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

小行星9527804 了解径流的动力学（或时间演变）及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研究的核心问题。 拟议中的研究旨在利用美国地质勘探局（USGS）长期记录（60至114年）的日径流量（据推测对人类影响不大），在美国站点开发径流量的可预测性和动力学相似性的定量概念。 直接从时间序列预测径流的方法（基于非线性动力学）将是研究的副产品。 在气候变化研究方面，今后许多年都可能需要利用外生模式气候数据预测径流量。 鉴于不确定的输入，重要的是要评估如何快速，以及在何种条件下，这种预测恶化为随机轨迹，无论模型的形式。 它也可能是感兴趣的知道，至少定性，流量的敏感性，不同的成因因素。 不同空间和时间尺度的径流建模有何影响？ 什么时候追求确定性、分布式或集总模型是有用的，什么时候必须诉诸纯统计方法？ 不严格地说，径流是大尺度大气环流与缓慢变化或固定的地面条件相互作用的结果。 后者可以将组织流作为感兴趣的空间尺度（例如，流域面积）增加，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，一个较大的流域在气候强迫中的许多动力学过程的空间平均值-具体地点的降雨量、流域的地理特征、蒸发和土壤特性，这些在任何流域都是不均匀的。 这种平均可以减少我们通过径流采样的响应的维度。 同样，在长时间尺度上具有“结构”的气候波动（例如，厄尔尼诺南方涛动（El Nino Southern Oscillation） 可以增加蒸汽流的可预测性。非线性动力学的最新进展提供了一个有趣的方法来深入了解这些过程，特别是非线性过程的时间序列分析。 其想法是单个状态变量的时间序列（例如，流）可用于几何重建“状态空间”，其中包含有关底层系统的可预测性和复杂性的基本信息。 可预测性是通过测量附近轨迹在状态空间中的发散率的李雅普诺夫指数在信息理论方面来测量的。 复杂性是通过检查状态空间被填充的密度以及状态空间上密度的变化来测量的。 在重构的状态空间预测的状态变量的策略。 我们的分析大盐湖量使用这些方法已经非常富有成效，并给了我们坚定的信念，显着的见解的性质，径流过程和发展的理论模型，在不同尺度的径流将是可能的。 本文提出的方法是系统地分析各种长的美国径流数据集，以（1）看看是否有可能从时间序列重建潜在的动态，（2）估计李雅普诺夫指数作为可预测性的度量，（3）估计广义维数来描述潜在的动态的复杂性，（4）开发有效的预测策略，为每日径流，以及（5）识别可预测性和复杂性以及预测能力如何改变气候属性和流域属性（例如流域面积）。 特别令人感兴趣的是物理阈值，在该阈值处，系统的响应经历了性质上不同的动态变化。 在使用非参数回归方法从时间序列中恢复系统不变量后，针对感兴趣的参数，探讨了这种阈值的存在。

9527804 Abarbanel 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 "stru cture" 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 sy stem invariants from the time series using nonparametric regression methods with respect to the parameters of interest.