Real-Time Adaptive Observation Guidance Using Singular Vectors for Typhoon Jangmi (200815) in T-PARC 2008

Hyun Mee Kim Atmospheric Predictability and Data Assimilation Laboratory, Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea

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Sung-Min Kim Atmospheric Predictability and Data Assimilation Laboratory, Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea

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Byoung-Joo Jung Atmospheric Predictability and Data Assimilation Laboratory, Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea

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Abstract

In this study, structures of real-time adaptive observation guidance provided by Yonsei University (YSU) in South Korea during The Observing System Research and Predictability Experiment (THORPEX)-Pacific Asian Regional Campaign (T-PARC) are presented and compared with those of no-lead-time adaptive observation guidance recalculated as well as other adaptive observation guidance for a tropical cyclone (Jangmi 200815). During the T-PARC period, real-time dry total energy (TE) singular vectors (SVs) based on the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) and the corresponding tangent linear and adjoint models with a Lanczos algorithm are provided by YSU to help determine sensitive regions for targeted observations. While YSU provided the real-time TESV guidance based on a mesoscale model, other institutes provided real-time TESV guidance based on global models. The overall features of the real-time MM5 TESVs were similar to those generated from global models, showing influences from tropical cyclones, midlatitude troughs, and subtropical ridges. TESV structures are very sensitive to verification region and forecast lead time. If a more accurate basic-state trajectory with no lead time is used, more accurate TESVs, which yield more accurate determinations of sensitive regions for targeted observations, may be calculated. The results of this study may imply that reducing forecast lead time is an important component to obtaining better sensitivity guidance for real-time targeted observation operations.

Corresponding author address: Hyun Mee Kim, Dept. of Atmospheric Sciences, Yonsei University, Shinchon-dong 134, Seodaemun-ku, Seoul 120-749, South Korea. E-mail: khm@yonsei.ac.kr

Abstract

In this study, structures of real-time adaptive observation guidance provided by Yonsei University (YSU) in South Korea during The Observing System Research and Predictability Experiment (THORPEX)-Pacific Asian Regional Campaign (T-PARC) are presented and compared with those of no-lead-time adaptive observation guidance recalculated as well as other adaptive observation guidance for a tropical cyclone (Jangmi 200815). During the T-PARC period, real-time dry total energy (TE) singular vectors (SVs) based on the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) and the corresponding tangent linear and adjoint models with a Lanczos algorithm are provided by YSU to help determine sensitive regions for targeted observations. While YSU provided the real-time TESV guidance based on a mesoscale model, other institutes provided real-time TESV guidance based on global models. The overall features of the real-time MM5 TESVs were similar to those generated from global models, showing influences from tropical cyclones, midlatitude troughs, and subtropical ridges. TESV structures are very sensitive to verification region and forecast lead time. If a more accurate basic-state trajectory with no lead time is used, more accurate TESVs, which yield more accurate determinations of sensitive regions for targeted observations, may be calculated. The results of this study may imply that reducing forecast lead time is an important component to obtaining better sensitivity guidance for real-time targeted observation operations.

Corresponding author address: Hyun Mee Kim, Dept. of Atmospheric Sciences, Yonsei University, Shinchon-dong 134, Seodaemun-ku, Seoul 120-749, South Korea. E-mail: khm@yonsei.ac.kr

1. Introduction

The Observing System Research and Predictability Experiment (THORPEX), a World Weather Research Program (WWRP) of the World Meteorological Organization (WMO), began in 2003 and is scheduled to end in 2012. From 1 August to 6 October 2008, the THORPEX-Pacific Asian Regional Campaign (T-PARC) was implemented in the western North Pacific to improve short- to medium-range typhoon forecasts. During the T-PARC period, multiple types of in situ and remotely sensed nonregular observations were deployed in this area (Elsberry and Harr 2008). In particular, intensive dropsonde observations using aircraft were performed, following the typhoon life cycle from tropical convection to extratropical transition. To perform these aircraft-based dropsonde observations, sensitive regions for future forecasts had to be determined in advance.

Methods for determining sensitive regions that influence forecasts verified in the future are called targeted observation strategies (or adaptive observation guidance). Various organizations have developed real-time adaptive observation guidance that suggests possible target regions for adaptive observations to improve tropical cyclone track forecasts (Kim et al. 2008). The real-time guidance employed for T-PARC includes total energy singular vector (TESV; Peng and Reynolds 2006; Reynolds et al. 2010) and adjoint sensitivity (Amerault and Doyle 2009; Reynolds et al. 2010) guidance, both used by the Naval Research Laboratory (NRL); TESV guidance, used by the European Centre for Medium-Range Weather Forecasts (ECMWF; Buizza et al. 2007), the Japan Meteorological Administration (JMA; Yamaguchi et al. 2009), and Yonsei University (YSU; Kim and Jung 2009b,a); adjoint-derived sensitivity steering vector (ADSSV) guidance, used by National Taiwan University (Wu et al. 2007); an ensemble transform Kalman filter (ETKF), used by the University of Miami (Majumdar et al. 2006) and the Met Office (Bowler et al. 2008); and analysis of ensemble deep-layer mean (DLM) wind variance, used by the National Oceanic and Atmospheric Administration (NOAA; Aberson 2003). These sensitivity products for adaptive observations were collected during the T-PARC period by the Earth Observing Laboratory (EOL) of the National Center for Atmospheric Research (NCAR), the Data Targeting System (DTS) of ECMWF, and the JMA T-PARC Web site, and were used to determine the target regions for adaptive observations of typhoons.

Using the real-time guidance provided by the organizations named above, flight plans were determined for individual typhoons. Once tropical convections that might develop into a typhoon were observed, meetings were held almost every day through the extinction of the typhoon to plan flight paths that cover the sensitive regions suggested by various strategies. With the exception of YSU in Korea, which provided real-time TESV guidance based on a mesoscale model, the other institutes provided the real-time TESV guidance based on global models. The impacts of real-time targeting guidance during T-PARC have not yet been fully reported, but the TESV guidance provided by YSU showed a positive effect on tropical cyclone (TC) track forecasts (Jung et al. 2010).

