65SOLA, 2010, Vol. 6, 065−068, doi:10.2151/sola.2010-017

AbstractA new parameterization scheme of air-sea momentum flux,

heat flux and moisture flux is introduced into the Japan Meteoro-logical Agency Non-Hydrostatic Model (JMA-NHM, Saito et al. 2006). The new formulation describes the saturation properties of bulk transfer coefficients of momentum, heat and moisture under high winds regime (> 30 m s−1). It also considers the effect of sea-wave drag in the roughness length. The proposed parameterization is applied to simulate an intense tropical cyclone Hagupit (0814). The impact of the new scheme on the tropical cyclone prediction is found in the increase of maximum surface wind speed and de-crease of central pressure. Improvements in the forecasts of distri-bution of high wind areas and precipitation are obtained. This may help to improve the model predicted wind-pressure relationship for intense tropical cyclones.

1. IntroductionPrediction of tropical cyclones motion using numerical

weather prediction (NWP) models has improved in recent decades due to the advance made in model design, data assimilation and ensemble prediction system. Meanwhile, efforts to improve the prediction of intensity and wind structures continue. Key physical processes related to the development of tropical cyclones like the air-sea interaction are inevitably important to simulate more real-istic structure and evolution of tropical cyclones in NWP model for both weather and climate predictions. In the current version of the Japan Meteorological Agency Non-Hydrostatic Model (JMA-NHM, Saito et al. 2006), or NHM in short, the bulk transfer coefficient for momentum is assumed to increase with wind speed when exceeding 15 m s−1. Recent studies by Powell et al. (2003) and Donelan et al. (2004), based on the findings from observation measurements and laboratory studies, have suggested that the drag coefficient of momentum or surface momentum flux levels off as wind speeds increase above hurricane force. Results from field experiments to determine bulk transfer coefficients under different sea conditions (Belamari 2005) also suggest larger values of coef-ficients with similar saturation properties in high wind regime. The existing formulation of bulk transfer coefficients based on extrapolation of results from past field studies under low and moderate wind speed conditions as adopted in NHM, is therefore likely to be inadequate when applied to simulate intense tropical cyclones and extreme wind conditions.

The change in surface drag and roughness due to different conditions of ocean waves is also important to study the develop-ment of tropical cyclones. For instance, in Kohno et al. (2006) using NHM coupled with a wave model, an increase in drag coef-ficient was obtained when wave parameters like wave induced stress, wave age and steepness were considered, leading to consid-erable differences in wave height and wind speed forecasts over sea surface.

In this study, a new formulation of bulk coefficients and roughness lengths is incorporated in NHM in the light of results from laboratory study (Donelan et al. 2004) and observation measurement experiments (Powell et al. 2003; Fairall et al. 2003; Belamari 2005).

In the next section, the design of the new scheme of bulk transfer coefficients and roughness lengths will be presented. Description of numerical experiments to study the impact of new scheme to simulate Typhoon Hagupit (0814), the most intense tropical cyclone affecting the South China Sea in 2008, will be given in Section 3. In Section 4, results and discussions will be made to compare intensity, wind structure and precipitation using the original scheme and the new scheme, followed by a summary in Section 5.

2. New formulation of bulk transfer coefficients and roughness lengths

In the bulk formulation of aerodynamics, the momentum flux, heat flux and moisture flux are calculated by the following equations to determine the covariance of perturbation of vertical velocity (w′) with horizontal wind (u′), potential temperature (θ′) and specific humidity (q′),

′ ′ =− =

′ ′ =− = −

′ ′ =− = −

w u u C U

w u C U

w q u q C U q q

*

* *

* *

,

( ),

( ),

2 2

m

h s

q s

θ θ θ θ (1)

where Cm, Ch, Cq are respectively bulk transfer coefficients for momentum, heat and moisture, and |U | the mean horizontal wind speed at a reference level, usually at 10 m above surface. θ (q) is the potential temperature (specific humidity) at a given height with its value at surface denoted by a subscript ‘s’. u* is the friction velocity or scaling parameter for wind, θ* and q* are the scaling parameters for potential temperature and specific humidity respectively. In the current version of NHM, several schemes of bulk transfer coefficients and roughness lengths over sea surface are available to compute the surface fluxes (Saito et al. 2006). For wind regime with wind speed exceeding 15 m s−1, the bulk coef-ficient for momentum increases with the wind speed in the current schemes based on Kondo (1975) and Beljaars (1995). According to Powell et al. (2003) and Donelan et al. (2004), ‘saturation’ behaviour of Cm for wind speeds exceeding 30 m s−1 were found from direct measurements and laboratory experiments. Similar level-off properties in high wind regime for Ch and Cq are also found from various field experiments (Belamari 2005). In Lebeau-pin et al. (2007), the surface flux parameterizations in SURFEX of the MesoNH are revised according to the above field experiment results, and shows positive impacts on the prediction of intense precipitation associated with the high wind conditions.

