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  • View in gallery
    Fig. 1.

    (a) The simulated wind at 10-m height (vectors; m s−1), overlapped with wind speed (shaded; m s−1) at 0000 UTC 6 Aug 2015 without cycling for Typhoon Soudelor; (b) as in (a), but at 51 cycles; (c) as in (a), but at 99 cycles; (d) as in (a), but for surface pressure (contours at an interval of 4 hPa) and temperature at 2-m height (shaded; K); (e) as in (d), but at 51 cycles; and (f) as in (d), but at 99 cycles. The mesoscale reference physics suite is employed in the experiment with the 60–15-km mesh.

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    Fig. 2.

    (a) The simulated wind speed at 10-m height (shaded; m s−1), overlapped with vertical velocity (contours at an interval of 0.4 m s−1), at the initial time of 0000 UTC 6 Aug 2015 for Typhoon Soudelor at the latitudinal cross section through the typhoon center at different cycles of (b) 40, (c) 51, and (d) 99. (e)–(h) As in (a)–(d), respectively, but at the longitudinal cross section. The mesoscale reference physics suite is employed in the experiment with the 60–15-km mesh. The best track data give 938 hPa for central sea level pressure and 45 m s−1 for maximum wind speed at the initial time.

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    Fig. 3.

    (a) The simulated tracks for Typhoon Soudelor for CTL (no cycling) in red, V-match (at 51 cycles) in blue, and P-match (at 99 cycles) in green and the CWB best track in black from 0000 UTC 6 Aug 2015 (0 forecast hours) to 0000 UTC 9 Aug 2015 (72 forecast hours). (b) As in (a), but for the track errors with time for CTL, V-match, and P-match; (c) as in (b), but for CSLP (hPa); and (d) as in (b), but for MWS (m s−1). The mesoscale reference physics suite is employed in the experiments with the 60–15-km mesh.

  • View in gallery
    Fig. 4.

    As in Fig. 3, but for Typhoon Megi starting from 0000 UTC 25 Sep 2016. V-match is at 35 cycles, and P-match is at 40 cycles.

  • View in gallery
    Fig. 5.

    As in Fig. 3, but for the track forecast of Typhoon Maysak starting from 0000 UTC 30 Aug 2020. V-match is at 12 cycles, and P-match is at 10 cycles.

  • View in gallery
    Fig. 6.

    (a) The simulated tracks for Typhoon Mitag with the 60–15-km mesh for CTL (initial with no cycling in red) P-match (green), and V-match (blue) using the DVI and DVIb with P-match (purple) and V-match (pink) and the CWB best track (black) from 0000 UTC 29 Sep 2019; (b) as in (a), but for track errors; and (c) as in (b), but for CSLP (hPa). (d)–(f) As in (a)–(c), respectively, but for Typhoon Lekima from 0000 UTC 6 Aug 2019. The matched cycle is indicated in the legend of the experiment. In (a)–(f), the mesoscale reference physics suite is employed.

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    Fig. 7.

    The simulated wind for Typhoon Soudelor at 10-m height (vectors; m s−1) and surface pressure (contours at an interval of 4 hPa), overlapped with wind speed (shaded; m s−1). (a) Initial analysis (no cycling) at 1200 UTC 7 Aug 2015; (b) as in (a), but at 26 cycles (P-match); (c) as in (a), but for azimuthal-mean tangential wind; and (d) as in (c), but at 26 cycles. The yellow dashed cycle in (b) indicates the radius of vortex updating (600 km). The mesoscale reference physics suite is employed in the experiments with the 60–15–3-km mesh.

  • View in gallery
    Fig. 8.

    The absolute forecast errors in 6-h bins from 0–72 h for all 16 typhoon cases (18 runs) in 2015–20 using 60–15-km resolution in Table 2 for CTL (black), V-match (blue), and P-match (red). (a) Track error (km) and (b) MWS intensity error (m s−1). The absolute forecast error is the absolute deviation from the best track data. The arrows above the bars indicate that the DVI performance is better than that of CTL by passing the Student’s t test of 95% confidence level. Each bin is calculated in the interval of 6 h before the analysis time, except for the 0-h bin that is the performance at the initial time.

  • View in gallery
    Fig. 9.

    (a) The forecast along-track (solid) and cross-track errors (dashed) from 0 to 96 h for all 16 typhoon cases (17 runs) in 2015–20 for CTL (red), V-match (green), and P-match (cyan). (b) As in (a), but CTL (red) and V-match (green) for the bias of forecasted Vmax. The numbers in the bottom indicate the total of homogeneous runs.

  • View in gallery
    Fig. 10.

    The daily forecast errors of track (km; blue), Vmax (m s−1; red), and CSLP (hPa; purple) summarized for four typhoon cases (Soudelor, Megi, Mitag, and Lekima) using V-match and P-match with (a) the M-suite and (b) the C-suite. There are 10 runs at 60–15-km resolution for comparisons on each suite. The forecast errors are relative to those of the counterpart (control experiment) without the DVI compared to the best track data, and positive and negative values indicate better and worse performances, respectively, than CTL.

  • View in gallery
    Fig. 11.

    Azimuthal-mean potential vorticity (shaded colors; PVU) in the radius–height cross section for CTL for Typhoon Lekima at (a) 0 h, (b), 12 h, (c), 24 h, and (d) 48 h. (e)–(h) As in (a)–(d), respectively, but for V-match. Both forecasts use the M-suite and 60–15-km resolution. The wind vectors indicate the radial and vertical wind components (m s−1) with the reference vector given at the bottom-right corner. The green line shows the radius of maximum horizontal wind speed.

  • View in gallery
    Fig. 12.

    (a) Evolution of tropospheric potential vorticity (PVU) averaged in a circle radius of 0°–1° and between 0- and 12-km height from the typhoon center in 0–72 h for Typhoon Megi. (b) As in (a), but for Vmax (m s−1). (c),(d) As in (a) and (b), respectively, but for Typhoon Lekima. (e),(f) As in (a) and (b), respectively, but for Typhoon Mitag. The dashed and solid lines indicate the forecasts for CTL and V-match, respectively. Both forecasts use the M-suite and 60–15-km resolution.

  • View in gallery
    Fig. A1.

    Updating the vortex using inverse distance weighted interpolation (IDWP). The original vortex within a solid circle at time t0 moves to a new position with the model-integrated vortex (marked by the dashed circle) at t1. Here, rj is the position vector of one cell center from the center of the original vortex, which is mapped into the same vector, but relative to the center of the new vortex. The model value at rj is obtained with IDWP using all the values at ri, where i is the index of a cell within the specified radius of interpolation R (marked by the dotted circle). Relocation can be combined when the best track vortex center is used instead to replace the vortex center at time t0.

  • View in gallery
    Fig. A2.

    Edge-normal wind reconstruction. The zonal and meridional components of the wind at the center of a cell, given by Ux and Uy with corresponding unit vectors ex and ey, contribute velocity components normal to an edge of the cell u (red vectors). Here, g is the unit vector normal to the edge. The total normal wind velocity at the edge is the average of the contributions from both cells that share the edge.