In this study, structures of real-time adaptive observation guidance provided by YSU during T-PARC are presented and compared with those of other adaptive observation guidance and no-lead-time TESVs. The purpose of this paper is to describe the real-time adaptive observation guidance produced to support the T-PARC field program, and compare those real-time products with no-lead-time TESVs. To compare TESVs provided from several institute during T-PARC, the effects of physics and norms on TESV structures are also discussed. The mathematical SV formulation, experimental framework, and real-time procedures are presented in section 2. The real-time adaptive observation guidance provided by YSU and by other institutes during T-PARC and the recalculated TESV guidance are presented and compared in section 3. Section 4 contains a summary and discussion.

2. Mathematical formulation and experimental framework

a. Total energy norm SVs

The calculation of SVs involves selecting an initial disturbance subject to the constraints that the initial disturbance has unit amplitude in a specified norm and evolves to have a maximum amplitude in a specified norm after some finite optimization time, . In this study, the initial and final norms were the dry total energy (TE), defined by Zou et al. (1997) and Kim and Jung (2009b,a) as
e1
where is the dry TE in a nonhydrostatic model; , , and are the zonal, meridional, and vertical wind perturbations, respectively; is the potential temperature perturbation; is the pressure perturbation; , , , and are the Brunt–Väisälä frequency, potential temperature, density, and speed of sound at the reference level, respectively; and x, y, and σ denote zonal, meridional, and vertical coordinates, respectively. While the first three terms on the right-hand side (rhs) of (1) are associated with the kinetic energy (KE), the final two terms in the rhs of (1) are associated with the potential energy (PE).
The ratio of the final and initial perturbation amplitudes is the Rayleigh quotient (the amplification factor) defined as
e2
where the inner product is denoted by , is a local projection operator that zeros out the state vector outside the verification region, is the tangent linear model (TLM) of the nonlinear model, is the dry TE norm, and is the initial perturbation state vector. In (2), the state vector at the initial time evolves linearly. By defining the local projection operator, the amplitude of the state vector with norm at the optimization time is maximized over a specific region. The maximum ratio is realized when is the leading SV of the TLM for the norm; that is, satisfies
e3

The generalized eigenvalue problem in (3) can be reduced to an ordinary eigenvalue problem by left-multiplying both sides of (3) by the inverse of the square root of (Zou et al. 1997). A Lanczos-type algorithm (e.g., Ehrendorfer and Errico 1995; Kim 2003; Kim et al. 2004; Kim and Jung 2009b,a) can then be used to solve for . The Lanczos algorithm is an iterative algorithm that is an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix or the singular-value decomposition of a rectangular matrix, and is particularly useful for finding decompositions of very large sparse matrices (Golub and Van Loan 1996).

Similar to Langland et al. (2002), the vertically integrated TESV energy is calculated to combine each component of the TESV with a different unit into a single two-dimensional TESV field with a unit of energy (J kg−1):
e4
where i, j, and k denote grid points in the x, y, and z directions, respectively.
To investigate the overall properties of the first to third TESVs, the composite of the first to third TESVs was calculated as in Kim and Jung (2009a). The formula of the vertically integrated energy composite of the first to third TESVs is
e5
where and are singular values for the first and nth TESVs, respectively, and denotes the nth vertically integrated TESV energy field.

b. Model and SV configurations

To calculate SVs in real time, this study used the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) adjoint modeling system (Zou et al. 1997) and a Lanczos algorithm. The model domains were centered at 25°N and 125°E, 30°N and 126°E, and 36°N and 125°E for verification regions corresponding to Taiwan, Japan, and Korea, respectively (Fig. 1), with 120-km horizontal grid spacing in a 50 × 50 domain and 14 evenly spaced vertical sigma levels from the surface to 50 hPa. The model initial and lateral boundary conditions used for real-time calculation were obtained from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS; 1° × 1° global grid). For recalculated SVs with more accurate basic states, the NCEP final analysis (FNL; 1° × 1° global grid) was used for the model initial and lateral boundary conditions. Physical parameterizations used for the nonlinear basic-state integrations included the Grell convective scheme, a bulk aerodynamic formulation of the planetary boundary layer, a simple radiational cooling scheme, horizontal and vertical diffusion, dry convective adjustment, and the explicit treatment of cloud water, rain, snow, and ice. The same physical parameterizations were used in the TLM and adjoint model integrations, except that the TLM and adjoint model considered the effects of moisture using a large-scale precipitation scheme rather than the Grell convective scheme and an explicit treatment of cloud water, rain, snow, and ice. These configurations of nonlinear and adjoint model integrations were used by Kim and Jung (2009b,a) to consider moist physics effects in linear integrations of SV calculations. As mentioned in section 2a, the dry TE norm was used for the calculation of real-time SVs to reduce the computation time, which was constrained by the real-time configuration as shown in Fig. 2.

Fig. 1.
Fig. 1.

Model domains (solid lines) and verification regions (dotted lines) for Taiwan (red), Japan (purple), and Korea (blue). Real-time TESV sensitivity products using MM5 were generated for the Taiwanese verification region of 18°–30°N, 118°–132°E (18°–30°N, 117°–140°E) from 0000 UTC 11 May to 0000 UTC 3 Aug 2008 (from 0000 UTC 4 Aug to 0000 UTC 26 Dec 2008); the Japanese verification region of 20°–40°N, 120°–150°E from 0000 UTC 18 Apr to 0000 UTC 26 Dec 2008; and the Korean verification region of 30°–42°N, 118°–132°E from 0000 UTC 4 Jun to 0000 UTC 26 Dec 2008.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Fig. 2.
Fig. 2.

A schematic diagram of the preparation procedure for MM5 real-time TESV guidance at YSU.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

c. Experimental setup and procedures

To provide real-time adaptive observation guidance during the T-PARC 2008 period, SVs and adjoint-based forecast sensitivities using the MM5 and its tangent linear and adjoint models were calculated at YSU for several typhoons that have occurred since 2006 (e.g., Kim and Jung 2006; Kim et al. 2008; Kim and Jung 2009b,a). Based on these prior experiences, real-time MM5 SVs were calculated for the period from spring to winter 2008 for each of three verification regions (Japan, Taiwan, and Korea; see Fig. 1), and were provided to the ECMWF T-PARC DTS and JMA T-PARC Web site during the T-PARC period to help determine targeting regions.