Following Donelan (2004) and Belamari (2005), a new scheme of bulk transfer coefficients of momentum, heat and mois-ture is implemented in NHM. Figure 1 shows the variation of Cm, Ch and Cq in the new scheme against wind speeds at 10 m under neutral condition. The diabatic bulk transfer coefficients in the above equations (1) are calculated by multiplying a factor depend-ing on surface stability conditions (Kondo 1975):

C S Cm,h,q m,h,q s mn,hn,qn= −( ) ,θ θ (2)

where Sm, Sh and Sq are functions of temperature difference between the surface and the 10 m level. Cmn, Chn and Cqn are respectively the bulk transfer coefficients of momentum, heat and moisture under neutral condition.

Similar to other NWP models, the velocity roughness length

Development of Air-Sea Bulk Transfer Coefficients and Roughness Lengthsin JMA Non-hydrostatic Model and Application

in Prediction of an Intense Tropical Cyclone

Wai-kin Wong1, Santi Sumdin2 and Edwin ST Lai1

1Hong Kong Observatory, Hong Kong, China2Thai Meteorological Department, Bangkok, Thailand

Corresponding author: Wai-kin Wong, Hong Kong Observatory, 134A Nathan Road, Tsim Sha Tsui, Kowloon, Hong Kong, China. E-mail: wkwong@hko.gov.hk. ©2010, the Meteorological Society of Japan.

66 Wong et al., New Air-Sea Bulk Coefficients and Roughness Lengths in NHM

3. Design of experimentsIn this study, NHM is configured in three domains with hori-

zontal resolution at 20 km (RF20), 10 km (RF10) and 5 km (RF5) (Fig. 2) to perform numerical simulations of Typhoon Hagupit (0814). The number of grid points, time steps and specification of boundary conditions of the three domains are given in Table 1. The initial and boundary conditions of RF20 are obtained from the analysis output of the operational 4-dimensional variational data assimilation system of the JMA Global Spectral Model (GSM) (JMA 2007) at 0000 UTC 22 September 2008 and the following 60 hours at 6-hour intervals. As the horizontal resolution of GSM analysis is 0.5 degrees, the RF20 experiment is thus necessary to provide initial and boundary for RF10 and RF5 to study the impact of new scheme on the simulation of Typhoon Hagupit at a higher resolution to resolve the cloud and convective processes. Sea surface temperature in RF20 is calculated from GSM surface temperature analysis, and it is kept constant during the time inte-gration. RF10 (RF5) is initialized at 0000 UTC 22 (23) September 2008 with forecast range of 60 (30) hours.

In all the NHM experiments, Kain-Fritsch convective parame-terization, 3-ice cloud microphysics (Saito et al. 2006), and Mellor- Yamada-Nakanishi-Niino Level-3 turbulence closure scheme (Hara 2007) are chosen. Default settings of the aforementioned physical processes are used. In this study, the average value of the two formulation of momentum roughness length (Eq. 4) is considered, giving a larger roughness length for winds up to about 23 m s−1, while keeping similar roughness length like the original scheme under large wind speeds. As a control, the bulk coef-ficients and roughness lengths following Beljaars (1995), i.e. the recommended options in the current NHM, are used to perform the same set of forecasts to compare the results.

4. Results and discussions4.1 Intensity and wind distribution

Figure 3a shows the time series of forecast maximum wind near the centre of Hagupit from RF20, RF10 and RF5 experi-ments. It can be seen that as a coarse horizontal resolution is used in RF20 that the model cannot resolve the convection and storm structure, the predicted maximum wind from both schemes are lower than the best track values by more than 10 m s−1. In RF10 and RF5, however, the new scheme can give a higher wind speed in general, and similar wind speeds are obtained compared with that of the best track. Maximum wind in RF10 exceeding 40 m s−1 is forecast from 1500 UTC 22 September to 0000 UTC 24 September and the highest maximum wind speed and minimum central pressure forecasts are respectively 48 m s−1 and 946 hPa. It agrees better with the Hong Kong Observatory (HKO) best track data (49 m s−1 and 940 hPa) than using the original scheme (42 m s−1 and 952 hPa). Similarly in RF5 experiments, the new

(zom) in NHM is specified using Charnock’s relation plus a smooth flow limit (Smith 1988):

z ug

auomm= +

α υ*

*

,2

(3)

where g is the acceleration due to gravity, ν is the kinematic viscosity, α is the Charnock parameter (α = 0.018) and am = 0.11. To include the effects of wave parameters like wave height and periods, modifications of roughness length are made according to Taylor and Yelland (2001) and Oost et al. (2002):

z h hL

auom s

s

p

m (Taylor and Yelland)=

+1200

4 5.

