# Establishing orthometric heights using GNSS — Part 6

## Basic procedures and tools for ensuring GNSS-derived orthometric heights meet the project’s desired accuracy

To date, this series of columns has addressed the following topics: basic concepts of GNSS-derived heights, National Geodetic Survey’s (NGS) guidelines for establishing GNSS-derived ellipsoid heights (NGS 58), differences between hybrid and scientific geoid models, procedures and tools for detecting GNSS-derived ellipsoid height data outliers, and basic procedures for estimating GNSS-derived orthometric heights (NGS 59). These columns are meant to provide the reader with basic concepts, routines, and procedures for analyzing, evaluating, and estimating GNSS-derived heights.

As mentioned in the last column “Determining ** valid** North American Vertical Datum of 1988 (NAVD 88) published heights is the most important process when using GNSS data and geoid models to estimate GNSS-derived orthometric heights.” In Part 5 (February 2016) of this series, we discussed NGS 59 guidelines and methods for evaluating the results of the GNSS project. It provided methods for evaluating the results of the project and identifying stations with valid NAVD 88 published heights. In this column, we will continue to analyze the changes in adjusted heights due to different height constraints and compare the results to the published NAVD 88 orthometric heights.

First, we need to discuss what should be considered an outlier when identifying valid NAVD 88 published heights to be used as constraints. According to NGS guidelines for performing GNSS adjustments, the rule of thumb for outliers are shifts greater than 2 cm horizontally and 4 cm vertically (see highlighted section in the box below). The guidelines also stated that *“It is important to realize that this threshold is merely a ‘rule of thumb.’ For individual projects, unconstraining a station may be necessary if shifts are less than the ‘rule of thumb’ threshold, and in some cases it can remain constrained even if shifts slightly exceed the threshold.”*

It is important to understand this concept because constraining the height of a station influences the heights of stations nearby that constraint. Also, not constraining a published height of a station will result in establishing a new height for that station which means it could be inconsistent with other published stations nearby that station. If the station had moved since the last time it was leveled to then *not* constraining the height is the appropriate action to take. However, if the shift is due to some other reason (such as a previous adjustment distribution correction, or ellipsoid and/or geoid issue), then constraining the height may be the appropriate action to take. Selecting constraints is not an exact science; as a matter of fact, at times, it appears to be more like an art or like solving an enigmatic puzzle.

Excerpt of NGS Adjustment Document, adjustment_guidelines.pdf, under section 5 titled Constrained Horizonal Adjustment.
As a general rule, if the adjusted values of the constrained coordinates of a station shift by more than 2 cm horizontally and/or 4 cm in height, its horizontal coordinates and/or ellipsoid height, respectively, should be unconstrained. Doing so means that the published values for the unconstrained passive control station will be updated by the adjusted values determined in the submitted survey (CORS coordinates will |

The NGS guideline mentioned above is for horizontal coordinates and ellipsoid heights. The NGS guidelines under section 6 implies that the user should apply the same guidelines for shifts between GNSS-derived orthometric heights and published NAVD 88 orthometric heights (see highlighted section in the box below). The guidelines also recommend that the user analyze the shifts of stations near each other to determine if stations nearby each other are shifting consistently or if one of the station’s value appears to be an outlier (see underlined section in box below).