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Typhoon Forecasts with Dynamic Vortex Initialization Using an Unstructured Mesh Global Model

Ching-Yuang HuangaDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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Jia-Yang LinaDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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William C. SkamarockbNational Center for Atmospheric Research, Boulder, Colorado

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Shu-Ya ChencGPS Science and Application Research Center, National Central University, Taoyuan, Taiwan

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Abstract

A dynamical vortex initialization (DVI) scheme is implemented on unstructured meshes for the global model MPAS for typhoon forecasts. The DVI extracts the departure vortex within a specified radius of the vortex center and implants this vortex at the observed vortex location in continuously cycled 1-h integrations of the model. The cycling integration is stopped when either the simulated central sea level pressure or maximum wind speed of the typhoon has reached the value in the best track data, denoted as P-match or V-match, respectively. The DVI may spin up the initial vortex with a more contracting eyewall, but still keeping the same size of the outer vortex. Forecasts for 16 typhoons over the western North Pacific in 2015–20 are investigated. Predictions from the experiments with the 60–15-km variable-resolution MPAS mesh show that both P-match and V-match significantly improve the track forecasts, where V-match mostly requires less cycle runs than P-match. Cycling results with P-match or V-match are also dependent on the choice of physics suites within MPAS. Positive impacts are larger for V-match than P-match using the mesoscale reference physics suite, with significantly improved track forecasts and earlier intensity forecasts. Intensity differences resulting from the DVI have gradually decreased with forecast time, which are closely correlated to the differences in the averaged tropospheric potential vorticity of the inner vortex. The DVI with the 60–15–3-km variable-resolution mesh also works well and improves intensity forecasts. The DVI can also help produce asymmetric structures and spin up inner vortex cores for typhoons near high topography, which leads to improved intensity forecasts.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ching-Yuang Huang, hcy@atm.ncu.edu.tw

Abstract

A dynamical vortex initialization (DVI) scheme is implemented on unstructured meshes for the global model MPAS for typhoon forecasts. The DVI extracts the departure vortex within a specified radius of the vortex center and implants this vortex at the observed vortex location in continuously cycled 1-h integrations of the model. The cycling integration is stopped when either the simulated central sea level pressure or maximum wind speed of the typhoon has reached the value in the best track data, denoted as P-match or V-match, respectively. The DVI may spin up the initial vortex with a more contracting eyewall, but still keeping the same size of the outer vortex. Forecasts for 16 typhoons over the western North Pacific in 2015–20 are investigated. Predictions from the experiments with the 60–15-km variable-resolution MPAS mesh show that both P-match and V-match significantly improve the track forecasts, where V-match mostly requires less cycle runs than P-match. Cycling results with P-match or V-match are also dependent on the choice of physics suites within MPAS. Positive impacts are larger for V-match than P-match using the mesoscale reference physics suite, with significantly improved track forecasts and earlier intensity forecasts. Intensity differences resulting from the DVI have gradually decreased with forecast time, which are closely correlated to the differences in the averaged tropospheric potential vorticity of the inner vortex. The DVI with the 60–15–3-km variable-resolution mesh also works well and improves intensity forecasts. The DVI can also help produce asymmetric structures and spin up inner vortex cores for typhoons near high topography, which leads to improved intensity forecasts.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ching-Yuang Huang, hcy@atm.ncu.edu.tw

1. Introduction

The performance of tropical cyclone (TC) prediction relies heavily on model initial conditions. Uncertainties exist in the initial conditions of forecast models in spite of the use of comprehensive data assimilation methods with various observations to improve initial analyses. Over the open ocean where TCs form and develop, the observations, mostly from satellites, are typically scarce and do not provide sufficient information to resolve the TC core structure in global analyses even with relatively high resolution. For the global analyses, the initial vortices associated with TCs are often too weak compared to the best track data from real-time operational estimation. Although intense TC core structures can be well resolved using data assimilation with airborne Doppler radar observations, these are typically available only in special field experiments and are case-dependent (e.g., Zhang and Weng 2015).

To better represent initial TC vortices, vortex initialization (VI), either through regeneration or implantation, is needed for numerical modeling. There are several ways to reach such a goal of VI and they have been described in detail in the literature (e.g., Van Nguyen and Chen 2011; Cha and Wang 2013). In brief, VI can be divided into two approaches, static vortex initialization (SVI) and dynamic vortex initialization (DVI). For SVI, empirical functions for surface pressure and tangential wind profiles (e.g., Fujita 1952; Holland 1980) usually are specified with the central sea level pressure and radius of maximum wind speed from the best track data used in solving the nonlinear balance equation (e.g., Davis and Low-Nam 2001). In spite of its simplicity and without having asymmetric components and vertical motions associated with TCs, SVI effectively produces more intense initial vortices that replace the original vortices, and it has often been employed in regional models (e.g., Davis and Low-Nam 2001; Kwon and Cheong 2010; Rappin et al. 2013). Kurihara et al. (1993) developed a DVI method to include both axisymmetric and asymmetric components for TCs, the former produced from integrating an axisymmetric version of the Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model and the latter from integrating the nondivergent barotropic vorticity equation on a beta-plane initialized with the former axisymmetric flow. Although the initial vortices are not completely produced by the full primitive equations forecast model, the integration of the simplified model is also a type of DVI. Use of DVI has greatly improved both TC track and intensity predictions of GFDL hurricane model (e.g., Kurihara et al. 1998).

Another approach that utilizes model dynamics and physics to generate a consistent initial vortex is to combine data assimilation with empirical vortex parameters from the best track data. The so-called bogus data assimilation (BDA) method is one specific type of DVI and it can be applied to different data assimilation systems. Using the adjoint of the forecast model, an initial vortex consisting of asymmetric components can be generated by the minimization of the cost function with the bogus observations (e.g., Xiao et al. 2000; Zou and Xiao 2000; Pu and Braun 2001; Park and Zou 2004). This data assimilation-based approach uses four-dimensional variational (4DVAR) data assimilation (DA) with a specified assimilation time window to consistently digest the prescribed vortex, and it offers a great advantage for vertical motions and moisture adjustment over SVI (Zou and Xiao 2000). Using various variations of BDA, significant improvements on both TC track and intensity forecasts have been shown in a number of studies (e.g., Zou and Xiao 2000; Xiao et al. 2000; Pu and Braun 2001; Wu et al. 2006; Zhao et al. 2007; Huang et al. 2011). However, the BDA approach based on 4DVAR is still not optimal as the adjoint model is usually a simplified version of the full-physics forecast model and the use of a lengthy time window of assimilation is very time-consuming. Recently, data assimilation based on ensemble Kalman filters can also effectively produce an initial spunup vortex from assimilation of a bogus vortex or real in situ observations and has shown remarkable improvement on TC prediction (e.g., Chen and Snyder 2007; Zhang et al. 2009; Wu et al. 2010, 2012; Kleist 2011; Yang et al. 2013; Kunii 2015). This is also a type of DVI as the forecast model is integrated in each DA cycle to obtain correlations among forecasts of ensemble members and thus corrections to the initial analysis of the TC as well as its environment. Using this approach, a larger number of ensemble members may improve the correlations. Specification of bogus vortex observations and real in situ observations are also critical to the performance of the ensemble correlations with respect to the initial TC analysis. In general, ensemble data assimilation with various observations not only helps to improve the initial vortex analysis but also reduces biases of the environmental background associated with the vortex.

