Introduction

Tropical cyclones (TCs) are well known for their destructive potential and impact on human activities. The recent Supercyclone Orissa (1999) has illustrated the need for the accurate prediction of inland effects of tropical cyclones. The inland devastation caused by the supercyclone was due to strong winds and a storm surge, which together caused the loss of 10 000 lives. With the availability of sophisticated numerical weather prediction (NWP) models some progress has been noticed in the tropical cyclone track prediction during recent years. However, the skill of the intensity prediction of tropical cyclones is still very much lacking (Bender et al. 1993). Until the time when NWP models can be used with reasonable success, there is an imperative need in the operational scenario to derive an empirical method for predicting wind fields associated with tropical cyclones after landfall. Kaplan and DeMaria (1995, 2001) described an empirical model for predicting the wind speed of tropical cyclones after landfall over the United States, but no such empirical study for predicting wind speed after landfall is presently available for the Indian region.

Very recently, following the technique of Kaplan and DeMaria (1995), Kalsi et al. (2003) attempted to study the decaying nature of the Orissa (Paradip) supercyclone (1999). The study warranted further investigation to calibrate the technique in a more general manner, incorporating a reasonably good number of cyclone cases of varying landfall intensities, coastal segments, and seasons. Toward this direction, an attempt has been made in this article to derive an empirical model for predicting the wind speed associated with a TC after landfall across the east coast of India, using the database of 19 recent cyclones.

Data and methodology

For the present study, we consider tropical cyclones to be those formed over the Bay of Bengal during the period 1981–2000. The data period includes 42 cases of landfalling TCs, but most of them lost their intensity of depression (wind speeds of less than 17 kt; 1 kt = 0.5144 m s⁻¹) immediately after landfall (within 1–2 h). In order to develop the empirical technique, we used only those 19 TCs (Table 1) that maintained the minimum intensity of depression (wind speeds of more than 17 kt) for more than 6 h after landfall. The tracks of these TCs are depicted in Fig. 1. The data used to derive the empirical equation consist of intensity estimates obtained from annual reports of the Regional Specialized Meteorological Centre (RSMC), New Delhi, India, operating in the India Meteorological Department’s (IMD)’s headquarters. Intensity estimates are basically inferred from all available observations (incorporating data received late). In India, surface wind observations are based upon 3-min-averaged winds. In this study, the landfall intensity is considered as the maximum sustained surface wind (MSSW) associated with a cyclone at the time the TC crosses the coastline. Intensity at landfall, tracks, and other synoptic informations are taken from the records of the Cyclone Warning Division of India Meteorological Department, as presented in Table 1.

As per the convention of the India Meteorological Department, the classification of tropical disturbances is as follows: low: wind speeds less than 17 kt; depression: wind speeds of 17–33 kt; cyclonic storm: wind speeds of 34–47 kt; severe cyclonic storm: wind speeds of 48–63 kt; very severe cyclonic storm: wind speeds of 64–119 kt; and supercyclone: wind speeds above 119 kt.

The data period (1981–2000) includes one case of a supercyclone and 14 cases of very severe cyclonic storms. It is observed that all 15 cases of intense tropical cyclones (wind speed more than 64 kt) maintained the minimum intensity of depression for more than 6 h after landfall. In order to illustrate the effect of landfall intensity on the decay rate of winds, the 19 TCs considered in this study are placed into one of two stratifications, namely, MSSW > 65 kt and MSSW ≤ 65 kt. This stratification is used to divide the 19 TCs into two equal groups. It may be seen from Table 2 that for the major cyclones (MSSW > 65 kt) the decay rate, during early hours after landfall, is significantly higher compared to weak cyclones (MSSW ≤ 65 kt). Decay curves (Fig. 2) are constructed taking the average intensity of each of these stratifications as a function of the elapsed time after landfall. This figure indicates that although the rate of decay of storms with MSSW > 65 kt (solid line) exceeds the decay rate for storms with MSSW ≤ 65 kt (dotted line), the shape of the decay curves is quite similar. It is interesting to note that the average intensity of the average major intense storm reduces below the strength of very severe cyclonic storm in 4–6 h, below severe cyclonic storm intensity in about 6–12 h, and below cyclonic storm intensity in about 12–18 h. The Supercyclone Orissa (Paradip) of 1999, which maintained the intensity of a cyclonic storm even 30 h after landfall is an exceptional case. Kaplan and DeMaria (1995) noted that over the United States (south of 37°N latitude) average major hurricanes fall below hurricane intensity in about 7 h and below tropical storm intensity in about 20 h after landfall. In 24–30 h after landfall, TCs decay to some constant MSSW independent of their initial intensity at landfall. Kaplan and DeMaria (2001) noted that for the northern latitudes (north of 37°N latitude) over the United States TCs decay to a constant MSSW in 12–24 h after landfall. In their study Kaplan and DeMaria (1995, 2001) termed this constant wind speed as the background wind speed. Background wind speed is simply the maximum wind speed that a tropical cyclone can maintain while over land under ideal conditions, as suggested by Kaplan and DeMaria (1995, 2001). Comparison reveals that for the Indian coast (east coast) TCs decay faster after landfall.

