1 Introduction

Tropical cyclones affect economic and sustainable social development in coastal regions (Liu et al. 2009; Haque 2003), causing severe casualties and economic losses to such regions every year (Xu and Gao 2005; Cheng and Wang 2004; Imamura and To 1997). With the rapid temperature rises associated with global warming, tropical cyclones will increase in intensity, causing even more serious damage (Emanuel et al. 2008; Wang et al. 2008; Webster et al. 2005). Tropical cyclones have been the most serious disasters affecting Zhejiang, located along the southeastern coastal region of China (Zhou and Liu 1995). For example, tropical cyclone No. 5612 claimed 4,925 lives in Zhejiang, causing direct economic losses of 150 million BMB, which accounted for 4.47% of its gross domestic product (GDP) in that year. With social and economic development and strengthened disaster prevention ability, the casualties resulting from tropical cyclones have greatly decreased, but the direct economic losses have been rising considerably (Liang et al. 1996). In recent years, governments at all levels in Zhejiang have put the prevention of disasters resulting from tropical cyclones at the top of their agendas. Governments have adopted the disaster prevention strategy of “no deaths and fewer injured” in an effort to minimize casualties (Yang 2005). For instance, tropical cyclones No. 0505 and No. 0509 caused three and four casualties, respectively, with corresponding economic losses to Zhejiang Province of 5.46 and 6.56 billion RMB.

Disaster assessment is the most important basis for disaster prevention and alleviation and for insurance indemnity (Pinelli et al. 2008; Symon et al. 2003). Evaluation studies of disaster grades of tropical cyclones in China have been carried out (Wang et al. 2010; Zhang et al. 2009; Liu et al. 2009), but quantitative disaster pre-assessment of tropical cyclones is currently only at the initial stage. Post-disaster data collection is mainly reported from lower-level authorities to those of the next higher level. However, such disaster-related figures are mainly rough calculations. The lack of uniform standards of disaster statistics and that of standardized calculation methods have led to artificiality in the statistics, so that figures from one department might exceed those of another by up to 10 times, and in some cases even more. Time-consuming and arduous but inaccurate such calculations have become the fetters of disaster-related statistics and disaster relief (Yuan and Zhang 2006; Xu 2006). Current research on tropical cyclone assessment is mostly conducted by combining disaster-inducing factors, disaster situations, and assessment models of tropical cyclone disasters using mathematical statistics approaches (Qian et al. 2001; Lu 1995), SAS systems (Meng and Kang 2007), fuzzy mathematics (Liang et al. 1999), analysis hierarchy processes (Li et al. 2006), and perception algorithms (Ye et al. 2004). However, since changes in disaster-formative environments and disaster-affected bodies have not yet been taken into account, these models have a wide margin of error when applied to actual assessments (Huo and Qian 2002). All three factors relating to tropical cyclone disasters, namely the disaster-inducing factor, the disaster-formative environment, and the disaster-affected body, need to be considered together for a comprehensive treatment of a model of disaster assessment (Patwardhan and Sharma 2005). In this paper, we attempt to do this, pre-processing data using the principal component analysis (PCA) method and applying the model of BP neural networks to the assessment of economic loss to Zhejiang Province.

2 Data and methods

2.1 Data collection

Disaster data of tropical cyclones from 1949 to 2008 are from the Zhejiang Civil Affairs Bureau; data of tropical cyclones and meteorological data are from the Shanghai Typhoon Institute and the Zhejiang Meteorological Station, respectively. GDP data from 1949 to 2007 in Zhejiang Province are from the Zhejiang Statistical Yearbook (1949–2007). Construction of almost two-third of meteorological stations in Zhejiang was completed before 1970, and others were completed between 1970 and 1971, to ensure the completeness and continuity of meteorological data, only the 67 tropical cyclones making landfall in or affecting Zhejiang from 1971 onwards are taken as research objects in this paper. A tropical cyclone has three disaster-inducing factors: rainstorm, gale, and storm tide. In view of statistics on their levels of damage to Zhejiang (Zhou and Liu 1995), 30 tropical cyclones making landfall in Ningde, Fujian province, and Zhejiang Province are categorized as landing tropical cyclones, while the other 37 are categorized as affecting tropical cyclones.

