Journal of Heat Island Institute International Vol. 9-2 (2014)

Academic Article

A Study on Structural Changes of Urban Air Temperature
in Japan- Data for 114 years of 1891-2004 at 36 observatories Takahiro Tashiro*1*1

Takahito Ueno*1

Department of Ecodesign, Faculty of Engineering, Sojo University

Corresponding author: Takahiro Tashiro, tashiro@eco.sojo-u.ac.jp

Abstract
The temperature data in Japan over 100 years is accumulated. The purpose of this study is to express the urban warming
phenomena in Japan through statistical analysis of such long-term data. The object data is the annual data of the daily mean
air temperature for 114 years from 1891 to 2004. There are 36 object observatory points. The main conclusions are as
follows. First, the air temperature fluctuations of all the observatories are judged with very high accuracy that it isexpressed more appropriately by two regression lines rather than one. Second, it turns out that the larger the city scale(administrative district population) in which observatory is located, the steeper the urban warming. Third, it becomes clearthat in most large cities or the middle-scale cities, in the second period, the air temperature rose rapidly. Therefore, it is
supposed that urbanization factor as well as geographical climate factor has influence on the urban warming in Japan.
Keywords: urban warming, long period air temperature data, statistical analysis, Chow test, regression analysis

long-term air temperature data of many observatories with the

1. Introduction

following statistical methods. From an expost viewpoint in
In Japan, there are many observatories from large cities toorder to represent air temperature fluctuation, using the Chow

rural areas where the weather observation data is accumulated

Test, it is investigated statistically whether one regression line

over more than 100 years. Air temperature data is one of theis appropriate or whether two regression lines are appropriate.

main weather observation data. In order to elucidate urban

If it is judged that two regression lines are proper, it is said thatwarming phenomenon, it is necessary to grasp the phenomenon

there is a 'structural change' of the air temperature data of theitself at various standpoints .The examination of a long-term air

observatory. To the second, when a 'structural change' exists,

temperature data can be one of these measurements.

the two regression lines are examined. As stated object data is

Incidentally, it seems that moving average method andannual data of the daily mean air temperature for 114 years

regression analysis are usually used as for analysis of thefrom 1891 to 2004, and there were 36 object observatories fromlong-term time series data about the weather. It seems thatlarge cities to rural areas.

regression analysis is effective in the point that air temperaturerise is expressed numerically. In a great deal of research,

2. Analytic procedure

however, it seems that one regression line is used to express air
Analysis of this study is executed with four steps of following

temperature fluctuation.
The purpose of this study is to express the aspect of theprocedures.

urban warming phenomenon in Japan by analyzing the- 113 -

The 1st step: Original Chow test of a single year

The Chow test, which was developed in econometrics,

divided for applicable arbitrary years, in order to dare to choose

judges statistically whether there was any structural change forone point here, target period are formally divided by the year ofa certain year. That is, the Chow test decides whether one

a maximum Fc-value. Such year is defined here a 'maximum

regression line is appropriate or not from an ex post viewpoint.

Fc-value year' described as FcMAX year, and the following year

The 'structural change', which is the technical term of

is a 'structural change year'. Then, the target period from 1891

econometrics, means that the parameter of a regression line

to 2004 is divided into two periods. The first period during thechanges.

former half is from 1891 to the FcMAX year, and the second

The numerical formulas necessary for this test are listed inTable 1. The regression line of all data for the target period isperiod during the later half is from structural change year to2004.

assumed as the formula (1). On the other hand, if the structural

The FcMAX year and structural change year here, of course,change year is assumed t0+1, two regression lines as formula (2)are judged by all the data from an expost standpoint, so thatand (3) are assumed for the data divided in before and after thesuch years never signified that something decisive occurred. In

structural change year. The following null hypothesis H0 andorder to avoid confusion, a structural change year is not used

the alternative hypothesis H1 are tested by these.

but FcMAX year is mentioned mainly.

H0 :

b0=c0

b1=c1

H1 : not H0

The 4th step: Examination of two regression lines

The null hypothesis H0 means ' two regression lines divided

If all the data is divided in this way, regression analysis isbefore and behind t0+1 are equal, that is, regression lines are one

applied to these two periods and two regression lines will be

line'. The Chow’s F-value of the formula (4) is distributed

obtained. The coefficient of each regression line is statisticallyunder F-distribution of the degree-of-freedom (k, T-2k). If in atested by a significance level α= 5%. The coefficient of year

given the Chow’s F-value is over the numerical value

variable xt such as a1, b1 and c1 means each air temperaturecorresponding to significance level α, H0 is rejected and H1 isgradient.

adopted. Hereinafter, the Chow’s F-value of the formula (4) is
described as Fc-value [1].

3. Data for specifications

Table 1 Formulas for the Chow test

The data used is annual data of the daily mean air

One regression liney t  a 0  a1 xt   t

Two regression lines

yt  b0  b1 xt  u t

t  t0 (2)

yt  c0  c1 xt  vt

t  t0 (3)Chow’s test statistics

temperature(1)

S  S 2  S3  kF 1
S 2  S 3  T  2k 

of

the

Meteorological

Agencyhomepage

publication, and the unit of the temperature is displayed indegrees Centigrade (°C) (1). In consideration of obtaining as
much long-term observational data as possible, and of
obtaining the data sets from large cities to local small size cities
in order to compare between cities, the time span of the data is(4)from 1891 to 2004 (this study was started in 2005). The

where, xt : calendar year t
yt : annual mean temperature of daily mean temperature of year tt0+1: assumed structural change year
a0, b0, c0 : constant terms
a1, b1, c1 : air temperature terms
F : Chow’s F-value
εt, ut, vt : error terms
T : number of target periodk : number of parameters,
S1 : residual square sum of the formula (1)S2 : residual square sum of the formula (2)S3 : residual square sum of the formula (3)observatories which gathered the data of the target period areplaced in 36 locations including metropolises, medium-sized
cities, and rural areas as shown in Fig.1.
Although this study does not deal with global warming
directly, it is because the observatories in rural areas are
expected that the influence of global warming appeared easily,
because the observatories in rural areas are expected to showless influence of global warming, the features of urban warming

