On the Fine Structure of the Bottom Layer of the Atmosphere on the Water Surface at Nagase dam

On the Fine Structure of the Bottom

Layer of the Atmosphere

       onthe Water

Surface

at Nagase

dam

       Hisashi

Ueta

Ｐｈ:ｙｓtｅａｌ Ｌａｂｏｒａtｏｒｙ，

Ｆａｃｕlりｏｆ

Ｌｉｔｅｒａtｕｒｅ

ａｎｄ

Ｓｃiｅｎｃｅ

      Abstract       。

 Some

features

of the

fine structure

of the

bottom

layer

of the atmosphere

on

the water

surface

at

Nagase

dam,

Kochi

prefecture,

in summer,

are made

clear by the analysis of the records

of fluctuations

of short

period

of wind

and

temperature｡

 The

minimum

temperature

appears

at

the height

of ３０cm

and

strong

inversion

of temperature

appears

in the night.

and

weak

inversion

appears

in the daytime.

Cross-correlation

functions

of the

fluctu゛itionsof the temperatures

at two

heights

are

examined

and

they

are conspicuously

affected by

stability. Autocorrelation

of the fluctuations

of vertical component

of wind

velocity w'

and

of along･

wind

component

of wind

velocity

≪' and

cross-correlation

of ｙ and

w'

are examined.

Austausch

coefEcient

and

eddy

diffusivity

for heat

and

amount

of evaporation

are

evalりated.

       1.

Introduction

 Mi crometeorologi cal study in the bottom layer in the atmosphere

on the water surface of

ａ lake of ａ dam

is important

to know

the amoiint of evaporation from

the water surface

and meteorological relation between

the water surface and the surrounding atmosphere. As

the bottom layer on the water surface is affected by the water having a large heat capacity

and by the land surrounding

the lake, it has ａ considerably different structure from the

bottom layer on the 日ａtland and some

studies have been devoted to the problem｡

 The

present study is attempted to make

clear the fine structure of the bottom layer in

the atmosphere

on the water surface at ａ dam

with the data gained by ａ few observations

carried out for this purpose by

the method

which

the author has used

in the previous

study".

This method

is based on the analysis of the records of fluctuationsof short period

of the wind

and

temperature gained

by using

a hot wire anemometer and

thermocouple

thermometers.

      2.

Method

of

Observation

 The

instruments

used

in the study are those which

have

been

used

in the previous

paper"

and

the outline of them

is expressed

here.

 Ａ hot-wire

anemometer

of thermocouple

type is used

as ａ total air-flow meter.

Its

hot-wire

is

stretched horizontally

on top of ａ

wind

vane

making

the wind

blow

normally

 across

the wire

and

ａ total air-flow

is measured

as ａ thermo- current

in ａ thermocouple

attached

to the hot-wire.

Another

Biram･type

anemometer

is also used

to measure

the

mean

wind

velocity.

 The

inclination

angle

(9') of air-flow is measured

by

two hot-wire

systems

of Wheatstone

bridge

type,

＼vhich show

different electric current

for different inclination

of ａ wind.

Then

278

高知大学学術研究報告  第21巻  自然科学  第15号

u°V.

COS 9°and

w=v.

sin ？.       ，

 To

measure

the fluctuations of miχing ratio, SheppaΓｄ and Elneser's"

circuit･is employed.

 To

measure

the fluctuations of temperature,

several thermocouples

of copper

and constantan

       ４

wires

are employed.

 The

mean

ｍｉχing ratios (r)

at the

two

points

of

vertical

distance

∠1z are

measured

successively

by

Assman゛s

aspiration

psychrometer.

 Ａ metallic

pan

(1.8

cm

in

diameter)

containing

some

water,

is

floated on

the

water

surface

of ａ bath

used

for photographic

development.

which

is also floating on the water

surface

of the lake.

(Fig.

1)

The

depletion

of

the amount

of water

in

the

pan

after ａ

constant

time interval is measured

with ａ precise balance.

-一一一一-一一一一

_{一一一一  一一一一}

- - - -  - ・ 一

Fig. 1.

A small metallic pan for estimation of amount

of

 evaporation from

water surface. 、

       3.

Data

of Observation

 The

observations

were

ｅχecuted on

the water

surface

at Nagase

dam,

Kochi

prefecture,

on Jul.

28, 29, 1964.

Durng

the observing

period

S-wi!id surpassed

and its running

distance

over

the water

surface

was

ca.

500 m and it

may

be thought

that the

surface

was

wide

and

homogeneous.

The

point

of observation

is selected in shallow

water

ca.

3 m

off the

shore

and ａ pole is erected

in the water

and

thermojunctions

are fixed on it at the heights

of 30, 75, 145,

220 cm respectively

above

the water

surface.

Hot-wire

to measure

wind

velocity and

wind

inclination.

and ａ thermojunction

to measure

ｍｉχing-ratio are fixed at

the level of 120 cm.

CFig. 2) The

outputs

of the circuit of the above

meteorological

elements

Fig.

2.

The

view

of observation

site.

are photographically

recorded

by

means

of two

sets of ･Takasu's

six points

simultaneous

self-recorder.

The

constants

of the recorder are

as follows ； preiod

of the free oscillation

of each

galvanometer

is 0. 5 sec. Time

scale of

the record

is ca. 0.２ cm

per second

and

the time

interval needed

for one rotation

of the recording

drum

is ca.

2 minutes. 。

 The

record

is divided into

120 subintervals

and

the mean

values

of the elements

ｖ,９’ａｎｄ

on the Water

SurfaceCH. UeTa) 279

‘the wind

u=v.

COS V, ■w=v. sin 'P for each interval and the mean

values of these elements

for 120 seconds u,iv, T are calculated. The

fluctuationsof the elements

at every second

are gained as u' =u―u,

for example.

The

vertical eddy

nｕχ for heat (H),

Austausch

coefficient{At)

and

eddy diffusivity(Kx)

for heat can be calculated by

the formulae

of

 一

石＝Ｃ≫ｐｕ.’ Ｔ’

   μ匹

λ＝一一- ７   ∂？/∂ｚ

Ｋｒ＝一

-ｔがｙｒ´

9T/9ｚ

where

Ｃ。= 0.24

cal. ｇ￣!. deg"^

is specific heat

of

the air at constant

pressure

and

ｐ＝

0. 00129

g/cm≫ is density

of the air. The

mean

values of these elements

for each

subinterval

０ｒone

second

are listed in table 6 about

l7 h 00 m

on

Jul.

