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The Science of Middle-earth -- How High the Mallorn?
-- Olog-Hai

Nothing exemplifies the spirit of Elvendom more than the majestic mallorn. This species of tree is almost entirely confined to Lothlorien, where it grows to a great size, supporting huge palaces even in its upper branches. But how high can mallorn trees grow? Some remarkable research, just published, establishes limits on the heights of the tallest trees.

George W. Koch of Northern Arizona University and his colleagues have been examining how the effort of pumping water to the tops of the tallest redwoods in California ultimately limits the heights these trees can attain. The researchers looked at five of the eight tallest trees in the world, including the tallest and second tallest -- all giant redwoods (Sequoia sempervirens) growing in the Humboldt Redwoods State Park, California. The tallest of these trees is 112.7 meters high, equivalent to a thirty-story building. Measurements of water pressure and other aspects of the physiology of these trees, some of which are more than 2,000 years old, suggest that tall as they already are, they still have some way to go. The researchers think that these trees cannot grow any higher than 130 meters -- even though some are still shooting upwards at a respectable 25 centimeters per year.

So what stops a tree growing to -- say, 200 meters, or a mile, or any height it chooses? The limit is set, ultimately, by gravity. The pressure of the atmosphere can, in certain circumstances, be set in opposition to gravity, by persuading it to support a column of fluid. The pressure is great enough to support a column of mercury 760 millimeters tall. Variation in the height of this column gives a clue to changes in atmospheric pressure -- and this is the basis of the mercury barometer. Water is much less dense than mercury, and the atmosphere can support a column of water about 10 meters tall. The tallest trees are more than ten times as tall as that. Clearly, trees can only grow tall by actively hauling the water up their trunks.

They do this by drawing up the water in networks of extremely fine tubes of woody tissue. Everyone knows how fluid spontaneously rises up very narrow tubes, a phenomenon known as surface tension. However, this is not enough to allow trees to surmount the 10-meter limit imposed by gravity. To get water all the way to the treetops, trees must drag the long but very thin columns of water from root to topmost leaf. They can do this by exploiting a tendency of water molecules to form loose associations with one another. They do this very effectively in the confined space of a microscopically thin water vessel, and trees have engineered it so that the water in each conducting vessel (it has many hundreds working simultaneously) is effectively linked up in a molecular chain, from top to bottom. Water reaching treetop leaves evaporates into the air and sunshine through small pores or 'stomata'. This evaporation provides the energy needed to drag the entire chain upwards.

One consequence of pulling a chain of water molecules to a great height is that the higher you go, the greater the tension in the chain becomes. Increased vertical tension means a sharp decline in pressure. Above 10 meters -- the upper limit that the atmosphere can raise water unaided -- the pressure actually becomes negative: that is, below that of a vacuum. The vessels must be physically very strong to conduct water in these conditions without collapsing. The greater this negative pressure, the greater the risk that the integrity of the vessel will suffer -- bubbles explosively appear and the chain will break. Because the tree has hundreds of water vessels working at once, it can afford for a few to fail every now and then, taking time to restore themselves by drawing up more water. However, the risk that all the vessels will fail at once increases with height: such failure is the arboreal equivalent of a coronary thrombosis. Such embolisms are the cause of local die-back in crowns and branches of tall trees. Koch and colleagues found that the pressure inside a redwood can gets so low that water vessels run a significant risk of collapse at around 100 meters.

The difficulty of getting water to the crown imposes constraints on the growth of the leaves -- the very leaves responsible for generating the energy needed to do the pulling. With increasing height, leaves are under ever greater water stress, and respond to this by becoming smaller, denser and with fewer stomata. The leaves in the crowns of giant redwoods are the densest of any leaves ever measured, and are the poorest at drawing in the carbon dioxide necessary to drive the process of photosynthesis, by which leaves grow. A height is reached, eventually, at which the leaves are too small and desiccated to grow, let alone pull water up from far below.

These various constraints -- on vessel integrity, on the size of leaves and consequently their ability to operate effectively -- converge on a relatively narrow height range of between 122 and 130 meters for maximum height. This value need not be absolute, but applies only to the conditions of soil, water and climate in which the trees grow. It is possible that trees could grow taller still -- but probably not very much.

How do you actually go about observing what goes on in these vertiginous treetops? By going there and looking for yourself, of course: in a decidedly Elvish mode of doing science, the researchers got to the topmost branches by shooting lines over them with bows and arrows, following these with ropes and then climbing up, with some mechanical assistance.

Mallorns have a reputation for greatness, although this is not qualified or quantified in The Lord of the Rings as published. However, a reference in The Treason of Isengard (Chapter XIII: Galadriel) is more specific, suggesting that the tallest mallorns in Caras Galadhon were "nearly 200 feet high", that is, about 60 meters, less than half the height of the tallest Californian redwood. Redwoods, however, are conifers, whereas mallorns are deciduous, resembling copper beeches (Fagus sylvatica) in their shape and leaf-shedding habits. The tallest deciduous tree in the world is the Australian mountain ash Eucalyptus regnans, one specimen of which reached 99 meters. However, accounts exist of specimens of this tree exceeding 152 meters -- though these may, of course, be tall stories.

-- Olog-Hai

I am grateful to Christopher Surridge for assistance with this article and for helping me equilibrate to the head-frying concept of negative pressure. The Science of Middle-earth, by my very good friend Henry Gee, will be published by Cold Spring on 1 November, and you can pre-order it now from Amazon.com. ISBN 1593600232 $14.00, here.

Sources: George W. Koch et al., 'The limits to tree height', Nature 428, 851-854 (2004); Ian Woodward, 'Tall storeys', Nature 428, 807-808 (2004).

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