Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp17-29

Long-term Change in Lightning Mortality and Its Relation to Annual
Thunder Days in Japan
Fumiaki Fujibe** Faculty of Urban Environmental Sciences, Tokyo Metropolitan University(Received: Nov. 14, 2016 Accepted: Mar. 22, 2017)

ABSTRACTLong-term variations in annual lightning deaths in Japan were examined in relation to the number of thunderdays, on the basis of death statistics for 1909 to 2014, and police data for 1968 to 2009. The number oflightning deaths was mostly 20 to 60 people without a remarkable trend before World War II, while it roseto over 100 just after the war, and then decreased during the latter half of the 20th century to less than 10 inrecent decades. For the period before 1970, the number of annual lightning deaths was positively correlatedwith that of warm-season thunder days (averaged over 39 stations) with a correlation coefficient exceeding
0.5. The correlation became low and insignificant after the 1980s as lightning mortality decreased,
although a high correlation of 0.6-0.8 was maintained between lightning damages and thunder days.
There was also a positive correlation of 0.4-0.6 between lightning deaths and warm-season mean
temperature until the 1980s, corresponding to a weak correlation between thunder days and temperature.
Key words Lightning Mortality, Lightning Deaths, Thunder Days, Vital Statistics

1. INTRODUCTION
As in many regions of the world, lightning is one of the causes of natural disaster in Japan. Lightning ismost frequent in summer, especially in the inland region (Japan Meteorological Agency, 1968; Shindo etal., 2012; Ishii et al., 2014), where daytime heating enhances thermal instability causing the developmentof convective clouds. Lightning also occurs in winter on the northwestern coast of Honshu under an outbreakof cold air that is heated and moistened over the Sea of Japan. Kitagawa (1989) and Yoshida (2002)
showed a long-term increasing trend of winter thunder days on the northwestern side of Honshu.
For lightning deaths in Japan, the data of the National Police Agency (NPA) have been used by someresearchers to document their change in the latter half of the 20th century (Hatakeyama, 1970; Kitagawa,
2001; Holle, 2008, 2010, 2016). The data show that annual lightning deaths amounted to 20 people or moreby the 1970s, but decreased to less than 10 in the 1990s. However, there is no documentation of lightning
fatalities for a longer period including the early 20th century. Neither is there information on the relationshipbetween lightning mortality and meteorological parameters.
The present study was conducted using death statistics compiled by the Ministry of Health, Labourand Welfare of Japan. The statistics are based on the International Classification of Diseases (ICD,
http://www.who.int/classifications/icd/en/), and provide annual numbers of lightning deaths since 1909. The
data are categorized by age and sex, as well as prefecture and month for some periods. The aim of the study
is to document long-term changes in lightning mortality for over 100 years, and its relationship tometeorological parameters such as the annual number of thunder days and temperature.

2. DATA
2.1 Lightning Mortality
The ICD-based death statistics of Japan were published annually in “Statistics on Causes of Death” until

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F.FUJIBE
1938 and in “Vital Statistics” thereafter. The item of lightning appeared in the second ICD (ICD-2), which
entered into use in 1909 in Japan. Since then, ICD has been revised eight times as shown in Table 1, andthe currently used version is ICD-10. The present study was made using data up to 2014. The area ofstatistics is almost unchanged during the analysis period, except the lack of data in Okinawa for 1947 to1972 and other minor changes. Data for 1944 to 1946 are missing due to war.

