Intercomparison of Targeted Observation Guidance for Tropical Cyclones
in the Northwestern Pacific
CHUN-CHIEHWU,* JAN-HUEYCHEN,* SHARANYAJ. MAJUMDAR,1 MELINDAS. PENG,# CAROLYNA. REYNOLDS,# SIMD. ABERSON,@ ROBERTOBUIZZA,& MUNEHIKOYAMAGUCHI,**
SHIN-GANCHEN,* TETSUONAKAZAWA,11ANDKUN-HSUANCHOU## * Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan 1 RSMAS Division of Meteorology and Physical Oceanography, University of Miami, Miami, Florida
# Naval Research Laboratory, Monterey, California @ NOAA/AOML Hurricane Research Division, Miami, Florida
& European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom ** Japan Meteorological Agency, Tokyo, Japan
11 Meteorological Research Institute, Japan Meteorological Agency, Tokyo, Japan ## Department of Atmospheric Sciences, Chinese Culture University, Taipei, Taiwan
(Manuscript received 19 August 2008, in final form 4 February 2009) ABSTRACT
This study compares six different guidance products for targeted observations over the northwest Pacific Ocean for 84 cases of 2-day forecasts in 2006 and highlights the unique dynamical features affecting the tropical cyclone (TC) tracks in this basin. The six products include three types of guidance based on total-energy singular vectors (TESVs) from different global models, the ensemble transform Kalman filter (ETKF) based on a multimodel ensemble, the deep-layer mean (DLM) wind variance, and the adjoint-derived sensitivity steering vector (ADSSV). The similarities among the six products are evaluated using two objective statistical techniques to show the diversity of the sensitivity regions in large, synoptic-scale domains and in smaller domains local to the TC. It is shown that the three TESVs are relatively similar to one another in both the large and the small domains while the comparisons of the DLM wind variance with other methods show rather low similarities. The ETKF and the ADSSV usually show high similarity because their optimal sensitivity usually lies close to the TC. The ADSSV, relative to the ETKF, reveals more similar sensitivity patterns to those associated with TESVs. Three special cases are also selected to highlight the similarities and differences among the six guidance products and to interpret the dynamical systems affecting the TC motion in the northwestern Pacific. Among the three storms studied, Typhoon Chanchu was associated with the subtropical high, Typhoon Shanshan was associated with the midlatitude trough, and Typhoon Durian was associated with the subtropical jet. The adjoint methods are found to be more capable of capturing the signal of the dynamic system that may affect the TC movement or evolution than are the ensemble methods.
1. Introduction
The tropical cyclone (TC) is one of the most threat-ening natural phenomena that cause great human and economic losses. The lack of observations over the ocean regions where TCs spend most of their lifetime seriously degrades the accuracy of forecasts (Wu 2006). Therefore, it is worthwhile to assimilate the special data
obtained from both aircraft (with dropwindsondes de-ployed) and satellites in areas that may have the maxi-mum influence on numerical model predictions of TCs. To achieve this, several mathematical targeted observ-ing strategies have been developed (Majumdar et al. 2006; Wu et al. 2007a). The primary consideration in devising such strategies is to identify the sensitive areas in which the assimilation of targeted observations is expected to have the greatest influence on improving the numerical model forecast, by minimizing the analysis error.
Recent research efforts in targeted observations have been associated with the National Oceanic and Atmospheric Administration (NOAA) Winter Storms Corresponding author address: Dr. Chun-Chieh Wu, Dept. of
Atmospheric Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan.
E-mail: cwu@typhoon.as.ntu.edu.tw DOI: 10.1175/2009MWR2762.1
Reconnaissance, NOAA synoptic surveillance, and The Observing System Research and Predictability Experiment (THORPEX). In 2003, the Atlantic Ocean THORPEX regional campaign was launched to improve forecasts of winter cyclones over Europe, using a wider variety of instruments than was possible during the Fronts and Atlantic Storm Track Experiment (FASTEX; Joly et al. 1997) and the North Pacific Experiment (NORPEX; Langland et al. 1999). Several of the objective methods considered previously were used, in addition to more recently developed methods such as Hessian singular vectors (Leutbecher 2003) and observation sensitivity (Langland and Baker 2004). In the Northern Hemi-sphere summer of 2006, the observation sensitivity and ensemble transform Kalman filter (ETKF; Bishop et al. 2001; Majumdar et al. 2002a) methods were used to provide guidance for deployments of driftsonde balloons traveling across the Atlantic Ocean from their launch site in Africa, as part of the African Monsoon Multidisci-plinary Analysis (AMMA). In 2008, targeted observa-tions have been one important facet of the THORPEX Pacific Asian Regional Campaign (T-PARC).
The synoptic surveillance missions to improve TC track forecasts have been conducted by NOAA in the Atlantic basin since 1997 (Aberson and Franklin 1999; Aberson 2002, 2003). In the northwest Pacific Ocean basin, since 2003, Dropwindsonde Observation for Typhoon Surveillance near the Taiwan Region (DOT-STAR) has been conducted under the support of the National Science Council (NSC) in Taiwan (Wu et al. 2005). Four objective methods, adapted from those used to study the winter storms, have been employed for the targeted observations for these surveillance missions of TCs. These products are derived from four distinct tech-niques. First is the ensemble deep-layer mean (DLM) wind variance of the deep-layer steering flows based on the National Centers for Environmental Prediction (NCEP) Global Ensemble Forecasting System (GEFS), specifically developed for the tropics (Aberson 2003). Second is the ETKF (Majumdar et al. 2002a), which predicts the reduction in forecast error variance for feasible deployment of targeted observations based on a combination of NCEP, European Centre for Medium-Range Weather Forecasts (ECMWF), and Canadian Meteorological Center (CMC) ensembles. Third are the total-energy singular vectors (TESVs; Palmer et al. 1998; Buizza and Montani 1999; Peng and Reynolds 2006), which maximize the linear growth of the per-turbation total energy in the Navy Operational Global Atmospheric Prediction System (NOGAPS; Rosmond 1997; Gelaro et al. 2002). Fourth is the adjoint-derived sensitivity steering vector (ADSSV; Wu et al. 2007a). By appropriately defining the response functions to
represent the typhoon steering flow at the verifying time, ADSSV demonstrates the sensitivity locations at the observing time that would affect the typhoon steering flow at the verifying time. The current ADSSV is calculated based on the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5; Grell et al. 1995) adjoint modeling system. In the Atlantic Ocean basin, the TC track forecasts have been improved by 15%– 20% within the 5-day forecast period for those missions designed by the targeted strategies (Aberson 2008). In the western North Pacific Ocean basin, an average of 20% improvement for the 12–72-h track forecasts over the NCEP Global Forecasting System (GFS), NOGAPS, Japan Meteorological Agency-Global Spectral Model (JMA-GSM), their ensembles, and the Weather Re-search and Forecasting (WRF) Model has been dem-onstrated (Wu et al. 2007b; Chou and Wu 2008).
In Majumdar et al. (2006), five targeted observing guidance products based on three different techniques for 2-day forecasts of 78 TC cases during the 2004 At-lantic hurricane season were compared. The products include the ensemble DLM wind variance from the NCEP model, two ETKF products based separately on NCEP and ECMWF ensembles, and two TESV pro-ducts based on ECMWF and NOGAPS. Majumdar et al. (2006) showed that the large-scale characteristics of the ECMWF and NOGAPS TESV guidance pro-ducts are relatively similar on synoptic scales, but are less similar in the local environment of the TC. For major hurricanes, all techniques usually indicate sensi-tive regions close to the storms. For weaker TCs, the TESVs only have 30% (20%) similar regions to that from the ETKF (DLM wind variance). The ETKF based on the ECMWF ensemble is more similar to that based on the NCEP ensemble and the DLM wind var-iance for major hurricanes than for weaker TCs.
Using the same database as Majumdar et al. (2006), Reynolds et al. (2007) identified and interpreted sys-tematic structural differences between these techniques. Their results showed that when the sensitive areas are close to the storm, the TESV presents a maximum in an annulus around the storm, but the ETKF shows a maxi-mum at the storm location itself. When the sensitive areas are remote from the storm, the TESV maxima generally occur northwest of the storm, whereas the ETKF maxima are more scattered relative to the storm location and of-ten occur over the northern North Atlantic.