Excerpt of NGS Adjustment Document, adjustment_guidelines.pdf, under section 6 titled Vertical Adjustment (Free and Constrained).
6-1. Create the vertical free Afile (Afilevf). Fix one position and one published orthometric height. They can be from the same station or different stations (e.g., good horizontal position in one CC record for a CORS, good OH in separate CC record for a bench mark). Leaving column 77 of the CC record blank indicates the record contains an orthometric height value. Standard deviations of the constrained coordinates and heights should NOT be entered (i.e., columns 15-32 of the CC record should be blank). 70-76 Height, units of millimeters (integer) 77-77 Height Code blank — orthometric height 6-2. Run Adjust with minimum constraints. Assuming the adjustment ran to completion, the statistics of this run will be identical to those of the horizontal free adjustment. Check adjvf.out for big shifts between published and free-adjusted heights. It would be helpful to compute the shifts between the results of the vertical free adjusted and the published heights. Additionally, plot these shifts on a project sketch to determine if several heights near each other are shifting consistently or a height appears to be an outlier and therefore should not be used as control. For inconsistent shifts use resources available such as recovery notes, photographs, and rubbings of the mark. Possible causes could include movement, an unintended mark was observed such as the underground mark instead of the surface mark, or occupying a reference mark rather than the parent station. Look for inconsistent shifts as opposed to areas where the shifts, even high shifts, are consistent. Likewise, look at the geoid heights to ensure they are consistent. If no cause for the shift can be found, the orthometric height may need to be readjusted. 6-3. Create the vertical constrained Afile (Afilevc). Constrain all previously adjusted orthometric heights as indicated above and one NAD 83 adjusted position. The same comments about CC records apply. All GPS-derived Ht Mod heights should be constrained along with bench marks. For ht mod stations the datasheet will read: HT_MOD – This is a Height Modernization Survey Station. 6- 4. Run Adjust with vertical constraints. Run PrePlt2 to list and sort the residuals. Investigate observations with large shifts or residuals to see if any heights should be readjusted. Apply the same rule as in the horizontal constrained adjustment: no rejections due to constraints. Free any heights in question and rerun as a test. Note the differences between the published and readjusted heights obtained from the vertical constrained adjustment. Consider the requirements of the project before deciding whether to readjust additional points. Save the output Bfile from the final constrained vertical adjustment. |

In Part 5, I highlighted a potential issue at station Phaniel. I’ve included the diagrams and tables from Part 5 that depicts the differences between GNSS-derived orthometric heights from a minimum-constraint adjusyment (using GEOID12B and xGeoid15b) and the published NAVD 88 height values (see figures 1-4, and tables 1-2). Looking at figures 1 and 2, there are several large differences between closely spaced constraints when using the hybrid geoid model – Phaniel, Buffalos 2, V 49, and Row 9. As stated in Part 2, the user should compute the results using both the hybrid and the scientific geoid models. Figures 3 and 4 depict the differences using the scientific geoid model xGeoid15b. Notice that the large differences between Phaniel and Buffalo 2 decreased from 4.9 cm using GEOID12B to 0.7 cm using xGeoid15b. However, the larger relative difference between Phaniel and V 49 (3.8 cm) and ROW 9 (5.2 cm) still exists. Also, the difference between Buffalo 2 and V 49 is large (3.1 cm), and Buffalo 2 to Row 9 is large (4.5 cm), but the difference between V 49 and Row 9 is less than 2 cm. The neighbor stations of Row 9 all seem to agree within a couple of centimeters indicating that Buffalo 2 may be a station that needs further investigation.

Next we need to look at the adjusted ellipsoid heights from a minimum-constraint solution compared to the published ellipsoid heights. This procedure was decribed and demonstrated in Part 4. Figure 5 is plot of adjusted ellipsoid height minus published NAD 83 (2011) ellipsoid heights for stations near Phaniel. Figure 5 indicates that the adjusted ellipsoid heights at Buffalo 2, Phaniel, and V 49 all agree within 2 cm. As a matter of fact, Buffalo 2 and Phaniel agree to better than 1 cm from the NAD 83 (2011) published heights. This is an indication that the orthometric height of station Phaniel may be an outlier and should not be constrained. The leveling network in the area requires investigation to validate this conclusion. This will be addressed in a future column. Looking at Tables 1 and 2, two other stations, stations Plaza and Row 3, have large differences between the GNSS-derived orthometric heights from a minimum-constraint adjustment and the published NAVD 88 heights, and they should be investigated.

