## 1. Introduction

There is ample observational and theoretical evidence that tropical cyclones (TCs) lose their intensity and finally dissipate as they move over land, because they are primarily maintained by the latent heat release of water vapor extracted from the oceans (e.g., Hubert 1955; Miller 1964; Rosenthal 1971; Tuleya and Kurihara 1978; Tuleya 1994). While TCs weaken because of this common and dominant effect, the decay rates have also been found to be variable. One reason for the difference is that the intensity change of TCs is controlled by some environmental conditions (e.g., sea surface temperature) that vary from case to case. For the decay over land, additional factors like the underlying topography and vortex structure could also play a role.

The ability to forecast the decay rate accurately is important not only in estimating how long the severe weather would last, but in some cases also how strong the wind would become after a change of wind direction. In Hong Kong, China, for example, it is not rare to see a strengthening of the wind after a TC has made landfall and begun to weaken. This occurs when a TC makes landfall around 100 km east of Hong Kong heading in a northwest direction. Because of topographic sheltering, the northerlies/northwesterlies near landfall are usually weak, but when the TC moved farther inland, the wind direction veered to the west/southwest, and many parts of the city become susceptible to the high winds.

Because numerical models have limited skills in predicting TC intensity change, empirical relationships have also been useful to forecast the decay (e.g., Kaplan and DeMaria 1995, 2001; Vickery and Twisdale 1995; DeMaria et al. 2006; Bhowmik et al. 2005; Vickery 2005). Generally speaking, these studies suggest that storm parameters [e.g., radius of maximum wind (RMW)] and environmental factors (e.g., background steering that determines the moving speed) could affect the decay rate. The decay models have recently been incorporated into the Statistical Hurricane Intensity Prediction Scheme (DeMaria and Kaplan 1994, 1999) for the Atlantic and eastern Pacific Oceans (DeMaria et al. 2005) and also into the Statistical Typhoon Intensity Prediction Scheme for the western North Pacific (Knaff et al. 2005) and have demonstrated improvements in the intensity forecasts.

The objective of this study is to examine the decay rate of TCs that made landfall along the south China coast (SCC) using the Hong Kong Observatory’s (HKO) best-track data. Moreover, the factors that affect the decay rate are identified. In some previous studies (Kaplan and DeMaria 1995; Vickery 2005), an underlying assumption is that the environmental conditions are neutral so that TCs exhibit little change in intensity just prior to landfall, and the decay rate after landfall would also not depend on them. This assumption may not be valid over other regions (Kaplan and DeMaria 1995), and we therefore also explore the possible relationship between the decay rate and the environmental factors.

Section 2 describes the various datasets and terminologies used in this study. Section 3 contains the results for the decay rates after landfall, and prediction equations are also developed. The results are summarized in section 4.

## 2. Method

### a. Data

#### 1) TC best track

Thirty years (1976–2005) of TC best-track data from the HKO are used. This dataset provides 6-h latitude–longitude positions of the center at 0.1° resolution, the minimum sea level pressure (MSLP), and the 10-m, 10-min maximum surface winds (MSW). The World Meteorological Organization standard synoptic report (SYNOP) and aviation routine weather report (METAR) stations are fairly close to the south China coast (Fig. 1), and there are also other stations with data that are not available through the Global Telecommuinications System and remote sensing techniques that can help provide a representative determination of the TC intensity at and after landfall in the best-track data.

#### 2) Terrain elevation and land use

Terrain elevation and vegetation data of the U.S. Geological Survey (USGS) at ∼4-km resolution are used to study their possible influence on TC decay. The vegetation categories are also used when defining landfall (see section 2b).

#### 3) Daily weather chart

The HKO’s daily weather charts are used to infer the average radius of the outer closed isobar (ROCI) and its associated pressure.

#### 4) National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis

The 2.5° × 2.5° latitude–longitude reanalysis provides the wind components at various levels to compute the vertical wind shear, and the temperature and specific humidity to compute the (specific) moist static energy. The relationships between these derived environmental variables and the TC decay rates are explored.