Formulation of the model

Ho et al. (1987) noted that the TC decay rate is proportional to landfall intensity and that the decay rate is highest immediately after landfall. From the decay curve (in Fig. 2), it is seen that the maximum wind speed decreases exponentially. Following Kaplan and DeMaria (1995), the MSSW after landfall at time t is written as

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where a is the decay constant, V₀ is the maximum sustained surface wind speed at the time of landfall, V_t is the wind speed at time t after landfall, and V_b is the background wind speed.

Studies of Powell (1982, 1987 and Powell et al. (1991) reported that MSSW decreases abruptly as the landfalling storm crosses the coastline, and a rapid decrease in the wind speed occurs during the early hours after landfall. Because of this consideration Kaplan and DeMaria (1995, 2001) introduced a reduction factor R as a multiplier to the landfall intensity (V₀). Their optimal value of R is 0.9.

From Eq. (1), the decay constant a can be written as

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The decay constant for the mean decay curve (Fig. 2), computed from Eq. (2) for t = 12 h, shows that for MSSW > 65 kt the decay constant is 0.163 h⁻¹, and for MSSW ≤ 65 kt the decay constant is 0.107 h⁻¹. Kaplan and DeMaria (1995) noted that for the U.S. region south of 37°N latitude, the decay constant is 0.115 h⁻¹. For the northern U.S. latitudes, it is 0.187 h⁻¹, as documented by Kaplan and DeMaria (2001) using the initial reduction factor 0.9. It is seen (Fig. 2) that for the stratification of MSSW > 65 kt, V_b is 21 kt and for the other stratification V_b is 19 kt. For the United States V_b ranges from 26.7 to 29.6 kt (Kaplan and DeMaria 1995, 2001).

In the model of Kaplan and DeMaria (1995), the reduction factor is applied right at the coast, and then the winds decay exponentially with time at the same decay constant. The decay constant is determined from a sample of U.S. landfalling TCs and is assumed to be constant. In the present version, the basic decay model is applied in a slightly different way than in the version of Kaplan and DeMaria (1995). We do not apply the reduction factor, but, instead, allow the decay constant to be determined at each time interval. It is seen from Table 2 that the decay rate of MSSW during the first 6 h is more than double that of the next 6 h. In order to take into account the effect of these changes of decay rate in the decay constant, in this study we compute decay constant a₁ for the first 6 h after landfall (for t = 0–6) as

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The decay constant a₂ for the remaining 12 h (for t = 6–18 h) is taken as

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It is presumed that for the first 6 h the decay constant is a₁ and, thereafter, it remains as a₂.

The corresponding 6-hourly “current reduction factors” are defined as

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Now, from Eq. (1), the decay equation for 6-hourly forecasts is written as

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The decay coefficients (a₁, a₂, R₁, R₂, and V_b) computed for the mean decay curves (Fig. 2) using Eqs. (3)–(6), taking the mean intensity as a function of time after landfall, are shown in Table 3. Once V₀, the landfall intensity, is known, 6-hourly forecasts valid up to 30 h can be made using parameters (R₁, R₂, V_b) from Table 3 in Eq. (7).

Correction procedure

Tuleya (1994) noted that the primary mechanism responsible for the rapid decay of TCs after landfall is the largely reduced latent heat and sensible fluxes. Regional variation in the decay rate of landfalling TCs was also reported by Schwerdt et al. (1979) and Ho et al. (1987). Kaplan and DeMaria (1995) introduced a correction factor as a function of inland distance to take into account the effect of the tropical cyclone’s proximity to water on the rate of decay after landfall. This effect was first discussed by Malkin (1959) and was confirmed in the study of Kaplan and DeMaria (1995).

