Hydrologic classification system: A data reconstruction approach

Abstract

Recent technological advances, such as powerful computers, remote sensors, geographic information systems and worldwide networking facilities, have brought hydrologic research to a whole new level. They have facilitated extensive data collection, better data sharing, formulation of sophisticated methods, and development of complex models to mimic real hydrologic systems. Despite these obvious advances, there are serious concerns about their use in practice and criticisms about our approach to hydrologic modeling. For example: (1) these developments naturally lead to more complex models (having too many parameters requiring too much data) than that may actually be needed; (2) to satisfy the data requirements for such models, we are certainly collecting more and more data, but this does not mean that we are collecting all the relevant data; (3) so, despite their complexity, these models do not perform sufficiently well, even for the situations they are developed for; and (4) since the models are often developed for specific situations, 'translation' of the results to other situations is difficult. Recent studies have addressed these concerns and criticisms, albeit in different forms, such as dominant processes, thresholds, model integration, and model simplification. A common aspect in these studies is that they recognize the need for a "classification system" in hydrology, so that an appropriate identification as to the model (type) and data requirements can be made. The studies also recognize that, in order to be of general use, such a framework must be: (1) able to provide guidelines for streamlining hydrologic complexity into classes and sub-classes, as appropriate, based on the general/specific information available; and (2) simple enough and commonly agreeable, so that it could provide a "universal" language for communications and discussions in hydrology. They opine that perhaps the identification of dominant governing processes may help in the formation of such a classification system. The present study explores one potential way to advance this classification system. The exploration involves use of a simple phase-space data reconstruction technique to identify the 'complexity' of hydrologic systems (defined especially in the context of dimensionality of relevant time series). The reconstruction involves representation of the given multi- (often large-) dimensional hydrologic system using only an available (representative) single-variable data series through a delay coordinate embedding procedure. The 'extent of complexity' of the system is identified by the 'region of attraction of trajectories' in the phase-space, which is then used to classify the system as potentially low-, mediumor high-dimensional. The investigation is carried out in two steps: First, the use of the phase-space concept for system complexity and classification is demonstrated on two artificially generated time series, whose characteristics are known a priori: a high-dimensional purely random series and a low-dimensional deterministic chaotic series. Then, phase-spaces are reconstructed for a host of river flow time series, representing different geographic regions, climatic conditions, river sizes and complexities, and scales. Two specific cases are discussed herein: (1) daily river flow data from different locations; and (2) river flow data of different scales from the same location. The results for the two artificial time series reveals that direct time series plots and other widely used linear statistical tools (such as autocorrelation function and power spectrum) may not be adequate for studying system complexity and classification. This may be attributed to the inability of these tools to represent the nonlinear properties of the deterministic chaotic series (an inherent property of hydrologic data). The river flow series yield 'attractors' that range from 'very clear' ones to 'moderately clear' to 'very blurry' ones depending on data, indicating the usefulness of this simple phase-space reconstruction concept for studying hydrologic system complexity and classification. The results also reveal the ability of the phase-space to reflect the river basin characteristics and the associated mechanisms, such as basin size, smoothing, and scaling.