As a follow-up study, this paper compares six dif-ferent targeted guidance products based on 84 cases (as described in appendix A) of 2-day forecasts of the northwest Pacific TCs in 2006, and highlights the unique dynamical features that affect the TC tracks in
this basin. There are six types of guidance: three TESVs from different global models, the ETKF based on the multimodel ensemble members, the DLM wind vari-ance, and the ADSSV (details are listed in Table 1). In the northwestern Pacific Ocean there are several in-teresting dynamical systems affecting the TC motion (Wu 2006), such as the subtropical high, the midlatitude trough, the subtropical jet, and the southwesterly mon-soon. The latter two systems appear to play less signif-icant roles in the Atlantic Ocean. Further analysis is thus conducted to identify the similarities and differ-ences between all these different targeted methods and to interpret their dynamic meanings. The methodologies of the four different techniques and the models adopted are presented briefly in section 2. Section 3 provides a comparison based on quantitative analyses. Some phys-ical interpretations of the dynamphys-ical systems in three special cases are discussed in section 4. The summary and future prospects are discussed in section 5.
2. Targeted observing techniques
Based on different models and techniques, the six targeted observing products are summarized in Table 1. The three TESV products, called ECSV, NGPSV, and JMASV, respectively, in this study, utilize the first three SVs from three global models, ECMWF, NOGAPS, and JMA/Ensemble Prediction System (EPS). The ETKF method uses multimodel ensemble members.1 For the TESV methods, the model initial time tiis 48 h prior to
the observing (analysis) time ta, while ensemble
mem-bers of the multimodel forecasts 48–66 h prior to the observing time are used for the ETKF calculation. The error propagation from ta to the verifying time ty is
considered for TESVs and ETKF. The period of ta–ti
is selected for planning synoptic surveillance missions, since the decision for aircraft deployment is required at least 36 h prior to ta in order to meet the air traffic
control requirement. For the ADSSV method, the ini-tial condition of the MM5 is based on the 48-h forecast of the NCEP/GFS. The trajectory of tato tyis then
ob-tained from the MM5 48-h forward integration. The DLM wind variance, also called NCVAR in this study, is calculated based on the ensemble forecast fields of the NECP/GEFS, with 10 bred-mode (Toth and Kalnay 1993) ensemble members before 31 May (for the first 8 cases, as shown in appendix A), and with 14 members based on an ensemble transform technique (Wei et al. 2008) after 31 May. This is a method in which only the period between tiand ta(48 h) is considered. The
reso-lutions of the trajectory and output of the six methods are also shown in Table 1.
a. TESV
The SV technique, introduced by Buizza (1994) in the ECMWF ensemble prediction system, and used by Palmer et al. (1998) and Buizza and Montani (1999) to identify targeted observing areas, is a particular type of the general class of targeted analysis error covariance (AEC) optimal. This method was applied to maximize the growth of a total energy perturbation into a fore-cast verification region for TCs in Peng and Reynolds (2006).
The leading singular vector (SV) represents the fastest-growing perturbation to a given trajectory (such as a weather forecast) in a linear sense (Peng and Reynolds 2006). The leading SV maximizes the ratio of the final perturbation energy to the initial perturbation energy. TABLE1. Summary of six targeted methods.
Method ECSV NGPSV JMASV ETKF ADSSV NCVAR
Model ECMWF NOGAPS JMA/EPS ECMWF NCEP/GEFS CMC MM5 NCEP/GEFS
No. ensemble/SVs 3 SVs 3 SVs 3 SVs ECMWF: 51
NCEP/GEFS: 60 CMC: 34 Tot 154 members — 14 ensembles (10 ensembles for first 8 cases) Resolution of trajectory T63L40 T239L30 T319L40 ECMWF: T399L62 NCEP/GEFS: T126L28 CMC: 1.28 60 km T126L28 Resolution of output T63L40 T79L30 T63L40 28 60 km 18 ti–ta 48 h 48 h 48 h 66–48 h — 48 h ta–ty 48 h 48 h 48 h 48 h 48 h —
1In this study, 145 ensemble members in total contribute to the ETKF method. Fourteen ensembles and 1 control run of NCEP/ GEFS are calculated from 0600, 1200, 1800, and 0000 UTC, re-spectively, 66, 60, 54, and 48 h prior to ta. In total, 50 ensemble members and 1 control run are from ECMWF initialized 60 h prior to ta. CMC offers 16 ensemble members and 1 control run 60 and 48 h before taat 1200 and 0000 UTC, respectively.
The second SV maximizes this ratio under the con-straint of being orthogonal to the first SV, the third SV maximizes this ratio under the constraint of being or-thogonal to the first two SVs, and so on. For complex models such as dynamical TC models, the eigenvector equation may be solved in an iterative fashion using the forward and adjoint propagators linearized about a particular forecast.
The ECSV and NGPSV have been computed using tangent linear and adjoint models of the ECMWF var-iational data assimilation system (Mahfouf and Rabier 2000) and the NOGAPS forecast system, respectively. Both systems contain surface drag and horizontal and vertical diffusion, but do not include moist processes.
Another SV method, JMASV, contains moist SVs calculated by JMA/EPS, which has been developed using the linearized model and its adjoint version adopted for the JMA global four-dimensional varia-tional analysis system (Yamaguchi et al. 2009). This system consists of full dynamics based on Eulerian in-tegrations and physical processes including representa-tions of vertical diffusion, gravity wave drag, large-scale condensation, longwave radiation, and deep cumulus convection.
b. ETKF
In this study, the ETKF (Majumdar et al. 2006) uses ensemble-based data assimilation theory (Bishop et al. 2001) to predict the reduction in 200–850-hPa wind forecast error variance within the verification area for feasible deployments of targeted observations, based on 145 ensemble forecast perturbations from three different models (Table 1). As explained in detail in Majumdar et al. (2006), the ETKF computation is a two-stage pro-cess. First, the analysis error covariance matrix Pr(ta) at
the observing time (ta) pertaining to the routine
obser-vational network composed of rawinsondes and satellite-based temperature fields is found by solving the Kalman filter error statistics equation. Next, the anal-ysis error covariance matrix Pq(ta) for the observational
network augmented by the qth hypothetical ‘‘test probe’’ of targeted observations is computed. The test probe comprises targeted observations of (u, y, T) in a 38 3 38 square lattice, at the 250-, 500-, and 850-hPa levels. The associated ‘‘signal covariance’’ matrix or reduction in forecast error covariance due to the targeted observa-tions, valid at the verification time (ty), is then deduced.
The trace of this matrix localized within the verification region is referred to in this paper as the ‘‘signal vari-ance.’’ The signal variance is then rapidly computed for each different test-probe location on a 18 3 18 grid. The ETKF guidance then represents this signal variance as a function of the central location of test probes. The
test-probe location that produces the highest signal variance is deemed the optimal location for targeting.
c. DLM wind variance
Using this technique, the sensitive regions at the observing time are represented by locations containing the largest variance of the NCEP/GEFS ensemble of mass-weighted DLM (850–200 hPa) wind (Aberson 2003). Prior to 31 May 2006, the NCEP/GEFS was initialized using bred vectors (Toth and Kalnay 1993). Since 31 May 2006, the ensemble transform (Wei et al. 2008) has been operational at NCEP. The DLM wind is chosen because TCs are generally steered by the envi-ronmental DLM flow, and the dropwindsondes from the jet aircraft tend to sample areas in which the un-certainty in this flow is predicted to be the largest. Aberson (2003) demonstrated that the assimilation of only the subset of observations in areas of high NCEP DLM wind variance improved NCEP GFS TC track forecasts more than the assimilation of uniformly sampled observations did.
d. ADSSV
Wu et al. (2007a) proposed ADSSV to demonstrate the sensitivity locations and the critical direction of the typhoon steering flow at the observing time, based on the MM5 adjoint modeling system. The goal of this method is to identify the sensitive areas at the observing time that would affect the steering flow of the TC at the verifying time. The DLM wind within the verifying area is defined as the response function in the MM5 adjoint model. Different from ETKF and SV methods, ADSSV includes a 600 km by 600 km square verifying area centered on the MM5-simulated storm location at the verifying time, which is used to calculate the back-ground steering flow. Two responses functions are then defined: R1, which is the 850–300-hPa deep-layer area
average (Wu et al. 2003) of the zonal component (u); and R2, the average of the meridional component (y) of
the wind vector.