2.2 Selection of assessment factors

A disaster results from the comprehensive interactions of disaster-inducing factors, disaster-formative environments, and disaster-affected bodies (Shi 2005). Disaster-inducing factors of a tropical cyclone include gale, rainstorm, and storm tide (Li 2009; Ramesh et al. 2007). For example, tropical cyclone No. 9417 made landfall in Ruian, Zhejiang, at 22:30, August 21st, 1994. The coincidence of the tropical cyclone and the spring tide on July 15th led to the integration of gale, rain, and tide, triggering an extra-high storm tide at a level that had not been seen in 100 years. It caused direct economic losses to Wenzhou of as much as 10.5 billion RMB. Data concerning tropical cyclone tides are difficult to collect. The storm tide triggered by a tropical cyclone is related to the central pressure of the storm and the maximum wind speed near the center (Mcconochie et al. 2004; Madsen and Jakobsen 2004). Current meteorological observation systems are capable of closely monitoring these two items and predicting them with relative accuracy 24–48 h in advance, together with the landfall position of the storms. Hence, in this paper, we use the central pressure and the maximum wind speed near the center when the tropical cyclone lands as the assessment factors of the storm tide.

The disaster-formative environment of a tropical cyclone is co-influenced mainly by the climatic conditions of its formation and landfall regions, the geographical conditions of its route and landfall regions, and the hydro, soil, and vegetation conditions of its landfall regions. These environmental conditions combine to strengthen or weaken the disaster-inducing factors of the tropical cyclone and its secondary disasters, thus directly affecting the disaster. Main disaster-affected bodies of the tropical cyclone include the inhabitants, buildings, crops, factories and mines, water conservancy facilities, coastal breeding farms, the arteries of communication and telecommunication. The combination of the quantity and quality (degree of fragility) of these indices is the major cause and most important factor of the tropical cyclone disaster. However, it is impossible to accurately obtain these indices, since they are continuously changing. The indices for a particular region are decided by its regional level of social and economic development. For example, with their increase in income, farmers can improve their housing condition, thus increasing their ability to prevent cyclone damage. Since the 1980s, the development of coastal wetland breeding and industrial development has contributed to the rapid rise of GDP. Meanwhile, the direct economic losses from tropical cyclones have also been rising dramatically.

Characterization factors of the disaster-formative environment and disaster-affected bodies vary in a non-linear way with time. Zhejiang Province is composed of 11 prefectures, and characterization factors of disaster-formative environment and disaster-affected bodies differ in each prefecture. Tropical cyclone disasters of Zhejiang are the sum of the disasters in the prefectures in Zhejiang Province, together with the effects of disaster-formative environments and disaster-affected bodies in each of the different prefectures (Li et al. 1995). In this way, the impacts of disaster-formative environment and disaster-affected bodies on a disaster can be estimated using the time and the temporal and spatial disaster-inducing factors in Zhejiang Province.

The extent of a tropical cyclone disaster is also related to disaster prevention awareness, regional prevention ability, and the emergency responding capability of the local government. In recent years, more accurate forecasts of the route of a tropical cyclone, its landfall time and position, precipitation, and gales have provided a more scientific basis for assessment. The improved understanding of tropical cyclones and raised public awareness of disaster prevention and alleviation, together with the construction of various water utilities, tropical cyclone prevention facilities and houses, have alleviated the extent of tropical cyclone disasters. Particularly in recent years, the Zhejiang provincial government has adopted a strategy of discharging reservoirs and evacuating people from areas likely to be affected before the tropical cyclone strikes, thus minimizing the casualties and direct economic losses. So, disaster prevention and mitigation capability changes with time (Yang 1998).

