Subject: [NEXTEL-1] GPS, GIS, and Removal of Airport Obstructions

From: [email-masked]
Date: Tue, 05 Aug 2003 02:50:58 -0400

GPS, GIS, and Removal of Airport Obstructions

July 1, 2003
By: Fred McCamic
GPS World

Late in 2001, the Federal Aviation Administration (FAA) alerted the San
Diego County Airport to the presence of numerous trees that appeared
to be intruding into airspace in runway approach fans and clear zones
adjacent to Gillespie Field. Because of the hazard that such
obstructions posed to aviation in these areas, FAA mandated that the
county airports division survey several dozen suspect trees and trim or
remove any that exceeded height limitations.

The federal agency allowed the county only about two months to
complete the project. That tight timeline and the absence of a
preallocated budget for the work were complicated by the county survey
section being overbooked and unable to respond in time to meet the
deadline. Consequently, the county's Airports Division and the
Department of Public Works GIS Division devised an inventory plan that
used real-time differential GPS (DGPS) positioning, geographic
information system (GIS) mapping. and other measurement instruments
to identify trees for trimming or removal.

The process required determining the location of each tree, plotting it on
a base map, and identifying the elevation of the top of each tree and the
elevation of the approach fan. Once county GIS personnel had
completed the inventory, the County Real Property Division contacted
affected land owners and supervised the trimming and removal of the
trees. The project demonstrated that ingenuity, good project design and
planning, and appropriate tools can solve a time-critical problem that
might suggest higher-tech and more expensive approaches under other
circumstances.

Solving the Problem

FAA regulations specify "imaginary surfaces" for various classes of
runway (see Figure 1 for an example of such surfaces associated with
one of the runways at Gillespie Field). According to FAA regulations
(Part 77), obstructions that are higher than an imaginary surface must
be removed or a waiver must be granted. Surface specifications are a
function of the class of runway and therefore differ from runway to
runway.

As shown in Figure 1, surfaces relevant to the San Diego County project
include the:

primary surface: a rectangle centered on a runway with elevation
the same as the runway centerline. For Gillespie Field Runway
27R, the surface is 500 feet wide and extends 200 feet beyond
the runway threshold or displaced threshold.
approach surface: a surface longitudinally centered on the
extended runway centerline and extending outward and upward
from each end of the primary surface. The inner edge of the
Runway 27R approach surface is 500 feet wide (same as the
primary surface) and expands to a width of 3,500 feet at a
distance of 10,000 feet at a slope of 34:1.
transitional surface: a surface extending outward and upward at
right angles to the runway centerline at a slope of 7:1 from the
sides of the primary surface and from the sides of the approach
surface.

The airports division staff conducted a preliminary inventory to identify
probable offending trees. We plotted a work map of the airport area
using a digital aerial photo overlain by parcel lines and street names.
The overlay data were from the San Diego Geographic Information
Source (SanGIS) database. Airport Division staff went into the field and
noted the approximate location of trees that appeared to be too tall.

The formal field survey by Public Works personnel to measure and
identify obstructing trees would require three steps:

determining the location of each tree by triangulation from
observation points whose location was established by corrected
GPS
calculating the elevation of each treetop by trigonometry using
the angle above horizontal, measured from eye height at one of
the observation points
comparing the elevation of the treetop to the calculated elevation
of the lowest imaginary surface at the tree location.

Instrumentation

We collected location data using a
real-time differential GPS system
that incorporates pseudorange
corrections transmitted via
geostationary satellites (GEOs). The
backpack system includes an
antenna, receiver, two camcorder
batteries, and a cable to a handheld
computer. The antenna was mounted
on a pole and cabled to the receiver,
which processed the GPS satellite
signals and correction data to
calculate the positions that
processed the GPS satellite signals
and correction data to calculate the positions, in three dimensions, from
which we triangulated the locations of the trees. The receiver was
cabled to the computer, where separate software read the GPS input
and further processed and captured data.

The commercial DGPS service provider uses what it calls "virtual" base
station calculations to generate corrections. This method uses a global
network of high-accuracy reference stations that monitor the GPS
satellite signals. These stations pass the GPS error data to network
control centers where it is compressed and uplinked to the GEOs for
broadcast. Users' receivers use the error data from the geosynchronous
earth orbit (GEO), plus atmospheric modeling, to generate a differential
correction.

The GEO that we used for this project is located above the equator at
101 degrees W longitude. In San Diego County, the satellite appears
approximately 50 to 55 degrees above the horizon in a south-southwest
direction (approximately 157 degrees T). As with GPS signals
themselves, these line-of-sight correction signals from the GEO can be
obscured by terrain or buildings.