After being averaged, the axisymmetric component of the strong cyclonic flow around the storm center is removed, and thus the vector of (R1, R2) represents the
background steering flow across the storm center at the verifying time. To interpret the physical meaning of the sensitivity, a unique new parameter, ADSSV is de-signed. It relates the sensitive areas at the observing time to the steering flow at the verifying time. The ADSSV with respect to the vorticity field (§) is
ADSSV [ ›R1 ›§ , ›R2 ›§ , (1)
where the magnitude of ADSSV at a given point indi-cates the extent of the sensitivity, and the direction of the ADSSV represents change in the response of the steering flow due to a vorticity perturbation placed at that point. For example, if at a given forecast time the ADSSV vector at one particular grid point points to the east, an increase in the vorticity at this point at the ob-serving time would be associated with an increase in the eastward steering of the storm at the verifying time.
3. Quantitative comparison
From the 2006 season, 84 cases in which the Joint Typhoon Warning Center (JTWC) issued forecasts at 0000 UTC and the storms still remained present at 48 (ta) and 96 (ty) hours were selected for this study
(see appendix A). These cases include studies of 19 TCs (Fig. 1), 14 of them made landfall in Japan, Korea, China, Taiwan, Vietnam, and the Philippines. Multiple cases from the same storm are separated by 24 h on successive days. To be consistent with the work in Majumdar et al. (2006), the verification area is chosen to be centered at the 96-h (ty) TC position forecast by the JTWC. The
values of the six guidance products are interpolated to latitude–longitude 1.58 grids and normalized by the
maximum value of each method for each case. Since the observations collected within the inner three degrees of the TC center generally provide little impact on im-proving the forecast of TC track (likely because the data were obliterated by the bogus vortex; Aberson 2002), all data within 333 km of the related model forecast TC center locations2 at time ta are ignored. Figure 2 is a
representative example to indicate the patterns of the six sets of guidance for a selected case [i.e., number 10 (WP04, Typhoon Ewiniar)]. More details of the tar-geted patterns for this individual case and the general characteristics are discussed in the following sections. In this section, the two statistical techniques introduced in Majumdar et al. (2006) are used to show the quantita-tive diversity of the six methods. In this study, we im-prove upon the statistical techniques of Majumdar et al. (2006) with varying threshold values to elucidate the extent to which two sets of guidance are similar. This allows for a more complete and useful comparison than the results provided in Majumdar et al. (2006). The FIG. 1. The JTWC best tracks of the 19 TCs. Each symbol is plotted at 12-h intervals. Except for ‘‘01C’’ (Typhoon
Ioke) from the central Pacific, all other TCs are numbered in northwest Pacific orders. For example, ‘‘02W’’ is Typhoon Chanchu whose annual cyclone number is 02 in the northwestern Pacific basin in 2006.
2The TC center information of ETKF at time t
ais adopted as the average of the forecast TC center locations weighted by the proportion of the number of ensemble numbers as 6051:34 of NCEP/GEFS, ECMWF, and the CMC model.
statistics here are also compared with the results of Majumdar et al. (2006) for the Atlantic TCs.
a. The common targeted locations
For each of the 84 cases, there are 15 pairs of maps for the six targeted methods to be compared. In this test, the gridpoint locations corresponding to the number of X highest grid points with leading sensitivity values are first stored for each map and then the number C of the common grid points between each of the 15 pairs are found in each case. A modified equitable threat score (METS; Majumdar et al. 2002b),
METS 5 C E(C)
2X C E(C), (2)
is used to show the commonality between any two maps. In (2), E(C) is the expected number of common grid points, which is estimated between all 84 cases. The first step to obtain E(C) is to compute the 83 values of C
between ECSV case 1 and each of NGPSV cases 2–84. The values of C between ECSV case 2 and each of NGPSV cases 1–84, except case 2 are then computed. The procedure is stopped when all 84 3 83 ECSV and NGPSV cases are computed. Similar procedures are preformed for the other 14 pairs of the targeted methods. The total number of C values for the inde-pendent pairs of maps is N 5 15 3 84 3 83 5 104 580. The average of the 104 580 C values is given as E(C) for a fixed X. More details of E(C) are introduced in ap-pendix B of Majumdar et al. (2002b). The values of METS for each pair of maps are calculated for each case. When the METS is equal to 1, the value of C is the same as that of X. That means the two maps contain identical targets. A METS greater than (less than) 0 indicates that a larger (smaller) number of common grid points occur than by chance. In the following discussion, the percentage of cases out of 84 in which METS . 0 (Majumdar et al. 2006) is adopted to show the similarity of the targeted methods.
FIG. 2. The large-domain common targeted location comparison of (a) ECSV, (b) NGPSV, (c) JMASV, (d) ETKF, (e) ADSSV, and (f) NCVAR for case 10, Typhoon Ewiniar, at ta50000 UTC 2 Jul 2006 and ty50000 UTC 4 Jul 2006. Except for (f), the verifying areas of the other five methods are indicated by the red squares. The JTWC best track and each model forecast of case 10 valid at taare denoted by the solid and empty typhoon symbols, respectively. The brown dots represent X 5 63 grid points with the highest value.
To provide a thorough comparison of all the guidance products, following Majumdar et al. (2006), we conduct the comparison based on two domains of different sizes. One is the larger domain (108S–658N, 808E–1808), the other is the smaller domain (3000 km by 3000 km cen-tered at each model storm center). The larger domains tend to highlight the large-scale sensitivity environment (away from the storm), which could be related to the targeting of extra satellite observations (such as rapid-scan winds). On the other hand, the smaller domains focus more on the local sensitivity features around the storm region, which is likely more relevant for synoptic surveillance (such as in DOTSTAR)
1) FIXED LARGE DOMAIN(108S–658N, 808E–1808)
A domain containing the northwestern Pacific basin and east Asia’s continental region including the Indian Ocean is chosen for the comparison based on METS. In total there are 3149 grid points in this 108S–658N, 808E–1808 area with 1.58 3 1.58 resolution. Figure 2 shows the targeted guidance for case 10, Typhoon Ewiniar at ta50000 UTC 2 July 2006. The 63 leading grid points,
which is 2% (this threshold value can be modified, as discussed later) of the total number of grid points, correspond to the sensitive regions (X 5 63). The value of E(C) is 2.48 under the 2% threshold mentioned above. In this case, the number of common grid points C and their corresponding METS for each of the 15 pairs of guidance are listed in Table 2. ECSV versus JMASV has the most common grid points (i.e., 44) and the highest METS value (i.e., 0.52). Both of them show sensitivity within several hundred kilometers to the east of the TC (Fig. 2). On the other hand, NGPSV, ETKF, and ADSSV show high sensitivity near the TC, but with the maximum value in different directions relative to the storm center. As for NCVAR, it does not share common grid points with the three TESVs and ADSSV, while having only 10 common grid points with ETKF.
Table 3 shows the percentages among the 84 cases of those with METS . 0 for X 5 63. ECSV and NGPSV
are highly similar (METS . 0) in 90% of the 84 cases. The three TESVs are quite similar to one another, consistent with the results in Majumdar et al. (2006) that the targeted methodology usually gives similar guidance irrespective of the model. The percentage of METS . 0 for the comparison of ETKF and the three TESVs are around 50%–60%. However, the percentage increases to around 89% when ETKF is compared with ADSSV. For ADSSV, the similarity reaches 70% when it is compared with NGPSV and around 50% when com-pared with the other two TESVs. The similarities be-tween NCVAR and other methods, except the 43% for ETKF, are generally lower than 10%, indicating that NCVAR persistently shows rather different sensitivity locations as compared with other targeted methods. On the other hand, NCVAR and ETKF usually show sen-sitivities around the midlatitude jet and extratropical cyclones, which are far from the TCs. Thus, the simi-larity is higher for this pair than that between NCVAR and other methods.
