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ISSN : 1225-6692(Print)
ISSN : 2287-4518(Online)
Journal of the Korean earth science society Vol.40 No.4 pp.382-391
DOI : https://doi.org/10.5467/JKESS.2019.40.4.382

# Application of Vertical Grid-nesting to the Tropical Cyclone Track and Intensity Forecast

Hyeon-Ju Kim, Hyeong-Bin Cheong*, Chung-Hui Lee
Department of Environmental Atmospheric Sciences, Pukyong National University, Busan 48513, Korea
Corresponding author: hbcheong@pknu.ac.kr Tel: +82-51-629-6642
July 31, 2019 August 17, 2019 August 19, 2019

## Abstract

The impact of vertical grid-nesting on the tropical cyclone intensity and track forecast was investigated using the Weather Research and Forecast (WRF) version 3.8 and the initialization method of the Structure Adjustable Balanced Bogus Vortex (SABV). For a better resolution in the central part of the numerical domain, where the tropical cyclone of interest is located, a horizontal and vertical nesting technique was employed. Simulations of the tropical cyclone Sanba (16th in 2012) indicated that the vertical nesting had a weak impact on the cyclone intensity and little impact on the track forecast. Further experiments revealed that the performance of forecast was quite sensitive to the horizontal resolution, which is in agreement with previous studies. The improvement is due to the fact that horizontal resolution can improve forecasts not only on the tropical cyclone-scale but also for large-scale disturbances.

## 초록

Korea Meteorological Institute

## 1. Introduction

Nesting-grid technique is widely used in numerical weather forecast models to achieve better performance by increasing resolution only in small part of the model domain (Warner and Hsu, 2000;Harris and Durran, 2010;Harris and Lin, 2013;Daniels et al., 2016;Mirocha and Lundquist, 2017). It is known to provide a cost effective forecasting by concentrating the finer-grid computations in the nested domain where the disturbance of interest is located. Nestinggrid technique places finer grid, usually finer by a few times, inside coarser grid in the model. Since in the nested domain computations are done in both finer and coarser resolution, information can be shared between two grids in either one-way or two-way (Harris and Duran, 2010;Harris and Lin, 2013). While the nest-grid has been used only in the horizontal domain from the early development stage of numerical weather prediction, the vertical nesting has started to be used recently. The WRF model, which is popular in numerical weather forecast for both research- or operation- sectors, recently has started to provide the option of vertical nesting (Daniels et al., 2016). Unlike the horizontal grid, which is usually quasi-uniform, it is common practice that the vertical grid is given quite nonuniform allowing usually better resolutions near lower and upper boundaries (Arakawa and Lamb, 1977;Haltiner and Williams, 1980;Lindzen and Fox-Ravinovitz, 1989;Skamarock and Klemp, 2008;Aligo et al., 2009;Leuenberger et al., 2010;Klemp, 2011;Choi and Hong, 2016). For this reason, the ratio of numbers of finer-grid to coarser-grid in vertical direction does not necessarily mean a uniform mesh-refinement-ratio throughout the vertical layers, unlike the case of horizontal mesh refinement.

Tropical cyclone is an intense vortex consisting of strong wind and sharp pressure gradient accompanying heavy rain. It is well defined disturbance whose horizontal range extends relatively in a limited area, as a result, the tropical cyclone is often simulated using nested-grid: A nested domain is placed in the area covering the tropical cyclone. Tropical cyclone is so intense that its observation is not easy, and consequently, it is poorly represented in the analysis data (Kurihara et al., 1993;Zhang and Wang 2003;Kwon and Cheong, 2010;Tom and Snyder, 2012;Galameau and Davis, 2013;Goerss and Sampson, 2014). This makes it necessary to adopt a special kind of initialization for the tropical cyclone (Kurihara et al., 1993;Nguyen and Chen, 2014). One of them is the bogus method which replaces the poorly resolved tropical cyclone with an empirically generated vortex (Kurihara et al., 1993;Kwon and Cheong, 2010;Cheong et al., 2011). The bogus method was found to provide improved forecast compared to the case without the bogus tropical cyclone.

In this study, the vertical nesting technique is applied to the tropical cyclone prediction using WRF model and its impact is examined in terms of errors for the central pressure and track. The paper is organized as follows. In the following section, the model and parameters are explained. Section 3 serves to describe the tropical cyclone initialization method. Results and discussion are provided in section 4, and concluding remarks are given in the final section.