### b. Some definitions

The SCC in this study is defined to be the rim of mainland China within the longitude interval 110.5°–117.5°E (Fig. 1). Note that this definition is somewhat arbitrary and may be different in other publications (e.g., Liu and Chan 2003).

Some objective criteria are used to select the landfall cases for the current study. The 6-hourly positions of the TCs are first interpolated to half-hourly positions by spline interpolation. The USGS vegetation categories are then used to determine whether the TC center is over the land or ocean. We consider a TC to have made landfall (seafall) if its center falls over land (sea) and stays there for at least three subsequent hours. We study those cases where the last landfall is along the SCC and the TC dissipates over land (i.e., does not move out to sea again).

Instead of the landfall of the TC center, one might also use the eye, leading eyewall, or trailing eyewall as the definition of TC landfall. For example, it might be possible that the decay commences as the leading eyewall reaches the coastline. If we could know better the intensity change near (at length scale of the eyewall) the landfall of the TC center, an alternative definition could be adopted. However, to date, there is no strong evidence to support an alternative definition and we therefore use a similar definition as in previous studies.

Note that a few cases are excluded under the selection rules. This includes Typhoon Hope (1979) that made landfall near Hong Kong and finally moved back to the sea. Typhoon Maggie (1999) made two landfalls over the SCC and only the second one is counted. There are 67 landfall cases left, with 33 (34) cases west (east) of 114°E. The deliberate differentiation between landfall cases east and west of 114°E would reflect the spatial influence of the decay, because the topography and vegetation categories are actually different over the two regions. There are more hills east of 114°E (Fig. 2a) and some regions belong to “evergreen needleleaf forest,” which has higher surface roughness (Fig. 2b).

## 3. Decay rate after landfall along SCC

### a. Decay model

As mentioned in the introduction, a few previous studies have investigated the decay rate of TC after landfall, either in terms of the decrease of MSW (e.g., Kaplan and DeMaria 1995, 2001; Bhowmik et al. 2005) or the increase of MSLP (e.g., Vickery and Twisdale 1995; Vickery 2005). One consideration in choosing either the wind or pressure decay model is the quality of the data. Although the wind reflects the direct influence of a TC and would be more desirable, obtaining standardized and representative measurements is not an easy task. This difficulty is partly due to the complex terrain and urbanization and is partly due to the inherent large temporal variations of the wind associated with turbulence and rainbands. On the other hand, pressure would be more stable and reliable in terms of the small errors involved in the measurement and the reduction to sea level. In actual practice, the pressure and wind data complement each other to give the best estimation.

According to Atkinson and Holliday (1977), a pressure–wind relationship of the form *V* = *A*(*p _{e}* −

*p*)

_{c}*would imply that the exponential decay model of the MSW (*

^{B}*V*) and the exponential decay model of the central pressure deficit (

*p*−

_{e}*p*) are equivalent. However, this is an empirical relationship for the western North Pacific that is not perfect and does not include the effect due to fast movements. More important, such a relationship may not be suitable for use with landfall, because in the transition from sea to land, the wind must decrease in response to the increased surface roughness even if the central pressure deficit remains unchanged. With these limitations, it is still possible that they are not entirely equivalent and one of the models might be better than the other. Therefore, we will present the results of both models.

_{c}*p*is the difference between the MSLP

*p*and SLP of the environment

_{c}*p*(here taken to be that associated with the outer closed isobar, determined from daily weather charts; see section 3c), Δ

_{e}*p*

_{0}is the difference at the time of landfall,

*t*is the hours after landfall, and

*λ*is the decay constant.

*V*is the 10-m, 10-min maximum wind,

*V*

_{0}is the landfall value,

*t*is the hours after landfall, and

*α*is the decay constant. Kaplan and DeMaria (1995, 2001) employed an extra factor

*R*to account for the sudden change of surface roughness on the wind and a background value

*V*that the wind would decay toward. Our results show that for

_{B}*R*= 1 or 0.9, most of the

*V*are zero while a few take unrealistic values. We therefore stick to the form (3.2). Note the similarity between (3.1) and (3.2).

