1 Introduction

Tropical cyclones (TCs) are one of the most destructing natural hazards (Emanuel 2005; Peng et al. 2014) and pose great scientific challenges to meteorologists. The planetary boundary layer (PBL) scheme and the microphysics scheme have been shown critical to the numerical forecasting of TCs, because the boundary layer processes regulate the sources of heat and moisture, and sink of momentum in TCs (Kepert 2012), while the cloud dynamical properties such as vertical velocity and cloud top height are determined by the microphysics scheme in numerical models (Khain and Lynn 2011).

Many studies focus on the effects of single PBL scheme (e.g., Rao and Prasad 2007; Kanada et al. 2012; Kepert 2012) or single microphysics scheme (e.g., Wang 2002, Khain and Lynn 2011; Pattanayak et al. 2012). However, effects by various combinations of PBL and microphysics schemes have only received limited attentions. Indeed, interactions between the PBL and the microphysical processes cannot be overlooked. On one hand, the condensation processes in PBL have interactions with the microphysics in clouds (Nakanishi 2000, 2001; Nakanishi and Niino 2004, 2006). On the other hand, the downward short-wave and long-wave radiations to PBL are governed by the cloud effects in microphysics schemes. Hence, various combinations of PBL and microphysics schemes may have different influences on TC simulations and forecasts. Study from Zhou et al. (2013) shows that the combination of YSU scheme (the Yonsei University PBL scheme, Hong et al. 2006) and Ferrier scheme (the Eta Grid-scale Cloud and Precipitation scheme, Ferrier et al. 2002) is the best choice for the track simulation of super Typhoon Megi (201013). However, this study may be case-dependent because only one TC was analyzed. In the present study, an ensemble of forecasting experiments using different combinations of PBL and microphysics schemes are carried out for five TCs in the South China Sea (SCS), one of the major active regions of TCs (Chen et al. 2014), to figure out the effects by various combinations of PBL and microphysics schemes on the track forecasts.

The present study is organized as follows. Sections 2 and 3 present the forecasting experiments with different combinations of physical schemes and analysis results, repectively. Conclusions and discussions are given in the final section.

2 The forecasting experiments

The experiments carried out in this study are based on the Weather Research and Forecasts (WRF) model (Skamarock et al. 2008), developed by the National Center for Atmospheric Research (NCAR) and the National Centers for Environmental Prediction (NCEP) in the USA. It is a next-generation meso-scale model for advancing the understanding and prediction of meso-scale weather and accelerating the transfer of research advances into operations. A dynamical downscaling technique is employed to obtain higher-resolution output with small- and meso-scale features from the lower-resolution output of a global atmospheric model. To realize this, a two-domain-one-way-nested configuration is designed, as shown in Fig. 1. The outer domain for the atmospheric model covers the Western North Pacific (WNP), the entire SCS, and the eastern Indian Ocean, with a horizontal grid resolution of 72 km. The inner domain covers the entire SCS and southern China, with a horizontal grid resolution of 24 km. Both domains have 27 layers in the vertical. The output from the Global Forecast System (GFS) maintained by NCEP with horizontal grid resolution of 1° × 1° is used to provide initial conditions and lateral boundary conditions for the outer domain. The Kain-Fritsch cumulus scheme (Kain and Fritsch 1990, 1993), Dudhia shortwave (Dudhia 1989) and RRTM longwave (Mlawer et al. 1997) radiation scheme are chosen for both domains.