28,

as

an

example.

By

the

same

way

as above,

vertical eddy

flux （ｑ).Austausch

coefficient (Ar)

and eddy

diffusivity

（Ｋｒ）foｒ water

vapor

were

gained

by the formulae

       -   一一

   q=

piv' r'   ム＝−{だjご一   drぶシ

for only

one

case

at 16 h

00 m

on Jul.

2 9 and

the values

are

data

are listed as appendix.

4.

Result

of

Observation

listed

in

table 4.

The

other

  (i)

Vertical

distribution of temperature

 In

the

daytime,

air temperature

rises to ca.

31°Ｃ and

the difference between

the

tern-perature

of

the upper

layer

and

that of

the lower

layer in

the bottom

of the atmosphere

under

2 m

height

touching

the water

surface,

is very

small

1 to 2°Ｃ at most.

The

tern-perature

of

the water

stirface is kept

between

２８°C and

29.5°C,

and

it is less

than

or

nearly

equal

to the air temperature.

Vertical temperature

profiles of the air and temperature

of the water

surface is illustrated in Fig.

3. In

the

night,

the

air temperature

is higher

than

the water

temperatiire.

This

is because

it is more

difficult for the water

of the lake,

which

has

been

warmed

by

solar radiation

in the daytime,

to be cooled

than

the air. The

temperature

at 30 cm

height

above

the water

surface is the

lowest

and

the temperatures

are higher

above

the height.

The

temperatures

at 30 cm

height

begins

to fall down

from

evening

to the next

early morning

and it seems

that the temperatures

in the higher

levels

are

pulled down

by

the temperature

at 30 cm

height.

It seems

that the temperature

of the

water

does

not fall so much

and it keeps

26 to

28°Ｃ because

of ａ large

heat

capacity

of

water

and

that

the

air cooled

by

the

surrounding

surface

of the

earth

advects

to the

warmer

water

surface.

  (ii)

Appearance

of extreme

temperature

 From

the simultaneous

records

of air temperature

gained

at several different heights,

it

is found

that there

are following

three

cases in appearance

of extreme

temperatures｡

       1

  (1)

Extreme

value

of air temperature

appears

early at high

level and it does

gradually

280

I l l : > 一 一 Ｃ ｀ , ￨ つ x l に Ｉ ・ 一

高知大学学術研究報告  第21巻  自然科学  第15号

          Ｅ ︵ ︶ Ｗ ９ t ’ｉ         t i l   > i Z   Ｌ Ｚ ． ６ ２     ' [ ” ｆ   ａ ｏ   ^ ０ ! '   Ｍ ９ Ｔ Ｅ ｏ ０ ４ ９ １         ｌ Ｕ Ｑ t ' Ｈ Ｓ Ｉ ｕ :   O f :   ａ ｚ           ｏ s :   ６ ２ O f :           f     ｚ ヴ ､ j ' N l

ぶmi

  Ｅ ｏ ｍ ￡   ６ ｚ -￨ ” ｒ ' . ) Ｚ ＼ ' Ｚ ７ . ／ . ' ■ｕ -            1 -０             ︵ ■ ︵ .           ｓ ＾           ｕ           ｆ ｔ ｚ             i ｖ :

ぶＵI1２

１ 二 l 心 -   一 一  

-Ｅ︵︶ワ一に Ｅｏ︵︶’一に必？一コ﹃

Ｓ Ｓ ３ 卜 ￢ {   " ｊ ａ ｊ Ｅ Ｍ   ａ Ｄ Ｂ ｊ ｊ ｎ ｓ   ａ ｑ j l o   ａ ｓ ｏ ｑ }   ａ ＼ ０ ｕ ｓ   Ｊ ３ ) ３ Ｕ ｉ   ０ Ｊ ３ Ｚ   } Ｅ   ｓ ａ ｊ ｎ ｊ Ｂ ｊ ｇ ｄ ｍ ａ ｊ   a i i   Ｔ ︶ Ｕ Ｏ Ｕ Ｉ Ｑ Ｑ   m i ｌ Ｕ Ｏ Ｊ Ｘ ９ Ｉ Ｕ ０ ｊ ｄ   ３ ｊ ｎ ｊ ８ Ｊ ３ ｄ Ｕ Ｉ ９ }   1 1 3 D T J J 3 A Ｊ Ｏ Ｕ Ｏ Ｉ Ｊ Ｅ Ｕ Ｅ Ａ Ｘ ] Ｉ Ｂ Ｑ ' ｇ ' Ｓ ｌ ｊ ;

   (2)Extreme

value

of air temperature

  appears early at low

level and it does

  gradually at high

level.

   (3)Extreme

values of air temperature

  appear at the same

time

at a11 levels.

  About these

three

cases,

the data

of

time,

height,

wind

velocity,

wind

in-clination

and

vertical component

of the

wind

at the appearance

of extreme

tem-peratures

are listed

in

table 1 (a)∼

Cc).

In this table, vertical component

of the

wind

is gained

by

the relations

でv^v. sin V and

ｗ771＝∠lｚZ∠dt.

Where∠1z

is the

difference of

the reference

two

heights and

/It is the time lag which

eχ-treme

temperatures

appear. Positive

ｕ/

means

upwarc!

and

negative

ｗ means

downward

transmission

of extreme

tern-perature.

 (1) When

extreme

temperature

appears

  early

at high

level and

then it does

  at

lower

level, ･P and ■u)are positive

  in

many

cases. It is thought

that the

  upper

wamer

air existing on account

  of temperatui･ｅ inversion comes

  down.

In table 1，the values of ｗ･are

  to be equal

to w^.

and in fact. the

  signs

of ７ｃagree

with

those

of ｗm

  but the absolute values do not

.

(Fig.4＼

 '℃      ｜    ｜     ｜

冽＿         ふ

29ニ       土        220

cm

31−

  −   ＿1＿-＿4   ￡

29

-− -− / ; ) c m

:j(l cm

29,￣

-       20    :30    '10

sec

Fig. 4.

