Results of Time-Frequency Analysis

Data Description

In this study, we apply the hydrologic time series data from 2000 to 2015 to analyze their relationship with dengue fever. The dengue fever time series data are obtained from Taiwan Center for Disease Control, and the hydrologic time series data are obtained from Taiwan Central Weather Bureau (TCWB). Moreover, it is thought that the extreme climate plays an important role of dengue fever outbreak. As such, the Southern Oscillation Index (SOI) and Oceanic Niño Index (ONI), index of El Niño, are used to analyze the dengue fever. From Table 6.2, all the hydrologic variables of time frequency analysis in our research are listed.

Table 6.2 Hydrologic variables of time frequency analysis

Factor Source Region Sampling time Resolution

Number of dengue fever Center for Disease Control Kaohsiung 2000-2015 Week

Rainfall Central Weather Bureau Kaohsiung (Cianjhen) 2000-2015 day Rainfall Water Resources Agency Kaohsiung (Qishan) 2000-2015 day

Temperature Central Weather Bureau Kaohsiung 2000-2015 day

Humidity Central Weather Bureau Kaohsiung 2000-2015 day

Southern Oscillation Index (SOI)

Bureau of Meteorology of

Australia World 2000-2015 month

Oceanic Niño Index

(ONI) Golden Gate Weather Services World 2000-2015 month

Result of Wavelet Spectrum

The wavelet spectrum shows the energy distribution of time series data in the time period domain. Moreover, different period components of original time series data can be observed. Change of different period component along the time axis is also observed.

Figure 6.16 is the wavelet spectrum of dengue fever, and higher energy is located at 2002, 2014 and 2015 in the spectrum. The periods of dengue fever are located at 1 to 16 years. It can be found that dengue fever is a multiple time scaled event, and the time scales of dengue fever are non-stationary. The regular events of dengue fever have only one specific time scale from 2003 to 2012 in Figure 6.18. It can be found that dengue fever has yearly variations with a period of one year. However, extreme events of dengue fever are complex multiple time scales located at 2002, 2014 and 2015 in Figure 6.16. The energy density in spectrum means the amplitude of signal, and it can be regard as the numbers of dengue fever in our case. There are fourth high energy parts in Figure 6.17 c) and Figure 6.19 c), and specific time scale of each high energy parts are 1 year, 2 years, 4 years and 16years. However, the data length of our research is 16 year, which means that time scale equal or larger than 16 year cannot provide significant physical meaning. Regular dengue fever usually occurs yearly, so we think the yearly time scale of dengue fever is 1-2 year. Therefore, it can be observed that significant time scales of dengue fever are 1-2 year (yearly time scale) and 4 years (extreme events).

In our next discussion we will focus on those characteristic time scales (i.e. 1-2years; 4 years). This result will be compared with different hydrologic and meteorological time series data. Moreover, the bold line means the limit of boundary effect, and the region out of the bold line will be affected by boundary. In our case some region of extreme events in 2014 and 2015 are affected by boundary. If we want to avoid this effect, we need to obtain longer data of dengue fever incidences.

Figure 6.16 Wavelet spectrum of dengue fever from 2000 to 2015

Figure 6.17 Wavelet spectrum of dengue fever from 2000 to 2010

Figure 6.18 Wavelet spectrum of dengue fever from 2003 to 2012

Figure 6.19 Wavelet spectrum of dengue fever from 2006 to 2015

Both Figure 6.20 and Figure 6.21 are the wavelet spectra of rainfall in Kaohsiung.

Figure 6.20 shows results for Qianzhen, which is a hotspot of dengue fever. Figure 6.21 shows results for Qishan which does not have significant number of incidences of dengue fever incidences. It can be found that the energy distributions of different geographical regions are very similar in Figure 6.22. The most significant time scale is 1 year (yearly time scale, which is consistent with Asian rainfall seasons). The spatial variation of rainfall can be neglected in this research, so the rainfall data for Qianzhen is selected to analyze the relationship with the dengue fever. Moreover, it can be observed that except for seasonal time scales there is some discontinuous energy located from period 0.125 year to 0.5 year. The period from 0.125 years to 0.25 years should be equivalent to 4~8 occurrences in one year (i.e. frequency equals to 4~8 (1/year)). These high frequency events can be found in typhoons and afternoon thundershowers typically seen in the area. Comparing Figure 6.16 and Figure 6.20, the dengue fever does not have high frequency components from year 2005 to 2010. Moreover, energy of high frequency incidences is concentrated from year 2005 to 2010 in Figure 6.20 b), and there are no extreme dengue fever incidences that can be found. Therefore, it is found that yearly time scaled rainfall may have more significant correlations between dengue fever than typhoons and afternoon thundershowers (i.e. high frequency events).

