Initial distribution spread: A density forecasting approach
Machete, R. L. and Moroz, I. M. (2012) Initial distribution spread: A density forecasting approach. Physica D: Nonlinear Phenomena, 241 (8). pp. 805-815. ISSN 0167-2789
To link to this article DOI: 10.1016/j.physd.2012.01.007
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.