Observing Rainbows of Planet Earth: The Saga

Observing Rainbows on Planet Earth with astronomical tools allows us to derive detailed information about terrestrial clouds with surprisingly high accuracy.  If only we could do this for other extra-solar planets! Or, maybe, ET’s from somewhere have already done this for Earth, and now know about our rainy paradise….

part I: Cloudbows are everywhere!

part II: Earthshine and Polarisation

part III: Phase Curve of Earth in Polarisation

part IV: The Cloudbow of Planet  Earth Observed in Polarisation: Sterzik, M. F., Bagnulo, S., Emde, C., & Manev, M. (2020): Astronomy and Astrophysics, 639, A89

Observing Rainbows of Planet Earth (III): the Phase Curve of Earth in Polarisation

Our measurements allow to derive the polarisation of planet Earth. But the value of polarisation depends on its viewing geometry, and changes with its viewing angle. Each observing date (epoch) corresponds to a specific and unique viewing geometry and viewing angle, under which the sun illuminates Earth, and reflects and scatters light towards the Moon, and then back to the telescope on  Paranal. The angle between Sun, Earth, and Moon is called phase angle. This phase angle varies between 0° and 180° every month. Different observing epochs allow to measure the polarisation of Earth as a function of its phase angle. This variation by phase angle is called the (polarimetric) phase curve. We made many observations of Earthshine between the years 2011 and 2013, and were able to measure several phase angles of this phase curve. We published our results in 2019, which are described in a previous post.

The first phase curve of Earth, however, had been measured and published by the French astronomer Audouin Dollfus already in 1957. Also he used the Earthshine techniques to observe Earth as a planet from the Pic du Midi Observatory in the years 1949-1952. The graph below is from his work: Étude des planètes par la polarisation de leur lumière. Supplements Aux Annales d’Astrophysique, 4, 3–114.


The variation of polarisation (denoted “P”, in relative units) with phase angle (denoted “V” on the x-axis, in degrees) is shown on page 63(!), somewhere in the middle of his research paper. Each black dot corresponds to one measurement, taken at a specific time. Polarisation of Earth  increases steadily with increasing angles to phases around 80-90° (quadrature) and then decreases again with further increasing phase angles up to 180°.  Different measurements yield different polarisation values for similar phase angle, and considerable spread can be noticed around 80°.

Our new measurements from 2019/2020 dramatically change this picture! We recall that our observation dates were chosen to sample phase angles where rainbow scattering occurs, namely around angles of 40°. The figure below compiles all our measurements from the years 2011 to 2020. New datapoints from the 2019-2020 observation campaign are indicated with larger symbols. Different colours refer to values of polarisation in different photometric bandpasses (Dollfus’ observation were done in only one bandpass around 550nm).

Earth_MRfitOur polarisation values agree (in broad terms) with those from Dollfus: maximum polarisation (for all colours and bandpasses) is roughly between 80-100° phase angle, around quadrature. However, the polarisation values do not steadily decrease with decreasing phase angle! They reach a minimum around 45°, but increase again near 40°. Dollfus apparently did not notice this more complicated behaviour of the phase curve, possibly due to insufficient observations at these phase angles.

The increase in polarisation around phase angles of 40° is indeed caused by rainbow scattering of clouds on Earth.  The curves in the figure indicate a few model calculations that fit the observed data points. The best-fitting models allow to make surprisingly precise descriptions of the physical state and micro-physical parameters of the clouds that cause rainbow scattering. With remarkably high accuracy, both the refraction index of water (~1.33) and the mean effective radii of water droplets (6-7µm) are retrieved. In addition, the optical depth (thickness) of the water cloud decks responsible for scattering is determined between 10-20, and at the same time the fractional cloud coverage on the illuminated side of Earth over the Pacific Ocean being around 30%. 