Our receiver equipment can also access
corrections from the U.S. Coast Guard
radiobeacon-based DGPS service or from
FAA's GEO-based Wide Area Augmentation
System (WAAS), both of which are free. In
the San Diego area both WAAS satellites are
approximately 12–14 degrees above the
horizon, making them prone to obstruction.
However, we chose to use the commercial
service because it is reportedly less subject
to signal blockage and provides greater
accuracy (one meter versus two to three meters horizontally).

Our GPS unit reportedly provides submeter accuracy 95 percent of the
time. We usually were able to obtain a differential position determination
within less than one minute from a cold start. Occupying a single
position for 10 seconds generally provided the claimed one-meter
horizontal accuracy. For quality control, we confirmed this accuracy by
operating our GPS receivers at survey control monuments selected from
the county's GIS database. These monuments seemed to confirm
submeter horizontal accuracy 95 percent of the time. Curiously, we
have experienced slightly better accuracy in the z (elevation) coordinate
than in x or y. Information from the DGPS service provider suggests that
one can expect vertical errors of 2 to 2.5 times that of horizontal errors.
This is an important consideration because, as this article notes later in
discussing error sensitivities, GPS vertical error in our methodology
converts directly into errors in the final calculations of tree height.
However, as the article will also discuss, our z-component results were
better than predicted.

Magnetic Compass. We determined bearings
using a handheld magnetic compass. The
compass proved to be the weakest link in the
instrumentation, being subject to several
problems. The circular card with the degree
marks attached to the compass needle
tended to stick unless the compass body
was held absolutely level. Moreover, the
compass was affected by masses of metal
such as chain link fence and automobile
engine blocks, and it was somewhat hard to
read.

We achieved quality control for the compass by comparing the
instrument's readings to those of another compass and by shooting
runway and road centerlines, whose true bearings were measured from
our map, and converted to magnetic bearings for comparison to the
compass. If we kept the compass away from sources of magnetic
deviation described earlier, we eliminated associated deflections.
Independent compass readings by various operators were generally
within one degree of each other.

Clinometer. We measured the angle above horizontal to the treetop with
a clinometer, which provides a split view of a bubble level and the target
(see accompanying photo). The instrument had been adjusted by the
vendor at the time of purchase. Comparing two additional independent
readings on the treetop supplied further quality control. In practice,
repeatable accuracy appeared to be within approximately one-half a
degree, the limitation being the observer's ability to determine when the
bubble level was centered.

We collected the GPS data in the handheld
computer using vendor-supplied software. We
configured the software to record data in
California State Plan Zone 6, North American
Datum 1983 (NAD83), because our other GIS
data were stored in that system. We exported
data as ascii text because it preserved elevation
and correction code data. A programmable
vertical offset allowed us to collect GPS
observation points with the elevation of the
ground rather than with the antenna. We later
transferred data from the handheld computer to a
desktop PC for processing.

Field Procedures

We collected data for clusters of trees by occupying a location,
indicating the placement of the GPS operator's right foot with a marker,
allowing 10 seconds of corrected GPS averaging, and then logging the
point to the handheld computer with an observation point identifier. We
could verify DGPS by checking a lock LED on the GPS unit, by a visual
message in the software display, and by the synthesized voice
messages "corrected GPS" or "no corrected GPS."

The compass and clinometer operator then replaced the GPS operator,
put his right heel on the same mark and took compass and clinometer
readings for one or more trees while the GPS operator recorded the
observations in a notebook. The team then moved to a second location
to observe the same trees and repeat the procedure.

Processing the Data

We organized data in two text files, one with observation points and the
other with tree data. Observation points were created by exporting them
from the software with one line per point configured as follows:

pointnumber, y, x, elevation, name

For example, the data for two observation points would look like this:

1,1881065.7505266,6343649.2749577,427.479,'Obs 1'

2,1881414.2322601,6343622.5847365,430.070,'Obs 2'

Tree information was placed in a file with data for each tree occupying
three lines as follows:

Tree_name

Obs_pnt_num,magnetic bearing, angle above horizontal

Obs_pnt_num,magnetic bearing, angle above horizontal

For example, the data for one tree would look like this:

"teton pine"

1,124,11

2,34,17

Horizontal Position of a Tree. We wrote scripts to process the data and
create two GIS feature files - one with observation points and one with
intersecting bearing lines and tree points. We converted bearings from
magnetic to true by adding the local magnetic variation of 14.5 degrees.
This step furnished an angle clockwise from true north, which we then
converted to an angle counterclockwise from true east. The slope (m) of
a linear equation representing the sightline is the tangent of the angle
counterclockwise from true east.

We derived equations in the form y 5 mx 1 b in which y is the
coordinate or "northing" in the California State Plane NAD 83, x is the x
coordinate or "easting," and b is the y intercept of the straight line for
each observation point and bearing. We solved the resulting pair of
simultaneous linear equations and added a point attributed with the tree
name to the coverage at the x,y coordinates of the solution.

