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  • View in gallery

    Panel of 500-hPa geopotential heights at (left) ET − 72 h, (middle) ET, and (right) ET + 72 h for (top) Kong-Rey (2001, reintensifier) and (bottom) Wutip (2001, dissipater). In each panel, the black dot represents the determined storm center based on storm tracking and MSLP. Sea level pressure is shaded when <1004 hPa in intervals of 4 hPa, and the geopotential heights are contoured at an interval of 40 m.

  • View in gallery

    Mean 850-hPa potential temperature field for (left) 53 post-ET intensifying storms and (right) 55 post-ET dissipating storms at (top) 72 h prior to ET, (middle) 36 h prior to ET, and (bottom) ET. All of the frames are centered on the TC. The 500-hPa geopotential upstream trough (dashed line) and downstream ridge (solid line) generally associated with ET are indicated. Whitened pixels represent those chosen by the CFS feature selection system as most useful for class discrimination. Both x and y axes are in units of degrees latitude–longitude.

  • View in gallery

    Plot of CFS merit for 850-hPa potential temperature fields as a function of the number of features (model grid points) used at 72 h prior to ET (ET − 72 h). Maximum merit is achieved at 39 features, but the improvement in performance as more features are added to the technique drops considerably around 20 features.

  • View in gallery

    Hypothetical example classification problem to demonstrate SVM decision boundaries. Situations of comfort based on relative humidity and wind speed (black dots), and situations of a lack of comfort (gray dots) are represented. The 0 curve represents the SVM-determined boundary (hyperplane in feature space) between the classes. Increasing (and decreasing) values correspond to regions of increasing confidence that points that fall in that region and are of one class or the other. These correspond to distances from the boundary in RBF kernel-induced feature space.

  • View in gallery

    Time series of average intensity for post-ET intensifiers (solid black line) and dissipaters (dashed gray line). One standard deviation is plotted for each set. Note that, on average, the two classes of storms undergo a very similar intensity evolution before ET and do not fully statistically diverge until ~ET + 30 h.

  • View in gallery

    Time series of raw SVM classifier performance for 850-hPa potential temperature data and 20 features chosen by CFS. Validation results are plotted (solid gray) and provide an estimated model error based on a 10-fold K-fold cross-validation procedure. Training results are plotted (dashed gray) and provide a metric of how well the model is forced to fit the original data from which it is trained. Testing results are plotted (solid black) and represent model performance on a randomly selected fully independent test set of 21 storms (20% of all data).

  • View in gallery

    The ROC curve for 850-hPa potential temperature test storms at (top left) 72 h prior to ET through (bottom right) 48 h after ET at 24-h intervals.

  • View in gallery

    Time series of intensity evolution for the 4 storms (1 intensifier and 3 dissipaters) that were consistently misclassified leading up to ET (at ET − 72 h, ET − 48 h, and ET − 24 h). Note that Hagibis (2007) was right on the edge of the classification criterion (3-hPa intensity change); Longwang (2000) appears to be a delayed intensifier as well.

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Forecasting Post-Extratropical Transition Outcomes for Tropical Cyclones Using Support Vector Machine Classifiers

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  • 1 Department of Atmospheric Sciences, University of Arizona, Tucson, Arizona
  • | 2 College of Optical Sciences, University of Arizona, Tucson, Arizona
  • | 3 Department of Atmospheric Sciences, University of Arizona, Tucson, Arizona
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Abstract

Intensity changes following the multistage process of extratropical transition have proven to be especially difficult to forecast because of the extremely similar storm evolutions prior to and during the first stages of the transformation from a warm-cored axisymmetric tropical storm to a cold-cored asymmetrical extratropical low pressure system. In this study, differences in surrounding synoptic environments between dissipating and reintensifying extratropical transitioning tropical cyclones are used to develop a predictive technique for extratropical transition intensity change that can be used to enhance the standard numerical guidance. Using a set of all historical transitioning storms between 2000 and 2008 in the western North Pacific, common differences between 850-hPa potential temperature fields surrounding extratropical transition intensifiers and extratropical transition dissipaters, respectively, were identified. These features were then used as inputs into a support vector machine classification system in the hopes of creating a robust prediction system. Once the system was trained on a random subset of the data (80%), performance was tested on the remaining test set (20%). Overall, it was found that the prediction system was able to correctly predict extratropical transition intensity outcome in >75% of the test cases at 72 h prior to extratropical transition. This paper discusses the feature selection and classification system used, as well as the performance results, in detail.