The 2nd step: transition of Fc-values

phenomenon are conspicuous in contrast [2]. However, the aim

As the Fc-values are calculated while moving t0+1 year byof using 36 points is to survey the global warming situation andyear, a transition diagram of Fc-values are made up. Then

urban warming situation of the whole of Japan, without

under any significance level α, it will be judged whether theexamining individually either each observatory points or its

structural changes exist.

specific location. In addition, the data were examined simply,

The 3rd step: Division year of the object period

and this analysis is only based on the information released by

Under standard significance levels of α＝5% and 1%, thethe Meteorological Agency [3].

year in which Fc-value exceed the significance levels may
become a large number. In that case, although a period may be- 114 -

comparative examinations of the observatories are explained
where the different city scales within the same climatic division.
A survey of all 36 observatories is shown in 4.3.
In addition, Tokyo, Kyoto and Osaka were relatively large
cities from old times, but they became large metropolitan areas
after the mid-1950s. Moreover, the rapid urbanization of otherlarge cities and the medium-sized cities followed. Below, thepopulation of administrative district in 2000 in which anobservatory is located shown as a reference index (2) [5].
4.1 Examples of large cities(1) No.14 Tokyo
The analysis procedure is expressed concretely with the caseof Tokyo as an example.
STEP1 and 2: When the Fc-value of each year is obtained,
the transition diagram of the Fc-value is as in Fig.2. The
Fc-values gradually show a reductive tendency to after having
risen in the early 1900s. As the horizontal line of significancelevel α = 5% and α = 1% are shown in the diagram, if the year
when the Fc-value is larger than these levels, the nullNumber and name of observatory
No.1 Asahikawa
No.2 Sapporo

No.10 Ishinomaki
No.11 Yamagata

No.19 Niigata
No.20 Fushiki

No.3 Suttsu
No.4 Abashiri

No.12 Fukushima No.21 Kanazawa
No.13 Utsunomiya No.22 Kyoto

No.30 Fukuoka
No.31 Oita

No.5 Nemuro
No.6 Hakodate

No.14 Tokyo
No.15 Nagano

No.23 Osaka
No.24 Wakayama

No.32 Izuhara
No.33 Saga

No.7 Aomori
No.8 Akita

No.16 Nagoya
No.17 Gifu

No.25 Hiroshima
No.26 Sakai

No.34 Kumamoto
No.35 M iyazaki

No.9 M iyako

No.18 Tsu

No.27 M atsuyama

No.36 Kagoshima

hypothesis H0 would be rejected, and representation by two

No.28 Kochi
No.29 Shimonoseki

regression lines would become appropriate.
STEP3: Most years are able to become dividing points witha significance level α = 5% and α = 1% as shown in Fig.2. For
the purpose of this study, the FcMAX-value year has been
conveniently chosen in order to divide the data into two periods,
and the next year is determined as ‘structural change year’. In

Fig.1 The object observatories

other words, the period from 1891 to the FcMAX-value year
becomes the first period, and from the structural change year to

The climatic division is also shown in Fig.1 [4]. Even when

2004 becomes the second period. In Fig.2, the year of the

only limited to Japan, the climate of each area is complicatedFcMAX-value is in 1909, the structural change year is 1910. The

and various. Thus, the results of this study are also

FcMAX-value is 12.879, and the P-value, that is, Prob.(FcMAX <fundamentally specific to the climate of each area and theFc) = 9.4×10-6. The structural change is identified with highinfluences of urbanization are assumed as being artificial

accuracy.

turbulence factor. The climatic divisions are displayed via two

STEP4: When regression lines are applied to the first period

numbers: the first, Roman numerals, display five kinds of large

data and the latter period data, they appear as in Fig.3. The

classification, and the second Arabic numerals are internal

regression coefficients are examined by testing statisticalclassifications. Classification names are regional names inhypothesis with a significance level α = 5%. As is shown by theJapanese. An explanation of the climate features of each

114 years data, in Tokyo the air temperature dropped fromclassification is omitted here.

1891 to 1909 and rose from 1910. As comparison, one
regression line is shown in Fig.4. When the temperature
gradient terms are compared, it turn out that the temperature

4. Result of analysis

gradient coefficient of one regression is a1=0.0271 while theAnalysis results are described in order of the following. In
4.1, in order to represent the area from the northern part oftemperature gradient coefficient c1=0.0303 in the second period
regression line show a rapid temperature rise［6］.

Japan to the southern part among large cities (with a populationof one million or higher) in 2000, the structural changesituation of the air temperature of Tokyo, Sapporo, Kyoto,
Osaka, and Fukuoka are shown illustratively. In 4.2, the- 115 -

No.14 Tokyo

14

8

12

7

8

4

6

Fc - value

Fc - value

106No.2 Sapporo

9

α＝1％

α＝1％

5
4

α＝5％

3

α＝5％

2

2

1

0
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 201001890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.2 Transition of Chow’s F-value for Tokyo

No.14 Tokyo

15

（℃）

y = 13.063 + 0.0303 x
r² = 0.778

17
16

11

y = 14.237－0.0484 x
r² = 0.453

temperaturetemperature

（℃）

18

Fig.5 Transition of Chow’s F-value for Sapporo

14
13

8
7

y =12.029－0.0275 x
r² = 0.061

651890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

16

No.14 Tokyo

No.2 Sapporo
11

（℃）

17

Fig.6 Temperature and two regression lines for Sapporo

y = 13.311 + 0.0271 x
r² = 0.784

10
9temperature

18

（℃）

9

y = 6.476 + 0.0200 x
r² = 0.600

121890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Fig.3 Temperature and two regression lines for Tokyo

temperature

10No.2 Sapporo

15
14
13

y =6.383＋0.0227 x
r² = 0.699

8
7
6

12
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 201051890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.4 One regression line for Tokyo

Fig.7 One regression line for Sapporo

If a comparatively long temperature change in the second
period is expressed by regression lines still more finely,
what is necessary is just to repeat the analysis by making
the second period into a new target period. Although thisanalytic procedure is slightly mechanical, it is because it
uses a technique that avoids choosing the dividing point of
the data arbitrarily but choosing it statistically. Moreover,in order to divide the period, it is desirable to consider
historical events which brought about serious changes in
the land use of Tokyo, such as the Great Kanto Earthquake(1923) and war disasters (1944-1945) at the end of World

Fig.8 Regression line with dummy variable for Sapporo

War II which brought about serious damage to Tokyo.