Table 1 Diagnosis code for lightning death in each version of ICD
ICD

Code

Period in Japan

2
3
4
5
6
7
8
9
10

196
195
192
192
E935
E935
E907
E907
X33

1909-1922
1923-1932
1933-1943
1947-1949
1950-1957
1958-1967
1968-1978
1979-1994
1995-

Data were provided for each sex and for four age categories of 0, 1-14, 15-59, and ≥60 years
old until 1935. From 1940, data are available for each of the five-year age classes up to 90 years old,and up to 100 years old since 1947. It is also possible to obtain data for each of the 47 prefectures (notclassified by age) for 1909 to 1942, 1947 to 1949, and 1999 onward. Monthly data are available for1937 to 1941.
There is no indication of erroneous data except for a case in 1914, for which the number oflightning deaths in Akita Prefecture is recorded to be 43. This is more than an order of magnitudelarger than other years (0.6 persons per year in Akita on average for 1909 to 1942 except 1914), despite
the fact that there is no literature regarding a big lightning disaster in Akita in that year. It seems
possible that some of the fatalities of the “Senhoku Earthquake”, which killed 94 people in Akita
in March 1914, were wrongly counted as lightning deaths, since the item of lightning death in“Statistics on Causes of Death” for 1909 to 1922 was labeled using the word shin-shi, which can bemistaken for “quake death.”
For supplementary analysis, the data compiled by the NPA in “The White Paper of Police” for1968 to 2009 were used. These data provide not only the number of deaths, but also the number of
injuries and damages due to lightning.
Analysis of the mortality rate was conducted using population data compiled by the Governmentof Japan. The definition of mortality rate is provided in Appendix A.
2.2 Meteorological Data

Data on monthly thunder days at observatories of the Japan Meteorological Agency (JMA; reorganizedfrom the Central Meteorological Observatory in 1956) are available in a data file of the JMA for theperiod from 1931 onwards, with some missing data in 1945. A thunder day is defined as a day on whichlightning of any intensity and/or thunder of intensity 1 or 2 are observed (Japan Meteorological
Agency, 2016). In this definition, intensity is based on a scale of three, 0, 1, and 2, which are judged
subjectively by an observer. The present study was made using data at 39 stations that lie in Honshu,
Shikoku, and Kyushu, and provide a continuous record up to 2014. The reason for limiting the area tothe three main islands is that the majority of lightning deaths occur in this area
(Fig. 8). Figure 1 shows the distribution of stations used for analysis.
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Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp17-29

Fig.1 Maps of East Asia and the analysis area, and meteorological stations used for the
analysis of thunder days, temperature, and precipitation. The region shown indashed lines in (a) is the region shown in (b). Shade indicates an area above 1000
meters from sea level.

Since a thunder day is a quantity of only
a fixed point, and does not give information on
frequency and intensity of the lightning of the day,its representativeness as lightning activity over a
region may be limited (Taszarek et al., 2015).
Figure 2 shows the number of cloud-to-ground (CG)flashes over Japan for 2002 to 2008 (Ishii, 2012),
and the number of thunder days averaged over the
39 stations. The former was analyzed using the dataof the JMA’s LF-wave lightning detection systemthat covers the most of Japan and its adjacentwaters (Ishii et al., 2014). The year-to-year
variation in thunder days, especially that for May to
September, is found to have some similarity to thatof CG flashes with respect to maxima in 2002,
2004, and 2008, although the agreement is not
perfect. The interannual variation in thunder days
also has partial similarity to that in CG flashes onanother location network for 1992 to 2008 (Fig. 3of Shindo et al., 2012). On this understanding, thenumber of thunder days was used for a correlation
analysis concerning annual lightning deaths,
because there is no other index of lightning activity
available over decades. Figure 3 shows annual
variations in thunder days and CG flashes. Both ofthem have sharp peaks in midsummer (July toAugust). However, the ratio of CG flashes tothunder days is much smaller in winter than insummer, reflecting the small number of lightning
flashes in a winter thunder event (Hayashi andMarui, 2016).

19

Fig.2

Interannual variations in cloud-toground (CG) flashes over Japan (bars;
after Ishii (2012)), and thunder days
(pink solid line for the whole year, andor a n g e da s h e d l i n e f or M a y to
September).

Fig.3

Seasonal variations in CG flashes overJapan (bars; after Ishii (2012)), andthunder days (pink solid line).

