Downscaled Climate Projections
Here we overview the statistical models that relate either temperature or precipitation at a weather station to variables averaged over a larger scale more representative of the scales resolved by climate models. The large-scale variables are the independent data and are denoted here by $x_i(t)$, where $i$ is an index which denotes the different large-scale variables used as predictors and $t$ is an index over time. The station data is the dependent variable and is denoted here by $y(t)$. The fitting of the statistical model is performed on the actual observed relationships between station data and large-scale variables and is therefore independent of the climate models. Because of the strong annual cycle in our downscaling domain, twelve separate statistical models are fit to each variable -- one for each calendar month.