Understanding Biases in Tropical Cyclone Intensity Forecast Error

Wei Na State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

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John L. McBride School of Earth Science, University of Melbourne, and Research and Development Division, Bureau of Meteorology, Melbourne, Victoria, Australia

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Xing-Hai Zhang State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, and Glarun Technology, Fourteenth Research Institute, China Electronic Technology Group Corporation, Nanjing, China

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Yi-Hong Duan State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

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Abstract

The characteristics of 24-h official forecast errors (OFEs) of tropical cyclone (TC) intensity are analyzed over the North Atlantic, east Pacific, and western North Pacific. The OFE is demonstrated to be strongly anticorrelated with TC intensity change with correlation coefficients of −0.77, −0.77, and −0.68 for the three basins, respectively. The 24-h intensity change in the official forecast closely follows a Gaussian distribution with a standard deviation only ⅔ of that in nature, suggesting the current official forecasts estimate fewer cases of large intensity change. The intensifying systems tend to produce negative errors (underforecast), while weakening systems have consistent positive errors (overforecast). This asymmetrical bias is larger for extreme intensity change, including rapid intensification (RI) and rapid weakening (RW). To understand this behavior, the errors are analyzed in a simple objective model, the trend-persistence model (TPM). The TPM exhibits the same error-intensity change correlation. In the TPM, the error can be understood as it is exactly inversely proportional to the finite difference form of the concavity or second derivative of the intensity–time curve. The occurrence of large negative (positive) errors indicates the intensity–time curve is concave upward (downward) in nature during the TC’s rapid intensification (weakening) process. Thus, the fundamental feature of the OFE distribution is related to the shape of the intensity–time curve, governed by TC dynamics. All forecast systems have difficulty forecasting an accelerating rate of change, or a large second derivative of the intensity–time curve. TPM may also be useful as a baseline in evaluating the skill of official forecasts. According to this baseline, official forecasts are more skillful in RW than in RI.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Duan Yi-Hong, duanyh@cma.gov.cn

Abstract

The characteristics of 24-h official forecast errors (OFEs) of tropical cyclone (TC) intensity are analyzed over the North Atlantic, east Pacific, and western North Pacific. The OFE is demonstrated to be strongly anticorrelated with TC intensity change with correlation coefficients of −0.77, −0.77, and −0.68 for the three basins, respectively. The 24-h intensity change in the official forecast closely follows a Gaussian distribution with a standard deviation only ⅔ of that in nature, suggesting the current official forecasts estimate fewer cases of large intensity change. The intensifying systems tend to produce negative errors (underforecast), while weakening systems have consistent positive errors (overforecast). This asymmetrical bias is larger for extreme intensity change, including rapid intensification (RI) and rapid weakening (RW). To understand this behavior, the errors are analyzed in a simple objective model, the trend-persistence model (TPM). The TPM exhibits the same error-intensity change correlation. In the TPM, the error can be understood as it is exactly inversely proportional to the finite difference form of the concavity or second derivative of the intensity–time curve. The occurrence of large negative (positive) errors indicates the intensity–time curve is concave upward (downward) in nature during the TC’s rapid intensification (weakening) process. Thus, the fundamental feature of the OFE distribution is related to the shape of the intensity–time curve, governed by TC dynamics. All forecast systems have difficulty forecasting an accelerating rate of change, or a large second derivative of the intensity–time curve. TPM may also be useful as a baseline in evaluating the skill of official forecasts. According to this baseline, official forecasts are more skillful in RW than in RI.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Duan Yi-Hong, duanyh@cma.gov.cn

1. Introduction

Tropical cyclones (TCs) are among the most serious natural disasters, bringing about large losses of life and property around the world. In recent decades, the skill of operational TC track forecasting has undergone continuous improvement. This is mainly due to continuous and rapid advances in numerical weather prediction capabilities, including the development of ensemble techniques (McAdie and Lawrence 2000; Powell and Aberson 2001; Franklin et al. 2003; Peng et al. 2017; Yamaguchi et al. 2012, 2015). In comparison, the forecasting of tropical cyclone intensity is improving much more slowly (DeMaria et al. 2007, 2014, Emanuel and Zhang 2016; Tallapragada et al. 2016).

In recent years, the improvements in TC intensity forecasting have been of deep concern to both forecasters and researchers (e.g., Gall et al. 2013). Many studies have attempted to improve forecast skill through advanced numerical models (e.g., Gopalakrishnan et al. 2011; Cha and Wang 2013; Zhang and Weng 2015; Liu and Tan 2016), in situ and remote sensing observations (e.g., Rogers et al. 2012; Ruf et al. 2016; Zhao et al. 2016, 2017), and statistical forecast models (Kaplan et al. 2015). As well as the importance of forecast skill development, insights into the characteristics of forecast errors from current operational forecasts can provide guidance for further improvement.

