[GIS] Inaccurate Buffer Distances

arcgis-10.2arcgis-desktopbuffercoordinate system

When buffering a point, the result is inaccurate to the basemap.

I specify a 200 foot buffer around a point however the resulting buffer has a distance from the point of about 260 feet. Both the measure distance tool and the scale bar on the layout view agree that the 200 foot buffer is indeed greater than 200 feet.

The .MXD uses a coordinate system of WGS84 Web Mercator Auxiliary Sphere as I am using some of ESRIs available online datasets, however I have added other data in different projections.

These data include:

State-provided data (multiple point shapefiles) in State Plane UTM Zone 13N
Field collected data in NAD27
Federally provided data in GCS North America 1983 (Datum NAD83)

I am using the buffer tool in the Analysis toolbox to buffer the point collected in the field (NAD27)

I have tried re-projecting both my location and the resulting buffer however this only results in moving the shapefiles relative to my basemap, with no resultant change is size.

How can I correct this issue?

Note: The displayed NAD27 Point is positioned accurately to the WGS84 Web Mercator basemap. (projected "on the fly" as it was added to the .MXD)

Steps:

Open .MXD
Add Base-layer from ESRI Online database (Aerial Imagery WGS84)
Add Data in the form of .csv; this is the field gathered location of interest in NAD27 Decimal Degrees
Export xy data to shapefile keeping it in NAD27
add exported data to map and remove .csv event
Analysis Tools -> Buffer
Buffer location .shp
Measure distance from point to buffer boundary = inaccurate

This happens because the buffer is in NAD27 as it is applied to the point. the basemap layer is in WGS Web Mercator Auxiliary Sphere and the measure distance tool is measuring the distance on the basemap. If I change the map properties to display in NAD27 I encounter distortion in the effect of oblation of my once round buffers. I also encounter a "stretched" appearance to the basemap and the shapefiles (excluding points of course). This does however plot the buffer boundaries in the correct location with correct distances (verified with on-the-ground references in the basemap) – but they are ovals.

Is there a way to preserve the roundness of my buffers yet still have them displayed accurately without changing the basemap projection (and distorting the image)

Best Answer

Try changing the buffer method from Planar to Geodesic Arguably, in such small scale features this shouldn't change much, but stranger things have happened before.

Here's a case where I buffered some points in a geographic CRS with a planar buffer of 250 meters and displayed on a projected CRS. Using a geodesic method solved this issue for me.

Related Solutions

[GIS] approximate error of Pythagorean Theorem vs. Haversine Formula in measuring distances on sphere at various scales

Using the Pythagorean formula on positions given in latitude and longitude makes as little sense as, say, computing the area of a circle using the formula for a square: although it produces a number, there is no reason to suppose it ought to work.

Although at small scales any smooth surface looks like a plane, the accuracy of the Pythagorean formula depends on the coordinates used. When those coordinates are latitude and longitude on a sphere (or ellipsoid), we can expect that

Distances along lines of longitude will be reasonably accurate.
Distances along the Equator will be reasonably accurate.
All other distances will be erroneous, in rough proportion to the differences in latitude and longitude.

The error depends on the start and end point of the distance calculations. However, because both the sphere and ellipsoid have a circular symmetry around the axis, the error depends only on the difference of the longitudes, so to study this error we might as well take the point of origin to be at the Prime Meridian. Because both the sphere and ellipsoid are symmetric under a north-south reflection, we only need to study points of origin in the southern hemisphere. For any such point we may draw a contour map of the relative error, equal to [Pythagorean calculation] / [True distance].

The Pythagorean formula, using the mean radius of the earth, is

Pythagorean distance =  6371000. * Sqrt[dx^2 + dy^2]] * pi / 180 meters

where dx is the difference in longitudes and dy is the difference in latitudes, both in degrees. (The difference in longitude values is reduced modulo 360 to give the correct value of dx when crossing the antimeridian; not doing so would introduce artificially large errors that tell us nothing about the Pythagorean formula itself.)

The following plots show the relative error compared to the correct distance on the WGS 84 ellipsoid for latitudes from -70 to 0 in increments of 10 degrees. The horizontal coordinate is the difference in longitudes and the vertical coordinate is the latitude of the destination. Light regions have relatively small error: the contour lines are at 1, 1.01, 1.02, 1.05, 1.1, 1.2, 1.5, 2, etc. (The pure white areas in the corners are places where the error goes beyond the range of these contours.) The red dots show the point of origin.

Plots

The vertical white bands testify to the correctness of expectation (1): Pythagorean distances are accurate when there is a small difference in longitudes. The horizontal white bands at low latitudes confirm expectation (2): near the Equator, horizontal distances are reasonably accurate. Otherwise, as witnessed by the extensive darker regions, at all other distances the Pythagorean formula is bad.

We can make quantitative estimates of the maximum error attained for pairs of nearby points (within, say, a few hundred kilometers of each other). Scale--using an appropriate value for the radius--is true along the meridian but along a circle of latitude it errs approximately by the secant of the latitude. For example, at a latitude of 40 degrees the secant is 1.31, implying the Pythagorean formula will give distances about 31% too large in the east-west direction. (This is evident in the upper right contour plot, for a point of origin at -40 degrees latitude, where the region immediately east-west of the red dot lies between the 1.2 and 1.5 contours.) Short distances in all other directions will be too large by some amount between 0% and 31%; longer distances may err by even more (as the contour plots show).

[GIS] Trying to convert coordinates from WGS84 Web Mercator Auxiliary Sphere to WGS84

My question is pretty much cleared up by mkennedy in the comments above.

The "Aux Sphere" version just has a parameter that says use the semimajor axis as the radius and then the sphere-based equations. -mkennedy

The code above transforms coordinates from WGS84 Web Mercator Auxiliary Sphere to WGS84 correctly. The issues I had were caused by a different problem within my data.

This post provides some excellent background on the two projections and their differences and uses.

Best Answer

Related Solutions

[GIS] approximate error of Pythagorean Theorem vs. Haversine Formula in measuring distances on sphere at various scales

[GIS] Trying to convert coordinates from WGS84 Web Mercator Auxiliary Sphere to WGS84

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