The dry TE norm SVs were calculated in real time for 48 h of lead time and 48 h of optimization time. Real-time TESVs were calculated based on the 48 h of model trajectory between Ta and Tυ, which is integrated from Ti with 48 h of lead time (Fig. 2). Real-time TESVs were perturbations at Ta that grew most rapidly from Ta to Tυ. Compared to TESVs based on model integrations starting from Ta, the real-time TESVs based on model trajectories from Ta to Tυ that are initialized from Ti use more uncertain model trajectories. This defect of real-time TESVs may lead to unrealistic sensitive regions, but TESVs should follow the real-time constraints as do other strategies.

The start time of the real-time TESV calculations was 0000 UTC. Between 6 and 6.5 h were required to download the NCEP GFS data for the initial and boundary conditions for the MM5 model, the subsequent TESV calculation and postprocessing took about 10 h, using a single processor of a 16-processor Linux PC cluster for each target region. The real-time TESVs were then uploaded to the ECMWF T-PARC DTS and JMA T-PARC Web site. Flight decisions were made by participating scientists at about 2200 to 0000 UTC.

The dry TESVs are recalculated after the T-PARC period to identify the impacts of uncertain model trajectories in real-time calculations on TESV characteristics. In contrast to the real-time TESVs, the TESVs are recalculated for 0 h of lead time and 48 h of optimization time. The recalculated TESVs are based on the 48 h of model trajectory from Ta to Tυ, integrated from the initial conditions at Ta as shown in Fig. 2.

3. Results

a. Real-time TESV products for the Taiwan verification region

The vertically integrated TESV energy is provided as real-time guidance to represent the general features of the sensitivities of typhoons. The real-time TESV guidance products for TC Jangmi (200815), one of the typhoons intensively observed during T-PARC, are shown in this study. The observed and simulated tracks of TC Jangmi are shown in Fig. 3. For this specific example, the model simulation started at 0000 UTC 25 September (Ti), and the real-time TESV is calculated based on the model trajectory from 0000 UTC 27 September (Ta) to 0000 UTC 29 (Tυ) September. TC Jangmi formed at 0000 UTC 24 September east of the Philippines, curved northeastward after 0000 UTC 29 September, and dissipated at 0000 UTC 1 October 2008.

Fig. 3.
Fig. 3.

The Regional Specialized Meteorological Center (RSMC)-Tokyo Typhoon Center best track (black line with + symbols), 48-h MM5 forecast track (red line with circles) with 48-h lead time, and 48-h MM5 forecast track (blue line with squares) with 0-h lead time, for TC Jangmi (200815). Green circles denote Ti, Ta, and Tυ in the best track. Each symbol is plotted at 6-h intervals.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

The vertically integrated energy of the first, second, and third TESVs, as well as the composite of the first to third TESVs, along with the 500 hPa geopotential height at the initial and final times, are shown in Fig. 4. For the leading TESV, the initial TESV shows large sensitivities north of the TC in the East China Sea (Fig. 4a). The sensitive regions are closely associated with the midlatitude trough. The second TESV has overall structures that are very similar to those of the leading TESV; however, the largest sensitivities, consisting of elongated structures from the southeast coast of China to the right-front quadrant of TC Jangmi, are much closer to the TC (Fig. 4b) than are those of the leading TESV. The third TESV had major sensitivities southwest of the Korean Peninsula (Fig. 4c). The amplification factors of the first, second, and third SVs are 52.3, 24.0, and 15.4, respectively, showing large growth of the initial SVs associated with the TC. Because of contributions from the first TESV, the composite TESV showed vertically integrated energy structures that are very similar to those of the first TESV (Fig. 4d). The first, second, and composite evolved TESVs after 48 h have the largest sensitivities over the TC center (Figs. 4e, 4f, and 4h). The first and third evolved TESVs have other sensitive regions on the boundaries of the Taiwan verification region, and the sensitivities northeast of the TC center for the first (third) TESV are much smaller (larger) in magnitude than those over the TC center (Figs. 4e and 4g). The second TESV has a secondary maximum far to the northeast of the TC center (Fig. 4f). These variations in evolved TESVs imply that the initial TESVs are associated not only with the TC itself but also with the midlatitude trough.

Fig. 4.
Fig. 4.

Vertically integrated energy distribution of the real-time TESV (10−3 J kg−1, colors with varied scales) for the Taiwan verification region (box) along with 500-hPa geopotential height (contours, interval of 50 m) at 0 h (0000 UTC 27 Sep 2008) for the (a) first, (b) second, (c) third, and (d) composite TESVs, and at 48 h (0000 UTC 29 Sep 2008) for the (e) first, (f) second, (g) third, and (h) composite TESVs. The thick solid line over the center of TC Jangmi denotes the 1002-hPa MSLP. The numbers at the bottom right of (a)–(c) denote the amplification factors associated with each TESV.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

The largest contributions to the vertically integrated leading TESV energy in Fig. 4a are from the lower part of the troposphere (Fig. 5). The TESV energy in the lower part (Fig. 5c) is associated with the sensitive region to the north of the typhoon in Fig. 4a, from southeast China to the East China Sea, whereas the TESV energies in the middle and upper regions are associated with the midlatitude trough (Figs. 5a and 5b). The largest contribution to the evolved TESV energy is from the lower part of the troposphere (Fig. 5f). The secondary maximum of the evolved TESV energy is located in the region between the midlatitude trough and the subtropical high to the east of the TC (Figs. 5e and 5f), indicating that the initial TESVs are associated with large-scale background systems as well as with the TC itself. The large sensitivities in the midlatitudes are located in the lower and middle parts of the troposphere, consistent with the results of Kim and Jung (2009b).

Fig. 5.
Fig. 5.

