This thesis covers several projects in predictability, prediction, and data assimilation of the Earth system:

1. The first is an analysis of the predictability of the atmosphere–ocean system. Due to the physical coupling between atmosphere and ocean, information about the ocean helps to better predict the future of the atmosphere, and in turn, information about the atmosphere helps to better predict the ocean. Here, we investigate the spatial and temporal nature of this predictability: where, for how long, and at what frequencies does the ocean significantly improve prediction of the atmosphere, and vice-versa?

We apply Granger causality, a statistical test to measure whether a variable improves prediction of another, to local time-series of sea-surface temperature (SST) and low-level atmospheric variables. We calculate the detailed spatial structure of the atmosphere-to-ocean and ocean-to-atmosphere predictability. We find that the atmosphere improves prediction of the ocean most in the extratropics, especially in regions of large SST gradients. This atmosphere-to-ocean predictability is weaker but longer-lived in the tropics, where it can last for several months in some regions. On the other hand, the ocean improves prediction of the atmosphere most significantly in the tropics, where this predictability lasts for months to over a year. However, we find a robust signature of the ocean on the atmosphere almost everywhere in the extratropics, an influence that has been difficult to demonstrate with model studies. We find that both the atmosphere-to-ocean and ocean-to-atmosphere predictability are maximal at low frequencies, and both are larger in the summer hemisphere.

The patterns we observe generally agree with dynamical understanding and the results of the Kalnay dynamical rule, which diagnoses the direction of forcing between the atmosphere and ocean by considering the local phase relationship between simultaneous sea-surface temperature and vorticity anomaly signals. We discuss applications to coupled data assimilation.

2. The second presents the analysis of the Lyapunov spectrum of a coupled quasi-geostrophic atmosphere–ocean model, the Modular Arbitrary-Order Ocean-Atmosphere Model.

We show that the Lyapunov spectrum of the forced ocean has a stepwise structure, unlike the smooth spectrum of the coupled ocean. The spectrum of the forced atmosphere, however, is nearly identical to that of the coupled atmosphere.

By computing the conditional Lyapunov exponent (CLE) spectrum, we find that the uncoupled atmosphere and ocean, when forced with output from the coupled system, do not synchronize with the coupled system. However, assimilating observations from the coupled atmosphere to the forced atmosphere makes the CLE spectrum negative, a necessary condition for synchronization with the coupled model. However, assimilating observations from the coupled ocean to the forced ocean does not make the CLE spectrum negative.

3. The third presents a novel forecasting method for leveraging the predictability of oscillatory modes. Oscillatory modes of the climate system are one of its most predictable features, especially at intraseasonal time scales. These oscillations can be predicted well with data-driven methods, often with better skill than dynamical models. However, since the oscillations only represent a portion of the total variance, a method for beneficially combining oscillation forecasts with dynamical forecasts of the full system was not previously known.

We introduce Ensemble Oscillation Correction (EnOC), a general method to correct oscillatory modes in ensemble forecasts from dynamical models. We compute the ensemble mean with only the best ensemble members, as determined by their discrepancy from a data-driven forecast of the oscillatory modes. We also present an alternate method which uses ensemble data assimilation to combine the oscillation forecasts with an ensemble of dynamical forecasts of the system (EnOC-DA). The oscillatory modes are extracted with a time-series analysis method called singular spectrum analysis (SSA), and forecast using an analog method.

We test the method using chaotic toy models with significant oscillatory components, and show that it robustly reduces error compared to the uncorrected ensemble.

4. The fourth applies EnOC to the South Asian monsoon. Prediction of the monsoon on intraseasonal timescales is critical for agriculture and flood planning. The summer monsoon season displays northward-propagating modes of convection known as the monsoon intraseasonal oscillations (MISOs). These modes, which have periods of about 45–50 days and 20–30 days, characterize the active and break phases of the monsoon, as well as much of the regional rainfall patterns. It has been recognized that MISO is a source of predictability for monsoon rainfall beyond the synoptic weather timescale, and several studies have shown it can be predicted well by data-driven methods.

We apply EnOC to the ECMWF ensemble seasonal hindcasts from 1998 to 2016, initialized in May, June, July, August, and September. We use analog-based forecasts of the leading MISO mode, as represented by a trajectory in a two-dimensional principal component (PC) space. Ensemble members are projected into the PC space using a lasso regression technique.

We see increases in forecast skill over the regular ensemble mean, as measured by the anomaly correlation and mean-square error, at lead times between 14 and 40 days, especially for forecasts starting in May and June. The largest error reductions are seen in the West and South regions of India, which contain the Western Ghats.