_{B}Past theoretical and modeling studies (e.g., Eliassen and Lystad 1977; Montgomery et al. 2001) also suggest the use of a wind decay model in the form *V*(*t*) = *V*_{0}(1 + *αt*)^{−1}, which can be obtained from (3.2) if we neglect the higher powers of *α*. However, the observational results show that it underperforms in the exponential decay model (not shown).

### b. Decay constants for SCC TCs

We use the (spline) interpolation to obtain the MSLP/MSW at landfall. The ROCI is also used to determine Δ*p*_{0}. The 6-hourly raw MSLP/MSW data at/after landfall are then used to determine the decay constants *λ* and *α*. Among the 67 selected cases (see section 2b), we further ignore weak TCs that have a dissipation time (time difference between that at landfall and that for the last warning) of less than 6 h because this may introduce larger errors in determining the decay constants. After all, it is of little interest to determine the decay rate of these weak TCs. After the elimination, 55 cases are left and 28 (27) of them made landfall west (east) of 114°E. Of these cases, the minimum intensity at landfall is Δ*p*_{0} = 2 hPa, and *V*_{0} = 30 kt (1 kt ≈ 0.5 m s^{−1}) for Tropical Depression Lisa in 1996.

The decay constants are determined numerically to minimize the errors in the least squares sense. The results for the landfall cases west and east of 114°E (Figs. 3, 4, respectively) indicate that the exponential decay model is fairly good for Δ*p* (e.g., Utor 2001 in Fig. 4). The results for the wind decay model are also satisfactory (not shown). However, there may also be a bias with the models. The actual intensity would be higher (lower) than that of the decay model during the former (latter) half of the decay period, as in the case of Typhoon Utor 2001 (Fig. 4). A plot of the errors further confirms the bias. The best-fit curves for the decay models both indicate an underestimation of intensity during the 12 h after landfall, with a positive MSLP error (Fig. 5a) and a negative MSW error (Fig. 5b). These errors may indicate that the model is imperfect, or that the decay constant is time-dependent, so that using a time-invariant decay constant introduces errors. One plausible explanation is that TCs may still be entraining sea fluxes just after landfall and the decay would be relatively slower. Despite the bias, the moving mean absolute error and the root-mean-square error remain near or below 2 hPa for the central pressure deficit decay model (Fig. 5a) and below 4 kt for the wind decay model (Fig. 5b).

*λ*and

*α*is only 0.80. As an attempt to compare the performance between the models, we first fit the postlandfall raw MSLP and MSW data for all 55 storms to a form of the Atkinson and Holliday (1977) equation:This gives

*A*= 15.14 and

*B*= 0.37 (Fig. 6). Then an error in wind could be converted to an error in the central pressure deficit by using the differential form of (3.3):The errors in wind, after converted to an error in Δ

*p*/MSLP by (3.4), might indicate that the wind decay model underperforms in the central pressure deficit decay model, because the moving root-mean-square error is a little bit higher (Fig. 5c) than that in the central pressure deficit decay model (Fig. 5a). However, such an interpretation should be made with caution. First, even if (3.4) is a perfect relation, it is easy to get a relatively large error for weak TCs during the conversion because of a potential error in estimating Δ

*p*. Second, the MSW in the best-track data is reported to the nearest 5-kt interval. A larger error would not be due to the model itself but rather would be due to this roundoff error.

As mentioned in the introduction, the decay constants are highly variable from case to case. For *λ*, the mean of all the 55 cases is 0.086 h^{−1}, but the standard deviation is 0.039 h^{−1}. For *α*, the mean is 0.047 h^{−1}, but the standard deviation is 0.021 h^{−1}. Therefore, it is important to identify the conditions that govern the variability of the decay constants.

