Statistical Prediction of Weekly Tropical Cyclone Activity in the Southern Hemisphere

Anne Leroy Météo France, Nouméa, New Caledonia

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Matthew C. Wheeler Centre for Australian Weather and Climate Research,* Melbourne, Australia

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Abstract

A statistical prediction scheme, employing logistic regression, is developed to predict the probability of tropical cyclone (TC) formation in zones of the Southern Hemisphere during forthcoming weeks. Through physical reasoning, examination of previous research, and some new analysis, five predictors were chosen for this purpose: one representing the climatological seasonal cycle of TC activity in each zone, two representing the eastward propagation of the Madden–Julian oscillation (MJO), and a further two representing the leading patterns of interannual sea surface temperature variability in the Indo-Pacific Oceans. Cross-validated hindcasts were generated, being careful to use the predictors at lags that replicate what can be performed in real time. All predictors contribute significantly to the skill of the hindcasts for at least some leads in the majority of zones. In particular, it is found that inclusion of indices of the MJO as predictors leads to increased skill out to about the third week. Beyond the third week, the skill asymptotically approaches that which can be achieved through consideration of the seasonal cycle and interannual variability alone. Furthermore, the importance of a simple consideration of the seasonal cycle of TC activity for intraseasonal TC prediction, for all forecast leads, is demonstrated.

* The Centre for Australian Weather and Climate Research is a partnership between the Bureau of Meteorology and CSIRO.

Corresponding author address: A. Leroy, Météo France, 5 rue Vincent Auriol, B.P. 151, 98 845 Nouméa, New Caledonia. Email: anne.leroy@meteo.fr

Abstract

A statistical prediction scheme, employing logistic regression, is developed to predict the probability of tropical cyclone (TC) formation in zones of the Southern Hemisphere during forthcoming weeks. Through physical reasoning, examination of previous research, and some new analysis, five predictors were chosen for this purpose: one representing the climatological seasonal cycle of TC activity in each zone, two representing the eastward propagation of the Madden–Julian oscillation (MJO), and a further two representing the leading patterns of interannual sea surface temperature variability in the Indo-Pacific Oceans. Cross-validated hindcasts were generated, being careful to use the predictors at lags that replicate what can be performed in real time. All predictors contribute significantly to the skill of the hindcasts for at least some leads in the majority of zones. In particular, it is found that inclusion of indices of the MJO as predictors leads to increased skill out to about the third week. Beyond the third week, the skill asymptotically approaches that which can be achieved through consideration of the seasonal cycle and interannual variability alone. Furthermore, the importance of a simple consideration of the seasonal cycle of TC activity for intraseasonal TC prediction, for all forecast leads, is demonstrated.

* The Centre for Australian Weather and Climate Research is a partnership between the Bureau of Meteorology and CSIRO.

Corresponding author address: A. Leroy, Météo France, 5 rue Vincent Auriol, B.P. 151, 98 845 Nouméa, New Caledonia. Email: anne.leroy@meteo.fr

1. Introduction

Tropical cyclones (TCs) pose a major threat to life and property in many parts of the world, and forewarning of their occurrence can be of great benefit for emergency preparedness and loss minimization. At the shortest lead times, high-resolution numerical weather prediction (NWP) models can provide skillful forecasts of the development and tracks of individual TCs out to about 5 days [(World Meteorological Organization) WMO 2006]. Beyond this time scale, however, the chaotic nature of the atmosphere necessitates that TC forecasts concentrate not on individual systems, but rather on statistics of the general level of TC activity, such as their numbers or frequency. Successful development and implementation of TC activity forecasts has been made on the seasonal time scale using both statistical methods (e.g., Gray 1984; Nicholls 1985; Gray et al. 1992; Jury et al. 1999; Chan et al. 2001; Saunders and Lea 2005) and dynamical models (e.g., Vitart and Stockdale 2001; Camargo et al. 2005). Little published work, however, exists on the prediction of TC activity on the intraseasonal time scale. In this paper we consider such intraseasonal variations, whereby we develop a scheme to make predictions of the probability of TC formation, over selected zones, during future week-long periods.

We focus this study on TCs of the Southern Hemisphere, forming in the Indian, western Pacific, and central Pacific Ocean domains, and the approach we take is statistical. Like the aforementioned seasonal statistical prediction studies, suitable predictors of future TC activity must be chosen. In those studies, that is, those concerned with TC activity averaged over a season, the El Niño–Southern Oscillation (ENSO) has consistently been included as one of the predictors. Given ENSO’s dominance as a large-scale climatic signal, its usefulness as a predictor of TC activity is likely to extend to week-long periods as well, especially in the south Indo-Pacific where its influence is particularly strong (Nicholls 1984; Kuleshov and de Hoedt 2003). Likewise, other predictors that are commonly used for seasonal TC prediction, such as large-scale patterns of sea surface temperature (SST) and the stratospheric quasi-biennial oscillation (QBO), will need to be considered.

In contrast with the seasonal statistical TC prediction studies, however, is our additional consideration of the Madden–Julian oscillation (MJO) as a predictor. The MJO is the strongest existing mode of tropical intraseasonal atmospheric variability (Madden and Julian 1994; Zhang 2005), and with its 30–80-day period, has good potential as a predictor of weekly TC activity. Supporting this notion are recent studies that have demonstrated the existence of a strong contemporaneous relationship between TC activity and the MJO (e.g., Maloney and Hartmann 2000; Hall et al. 2001; Dickinson and Molinari 2002; Bessafi and Wheeler 2006; Frank and Roundy 2006), together with studies showing the extended-range predictability (out to about 20 days) of the MJO (e.g., Waliser et al. 1999; Lo and Hendon 2000; Wheeler and Weickmann 2001). Nowhere in the published literature, however, have these two lines of supporting evidence yet been combined to generate skillful intraseasonal TC predictions. Here we demonstrate that inclusion of the MJO as a predictor leads to increased skill out to the third week of our TC activity forecast model. Furthermore, we demonstrate the importance of a consideration of the seasonal cycle for intraseasonal TC prediction.

The following sections of this paper will describe the TC dataset (section 2a), introduce the statistical method that will be used for prediction (logistic regression; section 2b), discuss the creation of a climatological seasonal cycle of TC activity (section 2c), and identify and physically justify the chosen predictors (section 3). Our analysis suggests the use of five predictors: one representing the climatological seasonal cycle of TC activity; two representing the MJO; and two representing the leading modes of SST variability in the Indo-Pacific, particularly that associated with ENSO. The forecast model is then developed, being careful to use the predictors at lags that replicate what can be performed in real time (section 4a). A formal stepwise selection procedure is then carried out, which shows the relative importance of each predictor in each regional zone, and as a function of forecast lead out to the seventh week (section 4c). Last, example cross-validated hindcasts are presented, and measures of skill and reliability are assessed (section 5).