As in Fig. 4, but for (top) the 100–400-hPa layer along with the layer-average potential vorticity (PV) of the 200–500-hPa layer [contour interval of 1 PV unit (PVU), where 1 PVU = 10−6 m2 s−1 K kg−1] at (a) 0 h (0000 UTC 27 Sep 2008) and (d) 48 h (0000 UTC 29 Sep 2008); (middle) the 400–750-hPa layer along with the layer-average PV of 500-hPa geopotential height (contour interval of 50 m) at (b) 0 and (e) 48 h; and (bottom) the 750 hPa–MSLP layer along with the MSLP (contour interval of 4 hPa) at (c) 0 and (f) 48 h.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Vertical profiles of the first, second, third, and composite TESV energy are shown in Fig. 6. The maxima of the leading TESV for both the TE and KE at the initial time (Fig. 6a) are located in the lower troposphere. In contrast, the leading TESV for the PE has a peak at the upper boundary, with much smaller contributions throughout the troposphere (Fig. 6a). The leading TESV at the final time (Fig. 6e) increased in amplitude by at least an order of magnitude and has a maximum near the lower troposphere. The PE has a smaller contribution and a more uniform structure, which also holds for the second and third TESVs. Major and minor peaks in the second TESV for both the TE and KE at the initial and final times are different from those of the leading TESV at the corresponding times, showing large TE and KE near the mid- to upper troposphere at the initial time (Fig. 6b) and near the upper troposphere at the final time (Fig. 6f). The PE of the second TESV also has a maximum at the upper boundary at the initial time (Fig. 6b) and a uniform distribution at the final time (Fig. 6f). The maximum of the third TESV for the TE and KE at the initial time (Fig. 6c) is located in the lower troposphere, and the maxima of the third TESV for the TE and KE at the final time (Fig. 6g) are located in the lower and upper troposphere. Because of the largest contribution of the leading TESV to the composite TESV, the composite and leading TESVs have very similar vertical structures (Figs. 6a and 6d). As shown in Kim et al. (2008) and Kim and Jung (2009b,a), the KE of the initial TESV is dominant, except at the upper boundary, and the KE of the final TESV is also dominant throughout the troposphere. Unlike the leading TESV, the second and third TESVs show upward energy propagation during the evolution, which implies that the second and third TESVs may be more closely associated with extratropical systems (e.g., Palmer et al. 1998; Morgan 2001).

Fig. 6.
Fig. 6.

Vertical energy distributions of the real-time TESV (J kg−1: TE, closed circles; KE, open circles; PE, open squares) at 0 h for the (a) first, (b) second, (c) third, and (d) composite TESVs, and at 48 h in the Taiwanese verification region for the (e) first, (f) second, (g) third, and (h) composite TESVs. Note the different magnitudes along the abscissas of the evolved TESVs after 48 h. The ordinate represents the vertical level (pressure) and the abscissa denotes the TESV energy (J kg−1).

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

b. Real-time TESV products for the Korean verification region

In addition to the two fixed verification regions of Taiwan and Japan, another fixed verification region centered on the Korean Peninsula is used for calculating real-time TESV guidance at YSU. The purpose of this fixed region is to assess the sensitive regions for weather systems affecting the Korean Peninsula during the T-PARC period, including typhoons. Because no typhoon activities occurred over the Korean Peninsula during the T-PARC period, the sensitive regions associated with TCs cannot be determined, but other interesting features are captured, as shown in Fig. 7.1 First, because the TC center is outside of the verification region, the evolved TESV structures have several maxima over the TC center, in the verification region, and east of the verification region (Figs. 7e, 7g, and 7h), which implies that the initial TESVs are associated with several weather systems including the typhoon, as indicated in Reynolds et al. (2009). Unlike the initial TESVs for the Taiwan verification region shown in Fig. 4, the initial TESVs are located north to the far northwest of the TC (Figs. 7a–d). In addition, amplification factors of 17.9, 14.0, and 12.6 for the first, second, and third SVs (Figs. 7a–c) are much smaller than those for the Taiwan verification region in Fig. 4, implying the smaller growth of the initial SVs, which are mostly associated with the midlatitude weather systems. The first TESVs in the upper, mid-, and lower levels at the initial and final times show large sensitivities primarily near the midlatitude trough (Fig. 8). Only the lower-level evolved TESV shows a large sensitivity structure over the TC center, with other maxima in the extratropics (Fig. 8f), indicating that initial lower TESV structures are associated with several weather systems including the typhoon.

Fig. 7.
Fig. 7.

As in Fig. 4, but for the Korean verification region (box).The thick solid line over the center of TC Jangmi denotes 1000 hPa MSLP.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Fig. 8.
Fig. 8.

As in Fig. 5, but for the Korean verification region (box). The thick solid line over the center of TC Jangmi denotes the 1000-hPa MSLP.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Vertical profiles of the first, second, third, and composite TESV energy for the Korean verification region are shown in Fig. 9. The maxima of the leading and third TESVs for both the TE and KE at the initial time (Figs. 9a and 9c) are located in the lower troposphere. Major peaks of the second TESV for both TE and KE at the initial and final times are different from those of the leading TESV at the corresponding times, showing large TE and KE in the midtroposphere at the initial time (Fig. 9b). At the final time, all the evolved TESVs (Figs. 9e–g) have increased in amplitude by at least an order of magnitude and have attained maxima in the midtroposphere. The PE makes a smaller contribution and exhibits a more uniform structure for the first and third TESVs and shows a peak at the mid- to upper troposphere for the second TESV. The contribution of PE for all the TESVs increased at the final time. The KE and PE of the second evolved TESV show comparable magnitudes. Even though the KE of the initial TESV is dominant, the contribution of PE is much larger than that for the Taiwan verification region, indicating that TESV structures that maximize energy in the Korean verification region, located far north of the Taiwan verification region, detect midlatitude weather systems instead of the TC.

Fig. 9.
Fig. 9.

As in Fig. 6, but for the Korean verification region.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

c. Comparison with TESV products with 0-h lead time

Unlike the case for the real-time calculation, the model simulation started at 0000 UTC 27 September (Ta), and the 0-h lead-time TESV for the Taiwan verification region is calculated based on the model trajectory from 0000 UTC 27 September (Ta) to 0000 UTC 29 September (Tυ). Because there is no lead time, the basic-state trajectory used for TESV calculation is closer to the real atmospheric state.