Fig. 1
figure 1

Model domains of WRF and the JTWC best tracks of the five selected TCs in 2012

Full size image

An ensemble of experiments using different combinations of three PBL schemes and four microphysics schemes are carried out. The three PBL schemes are the YSU scheme, the MYJ scheme (the Mellor-Yamada-Janjić PBL scheme, Janjić 1994) and the MYNN2 scheme (the Level 2.5 Mellow-Yamada Nakanishi Niino PBL scheme, Nakanishi and Niino 2006), while the four microphysics schemes are the Ferrier scheme, the Goddard scheme (the Goddard Cumulus Ensemble Model scheme, Tao et al. 1989), the WSM6 scheme (the WRF Single-Moment 6-class scheme, Hong and Lim 2006) and the Lin scheme (the Purdue Lin scheme, Lin et al. 1983), respectively. In order to reduce case dependence, five TCs that entered the inner domain of the model during 2012 are selected. In the WRF model, the surface environments are similar over the sea and varied over the continent, hence the effects by the PBL schemes are more significant near or on the continent. Thus, in order to enlarge the effects of the PBL schemes, the selected TCs should have made landfall. The TCs chosen for this analysis are Doksuri (201206), Vicnte (201208), Saola (201209), Kai-Tak (201213) and Gaemi (201220), respectively. Their observed tracks produced by Joint Typhoon Warning Center (JTWC, http://www.usno.navy.mil/JTWC/) are also shown in Fig. 1. The forecasting experiments are initialized at 72, 48 and 24 h before the landing of each TC. There are totally eighteen initialization times, six for Typhoon Kai-Tak, which landed for two times, and three for every other TCs.

3 Results from the experiments

3.1 The tracks

Based on the observed tracks produced by JTWC, the track position error (TPE) for 24-, 48- and 72-h forecasts by each combination of PBL and microphysics schemes is calculated using the following formula (Neumann and Pelissier 1981; Powell and Aberson 2001):

$${\text{TPE}} = 111.11\frac{180}{\pi }\cos^{ - 1} \left[ {\sin \varphi_{\text{O}} \sin \varphi_{\text{S}} + \cos \varphi_{\text{O}} \cos \varphi_{\text{S}} \cos (\lambda_{\text{O}} - \lambda_{\text{S}} )} \right],$$
(1)

where \(\lambda_{\text{O}}\) and \(\varphi_{\text{O}}\) are the longitude and latitude of the observed storm center, and \(\lambda_{\text{S}}\) and \(\varphi_{\text{S}}\) are those of the storm center forecasted by each combination. Further, in order to make a relative comparison between different combinations of physics schemes, the relative error (R i ) of each TC track predicted by each combination is calculated using the following formula:

$$R_{i} = \frac{{{\text{TPE}}_{i} }}{{\overline{\text{TPE}} }}\qquad (i = 1 \ldots ,N),$$
(2)

where \(\overline{\text{TPE}} = \frac{1}{N}\sum\nolimits_{i = 1}^{N} {{\text{TPE}}_{i} }\) and N denotes the number of combinations.

The mean TPEs and the relative error of various combinations, which is averaged over the ensemble forecasts for five selected TCs, are listed in Table 1. The combination of YSU and Ferrier schemes gets the smallest TPE and relative error for 24- and 72-h forecasts, while it ties the combination of MYNN2 and Lin schemes for the best in 48-h forecasts. Overall, as indicated by the rank based on the mean of relative errors of all forecast periods, the combination of YSU and Ferrier schemes provided the best prediction among all combinations, and thus we focus on this combination in the following analysis.

Table 1 Mean track position error (TPE, unit: km) and relative error (Ri) of 24-h, 48-h and 72-h forecasts as well as the rank for different combinations of three PBL schemes and four microphysics schemes, averaged over an ensemble of forecasts for five landed tropical cyclones during 2012
Full size table

As an example, Fig. 2 shows the 6 hourly observed track as well as the 60-h forecast tracks and the TPEs by each combination of physical schemes starting at 0000 UTC July 22, 2012, for Typhoon Vicente (201208), which made landfall on the coast of south China. The forecast for the last 12 h is ignored because the real TC was dying out at this period. The combination of YSU and Ferrier schemes performs slightly better than most of the other combinations with the 48-h and 60-h forecast TPEs of 154.5 and 279.4 km, respectively, while it performs significantly better than others for the 24-h forecast with a TPE of 15.7 km. Although the combinations of the MYJ scheme with most microphysics schemes perform well from the 30- to 54-h forecast, they do not work for the 60-h forecasts because the simulated vortexes are too weak, with their sintensity weaker than a tropical depression.

Fig. 2
figure 2

Six hourly observed and the predicted tracks by combinations of different microphysics schemes with (a) YSU, (b) MYJ, (c) MYNN2 PBL schemes and (d) the track position errors (TPE, unit: km) for the 60-h forecast for Typhoon Vicnte (201208) started at 0000 UTC July 22, 2012

Full size image

In the next two subsections, the reason why the combination of YSU and Ferrier schemes performed the best for TC track forecast is revealed from analyzing the steering flows and other atmospheric variables such as the 500-hPa geopotential height, 10-m winds and the water vapor distributions as well as the precipitation.

