Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

How vegetation competes for rainfall in dry regions

02.09.2013
The greater the plant density in a given area, the greater the amount of rainwater that seeps into the ground. This is due to a higher presence of dense roots and organic matter in the soil. Since water is a limited resource in many dry ecosystems, such as semi-arid environments and semi-deserts, there is a benefit to vegetation to adapt by forming closer networks with little space between plants.

Hence, vegetation in semi-arid environments (or regions with low rainfall) self-organizes into patterns or “bands.” The pattern formation occurs where stripes of vegetation run parallel to the contours of a hill, and are interlaid with stripes of bare ground. Banded vegetation is common where there is low rainfall. In a paper published last month in the SIAM Journal on Applied Mathematics, author Jonathan A. Sherratt uses a mathematical model to determine the levels of precipitation within which such pattern formation occurs.


Desert steppes in Yol Valley in Mongolia. Photo Credit: Christineg (Source: Dreamstime)

“Vegetation patterns are a common feature in semi-arid environments, occurring in Africa, Australia and North America,” explains Sherratt. “Field studies of these ecosystems are extremely difficult because of their remoteness and physical harshness; moreover there are no laboratory replicates. Therefore mathematical modeling has the potential to be an extremely valuable tool, enabling prediction of how pattern vegetation will respond to changes in external conditions.”

Several mathematical models have attempted to address banded vegetation in semi-arid environments, of which the oldest and most established is a system of partial differential equations, called the Klausmeier model.

The Klausmeier model is based on a water redistribution hypothesis, which assumes that rain falling on bare ground infiltrates only slightly; most of it runs downhill in the direction of the next vegetation band. It is here that rain water seeps into the soil and promotes growth of new foliage. This implies that moisture levels are higher on the uphill edge of the bands. Hence, as plants compete for water, bands move uphill with each generation. This uphill migration of bands occurs as new vegetation grows upslope of the bands and old vegetation dies on the downslope edge.

In this paper, the author uses the Klausmeier model, which is a system of reaction-diffusion-advection equations, to determine the critical rainfall level needed for pattern formation based on a variety of ecological parameters, such as rainfall, evaporation, plant uptake, downhill flow, and plant loss. He also investigates the uphill migration speeds of the bands. “My research focuses on the way in which patterns change as annual rainfall varies. In particular, I predict an abrupt shift in pattern formation as rainfall is decreased, which dramatically affects ecosystems,” says Sherratt. “The mathematical analysis enables me to derive a formula for the minimum level of annual rainfall for which banded vegetation is viable; below this, there is a transition to complete desert.”

The model has value in making resource decisions and addressing environmental concerns. “Since many semi-arid regions with banded vegetation are used for grazing and/or timber, this prediction has significant implications for land management,” Sherratt says. “Another issue for which mathematical modeling can be of value is the resilience of patterned vegetation to environmental change. This type of conclusion raises the possibility of using mathematical models as an early warning system that catastrophic changes in the ecosystem are imminent, enabling appropriate action (such as reduced grazing).”

The simplicity of the model allows the author to make detailed predictions, but more realistic models are required to further this work. “All mathematical models are a compromise between the complexity needed to adequately reflect real-world phenomena, and the simplicity that enables the application of mathematical methods. My paper concerns a relatively simple model for vegetation patterning, and I have been able to exploit this simplicity to obtain detailed mathematical predictions,” explains Sherratt. “A number of other researchers have proposed more realistic (and more complex) models, and corresponding study of these models is an important area for future work. The mathematical challenges are considerable, but the rewards would be great, with the potential to predict things such as critical levels of annual rainfall with a high degree of quantitative accuracy.”

With 2013 being the year of “Mathematics of Planet Earth (MPE),” mathematics departments and societies across the world are highlighting the role of the mathematical sciences in the scientific effort to understand and deal with the multifaceted challenges facing our planet and our civilization. “The wider field of mathematical modeling of ecosystem-level phenomena has the potential to make a major and quite unique contribution to our understanding of our planet,” says Sherratt.