The vertically integrated energy distributions of the first, second, third, and composite of the first to third TESVs superposed on the 500-hPa geopotential height at the initial and final times are shown in Fig. 10. For the leading TESV, the initial TESV has large sensitivities north of the TC in the East China Sea and in the right–rear quadrant of the TC (Fig. 10a). The sensitive regions are closely associated with the midlatitude trough and the inflow region between the TC and the subtropical ridge. These structures are similar to the real-time TESVs from the ECMWF and NRL (Figs. 13b and 13c), indicating that the basic-state trajectory for the TESVs at this time may be closer to the real-time basic-state trajectories from the ECMWF and NRL. Compared to Fig. 4a, the subtropical ridge for this case is extended westward (Fig. 10a), which indicates that the subtropical ridge may not be well represented in real time. The second TESV shows the largest sensitivities in the inflow region between the TC and the subtropical ridge (Fig. 10b), and the third TESV has major sensitivities north of the TC near the midlatitude trough (Fig. 10c). The amplification factors of 62.7, 42.2, and 22.5 for the first, second, and third SVs (Figs. 10a–c) are larger than those for the real-time SVs in Fig. 4, implying the initial SVs are more closely associated with the TC itself. All of the evolved TESVs after 48 h have their largest sensitivities over the TC center (Figs. 10e, 10g, and 10h), except for the second evolved TESV, whose largest sensitivities appear in the middle of the TC and the subtropical ridge (Fig. 10f). Compared to the real-time TESVs in Fig. 4, the structures of the evolved TESVs are more concentrated in the TC itself, implying that the initial TESVs with 0-h lead time are associated with the TC itself and experience a relatively small influence from the midlatitude system.

Fig. 10.
Fig. 10.

As in Fig. 4, but for the 0-h lead-time TESV. The thick solid line over the center of TC Jangmi denotes the 996-hPa MSLP.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

The largest contributions to the vertically integrated leading TESV energy, as shown in Fig. 10a, are from the mid- to lower troposphere (Fig. 11). The TESV energy in the lower part (Fig. 11c) is associated with the sensitive region to the north and northwest of the typhoon in Fig. 10a. The TESV energies in the middle and upper parts are associated with both midlatitude and inflow regions (Figs. 11a and 11b), with the largest amplitude being in the inflow regions for the upper TESVs (Fig. 11a). The largest contribution to the evolved TESV energy is also from the mid- to lower troposphere (Figs. 11e and 11f). The secondary maximum of the evolved TESV energy in the upper troposphere is located in the outflow region between the midlatitude trough and the subtropical high to the far northeast of the TC (Fig. 11d), but the amplitude is much smaller than that in the mid- to lower troposphere. As indicated in Fig. 10, the evolved TESV is located over the TC, which indicates that the initial TESVs are associated with the TC itself.

Fig. 11.
Fig. 11.

As in Fig. 5, but for the 0-h lead-time TESV. The thick solid line over the center of TC Jangmi denotes the 996-hPa MSLP.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Vertical profiles for the first, second, and third TESV energy are shown in Fig. 12. While the maximum of the leading TESV for both the TE and KE at the initial time (Fig. 12a) is located in the mid- to lower troposphere, the leading TESV for the PE makes a much smaller contribution throughout the troposphere. The leading TESV at the final time (Fig. 12e) increased in amplitude by at least one order of magnitude and has maxima in the mid- to lower troposphere. The PE has a smaller contribution and a more uniform structure, as is also the case for the third TESV. Major peaks of the second TESV for both TE and KE at the initial and final times are located in the upper troposphere (Figs. 12b and 12f). The PE of the second TESV has a maximum at the upper boundary at the initial time (Fig. 12b), and at the upper troposphere at the final time (Fig. 12f), similar to the TE and KE. The maximum of the third TESV for the TE and KE at the initial time (Fig. 12c) is located in the lower troposphere, whereas the maxima of the third TESV for the TE and KE at the final time (Fig. 12g) are located in the upper troposphere and mid- to lower troposphere. The PE of the third TESV exhibits a uniform distribution at the initial and final times (Figs. 12c and 12g). Even though the contribution of the leading TESV is the largest, the composite TESV differs from the leading TESV because the magnitude of the second TESV in the upper troposphere is much larger than that of the leading TESV (Figs. 12d and 12h). As discussed in the case of the real-time TESVs, the KE of the initial TESV is dominant, except at the upper boundary, and the KE of the final TESV is dominant throughout the troposphere. Compared to the leading and third TESVs, the second TESV shows quite different vertical energy structures, of which large sensitivities in the upper troposphere are associated with the interaction between the TC and the subtropical ridge. The mechanism underlying these large sensitivities in the upper troposphere in the right-rear quadrant of the TC will be discussed in a future paper on TC Man-Yi (200704).

Fig. 12.
Fig. 12.

As in Fig. 6, but for the 0-h lead-time TESV.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

d. Comparison with other sensitivity products

Figure 13 shows several real-time sensitivity guidance examples provided by many organizations to the ECMWF T-PARC DTS for TC Jangmi. While the overall features of the TESV guidance products from YSU, ECMWF, and NRL are similar (Figs. 13a–c), the TESV from JMA shows different structures (Fig. 13d). The largest sensitivities of the YSU TESV are elongated from the northwest of the TC to the right circle of the TC, as shown in Fig. 4a, indicating the influence of a midlatitude trough (Fig. 13a). However, the TESVs of the ECMWF (NRL) show the largest sensitivities on the right half-circle (right-rear quadrant; see Figs. 13b and 13c), indicating a substantial influence from the subtropical high to the right of the TC. In particular, the NRL TESV shows large sensitivities in the inflow region, as in Reynolds et al. (2010). The JMA TESV shows two large sensitivities in the northwest and northeast of the TC, with both maxima denoting the influences of midlatitude weather systems (Fig. 13d). The different structures of the JMA TESVs may be due to the model physics and normal configurations used for the TESV calculations (Komori et al. 2009). Komori and Kadowaki (2010) also showed that TESV structures of Typhoon Sinlaku depend on the model resolutions. Compared to the TESVs, the guidance provided by the ETKF method used by two organizations shows similar structures, with large sensitivities over the TC center (Figs. 13e and 13f). As reported in Majumdar et al. (2006), sensitive regions tend to be similar when using the same method with different models.

