1. A letter from the sky

Snow crystals, i.e., ice crystals grown from the water vapor during their fall in the cloud, have been among the most familiar natural crystals to people in cold climate regions on the earth. Everyone who has witnessed their natural beauty for the first time (Fig. 1) is undoubtedly fascinated.

Observations of natural snow crystals have a very long history beginning in 1611 with Kepler's[1] discussion of why snow crystals are hexagonal in his book entitled "A New Year's Gift on the Six-cornered Snowflakes". Furthermore, Descartes[2] made observations on snow crystals in Amsterdam and published his sketches on "Les Meteores" in 1637. In addition to this, many researchers have published sketches and photographs of natural snow crystals[3]. The historic transition on snow crystal observations is discussed in detail by Kobayashi and Kuroda[4].

The most famous publication about snow crystals may be a book published in 1931 by Bentley and Humphreys[5]. The book entitled "Snow Crystals" includes about 2500 photographs of natural snow crystals taken by Bentley, who devoted almost all of his life to photographing snow crystals. He was a farmer by trade not a scientist. However, his work impresses us deeply in light of the fact that "a simple farmer" revealed to the world the wonder and enigma of the snow crystal |its universal hexagonal shapes and its infinite number of beautiful patterns. In fact, we should note his earlier article[6] appearing in the Monthly Weather Review in 1902, in which he wrote "Was ever a life history written in more dainty or fairy-like hieroglyphics? How charming the task of trying to decipher them."

Having been inspired by Bentley's book, Ukichiro Nakaya (Physicist) of Hokkaido University, Sapporo was led to start his research of snow crystals in 1932. He began by observing natural snow crystals and took more than 3000 photographs in the mountain area of Hokkaido within several years[7]. Initially, he classified the snow crystals in about 40 categories of morphology. He subsequently succeeded in producing almost all natural snow crystal morphologies in the laboratory[8]. As a result, he elucidated the relationship between the shapes of snow crystals and the atmospheric conditions, i.e. the temperature and the supersaturation of atmosphere. He summarized his results in the form of a diagram[7], which is now referred to the "Nakaya diagram". This diagram allows one to "read" the meteorological information "written" on a snow crystal, because we can infer the weather conditions in the upper air by observing snow crystal morphologies on the ground. In this sense, Nakaya was often quoted referring the snow crystal as "a letter from the sky". He might be considered as the first researcher who discussed snow crystals as a topic of physics[9].

Nakaya's pioneering work, however, did not provide answers to basic questions such as why the morphology of snow crystals can change drastically with slight variations of meteorological factors (growth conditions), notably the temperature and supersaturation (see Fig. 2). Even though, during the last 50 years, many researchers have struggled with this difficult problem, they have not been able to obtain any critical understanding for the remarkable variety of observed snow crystal shapes. In this decade, we have also studied this fascinating mystery and have obtained an important clue in the formation mechanism in a variety of snow crystal shapes.

The purpose of this article is to introduce the beautiful patterns and the grandeur of snow crystals and to explain the recent advances in our understanding of the formation mechanisms of snow crystal shapes. First of all , let us show some beautiful pictures of natural snow crystals(Fig. 1), which I took in the mountain area of central Hokkaido using a modern technique[10].

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