Over the past few decades, the official forecasting agencies have accumulated large amounts of TC forecasting data. The official forecasts, made by operational forecast personnel, are expert judgments drawing on the output of numerical weather prediction models, objective statistical techniques, and interpretations of satellite imagery and evolving synoptic patterns that can represent the highest level of TC forecasts currently available. Prior studies of official forecast errors (OFEs) have focused mainly on track forecasts (McAdie and Lawrence 2000; Powell and Aberson 2001; Franklin et al. 2003; Peng et al. 2017). Some evaluation of intensity forecast errors is included in annual TC reports from the Joint Typhoon Warning Center (JTWC) and the National Hurricane Center (NHC) (http://www.usno.navy.mil/JTWC/annual-tropical-cyclone-reports). DeMaria et al. (2005, 2014) document the trends or improvements in NHC/JTWC official intensity forecast errors.

The primary purpose of the current paper is to gain insight into the nature of the intensity official forecast problem through examination of forecast error distributions and error characteristics. Section 2 describes the data sources and methodology used. Section 3 presents an examination of the OFE. Strong anticorrelation is found between OFE and intensity change, suggesting there is a significant bias in error such that rapidly weakening storms are almost always overforecast (positive errors) and intensifying storms are underforecast (negative errors). To address whether this anticorrelation is caused by characteristics of the forecast model, or whether it is a property of the life cycle and intensity growth curve of the tropical cyclone, in section 4 the forecast database is duplicated using a simple first derivative or “trend persistence” forecast model (TPM). With the help of TPM, it is possible to understand the reasons for the asymmetric error characteristics and so give insights into the official forecast process. The final two sections discuss implications of the analysis for intensity forecasting and summarize our findings.

2. Data description and processing

In this study, the official forecasts of TC intensity for three cyclone basins in the Northern Hemisphere—North Atlantic (NA), east Pacific (EP), and western North Pacific (WP)—are examined, as issued by the NHC and from the China Meteorological Administration (CMA). The forecast error and best-track databases at 6-h intervals for the NHC in the NA and EP can be found online (http://www.nhc.noaa.gov/verification/verify7.shtml). Since the CMA database provides only the official forecasts of TC track and intensity, the corresponding forecast error is calculated using the best-track data obtained from the International Best Track Archive for Climate Stewardship (IBTrACS; Knapp et al. 2010) which is provided by the Shanghai Typhoon Institute of the CMA (CMA-STI) over the western North Pacific. The NHC forecast error database spans from 1990 to 2015, while the CMA database covers only 12 years, from 2004 to 2015. Despite the shorter time series for the WP, the data sample sizes are similar as climatologically the WP has a greater number of cyclones per year. The analysis is restricted to the 24-h forecast error, though with a short discussion of longer lead times in section 5c. The sample counts for each basin are shown in Table 1. The ocean samples mentioned in the following analysis exclude the samples onshore or near coastlines, in order to exclude the influence of land. The distance from a coastline (including the mainland and large islands) is obtained from IBTrACS.

Table 1.

Samples of TC 24-h intensity forecast error databases. Ocean samples denote samples excluding those within 300 km of the coastline at forecast time.

Table 1.

3. Characteristics of official TC intensity forecast

For the datasets considered here, the average 24-h intensity OFEs over the three basins (NA, EP, and WP) are, respectively, 9.8, 10.6, and 9.9 kt (where 1 kt = 0.51 m s−1; Table 2). In comparison, the errors at 48 and 72 h are 14.6, 16.0, and 14.6 kt and 17.8, 18.6, and 17.8 kt, respectively (note that in WP the 72-h forecast is obtained from 2007). As for the trend, there have been steady improvements in intensity forecasts at the longer lead times, but only very small improvements at 24 h, which is consistent with the published literature (DeMaria et al. 2014). This is one of the reasons that the analysis in this paper will focus on the 24-h forecast.

Table 2.

The averaged absolute 24-h intensity OFE (kt) and TPM-E (kt). The “all” column denotes all samples, while RI and RW denote rapidly intensifying and rapidly weakening samples respectively. Numbers in parentheses are the same but for ocean samples.

Table 2.