Figure 6.20 Wavelet spectrum of rainfall in Kaohsiung, Cianjhen, from 2000 to 2015

Figure 6.21 Wavelet spectrum of rainfall in Kaohsiung, Qishan, from 2000 to 2014

Figure 6.22 Energy Contour of Cianjhen and Qishan

The temperature and humidity only have only one significant frequency component as can be seen in Figure 6.23 and Figure 6.24, and this corresponds to seasonal variation.

Such frequency is the same as that identified in the rainfall data, as expected. The humidity is affected very much by rainfall. Moreover, it can be found that energy of humidity is higher from year 2014 to 2016 in Figure 6.24 b). It means the variation of humidity from 2014 to 2016 is very large. Arcari et al. (2007) presented that humidity is significantly correlated with outbreaks of dengue fever.

Figure 6.23 Wavelet spectrum of temperature in Kaohsiung from 2000 to 2015

Figure 6.24 Wavelet spectrum of humidity in Kaohsiung from 2000 to 2015 A high correlation between incidences of dengue fever and extreme climates is expected. Figure 6.25 shows the wavelet spectrum of the Southern Oscillation Index (SOI). Southern Oscillation Index is an index of El Niño. Sustained negative values of the SOI below −7 normally indicate El Niño episodes. Although some short time-scale components are observed in Fig. 6.25 (b), these time scales are neglected here since the time-scale of El Niño exceeds one year. The short time-scale components correspond to fluctuations of SOI. The longer time scales of SOI found in Figure 6.25 c) are 1~2year and 4years.

Figure 6.25 Wavelet spectrum of Southern Oscillation Index (SOI)

The Oceanic Niño Index (ONI) is used to compare with the SOI. The National Oceanic and Atmospheric Administration (NOAA) defines the presence of an El Niño as occurring when the ONI is higher than +0.5. Figure 6.26 c) shows the significant time scales (i.e. 1~2year, and 4 years) of ONI. Such results are the same as SOI.

Figure 6.26 Wavelet spectrum of Oceanic Niño Index (ONI)

In this section, the wavelet spectrum is used to identify characteristic time scales in different hydrological and meteorological time series data. In the following section, some IMFs of different time series data will be selected according to their characteristic time scales. The correlation between variables will be discussed by using IMFs.

Result of IMFs of HHT

Dengue fever usually breaks out after the rain season. It is also observed the dengue fever has a frequency component that matches rain season in wavelet spectrum.

Although the dengue fever has the same frequency component as rain season, the outbreak time of dengue fever is not the same as the time of rainfall peak. Chien and Yu (2014) used the distributed lag nonlinear model (DLNM) to determine that the characteristic time lag between peak rainfall and an outbreak of dengue fever is 13-15 weeks (Chien and Yu, 2014). Figure 6.27 shows the comparison of IMF (seasonal time scale) of the dengue fever and IMFs (seasonal time scale) of the rainfall, and the IMF of rainfall is found to be delayed for approximately 14 weeks in Figure 6.27 b). The peak of a dengue fever outbreak considerably overlaps the peak of rainfall with a 14 week lag.

This identified lag between dengue fever events and rainfall events is an important reference for the Center for Disease Control.

Figure 6.27 a) IMF5 of dengue fever and IMF8 of rainfall, b) IMF5 of dengue fever and

IMF8 of rainfall lag 14 weeks

A lag effect is also found in relation to temperature. Figure 6.28 b) presents a substantial overlap of the peak of dengue fever incidences with the peak of temperature with a 14 week lag, indicating that rainfall and temperature share the same time scale.

