Cleaning Time Series with Hidden Markov Models: Time series data is pervasive and messy. In my PhD work I collected river temperature data at two hour intervals for four years at over 100 sites resulting in nearly 2 million data points. Identifying errors in these data would be time consuming and mind numbing. Given that time series are highly autocorrelated, our expectation of any given time step is highly informed by the previous time steps.

Hidden Markov Models leverage temporal autocorrelation to not only estimate the expectation of subsequent data given previous data but also can estimate when the system has transitioned into a new state.

The figure above uses a Hidden Markov Model to separate air and water temperature observations. On the left I've plotted data for ten sites over 4 years. The yellow data are believed by the model to be in the air state while the blue data are expected water temperature observations. The right portion of the plot zooms in on one site and provides the probability estimates for each data point and the mean estimate for each temperature state.

Mapping Heat Risk: Understanding risk is a pervasive problem and requires taking uncertainty extremely seriously. In my PhD work I used river network models and time series models using MCMC and parametric bootstrapping to explore the parameter space that describes stream temperatures. In this way I could return probability estimates of exceeding any thermal threshold anywhere in the river system at any time. This process also reveals the relative contribution to risk and uncertainty in these estimate. Below are the spatial predictors of the parameter estimates that describe the temperature time series.

Mapping Space and Time: Maps make understanding space intuitive but conveying time is a bit tricky. Here placing points that describe the location and contributing area of hydro-gauge stations in the Fraser River basin is rather simple. By delineating and coloring the basin by the changing annual air temperature and precipitation we can also describe the shifting climate. This helps understand how different basins are integrating different varieties of changing climate that then impact stream flow.

A Rivers Portfolio Effect... With Certainty: Here is one simple way to describe how river networks attenuate changing flow regimes. The colored dots represent the degree of climate complexity integrated by a given catchment. The blue line is the observed attenuation and the red/yellow lines describe what we might expect if the attenuation where to occur by random chance. These random chance lines demonstrate that what we observed would be unlikely to occur randomly. Overal we show how flow trend variability decreases as watershed size and climate trend complexity increases. The pattern is rather simple but the data is rich!

Changing Climate | Shifting Water: With warming annual temperatures, places that have traditionally seen snow in the winter are increasingly shifting to rain. This change has impacts on the timing of river flow events. Visualizing these shifts are difficult in a static image but dynamic images allow us to see these changes without complex analyses or multi-panel plots. I'm interested in knowing how the network might mitigate these shifts and what the impacts may be for fish either directly or indirectly via changing phenological events or shifting temperature regimes.

Match-Mismatch: I'm currently working on a project that aims to understand phenological match-mismatch under climate change. Here I'm showing distributions of predicted estuary arrival. As the local climate of a population diverges from that of the estuary, the shape of the arrival timing distribution becomes more broad, leaving a large portion of the migration well before or after the zooplankton blooms (grey vertical lines). These new ridgeline plots sure win out over boxplots or violin plots.