In an exploration of the relationship between TC intensity and its OFE, the observed signal is between OFE and TC 24-h intensity change, rather than with TC intensity itself. Specifically, the 24-h intensity OFE is strongly anticorrelated with the corresponding TC 24-h intensity changes with the linear correlation coefficients for NA, EP, and WP of −0.77, −0.77, and −0.68, respectively (Fig. 1). The large positive OFEs generally occur with large negative intensity changes (weakening TCs), and large negative OFEs occur with large positive intensity changes (intensifying TCs). In particular, following Kaplan and DeMaria (2003), we define rapid intensification (RI) as an intensification rate larger than 30 kt over 24 h and rapid weakening (RW) as the equivalent rapid weakening rate following Wood and Ritchie (2015); these rates are marked in Fig. 1 with vertical dashed lines. The results show that for almost all RI cases, their future intensities are underestimated in official forecasts, and conversely for almost all RW cases, their intensities are overestimated. This is perhaps not unexpected as the tails of the distribution are, by definition, climatologically rare events and so are presumably less predictable.

Fig. 1.
Fig. 1.

Distribution of 24-h intensity OFE frequencies with respect to TC 24-h intensity change over (a) NA, (b) EP, and (c) WP. All frequencies are calculated within 10-kt bins and are indicated by numbers in each box.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0106.1

Since OFE is highly correlated with intensity change, the distributions of the forecast 24-h intensity change are compared with the distributions of actual 24-h intensity change in Fig. 2. Both distributions are approximately Gaussian, with a small positive expectation (or median value). But the spread or standard deviation of the official forecasts (red curve) is only about ⅔ of that in nature (black curve). Thus, the official forecasts are conservative in terms of the extremes of intensity change prediction. This confirms that the RI and RW cases that occur in nature are generally underestimated in the forecasts.

Fig. 2.
Fig. 2.

Distribution of 24-h intensity changes in the best-track data (black) and official forecast (red).

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0106.1

The contributions of RI and RW to large OFEs are quantified through Venn diagrams in Fig. 3. Defining a large OFE as the upper and lower 5% of the OFE distributions, the thresholds are 20, 20, and 20 kt and −20, −25, and −20 kt in NA, EP, and WP, respectively. More than half of the RI samples produce large OFEs, particularly in NA (~75%) and WP (~80%). Looking at the contribution of RI to the largest negative OFE, RI contributes 54%, 78%, and 61%, respectively, in NA, EP, and WP. Therefore, the association between RI and large negative errors is strong, as previously noted by Cangialosi and Franklin (2014) and Lee et al. (2016). The average absolute error for RI samples is much larger than that of all samples, by about 2–3 times, as shown in Table 2.

Fig. 3.
Fig. 3.

Venn diagram representation of the overlap between the top 5% and bottom 5% (blue) of OFEs and the RW and RI processes (red). The labeled red numbers denote the total sample size for the RW/RI cases. The blue numbers indicate sample size and the top and bottom 5% of errors. Overlapped areas (purple numbers) denote coincident samples.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0106.1

In contrast, the overlap of RW and large OFE (top 5%) is relatively smaller, suggesting that the official forecasts are more skillful at RW than at RI. For all three basins, more than half of the RW events are well forecast to the extent they do not contribute to the top 5% of OFEs, especially in WP. Also, the average errors of the RW samples are less than those for RI, but still much larger than the whole averaged set of OFEs. This can also be seen by inspection of the relevant sectors of the graphs in Fig. 1. We will discuss this further in the next section.

4. Trend-persistence forecast model

The key finding of the earlier sections is encapsulated in Fig. 1: the presence of a large anticorrelation between TC intensity change and the corresponding OFEs. The question arises as to whether this is a characteristic of the forecast process or whether it is a characteristic of the life cycle of the system being forecast, that is, the tropical cyclone.

To address this, we introduce the simplest possible objective forecast model, the trend-persistence model. By definition, this model forecasts the 24-h intensity change to be equal to the observed intensity change over the preceding 24 h. Thus,
e1
where is the TPM forecast intensity at T + 24 h, and I denotes the TC intensity at time T, T + 24, etc., as denoted in the subscript. In the analysis here, TC intensities are obtained from the best-track datasets. Note that when is lower than the intensity of a tropical depression (TD; i.e., 20 kt), the samples are excluded. It may be not the best baseline to assess the OFEs, but it is very simple and adequate for answering the question.

The TPM has two appealing characteristics that aid in the analysis and interpretation of forecast errors. The first is that since the forecast intensity change is simply the change over the preceding 24 h, the distribution of forecast intensity changes from the model should be the same as that in nature. Thus, referring back to Fig. 2, for the TPM, the forecast changes do lie over the top of the black curve (not shown). The second characteristic is that the forecast intensity errors from the TPM (TPM-E) are inversely proportional to the curvature or concavity of the intensity–time curve of the cyclone. This can be deduced intuitively. Since the TPM continues the prior trend into the following 24 h, if the intensity graph curves upward (concave up), the continuation of the prior gradient will be below the curve, and so the TPM-E will be negative. Conversely, if the intensity–time graph from that point is concave down, the TPM-E will be positive. This is demonstrated quantitatively as follows.

