Improved Tropical Cyclone Forecasts with Increased Vertical Resolution in the TRAMS Model

Tropical cyclones (TCs) are extreme events that can cause some of the costliest and deadliest natural disasters, especially in the heavily populated coastal areas in southern China.For the track and intensity of landfalling typhoons, in addition to being influenced by the internal structure of the typhoon, large-scale circulation fields and complex underlying surfaces are also closely related factors.Therefore, there are difficulties in forecasting landfalling typhoons, and the forecasts of the current numerical prediction models still need further improvement (Wang et al.^[1]; Xu et al.^[2]).For example, Typhoon Hato (2017) made landfall in Zhuhai, Guangdong Province and killed a total of 11people, and incurred losses up to 28.91 billion RMB in southern China.The operational forecast of Typhoon Hato (2017) by the TRAMS model was characterized by a bias of northward path and weak intensity (cf.Fig. 3a1 and 3a2 in this paper), which caused some uncertainty for disaster prevention and mitigation.

Since boundary layer processes are the main source of energy for typhoon development, the vertical stratification design of the lower layers of the model can have a significant impact on the intensity and structure of typhoon forecasts (Zhang and Wang^[3]; Kimball and Dougherty^[4]; Bhaskar Rao et al.^[5]; Ma et al^[6]; Zhang et al.^[7]).Using sensitivity tests of an ideal typhoon, Kimball and Dougherty^[4]found that a sparse vertical layer in the boundary layer can also lead to an overestimation of the subsurface flux, and also indicated that the simulation results of typhoon intensity is very sensitive to the model minimum height.Zhang et al.^[7]further tested the effect of vertical resolution on hurricane forecasts with different weather circulation backgrounds and different intensities by using ideal experiments and found that hurricane intensity forecasts are less sensitive to the changes in circulation backgrounds at high vertical resolutions.Zhang et al.^[8]suggested that increasing the vertical resolution of the model may also improve typhoon track forecasts.

Vertical resolution affects typhoon forecasting mainly through both dynamic and physical aspects.Increasing the model's horizontal resolution can better identify the characteristics of small-and medium-scale weather systems, which is important for reducing forecast uncertainties and lowering forecast errors (Mass et al.^[9]; Clark et al.^[10]).While increasing the horizontal resolution, it is necessary to increase the vertical resolution accordingly to ensure the coordination of simulation results in terms of dynamical scales (Lindzen and Fox-Rabinovitz^[11]; Lu^[12]; Persson and Warner^[13]; Liao and Zhu^[14]; Wang et al.^[15]; Liu and Zhang^[16]; Waite^[17]; Cullen^[18]; Skamarock et al.^[19]).On the other hand, the impact of coordination between vertical stratification and physical processes on model forecasts is gradually gaining attention (Räisänen^[20]; Pope et al.^[21]; Yang and Gao^[22]; Lee et al.^[23]; Mc TaggartCowan et al.^[24]; Wang and Ping^[25]).Given the complexity of the physical processes of the model and the obvious differences in the design of different physical schemes, even if the vertical resolution of the model reaches a power-matching level with the horizontal resolution, it is still necessary to further specifically examine the coordination between it and individual physical processes to ensure the rationality of the physical feedback.

Great efforts have been made by the Guangzhou Institute of Tropical and Marine Meteorology (ITMM)to develop the TRAMS model for TC forecasts.The version TRAMS-v1.0 has been run in operational mode since 2014 and has been annually upgraded, establishing itself one of the best operational typhoon models used in China.TRAMS-v1.0 was implemented with a vertical resolution of 55 levels and a model top at 28km, with resolutions of approximately 36 km (Chen et al.^[26]; Xu et al.^[27]).During the 2016 typhoon season, the newer operational version of TRAMS, i.e., TRAMS-v2.0(Chen et al.^[28]), was implemented with only one domain, a horizontal resolution of approximately 18 km, an increased vertical resolution of 65 levels, and a model top set at 31 km.The operational version of the TRAMS model was further updated to v3.0 in 2019 (Xu et al.^[29]), with the horizontal resolution increased to 9km, while the vertical resolution was not changed.Although the horizontal resolution has been increasing from version1.0 to 3.0, the vertical resolution has changed relatively little.