Corresponding author address: Dr. E. A. Ritchie, P.O. Box 210081, Department of Atmospheric Sciences, University of Arizona, Tucson, AZ 85721-0081. E-mail: ritchie@atmo.arizona.edu

Abstract

Intensity changes following the multistage process of extratropical transition have proven to be especially difficult to forecast because of the extremely similar storm evolutions prior to and during the first stages of the transformation from a warm-cored axisymmetric tropical storm to a cold-cored asymmetrical extratropical low pressure system. In this study, differences in surrounding synoptic environments between dissipating and reintensifying extratropical transitioning tropical cyclones are used to develop a predictive technique for extratropical transition intensity change that can be used to enhance the standard numerical guidance. Using a set of all historical transitioning storms between 2000 and 2008 in the western North Pacific, common differences between 850-hPa potential temperature fields surrounding extratropical transition intensifiers and extratropical transition dissipaters, respectively, were identified. These features were then used as inputs into a support vector machine classification system in the hopes of creating a robust prediction system. Once the system was trained on a random subset of the data (80%), performance was tested on the remaining test set (20%). Overall, it was found that the prediction system was able to correctly predict extratropical transition intensity outcome in >75% of the test cases at 72 h prior to extratropical transition. This paper discusses the feature selection and classification system used, as well as the performance results, in detail.

Corresponding author address: Dr. E. A. Ritchie, P.O. Box 210081, Department of Atmospheric Sciences, University of Arizona, Tucson, AZ 85721-0081. E-mail: ritchie@atmo.arizona.edu

1. Introduction

Extratropical transition (ET) is a complex, multistage physical process during which a tropical cyclone (TC) interacts with the midlatitude environment and evolves from a warm-cored tropical system into a cold-cored midlatitude cyclone. A full review of extratropical transition and recent research is given in Jones et al. (2003). Although every tropical cyclone undergoes a unique evolution during and after the ET process, transitioning storms are often placed into one of two categories, either intensifiers or dissipaters, based on their relative intensity evolution following ET (e.g., Demirci et al. 2007; Kofron et al. 2010a,b). This binary classification system is useful in practice, because the main goal in forecasting these transitions is to determine which storms will regain strength after the transition process is complete, and potentially result in broad maritime and coastal impacts. The transition process itself has been defined by Klein et al. (2000) as a dominantly two-phase process: the first being the transformation stage and the second being the reintensification phase. Klein et al. (2000) found that intensifying and dissipating storms are especially difficult to distinguish during the first stage of ET, because all of the storms are generally moving into the midlatitude environment and weakening as they interact with the high levels of vertical wind shear associated with the midlatitude westerlies and low-level baroclinic zone in the midlatitudes (Fig. 1). Thus, the structure of all of the storms moving poleward tends to appear quite similar prior to the second stage of ET.

Fig. 1.
Fig. 1.

Panel of 500-hPa geopotential heights at (left) ET − 72 h, (middle) ET, and (right) ET + 72 h for (top) Kong-Rey (2001, reintensifier) and (bottom) Wutip (2001, dissipater). In each panel, the black dot represents the determined storm center based on storm tracking and MSLP. Sea level pressure is shaded when <1004 hPa in intervals of 4 hPa, and the geopotential heights are contoured at an interval of 40 m.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

Despite this lack of differentiation between dissipating and reintensifying classes in the storms themselves prior to the end of phase 1 of ET, recent studies have suggested that the spatial relationships between the TC and midlatitude upper-level trough are able to provide the capacity to predict the outcome of ET (Harr and Elsberry 2000; Ritchie and Elsberry 2007). Additionally, Hart and Evans (2001) found that 51% of Atlantic storms that underwent ET during the period of 1979–93 intensified post-ET. They also found a correlation between post-ET intensification and transit time between what they defined as the region supporting tropical development and the region supporting extratropical development. Those storms with rapid transit between these two boundaries were much more likely to intensify after transition, again suggesting that spatial relationships between TCs and midlatitude structures are important factors in determining post-ET intensity changes.