The TPM-E, namely the 24-h forecast error for the TPM, is equal to the difference between the forecast intensity and the actual intensity from the best track. Therefore, the TPM-E calculated at time T + 24, from an initial time T, is
e2
Substituting from Eq. (1),
e3
This is equal to minus the numerator of the second-order-accurate centered finite-difference algorithm for the second derivative. Thus, multiplying the right-hand side by ΔT2T2 yields
e4
where the partial derivative is approximated by its finite-difference form, and is the time step, which in this case is 24 h. Thus, the 24-h TPM-E is directly inversely proportional to the finite-difference form of the second derivative or the concavity of the curve of intensity plotted against time.

The 24-h TC intensity forecast in the previous section is repeated using the TPM. The TPM 24-h intensity forecast errors as a function of the actual 24-h intensity change are shown in Fig. 4, which is the equivalent figure to Fig. 1. The main feature is that the TPM shows the same linear relationship as the official forecast, with correlation coefficients of −0.69, −0.58, and −0.58 for NA, EP, and WP, respectively.

Fig. 4.
Fig. 4.

Distribution of 24-h forecast error frequencies with respect to TC 24-h intensity changes for TPM.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0106.1

Since this is the TPM whereby the errors are proportional to the negative of the concavity d2I/dT2, the relationship can be understood and is illustrated in Fig. 5. As illustrated, the top half of the graph corresponds to positive TPM errors, which in turn correspond to d2I/dT2 < 0, or a concave-down intensity time curve. Referring back to Fig. 4, the TPM errors for the three ocean basins are actually a plot of the climatology of observed −d2I/dT2 or concavity as a function of 24-h intensity change. As can be seen, in nature, large positive intensity changes tend to only occur in the presence of large upward concavity, with the converse being true for large negative changes or rapid decay rates. This behavior seems physically reasonable within the context of tropical cyclone dynamics. For example, samples shown in the bottom-right corners in Figs. 4 and 5 represent a concave-upward intensity change in time with dI/dT > 0 and d2I/dT2 > 0. That means the intensifying rate will grow with increasing intensity. This seems consistent with the Schubert and Hack (1982) and Vigh and Schubert (2009) paradigm, whereby as intensification occurs, the inertial stability increases, and so makes convective heating more efficient in terms of its impact on the tangential wind change or further intensification. Conversely, for the top-left quadrants in Figs. 4 and 5, a weakening system is presumably losing its dynamical structure and so the weakening process becomes accelerated. In summary, within the framework of the TPM, the fundamental reason that negative forecast errors accompany strongly intensifying systems and positive errors accompany strongly decaying systems is that in nature strongly intensifying systems generally follow a concave-upward intensity–time curve and strongly decaying systems follow a concave-downward intensity–time curve, which is dominated by TC dynamics.

Fig. 5.
Fig. 5.

Conceptual graph showing the relationship between 24-h intensity forecast error and 24-h intensity change in TPM.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0106.1

The question now is why do the official forecasts exhibit the same behavior? We propose it is for the same reason. As discussed, Figs. 4 and 5 of TPM-E versus intensity change are actually the climatology of intensity change versus concavity, as it occurs in nature. Thus, whenever moderate-to-large intensification rates occur, they occur in a concave-upward sense, that is, with an accelerating rate of intensification. The reason that the official forecasts have a negative error is that it is difficult to forecast an accelerating intensification rate. The same, but converse, reasoning explains why moderate-to-large cyclone weakening always has a positive error.

Figure 6 shows the OFE plotted against the TPM-E (proportional to −d2I/dT2). Since the sign of TPM-E can represent intensity–time concavity, it is confirmed that the official forecasts do behave such that the large positive errors occur when the intensity–time concavity is downward and the large negative errors occur when the concavity is upward. Therefore, similar to TPM, this feature of the OFE distribution is related to the nature of the TC intensity change. Specifically, all official forecasts have difficulty in forecasting an accelerating rate of change, especially for rapid intensification and weakening.

Fig. 6.
Fig. 6.

The 24-h intensity OFEs (x axis) vs the TPM forecast error (y axis) for the three ocean basins. The red dashed line indicates the two errors are equal.

