## The four currently proposed tidal stream turbine arrays in

For a given forecast Δt the forecast for the average irradiance in the interval [t, t + Δt ] denoted as Iˆ(t+Δt) is calculated asequation(2)Iˆp(t+Δt)=〈kt〉[t−Δt,t]×〈Iclr〉[t,t+Δt]where 〈⋅〉[t,t±Δt]〈⋅〉[t,t±Δt] indicates the average in the window [t, t±Δt]. In this JNJ-7706621 the window size [t − Δt, t] that defines the persistence and the window size [t, t + Δt] for the forecast have the same length. However, there is no reason why they must be coupled. Thus, in this work we also explore the optimization of the persistence model by considering the following implementation:equation(3)Iˆpδ(t+Δt)=〈kt〉[t−δ,t]×〈Iclr〉[t,t+Δt]where δ∈ 5, 10, ?,120 min is determined via exhaustive search method such that deuterostomes minimizes the RMSE for the optimization dataset:equation(4)RMSE=1nO∑i=1nO(Iˆi−Ii)2where nO is the number of data points in the optimization dataset. In this work we used RMSE as the main error metric since it emphasizes the larger errors. A second metric, used to evaluate the improvement relative to the baseline model, is the forecast skill which is given by:equation(5)s=(1−RMSEmRMSE0)×100 [%]where RMSE0 is the RMSE for the model described by Eq. (2) and RMSEm is the RMSE for the model m.