A simpler approach to generating a more representative initial TC vortex, compared to the more complex BDA, is to utilize a continuously cycling integration of the forecast model. After each cycle run within a certain time interval, e.g., one hour, the forecasted updated vortex is moved back to its original position at the start of the forecast. By continuously updating the vortex in the cycle runs, a more intense TC can be obtained possessing both axisymmetric and asymmetric components and vertical motions that often are too weak in global model analysis. Under favorable environmental conditions, TCs may intensify in response to model physics and dynamics. Iterative model integration may be stopped within several tens of cycle runs when either the simulated minimum central sea level pressure or maximum near-surface wind of the typhoon has reached the best track intensity, referred to P-match or V-match, respectively. Many experiments have shown that no quasi-stationary internal vortex can be attained as the continuously updated vortex keeps evolving (Van Nguyen and Chen 2011; Cha and Wang 2013). Stopping the cycled integrations when the TC intensity matches the best track intensity appears to be a reasonable choice, although either P-match or V-match can be chosen. This choice may not be optimal for maximizing positive impacts because the best track intensity is only an estimate. To hasten TC spinup, the best track data and empirical vortex observations, e.g., surface pressure or warm core structure, may also be nudged (e.g., Van Nguyen and Chen 2011, 2014).

Both typhoon track and intensity predictions have been further improved using the regional Weather Research and Forecasting (WRF) Model with DVI (e.g., Van Nguyen and Chen 2011, 2014; Cha and Wang 2013; Hendricks et al. 2013; Chen et al. 2014; Liu and Tan 2016; Liu et al. 2018) as compared to SVI. Van Nguyen and Chen (2014) found that the typhoon track and intensity predictions with DVI are considerably influenced by use of cloud microphysics schemes and cumulus parameterizations, while the prescribed auxiliary surface observations have little effect on the final updated vortices and ensuing forecasts. Based on a number of numerical experiments, DVI seems to give larger positive impacts on TC intensity prediction than on TC track prediction (Cha and Wang 2013). Indeed, minimal negative impact is induced by DVI on TC intensity prediction for various typhoon cases (e.g., Cha and Wang 2013; Van Nguyen and Chen 2014; Liu et al. 2018).

Use of higher resolution would enable global models to more reasonably capture TC core structures. Local enhancement of the horizontal resolution by stretching or nesting grids has further increased the capability of global models to predict TC intensity (e.g., Zarzycki and Jablonowski 2015; Hazelton et al. 2018; Chen et al. 2019). In particular, the high-resolution region of global models employing unstructured meshes (mostly hexagonal) can be focused on the TC regions (e.g., Park et al. 2014; Huang et al. 2017, 2019). For example, the multiple-resolution global model, i.e., the Model for Prediction Across Scales (MPAS), has been applied to simulate typhoons with 3-km resolution and is capable of simulating the development of typhoons in response to the effects of high topography (Huang et al. 2019). MPAS uses an unstructured centroidal Voronoi mesh that is convenient for employing variable horizontal resolution which gradually increases in specific regions of interest. Use of a 60–15–3-km variable-resolution mesh has enabled MPAS to improve typhoon intensity forecasts (Huang et al. 2019). The highest 3-km resolution region in that study is centered over Taiwan and covers the frequent paths of the typhoons near this region. With such variable-resolution, MPAS is able to demonstrate skill commensurable to that of multiply-nested regional models like WRF. However, there is currently no DVI implementation for MPAS nor for any other unstructured mesh models of which we are aware. In this study, we implement an unstructured-mesh DVI scheme for MPAS and evaluate MPAS performance for typhoon prediction using it. The DVI scheme can also be applied to typhoons near high topography. We investigate the relative impacts of cycled runs using P-match or V-match criteria, as well as investigating model performance with different physics suites.

The paper is organized as follows. The model description and configurations of the global model MPAS together with the DVI are given in section 2. The MPAS model performances for track and intensity predictions with and without the DVI are illustrated for several typhoons in section 3. The sensitivity of the DVI to different cycling integration methods is also tested for several typhoon cases in this section. The application of DVI to typhoons near significant topography and model performance in these regimes are given in section 4. The comparison between the performances with P-match and V-match is based on forecasts of 16 typhoons in 2015–20. Model performances with P-match or V-match, different physical suites, as well as enhanced model resolution are discussed in section 5. Vortex analyses are also provided to explain the forecast intensity differences resulting from the DVI. Finally, conclusions are given in section 6.

2. Model and experimental configurations

a. The MPAS model

The global model used in this study is MPAS-Atmosphere Version 5.1 developed at NCAR (Skamarock et al. 2012). MPAS has two suites of physics schemes, the mesoscale-reference suite and the convection-permitting suite, in which different physical parameterization schemes are combined (see Table 1). For all the experiments in this study, the model initial conditions were taken from the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System (GDAS) Final Analysis Data (0.25° × 0.25°) that have 31 vertical levels with a top at 1 hPa. There are 41 vertical levels with a model top of 30-km height in MPAS forecasts, where 19 levels are below 10-km height for the troposphere and 7 levels below 1-km height for the planetary boundary layer. The sea surface temperature (SST) in the MPAS experiments is from the GDAS dataset and is kept constant during the forecast.

Table 1

Physical parameterization schemes contained in the physics suites used in numerical experiments. Abbreviations of the physics schemes: Grell–Freitas: Grell–Freitas convective cumulus parameterization (Grell and Freitas 2014), New-Tiedtke: New Tiedtke convective cumulus parameterization (Zhang and Wang 2017), Thompson: Cloud microphysics scheme with prognostic ice, snow, graupel processes and rain number concentration (Thompson et al. 2008), Noah: Noah land surface model (Niu et al. 2011), MYNN: Mellor–Yamada–Nakanishi–Niino Level-3 PBL parameterization (Nakanishi and Niino 2009), YSU: Yonsei University planetary boundary layer parameterization (Hong et al. 2006), RRTMG: Rapid Radiative Transfer Model for General Circulation Models longwave (LW) and shortwave (SW) schemes (Iacono et al. 2008), Xu–Randall: Xu–Randall cloud fraction parameterization (Xu and Randall 1996), and WSM6: single-moment 6-class microphysics scheme of the Weather Research and Forecasting (WRF) Model (Hong and Lim 2006).

Table 1

b. Dynamic vortex initialization

The DVI is applied on the native MPAS unstructured mesh and consists of inner and outer steps. The inner step is the integration of the model over a specific time period. After completing this integration, the departure (original) vortex within a radius of Rυ is replaced with the arrival (updated) vortex using interpolation (as depicted in the appendix, see Fig. A1). This state is used for the next cycle. For scalars defined at cell centers, the interpolation formulas defined in the appendix equations, Eqs. (A1) and (A2), are used for the remapping. The MPAS prognostic horizontal wind velocity is defined as the velocity normal to the edge of a cell. These cell-edge velocities are used to diagnose zonal and meridional velocity components at each cell center using the appendix equation, Eq. (A3), to define the components. These zonal and meridional components are then interpolated using the appendix equation, Eq. (A4), to recover the new cell-edge velocities (as depicted in the appendix, see Fig. A2). The scalar interpolation uses a weighted sum of nearby values where the weights are proportional to the square of the inverse distance from the interpolation point. The radius of the circular region that determines the points used in the interpolation is chosen as 20 km for 60–15-km resolution and 5 km for 60–15–3-km resolution. The vortex replacement is combined with relocation fit to the best track position at each cycle. The size of Rυ for the updated vortex usually is set to 600 km to cover the original vortex. All the model prognostic variables in the original vortex are replaced so that wind, temperature, pressure, moisture and cloud hydrometeors are updated after each cycle. This process updates both axisymmetric as well as asymmetric components of the model variables in the vortex.