Propagation

of extreme

temperature

 from an upper layer t０lower layers.

 (Jul. 29, 15 h 40m)

i on the Water

Surface(H. UETa)

281

Table

1. ( a )

Propagation of ｅχtreme temperature from an upper layer to lower layers.

appearanceof extremetemperature

Wind

Vel.

(crn.sec￣1)

W°V.

sin (p

(ern.SeC￣1)

   <p

(degree)

   てtﾉ97S

（Crn.SeC￣1）

Date

Time

Heig旨）

Jul.

28

17h

00m

_{45 sec.}

48

220

30

200

−34

−10

−63

Jul.

29

3 10

72

73

220

30

230

０

０

-190

Juレ29

15 40

23

24

75

30

140

1 ・ ・

−13

−５

−45

27

28

220

 30

260

−10

−２

−190

36

37.5

220

 30

300

−36

−７

-126

73

75

220

30

170

０

０

−95

84

85

75

30

220

−20

−５

−45

Jul.

29

16 00

17

18

75

350

−11

−２

−45

Table

1. ( b )

Propagation

of ｅχtreme temperature from ａ lower layer to upper layers.

appearanceof extremetemperature

Wind

Vel.

(cΓΥ1.see￣1)

W°V.

sin (p

(Cln.SeC￣1)

   yﾌ

(degree)

   ■^■m.

(Ｃｍ．Ｓｅ(７１)

Date

Time

Height

    (cm)

Jul.

29

3｀h10m

Ｉ seC.

10

30

220

210

19

５

63

56

58

 30

220

220

０

０

95

Jul. 29

16 00

97

100

30

80

40

30

63

Table

1. ( c )

Extreme･temperatures

appear at the same

time at all levels

appearanceof extremetemperature

べA^ind Vei.

 (cm.

sec)

Ｗ°V. sin CO

(cm.

sec"')

   yﾌ

(degree)

  Zむ971

（Crn.SeC￣1）

Date

Time

Heightcm）

Jul. 28

17h

00m

_{14 see.}

37

一

一

’ 250

   120

−23

−31

−5

−15

一

一

Jul.

29

16 00

45

89

一

一

 O 、

150

 0

−18

 ０

−７

一

一

282         高知大学学術研究報告  第21巻  自然科学  第15号

 (2)

When

ｅχtreme temperature

appears

early

at low

level and

it does later at higher

level,

?> and ７むare positive. It is

thought

that

bubbling

warm

air masses

rise

apart

from

the lowest

level on

the warm

water

surface

to the upper

level. In

this case,

signs

of ７むgenerally

agree

with

those

of ｕ7771but the abusolute

values

do not.

 (3)

When

extreme

temperatures

appear

at the same

time

at a11 levels. the signs of ｗ

are indefinite. It may

be that the observing

points

at the different two

heights

enter into

the same

air mass

at the same

time

by

advection.

oａｓ ︵︶コ

o ｉ ｌ ○ ○ I ― ) つ e n つ Ｃ 心

○

ト

○ 〈 こ 〉 つ I J 7 S マ ･ Ｏ Ｃ り ○ C M ○ → ･ i n ｒ   ｕ ｏ   ｍ ｏ ｏ   Ｍ ｉ ｌ   ｌ ^ ^   ｕ i b ｑ -ｓ ｓ ｂ Ｓ ｂ ｗ   ｊ ｏ ｊ ｕ ａ ｕ ｏ ａ r ａ ｏ ｏ   ｉ ｅ ｏ ｕ ｊ ｓ ａ   ｊ ｏ   ｕ ｏ ｉ ｌ Ｂ ｎ ｐ ｎ ｎ   ｐ ｕ Ｂ

６Ｎ４

9 ■ ｄ ｚ ８ ． ９ ７ .                                                                 ･ ＾ 6 1       ' ８ ３ ９ ３ Ｂ Ｉ ｊ ｎ Ｓ Ｊ ３ ４ Ｅ Ａ ＼ S m ９ Ａ ０ ｑ ｅ     ３ ３ Ｓ ／ Ｕ Ｊ ０   a i       ｎ ｉ   j C j i o o t ｓ ａ   ｐ ｕ i M   ｊ ｏ Ｑ ｕ i   ａ ｊ r ｕ Ｂ ｊ ａ ｄ r a a j   ｓ ｎ ｏ ３ Ｕ Ｂ ︸ Ｕ Ｂ ; ｓ ｕ i   / ( ｑ   ｕ ｉ ａ Ｔ ｄ ｏ ｓ ｊ   。 ︵ Ｊ ９     -Ｓ U

笛呂 弓

ど

Ｑ

つ ７ り 0 1 ' -Ｏ Ｓ -ｏ ＾ -︵ ︶ ︷ ｌ ｏ ｏ ︷ 宛

泌

e S t J C M

２ぷ

ぱ り 卜

Ｑ

⊂ い っ ぐ り

on the Water SurfaceCH. tjeta)

285

に ｌ ヽ

旨−

∼−

( Ｄ     こ C り

踊

︵︶  .yＶ＼

０１

。ＪｒＱ

  (iii) Isopleths

 The

isopleths shown

in Fig. 5 (a)∼(

e ), may

be taken up

as ａ representation of the

thermal structure of the reference layer. As the temperature of 26.8°C of the surface water

is larger than the air temperature

of 23°Ｃon Jul. 29, 3h

10 m, convection takes place in

the lowest layer under 30 cm height by heating from the wamer

water surface but it does

not arrive at the upper layer. because the upper inversion layer suppress the convection.

The

intervals between

the successive cold （ｏｒwarm)

masses

are not definite, but the

O . J Ｓ 一 心 ･ C N i r - ｉ ︵ ︶ コ 一 一 -Ｗ Φ -Ｃ ･ ご り こ ; : 心 こ い こ こ

○

に

○ マ ｊ こ ７ ｔ じ 0 1 ･ ０ ７     -m ｒ   ｕ ｏ   ｕ i   ０ １   Ｕ Ｔ Ｊ   ︸ Ｂ   ａ ｏ Ｂ ｉ ｊ ｎ ｓ   ｊ ３ } ｂ ａ ｉ   ａ ｉ ｐ   ９ Ａ ０ ｑ Ｅ ヽ ｏ ｉ   ｕ ｏ ｑ E i ｔ ｏ ｎ ｕ   ｄ ｕ ｂ   ｍ ｇ ｉ ｄ ｏ ｓ ｊ

(ｑ︶ ｓ -３!＾

 Ｃ７.