### c. Predictors of the decay constant

In addition to the predictors (landfall intensity, moving speed, radius of maximum wind) examined in Vickery (2005), one can also hypothesize the decay to be related to the geographic location, because a rougher land surface would imply a faster decay, and a mountainous region would also impose a different effect than that imposed by flat land. Moreover, the environmental factors may also affect the decay rate. We have therefore chosen the following potential predictors for investigation:

- The first predictor is along-track surface roughness
*R*. At each half-hourly interpolated position after landfall, we obtain the average surface roughness length over a 2° × 2° latitude–longitude box. This is simply computed by taking the mean of the characteristic roughness length associated with the vegetation categories. The along-track surface roughness is then taken to be the mean of these averaged values over all the interpolated positions at and after landfall._{s} - The second predictor is the along-track terrain elevation
*Z*. At each half-hourly interpolated position after landfall, we obtain the average terrain elevation over a 2° × 2° latitude–longitude box. The along-track terrain elevation is then taken to be the mean of these averaged values over all the interpolated positions at and after landfall. - The third predictor is along-track terrain roughness
*R*. At each half-hourly interpolated position after landfall, the terrain elevation over a 2° × 2° latitude–longitude box is first fitted to a plane. The standard deviation of the terrain elevation relative to the plane is computed, and the along-track terrain roughness is then taken to be the mean of the standard deviations._{t} - The central pressure deficit at landfall Δ
*p*_{0}and maximum wind at landfall*V*_{0}computations were described in section 3a. - Prelandfall intensity change, denoted as Δ
_{pre}Δ*p*/Δ_{pre}*V*, is computed as the difference between two successive 6-h raw data at/before landfall. This could represent a time interval from 0–6 h before landfall to 6–12 h before landfall. - Landward speed at landfall
*c*is used instead of the translation speed (Vickery 2005). This approach gives a better determination of how fast the TC circulation is removed from the sea because the moving direction of the TC is also taken into consideration. Six hours after landfall, the distance of the TC from the closest shoreline point is divided by 6 to obtain the landward speed. - The seventh predictor is radius of the outer closed isobar at landfall. Vickery (2005) has found that the radius of maximum wind could influence the exponential decay rate. Although we do not have the RMW data for this study, we could examine the influence of another TC profile parameter, the ROCI. The ROCI could be estimated based on HKO’s daily weather charts (note that this is also used to infer the pressure of the environment). We have adopted the computation of Merrill (1984), using the average of the four distances from the TC center to the outermost closed isobar in the cardinal directions. The determination of the outermost closed isobar carries some subjectivity, and we further require that the shape of the outermost closed isobar not deviate too heavily from an ellipse. Note that because the weather charts are only available once a day, the ROCI at the time of landfall is simply taken to be that at or just before landfall. Therefore, the difference between the landfall time and the valid time of the weather chart could be close to 24 h in the worst situation, and there could be larger errors if the ROCI changes rapidly prior to landfall.
- The eighth predictor is vertical wind shear at landfall (VWS). We used the NCEP–NCAR reanalysis to estimate the 850–200-hPa vertical wind shear of the horizontal wind at the time of landfall and took a 9-point average (i.e., a square box with sides 7.5° latitude long) around the TC center. Linear temporal interpolation is also employed because the time of landfall usually does not coincide with the valid times of the reanalysis.
- The last predictor is the 850-hPa moist static energy at landfall Φ
. In a way similar to that for the vertical wind shear, the NCEP–NCAR reanalysis is also used to estimate this predictor._{m}

Although the along-track surface roughness, terrain elevation, and terrain roughness are statistically different over the two regions (Table 1), the differences of the decay constants between the two regions are not statistically significant. We would expect that these along-track terrain properties do not have a significant impact on the decay over the SCC region. Also, except for the 850-hPa moist static energy, there are no significant differences of the other predictors between the two regions. Therefore, we consider the two regions together in developing the prediction equations of the decay constants.

### d. Developing a prediction equation

The correlation between a particular predictor and the decay rates further shows that the along-track surface roughness, terrain elevation, and terrain roughness do not have significant impacts. For *λ*, the explained variance *r* ^{2} is 0.00 for either predictor (Table 2). For *α*, *r* ^{2} is also small (Table 3). As a result, we do not include them in the prediction equations.