- 116 -

(2) No.2 Sapporo

No.22 Kyoto

6

Similarly, the transition diagram of Fc-value of Sapporo is

5value, but two peaks are recognized in 1913 and in 1989. The

4

Fc - value

shown in Fig.5. The Fc-value generally changed with the low
data is divided automatically in 1989 when the Fc-value is at a
maximum. The fluctuation of air temperature and two

α＝1％

α＝5％

3
2

regression lines are shown as Fig.6. One regression line is1

shown in Fig.7. The temperature gradient of one regression is
a1=0.0227, whereas the temperature gradient of two regressions

0
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

becomes b1=0.0200 in the first period and c1=－0.0275 in theyear

second period. However, the air temperature term of theFig.9 Transition of Chow’s F-value for Kyoto

regression coefficient after 1990 was not significant under asignificance level α = 5%. It means that the regression line of

No.22 Kyoto

18

the second period might be horizontal.
（℃）

There is a difficult aspect to evaluating this type of urban

temperature

warming. If the air temperature jump of the end of the 1980s is
disregarded, the urban warming would be represented by
a1=0.0227, which is the coefficient of one regression line. If thejump in air temperature, that is, the structural change isconsidered important, the urban warming would be represented

y = 9.560 + 0.0610 x
r² = 0.428

1716

y = 13.292 + 0.0240 x
r² = 0.691

15
14
13

by b1=0.0200, which is the coefficient of the long regression

121890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

line of the first period. Although a structural change is acceptedyear

when is a temperature jump, if it is assumed that a warming

Fig.10 Temperature and two regression lines for Kyoto

tendency is constant, the regression lines which introduce thedummy variable would also be considered. The situation of18

in Fig.8. The coefficient of the dummy variable as 0.4767

17

（℃）

regression lines which introduced the dummy variable is shown
indicates the height of the temperature jump, and is significant

temperature

under α= 1%. It is shown like and the temperature gradientobtained using the whole data is 0.0199. In the end, from theviewpoint of this study, it would be natural to adopt Fig.6. That

16

No.22 Kyoto
y = 13.255 + 0.0248 x
r² = 0.769

15
14

is, urban warming advanced by b1=0.0200 untill 1989, air

13temperature jumped after that, and kept conditions at high121890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

[7]

levels .

Fig.11 One regression line for Kyoto(3) No.22 Kyoto
The transition diagram of the Fc-value of Kyoto is shown in
Fig.9. This diagram resembles that of Sapporo, but shows two

at a very high level until the late 1980s, and then decreased

peaks in 1911 and in 1980. When the data is divided at 1980

afterwards. When the data are divided at 1943 of FcMAX-value,

the FcMAX-value, air temperature fluctuation and two regression

the air temperature variations and two regression lines arelines are shown as Fig.10. A representation with one regression

shown as Fig.13. One regression line is shown in Fig.14. Theline is shown in Fig.11. The air temperature terms of two

air temperature terms of two regression lines are both

regression lines are significant at significance level α = 5%,

significant under significance level α = 5%. The temperature

respectively. Whereas temperature gradient term of one

gradient of one regression is a1=0.0204, temperature gradientregression is a1=0.0248, temperature gradient term of twoof two regressions becomes b1=0.0096 in the first half andregressions becomes b1=0.0240 in the first period and

c1=0.0328 in the second half.

c1=0.0610 in the second period.

(5) No.30 Fukuoka
In case of Fukuoka, the transition diagram of the Fc-value,(4) No.23 Osaka
The transition diagram of the Fc-value of Osaka is shown intemperature fluctuation and two regression lines, and one

Fig.12. In this case, the Fc-value rose until the 1930s, remained

regression line are shown in Fig.15, Fig.16 and Fig.17. Though- 117 -

No.30 Fukuoka

No.23 Osaka

16

18
16

14

14

Fc - value

Fc - value

12
10
8
6
4

6

α＝1％

4

α＝5％

2
0
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.15 Transition of Chow’s F-value for Fukuoka

Fig.12 Transition of Chow’s F-value for Osaka

No.23 Osaka19

y = 14.865 + 0.0096 x
r² = 0.142（℃）

y = 13.467 + 0.0328 x
r² = 0.630

18

temperaturetemperature

（℃）

19

16
15

No.30 Fukuoka
y = 13.800 + 0.0297 x
r² = 0.769

18
17
16
15

14

14

13
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010131890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

17

19

y = 14.540 + 0.0204 x
r² = 0.687

（℃）

18

No.23 Osaka

temperature19

y = 14.879 + 0.0007 x
r² = 0.0002

Fig.16 Temperature and two regression lines for Fukuoka

Fig.13 Temperature and two regression lines for Osaka

（℃）

8

α＝5％

0

temperature

10

α＝1％

2

17

12

16
15
14
13
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

18
17

No.30 Fukuoka
y = 14.350 + 0.0229 x
r² = 0.732

16
15
14
13
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.14 One regression line for Osaka

Fig.17 One regression line for Fukuoka

Fig.15 is somewhat similar to Fig.12 of Osaka, the Fc-value

4.2 Comparison of observatory in the same climatic divisionrose until the 1910s, remained at a high level until the 1950s,

In this section, at observatories within a comparatively closeand dropped afterwards while maintaining a high level. In

distance in the same climate division, it is examined whether

Fig.15, the data are divided at 1917, the FcMAX-value, and two

the difference of city scales in which the observatories areregression lines are shown.

located has an influence on the warming phenomenon. For

Temperature gradient of one regression is a1=0.0229, theconvenience, the city scale is represented by population oftemperature gradient of two regressions becomes b1=0.0007 inadministrative district. Like the former, the transition diagram

the first period and c1=0.0297 in the second period. However,FC-value, air temperature fluctuation and the regression line of

the air temperature term of the regression coefficient before

each observatory are shown. Since most coefficients of1917 is not significant under significance level α = 5% in casetemperature gradients become significant with a high level, it isof Fukuoka.

noted only when not significant under α= 5%.

