Formation of penitentes on earth

On Earth, penitentes reach their greatest heights of several meters in a restricted altitude zone on high subtropical mountains, in regions where summer is the dry season; they have been most intensively studied in the Andes of Chile and Argentina. Penitentes are exotic and beautiful (Fig. 1), but they can cause difficulty, for example by slowing the progress of mountaineers climbing Aconcagua. And Wentworth (Reference Wentworth1940) complained that snow spikes on Mauna Kea (Hawaii) made tobogganing impossible. More recently Hobley and others (Reference Hobley, Moore, Howard and Umurhan2018) have identified what is perhaps a more severe hazard, namely a risk to the Europa Lander, which I will critique below.

Fig. 1. A field of snow-penitentes in the Elqui Valley above La Serena, Chile, 21 December 2007.

Most of the tall penitentes found in the Andes (Fig. 1) consist of old snow, but they can also form in glacier ice. The explanation for their formation was given by Louis Lliboutry (Reference Lliboutry1954) in his classic paper ‘The origin of penitents’, and reviewed in his book (Lliboutry, Reference Lliboutry1964). [Lliboutry argued for use of the term penitent in English-language literature, but the original Spanish spelling penitente (4 syllables) is now almost universally used.] Penitentes result from a selection process in which surfaces facing the Sun absorb more radiation and ablate more quickly, so the surviving surfaces are nearly-vertical wedges oriented east-west, parallel to the solar beam. This selection process is most active during the midday hours of maximum irradiance, so in the Southern Hemisphere the wedges become tilted toward the north, at approximately the noontime solar zenith angle, which varies seasonally. They were given the name ‘penitentes’ because a field of these inclined spikes had the appearance of white-robed monks on a religious pilgrimage. Their mechanism of formation was concisely stated in Lliboutry's abstract: ‘The sublimation of the snow or ice allows the crests to maintain their temperature below 0°C, while in the spaces or passages between the penitents, where radiation is concentrated and removal of water vapour not so easy, melting takes place.’ The latent heat of melting is 335 J g⁻¹, whereas the latent heat of sublimation is 2838 J g⁻¹, a factor of 8.5 larger. The extreme topography of penitentes results from this 8.5-fold difference: the peaks remain dry and cold by sublimation, losing little mass, but in the troughs the air becomes stagnant and humid, so that sublimation cannot occur; the absorbed solar energy is instead consumed by melting, resulting in rapid loss of mass. In an example documented by Lliboutry (Reference Lliboutry1964, p. 375), on an afternoon at the end of November at 3500 m elevation, with air temperature above freezing but dew point below freezing, the sublimating spikes of 50-cm height were hard and dry with a temperature of −5°C, whereas in the troughs between them the snow was wet, containing 14% liquid water.

The lower limit to the altitude of penitente-formation was plotted as a function of latitude for North and South America by Troll (Reference Troll1942, Figure 14), from the Cascades at 50°N to the southern Andes at 40°S; this altitude-limit varied from 3000 m at 50°N to 5300 m at the Equator. Lliboutry (Reference Lliboutry1954) identified three zones of altitude in the Andes above Santiago, Chile, at latitude 33°S:

1. (1) In the lowest zone, below 4000 m, the snow surface developed the familiar scalloped surface called ‘suncups’, ‘ablation hollows’ or ‘honeycombed snow’, seen in summer on mountain glaciers and snow-fields worldwide (Post and LaChapelle, Reference Post and LaChapelle1971; Figure 2). Suncups are melting at all parts of the surface (both hollows and ridges), but some topography does develop from initial small irregularities, by two mechanisms: (a) Different orientations of surfaces relative to the Sun are illuminated differently; also the hollow is illuminated not only directly but additionally by radiation reflected from the neighboring walls. (b) Evaporation of meltwater occurs more readily at the ridges, which are exposed to wind and can therefore dispose of much of their absorbed solar energy without further melting, in contrast to the hollows where the air is more stagnant and therefore more humid. The effect of debris on the snow can either enhance or suppress suncup formation, depending on the degree of illumination (Rhodes and others, Reference Rhodes, Armstrong and Warren1987).

2. (2) In the highest zone of the Santiago Andes, above 5200 m, the snow was colder than 0°C everywhere, so melting could not occur; the dry snow surface remained nearly flat.

3. (3) The intermediate zone, 4000–5200 m, where penitentes developed, was characterized by sublimation at the peaks and melting in the troughs. In the troughs the air became stagnant and humid, so that sublimation was impossible, so the snow heated up to the melting point and then consumed the absorbed solar energy by melting. Penitentes are spikier than suncups because on penitentes there is no melting at the peaks. In this intermediate zone the snow was nearly flat in winter because only sublimation could occur then; the penitentes began to develop in late spring when the weather became warm enough that melting could begin in the troughs.