Skamarock et al.^[19]pointed out that for a horizontal grid resolution of 15 km, the vertical thickness must be about 200 m to meet consistency requirements.However, the current vertical thickness of the middle and upper levels exceeds 500 m in the 65-layer TRAMS-v3.0 model with a horizontal resolution of 9 km (cf.Fig. 3a in this paper). Obviously, the vertical resolution of the current TRAMS model is comparatively lower. To what extent does this low vertical resolution have an impact on the path and intensity forecasts of typhoons? What is the mechanism of its impact? These are the questions to be addressed in this paper. The rest of paper is organized as follows: Section 2introduces the model configurations, datasets, and experiment design, Section 3 presents a case study of Typhoon Hato (2017), the influence is further verified with landfalling storms occurred in the typhoon seasons during 2016-2017 in Section 4, and conclusion and discussion are given in Section 5.

The model domain of TRAMS-v3.0 covers the area of 0.8°-50.5°N, 81.6°-160.8°E (Fig. 1).A semi-implicit, semi-Lagrangian finite-difference scheme is applied to the Arakawa C grids and the terrain-following CharneyPhillips grids horizontally and vertically, respectively.Using a three-dimensional reference state to separate the atmosphere from the perturbations (Su et al.^[30]) in TRAMS-v3.0 can greatly improve the computational accuracy of its dynamic core.

Figure 1.  The domain of the model (filled colors in the figure indicate terrain height).

Currently, the physics options in TRAMS-v3.0include the modified medium-range forecast (MRF)model boundary layer scheme (Hong and Pan^[31]; Dai and Chen^[32]; Zhang et al.^[33]), the modified simplified Arakawa-Schubert (SAS) cumulus parameterization scheme (Pan and Wu^[34]; Han and Pan^[35]; Xu et al.^{[36, 37]}), the Weather Research and Forecasting (WRF)single-moment 6-class (WSM6) microphysics scheme(Hong et al.^[38]; Hong and Lim^[39]), the RRTMG longwave and short-wave radiation scheme (Iacono et al.^[40]), and the Slab land-surface model (Dudhia^[41]).

The TRAMS model uses the Integrated Forecasting System (IFS) analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) as both initial and boundary conditions for operational implementation.Because of the slow data transfer speed, the ECMWF data are selected at a very low vertical resolution of 17 levels, with a horizontal resolution of0.09°.The typhoon intensity and path observational data used for verification is released in real-time by the National Meteorological Centre typhoon network (http://typhoon.nmc.cn/web.html).

Although there are many different measures for the tracking of typhoon center (Tao et al.^[42]; Tory et al.^[43]; Biswas et al.^[44]), we just simply define the location of minimum geopotential height at 850 h Pa as the typhoon center and the minimum sea level pressure (denoted as P_min hereafter) as intensity, which was adopted in the operational verification system for the TRAMS model(http://www.grapes-trams.org.cn/TyphoonVerification.aspx).The same definition is used in the evaluation of TC track and intensity forecasts for other operational models including ECMWF-IFS, CMA/NMC CMA-GFS, NCEP-GFS, and CMA/NMC T639-GFS.In this paper, near-surface maximum wind speed (denoted as V_max hereafter) is also verified in typhoon intensity assessment, and it is computed according to P_min in the model according to the following wind-pressure relationship:

where a and b are adjustable parameters according to the maximum 10 m wind speed directly output by the model(vv0) and the latitude of TC center (TClat):

The above parameters are obtained by fitting

typhoon forecasts from the TRAMS model and observations, and they are used in the present study to diagnose V_max in real operational forecasts.

The Gal-Chen terrain-following vertical coordinates (Gal-Chen and Sommerville ^[45]) is adopted in the TRAMS model. According to their formulation, the transformation between physical height (z) and terrain-following coordinate (η) is assumed linear with the form:

where Z_S is the orographic height, and Z_T=constant is the model top boundary.

