Algorithm 1 Linear Trend Fitting and Deterministic Residual-Feature Engineering: Pipeline A

Require: Preprocessed, station-grouped dataset ${\mathcal{D}}_{\mathrm{pre}}$; target y; window sizes $\mathcal{K}=\{6,12\}$; MI top-K Ensure: Linear model $g_{\mathrm{lin}}$; residual targets $\mathbf{r}$; selected feature set ${\mathbf{X}}^{\det }$; ranked MI scores  Rolling Features (station-grouped): For each station s, variable z, and  $k\in \mathcal{K}$, compute rolling mean ${\mu }_t^{\left(k\right)}$ and rolling std ${\sigma }_t^{\left(k\right)}$ using Equations (7) and (8) within station s only (rolling and lag features for target-derived variables use strictly past observations $\{t-1,\dots ,t-k\}$ only; see Section 3.4)  Remove missing values; construct full deterministic feature matrix $\mathbf{X}$  Fit Linear Trend: $g_{\mathrm{lin}}\leftarrow$ OLS regression of y on $\mathbf{X}$ (training partition only), using Equation (5)  Compute Residual: $r_t\leftarrow y_t-g_{\mathrm{lin}}\left({\mathbf{x}}_t\right)$ for all t, using Equation (6)  MI Scoring: Compute $M{I}_i=I(X_i;r)$ for each feature using Equation (9)  Feature Selection: Sort by $M{I}_i$ descending; retain top-K features: ${\mathbf{X}}^{\det }\leftarrow \mathbf{X}\left[\mathrm{top}\text{-}K\right]$  return $g_{\mathrm{lin}}$, $\mathbf{r}$, ${\mathbf{X}}^{\det }$