So, finally, we can answer the initial question raised in part I: Indeed, if “Extraterrestrials” are able measure the polarisation of the cloudbow of planet Earth in a similar way as we do, they will learn: that the atmosphere of Earth contains thick liquid water clouds with typical droplet sizes of about 6-7µm; and that these clouds are typically covering 1/3 of the surface of planet Earth. Well done, ET’s… 

Observing Rainbows of Planet Earth (II): Earthshine and Polarisation

In order to observe Earth from groundbased telescopes and instruments (i.e. from Earth), we use Earthshine. Earthshine is scattered and reflected light originating from Earth, and then reflected back from the lunar surface. The Moon acts as a giant, diffuse mirror.  These observations thus mimic observations of Earth as if a (virtual) observer would be situated on the lunar surface, while (in reality) we are observing from the VLT site in Chile. We use the same techniques as described here

The crescent Moon and earthshine over ESO's Paranal Observatory

This view shows the thin crescent Moon setting over ESO’s Paranal Observatory in Chile. As well as the bright crescent the rest of the disc of the Moon can be faintly seen. This phenomenon is called earthshine. It is due to sunlight reflecting off the Earth and illuminating the lunar surface. By observing earthshine astronomers can study the properties of light reflected from Earth as if it were an exoplanet and search for signs of life. This picture was taken on 27 October 2011 and also records the planets Mercury and Venus.

Our own observations of Earth are recording polarised light, because scattered light usually is highly polarised. Also rainbow scattering  is much more prominent in polarised light than normal intensity. Therefore the simulated images of Earth in the previous post show polarised light for which the contrast of the cloudbow is much higher.

To observe the “rainbow” of planet Earth, we have selected a few different observing dates, roughly separated by a month between October 2019 and January 2020. Each of these dates cover a specific viewing geometry, and thus viewing angle under which the rainbow is seen from the lunar surface. The geometry allows to sample the variation of the cloudbow strength as expected from its physical origin as a giant rainbow,  distributed over large fractions of the visible surface of Earth, and varying according to its viewing geometry.


This time I pursued the observations not as usual from the control room in Paranal, but from home.  The image below shows my computer screen on December 30th, 2019. I am located about 1.200km south of Paranal, in a rural region in Chile near the coast. A prepaid internet connection suffices to link-up to the Observatory.  In the sky, the sunlit side of the Moon (and Venus) are visible in the evening dawn. Simultaneously, the dim, dark side of the Moon, can be seen on the acquisition image on the PC. This region is being observed; it contains Earthshine.



Observing Rainbows of Planet Earth (I): Cloudbows are everywhere!

Everyone has seen a rainbow on Earth. A colourful arc stretches across wide fractions above the horizon and below clouds, often after a rain shower. The sun always illuminates the clouds from behind the observer, and the angle between the sun, the coloured bow, and the eyes of the observer has a characteristic, constant, angle of about 40°. While the phenomena of natural rainbows has been there since ever on Earth, its physical explanation by reflection and refraction of light in small water droplets has only been accurately described in the early 20th century, based on Mie’s scattering theory.  Effectively, constructive interference leads to light concentration under a specific, favoured viewing geometry.

Is it possible that this phenomenon could actually be observed from outside Earth and remotely sensed by dedicated instruments? In other words: provided the ability exists elsewhere in the universe – could the terrestrial rainbow be “observed” and would these measurements allow to derive physical and chemical properties of Earth’s clouds?

And indeed, terrestrial rainbows can be seen from “above”. These are commonly called “cloudbows”,  and are formed by the same mechanisms as rainbows.  Usually, they can be seen from aircrafts, or from satellites, above clouds, sometimes even as complete  circles. In contrast to rainbows, cloudbows appear less colourful. The reason is the different “dispersion” of sunlight in its spectral colours, due to smaller water droplets on top clouds decks, opposed to larger droplet sizes involved below clouds.

Under specific, favourable conditions, cloudbows can also be seen from the ground. One morning around Christmas 2019, I witnessed this cloudbow, as can be seen in the left picture. The photo shows very low clouds above the Pacific ocean in Tunquen/Chile, usually called “vaguada costera”, which is often present in summer and during morning hours as a result of supersaturation and condensation of fresh ocean water in clear and cool nights. The cloudbow stretches in and above the clouds, and is visible as a relatively bright rim. Clouds disappear during sunny summer days and, as can be seen on the right picture, in the evening hours the sun slowly sets towards the cloudfree Pacific ocean.