()[

 284         高知大学学術研究報告  第21巻  自然科学  第!5号

predominance

of the intervals

of about

8

seconds

can be roughly

recognized

by inspection

 (Fig.

5 C C)).

Similar

isopleths

appear

at'1 7h

00 mしand

21h 10 m、 but

the

difference

between

the

water

temperature

and

the air temperature

is smaller

than

that at

3 h 10 m

and

the

turbulence

hy

convection

diminishes

尽nd longer

period

of 10

to 12 seconds

of

alternation

of warm

and

cold

air masses

appears

at 30 cm

height

and

the period

at 145 cm

level is ca. 30 seconds

at 17 h. The

vertical temperature

profile、 at 15 h

40 m

on Jul.

29、

shows

weak

inversion

and

the alternation

of warm

and

cold､air

masses

takes

place

at the

。。ポ已

S   Ｃ   つ   C I . r ご   マ   こ ら   へ l

Ξ ゜

  ≧

つ →

C

CM

C ） C y う

○

_寸

ブレ

）

o？ｚ

Ｅ０

Ｍ ． ｆ ︰ Ｍ η Ｎ

∼ｌ︷．．ＮＭ／ｖ１ど∼’／‘

ンー一‘．ＮＮトχ／いン＼ノ”

Ｑ Ｑ の ( ⊃ つ r 一 i

．Ｓ．︻ｎｆ ｕｏ ｕi QT

ｕｐ jE ３３ＥｉＪｎｓ Ｊ９ＪＥＡ＼ am ａＡＯＱＥヽm. ｕｏＵＢｎｐｎｇ ｐxre ｍａｊｄｏｓｊ

   ︵)５

０８

Ｏｉ

０９

(︶に   三ヽＯＫ

０７.

︵Ｑ︶〃

 ｏ［

. ｌ 皿 こ     ○ 7 り

of the Atmosphere

on the Water SurfaceCH.リＥＴＡ） 285

り り ㎝

．５２

 -ｐｆ ｕｏ rag＾ ｑgi JB ｇｏｅｊｊｎｓ ｊａｊＢＡｖ ３４; ａＡｏｑｅヽm ｕ０ｉｊＢｎｊｏｎｕ ｐｕＢ ｍａｊｄｏｓｊ

 ＯＧ

０８

ＯＺ

０９

Ｏ'Ｊ

01'

Ｏｆ:

ＯＺ   ︵︶一

period

of ca. 60 seconds

ａ‘ndpredominance

of downward

motion

during

the warming

stage

and

upward

motion

during

the cooling

stage

can

be recognized

at the level of 220 cm.

  (iv)

Correlation

functions

of fluctuations

of temperature

at various^ heights

 From

the

temperature

fluctuations T' 220、７≒5、Ｔ勺o at

the levels

of 220、75、30

cm

respectively above

the

water surface、cross･correlations

RTu

between

Ｔ≒2o and T≒5

as

well

as RTl

between

７‰５ and

^■'30 are calculated.

(Only

at 17 h

00 m

on Jul.

28、RTu

 Ｑ⊂）Ｏ

 ＱＩ口 ｔ

ポ

ロ

Ｑ

⊂ ） こ ･ つ

呂 邱 ｏ ヨ

       ｜

    ≧

つ   っ   っ       こ C 、 1   7 ヽ つ   寸     E C ､ ､ l 1 ｀   1   ¶     Ｑ へ 1 じ t 卜 ヽ

286

01'

０９

Ｕ８

。。♂ｙ

高知大学学術研究報告  第21巻  自然科学  第15号

１

匹

ぱ ） ｅ ヽ こ φ つ こ J ｈ ｔ t p : / / w w w . . . ( ︶ 一 一 こ ︵ 二 つ Ｓ

つ

父

一 一 １ ∼ 一 一 ・ 二-こ 1 ､ ・ 一 一 マ こ ７ で -り ､ l ． { . ７     " r ｎ ｆ   ｕ ｏ   ｕ i   ０ ０   i l   Q T   ︸ ｅ   ａ ｏ Ｅ ｊ ｊ ｎ ｓ   Ｊ ９ Ｊ ｂ ａ ＼   a m   ｓ ａ ０ １ ヽ ａ ｉ   ｕ ｏ Ｕ Ｂ ｎ ｊ ｏ ｎ ｕ   ｄ ｕ ｅ   ｍ ａ ｉ ｄ ｏ ｓ ｊ ( ３ ︶   Ｓ -Ｓ ｌ Ｊ     ( ︶ 一 ’

･Ｃ Ｃ Ｃ -Ｃ Ｃ Ｃ） 〃   ら

_{c｀l   αl マ こ cc 三  Ｅぷ５･}

    Ｉ Ｉ Ｉ Ｉ Ｔ  Ｑり､￨

  μ

is correlation between ７‰ｏ and

T'i45.) (Table

2.）

 In weak

stable layer、correlation of T'

at high and low levels is large and it indicates

that the temperature fluctuations at high

and low levels have

considerably close relation.

For example、 both RTl

and RTu

are 0.5 t0 0.8 at 17 h 00 m

on Jul. 28 and at 15h 40 m

and 16h 00 m

on Jul. 29、and RTu

is 0.8 at 21h 10 m

on Jul. 28.

 When

there is a temperature inversion、 cross-correlation iｓ▽ery small in the air under

the top of the inversion layer and in the weak

stablelayer above it RTu

shows large value.

287

Table

2.

Cross-corre】ation

of fluctuations of temperatures

at various

heights.

    RTl;

Tり５ and

Ｔり0.

RTu;

rり2o

and

Tり5.

Jul. 28

17h

00m

21  10

 0.53

−0.02

0.65

0.82

Jul. 29

3  10

15  40

16  00

-0.34

 0.79

 0.68

0.17

0.86

0.60

jｕａｉｏｍｇｏｏ ｕｏijＢiａｉＪＯＱ

１ ． ０ ０ ． ８ ０ ． ６ ０ ｡ 4 0 . 2     ０

−0.2

−0.4

       5   10   15  20  ｡25  30 ●

35  刳l  ･15

      Time-lag

(sec)

Fig.