2. Data and methodology

a. TC dataset

The TC dataset used is a best-track archive compiled at the Australian Bureau of Meteorology using data sourced from the individual National Meteorological Services responsible for TC warnings in the Southern Hemisphere (located in La Réunion, overseas department of France; Australia; New Zealand; and Fiji). It includes TCs that formed in the area 30°E–120°W for the TC seasons from 1969/70 to 2003/04 (Kuleshov and de Hoedt 2003). This dataset includes the name, position, time and central estimated pressure of the TCs. Inaccuracies in the dataset are known to exist, such as the overidentification of systems in the 1970s (Nicholls et al. 1998). Nevertheless, our results show that physically meaningful weekly TC variability exists in the dataset, which is predictable. Improvements to the dataset are likely to bring further improvements in the result.

During this investigation we applied our forecast methodology to both TC formation (i.e., using the genesis points only) and TC occurrence (i.e., including the whole track), but for brevity here we show only the results for TC formation; the results for TC occurrence are generally the same, although with higher base probabilities. To define TC genesis, we can either consider that the first noted record of each system in the dataset is the genesis point, or that genesis occurred when each system reached an estimated central pressure of 995 hPa (as used by Hall et al. 2001). The second definition is preferred because it excludes weak systems from the analysis. Figure 1 shows the genesis locations of TCs defined in this way during the November–April TC season.

TC activity will be predicted in four different zones, as defined in Fig. 2. The selection of these zones was based on both physical and operational considerations: the boundary at 90°E separates the areas of operational responsibility of La Réunion and Australia; the boundary at 135°E provides a natural geographical separation between TCs of the Pacific and Indian Oceans, with relatively few TCs crossing this longitude (5 in 40 yr; Kuleshov 2003); and the boundary at 180° approximately separates regions that are known to behave oppositely in response to ENSO (Basher and Zheng 1995; Kuleshov and de Hoedt 2003). Latitudinal boundaries were set at 0°and 30°S. Forecasts using smaller zones, which would potentially be more useful, were also tested (e.g., as small as 10° in longitude), and proved to be skillful only where there is a sufficiently dense number of TC formations. Thus, there exists some trade-off between forecast skill and usefulness. Nevertheless, our methodology is easily adapted to alternative zones. We will predict the probability that at least one TC forms for each zone. The simultaneous formation of two TCs in the one zone is not taken into account, although this is rare.

b. Logistic regression and stepwise predictor selection

The chosen method to predict TC activity is a purely statistical downscaling one. Once the large-scale sources of variability of TC activity are identified, if these sources have some predictability or memory, observed or analyzed indices representing them should be successfully used as predictors.

The statistical model we use is logistic regression. Logistic regression is particularly suited for making probabilistic forecasts as it has the property that it will never forecast a probability of less than 0 or greater than 1 (Wilks 2006). The logistic regression equation fit to the data is
i1520-0493-136-10-3637-e1
where is the predicted probability of TC formation, and (x1, x2, . . . , xm) are the multiple predictors. Input observations are in the form of a binary probability P that is assigned to be 0 if no TC genesis is observed during the week of interest, and 1 if a TC does form. To remove any potential biases associated with defining a specific start day for each week (e.g., Sunday versus Monday), we develop the model using overlapping weeks, starting on every day. The fitted coefficients (i.e., β0, β1, β2, . . . , βm) are computed through a least squares approach (Marquardt 1963). As with multiple linear regression, large uncertainties in the estimated coefficients may arise if the predictor variables are strongly correlated. In this study we thus seek to use predictors that are at best minimally correlated. We apply the statistical model separately for each regional zone, and for each forecast lead.

Also, like multiple linear regression, there are stepwise procedures for predictor selection in logistic regression. Once we identify potential predictors from physical considerations (section 3), we use the forward selection scheme of Hosmer and Lemeshow (2000) to select which predictors to use for each zone and each lead (section 4c). This procedure also determines an order of importance of the predictors, which is useful for physical interpretation. At the first step, models are developed using each predictor individually, and the most important of the predictors is determined from the model that returns the smallest p value for the log-likelihood statistical test. At the second step, all the models including the first selected predictor and one of each of the remaining predictors is fitted and the model that returns the lowest p value decides which is the second-most important predictor. The steps continue until the threshold p value of 0.15 (value suggested by Hosmer and Lemeshow 2000) is reached, that is, until it is determined that adding the new predictor is 15% likely to not provide any improvement to the model.

c. Creating a TC climatological seasonal cycle

For subsequent analysis it is useful to be able to construct a smoothly varying climatological seasonal cycle of weekly TC probabilities. Because of the relatively small size of the averaging set, however, the raw climatological probabilities computed from the daily data are quite noisy. Thus, we smooth by computing the annual harmonics (using Fourier transforms applied to the 365-day climatologies) and reconstruct using only the mean and first 8 of those harmonics, successively retaining only a smaller fraction of the amplitude of the third and higher harmonics. This effectively acts as a low-pass filter with a half-power point at 365/5 = 73 days. A relatively large number of harmonics is required to capture the tails of the season while minimizing the occurrence of negative probabilities in the smoothed climatology, and the amplitude tapering of the harmonics reduces the occurrence of Gibb’s phenomenon. In the rare situation that the reconstructed curve falls below zero, the climatology is set to zero. An example is provided in Fig. 3, with the smoothed version being what we expect, from physical considerations, to be a more accurate reflection of the true seasonal variation. Henceforth, we will use the smoothed version when discussing the climatological seasonal cycle of TC activity.

3. Identification and justification of predictors

The physical basis for TC activity prediction relies on the now well-documented influence of the large-scale environment on TC genesis (e.g., Gray 1979; McBride and Zehr 1981; Frank 1987; Landsea et al. 1998). Frank (1987) summarized the necessary conditions for TC genesis as warm sea surface temperatures coupled with a relatively deep oceanic mixed layer, significant values of absolute vorticity in the lower troposphere, weak vertical wind shear over the prestorm disturbance, and mean upward motion and high midlevel humidities. The challenge for TC activity prediction is to find slowly varying and predictable phenomena that influence these parameters and hence TC formation. Given the results of previous studies (as listed in the introduction and below), likely or possible candidates for predictions of weekly activity are the MJO, ENSO and other interannual variability associated with SST, the QBO, and the climatological seasonal cycle.

a. MJO

As discussed in the introduction, the contemporaneous relationship between the MJO and TC activity is already well established, as is the predictability of the MJO. However, the previous studies showing the MJO–TC relationship have only used indices of the MJO that cannot be determined in real time, usually relying on a bandpass time filter to diagnose its intraseasonal signal. Thus, it remains to be demonstrated how well a real-time MJO index performs, as this is what we will have available for actual TC predictions.

