Advances in Meteorology

Volume 2016, Article ID 2397873, 14 pages

http://dx.doi.org/10.1155/2016/2397873

## Evaluations on Profiles of the Eddy Diffusion Coefficients through Simulations of Super Typhoons in the Northwestern Pacific

^{1}Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong^{2}Division of Environment, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received 29 August 2016; Revised 29 October 2016; Accepted 14 November 2016

Academic Editor: Rossella Ferretti

Copyright © 2016 Jimmy Chi Hung Fung and Guangze Gao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The modeling of the eddy diffusion coefficients (also known as eddy diffusivity) in the first-order turbulence closure schemes is important for the typhoon simulations, since the coefficients control the magnitude of the sensible heat flux and the latent heat flux, which are energy sources for the typhoon intensification. Profiles of the eddy diffusion coefficients in the YSU planetary boundary layer (PBL) scheme are evaluated in the advanced research WRF (ARW) system. Three versions of the YSU scheme (original, K025, and K200) are included in this study. The simulation results are compared with the observational data from track, center sea-level pressure (CSLP), and maximum surface wind speed (MWSP). Comparing with the original version, the K200 improves the averaged mean absolute errors (MAE) of track, CSLP, and MWSP by 6.0%, 3.7%, and 23.1%, respectively, while the K025 deteriorates the averaged MAEs of track, CSLP, and MWSP by 25.1%, 19.0%, and 95.0%, respectively. Our results suggest that the enlarged eddy diffusion coefficients may be more suitable for super typhoon simulations.

#### 1. Introduction

The PBL is important for the typhoon intensification since the turbulent mixing in the PBL affects the momentum and heat in the typhoons. However, it is still not possible to fully resolve the diffusion processes within the boundary layer due to the limitations of physical models and grid resolution. Therefore, the boundary layer parameterizations are required to model the sub-grid-scale effects. Among various boundary layer schemes, the first-order turbulence closure schemes are widely used in the tropical cyclone studies and the weather research and forecasting (WRF) model. Comparing with higher-order turbulence closure schemes, the first-order schemes are computationally cheaper. The simplest first-order schemes are based on the local-K approach. However, the eddy transportation in the planetary boundary layer is mainly conducted by large eddies, which should be represented by bulk properties of the PBL, rather than local properties. Therefore, the nonlocal first-order schemes were developed to resolve this problem and keep the simplicity at the same time.

The eddy diffusivity’ modeling is fundamental to the first-order turbulence closure PBL schemes. We briefly go through the history of the eddy diffusivity’ developments. In the study of O’brien, the eddy diffusivity for momentum is parameterized aswhere is the von Kármán’s constant, is the friction velocity, and is the stability function [1].

In Brost and Wyngaard, the eddy diffusivity for momentum is represented bywhere is the boundary layer height and is the Monin-Obukhov length [2].

In Troen and Mahrt, is parameterized aswhere and is the wind profile function at the top of the surface layer [3]. They further assumed thatwhere is the convective velocity scale and is the fraction of the surface layer height and the boundary layer height. The Prandtl number in Troen and Mahrt is modeled aswhere is the eddy diffusivity for temperature and moisture and is the eddy diffusivity for momentum [3]. and are the profile functions for , and , , respectively.

Based on Troen and Mahrt, in Hong and Pan, a boundary layer diffusion package was implemented into the NCEP medium-range forecast model [3, 4]. The turbulence diffusion equations for a prognostic variable can be expressed bywhere is the eddy diffusivity for and is the counter-gradient term for , which was introduced by Deardorff [5]. can be , (horizontal wind components), (potential temperature), and (water vapor mixing ratio). Same as Troen and Mahrt, the eddy diffusivity for momentum is formulated aswhere is the profile shape exponent taken as 2 and is the mixed-layer velocity scale [3]. The counter-gradient terms for and are given bywhere is the corresponding surface flux for and . The boundary layer height is given bywhere is the critical bulk Richardson number, is the horizontal wind speed at , is the virtual potential temperature at the lowest model level, is the virtual potential temperature at , and is the temperature near surface. In Hong and Pan, the Prandtl number is a constant within the whole mixed boundary layer [4]. It is given byThe nonlocal scheme can improve the capability on representing the large eddy turbulence within a well-mixed boundary layer, and it is still computationally cheap as other first-order turbulence closure schemes.