Citation: Weather and Forecasting 33, 1; 10.1175/WAF-D-17-0106.1

Since TPM is the simplest TC intensity forecast model, it can also provide a baseline of forecast skill. The skill of the forecast, as measured by mean absolute error, is shown in Table 2. As would be expected, the official forecasts are significantly better than those from the TPM in all three basins averaged over “all” forecasts. For TCs with rapid intensity change, the skill of the official forecasts is much better for RW than for RI, which is a finding that is consistent with the above analysis. However, it is noteworthy that neither the official forecasts nor TPM could predict RI well, indicating that RI is more challenging for current official forecasts.

As mentioned above, official forecasts show much better skill than TPM for RW. The question arises as to whether the high level of skill for RW is due to the influence of landfall. With the improvements in TC track forecasts, the models and human forecasters may be able to take into account the fact that a cyclone will weaken when it approaches or crosses land. To ascertain this, all forecast origin points within 300 km of the continental coastline have been removed, and the corresponding results are shown in the numbers in parentheses in Table 2. For the official forecasts, removal of the land and near-land samples does not significantly affect the mean absolute errors for the North Atlantic and the east Pacific. However, for the WP, we can see that the absolute error for RW cyclones is increased by 50%. Thus, the higher skill for RW in WP is partly related to the better performance of official forecasts near and over land. Still, the error for RW is much smaller than that from TPM, suggesting that official forecasts do show a certain level of skill for RW. In addition, the TPM produces much larger error for RW than RI. A lot of RW cases occur when a TC is intensifying in the previous 24 h but weakens rapidly in the following 24 h, which results in TPM’s large forecast error. That is, the TPM could not catch the right time point for when the TC started weakening. Kowch and Emanuel (2015) claimed that, unlike RW, there may be no special process at work for RI, which is governed by randomly distributed environmental and internal processes. That means RI may be less predictable than RW.

5. Discussion

a. Systematic errors

As shown above, OFEs are generally negative for intensifying systems and positive for weakening systems. The question is whether this knowledge can be used operationally as a form of bias correction for a forecast. The authors carried out some preliminary investigation of this. However, to date we have found no simple relationship between the OFE and the intensity change in the preceding 24 h. Also, we have found no simple relationship between OFE and the concavity d2I/dT2 over the 24 h prior to the forecast period.

b. Predictability of intensity change

The above results show that official forecasts do not predict well large intensity changes, especially large positive changes or RI. Kaplan and DeMaria (2003) found that almost every intense TC (categories 4 and 5) would experience the RI process during its lifetime, and the proportion of intense TCs is believed to be increasing under global warming (Webster et al. 2005; Emanuel 2005; Curry et al. 2006; Mei and Xie 2016). The more RI processes that occur in the future, the larger the forecast errors will be (absent any major improvements in RI forecasts). This means the predictability of TC intensity may decrease. In fact, based on a model study, Emanuel (2017) has noticed this potential trend. Therefore, improvements in official forecast skill for RI are in urgent demand.

c. Longer forecast times

The reviewers requested comments on the application of these findings to longer forecast times, beyond 24 h. For the basic finding in Fig. 1, the large negative correlation between OFEs and actual intensity change does apply to longer lead times. In section 3 the correlations between 24-h OFEs and 24-h actual intensity change were stated as being −0.77, −0.77, and −0.68 (NA, EP, and WP). The equivalent correlations for 48-h OFEs versus 48-h intensity change and for 72-h OFEs and changes are −0.71, −0.70, and −0.67 and −0.71, −0.64, and −0.65, respectively. Thus, the basic findings of the paper apply equally well.

The analysis in Eqs. (1)(4) also applies if the TPM is based on the prior 48- and 72-h intensity changes. Application of a TPM model using the prior trend for the forecast length also yields the same negative correlations. For example, for the Atlantic basin the model forecasts were run for 6, 12, 24, 36, 48, and 72 h ahead, using in each case a TPM model derived from the same period trend. The correlations between TPM-E and actual intensity change were −0.37, −0.55, −0.69, −0.74, −0.78, and −0.82, respectively. Since the errors in the TPM are understood as being a function of the concavity of the intensity–time curve, and since both the OFEs and the TPM model show the same behavior for all forecast lead times, the discussion and findings of this paper seem to apply to all forecast lead times.

6. Conclusions

The characteristics of tropical cyclone intensity official forecast errors (OFEs) have been studied for three basins: the North Atlantic (NA), the eastern Pacific (EP), and the western North Pacific (WP). The trend-persistence model (TPM) has been introduced to aid in understanding the characteristics of the errors. Our major conclusions are as follows:

  1. The distribution of 24-h intensity change is approximately Gaussian, both in nature and in the official forecasts. However, the standard deviation of the forecast intensity change is only ⅔ of the actual changes, implying the forecasts will not reproduce the observed range of the intensity change.