The results of the present study apparently do not show any significant regional variation in the decay rate. In order to examine how the decay constant and current reduction factors change from cyclone to cyclone, decay constants (a₁, a₂) and current reduction factors (R₁, R₂) computed for each of the 19 cyclones (Table 1) are presented in Table 4. These coefficients for the individual cyclone are computed, taking V_b as the lowest intensity reached by each of them. Figure 3 shows a scatter diagram that explains a regression equation relating R₁ and R₂, as given below:

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In India, in the case of a cyclone situation, warnings/forecasts issued by the India Meteorological Department are updated at 3–6-h intervals, based on the latest available synoptic observations. In such a case, additional synoptic observations are taken at hourly intervals for the likely affected coastal stations, until the TC weakens into a low pressure area. Thus, in the Indian scenario, the first forecast (valid up to 24–30 h) issued at the time of landfall can be corrected and updated during the subsequent observation hours, taking into account the trend of the decay rate. Because a dense population resides at or near the Indian coasts, this update forecast has direct relevance to daily activities over a coastal zone (such as transportation, tourism, fishing, sports, etc.) apart from disaster management. The updated forecasts help people to modify their actions that they presumably initiated at the time of the first forecast.

In order to apply this method in operational forecasting and correct the forecast at 6-h intervals, the following steps are suggested:

• (i) At the time of landfall (at t = 0), employ the observed landfall intensity V₀ and climatological values of R₁, R₂, and V_b, which are obtained based upon the sample average decay rates (Table 3), to make 6-hourly predictions of V_t using Eq. (7).

• (ii) Six hours after landfall (at t = 6), use the observed V₀, V₆, and climatological V_b to compute the actual R₁ from Eqs (3) and (5). Then, get the new R₂ from Eq. (8) and use Eq. (7) to revise the forecast for 12 h after landfall and later.

• (iii) Twelve hours after landfall (at t = 12), employ the observed V₁₂ to make a 6-hourly prediction using Eq. (7).

• Eighteen hours after landfall, employ the observed values of V₀ and V₁₈ to calculate the actual R₂ from Eqs. (4) and (6) and revise the forecast for 24 h and beyond using Eq. (7).

• (v) Twenty four hours after landfall, use the observed V₂₄ to make a final forecast for V₃₀.

The climatological background wind speed (V_b) from Table 3 is considered for these computations.

By writing a simple FORTRAN program, the entire procedure (steps i–v) can be automated to be applied operationally.

Skill score

In order to verify the method, we apply the technique for the development database of 19 cyclones.

Results of 6-hourly forecasts after landfall for the 19 TCs, both with and without the correction procedure based on subsequent observations, are shown in Table 5. The table shows that there is generally good agreement between the predicted and observed values when the correction procedure is included. Table 6 shows the error statistics for the model with and without the use of the correction procedure. For the case without the use of the correction procedure, absolute mean error (AE) ranges from 6.1 to 4.9 kt and the root-mean-square error (rmse) from 7.9 to 5.6 kt, both decreasing with time. When the correction procedure to the forecast from the use of the current observations is applied, AE becomes 4.1–1.8 kt and rmse is from 5.0 to 2.9 kt. Kaplan and DeMaria (1995, 2001) obtained AE of 6.5 and 8.8 kt and rmse of 8.8 and 11.4 kt, respectively, for the southern (south of 37°E latitude) and northern latitudes over the United States. With the incorporation of the correction procedure, a significant improvement in the forecast skill is noticed for the case in which it is tested using the dependent sample in the present study.

There are some potential problems with the technique if it is applied in real time. Because the correction procedure is very sensitive to the availability of accurate real-time estimates, careful quality checks of the real-time data are essential before using them in the model. Real-time tests with independent data would be necessary to confirm the skill score obtained from the dependent evaluation.

Concluding remarks

The topic of inland wind is of great interest to the hurricane community. The present paper describes a method for predicting 6-hourly MSSW that is valid up to 30 h after landfall for a landfalling TC, using the decay equation of Kaplan and DeMaria (1995). A new correction procedure (current reduction factors) is introduced to update the first forecast (valid up to 24–30 h, issued at the time of landfall) at 6-h intervals, taking into account the trend of the decay constant and the use of current observations. With the application of the correction procedure, a significant improvement in the forecast skill is noticed. Results of skill score are well comparable with the results obtained by Kaplan and DeMaria (1995, 2001).

The method appears to be very promising for operational application in the Indian scenario in which a dense population lives in most coastal areas. Further research is required to refine the model with a larger dataset. Applying a similar technique, a separate model for the west coast of India (Arabian Sea) also could be developed.