6 (a)く Autocorrelation

of fluctuation

of vertical component

of wind

velocity ７む万´万（○）ａ万nd

 along-wind

component

≪' （□)

and

cross･correlation （●）of

u' and

w'

at a height

of 120 cm

 at 17h

00m

on

Jul.

28, 1964.

Sampling･duration

120 sec. ; Mean

wind

speed ・=

234 cm/sec.

j ｕ ｓ ｉ ｏ ｍ ｇ ｏ ｏ   ｕ ｏ Ｕ Ｂ ｐ ｊ Ｊ Ｏ Ｑ ] ． ( 1 0 . 8 ( ) . ( i ０ ． ４ ０ ． 2   0 0 . 2

−0

４

      Time-Lag(sec)

Fig. 6 (b).

Autocorrelation of fluctuation of ｗ´ and

u' and cross-correlation of u' and 7c/

288

jｕｇｉｏｍａｏｓ noijｕiａｉａＯＱ

１ ．０ ０ ． ８ ０ ． Ｇ ０ ０ ． , １ １ ０ 。 ２     ０

−０

−０

2 . ' I

高知大学学術研究報告  第21巻  自然科学  第15号

      5   ’10   15   20  25  :如  35  ●10  j15

      Time-Lag(sec)

Fig. 6 (c).

Autocorrelation of fluctuation of 7t/ 卯dがand

cross-correlationof ii' and 7cバ

 at 3h 10m on Jul. 29 ； Mean

wind

speed ｔ,＝195cm/sec.

5 Ｕ ３ t Ｏ Ｉ Ｊ １ ９ ０ ３   Ｕ Ｏ Ｕ Ｂ r Ｓ Ｊ Ｊ Ｏ Ｑ ｜ ． ０ ０ ． 8 0 . 6 ０ ． ･ １ ０ 。 ２     ０ - 0 . 2 − ０ 。 １ − ０ 。 ６ ５ 1 0

₁₅

   20｡，25

Time･Lag

(sec;

3 0

₃₅

4 0

45

Fig.

6

(d).

Autocorrelation

of

fluctuation

of

zv' and u' and

cross-correlation

of

v!

and

ｈttp:

/／www.h.coｍ.on.Jｕl.

29 ；

Mean

wind

speed

1^=253

cm/sec.

Fine Structure of the Bottom Layer of the Atmosphere

on the Water SurfaceCH. ueta) 289

１ ． ０

0.8

    ６       ４     ？ 一       ０   Ｊ     ０     ０     ０ Ｊ Ｕ ３ Ｉ Ｄ Ｉ Ｊ Ｊ ３ ０ ３ Ｕ Ｏ ｐ ｅ ｐ ｉ Ｊ Ｏ Ｑ ０ ． ２ ０ ． ４ ５ 1 0 １ ５ 2 0

25

3 0

35

4 0

_弱

      Time-Lag

(sec)

Fig. 6 (e).

Autocorre】ation of fluctuation of ７ｙ and

u' 池d

cross-correlationof ｙ

and ｚむ

 at 16h 00m on Jul. 29 ； Mean

wind

speed t;= 233 cm/sec.

For example、the

air above

the level of ７５ cm

and

the

air under

it shows

undoubtedly

individual

temperature

fluctuations at 21 h 10 m

on Jul.

28.

 At

3h 10 m

on

Tul. 29、inversion

is the largest

until

the height

of 220 cm

and

in this

strong

stable layer

both

RTl

and

RTu

are very

small

and it seems

that there is no relation

between

the upper

and

the lower

layer.

  (v)

Evaporation

from

the water

surface

 Vapor

tension

becomes

largest

from

13 h t0 15 h and

relative humidity

shows

ｍａχimum

value･of

90％fｒom

l h t0 4 h.

Daily

variations

of them

are illustrated in Fig.

7.

 The

amount

of evaporation

is calculated

by

the

next

two

ways.

The

one is by

the

evaporating

formula

of Thornthwaite-Holtzman

（９ぶ）、and the other is by ａ small evaporating

pan

(go').

Relative humidity

ｍｎｌ･Hk

り Ｉ Ｉ     Ｏ     Ｓ ソ ー   ２   １

V:ipc>i-tension

％00 90

 −

０     ０ ａ ; i -6 0

       U  2  ●1  6  8  10 1】2 M 16

hr

290

高知大学学術研究報告  第21巻  自然科学  第15号

 Thornthwaite- Holtzman' s formula

is as follows :     ・

      ρ尺2ヽけ1−ｒ2)(ﾌ■J2-V,)

    ’ ｑｔＫ ―   Un

ｚ2/21｀)2

where K is Karman!ｓ constant. Mean

wind velocities ﾌﾉland ｔﾉ2and relative humidities FI、

Ｆ２at the heights of ｚ1＝30 cm、2:.= 150 cm

are measured

and ｒ is calculated‘by the

following relations:

7-= 0.622×

こ

￡

×100＝Ｆ

  ε

ターε

where

^ is vapor tension. E is saturated vapor tension. F is relative humidity.

 The

amount

of water diminished by evaporation

from

the small evaporating pan during

two or three hours is measured

and reduced to time mean value. Another way

of measuring

       -evaporation from

the relation q= pwり'' was tried but it failed to measure ｒ and only one

case succeeded and is listed in table 3 (b)

as ａ reference. The

results show

that Qtn are

Table

3.( a ).

Amount

of evaporation calculated by Thornthwaite-Holtzmans'

formula.

Date

Time

height

   (cm)

Air Temperature

       (゜C)

どＬ

 (mb)

Wind Vel.

 Ccm.

s-i)

Amount of

詐ﾂﾞﾎ）

Jul. 28

13h 30m

 ､30

150

28.0

28.0

■

23.2

 22.4

103

120

0.036

1  30

30

150

23.6

23.7

20.1

19.1

33

36

0.006

Jul. 29

3  10

30

150

22.8

22.5

19.8

19.2

44

50

0. 009.

11  40

30

150

29.2

29.6

20.1

18.4.

83

137

・   0.23

Table

3 ( b ).

Amount

of evaporation measured

by ａ small pan.

