Why does Guan Yin ride a dragon?

Generally speaking Mahayana Buddhism employs skillful means to cleverly convey the message of Buddhism, and metaphors and symbolism are frequently used. The Avalokiteshvara represents the embodiment of the Dharma, and devotion to him is the central focus in the Universal Gate Chapter of the Lotus Sutra. In the Chapter he is described as having 33 transformations including that of Buddha, Pratyekabuddha etc. Whatever form as needed to teach sentient beings. The Dharma being present in all beings. This is also associated with 33 forms of Guanyin. I am uncertain of the origins of these forms but they are available in the following:

http://big5.xuefo.net/nr/article3/34985.html

The second form is the 龍頭觀音 the Dragon riding Guanyin described. This is also the form associated with the Pratyekabuddha transformation body. The Pratyekabuddha in Mahayana Buddhism is also associated with self realization. So based on these facts we can probably guess at the meanings of the iconic picture. The Dragon is the Chinese translation of the serpentine Naga, which is a powerful often destructive beast that has the form that twists and turns symbolizing impermanence. So the image of Guanyin on the head of a Dragon represents transcending and utilization of the impermanence by the Dharma.

I believe there are many metaphors and intrinsic meanings in this Avalokiteshvara Riding Dragon image. I would provide one of the many aspects, that the dragon is symbolic of Rage/Anger/Jealousy (嗔), riding the dragon is symbolizing conquered of Anger. Greed (貪), anger (嗔) and delusion (癡) are the Three Afflictions of the mind. Avalokiteshvara is respected as the Great Compassionate Bodhisattva (大悲菩薩). Compassion (大悲) termed 同體大悲, means "all differences but are one". The Chinese Character of 悲 graphically depicted the meaning, the upper is 非, means "not", "difference", the left and right are the reflection as if looking into a mirror, means all appeared different but in fact are reflections of the other. The lower is 心, a heart. A great heart will uphold all differences together, that's the meaning of compassion 悲. Now, rage, anger and jealousy are the greatest enemy to compassion. The extreme of rage and anger is hatred then escalated to war, then killing... By subduing the Dragon of Rage - a Chinese phrase 嗔心如毒龍 - heart full of rage is like a poisonous dragon - great compassion is achieved. Dragon is also symbol for energy, rage is a kind of energy but in bad use, if one could conquer it, one is able to turn the energy to great use, i.e., the reflection of rage is compassion, like the opposite of love is hate. ;)

P.S. Please be careful of modern rendering of the Buddha and Bodhisattva images, some of them are illegitimate. There are strict proportions and rules to abide when rendering these images, recorded in, such as 《佛說造像量度經》. These modern artists in this time of the world using their own habits and imaginations to freely draw these sacred images are full of blemishes. One should avoid but to find the good one if possible.

I to have this question. What I would like to share is that through my experience of studying the symbolism of dragons you need to carefully find the origin of the the dragon depicted because depending on the person, culture and/or artist that created the image the symbolism changes. Because the dragon symbolizes different things in different cultures there is confusion of what the dragon symbolizes. If you want the original meaning find the beginning of who Kwan Yin is. Then which ever culture first put her on a dragon will give you what it means for her to be riding the dragon.

Some facts from my research

1. Original name: Avalokitasvara The original form Avalokitasvara appears in Sanskrit fragments of the fifth century.

2. Refers to the Mahāyāna bodhisattva of the same name.

3. Because this bodhisattva is considered the personification of compassion and kindness, a mother goddess and patron of mothers and seamen, the representation in China was further interpreted in an all-female form around the 12th century. In the modern period, Guanyin is most often represented as a beautiful, white-robed woman, a depiction which derives from the earlier Pandaravasini form.
4. In Chinese art, Guanyin is often depicted standing atop a dragon.
5. For the most part, no theme would be accepted in traditional Chinese art that was not inspiring, noble (either elevating or admonitory), refreshing to the spirit, or at least charming.
6. All traditional Chinese art is symbolic, for everything that is painted reflects some aspect of a totality of which the artist is intuitively aware
7. In Chinese mythology there are nine classical types of dragons.
8. A turquoise dragons can symbolized the benevolent but potentially dangerous emperor
9. Of the nine dragons the horned dragon is the giver of rain. (I chose this because the dragon in the picture is a horned dragon.)

Still with this information the dragon could mean different things. So who is the artist and why did he paint this.

Wikipedia says that she is "protector of fishermen, sailors, and generally people who are out at sea".

A Chinese dragon is esteemed (a symbol of the emperor), and "traditionally symbolize potent and auspicious powers, particularly control over water, rainfall, typhoons, and floods", also prosperity and good luck and so on, rulers of weather and water.

So I assume that riding a dragon like that symbolizes control over the sea (part of being "protector of fishermen and sailors").