F.FUJIBE
For temperature, monthly and annual average data at 10 stations in Honshu, Shikoku, andKyushu were used (Fig. 1). These stations partly comprise the 15 stations used by the JMA for
monitoring climatic temperature change over Japan. For precipitation, data at 42 stations in the threemain islands were used (Fig. 1). They belong to the 51 stations used for monitoring climatic
precipitation change over Japan.

3. STATISTICS OF LIGHTNING MORTALITY

Figure 4 shows the time series of annual lightning mortality and thunder days. The number of deaths
varied mostly between 20 and 60 before World War II, without an obvious long-term trend, andsuddenly increased to over 100 in 1947 and 1948 after three years’ blank due to war. After that, it
decreased, and has stayed at fewer than 10 people since 1985. On the other hand, annual thunder days
fluctuated at around 15 days until the 1970s, and then gradually increased in the recent few decades.
However, an increasing trend of thunder days from May to September (hereafter denoted by the warm
season) is not obvious, reflecting the fact that an increase in thunder days is mainly found in winter(Kitagawa, 1989; Yoshida, 2002).

Fig.4 Annual lightning deaths for 1909 to 2014 except 1944 to 1946 (columns with the leftscale), and thunder days for 1931 to 2014 except 1945 (lines with the right scale).
Dotted vertical lines indicate the revision of ICD.

Figure 5 shows the time series of adjusted
mortality rate for three age groups from 1947 to2014, for which data are available for each fiveyear bin up to 100 years of age. An average overeach four-year period is shown in logarithm. The
nearly linear decrease on a logarithmic scale
indicates an exponential decrease in the mortality
rate. The linear regression in Fig. 5 yields adecrease rate of 7.4%/year for the 15-59 age group,and 5.7%/year for the ≥60 age group. These values
correspond to a decrease to 1/41 and 1/17 in 50
years, respectively. In comparison with these two
age groups, mortality at the age of 14 years old
and under is lower by a few times or more, and has
also decreased rapidly. The mortality rate for all of
the age groups (not shown) shows a decrease rateof 7.0%/year, corresponding to a decrease to 1/33 in
50 years..

Fig.5 Trends of lightning mortality in eachfour-year period from 1947 to 2014
for three age groups. The ordinate isscaledinlogarithm. Regression
lines are shown for groups of 1559 and ≥60 years old.

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Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp17-29

Figures 6 and 7 show lightning deaths and the mortality rate in each age category for the first
and the last 16 years in Fig. 5, namely, 1940-1958 (excluding 1944 to 1946) and 1999-2014. The
number of deaths is highest at around 20 years of age for the former period, whereas it is highest in
the 60s for the latter period. A shift toward higher ages is also found for mortality rate, but the change
in age dependence between the two periods is less striking than that in the number of deaths. The
different change between deaths and mortality rate is due to a relative increase in elderly people. The
population of the 15-59 age group increased by 1.4 times between the two periods, while that of the≥60 age group increased by 5.0 times. This fact and the differential decreasing trends of mortality
rate (Fig. 5) indicate that the relative increase in lightning deaths of elderly people is attributable toboth the higher increase in population and the slower decrease in mortality than young and middleaged people. It is to be noted that the very high mortality of the age category of 90-94 for 1940 to1958 (Fig. 7b) corresponds to only a man’s death during the 16 years, in which the population of thisage group was very small (8,742 people, which is 1/64 of that of the latter period), so that mortalityrose.

Fig.6 Lightning deaths for each five-year age group (0-4, ---, ≥95 years old) for 1999
to 2014, and 1940 to 1958 (except 1944 to 1946).