## 2. Model and Parameters

The model used in this study is the WRF v3.8 where the vertical mesh refinement for the horizontal nested-domain is available (Skamarock et al., 2000; Daniels et al., 2016;Mirocha and Lundquist 2017). Figure 1 presents the nested model domain, horizontaland vertical-grids, where model domain is specific to the simulation case of typhoon Sanba (16th 2012): Only sampled points, corresponding to full level, are illustrated for the horizontal grids, whereas all 36 points and 56 points of coarse (in dotted line) and fine (in solid line) resolution, respectively, are shown. The vertical grid interval is specified as a default setting of the WRF model. Model parameters and options for the physics are summarized in Table 1. Simulations were performed for 72 hours, starting from 1200 UTC, 14th SEP 2012.

## 3. Initialization of Tropical Cyclones

The initial field of the WRF model for the tropical cyclone simulations is the final operational global reanalysis (FNL) data of the National Center for Environmental Prediction whose horizontal resolution is 0.25° × 0.25°. All variables are provided with 6- hours interval except for the sea surface temperature (SST) which is provided with 24-hours interval. The horizontal resolution of the FNL is not considered sufficient to resolve properly the tropical cyclones in the aspects of the central pressure and large spatial gradient of meteorological variables including the pressure, temperature and wind speed. To represent better the tropical cyclones in the WRF model simulations, the bogus vortex method is introduced to the initialization procedure of the model (Kurihara et al., 1993;Kwon and Cheong, 2010;Cheong et al., 2011). In this method, the tropical cyclone is generated using the empirical formula based on the best track data of regional specialized meteorological center (RSMC) Tokyo. Used parameters from RSMC report are the locations (longitude and latitude), the central pressure, the maximum wind speed, and the radius of 30-kt wind-speed of the tropical cyclone of interest. The three-dimensional structure of the bogus vortex, which is adjustable depending on the tropical cyclone of target, is characterized by dynamical balances in terms of the mass, the hydrostaticity, and the gradient wind (hereafter, referred to as SABV). One minor update added to the original SABV is the inclusion of the asymmetric component in the bogus vortex: The disturbance field separated from the FNL data is decomposed into axi-symmetric and the asymmetric part with respect to the local coordinates whose origin is defined as the center of the tropical cyclone of interest. The axi-symmetric part is replaced by the symmetric bogus vortex, while the asymmetric part is retained without modification. The bogus vortex was produced with the horizontal resolution comparable to but slightly lower than that of the WRF model simulations.

Simulations were carried out for the tropical cyclone of Sanba (16th, 2012), which has passed over the Korean peninsula and is reported as the strongest tropical cyclone in the year 2012: The maximum wind speed in matured stage has marked 56 m s−1 , while the minimum (central) pressure was as low as 900 hPa. Sanba showed a gradual decrease of the central pressure with a maximum decrease rate of 55 hPa in 24 hours in the final stage of the simulation period.

## 4. Results and Discussion

Figure 2 compares the initial surface pressure fields for the cases with and without bogussing. As is well documented in previous studies (Kurihara et al., 1993;Kwon and Cheong, 2010;Cheong et al., 2011), the typhoon is better represented in the case of bogussing as intended. The minimum pressure of the bogussed field is the same as the RSMC report whereas it is deviated from the RSMC report by as much as 45 hPa in the case without bogussing.

Shown in Fig. 3 is the time variation of central pressure and track with time interval of 6 hours. Central pressure well matches with the best track data with the errors less than 5 hPa before 60 hour, but beyond that it increases almost linearly reaching 18 hPa by 72 hour. Although the case of vertical nesting exhibits slightly better results, the difference between the two cases appears quite small (cf. Zhang and Wang, 2003;Daniels et al., 2016). Furthermore, the simulated values are identical to each other by 72 hour. The results indicate that the tracks of simulated typhoons, which appear to be almost overlapped, closely follow the best track which is oriented from south to north. For both simulations, the typhoons are found to be located in the west side of the observed position. This kind of bias is maintained throughout the forecast period of 72 hours. Although the errors are quite small, they are shown to increase steadily with time: The largest error, which is about 120 km, is found between 60 and 66 hour. It is worthy to note that the moving speed of typhoon increases with time, and this was reproduced almost in the same way in the simulations. It appears that the speed of typhoon is almost doubled by 72 hour compared to the speed at the initial time.