- 118 -

No.16 Nagoya, No.17 Gifu and No.18 Tsu

No.2 Sapporo and No.3 Suttsu
35

98

No.16 Nagoya

30
25

6
5

Fc - value

Fc - value

7

α＝1％

4
3
2

α＝5％

20

10

No.2 Sapporo
No.3 Suttsu

001890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.21 Transition of F-value for Nagoya, Gifu and Tsu

Fig.18 Transition of F-value for Sapporo and Suttu

18

y = 6.476 + 0.0200 x
r² = 0.600（℃）

9No.2 Sapporo

temperature（℃）
temperature

10

No.18 Tsu

5

1

11

No.17 Gifu

15

8
7

y =12.029－0.0275 x
r² = 0.061

6

16
15
14
13

y = 14.533 + 0.0002 x
r² = 1E-05

121890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.22 Temperature and two regression lines for Nagoya

Suttu
18

11

y = 7.993 + 0.0037 x
r² = 0.046

（℃）

10
9

temperature（℃）

y = 12.874 + 0.0273 x
r² = 0.653

1751890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Fig.19 Temperature and two regression lines for Sapporo

temperature

No.16 Nagoya

87

y =11.443 －0.0246 x
r² = 0.045

6

No.17 Gifu
y = 13.024 + 0.0264 x
r² = 0.652

17
16
15
14
13

y = 14.339 － 0.0044 x
r² = 0.011

121890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 201051890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.20 Temperature and two regression lines for Suttu

Fig.23 Temperature and two regression lines for Gifu

(1) No.2 Sapporo and No.3 Suttsu in the climatic division I2

No.18 Tsu
18

exceeding one million people, Suttsu (4 thousand people) is a

17

（℃）

Whereas Sapporo (1,822 thousand people) is a large city
small town. In Fig.18, both observatories are in transition withtemperature

low level of Fc-value. The Fc-value of Sapporo is slightly
higher than that of Suttsu generally. Each Fc-values transition
pattern is similar. Both FcMAX-value years are in 1989, and are
significant under significance level α=1%. However, Fc-value16

y = 14.293 + 0.0086 x
r² = 0.282

1514

y = 10.936 + 0.0488 x
r² = 0.169

13121890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

exceeding α=1% in Suttsu only occurs this year.

year

Air temperature fluctuation and the regression lines of
Sapporo, Suttsus are shown in Fig.19 and in Fig.20. Neither

Fig.24 Temperature and two regression lines for Tsu

temperature gradient of the second period is significant at α=- 119 -

5%. Since the length of the first period is the same, it ispossible to compare the temperature gradient of each regression

14

line in the first period. Air temperature gradient of Sapporo is

12

much steeper than that of Suttsu.

10

Fc - value(2) No.16 Nagoya, No.17 Gifu and No.18 Tsu in the climatic
division IV5
Nagoya (2,172 thousand people) is a large city, Gifu (403

No.21 Kanazawa and No.20 Fushiki

No.21 Kanazawa

8
6

α＝1％

4

thousand people) is a mid-scale city, and Tsu (163 thousand2

people) is a small city. Transitions of Fc-value of these

α＝5％No.20 Fushiki01890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

observatories are shown in Fig.21. The Fc-value levels ofyear

Nagoya and Gifu are high through the 20th century. Nagoya
especially is changing with the very large Fc-value. Whereas

Fig.25 Transition of F-value for Kanazawa and Fushikitransition pattern of Fc-value of Nagoya and Gifu is similar,
Tsu is slightly different and increased to high Fc-value level inthe latter half of the 20th century.

17

（℃）

As for temperature fluctuation and regression lines, Nagoya,
Gifu and Tsu are shown in Fig.22, Fig.23 and Fig.24

temperature

respectively. Temperature gradients of Nagoya and Gifu are notsignificant in the first period, and the temperature gradient of
Tsu in the second period is not significant. Since FcMAX-value
year of Nagoya and Gifu is the same year at 1924, the16
15

No.21 Kanazawa

14
13
12
11
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

temperature gradient of the second period can be compared

year

with each other. The temperature gradient c1=0.0273 of Nagoya
is slightly larger than c1=0.0264 of Gifu, although one

y = 7.711 + 0.0670 x
r² = 0.494

y = 12.932 + 0.0123 x
r² = 0.352

Fig.26 Temperature and two regression lines for Kanazawa

regression line gradient a1 =0.0135 of Nagoya is slightly
smaller than a1 = 0.0170 of Gifu (shown later in Table2).

No.20 Fushiki

On the other hand, the temperature gradient in the first

17

（℃）

period of Tsu is b1 =0.0088, and the temperature gradient of

temperature

one regression line with a1 =0.0147 (shown later in Table2) areall also smaller than the temperature gradient in the second
period of Nagoya and Gifu.
(3) No.21 Kanazawa and No.20 Fushiki in the climaticy = 8.865 + 0.0490 x
r² = 0.320

1615

y =12.939 + 0.0068 x
r² = 0.135

14
13
12

division I4

111890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Kanazawa (456 thousand people) is a mid-scale city, andyear

Fushiki is an observatory of a rural area region, although it islocated in Takaoka city (172 thousand people). Transitions of

Fig.27 Temperature and two regression lines for Fushiki

Fc-value are shown in Fig.25. Although Fc-value of Kanazawa
is larger, Transition patterns between Kanazawa and Fushiki

Osaka city (2,599 thousand people) forms the megalopolis

are much alike. From the end of the 1970s, it was fundamental

with Kobe city and other cities. On the other hand, Wakayama

that Fushiki's Fc-value exceeded a line α= 1%.