Fig.7 Lightning mortality for each five-year age group.
A brief analysis of regional and seasonal features was conducted for the early 20th century, inwhich lightning mortality was high. Figure 8 shows the mortality rate (unadjusted; see Appendix A) for
each prefecture based on data for 1931 to 1949 (except 1943 to 1946). It can be seen that the mortality rate
is high in inland Honshu and southern Kyushu. This distribution is similar to that of the lightning frequency
in summer (Shindo et al., 2012; Ishii et al., 2014). For the 16 years from 1999 to 2014, however, each of the
top two prefectures in Fig.8 (Tochigi and Gumma Prefectures) had only one lightning death. This fact
implies that the distribution of mortality may have changed, but we refrain from entering into further
analysis because lightning deaths are so scarce in recent years (eight people at most in a prefecture for 1999
to 2014).

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F.FUJIBE

Fig.8 Lightning mortality (unadjusted) in each prefecture for 1931 to 1949 (except 1943 to 1946).
The top five prefectures are shown in callouts.

Figure 9 shows the monthly statistics of lightning deaths for 1937 to 1941. Over 95% of thetotal cases occurred from May to September with a peak in July to August. Although winter lightning
sometimes causes damage to outdoor equipment and aircraft (Kobayashi et al., 2007), it appears to beof a lesser threat to life. This may be because of low outdoor activity in winter, as well as thesparsity of flashes in winter thunderstorms (Hayashi and Marui, 2016; Fig. 3).

Fig.9 Monthly lightning deaths for 1937 to 1941.

Finally, time series of lightning casualties and damages in the NPA data are shown in Fig. 10.
The number of lightning deaths in this dataset does not exceed that in the Vital Statistics except in1987 (7 in the Vital Statistics and 14 in the NPA data). The ratio of deaths in the NPA data to those of the
Vital Statistics is nearly constant, with an average of 78% for the first 10 years (1968 to 1977) and 75%
for the last 10 years (2000 to 2009). In other words, lightning deaths in the NPA data decreased atnearly the same rate as those in the Vital Statistics.

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Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp17-29

Fig.10 Annual lightning deaths, injuries, and damages based on the NPA data, shown incolumns (left scale), red solid line (left scale), and blue dotted line (right scale),respectively. Deaths based on the Vital Statistics are also shown. The exceptional value(661 cases) of damages in 2005 is denoted by a callout.

In comparison, the decrease in lightning injuries in the NPA data is slower. The ratio of injuries
to deaths in the last 10 years is about three times higher than that of the first 10 years. The decrease indamages is still weaker, with an indication of increase in the 2000s. However, the exceptionally large
damage of 661 cases in 2005 is open to question. According to a report of National Association for Local
Autonomy (2011), monetary damage by lightning in 2005 was no more than that of other years in the
mid-2000s.

4. RELATIONSHIP BETWEEN LIGHTNING
PARAMETERS

MORTALITY AND METEOROLOGICAL

A series of correlation analyses was made for interannual variations in lightning mortality andmeteorological parameters. In view of the rapid decreasing trend of mortality, correlation was not
calculated for the whole period but for a moving window of fixed length, which was set to 15, 35,
and 55 years. The missing values for 1944 to 1946 were simply ignored without changing thewindow size. Correlation was calculated after subtracting the linear trend of each quantity during thewindow period, in order to avoid the influence of long-term change. The reliability of thecorrelation coefficient was evaluated using the jackknife method (Appendix B). It is to be noted thata wider window size tends to result in higher statistical confidence for the same value of correlation
coefficient.
Figure 11a shows the correlation coefficients for (1) lightning deaths and annual thunder days
with a 15-year window, (2) lightning mortality rate and annual thunder days with a 15-year window,and (3) lightning deaths and annual thunder days with a 35-year window. The analysis period is from
1931 for the number of deaths, and from 1940 for the mortality rate. Each calculated value is assigned
to the year at the center of the window (for example, the correlation for 1951 to 1965 is regarded as
the value for 1958). Figure 11b shows the result of similar analyses based on warm-season thunder days
instead. For both Fig. 11a and Fig. 11b, the results for the 15-year window indicate that lightning deaths
have a positive correlation that is mostly above 0.5 until the 1960s but decreases and loses significanceafter the middle of the 1970s as mortality decreases, although a significant correlation of about 0.6 isfound for the last two periods (1999-2013 and 2000-2014). The results hardly change if mortality rateis used instead. For the 35-year window, significant correlation is obtained until the 1980s. Hereafter,
the results based on warm-season thunder days are shown, with an understanding that similar results are
obtained for annual thunder days.