Based on these results, researchers have begun examining the practical application of these findings toward post-ET intensification prediction. Demirci et al. (2007) examined the problem from a spatial and spatiotemporal projection pursuit approach. The method involved empirical orthogonal function (EOF) analysis of the Navy’s Operational Global Assimilation and Prediction System (NOGAPS) 500-hPa geopotential height analyses centered on each storm every 12 h from 48 h before ET to 48 h after ET. In their method, the 10 EOFs that most separated the two classes (intensifiers versus dissipaters) were chosen by projection pursuit methods. Storms were then projected onto a vector that best separated the two classes in 10-dimensional EOF space, allowing for a projection distance for each storm, and classification based on threshold values. Overall, 57 storms from 1997 to 2004 were used as training data for the system, while 27 storms from 2003 to 2004 were used to test system performance. Using only spatial patterns, the system was able to correctly predict the post-ET outcomes of 60%–70% of storms between 12 and 24 h prior to ET. Spatiotemporal techniques allowed for peak performance ~82% using fields from 12 and 24 h before ET in combination. The full-physics NOGAPS model predictions with initialization times of 24 h prior to the ET time were assessed, and it was found that the general outcome of ET was correctly predicted approximately 84% of the time. However, the timing and amount of intensification were generally poorly forecast. Some previous authors (e.g., Jones et al. 2003) have noted that the numerical weather prediction (NWP) models (including the NOGAPS model) are not always consistent in their prediction of the outcome of ET between forecast cycles leading up to the ET time, although typically their performance improves within about 24 h of the ET time. A distinct, statistically based prediction technique [such as the Demirci et al. (2007) technique] that had predictability at, for example, a 72-h lead time would lend confidence to the NWP forecast by either supporting or disputing the basic forecast of ET outcome and providing useful additional information to the forecaster.

In this study, we have built on the work of Demirci et al. (2007) by looking at transitioning storms in high dimensional spaces and using advanced support vector machine (SVM) classification techniques in the hope of further increasing the range of forecast accuracy with respect to post-ET intensity change classification. The format of the paper is as follows. The methodology behind this new classification system is described in section 2. Some preliminary results are presented in section 3 using spatial patterns in one chosen atmospheric variable to show the potential effectiveness of such a pattern recognition system for forecasting the eventual outcome of ET up to 72 h in advance. These results, along with future work, are discussed in section 4.

2. Methodology

The overall method for this post-ET intensity classification system relies on a number of steps. The first of these steps comprise preprocessing of the data for training purposes, and would not need to be repeated in a forecasting situation. The overall outline of the methodology is as follows: 1) track the storms and diagnose the structural evolution through time to determine the timing of the ET, as well as the positions and post-ET intensity; 2) classify the storm based on intensity evolution; 3) preprocess the storm data; and 4) apply the SVM, select the model, and evaluate the error.

a. Tracking individual storms and ET time determination

Overall, 108 western North Pacific tropical cyclones that underwent extratropical transition between January 2000 and December 2008 were identified and processed. For each storm, ET time was defined as the first time that the storm appeared as an open wave on the midlatitude trough in the Global Forecast System (GFS) final analysis (FNL) 500-hPa geopotential height analyses using a 20-m contour (e.g., Fig. 1). This was the definition for “ET time” that was used in Demirci et al. (2007) and corresponded well to the end of the transformation time of ET in Klein et al. (2000). It was after this ET time that reintensification or dissipation of the TC would occur. A study by Kofron et al. (2010a) demonstrated that although the “open wave” definition could not be readily automated, it was objective, and did correctly identify all of the TCs that were beginning ET in their study.

After an ET time was established for each storm, the storm was then tracked in the model analysis from 72 h before the ET time (ET − 72 h) to 72 h after the ET time (ET + 72 h) at an interval of 6 h. Because the storm center in the analysis might not exactly match the location in the best-track archives, an automated procedure was developed that used the best-track location as the first-guess position in the analysis field and then searched an area ±5° latitude for the actual minimum sea level pressure in the analysis. The center location chosen by the system was checked and verified visually in case there were multiple low pressure centers within the search area. These tracking data were archived and used to center the model data around the storm center at a distance of ±30° longitude, and ±25° latitude, and to save pressure-level fields of all of the available atmospheric model variables for each storm at each relative ET time. Thus, each storm variable field for each relative ET time was composed of 3111 (61° × 51°) gridpoint values, corresponding to the storm itself and its surrounding environment before, during, and after ET.