A new scheme to determine vertical grid suggested by Jablonowski and Williamson ^[46] is implemented into the TRAMS-v3.0 model. The model levels η_k is calculated by the following quadratically stretched vertical grid:

where N is the total number of model levels. The stretching parameter ε is set as 5 to obtain an approximate resolution with TRAMS-v2.0. Once η_k is obtained from Eq. (5), the physical heights z can be obtained from Eq. (4).

To explore the sensitivity of typhoon forecasting to vertical resolution, we set up three sets of comparison tests including Test-65L (N=65), Test-95L (N=95), and Test-125L (N=125). To avoid the impacts of the lowest model height on typhoon forecast (Ma et al. ^[6]), the first model level above ground surface is uniformly set to 56 m in the above three sets of experiments. As shown in Fig. 2a, when the number of model vertical layers N increases from 65 to 125, the vertical layer thickness gradually decreases from 700 m to 250 m above 5 km altitude, which is basically close to the vertical resolution requirement proposed by Skamarock et al. ^[19]. Since the distribution of model layer is non-uniform in the vertical direction, computational instability in the vertical difference scheme would be easily caused by over-encryption of the low-level vertical layers (Lu ^[12]). To avoid this problem, we keep the distribution of model layers below 1 km for the three sets of tests (Fig. 2b).

Figure 2.  (a) Distribution of the thickness as a function of altitude, and (b) vertical distribution of vertical layers at low levels.

Super Typhoon Hato is selected as the main research object of this paper. It generated on the Pacific Ocean at 0600 UTC on August 20, 2017, and entered the South China Sea at 1800 UTC in less than 24 h. It started to strengthen rapidly after entering the South China Sea with its intensity level changed from tropical storm to strong typhoon within 24 h, and made landfall at Zhuhai city, Guangdong Province at 0500 UTC on August 23, with a central pressure of 940 hPa and a maximum wind speed of 48 km h^-1. The operational forecast provided by TRAMS-v3.0 has a relatively obvious bias of westward track and weak intensity at the early stage (refer to Fig. 3), which has brought uncertainties to the disaster prevention and mitigation before Typhoon Hato makes landfall.

Figure 3.  Composite plots of the track (a1-c1) and V_max intensity (a2-c2) forecasts of Typhoon Hato (2017) from 0000 UTC on August 20 to 1200 UTC on August 23, 2017 by the Test-65L (a), Test-95L (b), and Test-125L (c) models.

Figure 3 shows the composite plots of the track forecasts during the life cycle of Typhoon Hato at 12-hour intervals by the Test-65L, Test-95L, and Test-125L models.The forecast landfalls initialized from 0000UTC on August 20, 2017, to 0000 UTC on August 21, 2017 by the low vertical resolution model (Test-65L) are near eastern Guangdong, which is far from the actual landfall location shown in Fig. 3a1.When the number of vertical levels increases to 95, the track forecast errors decrease, as shown in Fig. 3b1.The highest vertical resolution model Test-125L predicts the exact landfall location and has the smallest track forecast errors (Fig. 3c1).The increase in vertical resolution also improves the intensity forecasts, as shown in Fig. 3a2, 3b2, and 3c2.

There are large differences in the intensity forecasts of Typhoon Hato by TRAMS with different vertical resolutions (e.g., initialized at 0000 UTC on August 20, 2017, as shown by the red curves in Fig. 3a2, Fig. 3b2, and 3c2).As the intensity differences are closely related to inner-core structural changes, it is necessary to compare the warm core structure to see the influence of higher vertical resolution on latent heat release.The warm core structure forecast by the high vertical resolution models of Test-95L and Test-125L, as shown in Fig. 4b and 4c(with a latitude-pressure level cross-section of temperature anomalies), is closer to that of the ECMWF IFS analysis at 0000 UTC on August 23, 2017, as shown in Fig. 4d, than that of Test-65L (Fig. 4a).

Figure 4.  The latitude-pressure level cross-section of temperature anomalies from the spatial mean over (15°N-35°N) at 115.4°E, 113.8°E, 113.3°E, and 114.5°E through the center of Typhoon Hato from the 72-hour forecasts by the Test-65L (a), Test-95L (b), and Test-125L (c) models (initialized from 0000 UTC on August 20, 2017) and the ECMWF analysis valid at the same time at 0000 UTC on August 23, 2017 (d), respectively.

