Abstract. Recent progress in nonlinear dynamic theory has inspired hydrologists to apply innovative nonlinear time series techniques to the analysis of streamflow data. However, regardless of the method employed to analyze streamflow data, the first step should be the identification of underlying dynamics using one or more methods that could distinguish between linear and nonlinear, deterministic and stochastic processes from data itself. In recent years a statistically rigorous framework to test whether or not the examined time series is generated by a Gaussian (linear) process undergoing a possibly nonlinear static transform is provided by the method of surrogate data. The surrogate data, generated to represent the null hypothesis, are compared to the original data under a nonlinear discriminating statistic in order to reject or approve the null hypothesis. In recognition of this tendency, the method of "surrogate data" is applied herein to determine the underlying linear stochastic or nonlinear deterministic nature of daily streamflow data observed from the central basin of Puget Sound, and as applicable, distinguish between the static or dynamic nonlinearity of the data in question.

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In part I of this study the strong teleconnections between large-scale atmospheric circulation patterns and the peak of snowpack measured by snow water equivalent (SWE) in Washington State were established by a linear regression model. However, the underlying dynamics of snowpack for each snow telemetry (SNOTEL) site are unknown. The statistically significant correlations between the peaks of snowpack and large-scale climate indices do not necessarily imply linear relationships among them. Moreover, these correlations do not imply a deterministic or stochastic dynamic process underlying snowpack SWE data. To better understand the complexity of snowpack dynamics in Washington State, a technique developed from nonlinear time series analysis and dynamic theory called surrogate data testing was used to investigate the complexity of snowpack dynamics in terms of determinism vs. randomness. Some relatively new concepts, such as embedding dimensions, time delay, phase reconstruction , correlation dimensions and prediction errors are introduced to hydrologists and water managers to characterize the complexity and predictability of the snowpack at specified sites.

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