Fig. 13.
Fig. 13.

Sensitivity guidance for the Taiwan verification region (box) with MSLP (hPa) at 0000 UTC 27 Sep 2008 for TC Jangmi: (a) YSU MM5 TESV, (b) ECMWF TESV, (c) NRL TESV, (d) JMA TESV, (e) UKMO ETKF, and (f) University of Miami–NCEP ETKF. (Courtesy of ECMWF T-PARC DTS.)

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Even though the overall features of the TESV guidance are similar, their detailed structures are different. Kim and Jung (2009a) showed that the TESV structures and evolutions of Typhoon Usagi (200705) highly depend on the moist physics and norms used to calculate the TESVs. To investigate the relative influence of physics, norms, and forecast lead time of the basic-state trajectory to the detailed TESV structures shown in Figs. 13a–d, additional experiments with different physics and norms used to calculate the real-time and 0-h lead-time MM5 TESVs are performed. Figure 14a (Fig. 14e) denotes the real-time initial (final) dry norm TESVs with dry physics for TLM and adjoint model integrations. Figure 14b (Fig. 14f) denotes the real-time initial (final) moist norm2 TESVs with the large-scale precipitation as the moist physics for TLM and adjoint model integrations as in section 2b. Because the SV in Fig. 14b is calculated by use of the moist TE norm, the TESV in Fig. 14b shows a larger amplification factor than that in Fig. 14a. However, the TESV structures in Figs. 14a and 14b are similar with those in Figs. 4a and 13a.

Fig. 14.
Fig. 14.

Vertically integrated energy distribution of TESV (10−3 J kg−1, colors with varied scales) for the Taiwanese verification region (box) with 500-hPa geopotential height (contours, interval of 50 m), for the real-time leading TESV at (a) 0 and (e) 48 h with the dry norm and dry physics and at (b) 0 and (f) 48 h with the moist norm and large-scale precipitation as the moist physics for the TLM and adjoint model integrations, for the 0-h lead-time leading TESV at (c) 0 and (g) 48 h with the dry norm and dry physics and at (d) 0 and (h) 48 h with the moist norm and large-scale precipitation as the moist physics for the TLM and adjoint model integrations.

Citation: Weather and Forecasting 26, 5; 10.1175/WAF-D-10-05013.1

Figure 14c (Fig. 14g) denotes the initial (final) dry norm TESVs with 0-h lead-time model trajectories and dry physics for TLM and adjoint model integrations. Figure 14d (Fig. 14h) denotes the initial (final) moist norm TESVs with 0-h lead-time model trajectories and the large-scale precipitation as the moist physics for the TLM and adjoint model integrations as in section 2b. Similar to the real-time TESVs, the TESV in Fig. 14d shows a larger amplification factor than that in Fig. 14c due to the moist physics and moist norm effects. Compared to the TESVs in Figs. 14a and 14b, the TESVs in Figs. 14c and 14d are much more similar to those in Figs. 13b and 13c, indicating that the basic-state trajectory for the TESVs at this time may be closer to the real-time basic-state trajectories from ECMWF and NRL. However, those sensitivities east of the TC center are more prominent in Figs. 10a and 14d than in Fig. 14c, indicating that those sensitivities to the right of the TC center become clearer by using large-scale precipitation physics for TLM and adjoint model integrations with a moist TE norm. Therefore, for this case, the structures of TESVs are more sensitive to forecast lead time than to the physics and norm configurations used to calculate the TESVs. While the short forecast lead time is a necessary condition for detecting sensitivities to the right of the TC center, the moist physics and norms are sufficient conditions for showing strong sensitivities there.

4. Summary and discussion

During the T-PARC period, real-time TESVs were provided by Yonsei University to help determine sensitive regions for targeted observations. In this study, structures of real-time adaptive observation guidance provided by Yonsei University in South Korea during T-PARC were presented and compared with those of other adaptive observation guidance and no-lead-time TESVs recalculated after T-PARC.

The overall features of the real-time MM5 TESVs are consistent with those found in previous works (e.g., Peng and Reynolds 2006; Chen et al. 2009; Kim and Jung 2009b), showing the influences of TCs, midlatitude troughs, and subtropical ridges. Unlike an extratropical cyclone system in which potential (kinetic) energy is generally dominant for the initial (evolved) TESV, kinetic energy was dominant for the initial and evolved TESVs of TC Jangmi, as indicated in Kim and Jung (2009b). Careful determination of the verification region was an important component for detecting sensitive regions associated with the TC considered. The real-time TESVs generated in a mesoscale model were generally similar to those generated from global models. As indicated in Majumdar et al. (2006), TESV methods using different numerical models (regional or global) produced similar results, whereas TESV and ETKF guidance differed significantly.

Structures of TESVs are sensitive to forecast lead time; given more accurate trajectory information, more accurate TESVs would yield more accurate sensitive regions for targeted observations that may be calculated. For the case in this study, structures of TESVs depend more on the forecast lead time than the physics and norm configurations used for TESV calculations. There are limitations in real-time operations due to the lengths of the lead time. If different observational methods (such as satellite remote sensing observation) are used for real-time targeting operations, then lead time can be significantly reduced, paving the way for more accurate sensitivity guidance for targeted observations.

Acknowledgments

The authors wish to thank two anonymous reviewers for their valuable comments. This study was supported by the Korea Meteorological Administration Research and Development Program under Grant CATER 2011-2211. The authors appreciate Dr. Prates at ECMWF and Mr. Yamaguchi at JMA for supporting the real-time MM5 TESV display for the T-PARC Web sites. Real-time sensitivity products of ECMWF T-PARC DTS used in this study have been obtained from the ECMWF Data Server.

REFERENCES

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    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
  • Wu, C. C., Chen J.-H. , Lin P.-H. , and Chou K.-H. , 2007: Targeted observations of tropical cyclone movement based on the adjoint-derived sensitivity steering vector. J. Atmos. Sci., 64, 26112626.

