  Ensemble forecasting of nonlinear systems involves the use of a model to run
forward a discrete ensemble (or set) of initial states. Data assimilation
techniques tend to focus on estimating the true state of the system, even
though model error limits the value of such efforts. This paper argues for
choosing the initial ensemble in order to optimise forecasting performance
rather than estimate the true state of the system. Density forecasting and
choosing the initial ensemble are treated as one problem. Forecasting
performance can be quantified by some scoring rule. In the case of the
logarithmic scoring rule, theoretical arguments and empirical results are
presented. It turns out that, if the underlying noise dominates model error, we
can diagnose the noise spread.
