Fig. 5

Effects of the bias and trend terms on \(\sqrt {{\text{d}}P}\), defined by Eq. (40). The black dotted and dashed lines and the cyan solid line indicate the MHD forecasts with \(k^{\prime} = 0\) (Eq. 16), i.e., the MHD simulations given the initial condition at 2004.25 obtained by the data assimilation. The dotted black line is with neither bias nor trend, while the dashed line includes only bias. The cyan solid line takes both bias and trend into consideration in minimizing Eq. (10) at the final iteration. The blue dashed line shows the ensemble-weighted sum with bias and trend terms, corresponding to Eq. (13). See Table 1 for details of each calculation