An extension of Demirci et al. (2007) showed that a multivariate strategy for ET projection-pursuit prediction had higher potential for success in forecasting the outcome of ET than pursuing a single variable (Demirci 2006). Rather than prejudice the process by determining a priori that particular fields (e.g., Harr and Elsberry 2000; Ritchie and Elsberry 2003, 2007) would be the most successful discriminators of ET outcome, all of the basic raw model output fields from the GFS FNL model and the potential temperature and equivalent potential temperature were tested using an SVM classifier and five testing sets of storms. Based on the results of these quick-look analyses, several variables were chosen for their success in correctly discriminating between reintensifying and dissipating TCs. These variables included geopotential heights at 500 hPa (as used in Demirci et al. 2007), vertical velocity at 600 and 100 hPa, meridional winds at 100 hPa, and potential temperature and equivalent potential temperature at 850 hPa. The greatest success was achieved using 850-hPa potential temperature, and the differences between the features in the two classes (reintensifying and dissipating) could be easily understood in terms of the evolution of the atmospheric circulation patterns in the potential temperature fields. In particular, 850-hPa potential temperature fields captured the structure of the TC itself, but perhaps more importantly they also captured the location and intensity of frontal zones and associated midlatitude features (Fig. 2). Therefore, these potential temperature fields were chosen as the inputs of choice for demonstrating the potential of the classification technique outlined in this paper.

Fig. 2.
Fig. 2.

Mean 850-hPa potential temperature field for (left) 53 post-ET intensifying storms and (right) 55 post-ET dissipating storms at (top) 72 h prior to ET, (middle) 36 h prior to ET, and (bottom) ET. All of the frames are centered on the TC. The 500-hPa geopotential upstream trough (dashed line) and downstream ridge (solid line) generally associated with ET are indicated. Whitened pixels represent those chosen by the CFS feature selection system as most useful for class discrimination. Both x and y axes are in units of degrees latitude–longitude.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

b. Storm classification

Classification for each tropical cyclone was determined by observing changes in the mean sea level pressure (MSLP) at the center of each storm (MSLPTC) through its ET evolution, as well as changes in the MSLP surrounding the storm (MSLPENV). The value of MSLPENV is defined here as the mean MSLP within the surrounding environment (between all 3111 grid points). Because the TC central pressures in the FNL analyses are most probably only accurate to within a few hectopascals at best, some freedom was introduced into the criteria for reintensification after ET. Storms for which MSLPENV–MSLPTC increased more than 3 hPa in the time interval starting at ET ± 6 h and ending in the period between ET + 36 h and ET + 72 h were categorized as positive storms; that is, storms that intensified substantially post-ET. The reasoning behind the time bounds around ET and following ET are as follows: 1) by including the two times adjacent to ET (i.e., ET ± 6 h), the definition is relaxed in case there are some storms for which the time of the open wave and the time of the maximum central pressure do not exactly coincide; and 2) by only considering intensity between ET + 36 h and ET + 72 h as post-ET time, we prevent storms that only intensified briefly after our defined ET from being considered as reintensifying (positive) storms. All of the other storms were categorized as dissipating (negative) storms. This system of categorization resulted in 53 positive storms and 55 negative storms overall.

c. Data preprocessing

Because of the large amount of data available in the form of 3111 spatial data points (the initial set of features available for classification), the first preprocessing step was to reduce the dimensionality of the inputs using feature selection, while attempting to best retain information content that would be useful for classification. Because it has been observed in practice that added features tend to degrade classification performance in situations where the number of cases is small relative to the number of features (Jain et al. 2000), and because the dataset in use here is comprised of only 108 cases and a total of 3111 features, it was decided that the dimensionality of the feature set must be reduced before classification. For this task the correlation-based feature selection (CFS) method developed by Hall (1999, 2000) was chosen. The main premise behind this selection method is that the features that are most effective for classification are those that are most highly correlated with the classes (intensifiers and dissipaters), and at the same time are least correlated with other features. The method is therefore used to choose a subset of features that best represent these qualities. For this study, a modified forward selection version of the CFS method, with the dot product representing the relationship between variables, was used; the system first chooses the best individual feature based on the metric
e1
where Ms is the merit metric, k is the number of features in the subset, rcf is the mean of the dot product between features and classes, and rff is the mean of the dot product between the features themselves. Subsequently, the first chosen feature is matched with each other feature out of the set of 3111 spatial model grid points, and Ms is recalculated for each set of two features. The feature combination that maximizes Ms is then chosen iteratively up until a chosen number of input features is reached.

To better explain the way the modified CFS system works, a sample dataset was created; this dataset is composed of basic meteorological variables (temperature, relative humidity, and wind speed) and associated human comfort levels (defined by the binary classification of either comfort or lack of comfort). The dataset itself is presented in Table 1. The results of the modified CFS system, when applied to this sample dataset, are provided in Table 2. When limited to selecting two features, the system first selects wind speed and then selects relative humidity to best complement it, based on highest merit. This same methodology is used to select spatial grid points from the 3111 available.

Table 1.

Sample classification dataset.

Table 1.
Table 2.

Calculated merit for one and two features. Chosen features are displayed in bold.