(387 thousand people) is a mid-scale city. Transition of

Temperature fluctuation and the regression line of Kanazawa,

Fc-value of each observatory is shown in Fig.28. Both forms

Fushiki are shown in Fig.26, in Fig.27. Although bothare comparatively similar, although Fc-values of Osaka exceed

FcMAX-value years are in 1980 and each air temperature rise is

those of Wakayama from the 1930s to 1990s. The FcMAX-value

seen from the first period, in second period it is steeper. As foryear of Osaka is at 1943, and Wakayama is at 1950.

each temperature gradient of the same period, Kanazawa

Temperature fluctuation and regression lines are shown forexceeds Fushiki.

Osaka and Wakayama in Fig.29 and Fig.30. Although the(4) No.23 Osaka and No.24 Wakayama in the climatic

regression line of the first period of Osaka shows thedivision V

temperature rose gently, the sudden rise is shown in the second
period.

- 120 -

No.30 Fukuoka ,No.29 Shimonoseki and No.32 Izuhara

No.23 Osaka and No.24 Wakayama

16

35

14

No.23 Osaka25

Fc - value

10

Fc - value

No.29 Shimonoseki

30

12

8

No.24 Wakayama

620

No.30 Fukuoka

15
10

4

5

α＝5％

2
0
1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

No.32 Izuhara

0

2010

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

2010

year

year

Fig.31 Transition of F-value for Fukuoka, Shimonoseki and

Fig.28 Transition of F-value for Osaka and Wakayama

IzuharaNo.23 Osaka

1917

y = 14.865 + 0.0096 x
r² = 0.142

y = 13.467 + 0.0328 x
r² = 0.630

（℃）

18

temperaturetemperature

（℃）

19

16
15

No.30 Fukuoka
y = 13.800 + 0.0297 x
r² = 0.769

18
17
16
15

14

14

13
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010131890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

y = 14.879 + 0.0007 x
r² = 0.0002

year

year

Fig.29 Temperature and two regression lines for Osaka

19

（℃）

y = 14.419 + 0.0213 x
r² = 0.344

18
17
16
15
14

18
17

temperature（℃）

No.29 Shimonoseki

No.24 Wakayama

19

temperature

Fig.32 Temperature and two regression lines for Fukuoka

y = 15.309 + 0.0002 x
r² = 8E-05

y = 15.036 + 0.0061 x
r² = 0.133

y = 11.017 + 0.0547 x
r² = 0.482

16
15
14

13
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010131890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

year

year

Fig.30 Two regression lines for Wakayama

Fig.33 Two regression lines for Shimonoseki

On the other hand, the coefficient of the temperature gradient19

significance level α= 5%. The temperature rise is shown at the

18

（℃）

in the first period of Wakayama is not significant undertemperaturesecond period.
(5) No.30 Fukuoka, No.29 Shimonoseki and No.32 Izuhara
in the climatic division II1
Fukuoka (1,341 thousand people) is a large city, whereas
Shimonoseki (252 thousand people) is a minor city, and17

No.32 Izuhara
y = 11.119 + 0.0443 x
r² = 0.523

y = 14.227 + 0.0124 x
r² = 0.260

16
15
14
13
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Izuhara town (15 thousand people) is a central town inyear

Tsushima islands.
In Fig.31, each transition of the Fc-value of 3 observatories

Fig.34 Temperature and two regression lines for Izuhara

is shown. Each form and Fc-value level differs considerably.

- 121 -

shape of the Fc-value of both observatories is similar, and theNo.34 Kumamoto and No.33 Saga

value level of Kumamoto is higher than that of Saga (in Fig.35).

20

No.34 Kumamoto

18

Both FcMAX-value years are the same in 1948.

Fc - value

16
14

As for temperature fluctuation and a regression line,

12

Kumamoto and Saga are shown in Fig.36 and Fig.37. Neither

10of the coefficient of the temperature gradient in the first period

No.33 Saga8

is significant under significance level α = 5%. At Comparison

6
4of the temperature gradient in the second period, Kumamoto2

shows the temperature rise which exceeds Saga.

0
1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

As mentioned above, in order to diminish the influence of

2010

year

climate factors, by comparing the observatory in the close

Fig.35 Transition of F-value for Kumamoto and Saga

distance within the same climatic division, the changes of the
air temperature structure of observatories were compared [8].

（℃）
temperature

As a result, it is supposed that the relative large scale city

No.34 Kumamoto

19(population of administrative district) in which an observatoryy = 14.048 + 0.0269 x
r² = 0.472

18

is located has an effect on higher air temperature.

17

4.3 General view of all the object observatories

16

A summary of the calculation results of all object

15
14

observatories are indicated in Table 2. The items of table 2 are

y = 15.541－ 0.0017 x
r² = 0.005

the FcMAX-value year, its P- value calculated mechanically, air

131890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

temperature gradient b1, c1 that are coefficient of xt of twoyear

regression lines in the first period and the second period. In

Fig.36 Two regression lines for Kumamoto

addition, as a reference, climatic division, air temperature
gradient a1 of one regression line, mean temperature for 114（℃）
temperature

years and administrative district population are shown.

No.33 Saga

19

Although most P-values are unrealistic and extremely small

y = 14.486 + 0.0196 x
r² = 0.341

18values, it is concluded that the structural change of air
temperature arose in remarkable accuracy. That is, in order to17

represent air temperature fluctuation of all the observatories, it

16

is judged that two regression lines are more appropriate.

15
14

In table 2, each observatory is classified into five types

y = 15.477 － 0.0013 x
r² = 0.003

according to the form of two regression lines in the first period

131890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

and the second period. Each coefficient of regressions is tested

year

under a significance level α = 5%. Five types are the same as

Fig.37 Temperature and two regression lines for Sagalarge cities types of 4.1. It is as follows when the account of thefeature of each type is carried out.