Figure 6 is a diagram depicting differences between GNSS-derived orthometric heights from a minimum-constraint adjustment using GEOID12B and published NAVD 88 heights surrounding station Plaza. The user should notice that the relative difference in height changes between Plaza and 37 DRD is -3.8 cm (-2.5 – 1.3) and between Plaza and Fifth it is -3.2 cm (-2.5 – 0.7). This is an indication that there is a potential issue with station Plaza. Next, we need to compute the results using xGeoid15b. Figure 7 is a plot of the differences surrounding station Plaza using xGeoid15b. Figure 7 shows that station Plaza outliers relative to station 37 DRD and Fifth are exactly the same, i.e., -3.8 cm (-3.2 – 0.6) and -3.2 cm (-3.2 – 0.0) respectively. Something interesting to note is that station J 181 difference decreased from 2.1 cm using GEOID12B (see figure 6) to 1.1 cm using xGeoid15b (see figure 7). Once again, this is a reason why users should use both the hybrid geoid model and the scientific geoid model when analyzing GNSS-derived orthometric heights.

The other station to investigate based on the large difference in table 2 is station Row 3. Figure 8 is a diagram depicting the differences near station Row 3 using GEOID12B. Notice that the difference at Row 3 is considerably less than the 4 cm; however, the relative difference between Row 3 (-2.7 cm) and station 384 JAS (0.2 cm) is -2.9 cm. This doesn’t seem too large but computing the results using xGeoid15b indicates something different. Figure 9 is a plot of the differences using the scientific geoid model xGeoid15b. Notice that the difference at station Row 3 increased to -3.8 cm and the relative difference between Row 3 and 384 JAS is -3.9 cm. Note, this again emphases the importance of using both the hybrid and scientific geoid models when analyzing GNSS-derived orthometric heights. This large relative difference is an indication that the height of station Row 3 may not have a valid NAVD 88 published height and should be further investigated before constraining the height in the final adjustment.

After analyzing the differences between GNSS-derived orthometric heights from a minimum-constraint adjustment and published NAVD 88 heights to help identify potential outliers, the user can perform a constrained adjustment holding the published height values as constraints. The user should ensure that a constraint does not significantly affect the adjusted heights of neighboring stations. To understand the effects of the constraints on the heights of stations that are not constrained, the user can plot the changes in adjusted heights between the constrained adjustment and the minimum-constraint adjusted heights (with a bias removed). As mentioned in Part 5, any constraint can be used to obtain a minimum-constraint solution so removing a bias based on the differences between the published height values and the adjusted height values obtained from a solution constraining one published height is appropriate. Figure 10 is a plot that depicts the differences between the adjusted heights from an adjustment with all published NAVD 88 height values constrained and the adjusted heights values from the minimum-constraint adjustment. Figure 10 highlights the large relative changes of closely spaced stations such as between Phaniel (-2.8 cm) and Open (-0.6 cm). This means that the constraint at station Phaniel has changed the relative height difference between station Phaniel and station Open by 2.2 cm. This is a large change when you trying to obtain 2 cm heights. Another method to see the effect of the constraints is by plotting the changes in “dU” residuals between the constrained adjustment and the minimum-constraint adjustment. Figure 11 is a plot of the differences in vector “dU” residuals between the constrained adjustment (with all published heights constrained) and the minimum-constraint adjustment.

Looking at figure 11, the user can quickly see that constraining station Phaniel has changed the three vectors associated with Phaniel by 1.9 cm, 2.1 cm, and 2.3 cm. This means that the observed vectors were changed by 2 cm to be consistent with the constraint at Phaniel. This could have an impact on a surveyor performing leveling between these two stations. The analyst should now perform an adjustment not constraining the stations identified as potential outliers. At this moment, in this study, stations Phaniel, Plaza, and Row 3 are considered questionable and their heights will not be constrained.