The outer step of the vortex initialization involves iterating the model integration. The forward-in-time cycle runs are conducted with a 1-h interval in this study, which is similar to Van Nguyen and Chen (2011). For different typhoons, cycling integration usually may be stopped within several tens of cycle runs when either the simulated minimum sea level pressure, i.e., central sea level pressure (CSLP), or near-surface maximum wind speed (MWS) of the typhoon has reached the value in the best track data, denoted as P-match or V-match, respectively. The current DVI does not prescribe a sea level pressure field or a near-surface wind field for nudging the typhoon circulation during the cycled integration. Thus, the intensifying vortex produced by the DVI will not have a fixed size for, e.g., the 34- or 50-kt winds (1 kt ≈ 0.51 m s−1). The computing cost for each match essentially depends on the total of cycle runs required for the convergence with the match. Note that CSLP and MWS are correlated as both are often estimated from satellite observations. As shown later, V-match is satisfied earlier than P-match in most of the experiments. Usually, only the cycle run at P-match is selected for initial conditions (e.g., Van Nguyen and Chen 2011, 2014). Cha and Wang (2013) adopted the V-match to stop the cycling integration. In this study, we will compare the performances of the DVI with both V-match and P-match since the best track wind and pressure intensity are available in real time, even with some uncertainties. The DVI will produce a warm startup of the vortex for the forecast run since all the prognostic model variables are updated from the cycle runs. This DVI is rather simple and easy to implement into a numerical model.

c. Cycling experiments with limitations on updating the vortex

Cycling experiments conducted in this study are listed in Table 2. The 60–15–3-km variable-resolution mesh centered at Taiwan is identical to that shown in Huang et al. (2019, Fig. 1). In total, 16 typhoon cases, chosen based on the important impacts they had on the Southeast and East Asia regions are investigated with different initialization times and physics suites. In this study, sensitivities of the DVI performance to match criteria, physics schemes, and horizontal resolution are examined. Experiments with TCs closer to mountain terrain are remarked as “near terrain.” Liu et al. (2018) used a spunup axisymmetric vortex generated over open ocean to replace the axisymmetric part of the vortex over the terrain. TCs across topography are not considered in this study because, over high topography, the internal vortex core becomes significantly affected with largely asymmetric flow and is typically not well reconstructed by cycling integration. TCs approaching to the mountain terrain can still be spun up using DVI, specifically when the vortex core as well as the primary outer cyclonic circulation are not greatly affected by the topographic effect. These near-terrain experiments are intended to show the sensitivity of DVI to the topographic effect and whether the forecasts will be influenced by this initial imbalance.

Fig. 1.
Fig. 1.

(a) The simulated wind at 10-m height (vectors; m s−1), overlapped with wind speed (shaded; m s−1) at 0000 UTC 6 Aug 2015 without cycling for Typhoon Soudelor; (b) as in (a), but at 51 cycles; (c) as in (a), but at 99 cycles; (d) as in (a), but for surface pressure (contours at an interval of 4 hPa) and temperature at 2-m height (shaded; K); (e) as in (d), but at 51 cycles; and (f) as in (d), but at 99 cycles. The mesoscale reference physics suite is employed in the experiment with the 60–15-km mesh.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

Table 2

Forecast experiments with different horizontal meshes (denoted resolution here) and with the mesoscale reference physics suite. The radius of vortex updating Rυ is set to 600 km for all the experiments, except for one experiment for Nesat using 400 km. The match (denoted by “V” or “P”) refers to V-match or P-match, respectively, with the required cycle runs included in the parentheses, where character “X” indicates no cycle needed at the initial time.

Table 2

3. Forecasts of typhoons away from topography

a. Sensitivity on cycling numbers

Since the TC circulation is changing during the cycling, we first examine how the vortex and environmental flow are evolving at different points in the cycling as the DVI scheme is performed using the unstructured hexagonal meshes. Figure 1 shows the simulated near-surface wind, surface temperature and pressure of Typhoon Soudelor at the initial time (0000 UTC 6 August 2015) without cycling, and after 51 and 99 cycles. The radius of vortex updating Rυ is 600 km for Typhoon Soudelor. The mesoscale reference physics suite (M-suite, hereafter) is employed in the experiments with the 60–15-km mesh spacing. The typhoon center is defined as the position of minimum sea level pressure in the typhoon circulation. The internal vortex core has intensified significantly at 51 cycles (Fig. 1b) with an enlarged core size also evident in the pressure field (Fig. 1e) in comparison with the initial wind, temperature and pressure fields (Figs. 1a,d). Both TC wind and pressure fields further intensify through 99 cycles (Figs. 1c,f) and there are no detectable differences in the peripheral regions of the updated vortex in its environment. Such very small differences result from the use of a large Rυ in updating the vortex. The use of a circular region for vortex relocation and the use of a large Rυ help to smooth discontinuities near the vortex boundary produced in the cycling process. The size of Rυ can be gradually reduced within the cycled integrations, but we do not find noticeable changes when using a gradual reduction of Rυ (figures not shown).

Figure 2 depicts the evolution of the horizontal wind speed and vertical velocity at zonal and meridional cross sections through the vortex center at 0, 40, 51 and 99 cycles. The vertical velocity is assumed to be zero in the MPAS initialization (Figs. 2a,e). At the initial time, the vortex core without cycling is smaller and rather weak with an initial wind intensity of about 35 m s−1 only. The horizontal wind speed of the vortex is greatly intensified at 40 cycles (Figs. 2b,f) and further increased at 51 cycles (Figs. 2c,g), with a well-developed eyewall with a MWS radius of about 80 km; this is, however, much larger than the best track MWS radius [the Central Weather Bureau (CWB) in Taiwan reports a radius of 80 km for the wind speed of 50 kt at this initial time]. The wind and updraft intensities of the eyewall, however, are not quasi-steady as seen, comparing results at 70 cycles (figures not shown) and 99 cycles (Figs. 2d,h). Thus, the continuously cycling integration remains stable but may not lead to a quasi-steady TC given the fixed large-scale environment. The azimuthal-mean tangential wind of the vortex exhibits only small changes after 51 cycles when the simulated MWS catches the value in the best track data (figures not shown). This figure also indicates that the DVI may not always force the vortex toward the best track vortex. In this study, we have not applied a forcing term to help spin up the vortex with a constraint on the RMW. Dynamically, the vortex may not persistently develop with cycled integrations under some specific environments.

Fig. 2.
Fig. 2.

(a) The simulated wind speed at 10-m height (shaded; m s−1), overlapped with vertical velocity (contours at an interval of 0.4 m s−1), at the initial time of 0000 UTC 6 Aug 2015 for Typhoon Soudelor at the latitudinal cross section through the typhoon center at different cycles of (b) 40, (c) 51, and (d) 99. (e)–(h) As in (a)–(d), respectively, but at the longitudinal cross section. The mesoscale reference physics suite is employed in the experiment with the 60–15-km mesh. The best track data give 938 hPa for central sea level pressure and 45 m s−1 for maximum wind speed at the initial time.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

b. Experimental results with 60–15-km resolution

Figure 3 shows the time evolutions of the simulated track, track errors, CSLP and MWS for Typhoon Soudelor without the DVI (denoted CTL hereafter), V-match, and P-match. The cycling integration matches the MWS and CSLP of the best track data (from CWB) at 51 cycles (V-match) and 99 cycles (P-match), respectively. The tracks for CTL and both matches are well predicted (Fig. 3a), in spite of the fact that both matches begin to display larger track errors after the first day of integration (Fig. 3b). At 72 h (0000 UTC 9 August 2015), the track errors for V-match and P-match are about 120 km and 60 km, respectively, which are considerably less than 200 km, the current operational prediction average track error at CWB. P-match obtains the same CSLP of 938 hPa at the initial time (0000 UTC 6 August 2015), 2 hPa stronger than V-match, and much stronger than CTL (955 hPa) (Fig. 3c). Both matches provide the MWS of about 48 m s−1, which is slightly over the best track wind intensity (45 m s−1) and much stronger than that for CTL (35 m s−1). However, the cycling integration needs 99 cycles in order to reach the P-match. CSLP for CTL gradually intensifies and is close to the values of both matches that do not further intensify, approaching the observed deepening at the early stage. Indeed, the CSLP values for CTL and both matches are quite close and exhibit similar trends as the observed CSLP after about 36 h (1200 UTC 7 August 2015). Similar performances are also found in MWS for the three experiments (Fig. 3d). There is no particular advantage of P-match over V-match in these forecasts.

