Establishing orthometric heights using GNSS — Part 5

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

So far, this series of columns has addressed the following topics: basic concepts of GNSS-derived heights (Part 1), National Geodetic Survey’s (NGS) guidelines for establishing GNSS-derived ellipsoid heights (NGS 58) (Part 2), differences between hybrid and scientific geoid models (Part 3), and procedures and tools for detecting GNSS-derived ellipsoid height data outliers (Part 4).

These four columns were meant to provide the reader with basic concepts and procedures for estimating GNSS-derived ellipsoid heights and understanding hybrid and scientific geoid models. Now that the reader has a basic understanding of GNSS-derived ellipsoid heights and geoid models, this column will discuss procedures for estimating GNSS-derived orthometric heights.

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. As mentioned in Part 4, NGS has developed procedures for estimating GPS-derived orthometric heights and these guidelines are documented in NOAA Technical Memorandum NOS NGS 59. The NGS 59 guidelines are separated into three basic rules, four control requirements, and five procedures that need to be adhered to for computing accurate NAVD 88 GNSS-derived orthometric heights. This column will address the NGS 59 guidelines and methods for evaluating the results of the GNSS project.

The three basic rules are fairly simple to understand and implement, provided that the reader has followed the previous columns in this series.

Three Basic Rules for Estimating GNSS-Derived Orthometric Heights:

Rule 1: Follow NGS 58 guidelines for establishing GNSS-derived ellipsoid heights when performing GNSS surveys (Parts 2 and 4 addressed this rule),

Rule 2: Use NGS’ latest National hybrid geoid model (such as GEOID12B) and latest experimental geoid model (such as xGeoid15B) — when computing GNSS-derived orthometric heights (Part 3 addressed this rule), and

Rule 3: Use the latest National Vertical Datum — for instance, NAVD 88 — height values to control the project’s adjusted heights (this column will address this rule).

The four basic control requirements are also simple, but, in certain regions of the country, may be difficult to implement.

Four Basic Control Requirements for Estimating GNSS-Derived Orthometric Heights:

Requirement 1: GNSS-occupy stations with valid NAVD 88 orthometric heights; stations should be evenly distributed throughout project.

Requirement 2: For project areas less than 20 km on a side, surround project with valid NAVD 88 benchmarks, i.e., minimum number of stations is four; one in each corner of project. [NOTE: The user may have to enlarge the project area to occupy enough benchmarks, even if the project area extends beyond the original area of interest.]

Requirement 3: For project areas greater than 20 km on a side, keep distances between valid GNSS-occupied NAVD 88 benchmarks to less than 20 km.

Requirement 4: For projects located in mountainous regions, occupy valid benchmarks at the base and summit of mountains, even if the distance is less than 20 km.

Figure 1 depicts the NCGS Rowan County Height Modernization project discussed in Part 4. Looking at Figure 1, there are stations with published leveling-derived NAVD 88 orthometric heights distributed throughout the project (requirement number 1).

What do I mean by published leveling-derived NAVD 88 orthometric heights? This is important to note because all NGS datasheets provide the NAVD 88 height with an attribute that describes what method was used to establish their height. The following is a list of attributes used on the NGS datasheet for NAVD 88 published heights:

During the design of the survey, the user should first select as many stations with the attribute of ADJUSTED or LEVELING. If there aren’t any stations in a certain area of the project with the attribute of ADJUSTED or LEVELING, then stations labeled as GPS OBS with values rounded to 2 decimal places should be occupied. The other types of NAVD 88 heights aren’t accurate enough to validate your GNSS results.

Looking at Figure 1, there appears to be a few void areas in the north and east sections of the project. Although, it should be noted that the design meets the 20 km spacing rule (Rule number 3). Figure 2 depicts the NAVD 88 published heights for all leveling-derived stations and GPS-derived orthometric heights published to two decimal places (i.e., cm level). The published GPS-derived orthometric NAVD 88 heights filled in the void areas of the project. This is the practical reality of implementing the guidelines of NGS 59.

In some areas of the United States it may be difficult to locate enough valid NAVD 88 heights in the project’s area. First, let’s define a valid NAVD 88 height. Valid NAVD 88 height values include, but are not limited to, the following: control points which have not moved since their heights were last determined, were not misidentified, and are consistent with NAVD 88. This appears to be fairly simple, but it may be difficult for some users to determine if a station has moved since the height was last determined. In addition, in some areas of the country the user may not find valid NAVD 88 benchmarks every 20 km due to crustal movement. The user then may have to perform some classical precise leveling observations to evaluate the existing NAVD 88 heights and determine the relative accuracy of the geoid model in the areal extent of the project.