To explore the similarity of the targeted methods under different TC intensities, according to the Saffir– Simpson scale, the 84 cases are divided into 27 major typhoons (MTY; maximum sustained wind .96 kt, i.e., category 3 and above), 38 typhoons (TY; 64–96 kt; categories 1 and 2), and 19 tropical storms (TS; ,64 kt). The percentages of METS . 0 for these three categories are listed in Table 4. The three TESVs have the highest similarities to one another in the TY category. But for the comparison between ETKF and each of the other methods, no specific intensity category shows any par-ticularly higher percentages. Comparing ADSSV to other methods, the highest percentages are identified in the MTY category when compared with ECSV, NGPSV, and ETKF, but in the TY category when compared with JMASV and NCVAR. The agreement of ADSSV ver-sus ETKF reaches 96% in the MTY category. For the NCVAR method, the highest percentage (52.6%) is shown in the TY category when it is compared with the ETKF. On the other hand, the similarity between NCVAR and each of the other methods is very low. The percentages even drop to zero when NCVAR is com-pared with NGPSV in the TY and TS groups and with TABLE2. Number of (left) large-domain common grid points C
and (right) the corresponding METS for each pair of targeted methods of case 10 (shown in Fig. 2). The METS is computed by (9) with X 5 63 and E(C) 5 2.48.
C/METS NGPSV JMASV ETKF ADSSV NCVAR
ECSV 29/0.28 44/0.52 29/0.28 32/0.32 0/20.02 NGPSV 28/0.27 30/0.29 27/0.25 0/20.02
JMASV 30/0.29 37/0.40 0/20.02
ETKF 31/0.31 10/0.07
ADSSV 0/20.02
TABLE3. Percentage of the 84 cases in which METS . 0 for X 5 63 in the large domain.
Methods NGPSV JMASV ETKF ADSSV NCVAR
ECSV 90.48 84.52 55.95 53.57 4.76
NGPSV 79.76 58.33 70.24 3.57
JMASV 53.57 51.19 5.95
ETKF 89.29 42.86
the ADSSV in MTY group. In all, the above compari-son shows that generally more agreement among the guidance products exists for the stronger storms (MTY and TY) than for the weaker storms (TS). This finding is consistent with the study of the Atlantic TCs (Majumdar et al. 2006), which pointed out that there is a stronger agreement between each comparison pair for major hurricanes than for TCs of weaker intensities.
2) SMALL DOMAIN(3000BY3000KM2)CENTERED AT EACH MODEL STORM CENTER
The common targeted locations are also examined in relatively smaller domains in which synoptic surveil-lance would typically be conducted. A 21 by 21 grid of 150-km resolution is created for every case in a storm-relative coordinate centered at each model storm center. The values obtained from the methods are interpolated linearly onto the grids. Figure 3 shows the targeted guidance in the small domain for case 10 with X 5 31 leading grid points, which is 7% of total 441 grid points. As mentioned earlier, the sensitivity regions outside of the inner 38 radius (333 km) of the storm center are shown. The E(C) is 5.30 for this 7% threshold. Table 5 contains the numbers of common grid points C and their corresponding METS for each of the 15 pairs for case 10. The comparison between ECSV and NGPSV shows the highest similarity (C 5 20; METS 5 0.4), while the comparison between ECSV and JMASV, as well as between JMASV and ADSSV, provides the second highest similarity (C 5 18; METS 5 0.33). In general, the comparison in the small domain (Table 5) is con-sistent with that in the larger domain (Table 2). One notable difference is that the similarities of NCVAR versus the three other TESV methods and ADSSV in the small domain (Table 5) are much higher than those in the large domain (Table 2), mainly associated with the leading grid points on the east side of Ewiniar for case 10 in NCVAR (see Fig. 3).
Table 6 shows the percentage of cases with METS . 0 for X 5 31 among the 84 cases in the small domain. As expected, the three TESV methods are very similar to one another. The percentages of ETKF compared with the three TESV methods are around 45%. The
simi-larity between NGPSV and ADSSV is 39%, the same as that between JMASV and ADSSV. The similarity is only 30% in the comparison between ECSV and ADSSV. Because some of the NCVAR leading grid points are shown to be closer to the storm for the small-domain comparison (i.e., the synoptic surveillance scale), larger similarities for NCVAR versus the TESV methods and ADSSV are found for the small domain than for the large domain. The similarity between NCVAR and ETKF reaches 69% which is the highest percentage among all 15 pairs in the small-domain comparison. The reason for this result is that the maximum sensitivities are usually around the TCs in both methods on the synoptic surveillance scale. Taking the TC intensity into consideration (table not shown), there is no consistently favorable similarity in any specific intensity categories (MTY, TY, and TS) in the 15 pairs.
3) VARYING THE THRESHOLDS OF THE LEADING GRID POINTS
To compare our results with those of the Atlantic Ocean, 2% (X 5 63) and 7% (X 5 31) of the leading grid points are used to calculate the METS in the common targeted location test as in Majumdar et al. (2006) for the large domain and small domain, respectively. To better understand the impact of the threshold values on the results in this test, in this section the comparison between various thresholds of the leading grid points are shown.
The leading grid points (X) vary from 1% to 10% of the total 3149 grid points in the large domain, and 1%–15% of total 441 grid points in the small domain. The METS of each of the 15 pairs for each case with respect to different values of X are then computed. Figure 4 shows the percentage (among the 84 cases) of cases with METS . 0 as a function of the threshold values for the 15 pairs. To show the results more dis-tinctly, the 15 pairs are divided into three groups. In the first group, there are four pairs, three pairs of TESVs and ETKF versus ADSSV, which usually show the high similarity (Figs. 4a,d). The second group contains six pairs for the comparison among ETKF/ADSSV and the three TESV methods (Figs. 4b,e). The third group is for TABLE4. As in Table 3, but divided into 27 major typhoons, 38 typhoons, and 19 tropical cyclones of less than typhoon intensity
(from left to right).
Methods NGPSV JMASV ETKF ADSSV NCVAR
ECSV 88.9/92.1/89.5 85.2/86.8/78.9 55.6/63.2/42.1 55.6/55.3/47.4 7.4/2.6/5.3
NGPSV 81.5/81.6/73.7 74.1/60.5/31.6 77.8/68.4/63.2 11.1/0.0/0.0
JMASV 55.6/60.5/36.8 51.9/63.2/26.3 3.7/5.3/10.5
ETKF 96.3/89.5/78.9 29.6/52.6/42.1
NCVAR versus the other five methods, which usually shows rather low similarity (Figs. 4c,f). It can be found that as the leading grid points (X ) increases, most of the similarity percentages also increase, especially for the second group in both the large and the small domains (Figs. 4b,e), as well as for the first group in the small domain (Fig. 4d). For each of the pairs in the large domain of the first group (Fig. 4a), the similarity per-centage remains unchanged for X larger than 3%. The third group pairs show almost no variation with respect
to X (Figs. 4c,f) with the exception of the ETKF– NCVAR pair, for which similarities increase with X in the large domain (Fig. 4c).
It can also be found that the three TESVs have the highest similarity among all pairs (Figs. 4a,d). The comparison of ECSV and NGPSV shows that they are the most similar pair while the similarities between ECSV and JMASV, and between NGPSV and JMASV are close in the large domain (Fig. 4a). In the small do-main, the comparison of ECSV and NGPSV produces FIG. 3. As in Fig. 2, but for the small-domain common targeted location comparison. The brown dots represent X 5 31 grid points with the
highest value.
TABLE6. As in Table 3, but for X 5 31 in the small domain.
Methods NGPSV JMASV ETKF ADSSV NCVAR
ECSV 66.67 61.90 44.05 30.95 29.76
NGPSV 60.71 44.05 39.29 26.19
JMASV 46.43 39.29 25.00
ETKF 51.19 69.05
ADSSV 21.43
TABLE5. As in Table 2, but for the small domain with X 5 31 and E(C) 5 5.30.