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F.FUJIBE

Fig.11 Correlation coefficients between lightning deaths and mortality, and (a) annual
thunder days and (b) warm-season thunder days. Values significant at the 5% levelare shown in circles and crosses.

Figure 12 shows the correlation calculated using the NPA data instead of the Vital Statistics.
Results for damages are shown for two cases in which the extraordinary value of 2005 (661 cases)
were included and discarded, respectively. For deaths, the result is almost the same as that obtainedusing the Vital Statistics (Fig. 11b), without significant correlation during the period covered by
the NPA data. The correlation between injuries and thunder days is slightly higher than that for
deaths, and is partially significant. For damages, a high correlation of about 0.8 is maintained until theend of the analysis period if the 2005 value is ignored (dotted line and crosses in light blue), althoughsignificant correlation is lost if the 2005 value is taken into calculation (dotted line in dark blue).

Fig.12 Correlation coefficients between lightning deaths, injuries, and damages from the
NPA data and warm-season thunder days with a 15-year window. There is no
significant value for deaths from the NPA data. For damages, results with and without
the 2005 value are both shown in dark and light blue lines, respectively.

As another index of the relationship between lightning deaths and thunder days, the amplitude
ratio of variations in the two quantities was defined by a regression

Σ (∆y - a∆x)2 → min.,(1)where ∆x and ∆y indicate the deviation of thunder days and lightning deaths from the linear trend ofeach quantity, summation is made over the window period, and a is a regression coefficientcorresponding to the amplitude ratio. Figure 13 shows the time series of a. The value of a fluctuated ataround 2 until the 1960s, namely for the period in which significant correlation exists. This fact meansthat lightning deaths vary by about 2% for a 1% variation in thunder days. The value of a is also 2-3
for injuries and damages using the NPA data (not shown).

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Fig.13 Same as Fig. 11b, but for proportional coefficients obtained from the regressionof Eq. (1).

Figure 14 shows the correlation between lightning deaths and warm-season temperature, andprecipitation amount. Until the 1980s, deaths and temperature have a positive correlation of 0.4-0.6, which
is significant according to the 35-year window. In recent years, the correlation between deaths andtemperature is insignificant, while lightning damages in the NPA data and temperature are positively
correlated (if the 2005 value is ignored) with a correlation coefficient of about 0.4, which is statisticallysignificant if the 35-year window is used (not shown). The correlation between deaths and precipitation
amount is negative and partially significant.

Fig.14 Correlation coefficients between lightning deaths, and warm-season temperatureand precipitation amount.

Fig.15 Correlation coefficients between warm-season thunder days, and temperatureand precipitation amount.