Fig. 3.
Fig. 3.

(a) The simulated tracks for Typhoon Soudelor for CTL (no cycling) in red, V-match (at 51 cycles) in blue, and P-match (at 99 cycles) in green and the CWB best track in black from 0000 UTC 6 Aug 2015 (0 forecast hours) to 0000 UTC 9 Aug 2015 (72 forecast hours). (b) As in (a), but for the track errors with time for CTL, V-match, and P-match; (c) as in (b), but for CSLP (hPa); and (d) as in (b), but for MWS (m s−1). The mesoscale reference physics suite is employed in the experiments with the 60–15-km mesh.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

Typhoon Megi (2016) is similar to Typhoon Soudelor in terms of track evolution. The predicted tracks for all the three experiments (CTL, V-match, and P-match) using the M-suite are similar with track errors of about 240 km at 72 h, as seen in Fig. 4. The impacts on track prediction from both matches are mixed (Figs. 4a,b), but the track for CTL appears to be more southward-biased near and after landfall in southeast Taiwan. All three forecast tracks result in significant positive speed bias and result in landfalls 12 h earlier than the best track. Both matches obtain quite consistent CSLP deepening in the first day, but overpredict CSLP in the second and third days. CTL significantly underpredicts both CSLP and MWS in the first three days, owing to the initial large deficiency of about 18 hPa (Fig. 4c). V-match provides the best agreement with the best track data for MWS in the first day (Fig. 4d). All three experiments considerably underpredict both CSLP and MWS after three days (0000 UTC 27 August 2016), which may be attributed to the southward-biased tracks near and after landfall that allow for more interaction of the inner vortex core with the higher central mountains of Taiwan’s topography.

Fig. 4.
Fig. 4.

As in Fig. 3, but for Typhoon Megi starting from 0000 UTC 25 Sep 2016. V-match is at 35 cycles, and P-match is at 40 cycles.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

The DVI impact on the reduction of cross-track errors is illustrated in Fig. 5 for the forecast of Typhoon Maysak starting from 0000 UTC 30 August 2020. V-match is obtained at 12 cycles and P-match is obtained at 10 cycles. The observed track is northward toward Japan and South Korea, in contrast to the previous two typhoons heading west-northwestward for Taiwan. Even though both matches only apply the runs at fewer cycles with vortex intensification of about 10 hPa for CSLP and 8 m s−1 for MWS (not shown), the eastward track deviation for CTL is considerably reduced in days 2 and 3. The largest reduction on track error is about 90 km around 48 h for both matches. However, it was also found that for both matches the typhoons move considerably slower than the observed typhoons after two days.

Fig. 5.
Fig. 5.

As in Fig. 3, but for the track forecast of Typhoon Maysak starting from 0000 UTC 30 Aug 2020. V-match is at 12 cycles, and P-match is at 10 cycles.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

c. Comparisons with backward-time DVI

There are two model integration approaches to spin up the vortex in DVI. The DVI performances shown previously were obtained using the forward-time integration, i.e., from t0 (the initial time) to t0 + 1 h. The forward-time DVI has been used in several studies to improve typhoon forecasts (e.g., Van Nguyen and Chen 2011, 2014; Chen et al. 2014). Alternatively, Cha and Wang (2013) has applied a different model integration from t0 − 6 h to t0 as the best track data are available for these times. The spunup vortex is relocated at t0 to the best track position when the vortex intensity has reached V-match or P-match. The latter method is denoted as DVIb starting with a backward-time integration, which is different from the DVI only in the time window of cycled integrations. For illustration with the devised DVI on unstructured MPAS mesh, it is interesting to compare the performances of DVI and DVIb. We have compared their performances for several typhoons. Figure 6 shows the comparisons between the forecasts with DVI and DVIb for the two typhoons (Mitag and Lekima) in 2019 where the M-suite was employed. The relative impacts on the track and intensity forecasts are mixed and are comparable for both DVI and DVIb. The V-match with the DVIb has the largest track deviation with landfall at the northeastern corner of Taiwan for Mitag (Figs. 7a,b). The DVI gives the underpredicted (weaker) CSLP, while the DVIb produces the overpredicted (stronger) CSLP (Fig. 7c). However, it appears that V-match (4 cycles) with the DVIb gives the weakest CSLP closer to that for CTL (with no cycling). For MWS, the impacts of the DVI and DVIb with different matches are rather mixed (figures not shown). For Lekima, both DVI and DVIb with V-match or P-match give similar tracks in better agreement with the best track than CTL, except for the DVI with the V-match (Figs. 7d,e) showing a larger detour at later times similar to the CTL track. The DVI with the V-match seems to provide slightly more consistent CSLP with the best track data in the first day (Fig. 7f). Note that in this case the cycle difference between the V-match and P-match is only one cycle (with a period of 6 h) for the DVIb, while it takes 8 more cycles from V-match to P-match for the DVI. From the above comparisons, both DVI and DVIb show comparable performance and can be fairly applied to typhoon forecasts with MPAS.

Fig. 6.
Fig. 6.

(a) The simulated tracks for Typhoon Mitag with the 60–15-km mesh for CTL (initial with no cycling in red) P-match (green), and V-match (blue) using the DVI and DVIb with P-match (purple) and V-match (pink) and the CWB best track (black) from 0000 UTC 29 Sep 2019; (b) as in (a), but for track errors; and (c) as in (b), but for CSLP (hPa). (d)–(f) As in (a)–(c), respectively, but for Typhoon Lekima from 0000 UTC 6 Aug 2019. The matched cycle is indicated in the legend of the experiment. In (a)–(f), the mesoscale reference physics suite is employed.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

Fig. 7.
Fig. 7.