To get insight on the simulation results, the velocity fields are decomposed into two parts, the typhoon scale and remaining large-scale. An accurate decomposition can be done by adopting spectral filtering technique. In this study, a local-domain high-order spectral filter of Park et al. (2011) is incorporated, which uses the same algorithm for the global domain filter (Cheong et al., 2015;Kang and Cheong, 2017;Lee at al., 2017). The local-domain filter adopts cosine Fourier functions to expand the grid-point data with the spectral method. Before applying the Fourier expansion, the grid-point data is extended to the buffer zone outside the local domain using smoothly decreasing function towards the end-point of the extended region. The buffer zone can be adjusted depending on the size of domain. In the present study, the buffer zone is kept 10 percent of the domain area. By doing this, the negative effect coming from the artificial boundary condition of vanishing gradient (i.e., adopting cosine series) is alleviated to a large extent. As shown in Park et al. (2011), the filtering (or decomposition) is performed by multiplication of filter matrix to the Fourier-cosine coefficients. For instance,

$d l , m = ∑ k = 1 N B l , k c k , m ,$
(1)

where N is the number of grid points in the meridional direction, ck,m and dl,m represents the Fourier-cosine coefficients of a variable to be filtered and the filtered variable, respectively, and B means the filter matrix.

The filter is applied to the velocity field of vertical level η = 0.7 at t = 24 hour with η denoting vertical coordinate of the model, which corresponds to about 700 hPa level (Skamarock and Klemp, 2008). Results of filtering are presented in Fig. 4, where the velocity fields of two simulation cases are compared for each scale. Shown in the lower panel is the difference between the two scale-components taken over the center of the tropical cyclone. The tropical cyclonescale shows almost axi-symmetric structure having a maximum speed at the radius of about 100 km for both cases. The large-scale velocity distribution exhibits very smoothly varying fields even near the tropical cyclone center as is expected. It is interesting that even though the wind vanishes at the center of the tropical cyclone, the large scale field obtained by filtering has non-zero, finite values there. This means that the tropical cyclone moves by the large-scale field (Kwon and Cheong, 2010;Zarzycki and Jablonowski, 2015). From the lower panel, it can be found that the difference for the tropical cyclone scale is less than one m s−1 with the maximum difference located slightly outside of the radius of maximum wind. It is worthy to note that the difference for the large-scale is even smaller than the case of tropical cyclone scale: The difference is so small that it is almost indistinguishable from the line plots.

If we consider that the movement of the tropical cyclone is determined by the large-scale, the result suggests that the tracks of simulated tropical cyclones with and without vertical nesting should be quite similar to each other. As presented in Figs. 3 and 4, the difference caused by the vertical mesh refinement is significantly small and it is mostly confined to the scale of the tropical cyclone. It was also found that this feature is not sensitive to the mesh refinement ratio: Simulations performed with fine vertical grid of 56 levels, which is slightly lower resolution than the cases in Figs. 3 and 4, revealed the insensitivity very clearly. However, even in this case, the difference in simulated fields have appeared mainly in the inner core region. To pursue this point further, the vertical cross sections of the wind-speed difference and the temperature difference are presented in Fig. 5. It is clearly demonstrated that the difference is mostly found for the tropical cyclone scale, and the difference for the large-scale is almost negligible, compared to the tropical cyclone scale. The magnitude of the windspeed difference is larger in the upper layers than in the lower layers. The maximum difference is about 5 m s−1 . Similar distribution is seen for the temperature with the maximum value being about 1 degree. Figure 6 illustrates the vertical profile of the relative humidity. The case of vertical nesting has higher humidity in the lower layers than the case without vertical nesting, whereas the tendency in the upper layers is in the reversed sense. Scale-decomposition of the humidity field also reveals that such a difference is mostly found in the field of tropical-cyclone scale, like the case of the wind-speed and the temperature (not shown).

Combining the results shown in Figs. 3-5, it may be said that the effect of vertical nesting is almost found in the tropical cyclone scale, though it is quite small. Vertical mesh refinement within the nested domain does not affect the large-scale field in the WRF model simulations. In other words, the vertical resolution of the models used for the simulations is already fine enough, even without vertical nesting grid, as compared with the horizontal resolution. To confirm this hypothesis, the simulations with coarser horizontal resolution of 12 km mesh and without vertical nesting were performed with all other model parameters being remained the same. The central pressure and track for 3 days simulation are presented in Fig. 7. It is clear that the performance of the coarser horizontal resolution is inferior to the finer horizontal resolution (cf. Warner and Hsu, 2000;Skamarock and Klemp, 2008). The difference of central pressure is larger than 15 hPa and the difference of track is about 100 km at 48 hour. Figure 8 shows the same results as Fig. 4 but for the simulations provided in Fig. 7. To focus on the horizontal resolution, the simulations were performed on a single domain, i.e, without grid-nesting. As might be expected from the results in Fig. 7, the difference for the large scale as well as the tropical cyclone scale is significantly larger than the simulation results with finer horizontal mesh. As in the Figs. 3 and 4, the effect of vertical nesting on the simulations with coarser horizontal resolution was also insignificant.

