Water temperature model

[nehill197]

Going to follow the variance components model of Peterson & Ver Hoef, 2010.

1. Start with a model with water temperature to get variance structure working.
2. Incorporate predictor variables as seen in the DAGs (e.g. air temperature)
3. Attempt kriging (spatial predictions between points)

[nehill197]

I've successfully combined tail-up, tail-down, and euclidean distance covariance structures into an SSN model with a simple model for expected weekly mean water temperature with day of year and its squared polynomial term as predictors. Note that the effective sample size (ess) is higher than suggested by glance due to using data as parameters in the model to impute missing water temperature values. Chains are mixing well.

Next I'm going to work on a mechanistic (causal) model for water temperature.

[nehill197]

Decided on a logistic curve between air temperature and water temperature for the mechanistic model. The model was able to predict water temperatures for all weeks for all sites across the three years of air temperature data I downloaded. This extends beyond the range of the observed water temperature (which cover, at most, ~18 months of data). I was able to predict GSDD with uncertainty for the sites across the network for these three years.