  2. Large negative correlations are observed between the OFEs and the actual 24-h intensity changes. In particular, rapid intensification (RI) and rapid weakening (RW) samples are underestimated with consistent large negative and positive OFEs, respectively.

  3. We have documented the contributions of RI and RW to major errors, arbitrarily defined as the top 5% of the positive and negative forecast errors. The association is close between RI and the largest negative OFEs, with RI cases contributing between 54% and 78% of these errors, depending on the basin. In contrast, there is a weaker association between RW and the largest positive OFEs, with RW contributing between 23% and 42%, implying more than half of the RW cases were well forecast.

  4. The TPM model was introduced as an example of a simple objective forecast algorithm, to determine whether the same error characteristics would be present. It was found that the large negative correlation between error and actual intensity change is also present in the distribution of forecasts from this model.

  5. Algebraic analysis demonstrates that the TPM model error is proportional to the finite-difference representation of the negative of d2I/dT2, or the concavity of the intensity–time curve. Thus, for the TPM the reason for the negative correlation between error and intensity change is completely understood. It is simply a function of the climatological characteristics of the cyclones’ intensity change: large positive and negative intensity changes almost always occur in the presence of a strongly concave-upward or concave-downward intensity–time graph, respectively.

  6. We contend that the same aspect of the climatology is the underlying reason for the presence of the negative OFE–intensity change correlation. In nature large intensity changes occur only in the presence of large positive or negative values of d2I/dT2, so that the official forecast is attempting to predict a rapidly changing or accelerating state, which is inherently difficult.

  7. It is also proposed that the TPM may have some use as a baseline forecast. Comparing absolute errors from OFE with those from TPM, official forecasts are skillful in predicting RW. This is true even when the influence of landfall on RW is excluded from the dataset. In contrast, for rapidly intensifying cyclones, the official forecasts are no better than the trend persistence forecasts.

Acknowledgments

The comments of three anonymous reviewers brought about substantial improvements to the clarity of the paper. This work was funded by the National Key Basic Research (973) Program of China (Grant 2015CB452804), the Natural Science Foundation of China (Grants 41375068, 41475055, and 41705038), and the Basic Research Foundation of Chinese Academy of Meteorological Sciences (2017Y016).

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  • Kaplan, J., and Coauthors, 2015: Evaluating environmental impacts on tropical cyclone rapid intensification predictability utilizing statistical models. Wea. Forecasting, 30, 13741396, https://doi.org/10.1175/WAF-D-15-0032.1.

    • Crossref
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  • Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Climate Stewardship (IBTrACS): Unifying tropical cyclone data. Bull. Amer. Meteor. Soc., 91, 363376, https://doi.org/10.1175/2009BAMS2755.1.

    • Crossref
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  • Kowch, R., and K. Emanuel, 2015: Are special processes at work in the rapid intensification of tropical cyclones? Mon. Wea. Rev., 143, 878882, https://doi.org/10.1175/MWR-D-14-00360.1.

    • Crossref
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  • Lee, C.-Y., M. Tippett, A. H. Sobel, and S. J. Camargo, 2016: Autoregressive modeling for tropical cyclone intensity climatology. J. Climate, 29, 78157830, https://doi.org/10.1175/JCLI-D-15-0909.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, H., and Z. Tan, 2016: A dynamical initialization scheme for binary tropical cyclones. Mon. Wea. Rev., 144, 47874803, https://doi.org/10.1175/MWR-D-16-0176.1.

    • Crossref
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    • Export Citation
  • McAdie, C. J., and M. B. Lawrence, 2000: Improvements in tropical cyclone track forecasting in the Atlantic basin, 1970–98. Bull. Amer. Meteor. Soc., 81, 989997, https://doi.org/10.1175/1520-0477(2000)081<0989:IITCTF>2.3.CO;2.

