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What Rainbows Can Teach Us About Dual-Band GNSS

Multiple Explanations for Rainbows

If someone asked you, "Why does a rainbow appear?," how would you answer?

"If you see a rainbow after the rain lets up and the sun comes out, it symbolizes a wish in your heart. Therefore, you see the rainbow because you have such a wish."

Depending on the situation, this might be a correct answer. In more scientific terms, however, you could answer as follows:

1. Airborne, globular droplets of rainwater receive parallel rays of sunlight.
2. The angle of reflection for outgoing light from these droplets after being reflected and refracted is consistent at approximately 42 degrees compared with the entry angle.
3. Droplets which fulfill the above conditions create what appears to be an arc, or "bow," in the sky from the viewer's perspective.

That's the reason which light reflected by the rain droplets appears as a bow—hence the term "rainbow." However, this does not explain the reason why a rainbow appears as a gradient of vivid colors. Further elaboration is needed:

4. The Sunlight comprises mixed-wavelength white light, which undergoes spectral dispersion when it passes through a prism.
5. This dispersion results in differing degrees of refraction, with the shorter-wavelength violet light being refracted more than the longer-wavelength red light.
6. Similarly, light passing through a raindrop experiences differing levels of refraction depending on the color (wavelength), resulting in spectral dispersion. The difference between the red and violet light seen over this spectrum is roughly two degrees.
7. In a rainbow, a gradient ranging from red to violet is visible based on the viewing angle difference of roughly two degrees. The overlapping raindrops encountered along one's line of sight when viewing a rainbow make the rainbow's colors appear more vibrant.

To summarize more succinctly, the explanation goes: Numerous uniform and globular raindrops in the sky receive vertical white light, which passes through and is reflected and dispersed to create the rainbow phenomenon. If you were asked to explain the concept on a test in 30 words or less, this answer would receive top marks.
Furthermore, by expanding this thinking beyond Earth to other planets within the Solar System, such as Venus with its dense atmospheric sulfuric-acid content, Saturn's moon Titan which is believed to have liquid methane, or other such celestial bodies, one could expect to encounter rainbows of differing sizes and colors due to the refractive indexes and wavelength-based light absorption characteristics of the relevant liquids, raindrop sizes and uniformity as affected by surface tension, and various other physical properties and factors. The mind boggles at the possibilities!
Ultimately, however, the above explanation of the principles behind a rainbow—differing refractive indexes for differing light wavelengths, resulting in dispersion—can still be applied.

Speed Changes by Wavelength

As a principle, refraction is the changing of direction experienced by light, sound waves and similar as they pass through the boundary of a given medium. This change occurs due to a change of the speed.
The relationship between refraction and speed change is often likened to that of a car's tires when they transition from a paved to an unpaved road surface. Refraction is similar to the speed-change phenomenon experienced by the tires as they cross the boundary between the two surfaces, at which time running resistance causes the vehicle to turn. The unpaved surface has a higher running resistance, which reduces speed and causes turning of the slowed tires—an analogy that, essentially, explains refraction accurately. In order to attain a more in-depth explanation, it would be necessary to delve into the field of quantum mechanics, which I believe is best to avoid in this type of article.

Going back to our rainbow: When light penetrates airborne rain droplets, the incoming light experiences a speed reduction. Let's look at some specific numbers in order to get a better understanding of this.
Red light, which has a wavelength of 700 nanometers or so, experiences a refractive index of approximately 1.33, with this value referring to the speed comparison when the light enters a medium. In this case, the red light's speed is reduced to 0.751 times its original speed (the approximate result of 1 divided by 1.33), which is a roughly 24.9-percent decrease. Violet light with an approximate wavelength of 400 nanometers, on the other hand, experiences a refractive index of about 1.34, resulting in a speed decrease of roughly 25.4 percent.
The seemingly slight disparity range between these two percentages—24.9% and 25.4%—results in the vibrant color gradient we see in a rainbow.
Going back to the original question about what produces rainbow coloring, one could rightly answer that the speed disparity between red and violet light as they pass through raindrops creates these colors. At the very least, this answer will make it look like you have a basic grasp on the concept!

GNSS Professionals Harnessing the Same Principle

In much the same way as the light which changes speed to create a rainbow, GNSS positioning signals transmitted from space to earth experience speed changes.
The biggest cause of this is the ionosphere in the earth's upper atmosphere.

The ionosphere is a low-density, plasma layer (comprising ions, electrons, etc.) ionized by solar and cosmic rays. Its internal conditions vary greatly by location and time due to the effects of various disturbances.
In highly simplistic terms, it is an electron cloud that exists between Earth's surface and outer space whose thickness—and thus its effects on radio waves—changes constantly over time.

The process of estimating the distance between a satellite and a GNSS receiver based on the time required for positioning signals to arrive is the most basic of the basics in the field of satellite-based positioning. However, the above "electron cloud" creates distance-measurement disparities ranging from several to several dozen meters. Therefore, it is important to predict such effects on signals and process them with disparity-canceling corrections as needed to improve measurement accuracy. In such instances, the physical principle of speed changes resulting from wavelength (frequency) differences can be applied. That thinking process is as follows:

1. GPS positioning signals are broadcast over multiple frequency bands, including the L1 band (1575.42 MHz), the L2 band (1227.60 MHz) and the L5 band (1176.45 MHz), among others.
2. Speed reductions experienced by a positioning signal as it travels from the vacuum of space to a terrestrial receiver varies depending on its frequency (calculated as the inverse proportion of the frequency squared).
3. It is possible at this point to calculate the propagation speed disparity based on disparities in signal arrival times for L1, L5 and so forth. As mentioned above, the thicker the electron cloud at the time of signal propagation, the greater the required time until arrival, and thus the greater propagation speed difference.
4. Based on this, one can predict ionospheric effects on a signal and make corrections to cancel their impact on measurements.

Data from fixed, continuous observation equipment can be used to better understand ionospheric effects. However, professionals often utilize the method described above to accomplish the same using just a single GNSS receiver. In terms of the rainbow principles we explored above, one might liken such GNSS measurements to the precise measurement of the visual viewing angle disparity between the two colors seen in a rainbow in order to estimate the medium's refractive index.
By harnessing such an approach to reduce ionospheric effects on GNSS signal measurement results, the disparities of multiple meters experienced by amateurs can be reduce by a pro to just several centimeters or millimeters. Moreover, advances in the field have resulted in shorter TTFF (time to first fix) results, which is a measurement of the time required to complete the initial positioning calculations by a navigation device, making the aforementioned approach much more accessible and convenient in real-life operations.

Recent years have seen the emergence of high-performance smartphones with dual-band GNSS capability. I think manufacturers are facing difficulty in making users understand such a feature, which is connected to an understanding of the above scientific principles. However, I believe you have already glasped the concept.