Characteristics and Nonlinear Growth of the Singular Vector Related to a Heavy Rainfall Case over the Korean Peninsula

In this study,singular vectors related to a heavy rainfall case over the Korean Peninsula were calculated using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) adjoint modeling system.Tangent linear and adjoint models include moist physical processes,and a moist basic state and a moist total energy norm were used for the singular-vector calculations.The characteristics and nonlinear growth of the first singular vector were analyzed,focusing on the relationship between the basic state and the singular vector.The horizontal distribution of the initial singular vector was closely related to the baroclinicity index and the moisture availability of the basic state.The temperature-component energy at a lower level was dominant at the initial time,and the kinetic energy at upper levels became dominant at the final time in the energy profile of the singular vector.The nonlinear growth of the singular vector appropriately reflects the temporal variations in the basic state.The moisture-component energy at lower levels was dominant at earlier times,indicating continuous moisture transport in the basic state.There were a large amount of precipitation and corresponding latent heat release after that period because the continuous moisture transport created favorable conditions for both convective and nonconvective precipitation.The vertical propagation of the singular-vector energy was caused by precipitation and the corresponding latent heating in the basic state.