Role of eyewall and rainband eddy forcing in tropical cyclone intensification

Abstract. While turbulence is commonly regarded as a flow feature
pertaining to the planetary boundary layer (PBL), intense turbulent mixing
generated by cloud processes also exists above the PBL in the eyewall and
rainbands of a tropical cyclone (TC). The in-cloud turbulence above the PBL
is intimately involved in the development of convective elements in the
eyewall and rainbands and consists of a part of asymmetric eddy forcing for
the evolution of the primary and secondary circulations of a TC. In this
study, we show that the Hurricane Weather Research and Forecasting (HWRF)
model, one of the operational models used for TC prediction, is unable to
generate appropriate sub-grid-scale (SGS) eddy forcing above the PBL due to
a lack of consideration of intense turbulent mixing generated by the eyewall
and rainband clouds. Incorporating an in-cloud turbulent-mixing
parameterization in the vertical turbulent-mixing scheme notably improves
the HWRF model's skills in predicting rapid changes in intensity for several past
major hurricanes. While the analyses show that the SGS eddy forcing above
the PBL is only about one-fifth of the model-resolved eddy forcing, the
simulated TC vortex inner-core structure, secondary overturning circulation,
and the model-resolved eddy forcing exhibit a substantial dependence on the
parameterized SGS eddy processes. The results highlight the importance of
eyewall and rainband SGS eddy forcing to numerical prediction of TC
intensification, including rapid intensification at the current resolution
of operational models.


Outlines 1. A brief discussion of TC intensification by eyewall/rainband eddy forcing 2. A short review on our previous attempt to include eyewall/rainband in-cloud turbulent mixing in the HWRF PBL scheme. 3. Our recent progress on improving in-cloud turbulent mixing parameterization in HWRF. 4. Diagnosing the role of eddy forcing in TC intensification from HWRF output.

Summary
Azimuthal-mean tangential wind budget equation in a cylindrical coordinate : model-resolved eddy forcing _ : parameterized sub-grid scale (SGS) eddy forcing where � = ̅ � + 1 2 2 is the azimuthal-mean absolute angular momentum While higher model grid resolution allows the eddy forcing to be better resolved during the simulation, the uncertainty arises from the parametrical determination of SGS eddy processes.
The importance of boundary layer turbulent transport to TC evolution has long been recognized and is a focus of current research. But the importance of SGS eddy forcing above the boundary layer has been largely overlooked.
• It is overshadowed by the critical role of radial inflow and surface latent heating in maintaining and intensifying a TC.
• Lack of observations largely limits our understanding of the aloft in-cloud turbulent mixing processes.
• For deep convection, the focus is on the cumulus parameterization.
• Historically, all turbulent mixing schemes used today were originally developed to represent turbulent processes in the PBL.
HWRF PBL scheme is a typical K-closure scheme In reality, there is no physical interface that separates the turbulence in the eyewall generated by the surface and cloud processes. From the nature of turbulent mixing, it is more logical to parameterize the turbulence in the eyewall and rainbands based on the integrated "Turbulent Layer (TL)".
12:00 UTC, 28 August, 2015 Eddy exchange coefficients from the same HWRF simulation of Jimena (2015) but with the inclusion of in-cloud turbulent mixing parameterization (12:00 UTC, 28 August, 2015) Comparison of HWRF simulated storm intensity and track of Jimena (2015) with the best track data In the default HWRF PBL scheme, the turbulent eddy exchange coefficient above the diagnosed boundary layer height is calculated by, , ( ) is a stability function of gradient Richardson number.
This method is also adapted by the YSU PBL scheme to treat turbulent mixing above the boundary layer. But they included the cloud effects on Brunt-Vaisala frequency by reducing stability using the following formula, For YSU made a couple of inappropriate assumptions: (1), they dropped .
Because of significantly over-reduced Brunt-Vaisala frequency in clouds, it generates unrealistically large , . What YSU did is to artificially reduce , by averaging incloud , and entrainment , , In HWRF, we recalculated Brunt-Vaisala frequency using, HWRF-1: parameterization of in-cloud turbulent mixing based on the TL concept HWRF-2: parameterization of in-cloud turbulent mixing by recalculating N 2 in clouds 20:00 UTC August 28, 2015 Comparison of TC innercore structure of Jimena (2015) between satellite observations and two HWRF simulations right before Jimena's RI.

Summary
• A successful prediction of TC intensity depends on the skills of a model to generate eddy forcing that drives the primary and secondary circulations of a TC, provided that the model simulates correct large-scale fields and SST. • While it is negative definite in the PBL, the sign of eddy forcing associated with eyewall/rainband convection above the PBL is indefinite. It can be positive depending on the detailed eddy processes, and thus, provides a mechanism to spin up a TC vortex. • In numerical models, the continuous eyewall/rainband eddy forcing is artificially split into two parts: the model-resolved and SGS components, but they are not independent. While higher model resolution allows the eddy forcing to be better resolved, the SGS eddy forcing is a source of uncertainty. At the resolution of operational HWRF, the resolved eddy forcing and the associated storm inner-core structure show a substantial dependence on the SGS eddy forcing. • With the correct determination of Brunt-Vaisala frequency in the clouds, the HWRF PBL scheme is shown to have the ability to appropriately generate in-cloud turbulent mixing in the eyewall and rainbands. • We developed a SEE-like diagnostic equation that allows us to quantify the contributions of different components of forcing including tangential and radial eddy forcing to TC intensification.