Earth's fractal water distribution system

Arteries carry blood from our heart to the rest of the body. Veins carry blood from our organs back towards the heart. It’s a circulatory system that distributes nutrients, not using channels all the same size, but rather using channels that exhibit a fractal distribution. Arteries branch into smaller blood vessels, which in turn branch into even smaller blood vessels. Wilhelm Ripl has made reference to the water circulatory system as being like the blood stream.

Our societal delivery systems are also similarly fractal. Large planes deliver mail to cities. Cities distribute the mail to multiple local post offices. Local post offices distribute the mail to peoples homes.

Our earth’s water network is also fractal in nature. It delivers in a manner that is both similar and different to the way our circulatory systems and our mail systems deliver.

Water vapor ascends upwards to form clouds. Clouds exhibit a power law distribution, which is a type of fractal behavior. [1] The probability of a finding a certain size cloud is the size of that cloud to a certain exponent (also called power). Interestingly this exponent is different for different geographical areas of the earth.

Power law distributions are different than bell curve distributions. An example of a bell curve distribution would be people’s height, where a lot of adults are around five foot seven inches, and far fewer adults who are seven foot or four foot. If people’s height were power law distributed we would find people who are ten times as tall, or a hundred times as tall. Clouds though are power law distributed, so we will find clouds which are ten times as big, a hundred times as big, or a thousand times as big as a small cloud we might see overhead. Each successively larger cloud is less common, but the probability is not zero.

[Satellite image of clouds on earth]

Water is not delivered from the sky in a steady stream, nor is it delivered in bursts that exhibit a bell curve distribution. Rather it comes in the form of fractal power law bursts. [2,3] There are a lot of tiny, barely drizzling, rain events, and then there are rain events which are ten times, a hundred times, a thousand times as big, with each successively large event less common.

After the rain falls to the ground in these power law bursts, it infiltrates the soil and feeds the plants. The runoff from the rain then turns into small brooks, which turn into medium creeks, which turn into large rivers, in the form of a fractal which flows into the ocean.

Evapotranspiration from the land, and evaporation from the ocean then brings the water back up to. A significant amount of water vapor is brought up on the upward leg of the large scale atmospheric circulations that is the Hadley cell, which is why we have more clouds around the equator. A significant amount of water is also brought up by the Amazonian forest and the Congo rainforest; they are like the heart of Gaia, pumping water into the air, a metaphor I first heard from Antonio Nobre. Winds, which also obey fractal power laws, then redistribute the atmospheric moisture around the globe.

The water vapor from the Amazonian forest forms a fractally-dimensioned atmospheric river that carries rain southward in South America. The water vapor from the Congo rainforest forms an atmospheric river that carries rain northwards in Africa.

The oceans can give rise to atmospheric rivers like the Pineapple Express that carries water from north of Hawaii towards the west coast of the US. The Indian Ocean can give rise to atmospheric rivers that carry water towards Australia. In 2022, a particular large atmospheric river, lead to huge rains, that then resulted in many cities in Australia being flooded.

Floods also follow power laws. [4] These power laws may be affected by the ability of the soil to absorb and hold water.

The vegetation and the soil is the intermediary between the fractal flow of water in the air, and the fractal flow of water on the ground. More vegetation and more absorbent soil leads to the slowing of the water in the landscape. Roads, tile drainage, and urban sewage pipes lead to the speeding up of water through the landscape. Land use changes thus affects the the rhythm of the global pulsing of water. The loss of nature affects the globe’s liquid circulatory system. An interesting question then arises, how does land use affect the power law exponents of water movement? Would restoring nature shift the power law distributions, and reduce the probability of extreme weather events, like huge rain events, long droughts, and massive floods?

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REFERENCES

[1] Teo, C‐K., H‐N. Huynh, T‐Y. Koh, K. K. W. Cheung, B. Legras, Lock Yue Chew, and L. Norford. "The universal scaling characteristics of tropical oceanic rain clusters." Journal of Geophysical Research: Atmospheres 122, no. 11 (2017): 5582-5599.

[2] Peters, Ole, Christopher Hertlein, and Kim Christensen. "A complexity view of rainfall." Physical review letters 88, no. 1 (2001): 018701

[3] Peters, Ole, Anna Deluca, Álvaro Corral, J. David Neelin, and Christopher E. Holloway. "Universality of rain event size distributions." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 11 (2010): P11030

[4] De Michele CA, La Barbera PA, Rosso R. Power law distribution of catastrophic floods. IAHS PUBLICATION. 2002:277-82