ENSO teleconnections with Australian rainfall in coupled model simulations of the last millennium

El Nino-Southern Oscillation is the major source of interannual rainfall variability in the Australian region, with the strongest influence over eastern Australia. The strength of this regional ENSO-rainfall teleconnection varies in the observational record. Climate model simulations of the "last millennium" (850-1850 C.E.) can be used to quantify the natural variability of the relationship between ENSO and Australian rainfall on decadal and longer time scales, providing a baseline for evaluating future projections. In this study, historical and last millennium (LM) simulations from six models were obtained from the Coupled Model Intercomparison Project Phase 5 and Palaeoclimate Modelling Intercomparison Project Phase 3. All models reproduce the observed negative correlation between September to February (SONDJF) eastern Australian rainfall and the NINO3.4 index, with varying skill. In the LM simulations, all models produce decadal-scale cooling over eastern Australia in response to volcanic forcing, as well as a long-term cooling trend. Rainfall variability over the same region is not strongly driven by external forcing, with each model simulating rainfall anomalies of different phase and magnitude. SONDJF eastern Australian rainfall is strongly correlated with ENSO in the LM simulations for all models, although some models simulate periods when the teleconnection weakens substantially for several decades. Changes in ENSO variance play a role in modulating the teleconnection strength, but are not the only factor. The long-term average spatial pattern of the ENSO-Australian rainfall teleconnection is similar in the LM and historical simulations, although the spatial pattern varies over time in the LM simulations.