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F.FUJIBE
As a supplement, a brief analysis was conducted for the relationship between thunder days
and temperature, and precipitation amount. Figure 15 shows the correlation for the warm season. The
correlation between thunder days and temperature is insignificant for the 15-year window, while it issignificant with a value of about 0.3 for most of the analysis period if the 55-year window is used.
The correlation between thunder days and precipitation amount is weak for most of the analysis period.
In view of the correlation among lightning deaths, thunder days, and temperature, a partial
correlation analysis was attempted using the three quantities. The result changed little from that of thesingle correlation analysis, although statistical significance decreased. The partial correlation between
deaths and thunder days is mostly insignificant for the 15-year window, but significant over most of theanalysis period if the 35-year window is used. The situation was similar according to a partial
correlation analysis for four quantities including precipitation amount.
Another supplementary analysis was made using thunder days at four stations in central
Honshu (blue dotted line in Fig. 1b), where the mortality rate is highest in Fig. 8. The result was
similar to that obtained using the 39 stations. The correlation between thunder days and mortality
rate was statistically significant with a value of 0.6 or more for the period until the 1960s, but
decreased afterwards.
5. SUMMARY AND REMARKS(1) The long-term change in lightning mortality in Japan was described using the ICD-based Vital Statistics
data for 1909 to 2014. The number of annual lightning deaths varied mostly between 20 and 60 people
without a remarkable trend until World War II, while it exceeded a 100 in 1947 and 1948, and thendecreased in nearly an exponential manner to less than 10 in recent decades. The rate of decrease in themortality rate after 1947 is 7.0%/year, which corresponds to a decrease to 1/33 in 50 years.
(2) The percentage of elderly people among lightning fatalities has increased after the mid-20th
century. This increase is due to a slower decrease in mortality rate and a higher increase in the
population of elderly people than those of young and middle-aged people.
(3) On the year-to-year variations, lightning deaths were positively correlated with thunder days until
the 1960s, with a correlation coefficient of over 0.8 in some periods. After 1970, the correlation decreased
and became insignificant as lightning deaths decreased. However, the number of lightning damages
compiled by the National Police Agency (NPA) maintained a strong correlation (~0.8) with thunder days
until recent years, if the extraordinary value of 661 damages in 2005 is discarded from the analysis.
(4) Lightning deaths were positively correlated with temperature for most of the analysis period witha correlation coefficient of 0.4-0.6. This corresponds to a weak correlation (~0.3) between thunder days
and temperature. There was also a weak negative correlation between lightning deaths and precipitation
amount for part of the analysis period.
The decreasing trend of lightning mortality has been reported for many other countries aswell (Mackerras, 1991; Holle et al., 2005; Holle, 2008, 2010, 2016; Mills et al., 2008; Ashley andGilson, 2009). For USA, the “best estimate” annual fatality by Ashley and Gilson (2009) shows adecrease to less than half during the period from 1959 to 2006. A similar change was reported byMills et al. (2008) for Canada. Elsom (2015) showed a decrease in lightning deaths in UK to about
1/20 of those in the mid-20th century. On a longer time scale, Holle et al. (2005) and Holle (2016)
reported a decrease in lightning deaths in USA by an order of magnitude during the 20th century, andElsom (2015) showed a decrease to about 1/100 in UK from the mid-19th century to the present. In
comparison with these countries, the change in lightning mortality in Japan is characterized by a lackof remarkable change in the former half of the 20th century and a sudden increase just after World War
II (1947 and 1948), followed by a decrease that was more rapid than that in USA and UK during thesame period.
Elsom (2015) stated that “industrialised nations have experienced marked reductions in theannual number of lightning fatalities”, but “changes in lightning fatality rates are much less incountries where people continue to engage in labour-intensive agriculture and fishing, live and work

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Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp17-29

