Geoid-Spheroid Separation

Models

A geoid model is required before N-values can be extracted, and the type of model is determined by the Interpolation Method in Job Configuration.

There are two types of model.

• The Points menu Form TIN Geoid Model option forms a triangular mesh from irregularly positioned fixed points and must be created within each job whenever required. The data required will be horizontal coordinates and N-values for established survey marks or other control points - these points may also be the control for the survey job at hand although they do not need to be. Triangle models may be more suitable for smaller project areas where a closer network of known points occurs but may also be useful where a large number of known points occur over an extensive area. The interpolation method must be set to Fixed-point TIN to use this model.
  
  
• The second type of model is where N-values (and perhaps vertical deflections) have been computed in a regular square grid pattern and may extend over extensive areas. In Australia, data is readily available for the AUSgeoid models for which N-values on a regular 1- or 2-minute geographic grid and relating to the GRS80 spheroid are published (Geoscience Australia - www.ga.gov.au/nmd/geodesy/ausgeoid/). Geoid data for many other countries may be interpolated from a number of other ASCII text and binary formats. The interpolation method must be set to Bi-cubic or Bi-linear to use this type of model and a grid-file covering the area of interest must be available (see the section Grid-file interpolation method below).

The display of the current geoid model is controlled by the Geoid model checkbox in Display Settings - refer to this topic for more information.

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Choice of interpolation method

Bicubic grid interpolation is the best method to use by reason of it being the most accurate method; it should be the method of choice wherever possible and is suitable for large or small areas. The bilinear grid method is less accurate but is used in the bicubic grid method at grid corners and edges. The triangle method is suitable for smaller areas when a grid model is not available but the geoid values for control points are already known. With a triangle model care should be taken if geoid values are extrapolated for points outside the model area.

Grid-file interpolation method

Interpolation of geoid and deflection values from a grid-file model may use either of the bicubic or bilinear methods.

• Bilinear interpolation uses the four corner nodes of the grid square to determine the value of the interpolation function at the position of the required point. However the gradient of the function changes discontinuously at the edges of the grid square.
  
  
• Bicubic interpolation is the more accurate method as it uses the four corner nodes of the grid square plus the twelve closest surrounding nodes; an interpolation function is derived where the gradient changes smoothly from one grid square to the next, thus more closely representing the continuous nature of the geoid surface. If the point for interpolation falls within a grid square which is next to a grid boundary, the interpolation method reverts to the bilinear method. The bicubic method should be the method of choice for normal use.

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Data file optimisation - Bilinear & bicubic interpolation

If Interpolation Method is set to Bilinear or Bicubic interpolation, one of the following optimisations may be applied, depending on the format of the gridded geoid data:

• Australian AUSGeoid .DAT/.TXT or South African .DAT formats

• Usually the coverage of the data contained in a selected geoid data file will be far greater than is actually required for a job even of large extent. Geoida may therefore window the area of interest from the nominated geoid grid file based on the extent of the job plus a margin 2 times the grid interval. This reduces (usually by a considerable amount) the amount of data to scan during interpolation - this is an important feature of Geoida that attempts to keep at a minimum the amount of time taken to interpolate geoid data and is necessary because, unlike other ASCII text formats available, the Australian AusGeoid formats and the South African DAT format are not converted to binary files to maximise speed and efficiency.

  To accomplish the best efficiency, the windowed data is re-written to a new file in the same format and named the same as the original file but with the current job name inserted to identify the original file and the job to which the new file relates. The Geoid File field in Job Configuration is then updated with the new file name and on a subsequent occasion when interpolation is required in a selected option, the windowed file will be used.

  The windowed file has an extra header line inserted, beginning with the keyword 'GEOIDA_LOCAL_WINDOW', that records the name of the original grid file. If the job later increases in size by the addition of new points or by adjustment and it no longer "fits" the windowed file or it extends beyond the previously-windowed area, a new window of data will be extracted from the original geoid file and written to a new window file.

  If the original geoid grid-file is small and not greater than 200kb in size, or if the windowed file is not a significant saving over the size of the original file (not less than 0.75 of the original file size), the windowed file will not be saved.

  For more information about working with Australian AUSGeoid .DAT/.TXT or South African .DAT geoid files, refer to Interpolation tips below.

  
  
• General ASCII text and binary formats - Geoid data in these formats (ie, not Australian AUSGeoid .DAT/.TXT or South African .DAT format) is not windowed, but Geoida will re-write the ASCII text data to a new file in the US-NGS binary (.BIN) format. Data can be read for interpolation from files in binary format much more efficiently than reading directly from a sequential ASCII text file. Files re-written to a binary file will be named as the original file but with the current job name inserted and with the .BIN extension; if a file of the same name already exists it will be over-written. The Geoid File field in Job Configuration is updated with the new file name and will be used thereafter.

