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.
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
In Brost and Wyngaard, the eddy diffusivity for momentum
In Troen and Mahrt,
Based on Troen and Mahrt, in Hong and Pan, a boundary layer diffusion package was implemented into the NCEP medium-range forecast model [
In Hong et al., a revised vertical diffusion package is developed on the basis of Noh et al. [
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 [
Gopalakrishnan et al. started to use flight-level observations to modify the eddy diffusivity in the first-order planetary boundary layer schemes [
In Gopalakrishnan et al., they studied the impacts of modifying
The eddy diffusivity
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 [
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
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.
The eddy diffusivity for momentum (
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:
Simulation periods and durations for super typhoon cases in 2014.
Name | Start time (UTC) | End time (UTC) | Duration (h) |
---|---|---|---|
Neoguri | 06:00, 4 Jul, 2014 | 06:00, 8 Jul, 2014 | 96 |
Rammasun | 00:00, 14 Jul, 2014 | 00:00, 18 Jul, 2014 | 96 |
Genevieve | 12:00, 9 Aug, 2014 | 12:00, 11 Aug, 2014 | 48 |
Phanfone | 00:00, 1 Oct, 2014 | 00:00, 5 Oct, 2014 | 96 |
Vongfong | 12:00, 5 Oct, 2014 | 12:00, 9 Oct, 2014 | 96 |
Nuri | 00:00, 1 Nov, 2014 | 00:00, 5 Nov, 2014 | 96 |
Hagupit | 06:00, 2 Dec, 2014 | 06:00, 6 Dec, 2014 | 96 |
Numerical simulations are conducted by WRF-ARW v3.5.1. The parent domain (D01) has a horizontal resolution of 27 km, with 199 × 172 grids; the middle nest domain (D02) has a resolution of 9 km, with 301
WRF domains: (a) all the domains; (b) D03.
There are 39 vertical layers in all the three domains. The map projection method used for the simulations is the Lambert projection. The time steps are 120 s, 40 s, and 40/3 s for D01, D02, and D03, respectively. The current settings for the time steps can satisfy the stability constraints and control the computational cost at the same time. The pressure at the top of the computational domains is set as 50 hPa. Two-way nesting has been used for all the simulations. Time varying (6-hourly) sea surface temperature has been used.
The YSU planetary boundary layer scheme is used. The long wave and short wave radiation schemes are the RRTMG schemes. The Grell-Freitas cumulus scheme is applied in D01 and D02. The microphysics scheme is the WRF Single-moment 6-class (WSM6) scheme. The surface layer scheme is the MM5 similarity scheme. The land surface model is the Unified Noah Land Surface Model. The initial conditions and the boundary conditions are generated by the FNL (NCEP Final Analyses) data.
The simulation results are compared with the observational data from the HKO. The variables to be compared are track, CSLP, and MWSP. The observational data is 6-hourly. Therefore, the simulated data are compared with observations at
To evaluate the three versions of YSU, we compare the simulated track, CSLP, and MWSP with their corresponding observational data. The computation of AE and MAE follows the definitions in Section
In Figures
Case 1-Neoguri: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track ( | AE of CSLP ( | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 94.8 (131.9) | 5.6 (19.1) | 5.7 (19.4) |
48 | 148.2 (210.7) | 22.3 (7.5) | 0.1 (19.7) |
72 | 181.2 (263.8) | 12.9 (6.0) | 3.9 (19.3) |
96 | 242.7 (310.5) | 6.5 (2.8) | 9.4 (15.9) |
6-hourly MAE | 140.5 (186.6) | 8.4 (9.2) | 4.5 (17.3) |
Case 1-Neoguri: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
In Figures
Case 2-Rammasun: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track (km) | AE of CSLP (hPa) | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 32.2 (51.8) | 16.3 (19.6) | 8.0 (15.5) |
48 | 57.8 (134.5) | 27.6 (18.5) | 15.4 (18.7) |
72 | 123.6 (320.4) | 11.7 (15.2) | 6.0 (13.1) |
96 | 130.7 (388.4) | 26.1 (45.0) | 16.9 (31.1) |
6-hourly MAE | 74.9 (176.2) | 18.5 (22.2) | 9.2 (17.0) |
Case 2-Rammasun: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
In Figures
Case 3-Genevieve: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track (km) | AE of CSLP (hPa) | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 39.8 (80.5) | 14.4 (10.7) | 8.5 (12.4) |
48 | 136.9 (74.1) | 2.1 (2.7) | 0.7 (2.4) |
6-hourly MAE | 71.8 (67.6) | 14.9 (12.4) | 5.6 (8.8) |
Case 3-Genevieve: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
In Figure
Case 4-Phanfone: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track (km) | AE of CSLP (hPa) | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 84.5 (69.2) | 16.7 (25.2) | 14.1 (23.7) |
48 | 112.8 (90.0) | 16.0 (9.6) | 4.2 (20.4) |
72 | 235.1 (109.9) | 13.1 (11.1) | 3.5 (19.0) |
96 | 572.5 (288.3) | 13.0 (14.7) | 2.5 (12.7) |
6-hourly MAE | 174.0 (106.8) | 12.2 (10.3) | 4.9 (16.9) |
Case 4-Phanfone: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
In Table
Case 5-Vongfong: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track (km) | AE of CSLP (hPa) | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 143.9 (143.9) | 1.9 (4.2) | 6.0 (12.9) |
48 | 149.2 (213.6) | 5.4 (11.3) | 15.0 (24.5) |
72 | 183.1 (273.3) | 20.7 (19.5) | 22.8 (31.2) |
96 | 288.0 (482.1) | 9.9 (14.3) | 16.9 (27.1) |
6-hourly MAE | 151.9 (222.2) | 11.1 (13.4) | 13.3 (21.3) |
Case 5-Vongfong: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
For the super typhoon Nuri (2014), the CSLP time series simulated by the K200 and the original YSU are very close (Figure
Case 6-Nuri: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track ( | AE of CSLP (hPa) | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 90.4 (111.2) | 4.2 (14.0) | 8.1 (18.6) |
48 | 78.2 (103.5) | 31.2 (45.4) | 29.1 (39.1) |
72 | 107.5 (115.3) | 14.9 (20.9) | 14.1 (25.5) |
96 | 99.2 (148.5) | 15.1 (33.6) | 4.7 (15.9) |
6-hourly MAE | 84.1 (98.8) | 14.1 (24.2) | 13.2 (22.5) |
Case 6-Nuri: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
During the first 2 days of the simulations, the CSLP time series are close to each other (Figure
Case 7-Hagupit: AE and MAE of track, CSLP, and MWSP.