*

υ ,,

,*

.

*

z L uC

auom p

p

m (Oost)=

+

502

4 5

πυ

(4)

where hs is the significant wave height, Lp the wavelength cor-responding to the peak of the wave frequency-size spectrum (or dominant wave period), and Cp the phase speed of dominant wave. Physically, the first terms on the right hand side in the above two expressions represent effects due to slope of the dominant waves and the wave age respectively. According to Fairall et al. (2003), Cp and Lp can be expressed in terms of wave period Tp if deep- water gravity wave relationship is taken. In case of fully devel-oped sea, the wave parameters hs and Tp can be computed from neutral wind condition (Taylor and Yelland 2001). The first rela-tion in (4) was also studied in Kohno et al. (2006) to account for effects in drag coefficients due to wave steepness using a wave model coupled with NHM. Both relations in (4) are implemented in the new scheme to include the effect of wave parameters (hs , Lp and Cp) in the velocity roughness length (Fig. 1b). The values of wave parameters under a general sea condition can be determined by using a coupled atmosphere-wave model. The roughness lengths for heat (zoh) and moisture (zoq) following Fairall et al. (2003) are also incorporated in the new scheme (Fig. 1b):

z z R

R z uoq oh r

rom

= = × ×

=

− − −min( . , . ),

,

.

*

1 1 10 5 5 104 5 0 6

υ

(5)

where Rr is the roughness Reynold number.

Table 1. Configuration of the NHM domains.

Domain No. of grids (NX × NY × NZ) Time step Boundary and

update interval

RF20RF10RF5

151 × 151 × 40201 × 201 × 40241 × 201 × 50

80 s40 s20 s

GSM; 6 hrRF20; 1 hrRF20; 1 hr

Fig. 1. (a) Variation of bulk transfer coefficients in the new scheme and Kondo scheme (thin lines) for momentum (Cm), heat (Ch), and moisture (Cq) against wind speed (m s−1) at 10 m above the surface. (b) Variation of roughness lengths for momentum (z0m), heat (z0h) and moisture (z0q) against wind speeds at 10 m altitude (in m s−1) under neutral condition.

Fig. 2. The three model domains of NHM in this study.

67SOLA, 2010, Vol. 6, 065−068, doi:10.2151/sola.2010-017

scheme gives an improved intensification trend and forecast the highest maximum wind at 53 m s−1 (minimum central pressure at 943 hPa), although the initial condition is obtained by downscal-ing the forecast of RF20 which has much weaker storm intensity than the best track data. RF5 forecast with the original scheme also produces the highest maximum wind at 50 m s−1 (minimum central pressure at 949 hPa), but the intensification trend is slower than that from the new scheme. Therefore, the improved forecasts of maximum wind speed and central pressure for Hagupit suggest that the new scheme works effectively to enhance the intensity of strong tropical cyclone in NHM with horizontal grid resolution of 10 km or above.

Another aspect of improvement with the new scheme can be manifested in the forecast of wind distribution. In both RF10 experiments using original and new schemes (Figs. 3c and 3d), areas of hurricane force wind are predicted but the latter generates a comma shape annular pattern. Hurricane wind radii are about one degree over the northwestern, northeastern and southeastern quadrants while a smaller radius is forecast to the southwest. This compares favourably with the wind distribution from the NOAA Multi-Platform Satellite Wind (MPSW) Analysis data (Knaff and DeMaria 2006) (Fig. 3b), with hurricane wind radii (red shade) ranged from 100 to 140 km over the four quadrants. Figures 3e and 3f show the wind distribution forecasts from RF5 experi-ments. Annular region of hurricane wind areas is also simulated by the original scheme, but the area over northwest quadrant is reduced from both the new scheme and the MPSW analysis in accordance with a slightly weaker predicted intensity.

4.2 Bulk transfer coefficientsThe ratio of heat and moisture bulk transfer coefficients to

drag coefficient (Ch/Cm and Cq/Cm) is an important parameter in tropical cyclone intensity (Emanuel 1995). Compared with the original scheme, the new scheme has higher values of heat and moisture bulk coefficients for moderate to high wind regimes that contribute to the enhancement of heat and moisture fluxes for the development of more intense tropical cyclone. Both the variations of Ch and Cq with wind speed and saturation properties exceeding 30 m s−1 follow the results of field experiments (Belamari 2005).