Figure 6.28 IMF5 of dengue fever and IMF7 of temperature, b) IMF5 of dengue fever and IMF8 of temperature lag 14 weeks

Figure 6.29 presents a trend of increasing temperature (of 1℃ from 2000 to 2015 in Kaohsiung), which indicates that higher latitudes are more suitable for Aedes mosquitoes. Incidences of dengue fever appear to be moving northward (Kaohsiung in 2015, and Tainan in 2016). The temperature in the study area is closer to the most comfortable temperature (27℃-30℃) for Aedes mosquitoes to live. This result is consistent with Padmanabha et al. (2012).

Figure 6.29 Trend of Temperature

After discussing the seasonal time scale of dengue fever, researchers are more interested in time scale of extreme events. In the preceding section, the time scale of extreme dengue fever events was identified as four years, which is also the time scale of El Niño. IMFs with time scales of close to four years are identified in Figure 6.30 a).

Long-term trends of the El Niño are easier to identify in the IMF than in the original data. In record there are four El Niño years (i.e. troughs of IMF) from year 2000 to 2015 in Figure 6.30 a). It can be found that El Niño becomes more and stronger from year 2000 to 2015. Moreover, the El Niño occurrences normally accompany extreme dengue fever incidences, and both trends of dengue fever and El Niño are increasing in Figure 6.27 b).

Figure 6.30 a) IMF5 of dengue fever and IMF5 of SOI, b) Trend of dengue fever and Trend of SOI

The ONI in Figure 6.31 a) supports the above finding. El Niño is associated with peaks of IMF, based on the definition of ONI (i.e. El Niño appears when ONI is higher than +0.5). The trend of ONI also presents that the El Niño effect is increasing in Figure 6.28 b).

Figure 6.31 a) IMF5 of dengue fever and IMF5 of ONI, b) Trend of dengue fever and Trend of ONI

In this section, we discuss two characteristic time scales of the dengue fever incidences. The regular seasonal dengue fever events have a high correlation with seasonal variations of hydrology and meteorology. Moreover, dengue fever has the lag effect, and the characteristic time lag is 13~14 week post seasonal rainfall events. On the other hand, the extreme dengue fever incidences have the same time scale of El Niño, and El Niño usually accompanies extreme dengue fever incidences. Both the number of dengue fever incidences and El Niño have increasing trends. In our result, signs of climate change can be observed (i.e. trend of temperature; trend of El Niño).

Hydrological and meteorological events influence each other. Dengue fever is a complex multiple-scaled disaster. This study elucidates the correlation between dengue fever incidences and hydrological/meteorological factors by time-frequency analysis, which is utilized to decompose events with different time scales into events with multiple time scales, which are easier to observe and discuss.

6.3 Summary and Conclusion

This section elucidates the correlation between dengue fever incidences and hydrological/meteorological variables. Relevant recommendations will be provided to the Center for Disease Control (CDC). Methods of time-frequency analysis (STFT, wavelet transform, HHT) will be compared.

As suggested above, the wavelet transform is more useful than STFT for analyzing data with long time scales. The dynamic length of the window in the wavelet transform can be used to identify accurately components with different time scales in time series data. The HHT can decompose original data into various IMFs. Extracting information from individual IMFs is easier than doing so from original complicated, nonlinear and nonstationary events with multiple time scales.

The results herein reveal that the characteristic time scales of dengue fever incidences are one, four year and eight years. Rainfall and temperature have the same seasonal time scale (one year) as dengue fever. The characteristic time lag of dengue fever is identified as 13-14 weeks. The characteristic time scale of extreme dengue fever events (four years) is close to that of El Niño. Interestingly, the characteristic time scales of extreme dengue fever and El Niño are found to be similar. The frequency of both extreme dengue fever events and El Niño events is increasing.

The above results demonstrate that extreme dengue fever events are highly correlated with El Niño events. Accordingly, the Center for Disease Control (CDC) should pay close attention to El Niño. We advise that precautions (such as mosquito eradication) should be taken in the middle of rainfall seasons to prevent dengue fever.

Lastly, spatial statistical analysis revealed nonlinear relationships of population and the number of transportation stations with dengue fever incidences. The dengue fever

hotspots in Kaohsiung city are located in Qianzhen district, Sanmin district and Fongshan district, to which more attention must be paid.

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APPENDIX

IMFs of dengue fever

IMFs of rainfall (Qianzhen)

IMFs of rainfall (Qishan)

IMFs of temperature

IMFs of SOI

IMFs of NOI