The fastest initial error growth (optimal growth) in the Zebiak and Cane (ZC) forecast model for the El Nino-Southern Oscillation (ENSO) is analyzed by singular value decomposition of a forward tangent model along a trajectory in a reduced EOF space. In this paper (Part I of II), optimal growth about the seasonally varying background and ENSO cycles from a long model run are discussed.Among the many forms of nonlinearity in ZC, the discontinuity of the slope in subsurface temperature at zero thermocline depth and the nonlinear advection of SST are the most significant. That positive perturbations grow much faster than negative perturbations around the seasonally varying background is first attributable to the discontinuity and, second, attributable to nonlinear advection.About the seasonally varying background, 6-month optimal growth is largest for early (boreal) spring starts, which is related to the enhanced atmospheric heating due to equatorward movement of the ITCZ. One dominant growing structure is found, characterized by north-south and east-west SST dipoles, convergent winds on the equator in the eastern Pacific, and a deepened thermocline in the whole equatorial belt. This structure is insensitive to start month and optimization time.Optimal growth about ENSO cycles in a long model run is generally much smaller than that about the seasonally varying background. As before, one dominant growing structure, insensitive to start time and optimization time, is found. During the warm phase of ENSO, optimal growth is modulated by season as is that about the seasonal varying background. During the onset and mature phases of ENSO, the final pattern of the optimal structure in 6 months is confined to the eastern Pacific; during the decay phase of ENSO, it spreads to the western Pacific as well. During the cold phase of ENSO, optimal growth has two maxima in a year-early spring and fall; the optimal perturbation propagates westward associated with surface layer-wind interaction.The authors also compare the singular vector analysis in EOF space and the standard one in physical space. The importance of norm definition to optimal growth and optimal structure is discussed.
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