C/METS NGPSV JMASV ETKF ADSSV NCVAR
ECSV 20/0.40 18/0.33 9/0.08 8/0.06 3/20.04 NGPSV 10/0.10 9/0.08 5/20.01 3/20.04
JMASV 10/0.10 18/0.33 4/20.02
ETKF 13/0.18 8/0.06
the highest similarity when X is below 8%. Beyond 8%, the similarity between ECSV versus JMASV is higher than that between other pairs (Fig. 4d). The comparison of ETKF and ADSSV also shows very high similarity in the large domain (Fig. 4a). In the small domain, besides the comparison between ETKF and ADSSV, the com-parison between ETKF and NCVAR also indicates higher similarity (Figs. 4d,f). Note that although ETKF bears some similarity to ADSSV and NCVAR, respec-tively, the comparison between ADSSV and NCVAR shows very low similarities in both the large and the small domains (Figs. 4c,f). As mentioned above, both ETKF and NCVAR usually show the same sensitivities associated with the midlatitude system far from the TCs in the large domain, which is different to the sensitivity patterns of ADSSV that is closer to the TCs. In the small domain, both ETKF and NCVAR show uniformly distributed patterns surrounding the TCs. However, ADSSV sensitivities occur in different directions for different cases, which are more similar to the sensitivity patterns associated with TESVs. Higher similarities are found between ADSSV and the three TESV products as compared with those between ETKF and the TESV in
the large domain when X is larger than 5% (Fig. 4b). Note that the comparison of ADSSV and ECSV shows less similarity than that of other pairs in the small do-main (Fig. 4e).
Regarding the similarity under different TC intensi-ties (MTY, TY, and TS; figures not shown), the simi-larities for the second group decrease as the intensity is reduced. However, this feature is not obvious in the first and third groups. In the first group, the comparison of ETKF and ADSSV shows the highest similarity (which reaches 100%) when the threshold is higher than 3% in the MTY category, with lower similarities in the TY category and much lower similarities in the TS category for the large domain. In the small domain, most of the results in the three intensity categories are consistent with that of all 84 cases as discussed above.
b. Ranking of neighboring regions
Following Majumdar et al. (2006), another ranking-based statistical technique is employed for this inter-comparison study. This method, based on a Spearman ranking, provides a separate means to compare the ranks of potential target areas around the storm. To FIG. 4. The ordinate shows the distribution of percentage among the 84 cases with METS . 0. The abscissa indicates the threshold (a)–(c) from 1% to 10% grid numbers of the total 67 3 47 grid points in the large domain and (d)–(f) from 1%–15% of the total 21 3 21 grid points in the small domain. To show the lines distinctly, the 15 pairs are shown in three groups. (a),(d) The comparison results of three TESVs and ETKF vs ADSSV. (b),(e) The results of ETKF and ADSSV vs the three TESVs. (c),(f) NCVAR vs the other five methods.
conduct the ranking, Y adjacent geographical regions in each targeted method are first set. The distance between each region is set at 1050 km (see appendix B for de-tails), thus each region represents a square of equal area of 7 3 7 grid points with 150-km resolution (boxes in Figs. 5 and 6). Comparisons are also performed in the large and small domains. For example, Figs. 5 and 6 show Y 5 60 and Y 5 16 square regions in storm-relative coordinates for the large and the small domains, re-spectively. For each of the 84 cases, the average value of each method within each region is computed, and these regions are ranked from the first to the Yth. The degree of similarity between any two methods is then computed via the Spearman rank correlation coefficient (Rs; Wilks
1995) for that case.
1) LARGE DOMAIN
In the large domain, for each case, Y 5 60 square regions are set around the storm as in Fig. 5. The whole domain contains five regions to the west and to the east side, four regions to the north, and two to the south of the storm center. Figure 7 shows the percentage of cases (out of the 84 cases) in which the Spearman rank cor-relation coefficient (Rs) of the rankings between any
set of two targeted methods are larger than 0.0, 0.2, and 0.5. When Rs. 0.0 is used as the threshold
(fol-lowing Majumdar et al. 2006), most of the pairs show high percentages (except for comparisons involving NCVAR), all of which exceed 80%, while most exceed 90%. Comparing this finding with that in Majumdar et al. (2006), which also uses the same threshold of Rs.
0.0, but with percentage ranging roughly between 8% and 100%, the comparison based on the ranking of neighboring regions shows that the targeted methods
applied to northwestern (NW) Pacific typhoons studied here have higher similarity than those applied to At-lantic storms.
To better distinguish the similarity of the 15 pairs of targeted methods, we also examine the statistics based on two higher thresholds (i.e., Rs.0.2 and Rs.0.5).
The comparison of ECSV and NGPSV shows similar rankings in all cases (i.e., 100%) for both thresholds of Rs.0.2 and Rs.0.5. Overall, for both Rs.0.2 and
Rs.0.5 thresholds, high similarities are shown in the
comparison among the three TESVs. Regarding the comparison of the three TESVs with ETKF and ADSSV, Fig. 7 shows that JMASV is more similar to ETKF than to ADSSV, while the similarities in the comparisons of the other two TESVs to ADSSV are higher than to ETKF when the threshold is Rs .0.2.
Under the same threshold, the ETKF–NCVAR pair shows high similarity (70%) while the similarity for the ETKF–ADSSV pair is around 37%. Note that unlike the results of common targeted location test, the com-parison between ETKF and ADSSV does not show very high similarity. When the threshold is Rs . 0.2, the
similarity between these two methods is much lower than the comparisons of either one to the three TESVs. The comparisons between NCVAR and other target methods still show low similarities, except when com-pared with ETKF. It is interesting that the comparison between NCVAR and JMASV shows much higher FIG. 5. Regions to be ranked for NPGSV for case 7 (ta 5
0000 UTC 16 May 2006) in the large domain. Each of the Y 5 60 square regions are plotted while each region consists of 7 3 7 grid points at 150-km resolution.
similarity than that between NCVAR and ADSSV and other TESVs. This may correspond to the high simi-larities of both ETKF versus JMASV and ETKF versus NCVAR.
To further assess the dependence of the similarity among the guidance products on TC intensity, Fig. 8
shows the percentage of 27 major typhoons (MTY), 38 typhoons (TY), and 19 tropical storms (TS) cases with the threshold of Rs.0.2. It can be found that most of
the pairs show that the TS category usually has lower sim-ilarity than the stronger groups, except for the ETKF– ECSV and JMASV–NCVAR pairs. The 5% similarity FIG. 7. Percentage of cases in which the Spearman rank correlation coefficient (Rs) of the
rankings between any set of two methods are larger than 0.0, 0.2, and 0.5 for the large domain.
FIG. 8. Percentage of cases with the Spearman rank correlation coefficient (Rs) set to be larger than 0.2. Results are shown for typhoons of three different intensity categories: 27 major typhoons (MTY), 38 typhoons (TY), and 19 tropical cyclones (TC).
between JMASV and NCVAR in the TS category may reveal that the higher similarity between JMASV and NCVAR mentioned above is mostly contributed by the weaker cases.
2) SMALL DOMAIN
The domain is reduced to Y 5 16 (Fig. 6) for the synoptic surveillance mission application. From Fig. 9, it can be found that a higher threshold (Rs . 0.5) is needed to better distinguish the similarities among the 15 pairs in the small domain than in the large domain (i.e., Rs.0.2). When the threshold is Rs.0.5, it shows
that the comparisons among the three TESVs have the highest similarities (over 65%), while the comparison between ETKF and ADSSV also show a high similarity of around 52%. The first four most similar pairs are consistent with the results of common targeted locations in the large domain. Among the six pairs of ETKF and ADSSV to the three TESVs, ADSSV and NGPSV shows the highest similarity (around 48%). Meanwhile, the similarity associated with the comparisons between ETKF and either ECSV or JMASV is higher than that between ADSSV and either ECSV or JMASV. For the comparisons of NCVAR with other methods, as pre-viously discussed, the highest similarity is shown for the ETKF–NCVAR pair. The comparisons of both JMASV and ADSSV with NCVAR show low percentages of 16% and 12%, while a percentage even lower than 8% is shown in the comparison between NCVAR and both ECSV and NGPSV.