The simulated wind for Typhoon Soudelor at 10-m height (vectors; m s−1) and surface pressure (contours at an interval of 4 hPa), overlapped with wind speed (shaded; m s−1). (a) Initial analysis (no cycling) at 1200 UTC 7 Aug 2015; (b) as in (a), but at 26 cycles (P-match); (c) as in (a), but for azimuthal-mean tangential wind; and (d) as in (c), but at 26 cycles. The yellow dashed cycle in (b) indicates the radius of vortex updating (600 km). The mesoscale reference physics suite is employed in the experiments with the 60–15–3-km mesh.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

4. Typhoon forecasts near topography

a. Refinement of DVI near topography

DVI can also be applied to typhoons near topography. Since terrain-following coordinates are used in MPAS, the vortex at arrival near topography will be situated over heights different from the heights at departure. We avoid use of vertical interpolation for the vortex near the topographic regions since updating the departure vortex with such an arrival vortex is more complicated. Instead, all the prognostic variables in the departure vortex remain unchanged when the terrain height at the arrival vortex point is greater than 10 m or the forecast difference at the same location between the two vortices (relative to their centers) is larger than an empirical values of 5 K in temperature or 10 hPa in pressure used in this study. In this way, most of the departure vortex is still updated by the arrival vortex if the departing vortex is not close to the high topography but over plain land. Note that the empirical constraints (10-m terrain height, temperature and pressure forecast differences) are set specifically for the DVI application near topography in this study. As the terrain height constraint is relaxed to be 100 m or higher, the thermodynamics deviation between the arrival vortex and departure vortex grows rapidly with cycle runs leading to unacceptably large noise. We find that the current DVI is only applicable when the vortex center is at least a distance of approximately 2 times the radius of MWS from the mountains. As listed in Table 2, forecasts of four typhoons with centers 250–600 km away from mountain terrain have been conducted with the refined DVI.

b. Experimental results

One example of the DVI impact is for Typhoon Mitag (2019) which was close to the northern Philippines at 0000 UTC 29 September 2019. The radius of vortex updating Rυ is chosen as 600 km so that the outer vortex circulation of Mitag is over Luzon Island. The forecast results for Mitag near topography using CTL, V-match and P-match have been shown in Fig. 6. In general, the forecasted tracks with the M-suite follow the best track quite well, with track deviations less than 120 km over the three days (Fig. 6a). On average, V-match (at 18 cycles) performs best in the track forecast with the smallest errors east of Taiwan, even though CSLP is considerably underpredicted (Fig. 6c). On the other hand, P-match (at 40 cycles) significantly overpredicts CSLP in the first two days.

Another experiment is for Typhoon Soudelor at 1200 UTC 7 August 2015, when it is moving closer to Taiwan’s topography and possesses a strong vortex core. We choose this time for a more stringent test of the DVI. Figure 7 shows the near-surface wind and surface pressure for CTL and P-match (at 26 cycles) with 60–15–3-km resolution at this initial time. A radius of 600 km is chosen for Rυ to update the vortex. For reference, V-match is obtained earlier at 22 cycles (not shown). The vortex core for P-match has been significantly intensified with eyewall contraction. Disturbances (noise) in the pressure field near Taiwan’s topography and south of the vortex center are induced by the DVI, as is a small discontinuity in wind speed northeast of the northern Philippines (Fig. 7b). The unsmooth development of the outer vortex circulation may be induced by the propagating effects of the differences between the arrival vortex and departure vortex and is not constrained to regions downstream of the mountain terrain. However, the primary vortex structure is well preserved for P-match with a shrinking and upward developing eyewall, as indicated by the associated azimuthal-mean tangential wind fields (Figs. 7c,d). It appears that there are no sizable negative effects of the initial disturbances generated by the DVI on the forecasts. The track and MWS intensity forecasts with the DVI show better performances than CTL (without the DVI) (figures not shown).

5. Forecast results for extended periods and discussion

a. Forecast impacts of the typhoons in 2015–20 (V-match versus P-match)

Figure 8 shows the average absolute forecast errors for track and intensity (MWS) in terms of stratified bins of 6-h interval for the experiments (at 60–15-km resolution) with both matches in Table 2. There are 16 typhoons in 2015–20 constituting 18 runs for testing on the DVI impact. Only the relocation is performed in V-match for the Hagibis case and in P-match for the Francisco case as the initial MWS or CSLP for CTL is already stronger than the best track intensity. The vortex relocation through DVI has reduced the track error of CTL by about 20 km at the initial time (Fig. 8a). The track forecast errors for CTL and both matches have linearly increased with forecast time, and are approximately 140 km at 72 h. Compared with the fairly good performance of CTL, the DVI still gives positive impacts with statistical significance at the 95% confidence level for all the bins, except 72-h bin. The largest improvement occurs in bins of 42–60 h with an error reduction of 10–20 km for both matches. In this period of large impact, V-match slightly outperforms P-match. For the 72-h bin, V-match still gives a smaller track error on average than CTL, but this improvement is not statistically significant. For the DVI impact on MWS intensity forecasts, the positive impacts are more significant at earlier stages and persist up to 36 h with statistical significance (Fig. 8b), while degrading with forecast time with comparable or slightly worse performance than CTL after 42 h. Both matches give similar maximum intensity errors of about 7 m s−1 by the end of forecast. The reduction on MWS intensity error is much larger for V-match than P-match at earlier stages since the former uses the cycle run that already matches with the best track wind intensity. On the other hand, the reduction on CSLP error is much larger at earlier stages for P-match than V-match (figures not shown), due to the similar reason. Nevertheless, the DVI impacts are mixed for both matches without overwhelming advantages for MWS or CSLP forecasts at later stages. Our DVI performances with the global MPAS are comparable to those with the regional WRF (Cha and Wang 2013), except for that the positive DVI impacts with WRF on intensity forecasts continue for a longer period, due to the fact that their CTL experiments have considerably larger initial deviations (about 16 m s−1 on average) from the best track wind intensity, compared to the smaller deviations (only about 5 m s−1 on average) for our CTL experiments. We have also found that the relative performances of CTL, V-match, and P-match on track forecasts for the eight typhoons in 2019 (figures not shown) are similar to those in 2015–20, with statistical significance at the 95% confidence level for all bins including the 72-h bin.

Fig. 8.
Fig. 8.

The absolute forecast errors in 6-h bins from 0–72 h for all 16 typhoon cases (18 runs) in 2015–20 using 60–15-km resolution in Table 2 for CTL (black), V-match (blue), and P-match (red). (a) Track error (km) and (b) MWS intensity error (m s−1). The absolute forecast error is the absolute deviation from the best track data. The arrows above the bars indicate that the DVI performance is better than that of CTL by passing the Student’s t test of 95% confidence level. Each bin is calculated in the interval of 6 h before the analysis time, except for the 0-h bin that is the performance at the initial time.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

To understand the systematic performance on track and intensity forecasts, Fig. 9 shows the along-track and cross-track errors and MWS intensity biases for all the forecasts in Fig. 8. The overall track errors at most times have the largest contribution from the along-track errors for both DVI run and CTL (Fig. 9a). Considering all the forecasts, the DVI run tends to reduce the along-track errors of CTL at later stages, but both produce similar cross-track errors. There is on average a speed-up in typhoon movement through 24–36 h (with enhanced along-track errors but less than 10 km) and a slowdown afterward, indicating a performance bias in the MPAS track forecasts. Such vortex acceleration has also been shown in the tracks prior to landfall at Taiwan for Soudelor and Megi in Figs. 3 and 4.

Fig. 9.
Fig. 9.