Although large vertical wind shear is usually believed to have a detrimental influence on a TC, it only explains about 0.01 of the variance in *λ* (Table 2) and 0.00 of the variance in *α* (Table 3). Likewise, although past studies suggest that the storm parameter could influence the decay rate of TCs after landfall (e.g., radius of maximum wind in Vickery 2005), our results show that the ROCI does not correlate significantly with the decay constants.

The prelandfall intensity change predictors Δ_{pre}Δ*p*/Δ_{pre}*V* are included to detect any persistence in intensity change. However, they do not have statistically significant relationships with the decay constants.

On the other hand, the 850-hPa moist static energy (*r* ^{2} = 0.19 for *λ*, 0.17 for *α*), landward speed (*r* ^{2} = 0.09 for *λ*, 0.14 for *α*) and landfall intensity (*r* ^{2} = 0.15 for *λ*, 0.18 for *α*) have significant correlations with both decay constants. Although none of these individual predictors gives a satisfactory correlation for prediction purposes, their relationships with the decay constants appear to be consistent with theoretical reasoning and past studies (Vickery 2005): the decay is slower for high moist static energy as could be anticipated from energy consideration (Fig. 7a), and is faster for intense TCs (Fig. 7b) and those with large landward speed (Fig. 7c). Moreover, as revealed by the similar best-fit lines in the figures, the consistency of the results between the cases east and west of 114°E further supports that the relationships are physical. Note that these dominant predictors are also virtually linearly independent (Table 4), which means that they should all be incorporated into a prediction equation.

The 850-hPa moist static energy at landfall also reflects a seasonal dependence. The low values are recorded during early or late typhoon season (Fig. 8a) when South China is intermittently influenced by the continental winter monsoon. In fact, the smallest moist static energy was for Typhoon Joe on 13 October 1983, which is also the case of the fastest decay (Fig. 8b).

Similar to Vickery (2005), simple combinations (or interaction terms) of these dominant predictors could be used to give better correlations. For example, the combination *c*Δ*p*_{0} gives an *r* ^{2} of 0.19 for *λ*, better than the individual predictors (Table 2), and *c*Δ*p*_{0}/Δ*ϕ _{m}* (Δ

*ϕ*=

_{m}*ϕ*− 335) gives even better results with

_{m}*r*

^{2}of 0.44. For the wind decay constant

*α*, the analogous combinations of

*cV*

_{0}and

*cV*

_{0}/Δ

*ϕ*have

_{m}*r*

^{2}of 0.25 and 0.42, respectively.

Both (3.5) and (3.6) give an *r* ^{2} of 0.51 and represent some skills for prediction purposes. However, there may also be a bias for the prediction. For TCs that have a larger decay constant, the predicted *α* would be less than the observed *α* (Fig. 9b). Such a bias appears less significant for *λ* (Fig. 9a). To prevent such a bias, one could assign unequal weights when deriving the prediction equations.

The foregoing results are developmental statistics. If we use the jackknife method instead, *r ^{2}* for

*λ*and

*α*reduces to 0.40 and 0.43, respectively. For the jackknife-predicted

*λ*, the running mean absolute error and root-mean-square error are 2.2 and 2.9 hPa at

*t*= 12 h, respectively, and remain at nearly the same level through

*t*= 21 h (Fig. 10a). For the jackknife-predicted

*α*, the running mean absolute error and root-mean-square error are 3.5 and 5.2 kt at

*t*= 12 h, respectively, and they increase with time after

*t*= 12 h (Fig. 10b). Although these errors may still be acceptable, the prediction equations may not be able to forecast the extremes. For example, one may be more interested in those cases where the landfall intensity is large but the decay constant is relatively small, for those TCs could give more threat after landfall. In the case of Typhoon Peggy (1986), which has the smallest decay constants among those TCs that have typhoon strength (>63 kt) at landfall, the prediction from (3.5) and (3.6) may not be acceptable, as the error associated with the jackknife-predicted constant is −24 kt at ∼20 h after landfall (Fig. 10b). However, the exponential decay model gives a much smaller error of −8 kt (Fig. 5b) even though the decay rate appears to be time varying (Fig. 4). If additional predictors become available, one would be able to reduce the error to an acceptable level.