Table 2.

To determine an optimal number of features to use, the CFS-based merit was computed as a function of the number of features used on a training set. The results suggested that 39 features would be ideal for maximizing merit at ET-72 (Fig. 3). Similar numbers of features were suggested throughout all of the times relative to ET, although a greater number of features tended to be chosen after ET, when there is considerably more difference between the potential temperature fields in, and surrounding, the transitioning storms.

Fig. 3.
Fig. 3.

Plot of CFS merit for 850-hPa potential temperature fields as a function of the number of features (model grid points) used at 72 h prior to ET (ET − 72 h). Maximum merit is achieved at 39 features, but the improvement in performance as more features are added to the technique drops considerably around 20 features.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

In the interest of further reducing dimensionality and preventing overtraining, as well as promoting consistency throughout the period of interest, only 20 features were used as inputs into the classification system at all times during ET evolution. Once a subset of features is selected by the CFS method, only these features are retained for all of the storms. This feature subset then comprises the set of inputs to the classification system and the means for distinguishing important spatial differences between storms that intensify following ET and those that dissipate following ET.

The second preprocessing step involved dividing the storms into training, validation, and testing data subsets, and centering and scaling all of the variable inputs between the storms using the mean and standard deviation within each subset. To evaluate the classification system, K-fold cross validation was used as a means of producing training and validation sets. In K-fold cross validation, the data are split into a designated number of equally (or nearly equally) sized subsets, or folds. The classification system is then evaluated using each fold as an independent validation set. This method is appealing because it allows all of the inputs to be used both in the training and in the validation of the classification system. The K-fold error estimation is commonly used in statistical pattern recognition and was chosen over other techniques, such as bootstrapping, because of its lower computational cost (Jain et al. 2000). For all of the evaluations, 20% (21 storms) of the data were held out for final testing and 10 folds were used for training and validation (the remaining 87 storms). By holding out 20% of the storms from the training and validation stages entirely, a completely independent testing set was established, from which true model error could be established.

d. Support vector machines and model selection

SVMs are a specific type of classifier that combines the concepts of a maximum margin with kernel techniques in an attempt to classify sparse datasets in a manner that maximizes generalization capacity. The basic premise is to find a hyperplane that perfectly classifies all of the inputs, while optimizing the normal margin between the classes to be as wide as possible (for a full review, see Burges 1998). There are two limitations to this basic implementation: 1) it is, in its basic form, limited to linear classification problems, and 2) it requires that the classes be perfectly separable. Neither of these is conducive to the problem of post-ET intensity change, but SVM methods have evolved to overcome both issues.

By using the dual form of the Lagrangian to optimize the width of the hyperplane boundary between classes, and substituting a kernel function in place of the inner product between data points in the optimization problem, it is possible to use a kernel trick to map the input variables into extremely high dimensional spaces where they are much more likely to be linearly separable, without ever carrying out explicit mappings. This overcomes the problem of the SVM theory being limited to linear problems, because when the SVM solves for the maximum margin hyperplane in this kernel-induced feature space, the separating boundary in input space becomes a nonlinear curve whose shape is related to the form of the kernel function. Commonly used kernel functions include all of the polynomial forms and orders, as well as radial basis functions (RBFs), as used here.

To overcome the second problem of perfect separability, SVM theory has added the concept of a soft-margin SVM, where slack variables are added to allow for the misclassification of outliers. In two-norm soft-margin theory, these slack variables are determined based on the addition of a margin parameter to the diagonal of the kernel matrix, thus making that matrix better conditioned. The margin parameter C controls the trade-off between the cost of misclassification and the width of the margin between classes. Unfortunately, there is no robust method for determining an appropriate value for C, and so a range of values must be tested in order to determine which results in the best model. Therefore, model selection for SVMs is an iterative process of varying both the kernel function parameters and C together, and determining through cross validation which combinations result in the best generalization performance for the classifier.

In this study, an RBF kernel function is used, as follows:
e2
where xi and xj are individual data point vectors and σ is a parameter that controls the areal influence of each data point. Both the margin parameter and sigma influence the number of support vectors, which are chosen by the trained SVM. The support vectors are those observations (storms in this case), which, if removed, would alter the hyperplane solution. In Fig. 4, a support vector machine solution, using an RBF kernel, is shown for the sample dataset established previously. Here, the two axes represent centered and scaled versions of the two features chosen by the modified CFS system (wind speed and relative humidity). The SVM is able to perfectly classify all of the cases with regard to human comfort with knowledge of the classes.
Fig. 4.
Fig. 4.