3.2 The steering flows

Previous studies (e.g., Holland 1983; Wu et al. 2005) have pointed out that TC tracks are strongly influenced by large-scale steering flows. Accurate prediction of steering flow would guarantee the accuracy of TC track prediction. Following this line, the biases of u- and v-components of the steering flows from the 72-h forecasts of each combination against the NCEP Final Analysis (FNL) are displayed in Fig. 3. The deep-layer mean steering flows are obtained through averaging the wind field between 925- and 300-hPa over a 3–8° radial band from TC center, based on the suggestions or experiences in previous studies (e.g., Chan and Gray 1982; Evans et al. 1991). Compared with other combinations, the combination of YSU and Ferrier schemes produces relatively small errors in both u- and v-components. This more accurate prediction of steering flows is beneficial to TC track forecasts.

Fig. 3
figure 3

Mean bias of (a) u- and (b) v-components of steering flow (unit: m s−1) from the 72-h forecast by different combinations of three PBL schemes and four microphysics schemes, averaged over an ensemble of forecasts for five landed TCs during 2012

Full size image

Note that the combinations of YSU PBL scheme with other three microphysics schemes did not perform as well as the MYJ and MYNN2 PBL schemes (e.g., the v-components of the steering flows), suggesting that interactions between different PBL and microphysics schemes is an important factor of the predictions of TCs.

3.3 Atmospheric structures

Based on a spatial correlation analysis, the forecast 500-hPa geopotential height, 10-m winds and the water vapor distributions as well as the precipitation predicted by each combination of different PBL and microphysics schemes are compared with observations. Here, the spatial correlation coefficients between the FNL analysis and the forecast variables that interpolated onto the grids of FNL through averaging, are calculated within a fixed region (100–130°E, 0–30°N) covering the range of the five TCs. Examples for this interpolation are shown in Figs. 4b, 5b, 6b, respectively. Comparing the interpolated fields with the original fields, we can see that although small-scale features are filtered out by the interpolation, the general features are preserved, suggesting that the interpolated data are suitable for this spatial correlation analysis. Besides, in order to amplify the impacts of the PBL schemes, the correlation analysis is made at the moment right before the landing of TCs. Table 2 lists the coefficients averaged over the ensemble of forecasts for the five TCs.

Fig. 4
figure 4

The 500-hPa geopotential height (unit: geopotential meters, GPM) by (a) the FNL analysis, (b) the interpolated fields from the forecast by the combination of YSU scheme and Ferrier scheme, and the original forecasts field by the combinations of (c) YSU and Ferrier schemes, (d) YSU and Goddard schemes, (e) YSU and WSN6 schemes, (f) YSU and Lin schemes, (g) MYJ and Ferrier schemes, as well as (h) MYNN2 and Ferrier schemes at the 30-h forecast time, valid at 0600 UTC July 23, 2012, for Typhoon Vicnte (201208) (shaded area for values larger than 5840 GPM in the FNL analysis, and for values larger than 5860 GPM in the model forecasts)

Full size image
Fig. 5
figure 5

Similar to Fig. 4, but for the 10-m winds (unit: m s−1, shaded area for the magnitudes of the winds with an interval and minimum value of 5 m s−1)

Full size image
Fig. 6
figure 6

Similar to Fig. 4, but for the precipitable water (unit: kg m−2, shaded area for values larger than 60 kg m−2)

Full size image
Table 2 Spatial correlations between the FNL and the forecast 500-hPa height, 10-m winds and precipitable water by each combination of three PBL schemes and four microphysics schemes, averaged over an ensemble of forecasts for five landed TCs during 2012
Full size table

The averaged spatial correlation coefficients for the 500-hPa geopotential height is shown in Table 2, showing that the combination of YSU and Ferrier schemes performs relatively better than other combinations with the coefficient of 8.97 × 10−1. Concentrating on this combination, a comparison between the FNL analysis and the forecast field with other combinations including YSU scheme or Ferrier scheme is carried out. An example is shown in Fig. 4. The structure of the geopotential height over the SCS is dominant by two atmospheric systems, one is the subtropical high, which steers the TCs westward along its southwest flank, and the other is the structure of TC itself. Though all of the forecasts overestimate the magnitudes by about 20 GPM, the structure of the subtropical high is well predicted by the combination of YSU and Ferrier schemes, especially over the southeast part of the fixed region. The structures of TCs are similar between different combinations, suggesting that the combination of different PBL and microphysics schemes exert relatively fewer effects on the prediction of TC intensities.