Jul. 28

13h

30m-15h

00m

15h

00m-17h

50 m

0.088

0.034

Jul. 29

9h

15m-12h

15m

12h

15m-17h

00m

16h

00m

0.051

0.072

0. 022*

      - ＊ is the value gained by

ｑ°ｐ-ｍ’が

small

values

of 0.006

tｏ‘0.009 g. cm'^'hour"' in

the night

and large

values

of 0.05

to 0.23

g.ｃｍ￣2hour

^in the daytime.

Agreements

of these

calculatec! results Qth. with

the observed

values

9o gained

by ａ small evaporating

pan

are not sｕ伍cient. (Tabl

3(a))

In the method

of evaporating

ｐａｎ、

turbulence

may

be produced

by the

brim

of the pan

and

heat

may

be

absorbed

by

the vessel、and

so

the amount

of evaporation

９ｏmay

differ from

true value

on the Water

Surface(H. ueta) 291

by the

pw'T'

-∠1ｔ/４ｚ

the water surface.

  (vi) Austausch

coefficientand eddy diffusivity

 Vertical temperature

profile at l m

height、 where

wind

velocity and mixing

ratio are

measured、shows

inversion all day long

and vertical eddy 丑ｕχfor heat calculated

  -formula

J-T=らpｕﾉhｔtｐ：／／ｗｗｗ.downward．

Austausch

ｃｏｅ伍ent

for

heat Ar=-and

eddy

diffusivity for heat Ｋ７＝

ぷyﾌﾞ

-/Iz

are given in table 4.

Table 4.

Austausch coefficient(A)

and eddy

diffusivity

（尺）

｜

Ｑ

ｌ

回

バ

ド

−͡

→ .4

い

レ｀

 で

い

い

   ７

   １

．々５

   ､ｊ

 て

 ぴ3

_々l

 心

Jul.

 28

 28

 29

 29

 29

17h

00m

21  10

3  10

15  40

16  00

234

 83

195

251

233

･125

 21

 55

 69

 32

-2.54

−0.28

-1.17

-15.4

-0.87･

0.085

0.055

0.089

0.94

0. U

65.4

42.9

68.1

725

 87.5･

卜

_Ｑ

《Ｕ

_Ｅ

Ｈ

バ

1

1’

ド

柚

きｊ

口

り｀ ＆

 Ｗ

 で

ぺ

     ら

     か･ｉ

．  ｜

     Ｑ

     Ｑ

     ぴ）

  Ｊｉ

     Ｑ

     Ｗ

Jul.

 29

16  00

233

-2.45

6.2

2.53

1950

 The

order

of the vertical eddy

flux heat

(H)

is 10−3 to 10−5 cal. cm"^

sec

^ and minimum

value

appears

at 21 h and

maximum

value

of i5;4 cal.，ｃｍ￣2 sec"' does

at 15 h 40

m.

Consequently,

At

and

尺T at 15 h 40 m

show

remarkably

large

values.

In

general.

K.T is

order

of 102 to 103 c

｢sec"^.      ｡ヽ

  (vii)

Correlation

function

of fluctuations of wind

velocities｡

 Autocorrelation

functions of time-series Ｒt。and Ru

for

fluctuation

of vertical wind

component

゛´ and

for that of along-wind

component

u' and

cross-correlation

Ｒｔゐ旬ofが

and

■w' are illustrated in Fig. 6 （ａ）∼（ｅ）｡      ’

The

values of 1/？ｒ/1/昌ﾗ'2

and intentity of turbulence

along-wind

（ソぷＴ/ｙ）ａｎｄ vertical

（1/昌ﾜﾌIV)

are calculated

and

they

are listed in table 5. The

values

of 1/m'2/Vw'2

are

1.5 t0 4.4

and

they

show

that

the turbulence

at the height

of ｌ meter

above

the water

surface

is ｎｏt‘isotropic'｡

 ’ln the‘night,

the values

of 沢。:;keep

Ｏ｡1 t0 0. 4 and

the life time

of

eddies （７い（ａt

which

Ri。= 0) are 33 t0 43 seconds.

The

value

of To is ca.

16 seconds

and

that of゛沢ｗis

larger

than

that of Ru.

In the daytime,

Tq

of Ｒ,6 is almost

the same

as that of K。and

292

一 一

   高知大学学術研究報告  第21巻  自然科学  第15号

Table 5.

The value of l/７ｒ/ソこフＴａｎｄintensity,of turbulence

Date

Time

 ソ誤￣

(Crn.SeC￣1)

-1/ご「

(cm. sec

O

-(cm.

sec"')

-

Vu'-ソフ「

-ソ誤￣

-1/ご「

-∂7/∂zXlO*

(゜C cm-1)

Jul.

 28

 28

 29

 29

 29

17h

00m

21 00

 3 10

15 40

16 00

40

16

27

89

150

25

 5

18

24

34

234

 83

195

251

233

1.6

3.2

1.5

3.7

4.4

0.17

0.19

0.14

0.35

0.64

0.11

0.06

0.09

0.09

0.14

125

21

55

69

32

 Some

curves

Ru

and

ＲＩ。decrease

to negative

minimums

and

again

increase

to positive

maximums

with

the increase

of time-lag.

For

example、at

17 h

00 m

on Jul.

28、from

the

subsequent

decrease

of 7侃tｏ

ａ negative

minimum

at 17 second

and

increase

of it to ａ

positive ｍａχimum

at 34 second、it

is concluded

that

there is ａ pattern in the wind

tending

to

repeat

itself in ca. 34 seconds、which

at the

wind speed

(V=2.3

m/s)

prevailing

corresponds

to ca. 80 meters.

At

21 h、Ru

repeats itself in ca. 30 seconds

(which

corres-ponds

to ca.

25 meters)

and

at 15 h 40 m

on Jul.

29 R,、repeats

itself in ca. 62 seconds

 （ｏｒ

ca.

144 meters)

and

Rt。in ca.

80 seconds （ｏｒca.190

meters').

It is remarkable

that

the interval

of the repeat

is nearly

equal

to the period

of the alternation of warm

and

cold

air masses

at 220 cm

height （ｏｒ145 cm

height)｡

       5.

Conclusion

 The

study

gives

only

some

information

on

the fine stucture

of

the lowest

atmosphere

touching

the water

surface of ａ lake

of ａ dam

in summer.