Hypothetical example classification problem to demonstrate SVM decision boundaries. Situations of comfort based on relative humidity and wind speed (black dots), and situations of a lack of comfort (gray dots) are represented. The 0 curve represents the SVM-determined boundary (hyperplane in feature space) between the classes. Increasing (and decreasing) values correspond to regions of increasing confidence that points that fall in that region and are of one class or the other. These correspond to distances from the boundary in RBF kernel-induced feature space.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

A matching procedure is used for the theta fields for ET cases, where the most effective SVM model parameters for classification are chosen in the following manner: 1) by iteratively testing classification performance for values of C (1 × 10−6, 1 × 10−5, … , 1 × 10−1) and RBF kernel parameter sigma (2, 2.25, … , 10), using a two-norm soft-margin SVM system on each of 10 cross-validation folds; 2) by determining the mean estimated true error based on generalization for each parameter combination for each fold, calculated as follows:
e3
where k is the number of folds and Ei is the generalization error for each fold; and 3) by choosing the “best” model parameters based on mean estimated true error, and using these model parameters to train an SVM and classify the held-out test data. From this procedure, ideal model parameters, mean training set error, mean estimated true error, and actual test set error are determined at each relative ET time (from ET − 72 h to ET + 72 h).

3. Results

A time series analysis of class-averaged MSLP for intensifying versus dissipating storms (Fig. 5) suggests that the two classes display almost identical intensity evolution during the 72 h leading up to ET. This trend is in agreement with the findings of Klein et al. (2000). In both classes, storms, on average, tend to slowly weaken from ~ET − 24 h to ET time, before quickly diverging in behavior after ET. Note that by ~30 h after ET, the two classes have statistically diverged. These results both suggest that the method of storm classification used in this study is reasonable, and that, as previously suggested, storms that intensify and weaken post-ET are very difficult to differentiate prior to the completion of the ET process using only data about their intensities leading up to ET.

Fig. 5.
Fig. 5.

Time series of average intensity for post-ET intensifiers (solid black line) and dissipaters (dashed gray line). One standard deviation is plotted for each set. Note that, on average, the two classes of storms undergo a very similar intensity evolution before ET and do not fully statistically diverge until ~ET + 30 h.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

Based on the CFS method outlined above, 20 features corresponding to individual gridcell pixels in the potential temperature fields were chosen from the original 3111 at each relative ET time to be used as input features in the SVM classification system. Figure 2 shows sample features that were chosen prior to ET for 850-hPa potential temperature fields, overlaid onto intensifier and dissipater mean fields at ET − 72 h, ET − 36 h, and ET, respectively. Note that the correlation-based feature selection method tends to select features that describe the midlatitude environment surrounding the storms over features of the storms themselves, particularly prior to ET.

Several contiguous gridpoint locations that correspond to the northern part of the midlatitude trough to the northwest of the storms tend to be chosen as the most useful for differentiating classes at ET − 72 h. This, coupled with the feature selections in the tropics, suggests that the north–south temperature gradient associated with the baroclinic zone may be important for discriminating between reintensifying and dissipating TCs after ET. This is supported by similar (but not exactly the same) feature selections in the 500-hPa geopotential height fields (not shown), which also suggest that environmental baroclinicity is important at the early time. In addition, the selection of features in the trough, rather than those spread along the northern perimeter, suggests that the structure of the midlatitude trough may be important. In the top panels of Fig. 2, the structure of the potential temperature field varies considerably. The positive case shows a southeast-to-northwest orientation of the contours, which reflects the structure of the midlatitude trough aloft nicely (dashed white line). The negative case, however, is opposite to the orientation of the midlatitude trough aloft. The location and orientation of the midlatitude trough has been shown in some studies (e.g., Klein et al. 2002; Ritchie and Elsberry 2003, 2007) to be extremely important to the outcome of ET. In addition, the structure and depth through the atmosphere of the midlatitude trough is also important for reintensification (Ritchie and Elsberry 2003). Interestingly, scattered data points to the south and southeast of the storm centers are also chosen, perhaps representing differences in thermodynamic properties of the tropics themselves, and they may be related to seasonality of the north–south temperature gradient discussed briefly in the final discussion. Also of note is the fact that the feature selection system tends to ignore the properties of the midlatitude ridge downstream of the storm centers. Despite their lack of selection here, features of the downstream ridge have been identified in past studies as important to the eventual outcome of ET. Because the downstream ridge is usually identified as building ahead of the TC from the anticyclonic outflow, its presence and impact may be better identified in upper-level fields. An important consideration when interpreting the meaning of the features chosen by the modified CFS system, however, is the fact that the system is selecting against those model grid points that are highly correlated with other grid points that have already been chosen. If the system were selecting features based only on correlation with the class of the storm (intensifying versus dissipating), it would tend to select for contiguous regions within the storm environment, causing broader selection areas instead of the more scattered features revealed in Fig. 2.