As mentioned above, in this paper, the following items have been selected as the assessment factors: the respective ratios of the number of stations recording precipitation of over 100, 150, 200, 250, 300 mm, with the maximum wind speed of over 17.2 m/s (8 on the Beaufort scale), 20.8 m/s (9 on the Beaufort scale), 24.5 m/s (10 on the Beaufort scale) during the landfall or period of effects of the tropical cyclones in Zhejiang to the total number of meteorological stations in each prefecture, the central pressure and maximum wind speed of the landing tropical cyclones when they make landfall, and the years the tropical cyclones made landfall or affected.

2.3 Indices of economic losses from a tropical cyclone disaster

Two methods of data processing are usually used in the assessment of direct economic losses from disasters. One is the direct value of direct economic losses in the year of the disaster, and the other is the quotient of the direct economic losses divided by the GDP in the year (Hao et al. 2004; Qian et al. 2001). Listed in Table 1 are the direct economic losses from tropical cyclones making landfall in Zhejiang since 1971. As shown in the table, with the advances of the years and the rise in GDP, direct economic losses from tropical cyclones of similar intensity have been increasing, so the disasters in the 1970s and 1980s would be relatively less serious than later ones if they were directly represented by the economic losses in the year. Since the 1990s, the GDP in Zhejiang has been increasing exponentially with time, while the direct economic losses from landing tropical cyclones of the same or similar intensity have not shown obvious increases with time. Therefore, the quotient of the direct economic losses divided by the GDP in the year cannot truly reflect the disasters since the 1990s, especially for the year 2004. Direct economic losses are related not only to the GDP in the year, but also to the price index at the time (Lei et al. 2009; Wei et al. 2004). In this paper, we first normalize direct economic losses to obtain an index of direct economic losses. The unit of direct economic losses is 10 thousand RMB; the unit of GDP of the preceding year is 100 million RMB; and the price index is calculated as follows: the year 1970 is assigned the base value of 100, and the calculation of the price index of each year is based on its relationship with 1970. The direct economic losses caused by most landing cyclones are greater than both the GDP and price indices numerically. To arrive at a value between 0 and 10 for the indices of direct economic loss of the majority of landing tropical cyclones, GDP is multiplied by 10, and price index is multiplied by 500. The index of direct economic loss is thus defined as:

Table 1 Economic losses to Zhejiang Province from landing tropical cyclone disasters
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$$ Y = Z \times \left( {\frac{1}{{{\text{GDP}} \times 10}} + \frac{1}{W \times 500}} \right) \div 2 $$

In the equation, Y denotes the index of direct economic losses; Z is the direct economic losses (with 10 thousand RMB as the unit); GDP is the GDP of the year preceding the loss (with 100 million RMB as the unit); and W is the price index of the preceding year.

2.4 BP neural networks based on principal component analysis

There is a strong coupling non-linear relationship between the tropical cyclone disaster and the assessment factors. However, since the data of the disaster and assessment factors are incomplete and continuously changing, it is extremely difficult, if not impossible, to depict their relationships in conventional mathematical terms. Assessment results from the linear statistical model are usually greatly different from the actual values. ANN (artificial neural network), the abstraction and simulation of some basic characteristics of a natural neural network or the human brain, is a non-linear dynamic system. It does not require a clear understanding of the mechanism; the output is dependent only upon the connection weight between the input and output of the system, the value of which can be obtained from learning a training sample. This method is highly effective in solving a fuzzy problem having certain inherent laws, but the mechanism of which is not yet clear. Its application in disaster prediction and assessment has achieved relatively good results (Lin et al. 2008; Kurt et al. 2008; Lu and Rosenbaum 2003), but there has not yet been any report of research applying it to the disaster assessment of tropical cyclones.

