The Problem with Parallax: Part 2

This is the second of a three part series about parallax problems with satellite data. Part 1 presented an overview of parallax in this context and reviewed differences in orbital characteristics of geostationary and polar satellites. In this section we’ll examine more closely parallax issues associated with geostationary satellites. Part 3 will cover the topic as it relates to polar satellite data.

As discussed in the previous post, a satellite must be very high in order to orbit at a rate equivalent to the earth’s rotation, making it geosynchronous. The diagram below shows the scale of this orbital distance relative to the diameter of the earth. “Nadir” is the point on the globe where a satellite is looking directly downward. For geostationary satellites, the longitude may vary, but the latitude will always be over the equator. Since the orbital distance is very far from earth, the viewing angle “off-nadir” initially changes slowly with increasing latitude, but then increases significantly near the edge of the visible earth disk. As a result, above 50 degrees north (and south) parallax displacement error grows significantly.

The parallax offset problem is not restricted to the poles and can occur near any edge of the full disk view of the earth. However, it is mitigated somewhat in lower latitudes by an array of geostationary weather satellites positioned strategically around the equator. While this provides most non-polar locations with narrow viewing angle options, it does not completely eliminate it. Here is an interesting blog from CIMSS that presents an example of parallax displacement differences in the mid-latitudes between three geostationary satellites.

The United States has two primary Geostationary Operational Environmental Satellites (GOES) in operation: GOES-West over the eastern pacific, and GOES-East over the eastern US and South America. Other geostationary satellites are operated by Japan, the European Union (EUMETSAT), China, Russia, and India.

In October 2016, the first in a series of next generation geostationary satellites, GOES-R, was launched. The advanced technology on this satellite has significantly improved detection and observation capabilities, directly affecting public safety and economic prosperity. Sensor capabilities on GOES-R are very similar to one of Japan’s geostationary satellites, Himawari-8, which is in orbit around 140° east. The example below is a “true-color” image from Himawari-8 in which the Australian continent is near the center of the southern hemisphere, while the Bering Sea and Aleutian Islands are near the far northern edge.

Although image resolution with the new GOES-R satellite will be four times greater, it is important to remember that parallax will continue to be a problem in polar regions. The graph at right is an easy way to estimate the effect of parallax cloud displacement in geostationary satellite data.

The “Normalized Cloud Offset” (NCO), plotted as a function of latitude, is the ratio of the northward cloud displacement to the height of the cloud (in equivalent units). For example, at 60 degrees in the graph, the NCO is around 2.5, so a cloud top of 20,000 ft (or 3.8 mi) is offset 9.5 miles (3.8 mi x 2.5). The direction of the apparent offset, is to the north (away from the satellite) along a great circle arc from the satellite’s nadir point at the equator. From the graph you can see that displacement error grows exponentially north (or south) of 50 degrees in latitude.
In the northern latitudes, polar satellite data can add critical information about the location and structure of weather features, since the center of a pass has virtually no parallax displacement, and resolution is significantly improved. Below is a comparison of two infrared (IR) satellite images of convective clouds near Chichagof Island in Southeast Alaska, one from GOES-West, and the other from a NOAA polar satellite passing overhead around the same time.
In addition to the obvious resolution differences, the polar data shows that GOES has a convective cell incorrectly displaced 6 miles to the north. From the Normalized Cloud Offset curve, at a latitude of around 58° N the NCO is around 2.0, but displacement is dependent on cloud top height as well as latitude. This height is not known but can be inferred from the cloud top temperature measured by the satellite, which is around -35° C. A nearby atmospheric radiosonde sounding at that time (below) shows temperatures in that range to be around 5000 m or 3.1 mi. Multiplying 3.1 mi by the NCO of 2.0 gets a displacement of 6.2 mi as verified by the two images.
Here is another example a little farther north over the Kluane and Wrangell-Saint Elias regions. In this case the displacement error is much greater, around 14-16 miles, because the clouds are located farther north and the tops are much higher. In the far northern regions of Alaska, the displacement error is so great that it is often difficult to quantify.
For northern latitudes, the high frequency of geostationary data is invaluable for tracking the movement and evolution of cloud features, however the displacement of these features due to parallax should always be taken into account. When following critical weather events, comparisons between geostationary and polar satellite data can be an important exercise in order to correctly determine the location of affected areas.

By Carl Dierking