Features from the downstream ridge are, however, chosen by the CFS system at ET − 36 h, suggesting that differences in these features, such as the low-level frontal development between positive and negative storms, may become more evident as ET time approaches. Features near the storm center, particularly to the southwest where the cold frontal development is occurring, also become more important in differentiating classes at this time. At ET time itself, features closest to the storm center begin to become the best for class differentiation, probably because by this time the details of the trough interaction with the TC itself are the important differentiators. This sequence completes a movement from concentration on the upstream trough, to the downstream ridge, to the storm itself from ET − 72 h to ET time.

Information related to the 21 storms that were held out for final testing of the detection system is given in Table 3. It can be seen that a certain subset of these storms were consistently classified correctly at 24, 48, and 72 h before ET, while some were never correctly classified at those three times. Overall, classification performances (for the test set and validation sets) for 850-hPa potential temperatures through time (from ET − 72 h to ET + 72 h) are given in Fig. 6. These performance numbers are based on raw outputs of the SVM classifier. It can be seen that the testing data have slightly poorer performance than the training data prior to the ET time and are comparable or even slightly better after the ET time. This is not an unexpected result, and improvements over this may be obtained simply by increasing the training set to ensure that a more representative sample of ET cases exist in the training statistics. Examination of the receiver operator characteristics (ROC) curves for times leading up to ET (Fig. 7) suggests that better performance could also potentially be obtained by changing the threshold of the classifier. The raw SVM output performance reflects only a single point on the ROC curve, and purposefully allowing a certain amount of false detection may provide for a more robust detection system overall. For example, one could potentially achieve a positive detection rate of 80%, at 72 h prior to the ET time if a false alarm rate of 27% were an acceptable risk (Fig. 7). Despite this fact, and even using raw SVM output, this prediction system correctly classifies ~76% of storms (16 out of 21) at 72 h prior to ET.

Fig. 6.
Fig. 6.

Time series of raw SVM classifier performance for 850-hPa potential temperature data and 20 features chosen by CFS. Validation results are plotted (solid gray) and provide an estimated model error based on a 10-fold K-fold cross-validation procedure. Training results are plotted (dashed gray) and provide a metric of how well the model is forced to fit the original data from which it is trained. Testing results are plotted (solid black) and represent model performance on a randomly selected fully independent test set of 21 storms (20% of all data).

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

Fig. 7.
Fig. 7.

The ROC curve for 850-hPa potential temperature test storms at (top left) 72 h prior to ET through (bottom right) 48 h after ET at 24-h intervals.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

Table 3.

Storms included in testing set. Each asterisk (*) in the error column represents a classification error at ET − 72 h, ET − 48 h, or ET − 24 h for that given storm.

Table 3.

Although it would be useful to compare the testing results with actual GFS predictions 72 h in advance of the ET time, an archive of the necessary 192-h forecast fields (72 h prior plus 120 h after) could not be located for the cases prior to 2005 (71% of our testing cases). Thus, a direct comparison of our results with the GFS model itself was not possible in this study. Instead, an examination of the cases that the technique failed to predict correctly is provided here. Overall five storms from the test set of 21 are misclassified at ET − 72 h. These include two intensifiers (Longwang from 2000 and Bavi from 2008) and three dissipaters (Mitag from 2002, Kirogi from 2005, and Hagibis from 2007). Of these storms, four (Longwang, Mitag, Kirogi, and Hagibis) are consistently misclassified at ET − 72 h, ET − 48 h, and ET − 24 h. A total of seven storms are misclassified at some point in that series. Figure 7 displays MSLP evolutions for the four consistently misclassified storms. Of these four storms, Mitag and Kirogi seem to undergo intensity changes that are fairly representative of dissipaters (see Figs. 5 and 8). Longwang, which is an intensifier, weakens for a considerable time after ET, and only begins to reintensify around ET + 48 h. Hagibis falls within the group of storms that are right on the edge of intensifying enough to be classified as an intensifier (Fig. 8). Therefore, it is not surprising that our pattern recognition system has some difficulty in classifying it as a dissipater prior to ET. Further analysis will be done to identify whether there are consistent physical reasons for these misclassified storms.

