Examining the pluvial to nival river regime spectrum using nonlinear methods: Minimum delay embedding dimension

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The nonlinear dynamics of streamflow time series from 667 reference hydrometric stations in North America spanning the pluvial-nival hydrological continuum are explored using minimum embedding dimensions as determined by False Nearest Neighbor (FNN) methods. Simulations using synthetic time series demonstrate that snowmelt dominated time series have lower embedding dimensions than those that are rainfall dominated, and that mixtures of the two processes result in a nearly linear change in the embedding dimension. The majority of the reference hydrometric stations drop below a 1% threshold at a dimension less than 30, showing a high degree of natural complexity in the signals ranging from annual snowmelt to weather-driven pseudo-stochastic systems. A less restrictive threshold, 5% is suggested to be more appropriate for streamflow time series. Time series smoothing impacts the embedding dimension and over-smoothing results in incorrect reductions of embedding dimensions. The relationship of the embedding dimensions to watershed and statistical properties of streamflow record showed the lowest embedding dimensions are restricted to large drainage areas, high elevations, and large mean annual flows and variance, high autocorrelations, and large fractions of the records with only small changes in magnitude. Times series that have a large proportion of consecutive days of equal streamflow typically result in higher embedding dimensions. Mapping of the embedding dimension shows spatial patterns related to the streamflow generating processes and geographical features. The use of embedding dimension resolved different dynamics across the hydrological continuum for rainfall to snowmelt over many climate zones. Changes in the embedding dimension might indicate process changes related to climate variability and change.