4. Discussion of some representative special cases As pointed out earlier, more dynamical systems (such as the midlatitude trough, the subtropical jet, the south-westerly monsoon, and binary interactions) may affect the TCs in the NW Pacific Ocean than those in the Atlantic Ocean. In this section, three special cases are analyzed to highlight the similarities and differences between different targeted methods and to interpret the dynamic meanings.
a. Case 2—Affected by the subtropical high
Figure 10 shows the sensitivities of the six targeted methods superposed with the geopotential height field in the NCEP final analysis (FNL; 18 3 18) at 500 hPa of Typhoon Chanchu, with 0000 UTC 11 May as the ob-serving time (ta; case 2). The zonal region of the
sub-tropical high extends from 1008 to 1508E, as indicated by the 5880-gpm contour, and the TC is located at 108N, 1288E, which is just at the edge of the subtropical high. Among the six guidance products, the three TESVs and ADSSV show similar sensitivity results. Namely, major sensitivities occur at about 500 km around Chanchu, though at different directions relative to the storm center. In general, the main sensitivities among the above four methods are located to the east of the storm center. Furthermore, ECSV and NGPSV show sensi-tivities to the south of the storm center, and NGPSV, JMASV, and ADSSV show sensitivities around the north to the northeast part of the storm. Note that these sensitivities are associated with the subtropical high. In FIG. 9. As in Fig. 7, but for the small domain.
general, locations with highest sensitivity collocate well with the border between the TC and the subtropical high in Figs. 10a,b,e. It can be assumed that the sensi-tivity results show the impact of the steering flow from the subtropical high on the TC movement. In contrast, in addition to the large values at the storm center, ETKF also shows sensitivity associated with midlatitude troughs north and the northeast of the TC. For NCVAR, the high sensitivity is located at the TC center and the midlatitude trough far away from the TC, which appears to have no physical link to the storm motion. b. Case 38—Affected by the midlatitude jet
Case 38 is Typhoon Shanshan with 0000 UTC 16 Sep-tember as the observing time (ta). The midlatitude trough
played an important role in affecting Shanshan’s track when it recurved from westward to northward and northeastward later in its life cycle (Wu et al. 2009). In
Fig. 11, the NCEP FNL geopotential height field shows that the midlatitude trough is located around 208–408N, 1158–1208E, while the TC is at 268N, 1238E. Figures 11a–c show that the adjoint methods (three TESVs) produce high sensitivities at the center and the up-stream region of the trough, while the ADSSV shows high sensitivity right at the trough location (Fig. 11e). On the other hand, the ensemble methods (ETKF and NCVAR) show some sensitivity downstream of the trough, while the maximum sensitivity is still located around the TC. In this case, all six methods consistently pick up sensitivity signals associated with the midlati-tude trough, which has a strong impact on the TC movement and evolution 48 h after the observing time. Nevertheless, ETKF, ADSSV, and NCVAR all show another region of sensitivity to the east of the storm, probably in association with the strength of the western extent of the subtropical ridge, whereas the three types FIG. 10. The sensitivities of (a) ECSV, (b) NGPSV, (c) JMASV, (d) ETKF, (e) ADSSV, and (f) NCVAR superposed with the geopotential height field (contour interval of 60 gpm) from NCEP FNL at 500 hPa of case 2, with 0000 UTC 11 May as the observing time (ta). The verifying areas of the other five methods are shown as the red squares in (a)–(e). The JTWC best track at tais denoted by the solid typhoon symbols.
of TESV also show the sensitivity information related to the subtropical high in this case.
c. Case 66—Affected by the subtropical jet
Typhoon Durian occurred very late into the typhoon season of 2006. The observing time (ta) for case 66 is
0000 UTC 28 November. From Fig. 12, it can be found that the gradient of the geopotential height field at 500 hPa is relatively large at latitudes north of 208N. To highlight the location of the subtropical jet, the wind vectors (with wind speed higher than 20 m s21) at 500 hPa are superposed in Fig. 12. There are two main branches of the jet over East Asia. One is located at higher latitudes (408–608N) and may be associated with the polar front jet. Another is located at lower latitudes (208–358N) and is likely associated with the subtropical jet. The two jets merge to the east of 1208E. At higher altitudes, such as 200 hPa (figure not shown), only one jet is observed with a maximum wind speed of about 90 m s21 near 308N. The above characteristics are
consistent with the analysis of the subtropical jet in Krishnamurti (1961), which indicated that the subtrop-ical jet usually occurs in winter in the Northern Hemi-sphere with the maximum wind around 70 m s21 at 200 hPa and the baroclinic zone above 500 hPa. Figures 12a–c show that the TESV guidance appears in a belt zone along 208–308N, collocated with the southern (anticyclonic) side of the subtropical jet. ADSSV also shows a relatively short belt pattern of sensitivity at the southern edge of the jet. For ETKF, besides the maxi-mum sensitivity around the TC, there is also a belt pattern located at 308–458N. However, this belt is more likely related to the midlatitude cyclone at lower levels (850–700 hPa, figure not shown). The sensitivity located at 408N, 1608E of NCVAR is also associated with the midlatitude cyclone, which has no relationship with the TC evolution in this case. The dynamic interpretation of this sensitivity associated with the subtropical jet is not completely understood at this point and merits future research.
5. Summary and future prospects
The improvement of TC predictive skill through the assimilation of targeted observations is among one of the most important research and forecasting issues for TCs. To optimize the aircraft surveillance observations using dropwindsondes, and for future targeting using satellite and novel in situ observations, several targeted observing strategies have been developed and examined. The primary consideration in devising such strategies is to identify the sensitive areas in which the assimilation of targeted observations is expected to have the greatest influence on improving numerical forecasts. To high-light the unique features that affect the TCs over the northwestern Pacific, in this study, three TESVs from different global models (ECMWF, NOGAPS, and JMA/EPS), the ETKF based on multimodel en-semble members (ECMWF, NCEP/GEPS, and CMC), the NCEP/GEPS DLM wind variance, and the MM5 ADSSV are compared with each other (i.e., six different
types of guidance with 15 comparison pairs) based on 84 cases of northwest Pacific TCs in 2006. The 84 cases consist of 19 TCs while multiple cases studying the same TCs are separated by 24 h on successive days. The values of the six types of guidance are interpolated to latitude–longitude 1.58 grids and normalized by the maximum value of each method for each case.
The similarities among the six guidance products are evaluated by two objective statistical techniques as in-troduced in Majumdar et al. (2006) to show the diversity of the sensitivity regions in these products. In this study the statistical techniques of Majumdar et al. (2006) are further elaborated upon by employing varying thresh-old values. The range of different threshthresh-old values allows for an examination of the sensitivity of the com-parison results with respect to the choice of the threshold values. We believe this provides a clearer and more detailed picture of the comparisons that that provided in Majumdar et al. (2006). The results show that the three TESVs are quite similar to one another in both the large FIG. 12. As in Fig. 10, but for the sensitivities superposed with the geopotential height field (contour interval of 60 gpm) and wind field (vector; the scale is indicated by the arrow to the lower right) at 500 hPa of case 66 with 0000 UTC 28 Nov as the observing time.
and the small domains, especially regarding the com-parison between ECSV and NGPSV. This is consistent with the findings in Majumdar et al. (2006) that the targeted methodology usually gives similar guidance irrespective of the model. Except for the comparison between NCVAR and ETKF, both of the statistical results show rather low similarities when NCVAR is compared with other targeted methods, especially on the synoptic scale (large domain). That is because the maximum sensitivity of NCVAR is usually located near the midlatitude jet or extratropical storm, where high winds may be collocated with large DLM wind variance or the baroclinity and related jet strength may allow for rapidly growing modes, which are probably captured by ETKF but may not be relevant to TC ev-olution. On the other hand, when focusing on the sur-veillance scale, the maximum sensitivity of NCVAR around the TC results in higher similarity when com-pared with the three TESVs and ADSSV in the small domain. In both the large and the small domains, ETKF and ADSSV show high similarity because their sensi-tivity results are usually close to the TC and in the TC itself. Meanwhile, higher similarities are found between ADSSV and the three TESVs methods as compared with those between ETKF and the TESVs especially in the large domain. This is primarily because ETKF tends to have high sensitivity uniformly distributed around the storm center as the highest error variance in the wind field corresponds to the spread in the location and structure of the TC in the ensemble. Furthermore, this large error variance always propagates into the verifi-cation region, since the verifiverifi-cation region is chosen to be centered on the TC. Therefore, the assimilation of observations in the storm location is expected to reduce errors in the wind field associated with the storm at the verification time. Both ADSSV and TESVs often cap-ture similar sensitivity patterns in particular areas around and outside of the storm center, thus leading to the higher similarity for the comparison of these two methods with ETKF.