Fig. 2. Suncups on Taku Glacier, southeast Alaska. [Figure 82 of Post and LaChapelle (Reference Post and LaChapelle1971).].

Quoting Lliboutry (Reference Lliboutry1954): ‘[We] have alternately troughs where the snow melts and penitents where it sublimes. In both cases the speed of the process depends on the thermal balance, so that melting goes further than sublimation… . Although sublimation is indispensible for penitent formation, in a field of penitents most of the ablation proceeds from melting’.

The mechanism identified by Lliboutry has been confirmed in subsequent studies, by Untersteiner (Reference Untersteiner1957) in the Pakistani Karakoram at 36°N, by Kotlyakov and Lebedeva (Reference Kotlyakov and Lebedeva1974) in the East Pamirs of Tajikistan at 38°N, and by Naruse and Leiva (Reference Naruse and Leiva1997) in the Argentinian Andes at 32°S. Quoting Untersteiner, ‘Evaporation/sublimation plays a definite role in the energy budget [of penitents] … but a significant contribution to ablation is ruled out… . Growth of penitents by sublimation-ablation appears not to be possible, … so it must come about by means of melting.’ Quoting Kotlyakov and Lebedeva, ‘The facets were dry, but in the hollows the firn was soft and humid… . The melting on the surface perpendicular to midday solar rays can reach 20–30 mm day⁻¹ in water equivalent… . The surface was smooth on the upper part of the glacier.’ Quoting Naruse and Leiva, ‘All the field data … support Lliboutry's hypothesis … enhanced melting at the bottoms due to absorbed shortwave radiation and ceased melting at the top due to cooling by sublimation … .’

On Earth, penitentes have not been observed to form under conditions of sublimation-only. Apparently, melting in the troughs is occurring wherever penitentes are forming on Earth. This claim by Lliboutry was substantiated by MacDonell and others (Reference MacDonell, Kinnard, Moelg, Nicholson and Abermann2013), who found no penitentes on a high-altitude Andean glacier where only sublimation was occurring.

Lliboutry did observe ‘micropenitents’ with heights of a few centimeters, in the spring before melting began, resulting from trapping of incident sunlight in incipient troughs. The lack of melting meant that only the trapping mechanism was active, limiting the microtopography to these tiny structures, two orders of magnitude smaller than typical penitentes (Figure 6 of Lliboutry, Reference Lliboutry1954). This process was also investigated in a laboratory experiment: with vertical illumination of a snow block, Bergeron and others (Reference Bergeron, Berger and Betterton2006) were able to create conical micropenitents by sublimation alone, to a height of 1.3 cm and with a constant aspect ratio (height/spacing) of 2. With further illumination, melting began in the troughs, and both height and aspect ratio increased; the experiment was terminated when the height reached 3 cm.

It is not clear what limits the height of sublimation-only penitentes in nature to a few centimeters; it may be that the combination of adequate sunlight and subzero temperature just does not persist long enough on Earth's subtropics. Where lack of melting does persist for years, even millenia, is in the interior of Antarctica, but micropenitents are not observed there, probably because of the continuous light snowfall (‘diamond dust’), as well as the low and nearly circular path of the Sun in the sky. Instead, a different kind of snow-surface roughness predominates, namely sastrugi, which are longitudinal erosion features aligned with the prevailing strong winds (Gow, Reference Gow1965; Doumani, Reference Doumani and Oura1967; Armstrong and others, Reference Armstrong, Roberts and Swithinbank1973; Filhol and Sturm, Reference Filhol and Sturm2015), with typical height 0.2 m, width 1 m and length 5 m (Table 2 of Warren and others, Reference Warren, Brandt and O'Rawe-Hinton1998).

Are penitentes possible on Europa?

Europa is one of the four large moons of Jupiter. It is about the same size as Earth's moon. Europa possesses a deep ocean of liquid water beneath a several-kilometer-thick surface layer of ice. Europa is cold; the noontime equatorial surface temperature is 134 K.

Development of a lander mission to Europa is underway as a massive undertaking by NASA (Hand and 286 others, Reference Hand2022). So it was alarming for the mission planners to read a prediction by Hobley and others (Reference Hobley, Moore, Howard and Umurhan2018) that the low-latitude surface of Europa would exhibit ‘metre-scale bladed roughness’ in the form of penitentes.

Hobley's group made some peculiar statements about penitentes on Earth. They cited Lliboutry's classic paper to claim that ‘On Earth, … formation of large and well-developed penitentes requires … a melt-free environment… . Sublimation in the absence of melting is particularly essential for penitente formation.’ Hobley and his coauthors thus attributed to Lliboutry a statement which is the exact opposite of what he wrote. The Hobley paper included a picture of penitentes near the ALMA telescope site, at 5100 m elevation on the Chajnantor Plain of Chile, but neglected to mention that melting occurs at that location in summer, when the penitentes form. (I visited that location in winter, when melting was absent, and found no penitentes, nor even micropenitents.)

