs