Fig. 4: Observed and model climatologies and biases.

Row a is the observed climatology, \({\langle {O}_{{\rm{train}}}\rangle }_{m,\tau }\), and set of model forecast climatologies, \({\langle {F}_{{\rm{train}}}\rangle }_{m,\tau }\), for the training period (as functions of calendar month and lead time). Row b shows the training period biases, \({{B}_{{\rm{train}}}}_{m,\tau }\), which are the differences between the model and observed climatologies in the training period, \({\langle {F}_{{\rm{train}}}\rangle }_{m,\tau }-{\langle {O}_{{\rm{train}}}\rangle }_{m,\tau }\). Row c is the observed climatology, \({\langle {O}_{{\rm{test}}}\rangle }_{m,\tau }\), and set of model climatologies, \({\langle {F}_{{\rm{test}}}\rangle }_{m,\tau }\), for the testing period. Row d shows the testing period biases, \({{B}_{{\rm{test}}}}_{m,\tau }\), which are the differences between the model and observed climatologies in the testing period, \({\langle {F}_{{\rm{test}}}\rangle }_{m,\tau }-{\langle {O}_{{\rm{test}}}\rangle }_{m,\tau }\). Row e is the difference in climatologies between the training and testing periods for observations, \({{\Delta }}{\langle O\rangle }_{m,\tau }={\langle {O}_{{\rm{test}}}\rangle }_{m,\tau }-{\langle {O}_{{\rm{train}}}\rangle }_{m,\tau }\) (first column) and models, \({{\Delta }}{\langle F\rangle }_{m,\tau }={\langle {F}_{{\rm{test}}}\rangle }_{m,\tau }-{\langle {F}_{{\rm{train}}}\rangle }_{m,\tau }\) (remaining columns). Row f is the difference between the model biases in the training and testing periods, \({{\Delta }}{B}_{m,\tau }={{B}_{{\rm{test}}}}_{m,\tau }-{{B}_{{\rm{train}}}}_{m,\tau }\). Row g is a bar plot for the month of March (month 3 above) of the observed change in climate, Δ〈O〉_March,τ, (blue bars), the change in model biases, ΔB_March,τ, (red bars), and the sum of these, which is the change in model climatology, Δ〈F〉_March,τ, (black outlines).