### Abstract

We explore the use of atmospheric Linear Inverse Models (LIMs) in the established context of Madden-Julian Oscillation (MJO) forecast verification to show that simple stochastic-dynamic representations of the climate system can provide competitive MJO hindcast skill. The LIM framework harnesses the covariability of climate signals to model the entire variance field, as opposed to statistical forecasts of only the real-time multi-variate MJO Index or other truncated or filtered MJO-only metrics. The modeled data channels may be time series of variables in physical space, or principal component (PC) time series of eigenmodes of the data in the desired forecast space. The LIM framework decomposes system dynamics into a deterministic component, which represents modal interactions (if data is modal) or propagation (if data is spatial), and a stochastic component that parameterizes turbulent or chaotic energy as correlated noise.

Results show that LIM skill is on the low end of current full-physics numerical models but within the model spread for both bivariate correlation and RMSE. The LIM performs particularly well during mature stages of the MJO. At these times, LIM skill is on par with numerical model skill.This study highlights that extremely simple empirical models perform competitively in MJO hindcasts. It also provides a skill baseline for future implementations of reduced tropical stochastic climate models.

There are many possible extensions to the LIMs presented. They include seasonal cyclostationary time-dependence, ocean-atmosphere coupling, non-Gaussian independent modes, correlative additive and multiplicative noise, and non-linear modal interactions. Current research efforts which relate to these extensions will be discussed.