This doesn’t mean that the user must perform a leveling survey such that all GNSS stations are leveled to or even perform a large leveling network survey. The purpose of the leveling is to evaluate the geoid model and properly connect to the NAVD 88. Since each case is difference, i.e., NAVD 88 height problems and geoid accuracy will vary in each region of the country, as well as each individual project accuracy requirement will be different, it is impossible to describe exactly what the user will have to do. NGS will, however, assist users when they’re planning their surveys. You can contact a NGS advisor through their Regional Advisor Program.

The five basic procedures for estimating GNSS-derived orthometric heights may appear to users to be the most complex and most difficult to understand. However, as users perform more GNSS surveys and discuss their results with others, they seem to quickly understand why these procedures are needed.

Five Basic Procedures for Estimating GNSS-Derived Orthometric Heights:

Procedure 1: Perform a 3-D minimum-constraint least squares adjustment of the GNSS survey project, i.e., constrain one latitude, one longitude, and one orthometric height value. This procedure was described in Part 4.
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Procedure 2: Using the results from the adjustment in procedure 1, detect and remove all data outliers. (NOTE: If the user follows NGS’ guidelines for establishing GNSS-derived ellipsoid heights (NGS 58), the user will already know which vectors may need to be rejected and following the GNSS-derived ellipsoid height guidelines should have already re-observed those base lines.)

The user should repeat procedures 1 and 2 until all data outliers are removed.

Procedure 3: Compute the differences between the set of GNSS-derived orthometric heights from the minimum constraint adjustment (using the latest National geoid model, for example GEOID12B, and National experimental geoid model, for example xGeoid15B) from procedure 2 above and the corresponding published NAVD 88 benchmarks.

Procedure 4: Using the results from procedure 3, determine which benchmarks have valid NAVD 88 height values. This is the most important step of the process. Determining which benchmarks have valid heights is critical to computing accurate GNSS-derived orthometric heights. (NOTE: The user should include a few extra NAVD 88 benchmarks in case some are inconsistent, i.e., are not valid NAVD 88 height values.)

Procedure 5: Using the results from procedure 4, perform a constrained adjustment holding one latitude value, one longitude value, and all valid NAVD 88 height values fixed.

As mentioned in Part 4, during the analysis of the GNSS-derived ellipsoid heights, the user needed to perform a minimum-constraint least squares adjustment and look for outliers. This ensures that the GNSS-derived ellipsoid heights meet the user’s desired standards. Now, the user must ensure that the NAVD 88 heights that are going to be used to control the final set of GNSS observations and geoid heights are valid.

Part 4 described in detail how to analyze the project’s ellipsoid heights. If the user followed the procedures outlined in Part 4, then procedures 1 and 2 were performed.

The techniques described below are meant to be fairly simple for users to implement. They are not rigorous and are not the only way to detect outliers. They will, however, assist the user in determining which NAVD 88 benchmarks are valid. Procedure 3 is simply computing the GNSS-derived orthometric heights and comparing the results with the published leveling-derived NAVD 88 heights. The set of GNSS-derived orthometric heights are obtained by performing procedure 1. Figures 3 and 4 provide the differences between the GNSS-derived orthometric heights using GEOID12B and published leveling-derived NAVD 88 orthometric heights. (NOTE: One station’s latitude, longitude, and orthometric height (Buffalo 2) was constrained in the minimum-constraint least squares adjustment. Since any of the stations with a published height could have been constrained in a minimum-constraint least squares adjustment, an average difference (a bias) computed using all of the differences was removed from each difference.)

All relative height differences between adjacent station pairs should agree within 2 cm for 2-cm surveys and 5 cm for 5-cm surveys to be considered valid NAVD 88 benchmarks. Relative height differences that do not meet this guideline should be investigated.

Part 3 discussed the difference between hybrid and scientific geoid models and that the user should use both models during their analysis of GNSS surveys. As mentioned above, Figures 3 and 4 provided the difference using GEOID12B; Figures 5 and 6 provide the differences using xGeoid15b. Tables 1 and 2 provide this information in tabular form.

Table 1. Differences between GNSS-derived orthometric heights from a minimum-constraint adjustment (using GEOID12B) and published NAVD 88 heights (GEOID12B results sorted and highlighted).

Table 2. Differences between GNSS-derived orthometric heights from a minimum-constraint adjustment (using xGeoid15b) and published NAVD 88 heights (xGeoid15b results sorted and highlighted).

The reader should note that most differences in Figure 3 are less than 2 cm, but there is a several differences greater than +/- 2cm. Eight stations have differences greater than +/- 2 cm [see Table 1, column labeled “GNSS-Derived Orthometric Height (using GEOID12B) minus Published NAVD 88 Height (cm)”]. These stations should be investigated as a potential outliers.
Looking at Figure 3, the reader should notice that several stations less than 20 km apart have a relative differences greater than 4 cm.

