Chaotic, Non-linear Dynamics of Aquatic Metabolism in a Florida Freshwater Spring River

Observations of the complex underpinnings of non-linear systems in ecology are often data limited, but increased sensor technology in recent years is resulting in novel analyses of river chemistry. Aquatic metabolism is the result of integrated ecosystem responses, and is therefore likely to reflect deterministic non-linearity. In this paper, we diagnose the metabolic dynamics of an aquatic ecosystem from observations on a single constituent biochemical marker collected from the Ichetucknee River in Florida. While dissolved oxygen is commonly used to measure aquatic metabolism, recent evidence suggests that other biochemical markers, such as nitrate, reflect metabolic responses in these rivers as well. We apply the following markers individually to diagnose ecosystem dynamics: Nitrate (NO3-; 15- minute measurements), dissolved oxygen (DO), and specific conductivity (both hourly). The nonlinear time series analysis literature calls this an 'inverse' approach because system dynamics are detected from observed output—not generated by a model of mechanistic processes. Dynamic variation in the data can be due to deterministic chaos, non-chaotic but nonlinear deterministic structure, linear correlations, or various colored-noise processes. Initial analysis include phase-space reconstruction (PSR) and surrogate data analysis. We then apply Singular Spectrum Analysis (SSA) to separate signal from unstructured noise in the observed data for each marker. We next apply Surrogate Data Analysis (SDA) to test the SSA-signal for consistency with low-dimensional, nonlinear, and deterministic behavior, and to suggest dynamic processes best suited to simulate detected real-world dynamics. Finally, we apply SDA to separated SSA-noise to test whether discrepancies between observed data and the SSA-signal are indeed unstructured random i.i.d variables; and Extreme Value Statistics to statistically model SSA-noise and calculate the likelihood of biochemical-marker extremes outside of the periodic patterns detected in the SSA-signal. Preliminary results are consistent with the possibility that river chemistry is regulated by low-dimensional and nonlinear deterministic dynamics that exhibit sensitivity to initial conditions. The SSA-signals for the DO and NO3- markers explain 81-96% of the observed variance. The deterministic structure of the SSA-signal is readily apparent in phase-space attractors reconstructed from the SSA-signal for each marker. Each attractor is characterized by diurnal and half-diurnal cycles that are distinctly different from cycles that would be created by red noise. One implication of this work is that the dynamic behavioral patterns detected in river chemistry might be simulated with a few deterministic variables.