Here we use the real-time multivariate MJO (RMM) index of Wheeler and Hendon (2004; available online at http://www.bom.gov.au/bmrc/clfor/cfstaff/matw/maproom/RMM/index.htm).

This index is based on the first two empirical orthogonal functions (EOFs) of the combined fields of near-equatorially averaged 850-hPa zonal wind, 200-hPa zonal wind, and satellite-observed outgoing longwave radiation (OLR), a proxy for convective cloudiness. As such, the index monitors the convection and tropospheric circulation of the MJO, and the projection of daily data onto the multivariable EOFs yields projection coefficients that vary mostly on the intraseasonal time scale of the MJO. The two projection coefficients are called RMM1 and RMM2.

The traditionally defined RMM index is available back to 1974 when satellite OLR data first became available. To maximize the use of the available TC data, however, for this study we have extended the RMM values back to 1969 using the two wind fields when the OLR was unavailable. Correlations between the RMM values computed with winds only, and those with all three fields (r > 0.9 during 1974–2004), suggest that the wind-only values should provide a good estimate during those times. A comparison of the hindcast skill score of forecast models trained with and without the 1969–74 data (not shown) confirms that its inclusion provides an overall positive impact.

The relationship between TC genesis and the RMM-measured MJO is well demonstrated by binning the TC genesis locations according to predefined MJO phase categories (Fig. 4). Here we use the same MJO phases as Wheeler and Hendon (2004), except we combine neighboring categories: phases “2 + 3” occur when RMM2 is strongly negative, phases “4 + 5” when RMM1 is strongly positive, phases “6 + 7” when RMM2 is strongly positive, and phases “8 + 1” when RMM1 is strongly negative. The “weak” category is when the amplitude of the MJO, as measured by (RMM12 + RMM22)1/2, is less than 1.

In Fig. 4, the role of the MJO in modulating TC genesis, and the utility of the RMM index, can be discerned. Consistent with previous studies in the Southern Hemisphere (e.g., Hall et al. 2001; Bessafi and Wheeler 2006; Frank and Roundy 2006), TC genesis locations tend to be clustered poleward and somewhat westward of the MJO’s enhanced convective envelope (as indicated by negative OLR anomalies). For example, most TCs occur over the Indian Ocean in phases 2 + 3 and 4 + 5, with relatively fewer in phases 6 + 7 and 8 + 1. The peak in TC activity near Australia, on the other hand, is during phases 4 + 5 and 6 + 7, and for the Pacific it is phases 6 + 7 and 8 + 1. When computing statistics of the modulation in each defined zone of Fig. 2, utilizing the same methodology as Hall et al. (2001), we find a 95% statistically significant modulation of 4 to 1 in z1; 2 to 1 in z2 and z3; and 8 to 1 in z4 (full results not provided). Thus, we will use RMM1 and RMM2 as two of our input predictors to the logistic regression selection procedure.

b. ENSO and other interannual variability associated with SST

The impact of ENSO on TC genesis in the Southern Hemisphere is also already well established. In the Pacific during El Niño event years, TCs are found to occur preferentially farther east and away from the Australian region, with the node of the displacement somewhere near the date line (Nicholls 1984; Basher and Zheng 1995; Kuleshov and de Hoedt 2003). In the Indian Ocean, on the other hand, TC genesis locations have been found to shift westward with El Niño, with a node near 85°E (Kuleshov and de Hoedt 2003), as is hypothesized to be caused by the remote effect of El Niño on local SSTs and ocean mixed layer depth there (Jury et al. 1999; Xie et al. 2002).

In this study we choose to measure ENSO using an SST-based index that is already operationally computed and used for seasonal rainfall prediction at the Australian Bureau of Meteorology. Namely, we use the projection coefficient of the leading rotated EOF of monthly Indo-Pacific SST anomalies, called SST1 (Drosdowsky and Chambers 2001). The spatial pattern of this EOF (Fig. 5a) shows strong loadings in the equatorial Pacific, and its associated time series (i.e., SST1) is well correlated with other typical sea surface signatures of ENSO (e.g., Niño-3).

We also consider the impact of the second rotated EOF of monthly Indo-Pacific SST anomalies, called SST2 (Drosdowsky and Chambers 2001). Its spatial pattern (Fig. 5b) is primarily a monopole extending from the coast of western Australia northwestward up to India, with strongest loadings in the southeastern quadrant of the tropical Indian Ocean. It is known to be an important predictor of Australian seasonal rainfall (Drosdowsky and Chambers 2001), and the pattern projects partly onto the structure of interannual dipolelike SST variability that has been identified in the Indian Ocean (e.g., Saji et al. 1999). Such Indian Ocean variability has been argued to have some independence from ENSO (e.g., Webster et al. 1999; Drosdowsky and Chambers 2001), and thus some potential for additional TC predictability.

We display the contemporaneous relationship between these two forms of interannual SST variability and TC activity in Figs. 6 and 7. We use SST1 and SST2 averaged over the TC season (November–April), and compute stratified weekly TC climatological probabilities (smoothed using the technique described in section 2c) separately for the 11 highest and 11 lowest years of SST1 or SST2. This allows for a demonstration of the magnitude of the relationships, and their seasonality, if any.

Figure 6 displays the TC activity relationship with SST1 (i.e., ENSO). Consistent with the above-mentioned previous studies, there is an increased probability of TC genesis during El Niño (high SST1) years in the central Pacific (z4) and the western Indian Ocean (z1), with the opposite occurring in the zones bordering Australia (z2 and z3). Taking the season as a whole (see values in parentheses), the greatest differences, when measured as a ratio, occur in z2 and z4. Furthermore, there appears to be no particularly strong seasonality in the relationships, with the shift in probabilities generally being in the same direction in all months (the exceptions to this rule being very early in the season in z1 and z3). Hence, it would appear adequate to use SST1 as an input predictor in all zones, irrespective of the month in the season. The statistical significance of using SST1 as a predictor will be determined through the formal stepwise selection procedure in section 4c.