The

chief points of

contribution

are as follows :

 (1)

The

minimum

temperature

appears

at 30 cm

height

and inversion

layer ｅχists above

it in the night.

Convection

takes

place in

the lowest

vinstable layer

under

30 cm

height、

but in the stable layer

of temperature inversion

above

it、turbulent

motion

is very

weak.

In

the daytime、the

temperature

of the

air is higher

than

that

of the water

surface

and

alternation

of warm

and

cold air masses、

takes

place

not only in

the lower

layer

but also

in the upper

layer.

 (2)

Cross･correlation

function

of the fluctuations

of

the temperatures at

two

heights in

the strong stable

layer

under

the top

of

the inversion

layer is very

small、but

it shows

large

value in the weak

stable layer

above

it.

 （3）The

life time

of eddy

of the fluctuations of vertical component

of the wind

velocity

is larger

than

th､at of the fluctuations of along･wind

component

of the wind

velocity.

 (4)

Some

curves

of autocorrelation

functions

decrease

to negative

minimums

and

again

increase

to positive maximums

with

increase

of time-lag、 and

there is ａ pattern tending

to

repeat itself in

a time

interval.

It is remarkable

that the interval of

the repeat is nearly

equal

to the period

of the alternation

of warm

and

cold

air masses

at 220 cm

height.

 (5)

Some

data

about

the

amount

of evaporation

and

Austausch

coefEcient

and

eddy

Fine Structure of the Bottom Layer of the Atmosphere

on the Water SurfaceCH. ueta) 29ろ

 The numerical calculationswere performed with the use of FACOM

270-20 Computer

at the Computation Center of Kochi University.

      Acknowledgments

 The

author

wishes

to express

his hearty thanks

to Ｍ. Hamada

and ｌ. Nagao、the

students of Kochi

University、for

their valuable assistance in the observation. This work

was partly supported by the Science Research

Fund

granted by

the Education

Ministry.

       References

1). H. Ueta: Study

on the Quantitative Determination of Eddy

Exchange

Coefficient.Research Reports

 of the Kochi

Univ.

Vol.

7, No.

7, 1958.       '

2). P. A.

Sheppard

and Ｍ. K.

Elneser:On

the Direct Measurement

of Humidity

Miχing

Ratio

 and its Fluctuations. Q.

J. of Royal Met.

Soc. 1951.

剛?ｊｊｊ゛ｓ

t ･ l ヽ ･ t ヽ ｊ ヽ ４ ●   ● t - o r o o j C / 1 t t ^ ･ ､ Ｊ   ・ ヽ 3 1 ヽ j C 一 八 ｊ １ ４ ０ ヽ ｏ α ） -  ∼ t ヽ ） I ― ■ e n J ^ ●   ●   ● S 3 e 心 つ -６ Ｊ t s J   Ｉ   r o r v J Ｓ ｊ ･ ( ⊃ Ｑ Ｉ ふ ｔ ､ ｙ ●   ・   ●   ● ｌ − ︱ −   ２ ２ . ０   ２ ４ . ８   ２ ５ . 0 1 1 . ８ ﾄ ｰ ｂ ､ ） ６ Ｊ り 1 l 心 心 ， l ヽ Ｊ ｂ ･ ） Ｕ １ ４ ０ α ） -t ヽ Ｊ -t ヽ Ｊ Ｑ １ ４ ●   ● ｏ ∽ -t o t ヽ ） り １ ･ ｐ -S 3 - - ､ l 心 -ﾄ ､ 3 ヽ ､ ４ ふ -r 心 ∼ ａ

、l-・ ｏ １

４０-り、。1

4ol・

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９．・ ・ ・

ｏいｏ□いｏﾄ￣‘

ＮバＱ ６ハＪ Ｎ）

芦:ヽ゜On

OS

OO

○い○㎝つＳ）

６ハＱ ｂ､にＱ fO

？7ヽ゜On

CT^

OO

t 心 . C X ン ６ Ｊ ∞ t o ∼ ａ t o ∼ ａ l ヽ ） l ヽ ） ロ ヽ り １ ●   ¶ ｏ ヽ Ｃ Ｘ ） Ｎ ） O N C O ひ 1 ← 4 1 ､ Ｊ ’ ∞ ヽ ､ I C ） -← つ 6 . ） ’ つ ･ ヽ J > C a > Ｎ ３ ゛ ← t o ﾄ ｰ ‘ ｀ ６ ｊ 口 − ･ ･ ６ ｊ ６ Ｊ t o ← Ｃ ヽ o r o ｀   Ｗ < z > < z > -← ｏ い ､ ） ・   Ｃ A 5 t 心 α Ｄ ト ｰ ゛ （ ｙ

  TH5

  ＾２２０

  w

  Ｔ'u5

W'Ｔ'ｕs

ぶ ● ， ふ つ C あ ｊ   ｌ ｀   Ｃ ） ｏ い ヽ ０ 一 一 ｔ 、 、 １ ‘   つ 心 ゜ ふ 口 C ･ J （ 卜 ６ Ｊ ∞ （ ｙD O し ヽ ５ １ ヽ ） o o o ヽ ６ ､ ） ヽ ､ ｺ

リ

･ ・ l ヽ J Q ヽ Ｃ Ｘ ） ●   ● ６ Ｊ C n

w=ｖ

ｕ=ｖ

t N > Ｏ Ｄ ← “   ４ ）       ｜ Ｓ い Ｊ     ふ ･ Ｃ 卜 O O C O v O ・   ・   ← ・ ( . J - t * ― - t b t t > -t v J i ○ へ t ヽ h t t ｐ : ／ / ｗ ｗ ｗ . ．   ・   r . 1 ふ ←

