IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v5y2017i4p69-d120120.html
   My bibliography  Save this article

Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation

Author

Listed:
  • Merlin C. Köhnke

    (Institute of Environmental Systems Research, School of Mathematics, Computer Science, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany)

  • Horst Malchow

    (Institute of Environmental Systems Research, School of Mathematics, Computer Science, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany)

Abstract

Semi-arid ecosystems made up of patterned vegetation, for instance, are thought to be highly sensitive. This highlights the importance of understanding the dynamics of the formation of vegetation patterns. The most renowned mathematical model describing such pattern formation consists of two partial differential equations and is often referred to as the Klausmeier model. This paper provides analytical and numerical investigations regarding the influence of different parameters, including the so-far not contemplated evaporation, on the long-term model results. Another focus is set on the influence of different initial conditions and on environmental noise, which has been added to the model. It is shown that patterning is beneficial for semi-arid ecosystems, that is, vegetation is present for a broader parameter range. Both parameter variability and environmental noise have only minor impacts on the model results. Increasing mortality has a high, nonlinear impact underlining the importance of further studies in order to gain a sufficient understanding allowing for suitable management strategies of this natural phenomenon.

Suggested Citation

  • Merlin C. Köhnke & Horst Malchow, 2017. "Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation," Mathematics, MDPI, vol. 5(4), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:69-:d:120120
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/5/4/69/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/5/4/69/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marten Scheffer & Steve Carpenter & Jonathan A. Foley & Carl Folke & Brian Walker, 2001. "Catastrophic shifts in ecosystems," Nature, Nature, vol. 413(6856), pages 591-596, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ian Hodge & William M. Adams, 2016. "Short-Term Projects versus Adaptive Governance: Conflicting Demands in the Management of Ecological Restoration," Land, MDPI, vol. 5(4), pages 1-17, November.
    2. Jenerette, G. Darrel & Lal, Rattan, 2007. "Modeled carbon sequestration variation in a linked erosion–deposition system," Ecological Modelling, Elsevier, vol. 200(1), pages 207-216.
    3. Rustici, M. & Ceccherelli, G. & Piazzi, L., 2017. "Predator exploitation and sea urchin bistability: Consequence on benthic alternative states," Ecological Modelling, Elsevier, vol. 344(C), pages 1-5.
    4. Rodrigues, João & Domingos, Tiago & Conceição, Pedro & Belbute, José, 2005. "Constraints on dematerialisation and allocation of natural capital along a sustainable growth path," Ecological Economics, Elsevier, vol. 54(4), pages 382-396, September.
    5. Xu Luo & Hong S. He & Yu Liang & Jacob S. Fraser & Jialin Li, 2018. "Mitigating the Effects of Climate Change through Harvesting and Planting in Boreal Forests of Northeastern China," Sustainability, MDPI, vol. 10(10), pages 1-20, October.
    6. Carlos Sanz-Lazaro, 2019. "A Framework to Advance the Understanding of the Ecological Effects of Extreme Climate Events," Sustainability, MDPI, vol. 11(21), pages 1-18, October.
    7. Teh, Su Yean & DeAngelis, Donald L. & Sternberg, Leonel da Silveira Lobo & Miralles-Wilhelm, Fernando R. & Smith, Thomas J. & Koh, Hock-Lye, 2008. "A simulation model for projecting changes in salinity concentrations and species dominance in the coastal margin habitats of the Everglades," Ecological Modelling, Elsevier, vol. 213(2), pages 245-256.
    8. Grolleau, Gilles & Ibanez, Lisette & Mzoughi, Naoufel, 2020. "Moral judgment of environmental harm caused by a single versus multiple wrongdoers: A survey experiment," Ecological Economics, Elsevier, vol. 170(C).
    9. Kong, Xiang-Zhen & Jørgensen, Sven Erik & He, Wei & Qin, Ning & Xu, Fu-Liu, 2013. "Predicting the restoration effects by a structural dynamic approach in Lake Chaohu, China," Ecological Modelling, Elsevier, vol. 266(C), pages 73-85.
    10. Paul L. G. Vlek & Asia Khamzina & Hossein Azadi & Anik Bhaduri & Luna Bharati & Ademola Braimoh & Christopher Martius & Terry Sunderland & Fatemeh Taheri, 2017. "Trade-Offs in Multi-Purpose Land Use under Land Degradation," Sustainability, MDPI, vol. 9(12), pages 1-19, November.
    11. Sonia Kéfi & Vishwesha Guttal & William A Brock & Stephen R Carpenter & Aaron M Ellison & Valerie N Livina & David A Seekell & Marten Scheffer & Egbert H van Nes & Vasilis Dakos, 2014. "Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-13, March.
    12. Monika Winn & Manfred Kirchgeorg & Andrew Griffiths & Martina K. Linnenluecke & Elmar Günther, 2011. "Impacts from climate change on organizations: a conceptual foundation," Business Strategy and the Environment, Wiley Blackwell, vol. 20(3), pages 157-173, March.
    13. Duncan A. O’Brien & Smita Deb & Gideon Gal & Stephen J. Thackeray & Partha S. Dutta & Shin-ichiro S. Matsuzaki & Linda May & Christopher F. Clements, 2023. "Early warning signals have limited applicability to empirical lake data," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    14. Can Askan Mavi & Nicolas Quérou, 2020. "Common pool resource management and risk perceptions," DEM Discussion Paper Series 20-25, Department of Economics at the University of Luxembourg.
    15. Shana M. Sundstrom & Craig R. Allen & David G. Angeler, 2020. "Scaling and discontinuities in the global economy," Journal of Evolutionary Economics, Springer, vol. 30(2), pages 319-345, April.
    16. Therese Lindahl & Anne-Sophie Crépin & Caroline Schill, 2016. "Potential Disasters can Turn the Tragedy into Success," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(3), pages 657-676, November.
    17. Yan Cheng & Stefan Oehmcke & Martin Brandt & Lisa Rosenthal & Adrian Das & Anton Vrieling & Sassan Saatchi & Fabien Wagner & Maurice Mugabowindekwe & Wim Verbruggen & Claus Beier & Stéphanie Horion, 2024. "Scattered tree death contributes to substantial forest loss in California," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    18. Mariani, Fabio & Pérez-Barahona, Agustín & Raffin, Natacha, 2010. "Life expectancy and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 798-815, April.
    19. Kong, Xiangzhen & He, Wei & Liu, Wenxiu & Yang, Bin & Xu, Fuliu & Jørgensen, Sven Erik & Mooij, Wolf M., 2016. "Changes in food web structure and ecosystem functioning of a large, shallow Chinese lake during the 1950s, 1980s and 2000s," Ecological Modelling, Elsevier, vol. 319(C), pages 31-41.
    20. Ignacio C. Fernández & David Manuel-Navarrete & Robinson Torres-Salinas, 2016. "Breaking Resilient Patterns of Inequality in Santiago de Chile: Challenges to Navigate towards a More Sustainable City," Sustainability, MDPI, vol. 8(8), pages 1-19, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:69-:d:120120. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.