As illustrated in Table 2, the combination of YSU and Ferrier schemes performs the best for the forecasts of v-components of the 10-m winds, and the second for those of the u-components. Because the position of TC center is also determined by the structure of surface winds, the well-predicted surface winds is beneficial to TC track forecasting. As shown in Fig. 5, the large-scale environment and the asymmetric structure of TC are well predicted by all of the combinations; however, the locations of the strong wind regions near the TC are mainly governed by the PBL schemes. For example, the strong wind region located south of the Hainan Island is absent in the forecasts by the MYJ and the MYNN2 schemes, suggesting that the YSU scheme is beneficial to the forecasting of surface winds during TC’s influence.

The combination of YSU and Ferrier schemes performs the last one for the forecast of the precipitable water (the total atmospheric water vapor contained in a vertical column of unit cross-sectional area) (Table 2). As shown in Fig. 6, the YSU scheme failed in forecasting the distributions of water vapor within the outer radii of TCs, as the sea area southeast to the Indo-China Peninsula is too wet; besides, the TCs simulated by the Ferrier scheme are relatively drier, as the shading areas in the combinations including the Ferrier scheme are relatively smaller than those in the combinations including other microphysics schemes. Figure 7 shows the comparison of the accumulated precipitation between the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) 3B42 and the combinations between the YSU scheme and different microphysics schemes. Although TRMM has superior skill in detecting TC heavy rains (Islam and Uyeda 2005; Chen et al. 2013), it tends to underestimate moderate to high rain (>50 mm h−1). Hence, the simulated precipitations are almost double that of TRMM. The precipitation south of the Hainan Island is not well simulated by the Ferrier scheme. Compared to the Lin scheme (Fig. 7f), the Ferrier scheme simulates fewer precipitations, while the position of the precipitation cell is about 2° easterner. Overall, the forecast of the water vapor distributions and the precipitations by the combination of YSU and Ferrier schemes do not perform as well as that of the geopotential height and the surface winds. Since this combination preforms the best in track forecasting, the relationship between the distribution of precipitation and TC tracks is worth discussing.

Fig. 7
figure 7

The 30-h accumulated precipitation (mm) valid at 0600 UTC July 23, 2012, for Typhoon Vicnte (201208) by (a) Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) 3B42, the combinations of YSU scheme and (b) Ferrier scheme, (c) Goddard scheme, (d) WSM6 scheme, and (e) Lin scheme, respectively. The difference between the combination of YSU and Lin schemes and the combination of YSU and Ferrier schemes is illustrated in (f)

Full size image

4 Conclusions and discussion

An ensemble of forecasting experiments using different combinations of three PBL schemes (YSU, MYJ and MYNN2) and four microphysics schemes (Ferrier, Goddard, WSM6 and Lin) are carried out for five landed TCs during 2012. Among all the experiments, the combination of YSU scheme and Ferrier scheme performs the best for the forecast of TC tracks. A further analysis indicates that the combination of YSU Ferrier schemes produces a more accurate steering flow as well as TC wind structure, leading to a more accurate TC track forecast.

It is worth noting that, although the combination of YSU and Ferrier schemes performs the best for the forecast of TC tracks, it does not perform the best for the forecast of precipitation which is affected by a number of factors besides the PBL and microphysical schemes. Studies have found that it can be effectively improved by some techniques, including “optimizing” the initial conditions through data assimilation (Zhou et al. 2010; Zhang et al. 2013; Zheng et al. 2015), increasing the model resolution (De Bruijn and Brandsma 2000; Lonfat et al. 2007), and adopting a “best” cumulus parameterization scheme that takes into account the specific region and model resolution (Nasrollahi et al. 2012; Ma and Tan 2009).

Finally, it should be aware that the effects of the physical schemes on the forecasts of TCs may vary with different synoptic situations. More experiments with different combination of the physical schemes for the TC track forecast in different synoptic situations should be carried out in the future.