## 5. Concluding Remarks

In this study, the effect of vertical nesting grid on the tropical cyclone intensity and track simulations was investigated using the WRF v3.8 model and the FNL reanalysis fields as initial conditions. For a better representation of the tropical cyclone, poorly resolved in the FNL data, the SABV method was incorporated to generate a bogus tropical cyclone based on analytic empirical formulas. The vertical-grid nesting was introduced to the nested domain to achieve a finer resolution in the vertical direction in and around the tropical cyclone. Tropical cyclone Sanba (16th 2012), which has passed through the Korean peninsula with the central pressure gradually increasing with time, was simulated. Simulation of 72 hours indicated that the vertical nesting has little impact on the tracks while it has weak impact on the intensity. This was because the influence was mostly concentrated in the small area surrounding the tropical cyclone, which is comparable to the tropical cyclone scale. As in previous studies, it was also confirmed through sensitivity experiments that the intensity and track forecast was sensitive to the horizontal resolution. The sensitivity difference between the vertical nesting (vertical grid refinement) and horizontal resolution is likely to be caused by the fact that the increase of horizontal resolution contributes to the disturbances of large-scale as well as tropical cyclone-scale. On the other hand, the vertical nesting-grid (mesh refinement) contributes only to the tropical cyclone-scale field but not to the large-scale field, probably because the vertical nesting is restricted to the nested horizontal domain. In the present study, only one case of simulation was carried out, therefore, it is difficult to generalize the results because the structure and strength of the tropical cyclones are so diverse. Nevertheless, it seems quite plausible to point out that the horizontal resolution of the numerical weather prediction models such as WRF model in general is not better than the vertical resolution, which as a result brings about weak impact of the vertical grid refinement as demonstrated above.

## Acknowledgments

This work was supported by Korea Meteorological Institute (KMI 2018-07310).

## Figure

Numerical domain and nested grid structure of the WRF model used for the tropical cyclone simulations. The model area consists of two domains, the parent (outer) domain and nested domain (child domain or inner domain). The lowest and highest vertical-level corresponds to the surface and 50 hPa level, respectively. Two kinds of vertical grid resolution, consisting of 56 levels and 36 levels, respectively, are illustrated.

Initial fields of surface pressure before (left panel) and after (right panel) bogussing of the typhoon Sanba at UTC 1200 on 14th SEP 2019, where the unit of scale bar is Pascal and contour interval is 5 Pa. Bogus typhoon was generated with the use of SABV based on the RSMC best track report.

Central pressure (left panel) and track (right panel) of simulated Sanba with the time interval of 6 hours. Red- and bluedots indicate the simulations without vertical nesting (35 layers) and with vertical nesting (70 layers), respectively.

Velocity fields of η =0.7 (corresponding approximately to 700 hPa level) for the simulations without vertical nesting (upper panels) and with vertical nesting (middle panels) by t =24 hour. Left and right panels show the velocity field of tropical cyclone scale and large scale, respectively. Shown in the lower panels are the west-east cross sections of meridional velocity with black (red) line denoting the simulation without (with) vertical nesting.

Vertical cross-section of wind speed difference (upper panels) between simulations with and without vertical nesting, where the left and right panel corresponds to the tropical cyclone scale and large-scale, respectively. Lower panels are the same as the upper panels except for the temperature difference. The cross section is taken over the center of Sanba by t =24 hour, and vertical axis means the vertical coordinate of the model (η) and the pressure of η =0 corresponds to model top (50 hPa). Units for the wind speed and the temperature are ms−1 and degree, respectively.

Vertical profile of relative humidity (RH) at the center of Sanba by t=49 hour for the simulations with (blue dots) and without (red dots) vertical nesting.

Central pressure (left panel) and track (right panel) of simulated Sanba with the time interval of 6 hours. Black (blue) dots indicate the best track and the control simulations (with the resolution of 12km x 12km), respectively, while red dots correspond to the simulations with 8km x 8km resolution.

The same as Fig. 4 but for the simulations with horizontal resolution of 12 km × 12 km (upper panel) and 8km x 8km (middle panel). The lower panel presents the west-east section of meridional velocity with black (red) line denoting the coarse (fine) resolution.

## Table

Model configuration used for the tropical cyclone simulations

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