in ungrounded buildings”. Holle (2016) also describedthe difference in lightning mortality between
developed and lesser-developed countries. The lifestyleof the Japanese people did not change significantly
during the first half of the 20th century, especially inthe countryside. The jump in lightning deaths justafter World War II may be attributable to a temporary
increase in agricultural workers in a situation where
Fig.16 Total population (with the leftmany people returned from outside the country due
scale) and agricultural population
to the end of war, while agriculture was promoted(withthe right scale) in Japanin order to cope with a serious food shortage. It may
for1920
to 2010.
also be related to poor housing after extensive war
damage. In the latter half of the century, Japan
underwent rapid industrialization that was accompanied by a drastic change in lifestyle including
mechanization of agriculture. Figure 16 populations of Japan for 1920 to 2010 according to decadal
data of the National Census. There was a gradual growth in total population with a nearly constantagricultural population until the middle of the 20th century, whereas the agricultural population began todecrease rapidly from 15% of the total population in 1960 (13.7 million) to less than 2% in 2010 (2.2
million). The change in lightning mortality appears to coincide with this change. It is also likely thatdevelopment of weather forecast and communication devices, as well as disaster-resilient infrastructure,contributed to the reduction in lightning casualties.
The relative increase in elderly people in lightning deaths is another noticeable feature in our
result. This may be partly related to the increase in the activity of elderly people. The percentage of≥60-year-old people among the agricultural population was 23% in 1960, while it increased to 62% in2010 according to the National Census. On the other hand, Holle et al. (2005) and Elsom (2015)
discussed the shift in lightning casualties from agricultural workers to those in recreation activities. It
is possible that a similar change has occurred in Japan. In this respect, the slower decrease ininjuries and damages than deaths (Fig. 10) may reflect a change in the quality of lightning disaster,although it may be an apparent trend due to the increasing capture rate of minor incidents.
The high correlation between lightning mortality and thunder days in the mid-20th century (Fig.
11) was an unexpected result, because thunder days may be poorly representative of regional
lightning activity as discussed in 2.2. The correlation decreased in the latter part of the analysis period,
but this is likely to be due to the increase in statistical uncertainty as a result of decrease in mortality,
since a high correlation has been maintained between lightning damages and thunder days. It will
be interesting to use data from a lightning detection system in order to examine the relationshipbetween lightning activity and damages in further detail.
The positive correlation between lightning deaths and temperature (Fig. 14) may reflect a tendencyof higher convective activity in a warmer year, as a result of a greater amount of atmospheric moisturethat is related to temperature through the Clausius-Clapeyron relationship (Fujibe, 2013, 2015). In
addition, a warmer summer implies a greater number of sunny days, which is favorable for the outbreakof local thunderstorms. The latter explanation may also apply to the negative correlation between lightning
deaths and precipitation amount, although the correlation is statistically significant for only a limited partof the analysis period.

ACKNOWLEDGMENTS
This study was supported by JSPS KAKENHI Grant Number 26220202.
APPENDIX A: Definition of Mortality Rate
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F.FUJIBE
The mortality rate of five-year age category k is defined bydk
mk = −− ,pk(a1)where mk, dk, and pk are mortality rate, number of deaths, and population of the category, respectively.
For more than one age category, the unadjusted mortality rate is defined byΣ dkk
M0 = −−−−− ,
Σ pk

(a2)

k

where summation is made over the categories considered. However, M0 is unsuitable for time series analysis
because it is affected by an uneven population change among ages. The adjusted mortality rate is definedby normalizing the population asΣ dk (Pk /pk)
Σ mk Pkkk
M = −−−−−−−−−−−−−− = −−−−−−−−−− ,
Σ Pk
Σ Pk
k

(a3)

k

where Pk is the population of category k in the reference year, which has been set to 1985 in the formal
statistics in Japan.
The present study is based on the adjusted mortality, which can be calculated for 1940 onward.
For regional analysis (Fig. 8), however, the unadjusted mortality was used because data for prefectures were
not categorized by age group.
APPENDIX B: Jackknife Method
The jackknife method consists of repeating the calculation of correlation by removing one of theyears in the window period in turn, the result being a set of correlation coefficients C'[i] (i=1, . . . , N;
N=window size), where C'[i] is the value obtained by removing the ith year. Then, the unbiased estimateof C' and its variance, denoted by Est[C'] and Var[C'], respectively, are given by
Est[C'] = NC'[0] –(N–1)µ ,Var[C'] = (N–1)v ,where C'[0] is the correlation obtained by using all the years in the window, and µ and v are the mean andvariance of C'[i] for N trials (e.g., Efron and Tibshirani, 1993).
The difference between C'[0] and Est[C'] is usually less than 0.1, but it can be larger for highly
skewed data. The negative peaks at 1940 and 1950 in Fig. 11 are due to the outlying values in 1947 and1948, and are not found for C'[0]. However, all of these values are statistically insignificant, so that the large
difference between C'[0] and Est[C'] does not matter in practice.

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