Regarding the similarity of the guidance products for different TC intensities, the three TESVs have high-est similarity to one another in the typhoon category (64–96 kt). As for the comparison between ETKF and other methods, no association is found between simi-larity and TC intensity. When comparing ADSSV with other methods, the highest similarities occur in the major typhoon category when compared with ECSV, NGPSV, and ETKF, but in the typhoon category when compared with JMASV and NCVAR. Generally speaking, more agreement among the guidance prod-ucts exists for the stronger storms (MTY and TY) than for the weaker storms (TS). This finding is roughly
consistent with the study of the Atlantic TCs (Majumdar et al. 2006), which found larger similarities for major hurricanes than for weaker storms.
There are several interesting dynamical systems af-fecting the TC motion (Wu 2006) in the northwestern Pacific region, such as the subtropical high, the midlat-itude trough, the subtropical jet, and the southwesterly monsoon. The latter two systems appear to play less significant roles in the Atlantic Ocean. In this study, we select three special cases to highlight not only the similarities and differences between different targeted methods but also to interpret them dynamically. The first case is affected by the subtropical high. In this case, the three TESVs and ADSSV show that major sensi-tivities are located to the east of the TC center by about 500 km. The locations with the highest sensitivity col-locate well with the border between the TC and the subtropical high. As shown in Wu et al. (2007a) and Peng and Reynolds (2006), such sensitivity patterns indicate that the steering effect of the subtropical high on storm movement and the sensitivity is almost al-ways strongest on the side of the storm associated with the radial inflow. This is consistent with perturbation growth facilitated through changes to the steering flow of the storm and subsequent changes to the forecast track of the storm. The second case is affected by the midlatitude trough. In this case, all six methods con-sistently pick up the sensitivity signals associated with the midlatitude trough while the four adjoint methods (TESVs and ADSSV) produce high sensitivities at the center and the upstream region of the trough and the ensemble methods show sensitivity in the downstream region of the trough. The strong impact of the midlat-itude trough to the movement and evolution of TC is well captured 48 h before the verification time. The third case is associated with the subtropical jet in the late typhoon season of 2006. The sensitivities of TESVs appear in a belt zone along the 208–308N, well collo-cated with the southern (anticyclonic) side of the sub-tropical jet. The ADSSV shows a relatively short belt pattern of sensitivity at the southern edge of the jet. The ETKF also shows a belt pattern located at 308–458N, but this is more likely related to a midlatitude cyclone at lower levels.
From the above analysis of the three cases, it is noted that the adjoint-based methods are more likely to cap-ture the signals associated with the dynamic systems that may affect TC movement/evolution than the en-semble methods. Furthermore, an enen-semble method including dynamic information and data assimilation information (i.e., ETKF) can provide more valuable information than a method that only considers the en-semble variance (i.e., NCVAR).
Regarding other issues related to targeted observa-tions, it is important to evaluate the influence of extra data based on the targeted guidance on the model forecast (Szunyogh et al. 2000, 2002). Kelly et al. (2007), Buizza et al. (2007), and Cardinali et al. (2007) designed a series of data denial experiments to evaluate the im-pact of targeted observational data on operational model forecast fields downstream. Their research is based on midlatitude systems. In contrast, the scientific basis be-hind how targeted observations influence forecasting of TC motion and structure remains unexplored. More work to assess the impact of the targeted data on TC forecasts is required.
Further research includes the interpretation of the dynamics of these targeting methods on a case-by-case basis (e.g., Wu et al. 2009). It is believed that results from this work would not only provide better insights into techniques, but also offer useful information to assist in targeted observations, especially for the DOTSTAR, Typhoon Hunting 2008 (TH08), and Tropical Cyclone Structure-2008 (TCS-08) associated with the THORPEX– Pacific Asian Regional Campaign (T-PARC) program conducted in the TC season of 2008, as well as the tar-geting of other data from satellites, radars, unmanned aircraft, and balloons.
Acknowledgments. The work is supported by the National Science Council of Taiwan through Grant NSC95-2119-M-002-039-MY2, the Office of Naval Re-search Grant N00014-05-1-0672, National Taiwan Uni-versity Grant 97R0302, and the Central Weather Bureau Grant MOTC-CWB-96-6M-02. The authors thank the Japan Meteorological Agency for providing the 2006
typhoon track forecasting by the JAM Global Spectral Model, and JTWC for providing the track forecasts. Helpful comments from the anonymous reviewers are also appreciated. Melinda S. Peng and Carolyn A. Reynolds acknowledge the support of their sponsor, the Naval Research Laboratory, through Program Element 0601153N, and partial computer support provided by the Department of Defense Higher Performance Com-puting Program at NAVO MSRC.
APPENDIX A
Summary of 84 Cases in Northwest Pacific 2006 Table A1 lists the characteristics of the 84 cases used in this research. The names and annual numbers of TCs in the NW Pacific basin are shown under the column ‘‘name.’’ Here WP stands for the northwest Pacific and CP for the central Pacific. Note that WP01 of case 1 is an unnamed tropical storm (TS). The model initial time (ti), observing (analysis) time (ta), and the verifying time
(ty) are at 0000 UTC. For example, 0305 represents 0000
UTC 5 March 2006. The ‘‘verifying area’’ is 208 by 208 centered at the 96-h TC position forecast by the JTWC, which is valid at ty for the ETKF and three TESV
methods (shown in the table). Note that for the ADSSV, the verifying area is different, which is defined as a box of 600 km by 600 km in Wu et al. (2007a). The northern, southern (in degrees N), western and eastern (in degrees E) peripheries of the verifying area are lis-ted. The ‘‘intensity’’ indicates the 48-h official forecast valid at ta.
TABLEA1. Summary of the 84 cases used in this study.