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  • Mei, W., and S. Xie, 2016: Intensification of landfalling typhoons over the northwest Pacific since the late 1970s. Nat. Geosci., 9, 753757, https://doi.org/10.1038/ngeo2792.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peng, X., J. Fei, X. Huang, and X. Cheng, 2017: Evaluation and error analysis of official forecasts of tropical cyclones during 2005–14 over the western North Pacific. Part I: Storm tracks. Wea. Forecasting, 32, 689712, https://doi.org/10.1175/WAF-D-16-0043.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., and S. D. Aberson, 2001: Accuracy of United States tropical cyclone landfall forecasts in the Atlantic basin (1976–2000). Bull. Amer. Meteor. Soc., 82, 27492767, https://doi.org/10.1175/1520-0477(2001)082<2749:AOUSTC>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., S. Lorsolo, P. Reasor, J. Gamache, and F. Marks, 2012: Multiscale analysis of tropical cyclone kinematic structure from airborne Doppler radar composites. Mon. Wea. Rev., 140, 7799, https://doi.org/10.1175/MWR-D-10-05075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruf, C. S., and Coauthors, 2016: New ocean winds satellite mission to probe hurricanes and tropical convection. Bull. Amer. Meteor. Soc., 97, 385395, https://doi.org/10.1175/BAMS-D-14-00218.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39, 16871697, https://doi.org/10.1175/1520-0469(1982)039<1687:ISATCD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tallapragada, V., and Coauthors, 2016: Forecasting tropical cyclones in the western North Pacific basin using the NCEP operational HWRF model: Model upgrades and evaluation of real-time performance in 2013. Wea. Forecasting, 31, 877894, https://doi.org/10.1175/WAF-D-14-00139.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vigh, J. L., and W. H. Schubert, 2009: Rapid development of the tropical cyclone warm core. J. Atmos. Sci., 66, 33353350, https://doi.org/10.1175/2009JAS3092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Webster, P. J., G. J. Holland, J. A. Curry, and H.-R. Chang, 2005: Changes in tropical cyclone number, duration, and intensity in a warming environment. Science, 309, 18441846, https://doi.org/10.1126/science.1116448.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wood, K. M., and E. A. Ritchie, 2015: A definition for rapid weakening of North Atlantic and eastern North Pacific tropical cyclones. Geophys. Res. Lett., 42, 10 09110 097, https://doi.org/10.1002/2015GL066697.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., T. Nakazawa, and S. Hoshino, 2012: On the relative benefits of a multi‐centre grand ensemble for tropical cyclone track prediction in the western North Pacific. Quart. J. Roy. Meteor. Soc., 138, 20192029, https://doi.org/10.1002/qj.1937.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., and Coauthors, 2015: Global distribution of the skill of tropical cyclone activity forecasts on short- to medium-range time scales. Wea. Forecasting, 30, 16951709, https://doi.org/10.1175/WAF-D-14-00136.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., and Y. Weng, 2015: Predicting hurricane intensity and associated hazards: A five-year real-time forecast experiment with assimilation of airborne Doppler radar observations. Bull. Amer. Meteor. Soc., 96, 2533, https://doi.org/10.1175/BAMS-D-13-00231.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, K., Q. Lin, W. Lee, Y. Y. Qiang Sun, and F. Zhang, 2016: Doppler radar analysis of triple eyewalls in Typhoon Usagi (2013). Bull. Amer. Meteor. Soc., 97, 2530, https://doi.org/10.1175/BAMS-D-15-00029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, K., F. Vitart, S. T. Lang, L. Magnusson, R. L. Elsberry, G. Elliott, M. Kyouda, and T. Nakazawa, 2017: Doppler radar analysis of a tornadic miniature supercell during the landfall of Typhoon Mujigae (2015) in south China. Bull. Amer. Meteor. Soc., 98, 18211831, https://doi.org/10.1175/BAMS-D-15-00301.1.

