Toward an Improved Understanding of Hydrologic Complexity

Abstract:

Are wet hydrologic basins easier to model than semi-arid ones? How does the basin size impact the number of parameters needed to fairly represent the basin hydrologic response? Are there any other variables that exert a first-order control on basin behavior? These questions are of paramount importance to hydrologists with far-reaching consequences to model selection and prediction in ungauged basins. A few studies have previously examined the complexity of hydrologic basins using a range of statistical, dynamical and information-theoretic concepts. However, given the lack of complete records on basin properties and hydrologic variables apart from precipitation and streamflow, it has been difficult to relate their findings to basins’ distinctive features. Here, we use methods of time-delay embedding grounded on the theory of chaotic dynamical systems along with an extensive dataset to examine hydrologic complexity of more than 250 basins across the contiguous United States. In addition to a dimensionality metric that was previously used in identifying the number of degrees of freedom in a basin, we present a new metric to measure the strength of nonlinearity in a basin. Our findings pinpoint consistent patterns that link the size and climatic properties of a basin to its dynamic’s dimensionality and nonlinearity.