The Hobley paper was widely publicized, for example in EOS (Kornei, Reference Kornei2018) and in Nature (Anonymous, 2018); both articles included a photograph of penitentes in the Chilean Andes, as had the Hobley paper, with no mention of the importance of melt in forming penitentes on Earth. Indeed, they perpetuated Hobley's misrepresentation of Lliboutry's elegant explanation. For many readers of Nature and EOS, those news items will have been their first introduction to penitentes. It is therefore most unfortunate that the publicity about the Hobley paper reinforced its misconception that melting not only does not contribute to the formation of penitentes, but that melting would actually prevent their formation!

With a maximum daytime surface temperature of 134 K on the equator of Europa, and a near-vacuum atmosphere, melting cannot occur, thus ruling out the terrestrial mechanism for formation of penitentes on that planetary body. But we must still consider the possibility of a different mechanism on Europa using sublimation only, because of the long time available. Penitentes on Earth have only about 4 months to grow before they melt away in late summer. But Hobley and coauthors estimated that the time available for penitente formation on Europa would be eight orders of magnitude longer, because the average age of the Europan ice surface before resurfacing is ~50 million years.

Inspired by the laboratory experiments of Bergeron and others (Reference Bergeron, Berger and Betterton2006), in which micropenitents were grown, Hobley and his coworkers estimated the height that penitentes could attain on Europa. They did not model the evolution of surface roughness. Instead they just assumed an aspect ratio (height-to-spacing ratio) of 2, and equated the energy of sublimation to the radiation energy budget, concluding that, at equator, 15 m of ice could sublimate in 50 million years. If most of this sublimation occurred from troughs (and if erosion of the spikes by sputtering and impact-gardening were slow), the penitentes could be 15 m tall. By contrast, modeling by Hand and others (Reference Hand2020), in a comment on the Hobley paper, has indicated that penitentes cannot grow on Europa, because of the absence of an atmosphere to impede the diffusion of water vapor. And a subsequent laboratory experiment by Hand's group (Berisford and others, Reference Berisford2021) showed that, in their words, ‘Pre-formed penitentes undergo sublimation erosion, evolving toward a flat morphology, during simulated solar irradiance.’

As evidence for penitentes on Europa, the Hobley group cited radar measurements of Europa at wavelength 12.6 cm, in particular the latitudinal variation of reflectivity and an anomalous polarization ratio, which might be explained by penitentes. But those observations could alternatively be explained by subsurface irregularities (Ostro and others, Reference Ostro1992), since the absorption-length in ice for 12.6-cm radar is 100 m.

A more-definitive test of the Hobley hypothesis can be made using visible wavelengths, by considering how penitentes would alter the reflection of sunlight. Penitentes trap solar radiation, resulting in reduced albedo of a field of penitentes relative to a flat horizontal surface, in the same way that crevasses reduce the albedo of glaciers (Pfeffer and Bretherton, Reference Pfeffer and Bretherton1987). Solar photons reflected by a horizontal surface will escape to space, but many of the photons reflected by a spike-wall will be intercepted by the neighboring wall, getting another chance for absorption.

The triangular-shaped penitentes of Glaciar Tapado in Chile, with heights 2 m and spacing 1.4 m, caused a reduction of broadband albedo from its flat-surface value of 0.64, down to 0.32, as estimated by Lhermitte and others (Reference Lhermitte, Abermann and Kinnard2014, Figure 2D and Table 4D). A similar albedo-reduction, from 0.60 to 0.33, was obtained for idealized penitentes in a radiative-transfer model by Cathles and others (Reference Cathles, Abbot and MacAyeal2014). If the flat-surface albedo of Europan ice at a particular wavelength is ~0.7, for example, penitentes would thus be expected to reduce the area-averaged albedo to ~0.4. But the area-averaged albedo of the leading hemisphere of Europa is actually quite high, averaging 0.72 at mid-visible wavelengths 550–750 nm (Figure 13c of Carlson and others, Reference Carlson, Pappalardo, McKinnon and Khurana2009), suggesting that penitentes, if present, are not prominent. The angular dependence of visible reflectance also argues against meter-scale surface roughness (Belgasem and others, Reference Belgasem, Schmidt and Jonniaux2020).

In conclusion, the low latitudes of Europa are likely to have smooth surfaces, suitable for a lander.

Penitentes on Pluto?

