Deterministic and Stochastic Models of Water Limited Ecosystems: Implications of Pattern Formation, Bifurcations, Model Reduction, and Data

水资源有限的生态系统的确定性和随机模型：模式形成、分叉、模型简化和数据的含义

• 批准号: 1517416
• 负责人: Mary Silber
• 金额: $ 39.44万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-15 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1517416&HistoricalAwards=false
• 关键词: Deterministic; Stochastic; Models; Water; Limited

The investigator and her students will contribute to mathematical modeling efforts for desert ecosystems, which may be vulnerable to desertification under climate change. These models address the underlying mechanisms behind the spatial patterns of vegetation biomass that occur when certain semi-arid ecosystems are stressed by decreased precipitation. Interfacing self-organizing spatial effects for vegetation with the enormous variability of precipitation that define drylands suggests new directions for fundamental pattern formation research. The research will also contribute a mathematical framework for testing the robustness of the ecological proposals that the spatial patterns may serve as early warning signs of tipping points associated with climate change.The research will be developed within a framework of deterministic and stochastic mathematical ecological models, with its objectives enhanced by the availability of rich satellite data that can be used to test model predictions. The first objective is to compare, qualitatively and quantitatively, a class of pattern-forming reaction-diffusion vegetation models to determine the robust transitions between distinct vegetation pattern states that may occur as the model system approaches its trivial desert state. This analysis will be based in bifurcation theory. The second objective is to develop and analyze vegetation models with temporally variable precipitation inputs, and spatially variable drainage networks. This will lead to the development of stochastic models with non-Gaussian noise. Model reduction methods will be used to further determine the consistency between model frameworks. Satellite image data of dry-land ecosystems will inform and verify the modeling effort. The project also has an education component with the goal of training undergraduate and graduate students in interdisciplinary applied mathematics research.

研究人员和她的学生将为沙漠生态系统的数学建模工作做出贡献，这可能在气候变化下容易受到荒漠化的影响。这些模型探讨了植被生物量的空间模式背后的潜在机制，而植被生物量的空间模式是在某些半干旱生态系统因降水减少而强调的。将自组织的空间效应与定义旱地的巨大降水差异提出了巨大的差异，这提出了基本模式形成研究的新方向。这项研究还将为测试生态提案的鲁棒性做出一个数学框架，即空间模式可以用作与气候变化相关的倾斜点的预警信号。该研究将在确定性和随机数学生态学模型的框架内开发，并通过其对象的可用性来增强其目标，从而可以使用丰富的卫星数据来测试模型。第一个目标是在定性和定量上比较一类形成模式的反应扩散植被模型，以确定随着模型系统接近其琐碎的沙漠状态，可能发生的不同植被模式状态之间的稳健过渡。该分析将基于分叉理论。第二个目标是开发和分析具有暂时性降水输入和空间可变排水网络的植被模型。这将导致具有非高斯噪声的随机模型的发展。模型还原方法将用于进一步确定模型框架之间的一致性。干地生态系统的卫星图像数据将告知和验证建模工作。该项目还具有一个教育部分，其目标是培训跨学科应用数学研究的本科生和研究生。