The above results may be understood as follows.Just like the impact of increased horizontal resolution(∆x) on the generation of larger mass convergence (Yau et al.^[47]; Chen et al.^[48]), increased vertical resolution(∆z) would facilitate the generation of larger vertical mass (ρ) convergence and moisture (q) flux convergence $ \text { (i. e., } \frac{\partial \rho w}{\partial z} \text { and } \frac{\partial q w}{\partial z} \text { ) }$ and gridbox saturation in thoselayers.The enhanced vertical mass convergence and moisture flux convergence will drive more vertical flux convergence and latent heating in the inner core, which is favorable for typhoon intensification.

The analyzed wind field forecasts (Fig. 5d) show that the circulation field of Typhoon Hato has obvious asymmetric structural characteristics, and the wind speed on the north side of the typhoon center is much larger than that on the south side.With the increase of vertical resolution (Fig. 5a-5c), the wind speed on the north side of the typhoon rapidly strengthens to more than 21 m s^-1. Especially when the vertical resolution increases to 125 levels (Test-125L), the vertical wind field forecasted by the model is basically close to the real situation.The strengthening of winds on the north side of the typhoon can cause the typhoon path to shift to the west in the way shown in Fig. 6. Applying the gradient wind equation in an asymmetric typhoon and considering equal flow rates at different cross sections between two isobars, we can obtain the relationship between the typhoon center shift and wind speed distribution (Chen and Ding^[49]):

Figure 5.  Same as Fig. 4, but for wind speed.

Figure 6.  Schematic diagram for the effect of typhoon asymmetric wind field on its movement. The solid blue dot is the typhoon center. u and v are the positive components of typhoon wind speed (i.e., easterly and southerly winds), and u' and v' are the negative components. C_x and C_y are the east-west and north-south movement speeds of the typhoon center, respectively. σ is the average radius of the typhoon range. The two black circles indicate different values of isobars.

where u and v are the positive components of typhoon wind speed (i.e., easterly and southerly winds), and u'and v'are the negative components.C_x and C_y are the east-west and north-south movement speeds of the typhoon center, respectively.σ is the average radius of the typhoon range.Ω and R are the angular velocity and radius of the Earth's rotation, respectively.φ is the latitude of the typhoon center.

Since the path of Typhoon Hato is east-west and the latitude of the typhoon center does not vary much, the third term at the right end of Eq.(6) is basically a constant.When the vertical resolution increases, the wind speed component u on the north side of the typhoon increases significantly, and C_x increases as well, leading to an overall shift of the typhoon path to the west, which is thus more realistic (refer to Fig. 3).Therefore, vertical resolution can influence typhoon track forecasting through changes in typhoon structure.

The improvement of TC forecasts brought by higher vertical resolution is evaluated with high impact and landfalling storms during the typhoon seasons in2016 and 2017 (Table 1).

Figure 7 shows the mean forecast errors of the track and the mean longitudinal and latitudinal biases of the intensity forecast for the high-impact TCs by the 65-, 95-and 125-level TRAMS regional models and the global ECMWF IFS model.As shown in Fig. 7a, the track forecast errors of the 125-level TRAMS model are slightly smaller than those of the 95-level model.Both are smaller than the errors of the 65-level TRAMS model at most lead times, although the errors are larger than the errors of forecast by the ECMWF IFS.During the 2017 typhoon season, the track forecast errors of TRAMS-125L are smaller than the ECMWF IFS errors at lead times from 36 hours to 66 hours (not shown).However, the forecasts during the 2016 typhoon season by the TRAMS models are much worse than those of the ECMWF IFS; therefore, the performance of TRAMS-125L is not as good as that of ECMWF IFS for storms spanning two typhoon seasons.The mean longitudinal and latitudinal biases in the tracks are shown in Fig. 7b and 7c, respectively.The differences in the latitudinal biases among the three TRAMS models are smaller.For the longitudinal biases, the 95-and 125-level models have smaller biases than that of the 65-level TRAMS model, which is consistent with the mean forecast errors.Thus, the longitudinal biases are the main causes of the mean track errors.

