Collaborative Research: Nonlinear Dynamics of Streamflow: Classification, Predictability and Forecasting

9508085了解径流的动态(或时间演变)、其在不同时间和空间尺度上的可预测性、因果关系和变异性是水文学研究的一个中心问题。这项拟议的研究试图利用美国地质勘探局(USGS)每日径流的长期记录(60年至114年)，开发美国站点径流的可预测性和动态相似性的量化概念，这些记录被认为对人类影响很小。直接从时间序列预测径流的方法(基于非线性动力学)将是这项研究的副产品。在气候变化研究的背景下，未来许多年可能需要使用外源模型气候数据预测径流。在输入不确定的情况下，重要的是评估这种预测恶化成随机痕迹的速度有多快，以及在什么条件下恶化，而不考虑模型的形式主义。至少在定性上，了解径流对不同致因因子的敏感性也可能是有意义的。在不同的空间和时间尺度上对径流进行建模意味着什么？什么时候追求确定性、分布式或集中模型是有用的，什么时候必须求助于纯粹的统计方法？粗略地说，径流是大尺度大气环流与缓慢变化或固定的地表条件相互作用的结果。后者可能会随着关注的空间尺度(例如，流域面积)的增加而促进径流的组织，从而限制了具有重大影响的“动力”因素的有效数量。我们将研究的一个想法是，一个更大的流域在空间上平均了气候强迫的许多动态过程--特定地点的降雨量、盆地的地理特征、蒸发和土壤性质，这些肯定在任何流域都是不均匀的。这种平均化可以减少我们通过流动采样的响应的维度。同样，在较长时间内具有“结构性”的气候波动也具有尺度效应(例如，厄尔尼诺南方涛动)。可能会增加秘密流量的可预测性。非线性动力学的最新进展为深入了解这类过程提供了一种有趣的方法，特别是对于来自非线性过程的时间序列分析。其思想是，动力系统的单个状态变量(例如，径流)的时间序列可以用来几何地重建包含关于底层系统的可预测性和复杂性的基本信息的“状态空间”。可预测性是通过李亚普诺夫指数以信息论的形式衡量的，李亚普诺夫指数衡量的是状态空间中附近轨迹的发散率。通过检查状态空间的填充密度和这种密度在状态空间上的变化，通过广义维度来衡量复杂性。设计了在重构状态空间中预测状态变量的策略。我们使用这些方法对大盐湖的水量进行了非常富有成效的分析，并使我们坚信，深入了解径流过程的性质和发展不同尺度的径流理论模型将是可能的。本文提出的方法是系统地分析各种美国长期径流数据集，以(1)看看是否有可能从时间序列中重建基本动力学，(2)估计Lyapunov指数作为可预测性的度量，(3)估计广义维度以描述基本动力学的复杂性，(4)开发有效的日径流预报策略，以及(5)确定可预测性、复杂性和预报能力如何改变气候属性和流域属性，如流域面积。特别令人感兴趣的是物理阈值，在该阈值下，系统的响应经历了本质上不同的动态变化。在利用关于感兴趣参数的非参数回归方法从时间序列中恢复系统不变量之后，探讨了这种阈值的存在。

9508085 Lall An understanding of the dynamics (or time evolution) of streamflow, its predictability, causality and variability at different time and space scales is a central issue in hydrologic research. The proposed research seeks to develop quantitative notions of predictability and dynamical similarity of streamflow at U.S. sites, using long USGS records (60 to 114 years) of daily streamflow that are presumed to have little human impact. Methods (based on nonlinear dynamics) for forecasting streamflow directly from the time series will be a byproduct of the research. In the context of climate change research, projections of streamflow using exogenous model climate data may be needed for many years in the future. Given uncertain inputs, it is important to assess how quickly, and under which conditions such predictions deteriorate into random traces, irrespective of model formalism. It may also be of interest to know, at least qualitatively, the sensitivity of streamflow to different causative factors. What are the implications for modeling streamflow at different space and time scales? When is it useful to pursue deterministic, distributed or lumped models, and when must one resort to a purely statistical approach? Loosely speaking, streamflow results from the interaction of large scale atmospheric circulation with slowly varying or fixed surface conditions. The latter may lend organization to streamflow as the spatial scale of interest (e.g., drainage area) increases, thus limiting the effective number of "dynamical" factors that have major influence. An idea which we will investigate is that a larger basin spatially averages over the many dynamical processes in the climatic forcing--rainfall at specific locations, geographical features in the basin, evaporation and soil properties which are certainly heterogeneous across any watershed. This averaging may reduce the dimension of the response which we sample by streamflow. Similarly, climatic fluctuations that have "structure " at long time scales, (e.g., El Nino Southern Oscillation). may increase stearmflow predictability. An interesting methodology for insights into such processes is provided by recent advances in nonlinear dynamics, and in particular for time series analysis from nonlinear processes. The idea is that time series for a single state variable (e.g., streamflow) for the dynamical system can be used to geometrically reconstruct a "state space" that contains the essential information on predictability and complexity of the underlying system. Predictability is measured in information theoretic terms through Lyapunov exponents that measure the rate of divergence of nearby trajectories in state space. Complexity is measured through generalized dimensions by an examination of how densely the state space is filled and variations in such a density over the state space. Strategies for forecasting the state variable in the reconstructed state space are devised. Our analyses of the Great Salt Lake volume using these methods have been very fruitful, and have given us the firm conviction that significant insights into the nature of the streamflow process and development of theoretical models for streamflow at different scales will be possible. The approach proposed here is to systematically analyze variety of long US streamflow data sets, to (1) see if a reconstruction of the underlying dynamics is possible from the time series, (2) estimate Lyapunov exponents as a measure of predictability, (3) estimate generalized dimensions to describe the complexity of the underlying dynamics, (4) to develop effective forecasting strategies for daily streamflow, and (5) identify how predictability and complexity and forecasting ability vary the climatic attributes and basin attributes such as drainage area. Of particular interest are physical thresholds at which the response of the system undergoes a change to qualitatively different dynamics. The existence of such thresholds is probed after the recovery of system invariants from the time series using nonparametric regression methods with respect to the parameters of interest.