(a) The forecast along-track (solid) and cross-track errors (dashed) from 0 to 96 h for all 16 typhoon cases (17 runs) in 2015–20 for CTL (red), V-match (green), and P-match (cyan). (b) As in (a), but CTL (red) and V-match (green) for the bias of forecasted Vmax. The numbers in the bottom indicate the total of homogeneous runs.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

The intensity differences, stemming from the spinup of the inner vortex core after the DVI, significantly change with forecast time. The CTL intensity gradually increases with time and is able to catch up the intensity of the DVI run (Fig. 9b). This improvement on intensity forecast after the early stage for CTL has been shown in Fig. 3 for Typhoon Soudelor and Fig. 4 for Typhoon Megi. This strongly suggests that the CTL vortex may intensify as well if the same initial vortex can be spun up in cycle runs by the DVI under the fixed environment. The DVI runs tend to exhibit similar negative intensity biases as CTL after 36 h, thus producing nonsignificant impacts on intensity forecasts. However, the track forecasts are still improved at later stages with statistical significance, mainly due to the reduction on negative along-track errors after 48 h.

b. Sensitivity to physics suites (mesoscale reference versus convection-permitting)

The average daily forecast errors of the three metrics (track, MWS and CSLP) from 10 homogeneous runs at 60–15-km resolution for four typhoons (Soudelor, Megi, Mitag, and Lekima) are shown in Fig. 10 using the M-suite or C-suite. Forecasts at two different initial times were conducted for Megi (see Table 2). The forecast errors of the sensitivity tests are relative to those of CTL and have included both V-match and P-match for each suite. For the M-suite, the day-3 track is significantly improved with an error reduction of about 11 km, even though the intensity forecast is only slightly improved in day 1, nearly neutral in day 2 and slightly degraded in day 3. The C-suite does show better intensity forecasts through day 2; there is an error reduction of 5 hPa in CSLP in day 3. However, such noticeable intensity improvement in day 2 and 3 is accompanied by a very poor track, due to some outliers produced by use of the C-suite (figures not shown). When considering all the metrics on average, the M-suite seems to be more preferred than the C-suite. It is certain that some combinations between the M-suite and C-suite may preserve the forecast merits of both suites and reduce the percentage of track outliers. Such alternative scheme combinations, in addition to the default M-suite or C-suite, may be investigated in another study.

Fig. 10.
Fig. 10.

The daily forecast errors of track (km; blue), Vmax (m s−1; red), and CSLP (hPa; purple) summarized for four typhoon cases (Soudelor, Megi, Mitag, and Lekima) using V-match and P-match with (a) the M-suite and (b) the C-suite. There are 10 runs at 60–15-km resolution for comparisons on each suite. The forecast errors are relative to those of the counterpart (control experiment) without the DVI compared to the best track data, and positive and negative values indicate better and worse performances, respectively, than CTL.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

c. Impacts of enhanced resolution (60–15–3 km)

The forecast performances with both 60–15-km resolution and enhanced resolution of 60–15–3-km MPAS configurations for two typhoons (Soudelor and Megi) are given in Table 3. Compared to the results with the 60–15-km resolution, the enhanced resolution can considerably accelerate the DVI cycling for both V-match and P-match. We note that the results with 60–15-km resolution are only slightly influenced by use of a much smaller time step of 18 s as for 60–15–3-km resolution, thus the track and intensity forecasts are not greatly sensitive to update frequency or the time-truncation errors of the model. Compared to CTL, the enhanced resolution generally does not lead to further improvement on the track forecast with the DVI even though a large improvement is obtained in the Megi experiments. CSLP prediction, however, has been considerably improved by the enhanced resolution, although it is associated with degraded MWS prediction on average. Since the impacts of the DVI with the enhanced resolution were investigated only for two typhoons, the increased positive impacts on CSLP prediction are promising, but still need more testing.

Table 3

Forecasts of two typhoons with the 60–15–3-km resolution and 60–15-km using the mesoscale reference suite. Positive (negative) values indicate improvement (degradation) relative to the CTL run without use of the DVI. The characters “P” and “V” in the case name indicate the DVI with P-match and V-match, respectively. The cycle runs required for P-match or V-match are given in the cycle column. Numbers in bold indicate the reduced forecast errors with 60–15–3-km resolution relative to those with 60–15-km resolution.

Table 3

d. Vortex analyses for forecast intensity differences

We have observed that the track errors and intensity errors in either specific-case forecasts or average over numerous forecasts do not show a strong correlation with each other at most forecast times. To limit the scope of the investigation, we choose several typhoons to illustrate the intensity differences resulting from using DVI with V-match and the M-suite. Lekima shows the strongest intensification rate over the first two days of the forecast as shown in Fig. 6. Both dynamic and thermodynamic processes are involved in the evolution of potential vorticity (PV). For typhoon circulations, their structural and intensification changes are related to the evolution of PV in the inner vortex (e.g., Guinn and Schubert 1993). The generation of the intense tropospheric PV in the inner vortex has significantly contributed to the intensification of Lekima based on the nonlinear balanced flow (Shi and Chen 2021). Figure 11 shows the azimuthal-mean PV within 2° of the vortex center at different times for CTL and V-match for Lekima. Both forecasts use the M-suite and 60–15-km resolution. At the initial time, the DVI has produced a more consolidated inner vortex core (herein defined within 1°) associated with the enhanced tropospheric PV (TPV) in V-match that develops higher than CTL (Figs. 11a,e). The inner vortex core tends to intensify with time associated with a contracting eyewall at 12 h for V-match (Fig. 11f). However, the eyewall in CTL also becomes stronger at this time (Fig. 11b), but still weaker than that of V-match. The intensifying TPV fields in the inner vortex core for both runs are closer in intensity and vertical development at 24 h (Figs. 11c,g). At 48 h, their eyewall structures are quite similar with an upper PV tongue extending outward near the radius of 0.5°, which is also found in simulations of Haiyan (2013) (Tsujino and Kuo 2020). In response to the similar development of TPV for CTL and V-match, their transverse circulations are similar at later stages (Figs. 11d,h).

Fig. 11.
Fig. 11.

Azimuthal-mean potential vorticity (shaded colors; PVU) in the radius–height cross section for CTL for Typhoon Lekima at (a) 0 h, (b), 12 h, (c), 24 h, and (d) 48 h. (e)–(h) As in (a)–(d), respectively, but for V-match. Both forecasts use the M-suite and 60–15-km resolution. The wind vectors indicate the radial and vertical wind components (m s−1) with the reference vector given at the bottom-right corner. The green line shows the radius of maximum horizontal wind speed.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

We choose the three typhoons, Megi, Mitag, and Lekima, to illustrate the relationship between the development of vortex intensity and PV with and without the DVI. Figure 12 shows the evolution of averaged TPV in 0–12-km height and within 1° from the vortex center in 0–72 h for CTL and V-match. As seen in Table 2, Megi, Mitag, and Lekima requires 35, 18, and 6 cycle runs in the DVI with V-match, respectively. The intensification rate of the vortex closely follows the evolution of the averaged TPV for the three typhoons. The initial vortex spinup by the DVI leads to noted differences in the averaged TPV that are gradually reduced with forecast time. The amount of the averaged TPV essentially controls the vortex intensity, and the strongest vortex is produced for Lekima with the largest PV value up to 12 PVU (1 PVU = 10−6 K kg−1 m2 s−1) at 54 h. The differences in the evolving TPV between V-match and CTL are in good agreement with their differences in Vmax, even though some small deviations remain. We have also found that the TPV intensity for CTL takes about 24–42 h to catch up with V-match for the three typhoons. At later stages, the positive differences in the TPV intensity appear to be reversed and the TPV of CTL can be stronger than V-match. Consequently, the typhoon intensity can be slightly stronger at later stages in CTL than V-match. Although the intensity differences produced by the DVI have significantly decreased with forecast time, the improvement on track forecasts remains statistically significant throughout the 72-h forecast period as shown in Fig. 8 for the 16 typhoons. This may be attributed to the impact of their structural differences in the evolving vortex between CTL and V-match since both CTL and V-match produce similar intensity biases at later stages as shown in Fig. 9. The larger along-track errors at later stages for CTL are related to the asymmetry of the evolving vortex. Most of the typhoons move closer to the terrain at later stages, which would complicate the vortex analyses for the resulted track errors.

Fig. 12.
Fig. 12.