Figure 12 is a diagram depicting the differences between the GNSS-derived orthometric heights from a constrained adjustment were the height values of stations Phaniel, Plaza, and Row 3 were not constrained. Figure 13 is a diagram depicting the differences between the dU residuals of baselines from the constrained adjustment with heights of stations Phaniel, Plaza, and Row 3 not constrained and the dU residuals from the minimum-constraint adjustment. Figures 14 and 15 provide more detail of the changes in residuals near station Phaniel. Figure 14 depicts the differences when all NAVD 88 heights are constrained and figure 15 depicts the differences when the suspected stations (Phaniel, Plaza, and Row 3) are not constrained. Comparing figures 14 and 15 clearly show that by constraining station Phaniel, the relative differences between station Phaniel and its neighbors are adversely effected by the constraint. For example, the difference in dU residuals between Phaniel and Brown Az Mk decreased from 2.3 cm to -0.2 cm resulting in a 2.5 cm relative height change.

As previously mentioned, station Plaza is another station with a large difference between the adjusted height from the minimum-constraint adjustment and its published height (see tables 1 and 2). Constraining station Plaza results in very large dU residuals between station Plaza and station 37 DRD, i.e, 3.7 cm over a distance of 1.1 km (see figure 16). By not constraining the height of station Plaza the dU residuals on the vector between station Plaza and station 37 DRD changed from 3.7 cm to 0.4 cm (see figure 17). Also, the dU residuals on the vector between station College and station Hudson changed from -1.8 cm to -0.1 cm, and dU residuals on the vector between station Dorsett and station Hudson changed from -1.7 cm to 0.2 cm. The distance between Dorsett and Hudson is 1.2 km. The allowable section closure for second-order, class 2 leveling in 1.2 km is 0.88 cm. If a user wanted to check their leveling work using these two stations they may not check within the allowable because of the large distribution correction applied to the adjusted heights due to constraining the height of station Plaza.

Next, the user should look at the differences in ellipsoid heights between minimum-constraint adjustment and published NAD 83 (2011) ellipsoid heights in the area of station Plaza (see figure 18). Station Plaza did not have a published NAD 83 (2011) ellipsoid height but the closest two stations (Dorsett and Salisbury CORS ARP) both agree within 0.6 cm of the published NAD 83 (2011) ellipsoid heights. This is a good sign tht the ellipsoid heights meet the desired accuracy but doesn’t help to explain the large difference at station Plaza.

The third station with a large relative difference highlighted in table 2 is station Row 3. Figures 19 and 20 provide more detail of the changes in residuals near station Row 3. Notice that the dU residual of the vector between station Railroad and Magna changed from 1.5 cm to 0.1 cm when the height of Row 3 is not constrained. The distance between the two stations is 4 km so the effect of constraining this station is not really significant. It should be noted that one of the reasons it’s being investigated is because of the large relative difference between Row 3 and station 384 JAS using xGeoid15b (-3.9 cm, see figure 9). Figure 21 is a plot of the differences in ellipsoid heights obtained from the minimum-constraint adjustment and their published NAD 83 (2011) ellipsoid heights in the vicinity of station Row 3. Station Row 3 does not have a published NAD 83 (2011) ellipsoid height but all of the stations surrounding the station are less than 2 cm. There does not appear to be any large outliers compared with the published ellipsoid heights in the area. Once again, this means that the next step in the process is to investigate the leveling network in the area.

Up to this point we have analyzed changes in adjusted heights due to different constraints and compared the results to the published NAVD 88 GNSS-derived orthometric heights to identity stations that should be constrained in the final adjustment. As one can see, performing GNSS-derived orthometric height adjustments is more like an art than an exact science. There are a lot of variables and unknowns. Every constraint has an influence on the final set of adjusted heights. Determining this effect and the consequences of selecting an invalid constraint has been described in this column.

When incorporating new geodetic data into the National Spatial Reference System, it is important to maintain consistency between neighboring stations. If the published height of a station is not constrained, it will be superseded by the newly adjusted height. If the station has moved since the last time its height was established then superseding the height is the appropriate action to take. If the difference is due to some other reason such as the results of a previous adjustment distribution correction then superseding the height may not be the appropriate action to take.

In my next column, Part 7, we will look at the design of the NAVD 88 leveling network and published heights in the area to help determine the final set of stations to constrain.

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