But cloudbows are always present and observable on Earth, provided a suitable viewing geometry. We can illustrate this in simulations of the cloudbow (simulations were performed using the MYSTIC code which is part of the libRadtran package www.libradtran.org and provided by M. Manev) below. Earth, with its characteristic cloud deck structures, is viewed from above, from various distances.


In the image to the left, Earth is observed from a height of 8.000km,  little more than Earth’s radius. The simulation corresponds to a proper viewing geometry with a scattering angle around 40° between sun, clouds and observer. Here, the cloudbow can be seen as a bright band stretching between the poles.  As the rainbow scattering extends over a narrow (but finite) range of angles on the curved Earth’s surface, the region of cloudbow becomes broader, the higher the observer is located (middle).  Finally, the bright cloudbow “band” covers entire Earth, in case the observer’s eye moves up, and located higher than about 100.000km  (image to the right).  However, if the viewing geometry is only slightly changed, the enhanced intensity of cloudbows vanishes.  In this case, Earth appears as usual in reflected light: dimmed, and without the special light  concentration effect that occurs within cloud droplets.

Polarization of Planet Earth

Research paper:

Spectral and temporal variability of Earth observed in polarization:
Sterzik, M. F., Bagnulo, S., Stam, D. M., Emde, C., & Manev, M. (2019). Astronomy and Astrophysics, 622, A41–19.  http://doi.org/10.1051/0004-6361/201834213

all spectra as ascii files (external on google drive)
txt files contain lambda [AA], I, Q/I , U/I  and Q/I, U/I (both corrected for lunar depolarization)

  • Earthshine polarization (uncorrected) Pacific (a<90) ES2_Pacific<90
  • Earthshine polarization (uncorrected) Pacific (a>90) ES2_Pacific>90
  • Earthshine polarization (uncorrected) Atlantic (a<90) ES2_Atlantic<90
  • Earthshine polarization (uncorrected) Atlantic (a>90) ES2_Atlantic>90
  • Earth polarization (corrected by lunar depolarization) Pacific (a<90) E2_Pacific<90
  • Earth polarization (corrected by lunar depolarization) Pacific (a>90) E2_Pacific>90
  • Earth polarization (corrected by lunar depolarization) Atlantic (a<90) E2_Atlantic<90
  • Earth polarization (corrected by lunar depolarization) Atlantic (a>90) E2_Atlantic>90

Bacteria for greening Mars?

My colleague Bob Fosbury from ESO shares (among many other beautiful and instructive photographs and anecdotes) and interprets intriguing spectra of samples of Atacamanian halites on his flicker account. These halites are populated by extremophiles, bacteria referred to as Chroococcidiopsis. Most interestingly, chlorophyll fluorescence between about 640nm and 780n can be clearly seen, opening possibilities to eventually search for chlorophyll signatures through fluorescence spectroscopy (and not, as usually suggested, through reflection).

Atacama halite and spectra

Earths Evolution over the past 5000 Mio years

Following the Earth’s history since its formation, we can identify some milestones of the Evolution of Life. Photosynthetic bacteria were formed very early (approx 3500 Mio years  ago), and had profound impact on the Earths atmosphere. They still exist, and survive in the most extreme environments on Earth. If one can rewind the “Tape of Life”, would they still emerge?

Animation: 1 second corresponds approximately to 100 Mio years (m4v  960×540, 26MB)

The Earth as a Benchmark

Research Paper:

Sterzik, M. F., Bagnulo, S. & Pallé, E. Biosignatures as revealed by spectropolarimetry of Earthshine. Nature 483, 64–66 (2012). [Supplementary Information]

News & Views:

Keller, C. & Stam, D. M. In search of biosignatures. Nature 483, 38–39 (2012).

Echoes & Waves: (social media: Altmetric)

The Earth in Time: One Month On the Moon (animation m4v 2m22s)

Frequenly Asked Questions:

1. What gave you the idea for this research? Did you start out thinking you were going to be able to get something that could be used to analyze exoplanets?
The final motivation is to establish a viable astronomical techniques to study and analyse the atmopsheres and surfaces of exoplanets, and in particular their biosignatures. However, we are convinced that the utilization of the Earth as still the only example of a life hosting planet is essential to be used as reference for earth-like exoplanets. Actually we had begun spectrapolarimetric Earthshine observations with the VLT already 6 years ago.

