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 Safeguarding sustainability through forest certification mapping
27.06.2017 | International Institute for Applied Systems Analysis (IIASA)

nachricht Dune ecosystem modelling
26.06.2017 | Albert-Ludwigs-Universität Freiburg im Breisgau

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: 3-D scanning with water

3-D shape acquisition using water displacement as the shape sensor for the reconstruction of complex objects

A global team of computer scientists and engineers have developed an innovative technique that more completely reconstructs challenging 3D objects. An ancient...

Im Focus: Manipulating Electron Spins Without Loss of Information

Physicists have developed a new technique that uses electrical voltages to control the electron spin on a chip. The newly-developed method provides protection from spin decay, meaning that the contained information can be maintained and transmitted over comparatively large distances, as has been demonstrated by a team from the University of Basel’s Department of Physics and the Swiss Nanoscience Institute. The results have been published in Physical Review X.

For several years, researchers have been trying to use the spin of an electron to store and transmit information. The spin of each electron is always coupled...

Im Focus: The proton precisely weighted

What is the mass of a proton? Scientists from Germany and Japan successfully did an important step towards the most exact knowledge of this fundamental constant. By means of precision measurements on a single proton, they could improve the precision by a factor of three and also correct the existing value.

To determine the mass of a single proton still more accurate – a group of physicists led by Klaus Blaum and Sven Sturm of the Max Planck Institute for Nuclear...

Im Focus: On the way to a biological alternative

A bacterial enzyme enables reactions that open up alternatives to key industrial chemical processes

The research team of Prof. Dr. Oliver Einsle at the University of Freiburg's Institute of Biochemistry has long been exploring the functioning of nitrogenase....

Im Focus: The 1 trillion tonne iceberg

Larsen C Ice Shelf rift finally breaks through

A one trillion tonne iceberg - one of the biggest ever recorded -- has calved away from the Larsen C Ice Shelf in Antarctica, after a rift in the ice,...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Closing the Sustainability Circle: Protection of Food with Biobased Materials

21.07.2017 | Event News

»We are bringing Additive Manufacturing to SMEs«

19.07.2017 | Event News

The technology with a feel for feelings

12.07.2017 | Event News

 
Latest News

Ultrathin device harvests electricity from human motion

24.07.2017 | Power and Electrical Engineering

Scientists announce the quest for high-index materials

24.07.2017 | Materials Sciences

ADIR Project: Lasers Recover Valuable Materials

24.07.2017 | Materials Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>