    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., Iriguchi T. , Nakazawa T. , and Wu C.-C. , 2009: An observing system experiment for Typhoon Conson (2004) using a singular vector method and DOTSTAR data. Mon. Wea. Rev., 137, 28012816.

    • Search Google Scholar
    • Export Citation
  • Zou, X., Vandenberghe F. , Pondeca M. , and Kuo Y.-H. , 1997: Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN-435STR, 110 pp.

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    • Export Citation
1

The model simulation and the real-time TESV calculation in this section are based on the same time frame as in section 3a.

2

The moist TE norm in this study is calculated as in Kim and Jung (2009a).

Save
  • Aberson, S. D., 2003: Targeted observations to improve operational tropical cyclone forecast guidance. Mon. Wea. Rev., 131, 16131628.

    • Search Google Scholar
    • Export Citation
  • Amerault, C. M., and Doyle J. , 2009: Applications of the COAMPS adjoint model. Preprints, 23rd Conf. on Weather Analysis and Forecasting/19th Conf. on Numerical Weather Prediction, Omaha, NE, Amer. Meteor. Soc., 14A.4. [Available online at http://ams.confex.com/ams/23WAF19NWP/techprogram/paper_152970.htm.]

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., Arribas A. , Mylne K. R. , Robertson K. B. , and Beare S. E. , 2008: The MOGREPS short-range ensemble prediction system. Quart. J. Roy. Meteor. Soc., 134, 703722.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., Cardinali C. , Kelly G. , and Thepaut J.-N. , 2007: The value of observations. II: The value of observations located in singular-vector-based target areas. Quart. J. Roy. Meteor. Soc., 133, 18171832.

    • Search Google Scholar
    • Export Citation
  • Chen, J. H., Peng M. S. , Reynolds C. A. , and Wu C. C. , 2009: Interpretation of tropical cyclone forecast sensitivity from the singular vector perspective. J. Atmos. Sci., 66, 33833400.

    • Search Google Scholar
    • Export Citation
  • Ehrendorfer, M., and Errico R. M. , 1995: Mesoscale predictability and the spectrum of optimal perturbations. J. Atmos. Sci., 52, 34753500.

    • Search Google Scholar
    • Export Citation
  • Elsberry, R. L., and Harr P. A. , 2008: Tropical cyclone structure (TCS08) field experiment science basis, observational platforms, and strategy. Asia-Pac. J. Atmos. Sci., 44, 209231.

    • Search Google Scholar
    • Export Citation
  • Golub, G. H., and Van Loan F. , 1996: Matrix Computations. The Johns Hopkins University Press, 728 pp.

  • Jung, B.-J., Kim H. M. , Kim Y.-H. , Jeon E.-H. , and Kim K.-H. , 2010: Observation system experiments for Typhoon Jangmi (200815) observed during T-PARC. Asia-Pac. J. Atmos. Sci., 46, 305316.

    • Search Google Scholar
    • Export Citation
  • Kim, H. M., 2003: A computation of adjoint-based sensitivities in a quasigeostrophic model. Korean J. Atmos. Sci., 6, 7183.

  • Kim, H. M., and Jung B.-J. , 2006: Adjoint-based forecast sensitivities of Typhoon Rusa. Geophys. Res. Lett., 33, L21813, doi:10.1029/2006GL027289.

    • Search Google Scholar
    • Export Citation
  • Kim, H. M., and Jung B.-J. , 2009a: Influence of moist physics and norms on singular vectors for a tropical cyclone. Mon. Wea. Rev., 137, 525543.

    • Search Google Scholar
    • Export Citation
  • Kim, H. M., and Jung B.-J. , 2009b: Singular vector structure and evolution of a recurving tropical cyclone. Mon. Wea. Rev., 137, 505524.

    • Search Google Scholar
    • Export Citation
  • Kim, H. M., Morgan M. , and Morss R. E. , 2004: Evolution of analysis error and adjoint-based sensitivities: Implications for adaptive observations. J. Atmos. Sci., 61, 795812.

    • Search Google Scholar
    • Export Citation
  • Kim, H. M., Jung B.-J. , Kim Y.-H. , and Lee H.-S. , 2008: Adaptive observation guidance applied to Typhoon Rusa: Implications for THORPEX-PARC 2008. Asia-Pac. J. Atmos. Sci., 44, 297312.

    • Search Google Scholar
    • Export Citation
  • Komori, T., and Kadowaki T. , 2010: Resolution dependence of singular vectors computed for Typhoon Sinlaku. SOLA, 6, 4548.

  • Komori, T., and Coauthors, 2009: JMA singular vector guidance for T-PARC 2008. Extended Abstracts, Fourth Japan–China–Korea Joint Conf. on Meteorology, Tsukuba, Japan, Meteorological Society of Japan, S5-03. [Available online at http://wwwsoc.nii.ac.jp/msj/jckjc09/JCKJC09-Abstract_Collection.pdf.]

    • Search Google Scholar
    • Export Citation
  • Langland, R. H., Shapiro M. , and Gelaro R. , 2002: Initial condition sensitivity and error growth in forecasts of the 25 January 2000 East Coast snowstorm. Mon. Wea. Rev., 130, 957974.

    • Search Google Scholar
    • Export Citation
  • Majumdar, S. J., Aberson S. D. , Bishop C. H. , Buizza R. , Peng M. S. , and Reynolds C. A. , 2006: A comparison of adaptive observing guidance for Atlantic tropical cyclones. Mon. Wea. Rev., 134, 23542372.

    • Search Google Scholar
    • Export Citation
  • Morgan, M., 2001: A potential vorticity and wave activity diagnosis of optimal perturbation evolution. J. Atmos. Sci., 58, 25182544.

  • Palmer, T. N., Gelaro R. , Barkmeijer J. , and Buizza R. , 1998: Singular vectors, metrics, and adaptive observations. J. Atmos. Sci., 55, 633653.

    • Search Google Scholar
    • Export Citation
  • Peng, M. S., and Reynolds C. A. , 2006: Sensitivity of tropical cyclone forecasts as revealed by singular vectors. J. Atmos. Sci., 63, 25082528.