Time (h) | AE of track (km) | AE of CSLP (hPa) | AE of MWSP (m s−1) |
---|---|---|---|
K ((1/4)K) | K ((1/4)K) | K ((1/4)K) | |
24 | 164.1 (129.0) | 23.5 (23.1) | 10.7 (17.8) |
48 | 175.7 (114.8) | 50.1 (57.5) | 26.6 (37.2) |
72 | 88.4 (159.8) | 35.9 (55.5) | 20.0 (33.6) |
96 | 139.1 (429.8) | 33.2 (49.2) | 13.7 (29.5) |
6-hourly MAE | 118.8 (151.9) | 32.5 (38.5) | 16.2 (25.5) |
Case 7-Hagupit: (a) track simulated by the original YSU; (b) track simulated by the K025; (c) track simulated by the K200; (d) comparisons of center sea-level pressure; and (e) comparisons of maximum surface wind speed.
In general, for all the 7 super typhoons, the simulations by the K200 always provide the best MWSP prediction, in the sense of lowest MAE. For track and CSLP, we use the averaged AEs and MAEs to evaluate the overall performance of these 3 versions. It is observed that the intensity simulated with larger eddy diffusivity is likely to be stronger.
The averaged AEs at
Averaged AEs and MAEs of track, CSLP, and MWSP simulated by the original YSU, the K025, and the K200.
Averaged | Original YSU | K025 | K200 | Improvement | Improvement |
---|---|---|---|---|---|
24 h-track | 92.8 | 102.5 | | −10.4% | 6.1% |
48 h-track | 122.7 | 134.4 | | −9.6% | 6.0% |
72 h-track | 153.1 | 207.1 | | −35.2% | 3.6% |
96 h-track | 245.4 | 341.3 | | −39.1% | 8.5% |
MAE of track | 119.8 | 149.8 | | −25.1% | 6.0% |
| |||||
24 h-CSLP | 11.8 | 16.6 | | −40.3% | 23.1% |
48 h-CSLP | 22.1 | | 23.2 | 1.3% | −5.0% |
72 h-CSLP | 18.2 | 21.4 | | −17.3% | 2.7% |
96 h-CSLP | 17.3 | 26.6 | | −54.0% | 20.8% |
MAE of CSLP | 16.0 | 19.1 | | −19.0% | 3.7% |
| |||||
24 h-MWSP | 8.7 | 17.2 | | −96.9% | 50.1% |
48 h-MWSP | 13.0 | 23.1 | | −78.1% | 16.1% |
72 h-MWSP | 11.7 | 23.6 | | −101.5% | 29.2% |
96 h-MWSP | 10.7 | 22.0 | | −105.9% | 32.0% |
MAE of MWSP | 9.8 | 19.2 | | −95.0% | 23.1% |
Comparing with the original version, the K200 improves the averaged MAEs of track, CSLP, and MWSP by 6.0%, 3.7%, and 23.1%, respectively. However, the K025 deteriorates the averaged MAEs of track, CSLP, and MWSP by 25.1%, 19.0%, and 95.0%, respectively.
To test the sensitivity of the enlarged eddy diffusion coefficients, the
Track, CSLP, and MWSP of super typhoon Phanfone (2014) simulated by the original YSU, the K025, the K200, and the K300.
In this article, WRF simulations for super typhoons are used to evaluate 3 versions of the YSU scheme. For all the averaged MAEs, the K200 can always provide the best performance. For all the super typhoon cases, the simulations with the K200 can always provide the best MWSP prediction.
Comparing with the original version, the K200 improves the averaged MAEs of track, CSLP, and MWSP by 6.0%, 3.7%, and 23.1%, respectively, whereas 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, because that larger eddy diffusion coefficients for heat and moisture can induce larger sensible and latent heat fluxes.
However, we shall also notice that this study is limited to the YSU PBL scheme and the WRF-ARW model. The modifications to the eddy diffusion coefficients also cannot be applied to the higher-order closure models, for example, Wyngaard and Coté [
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors appreciate the assistance of the HKO, which provided the meteorological data. This work was supported by NSFC/RGC Grant N_HKUST631/05, NSFC-FD Grant U1033001, and the RGC Grant 16300715.