The relationship between SST2 and TC activity is displayed in Fig. 7. In the far western zone (z1) it appears to be particularly strong, with more than a doubling of the genesis probabilities during periods of high SST2. In z2 the relationship is weaker, but reversed, with slightly fewer TCs forming during times of high SST2. Note that this is a reverse of the usual spatial relationship that exists between TCs and local large-scale SST, showing the complexity of what is possible, and further evidence that local SST is not the sole determinant of TC activity (e.g., Chan and Liu 2004). For the zones in the Pacific (z3 and z4) the relationship is also relatively weak, with some changes in sign toward the end of the season. Hence, the TC relationship with SST2 appears to be more diffuse than the relationship with SST1. Given the strong influence in z1, however, we shall still use it as an input to our logistic regression model, and let the predictor selection procedure decide whether or not to include it in each zone.

c. QBO

The QBO has previously been been shown to act as a useful predictor of TC activity in the Atlantic Ocean basin (e.g., Gray 1984; Gray et al. 1992), with the cause of the association hypothesized to be the QBO’s effect on the upper-tropospheric vertical shear of the zonal wind and/or its effect on upper-tropospheric static stability (Landsea et al. 1998). It would seem plausible that similar mechanisms may act for TCs in the other ocean basins, although previous work suggests that for the Southern Hemisphere it is only weak (see review by WMO 1993). We have thus investigated this possibility further, by examining the relationship between stratospheric zonal mean winds and TC activity in each of our zones of interest. Despite testing for a relationship with winds at a number of different levels (20, 30, 50, and 70 hPa), and at varying lags (it takes 6 months for the QBO’s wind signal to propagate from 30 to 70 hPa), we similarly find little evidence for a relationship, as we illustrate here for just one level and lag in Fig. 8. Thus, we choose not to use a QBO index as a predictor in this study.

d. Climatological seasonal cycle

Clearly, the probability of a TC forming during a week in November or April is much lower than at the peak of the TC season in February (e.g., Figs. 6 –8). Therefore, it is important that the forecast system includes a predictor of this seasonality. Usually, it is local SST that is thought to provide the strongest influence on the seasonal cycle of TC activity (e.g., Frank 1987). However, as is demonstrated in Fig. 9, in all but one (z3) of our selected zones, the seasonal cycle of SST (averaged for 10°–20°S) peaks over a month later than that for TC activity. There are presumably other large-scale factors (e.g., vertical shear) that affect TC climatology. Therefore, local SST would not be an entirely satisfactory predictor of the seasonal TC variation. Instead, we will use the climatological seasonal cycle of TC activity itself (as smoothed using the procedure outlined in section 2c), as a predictor.

4. Forecast model development

a. Simulating real predictions and definition of forecast weeks

The results of section 3 suggest the input of five predictors to the forecast model: RMM1, RMM2, SST1, SST2, and the seasonal cycle of TC activity for each region (Clim). By their construction, these predictors are essentially uncorrelated. We use each as daily values, using linear interpolation (in time) from the monthly values for the SST. To simulate a real-time prediction, however, lags must be introduced for the RMM1/2 and SST1/2 predictors. We use a conservative 2-day lag for the RMM values (it takes about 12 h for the index to become available for the previous day), and a 30-day lag for the SST values. No lag, however, needs to be introduced into the Clim predictor as it depends only on data from other years.

Defining our terminology for forecast weeks with an example, if today is 19 November, we would already have available RMM values for 17 November, and SST values from October (as above). Then we define the W1 (for week 1) forecast period as 19–25 November, W2 as 26 November–2 December, and so on. Additionally, we define W0 to refer to the 7-day period centered on 17 November, which provides no real predictive capability, but is used here as a useful diagnostic of the potential predictability that may be gained by having more accurate and up-to-date predictors.

b. Logistic regression validity check

Before proceeding, it is instructive to check the fit of the logistic regression model for each of the predictor variables to confirm the choice of model. Figure 10 shows examples of the model fit for the zone z3 (curves), using the W1 lag between the predictor variables and input TC observations. Also shown with plus symbols, are the observed probabilities when averaged for 20 equal-sized groups of neighboring observations (grouped according to the value of the predictor variable). Note that these averaged probabilities (plus symbols) are computed independently of the logistic regression model (curves), thus the match between the curves and plus symbols support the use of this model. In z3 for W1, it would appear that Clim and RMM2 have the strongest influence on TC genesis, with the greatest slope of the fitted logistic regression curves. This result will be confirmed by the formal predictor selection procedure (section 4c).

c. Formal stepwise predictor selection

The results of the formal stepwise predictor selection procedure (as described in section 2b), using the same five input predictors in each zone and for each forecast week, are summarized in Table 1. In all zones, at all leads, the climatological probability (Clim) is chosen first, that is, as the predictor that accounts for the most variability of the predictand. In z1, RMM2 is the next most important predictor at short lead times (W0 and W1), then SST2 takes over at longer lead times (W2 and later). In the other zones, SST2 is much less important, being either chosen after two or more other predictors (e.g., in z3), or not chosen at all (e.g., in z4 for W0, W1, W4–W7). SST1, by comparison, is always chosen before SST2 in z2, z3, and z4, showing the importance of ENSO, compared to Indian Ocean SST variability, in those zones.

Interestingly, the importance of the MJO (i.e., RMM1 or RMM2) exceeds the importance of the interannual SST variability for the W2 lag in both z2 and z3; RMM2 is favorably selected for W2 in z2, and RMM1 in z3. The contrasting importance of RMM1 versus RMM2, as a function of lag in each zone, is consistent with the time scale and eastward propagation of the MJO. At the longer lead times (W4 and greater), the magnitude of the logistic regression coefficients of the RMM1/2 predictors is only very small, indicating the loss of useful predictability by the MJO for leads greater than about 20 days (not shown). Nevertheless, RMM1 and RMM2 still sometimes exceed the threshold for inclusion for the longest (W7) lead, showing that a statistically significant relationship still exists. The coefficients for the Clim and SST predictors, on the other hand, change little with the forecast lead (also not shown).

d. Cross validation

An assessment of the skill and reliability of the forecast model requires testing it on a set of data that is independent to the data used to develop the model. To achieve this, a cross-validation technique is used, whereby 1 yr is successively left out of the complete record, and the model developed with the remaining years (called the training period). Then, hindcasts are made for the year left out (the test period), and the process is repeated over each year. Thus, 35 different sets of coefficients are estimated and 35 models are built (for each zone and each forecast lead), leading to a complete set of cross-validated hindcasts over all 35 yr of our observational record. Importantly, the climatological probability of genesis (Clim) is also recalculated for each different training period. Only minor changes appeared in the Clim predictor calculated with different training periods, confirming the robustness of the filter used to calculate it. We create such hindcasts from initial conditions starting on every day during the TC season, generating TC probability predictions for overlapping weeks.

5. Results

a. Hindcast examples

Examples of the (overlapping) weekly TC genesis probability hindcasts are shown in Fig. 11. Shown are the hindcasts in z3 for the W1 leadtime for three characteristic TC seasons: during a La Niña in 1973/74, during an El Niño in 1982/83, and a season with rather neutral ENSO conditions but with strong MJO variability in 1984/85. Also shown is the climatological seasonal cycle (Clim) for comparison.