Assessment factors of a tropical cyclone, because of their difference in units, cannot be directly added or integrated. Still, there are high correlations among these factors. PCA is a method that is particularly effective in reducing the correlation among factors, avoiding information overlap, and overcoming the subjectivity and one-sidedness in weight determination. It is capable of grasping the principal contradiction. In this paper, data are standardized, the PCA is conducted, and the principal component is taken as the input of the BP (Zhang 2007; Chen and Liao 2002). The PCA module and the BP neutral network module of the software DPS (Tang and Feng 2007) are used to establish the assessment model of economic losses from tropical cyclone disasters.

3 Results

For landing tropical cyclones, we adopt the following quantities as our original variables: the ratios of the number of stations with different levels of precipitation to the total number of meteorological stations per prefecture, the ratios of the number of stations with different levels of maximum wind speed to the total number of meteorological stations per prefecture, and the central pressure and the maximum wind speed when the tropical cyclone makes landfall. For affecting cyclones, the original variables are as follows: the ratios of the number of stations with different levels of precipitation to the total number of meteorological stations per prefecture and the ratios of the number of stations with different levels of maximum wind speed to the total number of meteorological stations per prefecture. Through data standardization and the calculation of the characteristic quantity of the variable variance and the covariance matrix, these variables are converted into fewer variables through dimension reduction. The cumulative variance contribution rates of the current principal components are above 85%; the principal components basically contain most of the information about the assessment factors. Therefore, the principal components are used to represent the indices of assessment factors, such as major winds and rains.

The principal component discerned by the PCA and the years in which tropical cyclones occurred are adopted as the neuron matrix of the input layer of the BP neutral network, while the index of direct economic losses becomes the neuron of the output layer. The BP network has three layers. The nodes of the hidden layer are set at 75% of the number of the input layer nodes. During the systematic training, one or two should be added or deleted for comparison to determine the most rational network structure. After training and testing, the BP structures of the assessment models of direct economic losses for landing tropical cyclones are shown as 13-9-1 and that of the affecting tropical cyclone are shown as 11-8-1. Historical fitting results show that the assessment value and the actual value of economic losses from landing tropical cyclones have a correlation coefficient of 0.9939, with the mean absolute error being 0.71, and that the assessment value and the actual value of economic losses from affecting cyclones have a correlation coefficient of 0.9807, with the mean absolute error being 0.85.

The PCA-BP neutral network assessment model was used to appraise the direct economic losses from 2007 and 2008 tropical cyclones “Sepat”, “Vipa”, “Krosa”, “Kalmaegi,” and “Fung-wong”. Assessment results and fitting results are shown in Table 2. The assessment values based on the actual precipitation, gales, the central pressure and the maximum wind speed near the center when the tropical cyclones making landfall are relatively larger than the values actually collected of indices of direct economic losses, with their differences reflecting the effects of disaster prevention and alleviation. Actually collected indices of direct economic losses from the affecting tropical cyclones “Sepat” and “Fung-wong” and one small-intensity landing tropical cyclone “Kalmaegi” are relatively small, and their assessment values thus agree with the actual values. “Vipa” made landfall as a strong typhoon, and its assessment value is higher than the actual value by 2.16, while “Krosa” made landfall with the intensity of a typhoon and its assessment value is higher than the actual value by 0.49. This shows that the greater the intensity of the tropical cyclone, the more severe its effects, the more attention should be paid to disaster prevention and alleviation, and the more results would be achieved. This is consistent with the actual work.