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    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaplan, J., and Coauthors, 2015: Evaluating environmental impacts on tropical cyclone rapid intensification predictability utilizing statistical models. Wea. Forecasting, 30, 13741396, https://doi.org/10.1175/WAF-D-15-0032.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Climate Stewardship (IBTrACS): Unifying tropical cyclone data. Bull. Amer. Meteor. Soc., 91, 363376, https://doi.org/10.1175/2009BAMS2755.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kowch, R., and K. Emanuel, 2015: Are special processes at work in the rapid intensification of tropical cyclones? Mon. Wea. Rev., 143, 878882, https://doi.org/10.1175/MWR-D-14-00360.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., M. Tippett, A. H. Sobel, and S. J. Camargo, 2016: Autoregressive modeling for tropical cyclone intensity climatology. J. Climate, 29, 78157830, https://doi.org/10.1175/JCLI-D-15-0909.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, H., and Z. Tan, 2016: A dynamical initialization scheme for binary tropical cyclones. Mon. Wea. Rev., 144, 47874803, https://doi.org/10.1175/MWR-D-16-0176.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McAdie, C. J., and M. B. Lawrence, 2000: Improvements in tropical cyclone track forecasting in the Atlantic basin, 1970–98. Bull. Amer. Meteor. Soc., 81, 989997, https://doi.org/10.1175/1520-0477(2000)081<0989:IITCTF>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mei, W., and S. Xie, 2016: Intensification of landfalling typhoons over the northwest Pacific since the late 1970s. Nat. Geosci., 9, 753757, https://doi.org/10.1038/ngeo2792.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peng, X., J. Fei, X. Huang, and X. Cheng, 2017: Evaluation and error analysis of official forecasts of tropical cyclones during 2005–14 over the western North Pacific. Part I: Storm tracks. Wea. Forecasting, 32, 689712, https://doi.org/10.1175/WAF-D-16-0043.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., and S. D. Aberson, 2001: Accuracy of United States tropical cyclone landfall forecasts in the Atlantic basin (1976–2000). Bull. Amer. Meteor. Soc., 82, 27492767, https://doi.org/10.1175/1520-0477(2001)082<2749:AOUSTC>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., S. Lorsolo, P. Reasor, J. Gamache, and F. Marks, 2012: Multiscale analysis of tropical cyclone kinematic structure from airborne Doppler radar composites. Mon. Wea. Rev., 140, 7799, https://doi.org/10.1175/MWR-D-10-05075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruf, C. S., and Coauthors, 2016: New ocean winds satellite mission to probe hurricanes and tropical convection. Bull. Amer. Meteor. Soc., 97, 385395, https://doi.org/10.1175/BAMS-D-14-00218.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39, 16871697, https://doi.org/10.1175/1520-0469(1982)039<1687:ISATCD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tallapragada, V., and Coauthors, 2016: Forecasting tropical cyclones in the western North Pacific basin using the NCEP operational HWRF model: Model upgrades and evaluation of real-time performance in 2013. Wea. Forecasting, 31, 877894, https://doi.org/10.1175/WAF-D-14-00139.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vigh, J. L., and W. H. Schubert, 2009: Rapid development of the tropical cyclone warm core. J. Atmos. Sci., 66, 33353350, https://doi.org/10.1175/2009JAS3092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Webster, P. J., G. J. Holland, J. A. Curry, and H.-R. Chang, 2005: Changes in tropical cyclone number, duration, and intensity in a warming environment. Science, 309, 18441846, https://doi.org/10.1126/science.1116448.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wood, K. M., and E. A. Ritchie, 2015: A definition for rapid weakening of North Atlantic and eastern North Pacific tropical cyclones. Geophys. Res. Lett., 42, 10 09110 097, https://doi.org/10.1002/2015GL066697.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., T. Nakazawa, and S. Hoshino, 2012: On the relative benefits of a multi‐centre grand ensemble for tropical cyclone track prediction in the western North Pacific. Quart. J. Roy. Meteor. Soc., 138, 20192029, https://doi.org/10.1002/qj.1937.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., and Coauthors, 2015: Global distribution of the skill of tropical cyclone activity forecasts on short- to medium-range time scales. Wea. Forecasting, 30, 16951709, https://doi.org/10.1175/WAF-D-14-00136.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., and Y. Weng, 2015: Predicting hurricane intensity and associated hazards: A five-year real-time forecast experiment with assimilation of airborne Doppler radar observations. Bull. Amer. Meteor. Soc., 96, 2533, https://doi.org/10.1175/BAMS-D-13-00231.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, K., Q. Lin, W. Lee, Y. Y. Qiang Sun, and F. Zhang, 2016: Doppler radar analysis of triple eyewalls in Typhoon Usagi (2013). Bull. Amer. Meteor. Soc., 97, 2530, https://doi.org/10.1175/BAMS-D-15-00029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, K., F. Vitart, S. T. Lang, L. Magnusson, R. L. Elsberry, G. Elliott, M. Kyouda, and T. Nakazawa, 2017: Doppler radar analysis of a tornadic miniature supercell during the landfall of Typhoon Mujigae (2015) in south China. Bull. Amer. Meteor. Soc., 98, 18211831, https://doi.org/10.1175/BAMS-D-15-00301.1.

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

    Distribution of 24-h intensity OFE frequencies with respect to TC 24-h intensity change over (a) NA, (b) EP, and (c) WP. All frequencies are calculated within 10-kt bins and are indicated by numbers in each box.

  • Fig. 2.

    Distribution of 24-h intensity changes in the best-track data (black) and official forecast (red).

  • Fig. 3.

    Venn diagram representation of the overlap between the top 5% and bottom 5% (blue) of OFEs and the RW and RI processes (red). The labeled red numbers denote the total sample size for the RW/RI cases. The blue numbers indicate sample size and the top and bottom 5% of errors. Overlapped areas (purple numbers) denote coincident samples.

  • Fig. 4.

    Distribution of 24-h forecast error frequencies with respect to TC 24-h intensity changes for TPM.

  • Fig. 5.

    Conceptual graph showing the relationship between 24-h intensity forecast error and 24-h intensity change in TPM.

  • Fig. 6.

    The 24-h intensity OFEs (x axis) vs the TPM forecast error (y axis) for the three ocean basins. The red dashed line indicates the two errors are equal.

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