In Hong et al., a revised vertical diffusion package is developed on the basis of Noh et al. [6, 7]. The turbulence diffusion equations for the prognostic variables can be expressed bywhere is the flux at the inversion layer. The Prandtl number is parameterized aswhere is the Prandtl number at the top of the surface layer. The profile functions and are given for different conditions. For unstable and neutral conditions,For the stable condition,

Comparing with the model proposed by Troen and Mahrt, the new model has the following main features: (1) incorporation of an explicit entrainment term into the heat fluxes; (2) the heat fluxes above the boundary layer height are also parameterized; (3) a profile of the Prandtl number is used, in contrast to the constant value; and (4) nonlocal mixing of momentum is also included [3].

Gopalakrishnan et al. started to use flight-level observations to modify the eddy diffusivity in the first-order planetary boundary layer schemes [8]. In Zhang and Drennan, they investigated the vertical eddy diffusivity in the surface wind regime between 18 and 30 m s^{−1} over the ocean [9]. They showed that the magnitudes of the eddy diffusion coefficients for momentum and latent heat fluxes are comparable, whereas the magnitude of the eddy diffusion coefficient for sensible heat flux is much smaller. The authors noted that the data were limited to wind speeds less than 30 m s^{−1}. However, it is quite common to have wind speed higher than 30 m s^{−1} in the super typhoons.

In Gopalakrishnan et al., they studied the impacts of modifying and to be 25% or 50% of the coefficients’ original values [8]. To the best of their knowledge, this is the first time that flight-level observations are used as the basis to provide an improvement to the existing boundary layer parameterization schemes. They found that reductions of and to 25% of their original values (for later references, this version is named as GFS-K025 in this article) produced eddy diffusion coefficients which were consistent with observations. It was also found that the GFS-K025 induced stronger hurricane intensity in the idealized frameworks, compared with the original GFS scheme and the GFS-K050. Since it is likely to underestimate the typhoon intensity in numerical models, it is possible that the GFS-K025 can provide better real-time predictions. In Gopalakrishnan et al., the boundary layer scheme used is the Global Forecast System (GFS) scheme [8]. The GFS scheme is a prior version of the YSU scheme, which is based on Hong and Pan [4]. The major difference between these two schemes is that the fluxes in the GFS scheme do not contain an entrainment component.

The eddy diffusivity in the YSU scheme and the in the GFS scheme have the same formulation:However, the mixed-layer velocity scales () are modeled differently:

In Gopalakrishnan et al., they pointed out that a reduction of diffusion would lead to a reduction in the dissipation of the angular momentum in the boundary layer, which would further lead to stronger spin-up and enhanced moisture convergence [8]. The enhanced latent heat flux provides better thermo conditions for tropical cyclones to develop and intensify. However, we also noticed that while the reduction of could reduce the sink of momentum and angular momentum, the reduction of would also reduce the sources of heat and moisture and weaken the tropical cyclones. It might still be difficult to determine whether the eddy diffusivity coefficients should be enlarged or decreased in the PBL schemes. To make an attempt at addressing this issue, we conduct simulations for the super typhoons in 2014 to evaluate 3 versions of the YSU scheme (original YSU, K025, and K200) in this article.

The YSU scheme is used because it is a state-of-the-art first-order turbulence closure scheme. In the K025 and the K200, the eddy diffusion coefficients are modified to be 25% and 200% of their original values, respectively. The rest of this article is organized as follows: in Section 2, methods and numerical simulations are introduced; in Section 3, simulation results are analyzed; and in Section 4, conclusions are provided.

#### 2. Methods and Numerical Simulations

In this section, we introduce the designs of the K025 and the K200, the simulated super typhoon cases, the WRF configurations, and the evaluation metrics.

##### 2.1. K-Profiles: Original, K025, and K200

The eddy diffusivity for momentum () is parameterized in (15). The eddy diffusivity for heat and moisture () is calculated by and the Prandtl number (). We introduce a new parameter to control the magnitudes of and :For the original YSU scheme, ; for the K025, ; and for the K200, . In the K025 and the K200, the eddy diffusion coefficients are modified to be 25% and 200% of their original values, respectively.

##### 2.2. Super Typhoon Cases

From 2009, the Hong Kong Observatory (HKO) divides the tropical cyclones into 6 intensity levels: (1) tropical depression: 22–33 knots; (2) tropical storm: 34–47 knots; (3) severe tropical storm: 48–63 knots; (4) typhoon: 64–81 knots; (5) severe typhoon: 82–99 knots; and (6) super typhoon: 100 knots. In this paper, the super typhoon cases in the northwestern Pacific in 2014 are simulated, which are Neoguri, Rammasun, Genevieve, Phanfone, Vongfong, Nuri, and Hagupit. The simulation periods and durations are shown in Table 1.