For example, the following three station pairs have large relative height differences: [Buffalo 2 (AB6805) – Phaniel (AB6836): 4.9 cm], [V 49 (FA0151) – Phaniel: 5.6 cm], and [Row 9 (DG5715) – Phaniel: 5.7 cm]. To investigate this further, we need to introduce the scientific geoid model in the analysis. Figures 5 and 6 are plots of the differences using xGeoid15b. The user should notice that the relative differences using the scientific geoid model (Figure 5) between the same stations pairs are all less than the differences using GEOID12B (Figure 3).

For example, the relative differences between Phaniel and Buffalo 2 is 4.9 cm [(2.8 – (-2.1)] using the GEOID 12B geoid model. The relative differences between the same two stations using xGeoid15b is only 0.7 cm [4.2 – 3.5]. This implies that the hybrid geoid model may have been distorted to agree with stations that may have moved since the last time they were observed. This could be an indication that station Phaniel and/or Buffalo 2 may have moved since they were last surveyed. If so, once again, they should not be constrained in the final adjustment.

It should also be noted that only five stations have differences greater than +/- 2 cm using xGeoid15b [see Table 2, columns labeled “GNSS-Derived Orthometric Height (using xGeoid15b) minus Published NAVD 88 Height (cm)”]. However, the five outliers are significantly larger than the rest of the differences (see highlighed section on Table 2). All other differences using xGeoid15b are less than +/- 1.7 cm. These five leveling-derived heights should be investigated for possible movement before constraining their heights in the final adjustment.

As previously mentioned, looking at Figures 5 and 6, stations Phaniel and Buffalo 2 seem inconsistent with the other stations in the southern half of the project. Another potential outlier highlighted in Table 2 is station Row 3 with a difference of -3.8 cm. These stations should definitely be investigated for potential movement.

When performing constrained GNSS-derived orthometric height adjustments, it is important to determine the effect of the constraints on the adjusted heights of the unconstrained stations. If a station’s published height is not valid, then constraining that value could distort the final set of adjusted coordinates. Users should compare the differences between the adjusted heights from the constrained adjustment with the adjusted heights from the minimum-constraint adjustment. Figures 7 and 8 are plots that depict the differences between the adjusted heights obtained from a fully constrained adjustment (using GEOID12B) and a minimum-constraint adjustment.

Looking at Figures 7 and 8, the reader should notice that several of the heights of stations in the southern portion of the network have changed by more than 3 cm. More importantly, some of the closely spaced stations have large differences in relative height changes. For example, the adjusted height at station Phaniel changed -4.9 cm (this station was constrained) and its neighbor station Moose (4 km from Phaniel) only changed -3.1 cm. This means the constraint changed the height difference between Phaniel and Moose by 1.8 cm. If the constraint is valid, then the user should use it in the constrained adjustment. However, during our analysis of this project, we identified station Phaniel as a potential outlier which means that station Phaniel may have moved since it was last surveyed. As previously mentioned, if a station moved since it was last surveyed it should not be constrained because it may distort the adjusted heights around it. Saying that, it is important to maintain consistency in a National Vertical Control Network, e.g., NAVD 88, when incorporating survey data into the network. If the station is not constrained and it did not move since it was last surveyed, then all stations surrounding the superceded station will be inconsistent with its neighbors. Therefore, if a user cannot determine that the station has moved since it was last surveyed, it should be constrained in the final adjustment.

To determine the effect of constraining station Phaniel, another constrained adjustment was performed constraining all published NAVD 88 leveling-derived orthometric heights except for station Phaniel. Figures 9 and 10 are plots that depict the differences in adjusted heights due to constraining all published NAVD 88 leveling-derived orthometric heights except for station Phaniel. The plots indicate that by not constraining Phaniel, the changes in adjusted heights due to that constraint were all reduced. All differences in the area of station Phaniel are less than 3 cm and the relative height changes have been significantly reduced. For example, the relative height change involving station Phaniel and Moose was reduced from -1.8 cm [-4.9 – (-3.1)] to -0.2 cm [-1.9 – (-1.7)], and from station Phaniel to Cold, the relative height change decreased from -2.9 cm [-4.9 – (-2.0)] to -0.6 cm [-1.9 – (-1.3)]. (See Figures 8 and 10.) This is a reason why it is very important to determine if a station’s published height is still a valid NAVD 88 height.

This column discussed procedures for estimating GNSS-derived orthometric heights following NGS 59 guidelines. It provided methods for evaluating the results of the project and identifying stations with valid NAVD 88 published heights. More analysis needs to be performed to identify all the valid stations to be constrained in this project. In the next column, we will continue to analyze the changes in adjusted heights due to different constraints, compare the results to the published NAVD 88 GNSS-derived orthometric heights observed in this project, and investigate the leveling network used to establish the published NAVD 88 leveling-derived orthometric heights.