Source Article:

Pattern Solutions of the Klausmeier Model for Banded Vegetation in Semi-arid Environments V: The Transition from Patterns to Desert

Jonathan A. Sherratt

SIAM Journal on Applied Mathematics, 73 (4), 1347–1367 (Online publish date: July 3, 2013).

The paper will be available for free access at the link above from September 4 – December 4, 2013.

About the author:

Jonathan A. Sherratt is a professor in the Department of Mathematics at Heriot-Watt University, and at Maxwell Institute for Mathematical Sciences in Edinburgh, United Kingdom.

About SIAM

The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of over 14,000 individual members, including applied and computational mathematicians and computer scientists, as well as other scientists and engineers. Members from 85 countries are researchers, educators, students, and practitioners in industry, government, laboratories, and academia. The Society, which also includes nearly 500 academic and corporate institutional members, serves and advances the disciplines of applied mathematics and computational science by publishing a variety of books and prestigious peer-reviewed research journals, by conducting conferences, and by hosting activity groups in various areas of mathematics. SIAM provides many opportunities for students including regional sections and student chapters.

Karthika Muthukumaraswamy | EurekAlert!
Further information:
http://www.siam.org

More articles from Ecology, The Environment and Conservation:

nachricht Machine learning helps predict worldwide plant-conservation priorities
04.12.2018 | Ohio State University

nachricht From the Arctic to the tropics: researchers present a unique database on Earth’s vegetation
20.11.2018 | Martin-Luther-Universität Halle-Wittenberg

All articles from Ecology, The Environment and Conservation >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Lethal combination: Drug cocktail turns off the juice to cancer cells

A widely used diabetes medication combined with an antihypertensive drug specifically inhibits tumor growth – this was discovered by researchers from the University of Basel’s Biozentrum two years ago. In a follow-up study, recently published in “Cell Reports”, the scientists report that this drug cocktail induces cancer cell death by switching off their energy supply.

The widely used anti-diabetes drug metformin not only reduces blood sugar but also has an anti-cancer effect. However, the metformin dose commonly used in the...

Im Focus: New Foldable Drone Flies through Narrow Holes in Rescue Missions

A research team from the University of Zurich has developed a new drone that can retract its propeller arms in flight and make itself small to fit through narrow gaps and holes. This is particularly useful when searching for victims of natural disasters.

Inspecting a damaged building after an earthquake or during a fire is exactly the kind of job that human rescuers would like drones to do for them. A flying...

Im Focus: Topological material switched off and on for the first time

Key advance for future topological transistors

Over the last decade, there has been much excitement about the discovery, recognised by the Nobel Prize in Physics only two years ago, that there are two types...

Im Focus: Researchers develop method to transfer entire 2D circuits to any smooth surface

What if a sensor sensing a thing could be part of the thing itself? Rice University engineers believe they have a two-dimensional solution to do just that.

Rice engineers led by materials scientists Pulickel Ajayan and Jun Lou have developed a method to make atom-flat sensors that seamlessly integrate with devices...

Im Focus: Three components on one chip

Scientists at the University of Stuttgart and the Karlsruhe Institute of Technology (KIT) succeed in important further development on the way to quantum Computers.

Quantum computers one day should be able to solve certain computing problems much faster than a classical computer. One of the most promising approaches is...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

VideoLinks
Industry & Economy
Event News

ICTM Conference 2019: Digitization emerges as an engineering trend for turbomachinery construction

12.12.2018 | Event News

New Plastics Economy Investor Forum - Meeting Point for Innovations

10.12.2018 | Event News

EGU 2019 meeting: Media registration now open

06.12.2018 | Event News

 
Latest News

New discoveries predict ability to forecast dementia from single molecule

12.12.2018 | Health and Medicine

CCNY-Yale researchers make shape shifting cell breakthrough

12.12.2018 | Physics and Astronomy

Pain: Perception and motor impulses arise in the brain independently of one another

12.12.2018 | Health and Medicine

VideoLinks
Science & Research
Overview of more VideoLinks >>>