Initial Distribution Spread: A density forecasting approach

TL;DR

This paper proposes a density forecasting approach that optimizes initial ensemble selection for nonlinear systems, focusing on forecasting performance rather than true state estimation, with theoretical and empirical support.

Contribution

It introduces a method to choose initial ensembles based on forecast performance, integrating density forecasting with ensemble selection, especially when noise dominates model error.

Findings

Diagnoses noise spread when noise dominates model error

Theoretical support for ensemble optimization

Empirical validation of the approach

Abstract

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.