## 4. Summary and discussion

In this study, the decay rate of TCs after landfall along the south China coast is examined using 30 yr (1976–2005) of best-track data from the Hong Kong Observatory. The central pressure deficit (pressure of the environment minus central pressure) and the 10-m, 10-min maximum wind after landfall are found to fit fairly well to an exponential decay model, consistent with the results of past studies (Kaplan and DeMaria 1995, 2001; Bhowmik et al. 2005; Vickery and Twisdale 1995; Vickery 2005).

The factors that affect the decay constants are then examined. The effects of geographic locations, storm parameters, environmental influences, and persistence have been tested. The most significant influence of the decay comes from the 850-hPa moist static energy, the landfall intensity, and the landward speed. The prediction equations in (3.5) and (3.6) based on these predictors are developed to forecast the decay rates after landfall. To further Vickery (2005), this study suggests that thermodynamic factors like the 850-hPa moist static energy have a significant effect on the decay rates in the SCC region, and could be included in a prediction equation to forecast the decay.

The prediction equations of the decay constants are ready for operational use. The landward speed *c* could be determined from the track forecasts, which have been undergoing continuous improvements; the intensity at landfall could be estimated by nowcasting; and the moist static energy at landfall could also be estimated from the global model forecasts.

The prediction equations are clearly not perfect, but further improvements can be anticipated. Previous studies have suggested that an even better prediction equation could be obtained if storm-size parameters are incorporated (e.g., radius of maximum wind in Vickery 2005). The ROCI, which is the only storm-size parameter available for the current study, is found to have no significant relationship with the decay. This might not be surprising, because the surface energy fluxes that drive the TC mostly come near the core, which is on the order of the radius of maximum wind and not necessarily related to the ROCI. As an improvement, recent best-track data that include size parameters could be used in the future. One could also utilize the passive microwave imagery to reveal the inner-core convective structures (Jones et al. 2006) that may influence the decay rate after landfall.

As in other similar studies, the reliability of the data could pose certain limitations in the applications of the results from the current study. Apart from the 6-h best-track intensity estimates that would be too coarse in temporal resolution, the moisture in the reanalysis would also be prone to errors. The incomplete understanding of the intensity change near the landfall of the TC center could also affect the definition of landfall and the estimation of the decay rates. Nevertheless, given the improved resolution of the NWP products and remotely sensed data, such an approach should prove to be useful in such estimations.

As a further step, the results of the current and other similar studies may be used for the validation and development of numerical models to predict the decay after landfall. A good numerical model would ultimately be more desirable to predict the decay rate, because the decay rate could change with time and may not be conveniently modeled by an empirical formula.

We thank the Hong Kong Observatory for their TC best-track data and daily weather charts. This research is sponsored by the Research Grants Council of the Hong Kong Special Administrative Region, China Grant CityU 100203. The work of Wen Zhou is supported by the City University of Hong Kong Research Scholarship Enhancement Scheme.

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Mean and std dev of the exponential decay constants (*λ* for the central pressure deficit and *α* for the wind) and their predictors (along-track surface roughness *R _{s}*, terrain elevation

*Z*, and terrain roughness

*R*; central pressure deficit Δ

_{t}*p*

_{0}and max wind

*V*

_{0}at landfall; prelandfall intensity change in central pressure deficit Δ

_{pre}Δ

*p*and max wind Δ

_{pre}

*V*; landward speed

*c*; ROCI; 850–200-hPa VWS; 850-hPa moist static energy Φ

*), for the landfall cases west/east of 114°E. The*

_{m}*p*values (values <0.1 in boldface) of the two-tailed

*t*and

*f*tests to determine the significance of the differences between the means and std dev, respectively, are given. See section 3c for detailed descriptions of the predictors.

The *p* value (values < 0.1 in boldface), std dev, and *r* ^{2} of single-variable linear regression of *λ*. See caption of Table 1 for a description of the predictors.

As in Table 2, but for the wind decay constant *α*.

Correlation coefficients between dominant predictors. See caption of Table 1 for a description of the predictors.