Influence of Moist Physics and Norms on Singular Vectors for a Tropical Cyclone

Abstract

In this study, the structures and growth rates of singular vectors (SVs) for Typhoon Usagi were investigated using different moist physics and norms. The fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) and its tangent linear and adjoint models with a Lanczos algorithm were used to calculate SVs over a 36-h period. The moist physics used for linear (i.e., tangent linear and adjoint model) integrations is large-scale precipitation, and the norms used are dry and moist total energy (TE) norms. Overall, moist physics in linear integrations and a moist TE norm increase the growth rates of SVs and cause smaller horizontal structures and vertical distributions closer to the lower boundary. With a dry TE norm, the SV energy distributions show similar (dissimilar) large-(small-) scale horizontal SV structures for experiments, regardless of physics. The SVs with moist linear physics and a moist TE norm have maximum horizontal energy structures near the typhoon center. With a small weighting on the moisture term in the moist TE norm, both the remote and nearby influences on the TC are indicated by the horizontal SV energy distributions. The kinetic energy shows the largest contributions to the vertical SV TE distributions in most of the experiments, except for the largest moisture (potential energy) contributions to the SV TE at the final (initial) time in the moist TE norm (dry and weighted moist TE norms at uppermost levels). In contrast, the SV vorticity distributions show more consistent structures among experiments with different linear physics and norms, implying that, in terms of the rotational component of the wind field, the SVs are not sensitive to the choice of moist physics and norms. Given large-scale precipitation as the linear moist physics, the SV energy structures and growth rate with a moist TE norm show the largest difference when compared with those with other norms.

Interaction of Typhoon Shanshan (2006) with the Midlatitude Trough from both Adjoint-Derived Sensitivity Steering Vector and Potential Vorticity Perspectives

“…This study utilizes the MM5 adjoint modeling system (Zou et al 1997;Kim and Jung 2006;Wu et al 2007b), which includes the nonlinear MM5, its tangent linear model (TLM), and a corresponding dry-physics adjoint model. The domain for the nonlinear and adjoint models used is a 60-km resolution, 85 3 115 (latitude by longitude) horizontal grid points, with 20 even-interval sigma levels in the vertical.…”

Statistical distributions of singular vectors for tropical cyclones affecting Korea over a 10-year period

“…The same physical parameterizations were used in the TLM and adjoint model integrations, although the moist physics scheme used in the TLM and adjoint model integrations was large-scale precipitation instead of the Grell convective scheme and explicit treatment of cloud water, rain, snow, and ice, used in basic state integrations. These configurations of physics parameterizations are appropriate to show large-scale sensitivities due to the environmental effects as well as small-scale sensitivities close to the TC center, as indicated in Kim and Jung (2009b).…”

“…As a case study, Kim and Jung (2009a) evaluated the SV sensitivities near a TC center and at midlatitude and interpreted the dynamical interactions between the recurving TC and the mid-latitude system. In addition, Kim and Jung (2009b) investigated the effects of moist physics and norm on SV structures of Typhoon Usagi (0705). As a composite analysis, Peng and Reynolds (2006) studied 85 TC cases that were generated in the western North Pacific from July to October 2003 and divided them into two groups (straight-and non-straight moving TCs) to determine the SV characteristics due to TC movements.…”

“…2 Methodology and experimental framework 2.1 Singular vector calculation As described in Kim and Jung (2009b), the calculation of SVs involves selecting an initial disturbance with the constraint that it has the unit amplitude and evolves to have maximum amplitude in a specified norm after some finite optimization time. In this study, the initial and final norms used were the dry total energy (TE) defined by Zou et al (1997) as:…”

“…where i and j denote grid points in the x and y directions, k 2 1 and k 2 n are singular values for the first and the nth TESVs, respectively, and S n ij denotes the nth vertically integrated TESV energy field as in Kim and Jung (2009b) and Kim et al (2011a).…”