  Note: In some ASCII text formats the data is stored from the southern-most edge of the coverage area increasing towards the north (latitude increasing northwards through the file) whereas other formats are recorded in the opposite direction, from northern-most with latitude decreasing southwards. Since the US-NGS binary (.BIN) format convention is southern-most first with latitude increasing northwards throughout the file, to account for some formats being recorded in the opposite direction, when Geoida re-writes the original data to the BIN format the number of rows in the header line is recorded as a negative number - this may be an issue if the Geoida-created BIN file is subsequently used in another software application.

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Interpolation and data reduction

Direct interpolation of geoid-spheroid separation for individual or multiple points may be done at any time in a number of different ways once a model has been formed or is otherwise available. For individual points (i.e., one at a time) use the Interrogate Point option, the Modify function in List Points / Export option, or when creating new points (or provisional points for least-square adjustment) use the Digitise Provisional Points option. To interpolate for multiple points at once, use Interpolate Geoid values in Window.

When processing survey field observations, interpolation of N-value is made differently depending on the processing option to be used but is generally made in the following stages:

1. an initial value for reducing a distance observation to spheroid, and
2. deriving the N-value for the resulting computed point, according to the processing option:
   • Radiations and Traverse (Bowditch or None adjustment) - derive N-value at first approximation of the new point's coords
   • Least-Squares adjustment - derive N-value for first provisional coords before reducing distance observation
3. evaluate a final value for all non-fixed points upon exit from the option.

Note - Vertical gravitational deflections are available only from the Australian AUSGeoid .DAT/.TXT formats and are interpolated together with the undulations and applied to individual points, however the deflections are otherwise applied only to certain observation types in Least Squares Network Adjustment - refer to Corrections Applied.

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Interpolation tips

The following tips apply only to the Australian AUSGeoid .DAT/.TXT or South African .DAT formats. All other formats are either binary formats or are ASCII text formats that Geoida will automatically convert to binary; binary files are handled differently by Geoida and do not require creation of windowed files.

1. Creating new points with the Digitise Provisional Points option - If the current geoid file is a windowed portion of a larger original file and a new point falls outside the windowed area, Geoida will automatically reassess the geoid extents from the original file (named in the inserted GEOIDA_LOCAL_WINDOW keyword line - see above) and create a new windowed file to cover the larger job area. This could potentially occur with every new point created. To prevent this happening, create the first new points at the limits of the area and work inwards. Geoida will not re-window the geoid area for new points falling inside an existing windowed area. Note - new points may also be created with numerous other options, but even though these points may fall outside an existing windowed geoid area, the geoid extents are not reassessed automatically - see next item.
   
   
2. To manually reassess the windowed area after new points have been inserted, imported or computed, use the Reset Geoid Window option, or double-click an existing point outside the existing area (Interrogate Point option) and click the Interpolate button. This will cause Geoida to re-assess the windowed area by re-reading from the original geoid file.
   
   
3. If points are deleted that effectively reduces the area covered by the remaining points in the job, Geoida does not automatically reduce the windowed geoid area. To re-size the windowed area downwards, use the Reset Geoid Window option; this will usually create a new, smaller file. If there is no change in the file, it may be necessary to use the Reset (Fix) Bounds option first (Refresh/Review Options).
   
   
4. If the size of the windowed geoid area cannot be reduced, it may be because there are other points that still exist outside of the area currently displayed on-screen. Locate these points by Zoom Bounds (Zoom Options) or the List Points / Export option. It may also be necessary to check the Zoom Point Range option to ensure that all available points are displayed.
   
   
5. Sometimes Geoida may be found to be frequently attempting to re-size the geoid extents but the windowed area remains unchanged at the same as the maximum size of the original area. This may be frustrating to the user because of the time taken for each failed re-assessment, but may occur because there are valid points that exist in the job but fall outside of the geoid extents as defined by the original file. Or the user may wish to retain the nominated original file and geoid window as-is and prevent the window being down-sized to a smaller area. Geoida can be prevented from making any further attempts to re-size the geoid extents by the use of the 'NO_RESIZE' keyword in either of two ways:
   
   
   1. Windowed file: Edit the file and add the [NO_RESIZE] tag at the end of the GEOIDA_LOCAL_WINDOW header line, eg

   2. GEOIDA_LOCAL_WINDOW,"D:\Geoida Reference\Geoid Files\SH50-14.dat",[NO_RESIZE]

   3. Original (non-windowed) file: Insert the tag [NO_RESIZE] into the file name, eg

   4. SH50-14[NO_RESIZE].dat

   The required geoid file with either of these changes applied should then be re-selected in Job Configuration. Note that the NO_RESIZE keyword is not case-sensitive but must be enclosed in the square brackets.
   
   

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