As expected from our preliminary investigations (section 3), the predicted probability in z3 is reduced during El Niño and increased in La Niña. During such ENSO events, the probabilities are increased or decreased during most of the season by about 10%– 20% relative to Clim. At the intraseasonal time scale, the genesis probability is modulated by the MJO as shown in February–March 1984/85 with a large increase in the predicted probability (more than 20% above the climatological genesis probability), giving a peak of greater than 60% in the probability curve concomitant with a strong MJO over the western Pacific. These results are consistent with the results from section 3 that were found without using a statistical model, hence, it confirms a correct use of the logistic regression model.

Hindcasts for lead times from W1 to W6 in z3 during 1984/85 are presented in Fig. 12. The strong influence of intraseasonal variability is still readily apparent in W2 and W3. At longer leads, the intraseasonal variation of the predicted probabilities can be seen to decrease. This confirms that at these longer leads, although RMM1 or RMM2 may still be selected by the formal predictor selection, the magnitude of their logistic regression coefficients is relatively small, so it takes a very strong MJO event for there to be an influence.

b. Hindcast reliability

The reliability of probabilistic predictions is perhaps best demonstrated with the use of what is known as a reliability diagram (Wilks 2006). To plot reliability diagrams, hindcasts made during the whole period (1969–2004) are grouped into 20 equal-sized groups according to the predicted values, separately for each zone. The mean observed/predicted probabilities for each group are plotted in Fig. 13 and form the reliability curve. The plotted points are concentrated near the lowest probabilities (especially in z4 where the base climatological probability is the lowest) as the formation of a TC is a relatively rare event. The plotted points globally follow the diagonal line (reliability curve of a perfect forecast) and are mostly within the 10% interval centered on the observations (dashed lines). Nevertheless, in z4 the predicted probabilities of the highest group (i.e., the 20th group) are overestimated, with the plotted point lying well below the line of perfect reliability. Poor predictions of such high values seems to come from an incorrect representation of MJO events in that zone, as it is only during the convectively active phase of an MJO that such high probabilities are possible in z4. This may be explained by the modification of the MJO’s structure by ENSO as it nears the central Pacific (e.g., Kessler 2001).

An increase in forecast reliability in z4 may require the incorporation of indices that diagnose that interaction.

c. Hindcast (Brier) skill

For evaluating the skill of our probabilistic hindcasts, we use the Brier skill score (BSS; Wilks 2006). The BSS provides an indication of the percentage of improvement of a set of forecasts or hindcasts compared to a reference forecast strategy. A positive value of the BSS indicates that there is an improvement over the reference strategy, and a BSS of 100% is reached when the forecast is perfect (i.e., each prediction is either for a probability of 0 or 1, and is always correct). Here we use a reference model that predicts for every day within the TC season a constant value that is the mean seasonal probability of a TC to form in a week in that zone. This is a very basic forecast strategy that is a function of location only, and whose value is represented by the horizontal lines in Fig. 13.

We present the BSS for each zone and each lead time in Fig. 14. To establish the relative importance of the predictors used, we show the BSS for both the full forecast model using all selected predictors (solid curve), as well as models using only a subset of the predictors (other curves, as labeled and described in the figure caption).

Using the daily climatology (i.e., Clim) alone, results in a skill improvement over the reference strategy (i.e., a constant climatology) of from 1% to 6%, depending on the zone. It does not depend on the lead time as no lag is needed to be introduced to the Clim predictor. The improvement is greatest in z3 where the daily climatology is the most sharply peaked (see Fig. 9), and least in z4 where the daily climatology shows the least variation.

Adding interannual predictors (i.e., SST1 and SST2) to the model adds up to 2% in additional improvement to the BSS, depending on the forecast lead and zone. The interannual variability adds the most skill in z1, and the least in z3, showing the importance of SST2 for the TC variability in the western Indian Ocean. There can be a relatively large difference between the BSS for W0 and W1 using the interannual predictors as the SST values used for these lead times are separated by more than 30 days. Besides this, the improvement gained by adding the interannual predictors depends little on the lead time as SST1 and SST2 change very little from week to week, and the predictability afforded by these predictors extends several months into the future.

Adding the MJO predictors (i.e., RMM1 and RMM2) to the model, on the other hand, provides additional skill that varies greatly with lead time. For the W1 lead, the additional improvement gained by adding the MJO predictors (over that from using Clim alone) varies from 1.5% to 3%, being greatest in z4 and least in z3, consistent with the MJO-associated TC modulation quoted for these zones in section 3a. While this skill improvement exceeds that for the interannual variability at W1, the improvement with the MJO is only significant at W1 and W2, and up to W3 in z2, consistent with the previously quoted useful predictability of the MJO being only out to about 20 days. Beyond these lead times, RMM1 and RMM2 are either not selected or selected with relatively small coefficients, which does not change much the predicted probability, except in the case of a very strong MJO (more later).

We are now in a position to more easily understand the skill of the model using the full selection of predictors (solid curve; Fig. 14). The skill of the full selection almost always exceeds that of all other subsets of predictors (in all zones except z4). The overall improvement provided by the full selection varies from about 4.6% to 9% for W1, and then asymptotically approaches the skill of the model using only the daily-varying climatology and interannual predictors at the longest leads.

Is the skill improvement enhanced further when considering only days when the MJO is very strong? We look at this by computing the BSS, using the same reference forecast strategy as above, but including only days when the amplitude of the MJO predictor, as measured by (RMM12 + RMM22)1/2, is greater than 2. This represents 16% of all days. For W1 hindcasts, the improvements relative to the scores computed using all available hindcast days are substantial in every zone (Table 2), being greatest in z1 (up from 8.7% to 19.6%) and least in z4 (up from 4.6% to 7.0%). Thus, when the MJO is very strong, greater skill is achieved by the hindcasts, consistent with predictions that are more emphatic (i.e., with greater probability swings), yet still quite reliable. Furthermore, when the initial state of the MJO is very strong, the increased skill provided by it extends to greater leads. In z3, for example, when comparing the BSS of the full model (i.e., including the MJO) to the model with the daily-varying climatology and interannual predictors only (i.e., not including the MJO), our calculations indicate an enhancement of skill out to at least W5 (Fig. 15). For the other three zones, the enhancement occurs out to at least W3 (not shown). Thus, there will be times that can be known in advance for which the MJO provides skill beyond the previously quoted 20-day limit.

6. Summary and conclusions

A statistical scheme to predict the weekly TC activity in the Southern Hemisphere has been developed. The quantity predicted is the probability that at least one cyclone forms in a zone during a week (with similar results for TC occurrence). Four different zones in the Southern Hemisphere were considered: the southwestern Indian Ocean, the southeastern Indian Ocean, the southwestern Pacific Ocean, and the south-central Pacific Ocean, although the technique may easily be adapted to other zones.