Shimonoseki shows the very large Fc-value from the end of theType A (Tokyo type): Both regression coefficients are

1960s to the end of the 1970s. The FcMAX-value year, Fukuoka

significant. The air temperature gradient in the first period

is at 1917, Shimonoseki is at 1978 and Izuhara is at 1978.

descends and in the second period rises.

As for air temperature fluctuation and regression lines,- It is only No.31 Oita except Tokyo.

Fukuoka, Shimonoseki, Izuhara are shown in Fig.32, in Fig.33- Naturally the temperature gradient of the second period

and in Fig.34. The temperature gradient at the second period is

becomes larger than the first period.

larger than at the first period in each case.

- The temperature gradient of the second period became larger(6) No.34 Kumamoto and No.33 Saga in the climaticthan that of one regression line.
Type B (Sapporo type): Temperature gradient in the firstdivision II2
Kumamoto (662 thousand people) is a large middle-scalecity, and Saga (168 thousand people) is a small city. Transition

period is significant and in the second period is not significant.
The air temperature gradient in the first period rose.

- 122 -

Table 2 Summary of all the object observatories
Structural change
Type

Ａ

Ｂ

Observatory

No.14 Tokyo
No.31 Oita
No.2 Sapporo
No.12 Fukushima
No.8 Akita
No.13 Utsunomiya
No.19 Niigata
No.11 Yamagata *No.15 Nagano *No.7 Aomori
No.4 Abashiri *No.25 Hiroshima
No.10 Ishinomaki *No.3 Suttsu *No.18 Tsu
No.35 Miyazaki *

Ｃ

Ｄ

Ｅ

No.22 Kyoto
No.21 Kanazawa
No.27 Matsuyama
No.20 Fushiki *No.26 Sakai *No.32 Izuhara
No.29 Shimonoseki

Climatic
division

Two regression lines

Maximum
Fc -valueyear

P -value

1909

9.4×10Ⅳ3
Ⅴ or Ⅲ8
Ⅰ2
Ⅳ3
Ⅰ3
Ⅳ3
Ⅰ4
Ⅰ3
Ⅰ4 or Ⅳ4
Ⅰ3
Ⅰ1
Ⅴ
Ⅳ3
Ⅰ2
Ⅳ5
Ⅲ8
Ⅰ4 or Ⅴ
Ⅰ4
Ⅴ
Ⅰ4
Ⅰ5
Ⅱ1
Ⅱ1

1948
1989
1989
1989
1989
1989
1989
1989
1989
1989
1989
1989
1989
1987
1987

Mean
temperaturefor 114 years

Population ofadministrative
area in 2000
(in thousands)

The first
periodtemperature
coefficientb1

The second
periodtemperature
coefficient
c1-0.0484-0.00650.03030.027114.9

8135

0.0276-0.0275
0.00460.01500.03040.01860.00540.0107-0.0243-0.02210.1000-0.0096-0.0246
0.04880.01330.02270.01380.01450.01520.01320.01190.01100.01180.00920.01380.00750.00610.0147

15.4
7.7
12.3
10.8
12.8
13.0
11.0
11.3
9.5
5.9
15.0
11.1
8.3
14.9

436
1822
291
318
444
501
255
360
298
43
1126
120
4
163

-6

-10

6.4×100.000570.001800.000040.02000.01800.01060.00970.00890.00760.00750.00630.00580.00520.00440.0037-8

6.1×100.00001
0.00001
0.00111-7

1.4×100.00288-16

8.1×100.005210.00664temperature
coefficient

（℃）

a1

-10

0.0086-90.00480.04220.010316.9

306

0.02400.01230.01250.00680.00700.01240.0061

0.06100.06700.05770.04900.06180.04430.05470.02480.01620.01710.00940.00970.01310.0151

14.7
13.7
15.4
13.4
14.5
14.9
15.6

1468
456
473
172
37
15
252

0.00960.01070.03280.020415.7

2599

0.02300.00488.5

2880.00070.0121-0.0391-0.01370.00020.02970.01540.00650.00530.02730.02290.01890.00790.00650.0135

15.7
6.0
5.8
10.3
14.8

1341
360
33
55
2172

7.3×107.2×100.007780.000020.00001
0.002240.000020.00008

1980
1980
1980
1980
1980
1968
1978

1.6×101943

2.3×10No.6 Hakodate

Ⅴ
Ⅰ2

1941

1.6×10No.30 Fukuoka
No.1 Asahikawa
No.5 Nemuro *No.9 Miyako
No.16 Nagoya

Ⅱ1
Ⅰ2
Ⅳ１
Ⅳ2
Ⅳ5

1917
1914
1914
1914
1924

5.2×100.00732
0.00253
0.02318
7.1×10No.17 Gifu

Ⅳ5

1924

2.7×10No.23 Osaka

One regression
line

-11
-6
-8
-7

-12
-7

-0.00440.02640.0170

14.8

403

-13

-0.0047

0.03660.0179

17.2

552

-7

-0.00170.02690.014615.9

662

0.01450.01190.0150

16.0
15.8
15.8

331
168
387

No.36 Kagoshima

Ⅱ2

1948

2.8×10No.34 Kumamoto

Ⅱ2

1948

1.0×10-6-0.00201948
Ⅲ80.0201
1.2×101948
0.00001-0.0013Ⅱ2
0.0196-61950
0.0002
Ⅴ
0.0213
3.0×10Notes 1) Asterisk ：Relatively suitable observatories for observing global warming by the Meteorological Agency
2) Temperature coefficient ・Gotyic type number： significant under α = 1%
・Under line number： signuficant under α=5%・Except above： not significant under α=5％No.28 Kochi
No.33 Saga
No.24 Wakayama- There are 14 observatories of this type. When it is- Nine observatories in 1989 could be compared, there is a

FcMAX-value in the same year, in Table 2, observatories aretendency that the larger city scale (administrative districtarranged in order with a large temperature gradient of the

population) except No.25 Hiroshima, the larger temperature

first period.

gradient of the first period is [9].

