Towards a Qualitative Theory on Non-Linear Geographic Systems: Regular and Stochastic Evolution in Fluvial Landforms

走向非线性地理系统的定性理论：河流地貌的规则和随机演化

• 批准号: 9819095
• 负责人: Terence Smith
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-03-15 至 2003-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9819095&HistoricalAwards=false
• 关键词: Towards; Qualitative; Theory; Non; Linear

Spatial patterns and processes characterizing geographical entities and phenomena, such as drainage basins, systems of cities, and flows of information, often show a remarkable mix of organization and complexity. These arise from a large number of interactions that are spatially distributed and characterized by non-linear processes involving stochastic effects and instabilities. The dominant objective of this research is to refine and extend a family of physically based models for simulating key aspects of drainage basin evolution. The project will incorporate theoretical, computational, and field-based investigations to accomplish the following: (1) apply emerging methodologies for characterizing the qualitative behavior of infinite-dimensional, non-linear dynamical systems in explaining the emergence of spatial patterns in the evolution of drainage basins; (2) demonstrate that such methods must be used in conjunction with traditional methods in developing a full characterization of the evolution of fluvial land surfaces and an understanding of various scaling laws; (3) develop additional tools for such analyses and apply them to other examples of complex geographic phenomena; and (4) disseminate an understanding of these methods and their value. The mathematical and modeling results will provide a basis for qualitative and quantitative predictions that may be compared with observations on real landscapes, and ultimately, models of analogous geographic phenomena, such as population movements, diffusion of innovations, and information flows can be developed based on this understanding.

表征地理实体和现象的空间格局和过程，如流域、城市系统和信息流，往往表现出组织和复杂性的显著混合。这些是由大量的相互作用产生的，这些相互作用是空间分布的，并以涉及随机效应和不稳定性的非线性过程为特征。本研究的主要目标是完善和扩展一系列基于物理的模型，以模拟流域演化的关键方面。该项目将结合理论、计算和实地调查来完成以下工作：(1)应用新兴方法来描述无限维、非线性动力系统的定性行为，以解释流域演化过程中空间模式的出现；(2)证明这些方法必须与传统方法结合使用，以全面描述河流陆面演变并了解各种标度规律；(3)开发用于此类分析的其他工具，并将其应用于复杂地理现象的其他示例；(4)传播对这些方法及其价值的理解。数学和建模结果将为定性和定量预测提供基础，可与对真实景观的观察结果进行比较，并最终可根据这种理解开发类似地理现象的模型，如人口流动、创新的扩散和信息流。