The values of Ch and Cq and their increasing trend with wind speed up to 20 m s−1 are both similar to the measurement results as described in Weill et al. (2003). However, it is also discussed in the same study that wind speed dependence is quite uncertain even in this medium wind regime due to instrumental noise.

In the new scheme, the ratio of Ch/Cm varies from 0.96 in low wind condition to 1.27 in high wind regime. It is qualitatively consistent with the range of ratio given by Emanuel (1995) that ratio lies within 0.75 and 1.5 and increases with maximum wind when tropical cyclones intensify. On the other hand, a decreasing trend of Cq/Cm is taken in the new scheme that is similar to the original scheme. The ratio (Cq/Cm) decreases from 0.99 to 0.69 as wind speed increases. In Weill et al. (2003), several experiments show that the moisture coefficient against wind speed increases more slowly than that of heat coefficient in medium wind regime (< 20 m s−1). Hence the decreasing trend of Cq/Cm in the new scheme is consistent with these measurement results.

4.3 Surface fluxesFigures 4a−4f show the 24 hour forecasts of surface momen-

tum, sensible heat and latent heat fluxes at 0000 UTC 23 Septem-ber 2008 in RF10 experiments. The reduction of drag coefficient over the high wind regime in the new scheme results in decrease of momentum flux near the centre of Hagupit, leading to increase in maximum wind speed and larger hurricane wind area. Heat and moisture fluxes are enhanced due to larger heat and moisture bulk coefficients. The new scheme improves air-sea flux exchange processes that provide better support in the vertical eddy transport of moisture and heat to sustain the development of Hagupit.

The enhancements of moisture and heat transport from surface contribute to the increase of moisture in cloud and convective parameterization processes of NHM. Figures 5a and 5b show the forecasts of sea level pressure and 1-hour accumulated rainfall at 1400 UTC 23 September 2008 from RF10. Using the new scheme, spiral rainbands are better predicted when compared to radar reflectivity and TRMM rainfall rate. Similar findings are also seen in RF20 and RF5 experiments (not shown). Improvements in the model prediction of spiral rainbands and rainfall intensity are useful for nowcasting applications and very-short-range forecast

Fig. 3. (a) Time series of maximum wind near the centre of Hagupit from RF20, RF10 and RF5 using the original (dashed line) and new schemes (solid line). Maximum winds from HKO best track analysis are given in black dots. (b) Surface wind distribution at 1200 UTC 23 September by NOAA MPSW Analysis. (c)−(d) Forecasts of surface wind barbs and isotach at 1400 UTC 23 September 2008 using the original and new schemes in RF10 experiments. The color shading of green / blue / red / violet / yellow represents areas of fresh (8.0−10.7 m s−1) / strong / gale / storm / hurricane force winds respectively. (e)−(f) Similar forecasts from RF5 experiments. Area in (b) is shown by dashed line boxes in (c)−(f).

68 Wong et al., New Air-Sea Bulk Coefficients and Roughness Lengths in NHM

of the heavy precipitation associated with the passage of intense tropical cyclones (Lai and Wong 2006).

5. ConclusionIn this study, a new scheme of air-sea bulk transfer coef-

ficients and roughness lengths is introduced into JMA-NHM. With drag coefficient reduced over high wind regime and heat and moisture bulk coefficients increased, the predicted maximum wind is strengthened and the central pressure is decreased in the simulation of Typhoon Hagupit. They contribute positively to the exchange of surface fluxes to sustain the development of Hagupit, distribution of high wind areas and rainbands near the centre of Hagupit. The new scheme thus provides promising application of NHM to simulate other intense tropical cyclones and effects of bulk coefficients in high wind regime for weather forecasts and climate studies on wind-pressure relationship of intense tropical cyclones. The roughness lengths are revised and sea-wave effect is considered in the momentum roughness length, although accu-rate specification of wave parameter values requires further study using coupled atmosphere-wave model.

AcknowledgmentsFinancial support to Mr. Santi Sumdin for his attachment to

the Hong Kong Observatory was made under the ESCAP/WMO Typhoon Committee Research Fellowship Scheme 2008.

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Manuscript received 11 December 2009, accepted 15 April 2010SOLA: http://www. jstage. jst.go. jp/browse/sola/

Fig. 4. 24 hour forecasts of surface momentum flux (MF, in kg m s−2), sensible heat flux (SHF, in W m−2) and latent heat flux (LHF, in W m−2) at 0000 UTC 23 September from RF10.

Fig. 5. 1 hour accumulated rainfall forecast at 1400 UTC 23 September 2008 using (a) original and (b) new schemes respectively. (c) Rainfall rate at 1425 UTC from TRMM (2A12 product from JAXA/EORC Tropical Cyclone Database). (d) Plan position indicator (PPI) display of radar reflectivity at 1405 UTC.