- FcMAX-value years are many as 12 the same in 1989, the- Since the temperature jump of the end of the 1980s is notothers are two in 1987. An air temperature jump of the end

considered, the temperature gradient in the first period isof 1980s in whole Japan might be related to this.

smaller than that of one regression line.

- Most of the observatories are located in northern part region,

Type C (Kyoto type): Both regression coefficients are

and Sea of Japan sides. The climatic divisions except No.25

significant. Both air temperature gradients have risen. The

Hiroshima and No.56 Miyazaki are I or IV.

FcMAX-value year is around 1980.

- 123 -

- The FcMAX-value years are 7 in 1980, the others are in 1968

the temperature gradient of the second period to become large

and in 1978.

can be guessed [10].
That is, although the urban warming in Japan is- There are locations of 6 observatories beside the Sea ofJapan. No.27 Matsuyama is exceptional.

fundamentally subject to geographical and climate influence, it- The temperature gradient in the second period is larger thanis supposed that the urban warming increases and the air

the first period. In this sense, the warming phenomenon has

temperature rises rapidly in the latter half mainly [11].
Incidentally, this study does not explore the cause of urban

accelerated.
- The temperature gradient in the second period is larger thanwarming directly. However, it is very interesting to investigate

one regression line.

the cause of urban warming, and taking measures is, of course,Type D (Osaka type): Both regression coefficients arevery important. Here, except climate factors, the following

significant. Both air temperature gradients have risen. The

matters are pointed out from the result of this study. That is,

FcMAX-value year is around 1940.

first, many cities more than middle-size in Japan were in ashes- The difference from Type C is only the times ofas a result of the destruction caused by World War II (in 1945).

FcMAX-value year, and this Type is earlier than Type C.

After that, from the 1950s, it is supposed that rapid- It is only No.6 Hakodate except Osaka.

urbanization invited the rapid urban warming. Second, it is- The character of a temperature gradient is the same as Typeguessed that though an increase in population is aC.

comprehensive index, physical changes of urbanization such as

Type E (Fukuoka type): The temperature gradient of the firstchange of land use, increase of energy consumption and so on,term is not significant and the second period is significant.

have a greater essential influence on urban warming. It is- The regression line in the first period might be horizontal.

because of this that in recent years, in mainly rural regions,

And after that, the temperature gradient in the second periodquite a few not only urban substantial population but the urban

expresses subsequently warming phenomena. This type ofadministrative district population decrease, while urban air

air temperature variation might change from the stationary

temperature rise continues in the middle-scale city.

process in the first period to the non-stationary process in thesecond period.

5. Conclusion- The areas where the observatory belongs are divided
roughly into two. One is in the northern region where

Main results of this study are as follows.

observatories of FcMAX-value year in 1914 are located, andFirst, in order to represent air temperature fluctuation, by thethe other is the Pacific Ocean side of the central area and a

Chow test, it was judged with high accuracy that there were

southern area.

structural changes of air temperature all over object- The temperature gradients in the second period of the former

observatories, that is, two regression lines are more appropriate

type show a small and moderate temperature rise, whereas

than one regression line.

those of the latter type show a rapid and steep temperature

Second,bythecomparative

examinations

of

the

rise. And observatories of the former are located in small

observatories where the different city scales within the same

cities, whereas the latter are located in relative large cities.

climatic division, it turned out that more remarkable warming- The temperature gradient of the second period of the latterphenomenon is, the larger city scales in which observatories aretype is larger than that of one regression line. That is, thelocated.

rapid urban warming occurred rather than having thought

Third, in the large city or the mid-scale city, it becomes clear

conventionally.

that the urban air temperature rose rapidly in the second period

In general, it is certain that global warming or urbanof the target period.

warming advanced for these 114 years. If Type B is excluded

By these facts, although the urban warming in Japanespecially, the temperature gradient of the second period isreceived regulation of geographical and a climate factor, it islarge altogether (although Type B is temperature jump).

clear that urbanization factor has influence on urban warming.

Moreover, if Type B and Type E of the FcMAX-value years in

There are many future examination subjects.

1914 are excluded, it turns out that the temperature gradient ofFirst, the period covered and object observatories need to be

the second period is larger than that of one regression line at 19

expanded. If the covered period is different, transition figure,observatories. Furthermore, if the length of the second period is

the FcMAX-value year and the structural change year might beshorter and the city scale (population of administrative district)different. It is necessary to adopt various period covered.

in which an observatory is located is larger, the tendency for

Moreover, if time has decreased, the data of the observatory in- 124 -

various areas from other large cities to rural areas will be able

Next, under the assumption of a constant error, multiple

to be used.

regression analysis with the dummy variable and theSecond, another method of presuming a structural change

coefficient test were carried out. Those are adapted about theyear is required. The Chow's F-values were too large and longdata before or after the discontinuous year of someperiod in order to specify the structural change year in someobservatories. Although at the three above-mentioned

large cities such as Tokyo, Nagoya, Osaka and Fukuoka. In

observatories, it was difficult to distinguish between thesuch a case, probably, it will be more desirable to use thisinfluence of relocation of an observatory and the influence

method together with another method, in order to presume aof temperature change, at almost all other observatories withstructural change year.

the discontinuous data points, the null hypothesis (theThird, the transition figures of Chow's F-value need further

coefficient of a dummy variable is Zero) was not rejectedinquiry. There are various patterns of them, and it is guessed

under a significance level α = 5%. Even if there is influencethat they have a useful piece of information on the difference inof data discontinuity, it is surmised that it is a grade which isurban warming concerning climates and city scales.

not detected statistically. Such statistical tests need to be

Thereby, it will be expected that the further knowledge

carried out about all the discontinuous points of all theconcerning urban warming is acquired.

observatories, and there is room for improvement of the test.