The first step was to identify climate phenomena that provide a predictive influence on weekly TC activity in the region, and find indices/predictors that adequately represent these phenomena. Five predictors were chosen: one was the daily-varying climatological seasonal cycle of TC activity, two others were to represent the MJO, and two more to represent the leading modes of SST variability in the Indo-Pacific basin. Indices of the QBO and local SST variability, however, were not found to be as useful, and hence not included.

Logistic regression was the method chosen for developing the prediction model, and a formal stepwise selection procedure was run in order to decide which predictors needed to be used for each lead time and for each zone. Hindcasts were generated for all years of the observational record, employing a strict cross-validation method and using the predictors lagged according to their availability in real time.

Skill of the hindcasts was computed as a percentage improvement in the Brier score over a reference forecast strategy of a constant mean climatological probability. Improvements using the full model selection in the first forecast week were between 4.6% and 9%. In this first week, the majority of this improvement is derived from the inclusion of the MJO as a predictor. Indeed, by considering hindcasts during very strong MJO events only, the percentage improvement can be as great as 20%. In the second and third weeks when considering all hindcasts, however, the relative importance of the different predictors is mixed. Beyond the third week, no significant overall improvement is derived from the MJO, in all regions, except during predetermined very strong MJO cases in z3. For these longer leads, the skill asymptotically approaches that provided by the climatological seasonal cycle and interannual variability alone. By the seventh week, the skill improvement varies from 2% to 6%, being greatest in the southwest Indian Ocean (z1) and southwest Pacific (z3), and dominated by the seasonal cycle component. This dominance demonstrates the importance of a simple knowledge of the seasonal cycle of TC activity for intraseasonal TC forecasts.

Based on these results, an operational implementation of the forecast scheme is being maintained, with plans for some further development and improvement (see online at http://www.meteo.nc/espro/previcycl/cyclA.php).

Finally, it is of interest to consider how improvements in the skill of the prediction scheme, and its utility for decision making, could be made. There are several obvious avenues that could be followed: by adding to the model new predictors that represent phenomena not yet considered, by finding better indices that afford greater predictability of the phenomena already considered, by the use of more sophisticated statistical techniques, and/or by the refinement of the forecast zones and time horizons for greater utility and/or skill. For example, some incremental skill improvement would be expected by taking into account the influence of equatorial Rossby waves, which are known to also modulate TC activity (Bessafi and Wheeler 2006). Given their shorter time scale than the MJO, however, this improvement would not be expected to extend much beyond the first or second week. Other shorter time-scale phenomena also show relationships with TC genesis (e.g., Frank and Roundy 2006), each of which may provide an incremental improvement. Furthermore, except for our use of November–April data only, our scheme makes no consideration of the possibility of a strong seasonality to the relationships between the predictors and TC activity. For example, the MJO modulation of TCs could be quite different in November compared to April. We thus see the further development and provision of intraseasonal TC activity forecasts, either by statistical or dynamical means, as a productive area for future research and applications work.

Acknowledgments

We thank Yuriy Kuleshov of the National Climate Centre of the Australian Bureau of Meteorology for providing us with the TC best-track archive. The majority of the work presented in this paper was completed while Anne Leroy was participating in a 5-month research program at the Bureau of Meteorology Research Centre as a student trainee of Météo-France. The advice of Bertrand Timbal, Neville Nicholls, Adam Sobel, and John McBride is acknowledged, as are the reviews of Paul Roundy, George Kiladis, and an anonymous reviewer.

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Fig. 1.
Fig. 1.

The TC genesis locations, as defined to occur when the estimated central pressure reaches 995 hPa, during the TC season defined from 1 Nov to 30 Apr for the period from 1969/70 to 2003/04.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 2.
Fig. 2.

Prediction zones used in this study. Longitudinal boundaries are at: 30°E, 90°E, 135°E, 180°, and 120°W. Latitudinal boundaries are at 0°and 30°S.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 3.
Fig. 3.

Climatological seasonal cycle of weekly TC genesis probability in z3 from raw observations (histograms) and filtered (smoothed curve) using methodology described in section 2c. The tick marks on the horizontal axis denote the first day of each month, and the probabilities refer to the probability of a TC forming in the week starting on the day that is specified on the axis.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 4.
Fig. 4.

TC genesis locations (dots) according to the phase of the MJO, as defined by the RMM index of Wheeler and Hendon (2004). November–April TC data used for years 1969–2004. Also shown are contours of OLR anomalies for each averaged MJO phase using only 1974–2004 data. The contour interval is 7.5 W m−2, with negative contours solid and positive contours dashed. The zero contour is omitted. Also listed is the number of TCs counted within each phase and the number of days for which that MJO phase category occurred. Note the many greater number of days contributing to the weak MJO category, as defined to occur when (RMM12 + RMM22)1/2 < 1.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 5.
Fig. 5.

Spatial patterns of loadings of the leading two VARIMAX rotated principal components of standardized monthly SST anomalies (using data from all months of the year), as used to define the indices (a) SST1 and (b) SST2. Contour interval is 0.2, with zero contour heavy, negative contours dashed, and areas above +0.2 and below −0.2 shaded. Adapted from Drosdowsky and Chambers (2001).

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 6.
Fig. 6.

Climatologies of weekly TC genesis probabilities stratified for (November–April) seasons of 11 highest and lowest values of SST1 for each of the four zones (z1, z2, z3, and z4). High SST1 years are 1972/73, 1982/83, 1986/87, 1987/88, 1990/91, 1991/92, 1992/93, 1994/95, 1997/98, 2002/03, and 2003/04. Low SST1 years are 1970/71, 1971/72, 1973/74, 1974/75, 1975/76, 1980/81, 1983/84, 1984/85, 1985/86, 1988/89, and 1999/2000. The average probability during the TC season is in parentheses. The tick marks on the horizontal axis denote the first day of each month, and the probabilities refer to the probability of a TC forming in the week starting on the day that is specified on the axis.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 7.
Fig. 7.

As in Fig. 6, but for high and low SST2 seasons. High SST2 seasons are 1977/78, 1982/83, 1987/88, 1988/89, 1990/91, 1994/95, 1995/96, 1997/98, 2001/02, 2002/03, and 2003/04. Low SST2 seasons are 1970/71, 1971/72, 1973/74, 1974/75, 1975/76, 1980/91, 1981/82, 1985/86, 1986/87, 1992/93, and 1999/2000.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 8.
Fig. 8.

As in Fig. 6, but for weekly TC genesis probabilities stratified by the phase of the QBO at 30 hPa during May–June–July. “Westerly” and “easterly” refer to the 11 yr of strongest zonal-mean westerlies or easterlies, respectively. Wind data were sourced from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis (available online at http://www.cdc.noaa.gov).