(a) Evolution of tropospheric potential vorticity (PVU) averaged in a circle radius of 0°–1° and between 0- and 12-km height from the typhoon center in 0–72 h for Typhoon Megi. (b) As in (a), but for Vmax (m s−1). (c),(d) As in (a) and (b), respectively, but for Typhoon Lekima. (e),(f) As in (a) and (b), respectively, but for Typhoon Mitag. The dashed and solid lines indicate the forecasts for CTL and V-match, respectively. Both forecasts use the M-suite and 60–15-km resolution.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

6. Conclusions

Dynamic vortex initialization (DVI) for unstructured meshes has been implemented in this study to help improve typhoon forecasts from the global variable-resolution model MPAS. The DVI applies cycling integration of the model that repeatedly updates the departure vortex within a specific radius, thus allowing the vortex to gradually intensify and match the MWS or CSLP value of the best track data, V-match or P-match, respectively. Typhoon forecasts with the DVI are investigated with two default physics suites, the mesoscale reference physics suite (M-suite) and the convection-permitting physics suite (C-suite). For application to typhoons near terrain, the DVI has been refined to perform only partial updating of the vortex to avoid the problem of interpolation over topography, which introduces noise near the outer boundary of the updated vortex.

The MPAS-based DVI has been tested in forecasts of 16 typhoons observed over the western North Pacific in 2015–20. Using a 60–15-km varying resolution mesh, DVI produces more consolidated vortex cores with clearer eyewall structures compared to the global analyses, thus leading to improved track and intensity predictions. V-match appears to slightly outperform P-match in track and intensity forecasts, while the latter requires more cycle runs with a stronger vortex core than the former. On the other hand, the M-suite appears to provide better track forecasts but is associated with slightly degraded intensity forecasts in comparison to the C-suite.

The DVI can also be applied to typhoons near but not over high topography. The typhoon vortex is only partially updated in the DVI, allowing for a spinup of the inner vortex core in response to the primary typhoon circulation across or around topography. The small amount of noise introduced by partial vortex updating is quickly damped by the model during the forecast. Several typhoon cases have illustrated the feasible performances of the DVI near high mountains with improvement on track and intensity forecasts.

Most of the DVI performances have shown improved typhoon intensity forecasts at the early stage since the DVI performs either P-match or V-match in the cycling runs. However, intensity forecasts have gradually degraded with time and become comparable with that without the DVI at later stages. These forecast differences in intensity have been explained by the evolution of the averaged tropospheric potential vorticity in the inner vortex core that closely correlates with the development of the vortex intensity and thus the resulting intensity differences from the DVI. The earlier impact of intensity differences produced by the DVI has been extended to the improvement on longer track forecasts with statistically reduced negative along-track errors for the 16 typhoons. We have observed similar performances of the DVI with the regional model on the intensity forecasts as shown by other studies (e.g., Van Nguyen and Chen 2014; Cha and Wang 2013; Liu et al. 2018). It is believed that the degrading intensity forecast with time for the DVI is due to the fact that the initial state is only adjusted for the typhoon vortex at a fixed inner core size, while holding fixed the environmental conditions within cycling runs thus producing an artificial transition zone around the peripheral of the vortex. A further study is worthy to establish a scenario that can largely remedy the impact of the artificial transition zone on the performance of the DVI.

The current experimental results seem to show an advantage of V-match over P-match on some aspects of performance and the former typically requires considerably fewer cycle runs in the DVI. More experiments still need to be conducted to further investigate whether P-match is really less preferable than V-match. Note that the currently refined DVI, although applicable to TCs near topography, has not been developed for TCs over topography. At present, forecasts at a lead time of 1–3 days may be considered when applying the DVI to initialize TCs near terrain. In situ and remote observations can be assimilated as well for improving the internal structure and intensity of TCs near terrain after application of the DVI.

Acknowledgments.

This study was supported by the Ministry of Science and Technology (MOST) in Taiwan. Support for author Skamarock was provided by the National Center for Atmospheric Research through support from the National Science Foundation under Cooperative Support Agreement AGS-0856145. Wen-Hsin Teng and Thi Chinh Nguyen helped on some figure plots.

Data availability statement.

The FNL data used for the model initial conditions were obtained from the website of the NCEP and the best track data were obtained from the CWB. All the model setups and simulation results in this study are available from the leading author, Dr. C.-Y. Huang (hcy@atm.ncu.edu.tw), at National Central University.

APPENDIX

Dynamic Vortex Initialization

Within DVI, the vortex at the initial time in the cycle is replaced by the vortex produced after the integration in that cycle is completed (here after 1 h). Spatial interpolation is required to relocate this new displaced vortex, and the interpolation consists of the sum of weighted averages of the prognostic model variables (including zonal and meridional wind speeds) from the relocated cells within a specified distance from the original cell, as depicted in Fig. A1. The weighting coefficients are inversely proportional to the square of the distance rj given in Fig. A1, and the interpolated value of mesh cell ϕj within the original vortex region is given by
ϕj=i=1Nwiϕi,
where
wi=dipi=1Ndipand di=|rirj|,
and N is the number of cell values used in the interpolation at a position vector ri with diR (R is the limiting radius of influence on ϕj at a position vector rj mapped to the updated vortex center). As noted, we choose p = 2 as inverse distance weighted interpolation (IDWP).
The MPAS prognostic horizontal wind is defined at each edge of a cell and is normal to the edge. DVI needs to update the horizontal wind at all the edges of each cell using the updated zonal and meridional wind speeds. To accomplish this updating, the unit vectors along the eastward and northward directions are projected into three orthogonal Cartesian unit vectors, i, j, and k in x, y, and z, respectively, and are given by
ex=sinϕi+cosϕj+0k,  ey=sinθcosϕisinθsinϕj+cosθk,
respectively, where ϕ is longitude and θ is latitude. The xy plane is parallel to the equatorial plane of Earth with the positive x pointing to 0° longitude and the positive y pointing to 90°E longitude, and thus the positive z is defined (pointing to 90°N latitude). This projection of the updated wind at the cell centers onto the normal direction of the cell edges is as depicted in Fig. A2, and it is accomplished by averaging the cell center projections from the two cells sharing that edge, and then computing the normal component of that average. Thus, a contribution from a cell to a given edge normal velocity is given by
u=0.5[Ux(gex)+Uy(gey)],
where g is the Cartesian unit vector normal to the edge of the cell, and Ux and Uy represent the zonal and meridional components, respectively, of the updated wind at the cell center. The other contribution of same weighting is given by the other cell joined on the same edge.
Fig. A1.
Fig. A1.

Updating the vortex using inverse distance weighted interpolation (IDWP). The original vortex within a solid circle at time t0 moves to a new position with the model-integrated vortex (marked by the dashed circle) at t1. Here, rj is the position vector of one cell center from the center of the original vortex, which is mapped into the same vector, but relative to the center of the new vortex. The model value at rj is obtained with IDWP using all the values at ri, where i is the index of a cell within the specified radius of interpolation R (marked by the dotted circle). Relocation can be combined when the best track vortex center is used instead to replace the vortex center at time t0.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

Fig. A2.
Fig. A2.

Edge-normal wind reconstruction. The zonal and meridional components of the wind at the center of a cell, given by Ux and Uy with corresponding unit vectors ex and ey, contribute velocity components normal to an edge of the cell u (red vectors). Here, g is the unit vector normal to the edge. The total normal wind velocity at the edge is the average of the contributions from both cells that share the edge.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-21-0235.1

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