Acknowledgment

revision concerning the past data was been noted. It is said

However, a more serious problem is that the necessity ofThis work was supported by JSPS, KAKENHI 24560672.

that the past data was influenced by not only changes inlocation but also in charges of used but the situation of theNotes

observation methods, such as the number of observations per[1] Strictly, the Chow test is performed in two steps. First, inday, the circumference of observation equipment, etc(3).

the test of the dispersibility such as error terms ut, vt. F-test

Probably, it will be impossible at least for the mainof the normal equal dispersibility is used for this. If

observatories to investigate such details over a long period

homogeneity of variance is adopted by this test, the FC-valueof time, if the Meteorological Agency does not carry out its

will be tested. In addition, homogeneity of variance wasdata gathering systematically. Archives that contain more

adopted under the significance level α= 5% in almost all thecomprehensive data, however, might no longer exist.

object observatories and in almost all covered periods, and[4] Japanese archipelagoes are surrounded by sea, and are adishomogeneity of variance data were excepted from thegentle bow-formed from the northeastern part to theannual judgment of the Chow test, hereinafter, only thesouthwestern part, and mountain ranges run along the central

FC-values are described.

part of the islands. Because of them, the climatic divisions

[2]

With

observational

theof regions in Japan are complicated and varied. For thisMeteorological Agency notes the air temperature change ofreason, various climatic division figures are proposed. Fig.1

17 observatories as being 'comparatively little although theis made based on Takeshi Sekiguchi's climatic divisioninfluence of urbanization has won general influence'. The

figure which is most often used (4). Although the original

targeted observatories of this study are located at 9 points,

drawing had the transitional zones where Kyoto, Nagano

No.3

and Oita were established in, those are simplified in Fig. 1.

Suttsu,

No.4

data

of

Abashiri,globalNo.5

warming,

Nemuro,No.10

Ishinomaki, No.11 Yamagata, No.15 Nagano, No.20 Fushiki,[5] For convenience, as a single index which guesses a city’s

No.26 Sakai and No.35 Miyazaki.

scale, administrative district population is adopted as a[3] Examination of the temperature data across 114 years isreference. It is because the present administrative districtdifficult. The discontinuous year points caused by relocation

population is not necessarily expressing a city scale. Theof observatories, changes in apparatus used, etc. are apparent

current large cities and medium-sized cities had populationin the annual data of the Meteorological Agency homepage.

influx from outside of the city and repeated municipal

In this study, the data used was checked with a simple

mergers after the 1950s. Consequently, the spatial domain

method. First, there are no points that the FcMAX-value year

expanded and administrative district population increased.

or a structural change year coincides with the discontinuous

The merger of municipalities, which were government led,

data years. And it is three places, No.6 Hakodate, No.16

included 'a large municipal merger of Showa era' (1953 to

Nagoya, and No.25 Hiroshima, that a discontinuous year

1956), and 'a large municipal merger of Heisei era'corresponded to one year before the FcMAX-value year.

(1999-2010). Thus, since the large city has repeated themunicipal mergers, it is not so easy to pursue the population- 125 -

change of a city concerning the present district (Every fivex1 : the urban scale (administrative district population.

years from 1920, there are Population Census which is madeunit: in thousand)x2 : the length of the second period

for every cities, towns and villages before mergers). On theother hand, according to a map or aerial photograph, cities

Multiple correlation coefficient R = 0.898

where observatories are located and their land use patterns

Multiple correlation coefficient adjusted for degrees ofare various. When examining the urban warming of each

freedom R = 0.887

city over a long period, it is necessary to examine the actualy  0.06826  3.5  106 x1  00067x2

conditions of the city where observatories have been located[11] It is not easy to distinguish global warming and urban
warming only by local air temperature data. In this study

from its historical context.

also, warming phenomenon of a relative large scale city is[6] Here, x is the natural number which set 1891 to x= 1 and set

only called 'urban warming'.

2004 to x= 104. The coefficient of the regression line istaken of more decimal places below the decimal point thanthe usual o.oo or o,ooo so that it might be easier to carry out

Referencescomparison between observatories. Rather than an actual(1) Japan Meteorological Agency: Search past meteorologicalconditional numerical value, a small number is an expedientobservation data, http://www.data.jma.go.jp/ [in Japanese](2) Ministry of Internal Affairs and Communications: The

numerical value.

Population Census in Japan in 2000

[7] Although Fig.8 is also interesting, there is no guarantee thata warming tendency is constant. And if the coefficient of a(3) Kondo, J.: M41. The amount of background warming anddummy variable is not significant, Fig.6 will be adopted

urban warming of Japan,

after all.

http://www.asahi-net.or.jp/~rk7j-kndu/kisho/kisho41.html/[in Japanese][8] The transition form of Fc-value has various patterns byobservatories. However, it may have common case under(4)

Sekiguch,T.

(1959): Climatic

regionsinJapan.

certain circumstances. It is observed that there is a tendency

Geographical Report of Tokyo University of Education. [inwhich shows the similar form with the low value level in theJapanese]

northern part region of Japan, and that there is another(5) Yoshino, M. (2003): Regional classification in Japantendency which shows the similar form with the high value

according to bioclimatology. Chikyu Kankyo,8. [in Japanese]level in a southern part region etc. It is given impression
generally that Fc-value is large in the southern part region or(Received Dec. 26, 2014, Accepted Jan. 17, 2015)

relative large city where mean of air temperature is high andits fluctuation is large, in contrast, and that Fc-value is small
in the northern part region or relative small city where meanof air temperature is low and its fluctuation is small (Since
there are many large scale or medium-sized cities in which
an object observatory is located in the southern part region,
it is not easy to distinguish the influence of a city scale andthe influence of a climatic factor clearly). However, this is
not always certain statistically. Therefore, in this study, theinterpretation of Fc-value considers only the formal meaningof the numerical formula (4) in Table 1.
[9] If No.25 Hiroshima is included, the coefficient-ofdetermination between city scale and the temperature
gradient in the first period is r2=0.335 (correlation
coefficient r = 0.579). And if Hiroshima is excluded, r2 =0.571 (r = 0.775).
[10] The next multiple linear regression analysis is carried out
about Type A, Type C, Type D and Type E. An explaining
variables fulfill sign conditions and are significant under α= 1%.
y: the temperature gradient in the second period- 126 -