｡ ｜

oo

to

← 卜   ｜ ４

-トーｔ

s一．ヌし９しO

,j:>.O^ヽａＯＯ__

 ，ｌ         ｌ

 ２８.1

 12.６

 -０.1

11.２６

 ｗふ

１Ｐ︷

−Ｐ鴎

← あ ← ← ● e 心 ∞ ← -l 心 ∞

 路旨

︲心心

ＩＰ︸

 Ｐ心

  ２ ８ .   １ -２ ２ . ２ -０ . 1   2 . ２ ２ 卜 ● ６ Ｊ 口

←

心

９ ﾄ ｰ ｀   ｌ つ ド ー ゛ 心 t ヽ ） l ヽ J I ヽ Ｊ Ｃ ヽ ｏ ヽ Ｃ Ｘ ） ●   ●   ● Ｋ ） C T ^ t 心 < D ^ t o t 心 ｏ ヽ Ｃ Ｏ ●   ● ６ Ｊ ふ -t ヽ ｏ  t ｏ ｏ ヽ ∽ C 。 ｊ O J １ Ｑ ン 6 ､ ） Ｃ ｡ j

−？゜

  ２

 昆’

 ほ‘

 ま’

・ ヽ ） t ヽ . ･ l ヽ ･ t s 3 C X ） ロ ヽ Ｃ ヽ Ｑ ⊃ ･ Ｓ − -b ､ ） Ｃ べ ） t 寸 α ）       ６ Ｊ ４ α ⊃ つ O J t o t ヽ ｈ t ｔ ｐ : ／ / ｗ w ｗ . ●   ●   ● り l t ･ ４ 一 一 Ｑ Ｑ Ｉ ヽ ） ロ ヽ ｏ ヽ α ］ ●   ●   ● ･ ヽ ５ ０ ヽ l ･ ４ つ つ 卜 ヽ ) ( カ

昆に

Ｉ﹁沁

- Ｑ ヽ 3 O O l 心 （ ㎝ ∼ ､ ｌ -t S J c r ≪ ６ Ｊ く ㎝ l 心 -Ｓ ） □ N Ｑ Ｉ ヽ ｊ Ｏ ヽ ロ ヽ l ヽ J I ヽ ） Ｃ ヽ Ｃ ヽ ●   ● ６ Ｊ ( Ｘ ) ６ Ｊ Ｃ Ｏ t ヽ ａ ‘   ∼ ａ C O Ｃ Ｘ ） I Ｑ ｈ t ｔ ｐ ： / ／ ｗ ｗ ｗ . ． ∽ ●   ●   ■   Ｉ   ● ← ４ ⊃ ト ー ゛ c n i v j I > O t o C O α ） ひ ひ α ） ●   ●   ●   ● l ･ ヽ ヽ l t ヽ ） t Ｑ -ｌ ､ ） Ｑ t s J t o O O C 7 ヽ ｏ ヽ o o ●   ・ ・   ●   ●   ¶   ４ Ｑ Ｑ ｈ t ｔ ｐ : ／ ／ ｗ ｗ ｗ . . ． . ． . ． . ． . ．   > C k t o O J t o t o ｏ ヽ - o o o ロ ヽ ｏ ヽ C X ） ●   ・   ●   ●   丿   ● に ４ （ Ｘ り e 。       -  ４ ｈ t t ｐ : ／ ／ ｗ ｗ w ． ひ ∽ ひ ひ α ） ●   ・   ●   ●   Ｉ   ● ・ ■ J >C Z > C ^ C K コ ４ t ・ -  , ａ ･ O J C O t s S t > J ^ O J O O ヽ コ ロ ヽ （ Ｘ ） ・   ●   ●   ●   ●   ●

1２５.４

  ０.７

−17.7!

C ／ １ l 心 N ） ふ , ａ -ふ -C J 1 つ Ｃ ） つ つ 口 ← Ｆ ２   １ ぶ t o α 3 ６ Ｊ 口 t n （ ｙ -  1 心 ● ふ 心 ･ -  １ り 1 e n I > O r N > D O t o （ Ｘ ） ヽ a O ヽ α ） ●   ●   ●   ● ｂ ､ ) 心 ( つ -Ｎ ) ( カ ふ ６ Ｊ Ｎ ） ∼ ａ C n -ｔ 心 ∼ ａ t ヽ Ｊ ｔ ヽ - ） o o c r ヽ ・   ● e n o o 一 一 e ヽ J I ヽ ） （ カ ロ ヽ ４ ･ - u - i -l ヽ j e ヽ ｊ o o o ヽ t o ∞ ６ Ｊ ( Ｘ ) N 3 C μ C O Ｃ へ Q ｔ ヽ ） α コ ロ ヽ ●   ● ω り 1 t 、 Ｊ t ヽ ・ Ｃ い Ｘ ］ Ｏ t ヽ ａ -r ヽ j l ヽ Ｊ ヽ 3 C カ o o t o -t ヽ J e ヽ Ｊ ヽ ａ o o ●   ● Ｑ ⊃ Ｑ -t ヽ ・ -t ヽ ａ ヽ ４ Ｃ Ｏ − l ヽ Ｊ 一 一 ･ ｔ ヽ ３ Ｑ Ｏ ヽ α ） t o Ｏ N l 心 O N ６ ､ ） c r ＼ t o Ｑ ⊃ C > J -６ Ｊ ∞ t 口 o o ← ４ ← ｀ t * i I 心 ∞ ふ

−？﹁

︲心心

 ︲Ｐ︸

 ９ａ

← ゝ Ｏ

Ｚ Ｉ

e n Ｑ t 口 ∼ ａ ト Ｊ -  ｌ t o C O ふ -  l c 4 3 1 ､ ） ６ Ｊ N ） ６ Ｊ ( Ｘ ) 4 ， Ｃ ･ 5 C J 1 9 ｀ ２ ｜ 刄 O J α ） C . J ← l 心 口     ふｰ -い ’ ４ ４ へ ← ｀     し Ｊ ･ ヽ ヽ ･ ∽ ← ゛ １ l 心 ← ● e 心 − ド ー 4 L n （ ｙ ｜

。 ｜

§じ;

-e､。1

呂こ

ｰ

。。｜

t > J １ ← C O 心 ， t o つ 心 ， T ａ ｂ ｌ ｅ   ６ .         Ｔ ｈ ｅ   ｍ ｅ ａ ｎ   ｖ a l ｕ ｅ ｓ   ｏ ｆ   ｔ ｈ ｅ   ｅ ｌ ｅ ｍ ｅ ｎ t ｓ

fｏｒ ｅｖｅｒｙ ｓｅｃｏｎｄ ｏｎ Ｊｕl.

 ２８｡

  17 ｈ ００ mI∼日・