## 1 Introduction

[2] The observational record of tropical sea surface temperature (SST) is suggestive of a significant change in the character of El Niño–Southern Oscillation (ENSO) since the late 1970s. The following decades saw a decrease in the frequency of ENSO events and an increase in their intensity, plus a change in the predominant direction of ENSO SST anomaly phase propagation along the equator [e.g., *An and Wang*, 2001; *Wang and An*, 2002]. During the 1960s and 1970s warm anomalies appeared first in the eastern Pacific and expanded westward, but since then they have developed in the central Pacific either prior to or concurrently with the eastern Pacific [*Fedorov and Philander*, 2000; *Wang and An*, 2002; *Trenberth et al.*, 2002].

[3] It has been demonstrated that such changes may be consistent with a change in the mean state of the coupled tropical ocean‒atmosphere and hence in the stability of the system's coupled modes [*An and Jin*, 2000; *Fedorov and Philander*, 2001]. In particular, the deepening of the eastern Pacific thermocline, resulting from the mean weakening of the trades, favors the longer period delayed oscillator mode and decreases the growth rate of the shorter period SST mode. However, while the observations appear to be consistent with a significant change in the underlying dynamics of coupled modes in the tropics, the possibility still exists that at least some of the observed alteration in ENSO character may result from either trends in the forcing [*An and Wang*, 2000; *Wang and An*, 2001] or noise-induced variability [*Kirtman and Schopf*, 1998; *Thompson and Battisti*, 2001; *McPhaden et al.*, 2011; *Newman et al.*, 2011]. There is also evidence to suggest that there has been no statistically significant changes in ENSO frequency and intensity [*Mendelssohn et al.*, 2005; *Douglass*, 2010].

[4] While a range of studies have investigated the natural modes of the coupled tropics via reduced‒physics analytical or numerical models, in which the governing physics were assumed a priori and the choice of parameter values was to some extent arbitrary, it has also been shown that ENSO dynamics can be inferred to a surprisingly good degree using inverse methods. In particular, skillful models have been constructed under the sole a priori assumption that ENSO is governed by a stochastically forced dissipative linear system that obeys a fluctuation‒dissipation relationship [*Penland and Magorian*, 1993; *Penland and Matrosova*, 1994; *Penland and Sardeshmukh*, 1995; *Newman et al.*, 2009; *Newman et al.*, 2011]. Thus, the empirical estimation of ENSO dynamics via Linear Inverse Models (LIMs) offers an alternative with which to investigate causes of the shift in ENSO character.

[5] In order to minimize the uncertainty in the inferred dynamical system, previous LIM‒based studies of ENSO have commonly used the entire data record since the 1950s for building the model, with the implicit assumption that the underlying dynamics of ENSO have not changed over this period. Here, we investigate whether the LIM based on the entire period can plausibly explain the climate shift, or alternatively whether the observed differences in ENSO imply a fundamental change in ENSO dynamics. It is found that, while the observed change in ENSO frequency and amplitude does not necessarily require altered linear dynamics, the change in the direction of propagation of SST in the equatorial Pacific does.