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 9.
Fig. 9.

Climatological seasonal cycle of TC activity (solid curves) and local SST (dotted curves) for each of the selected zones, using all years 1969–2004. SST data were averaged for the latitudes 10°–20°S in each zone and were sourced from the International Comprehensive Ocean–Atmosphere Dataset (ICOADS; available online at http://www.cdc.noaa.gov). The labeling of the horizontal axis is the same as that in Fig. 6.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 10.
Fig. 10.

Example logistic regression models (curves) fitted for zone z3 and lead W1, shown separately for each predictor variable. Also shown as plus symbols are calculated averages of the observed probabilities and predictor values, binned into 20 equal-sized groups of about 310 observations each.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 11.
Fig. 11.

Example cross-validated hindcasts (solid curves) and cross-validated climatological probabilities (Clim; dashed curves) for W1 of the 1973/74, 1982/83, and 1984/85 TC seasons in z3. The dates along the horizontal axis refer to the starting day of the verifying week of the hindcast, with the tick marks denoting the first day of each month. Solid rectangular boxes at the top of each plot indicate the verifying observations, that is, the periods when a TC was observed to form. By definition, each rectangular box spans at least 1 week (7 days) because of our use of overlapping weekly probabilities.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 12.
Fig. 12.

As in Fig. 11, but for z3 in 1984/85 at different leads (W1–W6).

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 13.
Fig. 13.

Reliability diagrams comparing observations with W1 cross-validated hindcasts. All (overlapping) hindcasts are grouped into 20 equal-sized groups of about 310 each, according to their predicted probabilities. For each group, the average of the observed and predicted probabilities are calculated, and each is indicated with a plus symbol. These symbols are linked together forming the reliability curve. The horizontal lines indicate the mean observed probabilities, and the diagonal lines indicate the perfect forecast (full lines) and a 10% interval centered on the perfect forecast (dashed lines).

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 14.
Fig. 14.

Hindcast BSSs for each region and each lead time. Shown are the scores for the full model (solid curve), and comparison models using only a subset of the full set of predictors, if they are selected. The label “daily clim” uses only the daily-varying climatology (i.e., Clim) as a predictor; “daily clim + inter” uses Clim and interannual predictors (i.e., SST1 and SST2); and “daily clim + MJO” uses Clim, RMM1, and RMM2 only. The reference forecast used to calculate the BSS is the mean seasonal TC climatology, which varies with region only, and not with time of year. Note that the scales change.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Fig. 15.
Fig. 15.

As in Fig. 14, but for very strong MJO days only (see text for definition), and for z3 only.

Citation: Monthly Weather Review 136, 10; 10.1175/2008MWR2426.1

Table 1.

Predictor selection order as determined by the formal stepwise selection procedure of Hosmer and Lemeshow (2000), with a threshold p value of 0.15 (see section 2b), using all available input data. The number “1” indicates the predictor selected first, “2” for the predictor selected second, and so on. A blank space indicates that the predictor failed the selection test.

Table 1.
Table 2.

Hindcast BSSs for all days and very strong MJO days, in each zone for lead time W1, expressed as a percent improvement over the reference forecast strategy that uses a constant climatology. “All days” uses hindcasts from all November–April days, while “strong MJO” uses hindcasts when at the initial time (RMM12 + RMM22)1/2 > 2.

Table 2.
Save
  • Basher, R. E., and X. Zheng, 1995: Tropical cyclones in the Southwest Pacific: Spatial patterns and relationships to Southern Oscillation and sea surface temperature. J. Climate, 8 , 12491260.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bessafi, M., and M. C. Wheeler, 2006: Modulation of South Indian Ocean tropical cyclones by the Madden–Julian Oscillation and convectively coupled equatorial waves. Mon. Wea. Rev., 134 , 638656.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Camargo, S. J., A. G. Barnston, and S. E. Zebiak, 2005: A statistical assessment of tropical cyclone activity in atmospheric general circulation models. Tellus, 57A , 589604.

    • Search Google Scholar
    • Export Citation
  • Chan, J. C. L., and K. S. Liu, 2004: Global warming and western North Pacific typhoon activity from an observational perspective. J. Climate, 17 , 45904602.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chan, J. C. L., J-E. Shi, and K. S. Liu, 2001: Improvements in the seasonal forecasting of tropical cyclone activity over the western North Pacific. Wea. Forecasting, 16 , 491498.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dickinson, M., and J. Molinari, 2002: Mixed Rossby–gravity waves and western Pacific tropical cyclogenesis. Part I: Synoptic evolution. J. Atmos. Sci., 59 , 21832196.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Drosdowsky, W., and L. E. Chambers, 2001: Near-global sea surface temperature anomalies as predictors of Australian seasonal rainfall. J. Climate, 14 , 16771687.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frank, W. M., 1987: Tropical cyclone formation. A Global View of Tropical Cyclones, R. L. Elsberry, Ed., Office of Naval Research, 53–90.

    • Search Google Scholar
    • Export Citation
  • Frank, W. M., and P. E. Roundy, 2006: The role of tropical waves in tropical cyclogenesis. Mon. Wea. Rev., 134 , 23972417.

  • Gray, W. M., 1979: Hurricanes: Their formation, structure, and likely role in the tropical circulation. Meteorology over Tropical Oceans, D. B. Shaw, Ed., Royal Meteorology Society, 155–218.

    • Search Google Scholar
    • Export Citation
  • Gray, W. M., 1984: Atlantic seasonal hurricane frequency. Part I: El Niño and 30 mb quasi-biennial oscillation influences. Mon. Wea. Rev., 112 , 16491668.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gray, W. M., C. W. Landsea, P. W. Mielke, and K. J. Berry, 1992: Predicting Atlantic seasonal hurricane activity 6–11 months in advance. Wea. Forecasting, 7 , 440455.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, J. D., A. J. Matthews, and D. J. Karoly, 2001: The modulation of tropical cyclone activity in the Australian region by the Madden–Julian oscillation. Mon. Wea. Rev., 129 , 29702982.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hosmer, D. W., and S. Lemeshow, 2000: Applied Logistic Regression. 2nd ed. Wiley, 373 pp.

  • Jury, M. R., B. Pathack, and B. Parker, 1999: Climatic determinants and statistical prediction of tropical cyclone days in the Southwest Indian Ocean. J. Climate, 12 , 17381746.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kessler, W. S., 2001: EOF representation of the Madden–Julian oscillation and its connection with ENSO. J. Climate, 14 , 30553061.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuleshov, Y., 2003: Tropical cyclone climatology for the Southern Hemisphere. Part I: Spatial and temporal profiles of tropical cyclones in the Southern Hemisphere. National Climate Center, Commonwealth Bureau of Meteorology, 20 pp.