Table 2 Assessment results of direct economic losses from tropical cyclone disasters in 2007 and 2008
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The pre-disaster assessment indices are shown in Table 2, using as forecast values the central pressure, the maximum wind speed near the center, the precipitation, and the gale 24 h before the landing tropical cyclones land or at the time when affecting cyclones start to affect Zhejiang. Except for “Vipa”, the assessment values of the four tropical cyclones according to the forecast values of wind and rain when they started to affect Zhejiang differ greatly from the actual values, and for the two affecting typhoons, there are extraordinary differences between their loss assessment values and the actual losses, which is related to the ability of meteorological departments to predict the precipitation and the gale strength of the tropical cyclone. The assessment value of the tropical cyclone “Vipa” comes close to the actual situation (see Fig. 1), and the pre- and post-disaster assessments are nearly the same. The forecast values of the precipitation and the gale strength at the time the four tropical cyclones including “Kalmaegi” started affecting Zhejiang are obviously higher (see Fig. 2), resulting in the higher pre-assessment values. Therefore, the accurate forecast of the precipitation and the gale strength before the tropical cyclone affects is crucial to improving the accuracy of post-disaster assessments.

Fig. 1
figure 1

a Precipitation forecast 24 h before Vipa’s landfall. b Actual precipitation during Vipa

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Fig. 2
figure 2

a Precipitation forecast 24 h before Kalmaegi’s landfall. b Actual precipitation during Kalmaegi

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4 Conclusions and discussions

  1. (1)

    Disaster assessment is an important step toward disaster prevention and alleviation. Pre- and post-disaster assessments of tropical cyclones would provide objective proof of the effectiveness of disaster prevention and relief measures. Along with social economic development and rising disaster prevention ability, the tropical cyclone disaster changes dynamically with time. Therefore, changes in the disaster-formative environment, the disaster-affected body, and disaster prevention ability must be taken into account to improve the accuracy of the disaster assessment.

  2. (2)

    In current methods employed in the disaster assessment of tropical cyclones, disaster degree is denoted by disaster grade. However, as the classification of disaster grades is mostly subjective and the value of direct economic loss corresponding to a specific disaster grade varies greatly, an accurate value of direct economic loss cannot be obtained. The direct economic loss caused by tropical cyclones is closely associated not only with disaster-caused factors, disaster-formative environment, and disaster-affected bodies, but also with GDP and price index. In this paper, we recognize these associations by indexing the value of direct economic loss using GDP and the price index. The direct economic loss can thus be translated into disaster grade and used for public announcement. These values can then guide the public in disaster prevention and alleviation. The specific value of direct economic loss can also serve as the disaster data to be used as a basis for disaster prevention, alleviation, and relief, as well as for post-disaster insurance claims undertaken by the government. As the disaster assessment of tropical cyclones unfolds, qualitative assessment gradually shifts to quantitative assessment. We offer our method as an effective tool for assessment of disaster loss, not only for tropical cyclone damage, but also for losses caused by flood, earthquake, etc.

  3. (3)

    There are many uncertainties affecting the assessment of loss caused by tropical cyclones, of which imperfect weather forecasting is only one. For instance, No. 9615 tropical cyclone in Guangdong Province caused accidental loss of billions of RMB, partly due to damage to several aircraft. Because of the highly uncertain non-linear relationship between assessment factors for tropical cyclones, we propose the use of a BP nerve network model. Based on PCA methods, we identify three assessment factors: disaster-caused factors, disaster-formative environments, and disaster-affected bodies, and the principal components are used as the input for a BP nerve network model to reduce data dimension and eliminate the relevance among the samples. In this way, realistic disaster simulation and forecast results can be obtained, making our method also applicable to the assessment of losses caused by flood, earthquake, etc.

  4. (4)

    Accurate forecasts of a tropical cyclone’s route, the precipitation, and the gale strength are crucial to improving the accuracy of a disaster assessment. The intensity and frequency of tropical storms are also changing, as a result of global warming, so the meteorological departments need further current research on tropical cyclones, if they are to improve the accuracy of their forecasts.

  5. (5)

    In this paper, we establish an assessment model of direct economic losses resulting from tropical cyclones for Zhejiang Province. For future research directions, we hope that by using geographical information technology, collecting detailed economic geography environmental data, and combining these with the weather forecasts at designated points provided by meteorological departments, we can obtain even further refined fixed-point and quantitative assessments of tropical cyclone disasters.