No. Name ti ta ty
Verifying area
Intensity (kt)
N lat S lat W lon E lon
1 WP01TS 0305 0307 0309 21.6 1.6 113.1 133.1 55 2 WP02 Chanchu 0509 0511 0513 24.0 4.0 114.4 134.4 65 3 WP02 Chanchu 0510 0512 0514 26.4 6.4 110.1 130.1 85 4 WP02 Chanchu 0511 0513 0515 25.5 5.5 108.6 128.6 65 5 WP02 Chanchu 0512 0514 0516 27.2 7.2 105.0 125.0 85 6 WP02 Chanchu 0513 0515 0517 29.9 9.9 103.7 123.7 110 7 WP02 Chanchu 0514 0516 0518 33.1 13.1 104.1 124.1 125 8 WP02 Chanchu 0515 0517 0519 37.5 17.5 106.4 126.4 125 9 WP04 Ewiniar 0701 0703 0705 28.0 8.0 121.9 141.9 90 10 WP04 Ewiniar 0702 0704 0706 30.2 10.2 119.4 139.4 85 11 WP04 Ewiniar 0703 0705 0707 32.5 12.5 118.4 138.4 100 12 WP04 Ewiniar 0704 0706 0708 38.3 18.3 120.5 140.5 105 13 WP04 Ewiniar 0705 0707 0709 41.6 21.6 121.3 141.3 100 14 WP04 Ewiniar 0706 0708 0710 46.8 26.8 122.4 142.4 110 15 WP04 Ewiniar 0707 0709 0711 50.4 30.4 122.6 142.6 90 16 WP05 Bilis 0710 0712 0714 33.3 13.3 113.7 133.7 50
TABLEA1. (Continued)
No. Name ti ta ty
Verifying area
Intensity (kt)
N lat S lat W lon E lon
17 WP05 Bilis 0711 0713 0715 34.8 14.8 110.7 130.7 70 18 WP05 Bilis 0712 0714 0716 40.1 20.1 106.3 126.3 50 19 WP06 Kaemi 0719 0721 0723 31.8 11.8 117.6 137.6 60 20 WP06 Kaemi 0720 0722 0724 28.7 8.7 116.3 136.3 105 21 WP06 Kaemi 0721 0723 0725 33.9 13.9 111.3 131.3 110 22 WP06 Kaemi 0722 0724 0726 34.4 14.4 107.2 127.2 110 23 WP06 Kaemi 0723 0725 0727 38.7 18.7 107.5 127.5 75 24 WP08 Saomai 0806 0808 0810 34.7 14.7 115.7 135.7 75 25 WP08 Saomai 0807 0809 0811 38.6 18.6 109.7 129.7 115 26 WP08 Saomai 0808 0810 0812 38.0 18.0 104.4 124.4 90 27 WP09 Maria 0806 0808 0810 46.5 26.5 121.8 141.8 55 28 WP10 Bopha 0807 0809 0811 35.2 15.2 107.2 127.2 60 29 WP10 Bopha 0808 0810 0812 34.0 14.0 104.6 124.6 35 30 WP10 Bopha 0809 0811 0813 32.2 12.2 101.0 121.0 40 31 WP11 Wukong 0813 0815 0817 50.9 30.9 125.7 145.7 65 32 WP11 Wukong 0814 0816 0818 41.4 21.4 120.6 140.6 65 33 WP11 Wukong 0815 0817 0819 43.3 23.3 122.2 142.2 70 34 WP11 Wukong 0816 0818 0820 43.3 23.3 116.7 136.7 60 35 WP14 Shanshan 0911 0913 0915 33.2 13.2 115.7 135.7 80 36 WP14 Shanshan 0912 0914 0916 34.1 14.1 117.1 137.1 115 37 WP14 Shanshan 0913 0915 0917 36.7 16.7 118.4 138.4 105 38 WP14 Shanshan 0914 0916 0918 42.6 22.6 118.8 138.8 90 39 WP14 Shanshan 0915 0917 0919 51.8 31.8 127.9 147.9 90 40 WP16 Yagi 0918 0920 0922 30.3 10.3 137.3 157.3 75 41 WP16 Yagi 0919 0921 0923 36.1 16.1 131.6 151.6 80 42 WP16 Yagi 0920 0922 0924 43.3 23.3 133.5 153.5 130 43 WP16 Yagi 0921 0923 0925 48.0 28.0 139.1 159.1 125 44 WP16 Yagi 0922 0924 0926 51.7 31.7 156.5 176.5 100 45 WP18 Xangsane 0926 0928 0930 26.6 6.6 110.0 130.0 60 46 WP18 Xangsane 0927 0929 1001 26.2 6.2 101.3 121.3 85 47 WP18 Xangsane 0928 0930 1002 25.3 5.3 96.0 116.0 115 48 WP19 Bebinca 1003 1005 1007 33.9 13.9 124.5 144.5 60 49 WP19 Bebinca 1004 1006 1008 34.1 14.1 125.9 145.9 65 50 WP21 Soulik 1010 1012 1014 33.4 13.4 126.4 146.4 60 51 WP21 Soulik 1011 1013 1015 33.8 13.8 127.7 147.7 80 52 WP21 Soulik 1012 1014 1016 37.7 17.7 131.1 151.1 75 53 WP21 Soulik 1013 1015 1017 46.8 26.8 142.1 162.1 95 54 WP21 Soulik 1014 1016 1018 48.8 28.8 155.8 175.8 75 55 WP22 Cimaron 1027 1029 1031 26.7 6.7 107.4 127.4 65 56 WP22 Cimaron 1028 1030 1101 26.2 6.2 103.9 123.9 85 57 WP22 Cimaron 1029 1031 1102 25.8 5.8 102.4 122.4 90 58 WP22 Cimaron 1030 1101 1103 26.1 6.1 99.5 119.5 90 59 WP22 Cimaron 1031 1102 1104 26.3 6.3 96.6 116.6 90 60 WP22 Cimaron 1101 1103 1105 30.4 10.4 101.1 121.1 65 61 WP22 Cimaron 1102 1104 1106 29.5 9.5 106.6 126.6 45 62 WP23 Chebi 1110 1112 1114 24.0 4.0 105.3 125.3 50 63 WP23 Chebi 1111 1113 1115 27.4 7.4 99.7 119.7 90 64 WP23 Chebi 1112 1114 1116 29.6 9.6 98.7 118.7 65 65 WP23 Chebi 1113 1115 1117 30.9 10.9 98.8 118.8 45 66 WP24 Durian 1126 1128 1130 25.0 5.0 116.0 136.0 95 67 WP24 Durian 1127 1129 1201 25.4 5.4 111.4 131.4 100 68 WP24 Durian 1128 1130 1202 26.7 6.7 112.7 132.7 105 69 WP24 Durian 1129 1201 1203 26.5 6.5 108.4 128.4 105 70 WP24 Durian 1130 1202 1204 25.6 5.6 106.5 126.5 85 71 WP24 Durian 1201 1203 1205 22.9 2.9 99.6 119.6 45 72 WP24 Durian 1202 1204 1206 21.3 1.3 96.2 116.2 45 73 WP25 Utor 1208 1210 1212 23.1 3.1 105.2 125.2 50 74 WP25 Utor 1209 1211 1213 24.0 4.0 103.9 123.9 90
APPENDIX B
The Size of the Square Region for the Ranking of Neighboring Regions
The size of the square regions should be sufficiently large so that the values in adjacent regions are not strongly correlated (Majumdar et al. 2006). Based on 84 cases, the correlations for the six methods at different distances are computed by first setting Y 5 286 square regions containing 3 3 3 grid points at 150-km reso-lution within each region. For each method, the corre-lation coefficient between any two square regions is calculated by
r 5 Sxy
SxSy. (B1)
Here, Sxand Syare the standard deviations of the
av-erage values within these two square regions of the 84 cases, and Sxyis their covariance. The definitions of
Sx, Sy, and Sxyare Sx5 1 n 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
å
n i51 (xi x)2 s , (B2) Sy5 1 n 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiå
n i51 (yi y)2 s , (B3) and Sxy5 1 n 1å
n i51 (xi x)(yi y), (B4)FIG. B1. Correlation between points as the function of distance among all regions for the six targeted methods.
TABLEA1. (Continued)
No. Name ti ta ty
Verifying area
Intensity (kt)
N lat S lat W lon E lon
75 WP25 Utor 1210 1212 1214 26.5 6.5 100.9 120.9 135 76 WP25 Utor 1211 1213 1215 26.8 6.8 102.2 122.2 85 77 WP25 Utor 1212 1214 1216 26.8 6.8 100.2 120.2 55 78 CP01 Ioke 0828 0830 0901 32.7 12.7 152.3 172.3 125 79 CP01 Ioke 0829 0831 0902 33.9 13.9 150.1 170.1 130 80 CP01 Ioke 0830 0901 0903 34.0 14.0 145.7 165.7 130 81 CP01 Ioke 0831 0902 0904 35.6 15.6 140.6 160.6 125 82 CP01 Ioke 0901 0903 0905 37.7 17.7 133.5 153.5 115 83 CP01 Ioke 0902 0904 0906 41.6 21.6 133.2 153.2 110 84 CP01 Ioke 0903 0905 0907 53.8 33.8 141.5 161.5 80
with n 5 84, x and y are the values (average over the 3 3 3 grid points) in these two square regions for each case, and x and y are the mean values of x and y for all 84 cases. Therefore, the correlation coefficient can be represented by the following function:
r 5
å
n i51 (xi x)( yi y) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiå
n i51 (xi x)2 s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiå
n i51 ( yi y)2 s , (B5)whose value is between 21 and 1.
There are 40 755 combinations between any two of the 286 square regions. The 40 755 correlation coeffi-cients and their corresponding distances can be shown in Fig. B1, which shows the smoothed curve represent-ing the correlations as the function of distance among all regions for the six targeted methods. When the dis-tance is shorter than 4000 km, all methods show a de-creasing correlation. However, beyond 4000 km, ADSSV shows an increasing correlation. It means that the sen-sitivities of ADSSV are usually located closer to the TC than other methods. It is also found that for three TESVs and ADSSV, the corresponding distance is around 1000 km for a correlation coefficient of 0.5, a threshold smaller than which the two square regions appears more independent. However, for ETKF and NCVAR, the correlation coefficients are larger. That is because the distributions of sensitivities are more ran-dom for these two methods than for the other methods. Based on Fig. B1, in this study, 1000 km is adopted as the distance between two regions for the ranking of neighboring regions test.
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