D. How OP Assigns Sigmas on Constrained Marks

In both session processing and network adjustments, realistic estimates of a CORS or user mark’s positional uncertainties are very important in deriving an accurate solution. In this appendix, we present additional information on the sources of these uncertainties within OPUS Projects.

D.1. Source of Uncertainties for Session Processing

The uncertainties associated with each coordinate are used to construct constraints in session processing. The uncertainties come from four possible sources:

  1. Unpublished user uploaded marks: the coordinate uncertainties come from the source OPUS-S solution used for the mark’s a priori NAD 83 and ITRF2014 coordinates. The reported OPUS-S peak-to-peak uncertainties are scaled by 1.6929 (Schwarz 2006) thereby estimating one sigma uncertainties. The uncertainty is never allowed to be smaller than 0.001 m. The mark’s velocity comes from the HTDP program and given 0.01 cm / yr uncertainties.

  2. Published user uploaded marks: the NAD 83 coordinates and uncertainties are taken from the datasheet for a mark (created from information in the NGS database) when the PID for that mark is associated with the mark in the project. From these coordinates, ITRF2014 coordinates are computed using HTDP. The NAD 83 coordinate uncertainties are transferred to the ITRF2014 coordinates without modification. The mark’s velocity comes from the HTDP program and given 0.01 cm /yr uncertainties.

  3. CORS: a database of ITRF2014 coordinates, velocities and uncertainties derived from the latest Multi-Year CORS Solution (MYCS; see Glossary) adjustment are kept by the CORS data center and used in OP. Occasionally, a CORS’s coordinates are updated because of divergence seen in daily NCN monitoring. In these cases, the coordinates and/or velocity are updated, the coordinates are given 0.1 cm uncertainties; the velocity 0.01 cm / yr uncertainties.

  4. Users can change user mark coordinates and uncertainties (i.e., sigmas) from their defaults (the sources given above) for unpublished marks from the individual mark web pages (not published marks or CORS). In addition, users can change constraint coordinates on the session processing form, but cannot change constrained coordinate sigmas from that form (again, not published marks or CORS).

In addition, a scaling factor specified by the user is applied to those uncertainties in session processing. Labeled the “Constraint Weights” on the session processing setup form, the options are: LOOSE, NORMAL or TIGHT. LOOSE scales constraint uncertainties to be approximately 1 m in magnitude; NORMAL scaled them to be approximately 0.01 m; and TIGHT scales them to be approximately 0.0001 m.

D.2. Source of Uncertainties for Network Adjustments

OP assigns uncertainties to all coordinates that are constrained by the user during a network adjustment. The Preliminary adjustment is best thought of as an extension to the session processing. Uncertainties are assigned to the constrained coordinates the same as in session processing, as explained above.

Geometric coordinates (e.g., latitude, longitude, ellipsoid height) constrained in the horizontal-free, horizontal-constrained, vertical-free and vertical-constrained coordinate constraints follow the guidelines required for submission to NGS:

  1. Unpublished user marks can be constrained (but this is not recommended). By default, OP will constrain the a priori coordinates of an unpublished mark and will assign uncertainties for these coordinates the same as in session processing, as noted above. Users can change the constraint coordinates and/or their sigmas from the mark web page.

  2. Published user marks will be constrained to their published coordinates and uncertainties, taken from the datasheet for a mark.

  3. CORS will be constrained to their published, NCN coordinates. However, the coordinates’ uncertainties are set to equal the root-mean-square (RMS) error values computed from network monitoring results around the time of the project 5. For examples of the most recent RMS values, see the CORS short-term plots. Adjustments using CORS outside of those monitored by the NCN are not allowed.

  4. There are circumstances where published mark or CORS constrained coordinates can appear to be modifiable by the user, but in these cases the marks are treated as unpublished user marks with 0.10 cm coordinate uncertainties.

OP suggests only constraining orthometric heights in the vertical-free and vertical-constrained adjustments following the guidelines required for submission to NGS. All orthometric height uncertainties are computed according to Table D-1, below.

  • For constrained marks with published orthometric heights determined by leveling, uncertainties are based upon the vertical source type and the order and class descriptions in the datasheets as noted in the table above.

  • For constrained marks or CORS with GPS-derived, published orthometric heights that meet height modernization standards (i.e., procedures outlined in NGS-59), constraints are derived from the ellipsoid and geoid height uncertainties appropriately computed using error propagation per the equation in the table above. For these marks or CORS, the datasheet will have a vertical source equal to GPS OBS, and HT_MOD will be listed at the top of the datasheet. Note that the same equation will be used to estimate uncertainties for GPS-derived orthometric heights constrained by the user that do not meet height modernization standards (although such constraints are not recommended).

  • For constrained, unpublished marks labeled as “LEVELING NOT PUBLISHED” in the adjustment setup form, uncertainties are treated as third order leveling . This option allows users to constrain leveling-derived orthometric heights that have not yet been published. If the project is to be submitted to NGS for publication, prior approval of this option is required; please contact the Bluebook Team at ngs.bluebook@noaa.gov.

Table D.1 Vertical uncertainties (sigmas) assigned in OP based on the source of the published orthometric height

Vertical Source on Datasheet

Vertical Sigma (cm)

ADJUSTED or ADJ UNCH*

VERT ORDER - FIRST CLASS 0

0.2

VERT ORDER - FIRST CLASS I

0.3

VERT ORDER - FIRST CLASS II

0.5

VERT ORDER - SECOND CLASS I

0.7

VERT ORDER - SECOND CLASS II

0.9

VERT ORDER - SECOND CLASS 0

0.9

VERT ORDER - THIRD

1.3

RESET or N-HEIGHT

1.3

POSTED or GPSONLV

1.5

GPS OBS and Height Modernization Station (as indicated by HT_MOD special category at the * - top of the datasheet)

where SD_h is ellipsoid standard deviation

No additional scaling of constraint uncertainties is applied for these adjustments.

Literature Cited:

Schwarz, C. R. 2006, “Statistics of Range of a Set of Normally Distributed Numbers”, “CORS and OPUS for Engineers”, ed. T. Soler, American Society of Civil Engineers, Reston, VA, USA, pp. 41-45

Footnotes:

5

If possible, OP uses a 90-day interval centered at the midpoint of the survey to compute RMS. If processing a recent survey, OP will use the nearest 90 days to the midpoint of the survey.