    • Search Google Scholar
    • Export Citation
  • Reynolds, C. A., Peng M. S. , and Chen J.-H. , 2009: Recurving tropical cyclones: Singular vector sensitivity and downstream impacts. Mon. Wea. Rev., 137, 13201337.

    • Search Google Scholar
    • Export Citation
  • Reynolds, C. A., Doyle J. D. , Hodur R. M. , and Jin H. , 2010: Naval Research Laboratory multiscale targeting guidance for T-PARC and TCS-08. Wea. Forecasting, 25, 526544.

    • Search Google Scholar
    • Export Citation
  • Wu, C. C., Chen J.-H. , Lin P.-H. , and Chou K.-H. , 2007: Targeted observations of tropical cyclone movement based on the adjoint-derived sensitivity steering vector. J. Atmos. Sci., 64, 26112626.

    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., Iriguchi T. , Nakazawa T. , and Wu C.-C. , 2009: An observing system experiment for Typhoon Conson (2004) using a singular vector method and DOTSTAR data. Mon. Wea. Rev., 137, 28012816.

    • Search Google Scholar
    • Export Citation
  • Zou, X., Vandenberghe F. , Pondeca M. , and Kuo Y.-H. , 1997: Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN-435STR, 110 pp.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Model domains (solid lines) and verification regions (dotted lines) for Taiwan (red), Japan (purple), and Korea (blue). Real-time TESV sensitivity products using MM5 were generated for the Taiwanese verification region of 18°–30°N, 118°–132°E (18°–30°N, 117°–140°E) from 0000 UTC 11 May to 0000 UTC 3 Aug 2008 (from 0000 UTC 4 Aug to 0000 UTC 26 Dec 2008); the Japanese verification region of 20°–40°N, 120°–150°E from 0000 UTC 18 Apr to 0000 UTC 26 Dec 2008; and the Korean verification region of 30°–42°N, 118°–132°E from 0000 UTC 4 Jun to 0000 UTC 26 Dec 2008.

  • Fig. 2.

    A schematic diagram of the preparation procedure for MM5 real-time TESV guidance at YSU.

  • Fig. 3.

    The Regional Specialized Meteorological Center (RSMC)-Tokyo Typhoon Center best track (black line with + symbols), 48-h MM5 forecast track (red line with circles) with 48-h lead time, and 48-h MM5 forecast track (blue line with squares) with 0-h lead time, for TC Jangmi (200815). Green circles denote Ti, Ta, and Tυ in the best track. Each symbol is plotted at 6-h intervals.

  • Fig. 4.

    Vertically integrated energy distribution of the real-time TESV (10−3 J kg−1, colors with varied scales) for the Taiwan verification region (box) along with 500-hPa geopotential height (contours, interval of 50 m) at 0 h (0000 UTC 27 Sep 2008) for the (a) first, (b) second, (c) third, and (d) composite TESVs, and at 48 h (0000 UTC 29 Sep 2008) for the (e) first, (f) second, (g) third, and (h) composite TESVs. The thick solid line over the center of TC Jangmi denotes the 1002-hPa MSLP. The numbers at the bottom right of (a)–(c) denote the amplification factors associated with each TESV.

  • Fig. 5.

    As in Fig. 4, but for (top) the 100–400-hPa layer along with the layer-average potential vorticity (PV) of the 200–500-hPa layer [contour interval of 1 PV unit (PVU), where 1 PVU = 10−6 m2 s−1 K kg−1] at (a) 0 h (0000 UTC 27 Sep 2008) and (d) 48 h (0000 UTC 29 Sep 2008); (middle) the 400–750-hPa layer along with the layer-average PV of 500-hPa geopotential height (contour interval of 50 m) at (b) 0 and (e) 48 h; and (bottom) the 750 hPa–MSLP layer along with the MSLP (contour interval of 4 hPa) at (c) 0 and (f) 48 h.

  • Fig. 6.

    Vertical energy distributions of the real-time TESV (J kg−1: TE, closed circles; KE, open circles; PE, open squares) at 0 h for the (a) first, (b) second, (c) third, and (d) composite TESVs, and at 48 h in the Taiwanese verification region for the (e) first, (f) second, (g) third, and (h) composite TESVs. Note the different magnitudes along the abscissas of the evolved TESVs after 48 h. The ordinate represents the vertical level (pressure) and the abscissa denotes the TESV energy (J kg−1).

  • Fig. 7.

    As in Fig. 4, but for the Korean verification region (box).The thick solid line over the center of TC Jangmi denotes 1000 hPa MSLP.

  • Fig. 8.

    As in Fig. 5, but for the Korean verification region (box). The thick solid line over the center of TC Jangmi denotes the 1000-hPa MSLP.

  • Fig. 9.

    As in Fig. 6, but for the Korean verification region.

  • Fig. 10.

    As in Fig. 4, but for the 0-h lead-time TESV. The thick solid line over the center of TC Jangmi denotes the 996-hPa MSLP.

  • Fig. 11.

    As in Fig. 5, but for the 0-h lead-time TESV. The thick solid line over the center of TC Jangmi denotes the 996-hPa MSLP.

  • Fig. 12.

    As in Fig. 6, but for the 0-h lead-time TESV.

  • Fig. 13.

    Sensitivity guidance for the Taiwan verification region (box) with MSLP (hPa) at 0000 UTC 27 Sep 2008 for TC Jangmi: (a) YSU MM5 TESV, (b) ECMWF TESV, (c) NRL TESV, (d) JMA TESV, (e) UKMO ETKF, and (f) University of Miami–NCEP ETKF. (Courtesy of ECMWF T-PARC DTS.)

  • Fig. 14.

    Vertically integrated energy distribution of TESV (10−3 J kg−1, colors with varied scales) for the Taiwanese verification region (box) with 500-hPa geopotential height (contours, interval of 50 m), for the real-time leading TESV at (a) 0 and (e) 48 h with the dry norm and dry physics and at (b) 0 and (f) 48 h with the moist norm and large-scale precipitation as the moist physics for the TLM and adjoint model integrations, for the 0-h lead-time leading TESV at (c) 0 and (g) 48 h with the dry norm and dry physics and at (d) 0 and (h) 48 h with the moist norm and large-scale precipitation as the moist physics for the TLM and adjoint model integrations.

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