Mathematical Sciences: Multiscale Processes and Stochastic Dynamics in Geosciences

数学科学：地球科学中的多尺度过程和随机动力学

• 批准号: 9504557
• 负责人: Rabindra Bhattacharya
• 金额: $ 9万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1999-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504557&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multiscale; Processes; Stochastic

9504557 Bhattacharya Abstract Probabilistic methods are proposed for the analysis of three broad classes of problems in hydrology, climatic prediction and global change phenomena. All these phenomena are governed by nonlinear dynamics with a hierarchy of scales in space and time, which make their analysis and prediction complex and challenging. Of the three broad topics considered here, Topic 1 is devoted to the problem of contaminant transport in natural media such as aquifers. The class of Fokker-Planck equations which govern this transport involve multiple spatial scales of heterogeneity. Topic 2 concerns the fine scale structure of a class of random measures which arise in the statistical theories of turbulence and rainfall. The mathematical theory to be employed for such highly singular phenomena is that of random cascades. Topic 3 is concerned with climatic changes and global change phenomena over much larger scales of time than envisaged under Topic 2. Here the aim is to analyze interannual climatic events using randomly perturbed dynamical systems. The main objective of the proposal is the development of nonlinear stochastic dynamical theories for (1) the prediction of the spread of pollutants in the environment with time, (2) making improvements in short-term weather forecasting, and (3) the understanding and eventual prediction of long-term climatic and global change phenomena. An important example under Topic 1 is the problem of the spread of chemical and other pollutants in natural underground water systems. Since even slightly different velocity fields of water in these systems often lead to dramatically different rates of spread of the pollution in the long run, careful and precise modeling and analysis are required and proposed here. With regard to Topic 2, different techniques are needed for the study of the space-time distribution of thunderstorms and rainfall. These are expected to provide better inputs into the numerical models which are generally used for we ather forecasts, thus improving their predictability. Although scientists have been somewhat successful in such short-term weather forecasting, they have had little success in the understanding and prediction of long-term climatic phenomena. Since it is impossible to provide an adequate deterministic model for the latter, the main aim under Topic 3 is the analysis of these long-term phenomena using models with random perturbations. An example considered is the prediction of the advent and intensity of the El Nino--a warming of the Tropical Pacific causing extensive rainfall and flooding--and its opposite the dry La Nina. Realistic nonlinear stochastic models are sought here and their analysis is proposed.

提出了9504557 Bhattacharya抽象的概率方法，用于分析三种广泛的水文学，气候预测和全球变化现象的问题。 所有这些现象都受时空和时间范围层次结构的非线性动力学的控制，这使得他们的分析和预测复杂和具有挑战性。 在此处考虑的三个广泛主题中，主题1致力于自然媒体（例如含水层）在自然媒体中的污染物运输问题。 控制该运输的福克 - 普兰克方程类别涉及多个空间尺度的异质性。主题2涉及一类随机度量的精细规模结构，这些结构是在湍流和降雨的统计理论中产生的。 用于这种高度奇异现象的数学理论是随机级联反应。主题3关注的是，比主题2所设想的时间更大的时间尺度上关注的气候变化和全球变化现象。在这里，目的是使用随机扰动的动力学系统分析年际气候事件。 该提案的主要目的是（1）随着时间的推移预测污染物在环境中的传播，（2）改善短期天气预报，以及（3）对长期气候和全球变化现象的理解和最终预测。 主题1下的一个重要例子是化学和其他污染物在天然地下水系统中传播的问题。 由于这些系统中的水速度场略有不同，从长远来看，污染的传播速度通常很大，因此需要仔细而精确的建模和分析。 关于主题2，需要不同的技术来研究雷暴和降雨的时空分布。 这些预计将提供更好的投入到数值模型中，这些模型通常用于我们的预测，从而提高了它们的可预测性。尽管科学家在如此短期的天气预报中取得了成功，但他们在理解和预测长期气候现象方面几乎没有成功。 由于不可能为后者提供适当的确定性模型，因此主题3下的主要目的是使用具有随机扰动的模型对这些长期现象进行分析。 考虑的一个例子是预测了埃尔尼诺（El Nino）的出现和强度，这是热带太平洋的温暖，导致了大量降雨和洪水 - 及其对面是干燥的拉尼娜（La Nina）。 在这里寻求现实的非线性随机模型，并提出了它们的分析。