The surface of Pluto consists mainly of nitrogen ice and methane ice, at temperatures ~40 K. In 2015 the New Horizons spacecraft obtained images of Pluto at a resolution (pixel size) of 320 m, which showed some large areas of long parallel ridges, consisting mostly of methane ice, on high plateaus at low latitude. These areas have been called ‘bladed terrain’ (Moore and others, Reference Moore, Howard, Umurhan and White2018), ‘penitentes’ (Moores and others, Reference Moores, Smith, Toigo and Guzewich2017) or ‘megadunes’ (Traversa and others, Reference Traversa, Fugazza and Frezzotti2023). With their heights of 300 m and spacing 3–7 km, they might better be called ‘rolling hills’ or ‘undulating terrain’. Their aspect ratio of 0.1 is 1–2 orders of magnitude smaller than that of Andean penitentes, and two orders of magnitude larger than that of Antarctic megadunes, which are only 2–4 m tall but spaced 2–5 km apart (Frezzotti and others, Reference Frezzotti, Gandolfi and Urbini2002).

Snow megadunes are found on large areas of the East Antarctic Plateau, as long low ridges of length 10–100 km, aligned perpendicular to the katabatic wind direction. They can be seen in satellite images, but because of their low profile they are difficult to discern from the surface. Field expeditions inspired by the satellite images have found that they are formed by sublimation from the leeward side of a dune and deposition on the windward side of the next dune down-wind, causing the entire dune field to migrate slowly upwind (Frezzotti and others, Reference Frezzotti, Gandolfi and Urbini2002; Dadic and others, Reference Dadic, Mott, Horgan and Lehning2013).

Pluto, unlike Europa, does possess a thin atmosphere, with a surface pressure of about 10 μbar or 1 Pa (Stern and others, Reference Stern2015), so a wind-driven mechanism for formation of Pluto's ridges may be possible, analogous to that which forms the Antarctic snow-megadunes. Some of the published images of Pluto (Moore and others, Reference Moore, Howard, Umurhan and White2017; Moores and others, Reference Moores, Smith, Toigo and Guzewich2017) do resemble satellite images of Antarctic megadune fields (Fahnestock and others, Reference Fahnestock2000; Frezzotti and others, Reference Frezzotti, Gandolfi and Urbini2002). In any case, since the aspect ratio and mechanism of formation of Pluto's ridges are so different from those of Andean penitentes, it seems inappropriate to label them ‘penitentes’. A news article in Nature about the images from Pluto (Hall, Reference Hall2020) included the same photograph of Andean penitentes that had been used in Nature's earlier news story about Europa cited above, unfortunately again neglecting to mention the crucial role of melting in the Andes, so it was similarly misinforming the readers about Earth's penitentes.

Recommendations for future work

Several groups have designed computational models to explain the growth of penitentes by sublimation alone (Betterton, Reference Betterton2001; Tiedje and others, Reference Tiedje, Mitchell, Lau, Ballestad and Nodwell2006; Cathles and others, Reference Cathles, Abbot and MacAyeal2014; Claudin and others, Reference Claudin, Jarry, Vignoles, Plapp and Andreotti2015). Those models accounted for such factors as the diurnal cycle of the direction of incident sunlight and its dependence on latitude, the ‘trapping’ of solar energy in topographic depressions, and resultant temperature gradients and sublimation rates. Those models could still be improved, even when considering only sublimation. For example, a recent highly-cited model (Claudin and others, Reference Claudin, Jarry, Vignoles, Plapp and Andreotti2015) completely ignores emission and absorption of thermal infrared radiation, and its lack of spectral resolution for the near-infrared solar radiation (and its attribution of visible-wavelength attenuation to absorption instead of scattering) lead to an absorption-depth that is at least an order of magnitude too large (Brandt and Warren, Reference Brandt and Warren1993).

Those published models have limited themselves to what can be achieved by sublimation alone. Modelers are of course wise to start out simple, and modeling the onset of penitente growth by consideration of sublimation alone was a good first step. But to make the models relevant to the tall penitentes that have reliably amazed travelers in the Andes, it will be necessary to include melting. This will require modeling of air turbulence within a trough to compute the humidity-gradients that are central to Lliboutry's explanation. Models should be structured to compute vertical profiles of humidity and temperature within the trough, thus allowing them to diagnose the vertical profiles of sublimation rates and melting rates as penitentes grow through the spring and summer, and then finally decay in late summer as the melting/sublimation boundary migrates upward.

Some fieldwork would be desirable to support the modeling. Several papers describing penitentes in the Andes (e.g. Nicholson and others, Reference Nicholson, Petlicki, Partan and MacDonell2016) have commented on the saturated humidity in the troughs, which is essential for preventing sublimation and leading to warmth and melting, but measurement of vertical profiles of humidity within the troughs has not been reported.