Figure 7.  The (a) mean error in the track (km), (b) mean longitudinal bias of the track (°), and (c) mean latitudinal bias of the track (°) during the typhoon seasons in 2016 and 2017 by the Test-65L (red), Test-95L (green), Test-125L (blue), and ECMWF IFS (cyan) models. The number located at the bottom of Fig. 7a indicates the number of samples used to count the error.

Figure 8 compares the mean errors and biases of the V_max and P_min intensity forecasts from the TRAMS models (with different vertical resolutions) and the ECMWF IFS global model during the typhoon seasons in 2016 and 2017. The ECMWF IFS global model shows a better performance for both the V_max and P_min intensity errors at the first 24-hour lead time, which is due to the spin-up/down when the TRAMS models use the global ECMWF analysis as the initial condition. For most longer lead times, the TRAMS models have smaller mean intensity errors than that of the ECMWF IFS. In Fig. 8a and 8b, the V_max and P_min mean forecast errors of the 125-level TRAMS model are slightly smaller than those of the 95-level model, and both are smaller than the errors of the 65-level TRAMS model at lead times of 36-60 hours. Thus, increasing the vertical resolution improves the intensity forecasts of TCs at those lead times.

Figure 8.  The (a) mean errors and (b) bias of V_max intensity (m s^-1) and (c) mean errors and (d) bias of P_min intensity (hPa) during the typhoon seasons in 2016 and 2017 by the Test-65L (red), Test-95L (green), Test-125L (blue), and ECMWF IFS (cyan) models. The number located at the bottom of Fig. 8c indicates the number of samples used to count the error.

This paper provides a preliminary assessment of the effect of increasing the vertical resolution on the potential improvement of typhoon forecasts in the TRAMS-v3.0 model. A case study of Typhoon Hato (2017) shows obvious benefits of increasing the vertical resolution. With water vapor convergence and vertical transport increased, the high vertical resolution model can more accurately simulate the rapid strengthening process. The improvement in track forecasting mainly comes from more accurate simulation of the asymmetric structure of typhoons. The improvement of high vertical resolution is validated by using the batch test with multiple cases during the 2016-2017 typhoon seasons.

As can be seen in this paper, the typhoon forecasts of the TRAMS model become consistent with the observations only when the vertical resolution of 125 layers is reached. However, running the TRAMS model with 125 levels in real operation still faces difficulties in terms of computational efficiency. Our test results show that the integration time almost doubles when the number of vertical layers is increased from 65 to 125, which is obviously not able to meet the business timeliness requirements. According to our study, the influence of vertical resolution on typhoon forecasts is mainly limited to the troposphere, while we increase the resolution at all heights in the vertical distribution setting (c. f., Fig. 2a), which leads to an unnecessary computational burden to some extent. McTaggart-Cowan et al. ^[50] proposed an upper-boundary nesting technique to reduce this computational cost in limited area models. This technique allows information from high-topped driving grids to influence the evolution of a lower-topped model integration in a manner analogous to the treatment of lateral boundary conditions. It offers the possibility of achieving high vertical resolution in the TRAMS model without increasing computational burden. This is one of the work we will carry out in the next step.

It has been pointed out in the introduction that vertical resolution can affect model forecasts through both dynamical and physical processes, while the degree of influence and interaction mechanism of different model components are still not clear at present. With the model forecast tendency decomposed into the dynamical and physical components, the variation of the different component tendency forecasts can provide more insight into the specific effects of vertical resolution, and such studies can also provide a basis for the diagnosis of model parameterization schemes. Recently, Zhang et al. ^[51] developed a tendency output module for the TRAMS-v3.0 model for both the dynamical and physical processes, and preliminarily analyzed its simulation of the heat balance in the South China Sea and its surrounding region. This work provides a basis for further analysis of the impact of vertical resolution on model forecasts later.

Although we have also noted the sensitivity of the model first layer height setting to the simulation of typhoon near-surface flux, the current research in this area is still mainly at the stage of phenomenological analysis (Wei et al. ^[52]; Zängl et al. ^[53]; Shin et al. ^[54]; Ma et al. ^[6]; Yang et al. ^[55]). The physical mechanism behind it remains unclear, and in later studies we will try to answer this question as well.