Elevation of a Treetop. The height of a treetop above the observer's eye
is calculated by

h3 5 d 3 tan(u) in which:

h3 is the height above eye height
d is the distance from the observation point to the tree
u is the angle above horizontal to the treetop.

In each case, we used the observation nearer the tree for this
calculation.

As Figure 2 shows, the elevation of the treetop was
calculated as follows:

Elev(treetop) 5 elev(obs pt) 1 eye height 1 h3 in which:

Elev(treetop) is elevation above mean sea level
of the treetop
elev(obs pt) is ground elevation above mean
sea level of the observation point - the GPS
data collection software includes a
user-settable correction for the antenna height
eye height is eye height (and thus clinometer
height) above ground - assumed to be 5.5 feet
h3 is treetop height above eye as calculated
above.

This data collection and analysis process resulted in a coverage with
tree locations and the elevation above mean sea level of the treetops.

Imaginary Surface Elevation. Once we determined the locations and
elevations of the treetops, we then compared each treetop elevation with
the elevation of the applicable FAA imaginary surface. A detailed and
careful reading of FAA regulations yielded descriptions of a set of
imaginary surfaces for each runway.

To accomplish the comparisons we followed these steps:

constructed footprints using the GIS editing software, including
its COGO functions
identified the slope of surface
approximated the elevation of the surface at the tree location for
each treetop and each footprint containing the tree location
identified trees with tops higher than the lowest imaginary
surface.

For example: The approach surface footprint for
runway 27R begins 200 feet east of the displaced
threshold and extends 10,000 feet eastward. Width is
500 feet at the west end and 3,500 feet at the east
end. Slope is 34:1. As shown in Figure 3, elevation
above runway elevation of the surface at any point was
approximated by

h2 5 d/slope in which h2 is the elevation above runway
elevation, d is the distance from the centerline at the
west end to the point, and slope is the slope for the
specified fan (e.g., 34:1).

Note that it would be strictly correct, on the basis of the FAA
description, for d to be the distance from the tree location point to the
line (extended) marking the western end of the fan. In the worst case,
for trees closest to the runway and farthest from the centerline, the
approximation overstates h2 by slightly more than one foot. For most
trees the error resulting from approximation was much less.

Sensitivity Analysis

The sensitivity of analysis of tree elevation and
imaginary surface elevation to instrument reading
errors presented some concern. Total sensitivity
depends on the particular geometry of observation
points and trees. The following analysis addresses
typical rather than worst-case geometry. It assumes
that site lines intersect at 60 to 90 degrees (smaller
angles would produce greater sensitivity), that the
distance from the observation point to the tree is
approximately 200 feet (longer distances produce
greater sensitivity), and that the GPS unit delivers
accuracy similar to what we observed relative to
survey monuments (we actually experienced better
vertical accuracy than the vendor has claimed). The
elements of analysis are:

error: GPS elevation
maximum expected error: 1–2 meters
sensitivity: 1:1; that is, a 1-meter error in
observation point elevation causes a 1-meter
error in treetop elevation
error: GPS xy
maximum expected error: 1 meter
sensitivity: low; elevation error is horizontal
error times slope, so for an altitude angle of 15
degrees, a 1-meter horizontal error causes, at
most, a vertical error of 1 3 tan(15
degrees)meters or 0.27 meters (approximately
0.9 foot). For an imaginary surface with 34:1
slope, a 1-meter horizontal error causes a
vertical error of 1 meter 3 (1/34) or
approximately 0.1 foot vertical error.
error: compass
maximum expected error: 1 degree
sensitivity: low; for site lines intersecting at 90
degrees and distance of 200 feet, a 1-degree
error moves the intersection by 3.5 feet. The
sensitivity of the elevations to that movement is
low (see prior item); given the above
assumptions, a 1-degree error in compass
reading causes about 0.1-foot vertical error.
Note that more-acute intersection angles
increase the sensitivity: at 60 degrees, a
1-degree error moves the intersection 4.6 feet
and at 30 degrees a 1-degree error moves the
intersection 14.4 feet.
error: clinometer
maximum expected error: 1 degree
sensitivity: moderate to high; at a distance of
200 feet and an angle above horizontal of
approximately 15 degrees, a 1-degree error in
clinometer reading causes an elevation error of
approximately 3.7 feet.

Targeting for Trimming

We surveyed 30 trees using GPS and the other
means of instrumentation and one more using a
measuring wheel and the clinometer. Of those 31
trees, 22 were identified as too tall with respect to
the relevant imaginary surface.

If the treetop elevation of each tree was higher than
any imaginary surface elevation, we earmarked
that tree for trimming and calculated the amount of
height to be trimmed.

