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The WRF-ARW model (Skamarock et al., 2008) was used to simulate idealized tropical cyclones on an f-plane with the latitude set at 15°N. Three vortex-following, two-way nested domains were used with model sizes of (311 × 251), (271 × 271) and (211 × 211) and grid spacings of 18, 6 and 2 km, respectively, and 50 model levels in the vertical direction with the model top at 25 km. The tropical cyclones in the simulation were initiated by a Rankine bogus vortex with a maximum wind speed of 20 m s−1 and a maximum wind speed radius of 90 km. The bogus vortex was inserted into a quiescent environment without steering flow and wind shear over the sea surface. Thus, the TC barely propagated in the absence of a steering flow in the environment during the simulation, though its motion might still be influenced by TC structure. In other words, the storm is not static, but its movements are relatively small. The initial thermodynamic structure was initiated by Jordan’s Caribbean humidity and temperature sounding (Gray et al., 1975) with a sea surface temperature of 29°C. All the simulations were integrated for 120 h.
The model physics used were the Yonsei University (YSU) PBL scheme (Hong and Pan, 1996), the Kain–Fritsch cumulus scheme (Kain and Michael Fritsch, 1993; Kain, 2004), the Dudhia shortwave radiation scheme (Dudhia, 1989), the Rapid Radiative Transfer Model (RRTM) (Mlawer et al., 1997) longwave radiation scheme and the WSM6 microphysics scheme (Hong and Lim, 2006). The cumulus scheme was only applied to the outermost domain (18 km).
In the YSU PBL scheme, the diffusivities Kq and Km are determined as:
here, k is the von Kármán constant with a value of 0.4, ws represents the mixed-layer velocity scale, z represents the height above ground, and h is PBL depth. The values of Kh and Kq are calculated from Km using the Prandtl number (
$ \mathrm{P}\mathrm{r} $ ) and Schmidt number (Sc), respectively. In YSU PBL scheme, Sc is approximately equal to Pr. Note that Km is changed after calculating Kq and Kh to ensure that Kq and Kh are not influenced by artificial modulation of Km. Based on the uncertainties of estimating the Km and Kq in the YSU PBL scheme, two sets of sensitivity simulations were conducted by artificially varying the Km and Kq. The Km and Kq in the YSU PBL scheme were multiplied by factors of α and β, respectively. In the CTRL experiment, the default value α and β are set to 1.Table 1 lists the sensitivity simulations with artificially altered diffusivities for momentum (Km) and moisture (Kq). Given that the observational peak value of the calculated diffusion coefficient ranges from 38 to 101 m2 s−2 (Zhang et al., 2011), the original diffusion coefficients were reduced to a minimum value of 50% in these sensitivity experiments and increased to 200% of the default YSU PBL scheme with a maximum of about 110 m2 s−2. The control experiment is conducted using the default YSU PBL scheme. The default Kq value of the YSU PBL scheme in the CTRL run was decreased to 50% in experiment 2 (Kq_50%) and increased to 200% in experiment 3 (Kq_200%) to investigate the influence of Kq on the simulated evolution of the tropical cyclone. Experiments 4 (Km_50%) and 5 (Km_200%) are the same as experiments 2 (Kq_50%) and 3 (Kq_200%), but for Km.
Experiment No. Name Remarks 1 CTRL Vertical eddy diffusivity calculated by default YSU PBL schemes in WRF version 3.8.1 2 Kq_50% As CTRL, but Kq is reduced to 50% 3 Kq_200% As CTRL, but Kq is increased to 200% 4 Km_50% As CTRL, but Km is reduced to 50% 5 Km_200% As CTRL, but Km is increased to 200% Table 1. Numerical experiments
Figure 1 shows the Km (shaded) and Kq (contour) results from the five sensitivity simulations. The Kq and Km results in the sensitivity experiments differ markedly from those in the CTRL experiments. The Km and Kq values calculated directly by the PBL schemes agree with the change in Km and Kq (Fig. 1), indicating that the eddy diffusivity is effectively changed in these simulations. For example, in the Kq experiments, the Kq maximum increases from about 46 to 133 m2 s−1 as the vertical moisture diffusivity increases from Kq_50% (Fig. 1b) to Kq_200% (Fig. 1d), corresponding to a maximum of about 72 in the CTRL experiment (Fig. 1e). The maximum Km increases about 23 m2 s−1 (about 30% that of CTRL run) from the Kq_50% to the Kq_200% experiment (Figs. 1b, d), indicating the internal interaction between moisture and momentum mixing in the YSU PBL parameterization. By contrast, the maximum Km in the Km experiments increases from about 49 to 177 m2 s−1 as the vertical momentum diffusion increases from Km_50% (Fig. 1a) to Km_200% (Fig. 1c) compared with a maximum of about 78% in the CTRL experiment (Fig. 1e).
Figure 1. Azimuthally and 12–36 h averaged radius–height cross-sections of the momentum exchange coefficients (shading, m s−1) superimposed on the moisture exchange coefficients (black contours; m s−1) for the (a) Km_50%, (b) Kq_50%, (c) Km_200%, (d) Kq_200% and (e) CTRL runs.
The objective of this study was to change vertical diffusivity separately for each atmospheric variable. The momentum eddy process can still be influenced by modulating the moisture diffusivity and varying the intensity and structure of the tropical cyclone. There still are some differences between these sensitivity simulations because the changes in turbulence in the PBL and the intensity of the tropical cyclone caused by varying Km (Kq) produce feedbacks to Kq (Km).
Figure 2 shows azimuthally and 12–36 h averaged radius–height cross-sections of the gradient Richardson number. All simulations show weakly unstable or neutral conditions in the lower PBL. Compared to moisture diffusivities, momentum diffusivities (Figs. 2a, e, c) have much more influence on Ri. The greater differences in the Ri vertical distribution between the Km sensitivity experiments are attributed to larger difference in vertical wind gradients. In the case of the Kq sensitivity experiments, the wind and temperature gradients indirectly related to the moisture diffusivities have weaker influence on Ri. The differences in Ri by varying the moisture diffusivities and momentum diffusivities reveal different influence on vertical mixing in TC PBL, which may impact the TC intensity and structure through different physical mechanisms. The following section discusses the impact of the modulation of moisture (Kq_50% and Kq_200%) and momentum (Km_50% and Km_200%) diffusivities on the evolution of tropical cyclones.
Experiment No. | Name | Remarks |
1 | CTRL | Vertical eddy diffusivity calculated by default YSU PBL schemes in WRF version 3.8.1 |
2 | Kq_50% | As CTRL, but Kq is reduced to 50% |
3 | Kq_200% | As CTRL, but Kq is increased to 200% |
4 | Km_50% | As CTRL, but Km is reduced to 50% |
5 | Km_200% | As CTRL, but Km is increased to 200% |