2. Why do you use (spectro-)polarimetry?
Most astronomical observations measure the brightness (or intensity) of the light coming from stars and other objects, often stretching the light into the familiar rainbow of colours that provides us with information on the nature of the emitting bodies, such as their temperatures and chemical makeup. For example, stars that appear predominantly white or blue will tend to be hotter than those that seem to be red, or yellow like our Sun. This new work exploits a different property of light, called polarisation, which tells us not only how bright an object appears, but also the direction of oscillation of the electromagnetic waves. This can sometimes reveal more about the emitting source and the materials through which it has passed on its journey to Earth.
There are many examples of polarisation all around us. Occasionally, we need to orientate a television aerial to receive a signal from a particular transmitter: by so doing, we are aligning the aerial so that it better picks up the horizontally or vertically polarised signal from that transmitter. Light reflected by certain surfaces such as a wet road, a lake, or a polished table, is polarised, and some people may have noticed that polarised sunglasses (polaroids) suppress part of the reflected light. Polarised light can tell us about the reflecting surface. In the case of the reflected light called Earthshine, it can tell us certain properties of the Earth’s atmosphere and surface. 

3. What’s the difference in the spectrum of light that’s been bounced back to Earth from the moon and light that is just bouncing off the Earth? Why does this matter for exoplanet studies?
We have used the moon as a giant mirror. This is the only way to see the Earth how it looks from space, but actually observing from the ground! Unfortunately, the Moon is not an ideal mirror and the signal to which we are interested in (the polarised reflected light) is modified when it bounces back from the Moon. The lunar surface damps the signal in which we are interested by a factor of 3, and this should be taken into account when our results are used as a benchmark for studies of extra-solar planets. Expected fractional polarization signals intrinsic to exoplanets are actually 3 times higher (but of course it would be strongly diluted by the hosting star)!

4. What are biosignatures?
We do not expect to see intelligent forms of life with our telescopes, but hope to detect characteristics associated with life, for instance gases such as oxygen, ozone, methane, and carbon dioxide. While these gases may also occur without the presence of life, their simultaneous presence with the abundances far from chemical equilibrium is only compatible with the existence of life. If life were suddenly to disappear, these gases would quickly react and combine with each other, and these characteristic “bio-signatures” would disappear too. 

5. How would a scientist use this technique to study an exoplanet? Does it need continuous observation? How detailed a picture do you think this could give us of an exoplanet’s atmosphere and potential biosphere?
A rough characterisation of the atmospheres of giant exoplanets is already in reach with present-day instrumentation and telescopes. For a more refined characterisation we need to wait for the next generation of extremely large telescopes.  Detection of spectroscopic features (such as O2, O3, H2O or an equivalent of the terrestrial vegetation red edge) that allow to infer biosignatures in Earth-like planets will be much more challenging.

6. Why is the spectro-polarimetric techniques  in particular well suited for ground-based studies of exoplanets?
While the precision of (normal) intensity spectra is affected by the Earths atmosphere when observing with ground-based telescopes (e.g. by spatially and temporally varying telluric lines), spectro-polarimetric signals are largely unaffected by atmospheric perturbations due to its intrinsically differential measurement character. Thus spectro-polarimetry with extremely large telescopes may become an interesting alternative to space-based missions for the characterization of exoplanets.

7. What follow-up work is planned?
We will continue to observe the Earth as a benchmark of a life hosting planet. We plan to obtain a better phase coverage (i.e., to observe the Earth under many different conditions) and in particular to follow the polarized “glint” of the suns reflex on the ocean. Our immediate objective is to compare the observed spectra with theoretical models of the Earth’s atmosphere and surface, as to improve on theoretical models, and eventually to apply them to observations of exo-solar planets.  We will also analyse circular spectropolarimetric data, that may contain “chiral” signatures of the Earth.