  • Kuleshov, Y., and G. de Hoedt, 2003: Tropical cyclone activity in the Southern Hemisphere. Bull. Aust. Meteor. Oceanogr. Soc., 16 , 135137.

    • Search Google Scholar
    • Export Citation
  • Landsea, C. W., G. Bell, W. M. Gray, and S. B. Goldenberg, 1998: The extremely active 1995 Atlantic hurricane season: Environmental conditions and verification of seasonal forecasts. Mon. Wea. Rev., 126 , 11741193.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lo, F., and H. H. Hendon, 2000: Empirical extended-range prediction of the Madden–Julian oscillation. Mon. Wea. Rev., 128 , 25282543.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1994: Observations of the 40–50-day tropical oscillation—A review. Mon. Wea. Rev., 122 , 814837.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maloney, E. D., and D. L. Hartmann, 2000: Modulation of eastern North Pacific hurricanes by the Madden–Julian oscillation. J. Climate, 13 , 14511460.

    • Crossref
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  • Fig. 1.

    The TC genesis locations, as defined to occur when the estimated central pressure reaches 995 hPa, during the TC season defined from 1 Nov to 30 Apr for the period from 1969/70 to 2003/04.

  • Fig. 2.

    Prediction zones used in this study. Longitudinal boundaries are at: 30°E, 90°E, 135°E, 180°, and 120°W. Latitudinal boundaries are at 0°and 30°S.

  • Fig. 3.

    Climatological seasonal cycle of weekly TC genesis probability in z3 from raw observations (histograms) and filtered (smoothed curve) using methodology described in section 2c. The tick marks on the horizontal axis denote the first day of each month, and the probabilities refer to the probability of a TC forming in the week starting on the day that is specified on the axis.

  • Fig. 4.

    TC genesis locations (dots) according to the phase of the MJO, as defined by the RMM index of Wheeler and Hendon (2004). November–April TC data used for years 1969–2004. Also shown are contours of OLR anomalies for each averaged MJO phase using only 1974–2004 data. The contour interval is 7.5 W m−2, with negative contours solid and positive contours dashed. The zero contour is omitted. Also listed is the number of TCs counted within each phase and the number of days for which that MJO phase category occurred. Note the many greater number of days contributing to the weak MJO category, as defined to occur when (RMM12 + RMM22)1/2 < 1.

  • Fig. 5.

    Spatial patterns of loadings of the leading two VARIMAX rotated principal components of standardized monthly SST anomalies (using data from all months of the year), as used to define the indices (a) SST1 and (b) SST2. Contour interval is 0.2, with zero contour heavy, negative contours dashed, and areas above +0.2 and below −0.2 shaded. Adapted from Drosdowsky and Chambers (2001).

  • Fig. 6.

    Climatologies of weekly TC genesis probabilities stratified for (November–April) seasons of 11 highest and lowest values of SST1 for each of the four zones (z1, z2, z3, and z4). High SST1 years are 1972/73, 1982/83, 1986/87, 1987/88, 1990/91, 1991/92, 1992/93, 1994/95, 1997/98, 2002/03, and 2003/04. Low SST1 years are 1970/71, 1971/72, 1973/74, 1974/75, 1975/76, 1980/81, 1983/84, 1984/85, 1985/86, 1988/89, and 1999/2000. The average probability during the TC season is in parentheses. The tick marks on the horizontal axis denote the first day of each month, and the probabilities refer to the probability of a TC forming in the week starting on the day that is specified on the axis.

  • Fig. 7.

    As in Fig. 6, but for high and low SST2 seasons. High SST2 seasons are 1977/78, 1982/83, 1987/88, 1988/89, 1990/91, 1994/95, 1995/96, 1997/98, 2001/02, 2002/03, and 2003/04. Low SST2 seasons are 1970/71, 1971/72, 1973/74, 1974/75, 1975/76, 1980/91, 1981/82, 1985/86, 1986/87, 1992/93, and 1999/2000.

  • Fig. 8.

    As in Fig. 6, but for weekly TC genesis probabilities stratified by the phase of the QBO at 30 hPa during May–June–July. “Westerly” and “easterly” refer to the 11 yr of strongest zonal-mean westerlies or easterlies, respectively. Wind data were sourced from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis (available online at http://www.cdc.noaa.gov).

  • Fig. 9.

    Climatological seasonal cycle of TC activity (solid curves) and local SST (dotted curves) for each of the selected zones, using all years 1969–2004. SST data were averaged for the latitudes 10°–20°S in each zone and were sourced from the International Comprehensive Ocean–Atmosphere Dataset (ICOADS; available online at http://www.cdc.noaa.gov). The labeling of the horizontal axis is the same as that in Fig. 6.

  • Fig. 10.

    Example logistic regression models (curves) fitted for zone z3 and lead W1, shown separately for each predictor variable. Also shown as plus symbols are calculated averages of the observed probabilities and predictor values, binned into 20 equal-sized groups of about 310 observations each.

  • Fig. 11.

    Example cross-validated hindcasts (solid curves) and cross-validated climatological probabilities (Clim; dashed curves) for W1 of the 1973/74, 1982/83, and 1984/85 TC seasons in z3. The dates along the horizontal axis refer to the starting day of the verifying week of the hindcast, with the tick marks denoting the first day of each month. Solid rectangular boxes at the top of each plot indicate the verifying observations, that is, the periods when a TC was observed to form. By definition, each rectangular box spans at least 1 week (7 days) because of our use of overlapping weekly probabilities.

  • Fig. 12.

    As in Fig. 11, but for z3 in 1984/85 at different leads (W1–W6).

  • Fig. 13.

    Reliability diagrams comparing observations with W1 cross-validated hindcasts. All (overlapping) hindcasts are grouped into 20 equal-sized groups of about 310 each, according to their predicted probabilities. For each group, the average of the observed and predicted probabilities are calculated, and each is indicated with a plus symbol. These symbols are linked together forming the reliability curve. The horizontal lines indicate the mean observed probabilities, and the diagonal lines indicate the perfect forecast (full lines) and a 10% interval centered on the perfect forecast (dashed lines).

  • Fig. 14.

    Hindcast BSSs for each region and each lead time. Shown are the scores for the full model (solid curve), and comparison models using only a subset of the full set of predictors, if they are selected. The label “daily clim” uses only the daily-varying climatology (i.e., Clim) as a predictor; “daily clim + inter” uses Clim and interannual predictors (i.e., SST1 and SST2); and “daily clim + MJO” uses Clim, RMM1, and RMM2 only. The reference forecast used to calculate the BSS is the mean seasonal TC climatology, which varies with region only, and not with time of year. Note that the scales change.

  • Fig. 15.

    As in Fig. 14, but for very strong MJO days only (see text for definition), and for z3 only.

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