Fig. 8.
Fig. 8.

Time series of intensity evolution for the 4 storms (1 intensifier and 3 dissipaters) that were consistently misclassified leading up to ET (at ET − 72 h, ET − 48 h, and ET − 24 h). Note that Hagibis (2007) was right on the edge of the classification criterion (3-hPa intensity change); Longwang (2000) appears to be a delayed intensifier as well.

Citation: Journal of Atmospheric and Oceanic Technology 28, 5; 10.1175/2010JTECHA1449.1

4. Discussion

Our SVM-based classification system for post-ET intensity forecasting displays encouraging results, with over three-quarters of the storms being correctly classified at 72 h prior to ET in the randomly chosen testing set. Performance is consistently in the range of 60%–75% leading up to ET, with the exception of the few times immediately before the start of the ET process. Performance falls off at this point, which is potentially an artifact of the lack of spatial pattern differences at these times. Once the storms begin the ET process, both post-ET intensifiers and dissipators become features on the midlatitude trough and generally weaken and undergo structural changes associated with interaction with the baroclinic zone. The decrease in performance is thus likely due to the loss of large-scale spatial pattern differences at this point, and a movement toward differences in TC structure itself. However, as expected, model performance quickly increases after the completion of ET (around ET + 12 h), because the process has been completed and the storm is now either intensifying or dissipating. At this point, the pattern recognition system is able to focus on features within and immediately surrounding the TCs, which suggest considerable differences in relative size and strength of the disturbance between classes.

Of the four storms that are consistently misclassified leading up to ET (one intensifier and three dissipaters), two seem to undergo intensity changes that are fairly representative of dissipaters, and it is not yet clear why they were misclassified at so many time periods. One other dissipater actually reintensifies almost enough to have fallen into the reintensification class and so the classifier may have difficulty with this storm. The one misclassified reintensifying TC actually weakens for a considerable time after ET, and only begins to reintensify around ET + 48 h. Therefore, it is not surprising that our pattern recognition system has some difficulty in classifying it as a reintensifier prior to ET.

One other topic that should be discussed is the discrepancy between the K-fold estimates of classification performance and the test set evaluations of true performance. True performance values from the test set tend to be ~10% higher than K-fold estimates based on the series of 10 validation sets. There are two possible explanations for this discrepancy: 1) the randomly selected test set happens to include storms that are more easily classified by the system, or 2) the K-fold estimates of error are simply pessimistic and do not fully represent the level of performance possible on a true test set. In future work it will be important to examine whether this trend continues between atmospheric variables and different test sets.

Although the method presented in this paper provides encouraging results for pattern recognition use in the forecasting of post-ET reintensification, there are several limitations that will be addressed in the future. First, the system uses analysis fields produced from the GFS, which has been modified over the period of study and will continue to be modified into the future. These changes will be reflected in the FNL analyses used for training the system, and this is not something that can be rectified. A more stable analysis set to use would be a reanalysis dataset. However, the limitations with using a reanalysis dataset is that it would not match the current version of the forecast model, and so it could not be matched with forecast fields. Second, the overall system is highly nonstationary (the earth’s atmosphere), and seasonal and interannual variability of the input variables (850-hPa potential temperature) are not accounted for. Therefore, the mean that is removed from the positive and negative storms individually may not be representative for many off-season storms or storms from strong El Niño or La Niña years. A movement toward either the removal of a seasonal mean or the inclusion of temporal information as a feature in the classification system is needed, and is likely to improve the system’s performance. Third, it will be vital to test more atmospheric variables both individually and in combination to see if there are certain fields that provide even better predictive ability. Last, the system simply needs a larger set of training data for improved performance. The CFS method has suggested that ~40 features are useful in class discrimination, but this number is simply unreasonable in a pattern recognition problem with less than 100 training samples. It will be vital, therefore, to continue growing the training set as new model data become available for TCs that have undergone ET.

The ultimate goal is to refine the SVM-based classification system to the point where it can be used as an effective complement to NWP models in forecasting the post-transition intensity of tropical cyclones. By contributing a separate statistical view of the likely outcome of extratropical transition for a given storm at least 72-h in advance of the common ET time, the SVM system will provide confidence in the NWP products to the forecasters in the period when the forecast models tend to be least reliable.

Acknowledgments

The GFS FNL analyses were kindly provided by Mr. Bob Creasey at the Department of Meteorology, Naval Postgraduate School, Monterey, California. The paper has been improved by the suggestions of three anonymous reviewers. This research was supported by the National Science Foundation under Grant ATM-0730079.

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