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: 1639761
• 负责人: Mary Silber
• 金额: $ 36.7万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-01-01 至 2020-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1639761&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.

这位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，在气候变化下，沙漠生态系统可能容易受到荒漠化的影响。这些模型探讨了当某些半干旱生态系统受到降雨量减少的压力时，植被生物量的空间模式背后的潜在机制。植被的自组织空间效应与定义旱地的降水的巨大变异性相结合，为基本格局形成研究提供了新的方向。这项研究还将提供一个数学框架，用于测试生态建议的稳健性，即空间格局可能作为与气候变化相关的临界点的早期预警信号。这项研究将在确定性和随机性数学生态模型的框架内进行，其目标将通过丰富的卫星数据来加强，这些数据可用于测试模型预测。第一个目标是定性和定量地比较一类模式形成反应扩散植被模型，以确定当模型系统接近其平凡的沙漠状态时可能发生的不同植被格局状态之间的稳健转换。这种分析将以分叉理论为基础。第二个目标是开发和分析具有时间可变的降水输入和空间可变的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。将使用模型简化方法进一步确定模型框架之间的一致性。旱地生态系统的卫星图像数据将为建模工作提供信息并进行验证。该项目还有一个教育部分，目的是培养本科生和研究生进行跨学科的应用数学研究。