We produced maps using mapping software that shows fan boundaries,
trees, parcel boundaries and assessor parcel numbers, and street
names, all overlaid on a geo-orthorectified digital aerial photo. We
identified trees by number and prepared a table that listed trees, treetop
elevation, fan elevation, and the amount of necessary trimming. We then
provided this information to the county's Real Property Division, which
would be responsible for arranging the tree trimming.

The Real Property Division staff asked us to complete the table by
adding the after-trimming height of the treetop from the ground. This was
somewhat of a problem because, in most cases, we had not occupied
the location of the tree and therefore had not collected the elevation at
the base of the tree. Instead, we used the elevation of the nearest
observation point as a base elevation, and in a limited number of cases,
we revisited the tree and collected or estimated a corrected base
elevation. The revised table provided the Real Property Division with the
information it needed to complete the project.

Real Property staff made one additional request - they asked for a
general height-above-ground limitation for tree height by neighborhood to
help them manage tree trimming in the future. We were unable to
accommodate their request because the sloping terrain made it
impossible to provide a single valid number for a neighborhood.

Trimming the Trees

Property owners are legally responsible for trimming their trees so they
are not obstructions. In some cases, the Real Property Division
determined ownership of a tree simply by examining the map. Many
tree crowns straddle property lines, however, so sometimes Division
staff determined ownership in the field by observing the location of the
base of the tree.

Several property owners doubted their trees were obstructions. Airport
staff responded by providing a tour during which owners stood at the end
of the runway and looked back toward their homes. From that vantage
point the tall trees were conspicuous; property owners recognized their
trees, generally accepted that they were obstructions, and most
submitted to the work within the necessary time frame. Only one
homeowner has not complied and is applying for an FAA exemption.

Conclusion

For all practical purposes, the tree survey project was a success. The
work was completed in a timely manner, and, given effective follow-up
by the county's Real Property Division, the trees were trimmed or
removed as required, and the airport operations continued without
interruption.

Still, in looking at the error analysis, it is impossible not to ask, Could it
have been done better? Assuming that we had allowed the worst case
for every variable identified in the error sensitivity analysis and that all
the errors were in the same direction, the error total would be
approximately 10.7 feet. We used a typical distance of 200 feet from
observation point to a tree even though most distances were less than
200 feet. A couple of distances were a bit more than 300 feet, making
the worst-case error closer to 12–15 feet. The majority of cumulative
elevation errors, however, were approximately 3–6 feet.

Could we have done better? Yes and no.

The largest single source of potential error was the elevation of the
observation point, as captured by the GPS unit. The most salient factor
driving the way we did the project was the pressure and tight deadline
imposed by FAA. So, in a sense, we couldn't have done much
differently.

On the other hand, we did pass up the opportunity to use a conventional
transit that would have provided better accuracy. We used the compass
and clinometer in part because we wanted to travel light and avoid
drawing too much curiosity from local residents. Although the
clinometer and compass appeared to give us repeatable measurements
to within about one degree, the transit would have read angles to one
minute, or one-60th of a degree. That would have reduced the error from
vertical angle measurement from approximately 3.25 feet to
approximately 0.05 feet, or effectively zero for our purpose. In
retrospect, we should have borrowed the transit.

Since project completion, non–survey grade GPS units with decimeter
accuracy have become available at moderate prices. Their ability to
reduce possible error from approximately six feet to approximately four
inches is pretty close to eliminating it entirely.

Acknowledgments

Eric Nelson, an engineer in the San Diego County Department of Public
Works Airports Division and the project coordinator, interpreted the Part
77 regulations, classified the function of each runway, and determined
the dimensions and slope of the various surfaces.

Mike Binge, San Diego County Department of Public Works GIS
section manager, enabled DPW/GIS to acquire GPS equipment and
apply it to current projects.

SanGIS, a joint powers agency of the city and county of San Diego, is
responsible for regional digital geographic databases (map records)
used with GIS software products. This project used data from the
SanGIS data warehouse.

San Diego Association of Governments (SANDAG), the forum for
regional decision making, builds consensus, makes strategic plans,
obtains and allocates resources, and provides information about a broad
range of topics pertinent to the region's quality of life.

This article is based on a paper presented at the Environmental
Systems Research Institute (ESRI) 2001 International User Conference
held in San Diego, California.

Manufacturers

The GIS software for this project was developed by ESRI (Redlands,
California) and includes ArcInfo GIS, ArcEditor, ArcPlot, and Arc Macro
Language. The project used a Sokkia (Olathe, Kansas) AXIS3 GPS unit
and the company's Imap software, Virtual Base Station DGPS
corrections from OmniSTAR (Houston, Texas), a Hewlett-Packard
Company (Palo Alto, California) Compaq iPAC handheld computer, and
Activesync software from Microsoft (Bellevue, Washington)

http://www.gpsworld.com/gpsworld/article/articleDetail.jsp?id=63227

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