Tail-up models allow covariance unilaterally in the upstream direction.
Tail-down models allow covariance in both directions, but at present cannot generate a case with stronger spatial autocorrelation for flow-connected sites than flow-unconnected sites.
For our purposes (modelling water temperature), neither of these cases are a good fit, so I suggest we use the variance component structure combining tail-up, tail-down, and nugget variances to allow the model to select which ones are most relevant to the data.
Model requirements:
Downstream hydrologic distance matrix
Total hydrologic distance matrix
Watershed areas upstream of each confluence point in the stream network
I've used the freshwater atlas to extract a stream network, and have calculated a downstream hydrologic distance matrix between the sites in the Nechako water temperature dataset.
Spatial Stream Network model development is described in Ver Hoef & Peterson 2010 and Peterson & Ver Hoef 2010
For our purposes (modelling water temperature), neither of these cases are a good fit, so I suggest we use the variance component structure combining tail-up, tail-down, and nugget variances to allow the model to select which ones are most relevant to the data.
Model requirements: