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imprecise initial state of the system. It could also stem from the more or less precise identification of forcings of the dynamical systems, such as emission fields (in atmospheric chemistry), radiative forcing, boundary conditions, and couplings to other models that may be imperfect. The deficiency of the model itself is another source of uncertainty. To account for this type of uncertainty, models could explicitly be made probabilistic. This occurs when some stochastic forcing is implemented to
imprecise initial state of the system. It could also stem from the more or less precise identification of forcings of the dynamical systems, such as emission fields (in atmospheric chemistry), radiative forcing, boundary conditions, and couplings to other models that may be imperfect. The deficiency of the model itself is another source of uncertainty. To account for this type of uncertainty, models could explicitly be made probabilistic. This occurs when some stochastic forcing is implemented to
1. Introduction Heavy rainfalls are extreme meteorological phenomena and often cause disasters with loss of human life. Recent progress in numerical modeling and assimilation techniques has made it possible to predict to some extent the occurrence of heavy rainfalls induced by orographic or synoptic forcing. However, predicting small-scale convective rainfalls with weak forcing is still a numerical weather prediction (NWP) challenge. In Japan, such local heavy rainfalls are sometimes called
1. Introduction Heavy rainfalls are extreme meteorological phenomena and often cause disasters with loss of human life. Recent progress in numerical modeling and assimilation techniques has made it possible to predict to some extent the occurrence of heavy rainfalls induced by orographic or synoptic forcing. However, predicting small-scale convective rainfalls with weak forcing is still a numerical weather prediction (NWP) challenge. In Japan, such local heavy rainfalls are sometimes called
correlations defined through The solution in (B3) represents the best fit to the observations and to the dynamical model according to the penalty function in (16) . However, (B3) is coupled to (B4) through the model error term, which appears as a forcing; conversely, the observation term, depending on x ( t ), acts as a forcing in (B4) . As mentioned in section 2 , the method of representers can be used to decouple and solve the Euler–Lagrange equations in the
correlations defined through The solution in (B3) represents the best fit to the observations and to the dynamical model according to the penalty function in (16) . However, (B3) is coupled to (B4) through the model error term, which appears as a forcing; conversely, the observation term, depending on x ( t ), acts as a forcing in (B4) . As mentioned in section 2 , the method of representers can be used to decouple and solve the Euler–Lagrange equations in the
diabatic forcing and divergence. Recently, Pagé et al. (2007) demonstrated the ability of another form of the omega equation to diagnose summertime mesoscale convective systems with a significant accuracy and envisage its utility as a balance constraint in a mesoscale Var system. These new approaches are currently being examined in the Environment Canada (EC) limited-area Var system ( Fillion et al. 2005 ). In terms of rotational wind balance, EC’s limited-area Var system uses, like other mesoscale
diabatic forcing and divergence. Recently, Pagé et al. (2007) demonstrated the ability of another form of the omega equation to diagnose summertime mesoscale convective systems with a significant accuracy and envisage its utility as a balance constraint in a mesoscale Var system. These new approaches are currently being examined in the Environment Canada (EC) limited-area Var system ( Fillion et al. 2005 ). In terms of rotational wind balance, EC’s limited-area Var system uses, like other mesoscale
) approach. The vertical localization is configured to force the covariances to 0 at a distance of (a) 2, (b) 4, or (c) 100 scale heights. Fig . 2. As in Fig. 1 , but for a single observation of AMSU-A channel 10. Fig . 3. The analysis increment of temperature from assimilating either (a) the full set of AMSU-A channels (4–10) at the same location used for Figs. 1 and 2 or (b) the vertical profile of temperature observations from a
) approach. The vertical localization is configured to force the covariances to 0 at a distance of (a) 2, (b) 4, or (c) 100 scale heights. Fig . 2. As in Fig. 1 , but for a single observation of AMSU-A channel 10. Fig . 3. The analysis increment of temperature from assimilating either (a) the full set of AMSU-A channels (4–10) at the same location used for Figs. 1 and 2 or (b) the vertical profile of temperature observations from a
