Tracking down the ENSO delayed oscillator with an adjoint OGCM

According to the delayed-oscillator picture of ENSO, a positive SST anomaly in the eastern tropical Pacific will cause westerly wind anomalies closer to the date line to first give a positive feedback, and later, via planetar y wave reflection at the western boundary, a negative feedback. The aim of this study is to follow a chain of sensitivities that lead to a delayed-osc illator mechanism in a general circulation model. To this end, the adjoint of such an ocean model is used for studying sensitivities of ENSO indices. The ocean model used in this study is the Hamburg Ocean Primitive Equation (HOPE) ocean general circulation model. Its adjoint has been constructed us ing the Adjoint Model Compiler. Applied to a scalar function computed with a forward model run. an adjoint run goes back in time and calculates sensit ivities as the derivatives of this function to forcing fields or oct:an sta te variables at earlier times. Results from six adjoint runs are reported, tracing the sensitivities of th e NINO3 and NINO3.4 indices in October 1987. December 1987, and December 19 88, as simulated by a Pacfic-only version of HOPE forced by ECHAM-3 fluxes. The sensitivities to sea level can be followed back in time for more than a year. They are nonlocal: patterns propagate back in time that are identif ied as adjoint Kelvin and n = 1, 2, and 3 Rossby waves, with speeds compati ble with those obtained from model density profiles. Both thr first and the second baroclinic modes seem to play a role. In contrast, the model sensit ivities to heat flux, zonal surface currents, and SST are local and decay i n about a month. The sensitivities to the wind stress agree with the wave interpretation of the sea-level sensitivities, but only the n = 1 Rossby wave is visible. Goi ng back in time, the sensitivity to westerly anomalies along the equator ch anges sign, in agreement with the delayed-oscillator picture. Finally, a statistical atmosphere model is used to convert sensitivities to wind stress at a given time to sensitivities to SST through the atmosphere at that rime. Focusing on the sensitivities to the ENSO index region itsel f at an earlier time then closes the circle. These sensitivities have a nat ural interpretation as delayed-oscillator coefficients and show the expecte d behavior of a. positive sensitivity in the recent past changing to a nega tive sensitivity at longer lags. However, the strength of these feedbacks, and hence the relevance of this mechanism in ENSO simulated in HOPE. cannot be determined accurately.