Report

of

the

National

ResearchCenterfor

DisasterPrevention，No，5，March1971

551，579．1：551，577．21：551，501．7／．8

A

SystemComposedofa

Cemtm1Computer汕dRadarsfor

Measuring

Weather

Area1Precipitatio皿

By

M．Sugawara，Y．Katsuyama

andK．OhmuraM〃o舳1肋∫〃κ乃Cθ〃θγ∫oγ1泌α∫〃P閉θ〃ゴo刎，τo妙o

Abstmct
The

only

way

to

measure

the

areal

precipitation

direct1y

atpresent

istO

use the weather radar． Unfortunately，however，the re1ation between radar echo
and precipitation▽aries with conditions so much that it is di冊cu1t to use theradar as rain gauge．0ne of the ways to overcome this di冊cu1ty is to ca1ibrate
the measurement of radar by rainfa11telemeters．For this purpose，it is possi−
b1e to construct a system composed of a central computer，weather radars andrainfal1telemeters，but there arise other di伍cu1ties，because the transmissionof the high−frequency radar signa1s necessitates a very expensive communicatiOnsystem and the data processing of the computer becomes di冊cult．In consider・

ation

of

tion

the

very

low

of

the

radar

proposedanddiscussed

frequencyofintegration

of

the

site

to cut o耐its high−frequency components．
With gate circuits and integrators it is possible

toconstmct

vice

which

on

polar

coordinate

order

to

the

is

gives16ca1averages

necessarytorotate

the

of

to

radar

antemasignals

slow1yinsuperHuous，andcommunica・

theregardsomewhat

a

be

with

seems

hydrologica1phenomena，suchtoItsigna1itse1f

radar

make

an

an

idea

is

signa1attheEanalogde−meshes．

communication

density1ow，and thus the data can be transmitted by usual telephone1ine at
low cost．The processing has another important merit in making the informa−tion density1ow，so that many radars can be controned with one centra1com−
puter．In this system the radars need not be powerful and of1ong range．The
aimed region can be covered with circles of radar ranges，so as to avoid theinterruption of mountains．The results of experiment show that this system is
promising．

1．Pu叩ose
1．1

and011tlim

of

0ne

most

of

the

the

Systemimportantanddi冊cu1t

problems

in

water

ba1anceisthemeasurement of area1precipitation．We can on1y estimate it from a set of rain
gauges，and as we cannot measure direct1y area1precipitation itse1f，the errorof estimated area1precipitation must be a theoretical one，that is，the error isderivedfrom some hypotheses，and camot be evident1y proved．
1．2We consider that the only way of measuri㎎the area1precipitation
directly at present is to use the weather radar．Unfortunate1y，however，there1ation between the intensities of radar echo and precipitation varies with con−ditions so much that it is very di冊cu1t to use the radar for rain gauge．One of

the ways to overcome this di蘭cu1ty is to ca1ibrate the measurements of radarby rainfal1te1emeters．For this purpose，we can use the centra1computer con−nected with the radar and rainfa11te1emeters．Moreover，with the use of a cen・1

Reportofthe

National

ResearchCenterfor

DisasterPrevention，No． 5，March1971

tra1computer we can construct a system for iood forecasting，heavy rain warn−
ing，dam−gate contro1，etc．（M．Sugawaraθ6αZ．，1968；M．Sugawara，1968）．
1．3 There1ies in communication another di伍cu1ty that the radar signa1re−quires very high frequencies，and so the communication system becomes expen−
sive and moreover the data processing of the centra1computer becomes di冊cu1t．

As the hydro1ogica1phenomena are of very1ow frequency，there must be somesuperiuousness to communicate radar signa1itse1f．And we have got an idea of
radar

site

components（M．Sugawara，1968；E．Kess1er

integrating

the

radar

signa1at

the

and

by

cutting

off

its

high

frequency

K．E．Wi1k，1968）．

1．4 If we integrate the radar signa1at each of sequential intervals with theuse of gate circuits and integrators for time duration〃，setting the radar an−tema in a ixed direction，we obtain the loca1integra1of radar echo in time andspace，wheretheintegra1domains

are

as

一口・雫工口㍑0㌶㌔ll；1．r㍑i楓i1鴛
〃

〃is

the

width
1．5

Fig．1．

antenna

of
By

radar

beam．

stepwiserotationwithrotatingofthe

ang1e〃，after

radar

ix−

ing it for time interval〃，we can get the1oca1integra1of radar echo on polar
coordinate meshes．
But the stepwise rotation is not essentia1，and we may rotate the antenna
continuous1y at a constant speed．
1．6 It is important to rotate

the antenna s1ow1y，and then we can set thetime interva1〃，which causes the fo11owing1arge merits：
1） The noises with cance1each other during the integration interva1〃，sothat the noise1eve1becomes1ower by inverse proportion to the square root of〃．
2）The communication density becomes lower by inverse proportion to ．

1ong

1．7 For examp1e，1et∠θbe3o and〃be1second，then the rotation period
is2minutes．If we divide the radar range into30inter▽a1s，and as each of
integra1va1ues can be expressed in7bits，we can transmit the obtained infor−
mations with210bits per second or it may be su冊cient with300bits per second
even when other necessary signa1s are inc1uded．Therefore，it is easy to com−municate with the usua1te1ephone1ine at1ow cost．
1．8 As the result of low communication density，there arises the possibi1ityof contro11ing many radars with one central computer．In this system the radars
need not have1ong ranges，because our purpose is to cover the area with a setof radar ranges over1apping at their peripheries（M．Sugawara，1969a and1969b）．
1．9

The use of a set of short−range radars has severa1merits as fo11ows：
1） The radars need not be powerfu1because of their short range．
2）The interruption by high mountains can be avoided by appropriate dis−tributionofradars．

3）An inadequate height of radar beam，which is caused by the curvatureof the g1obe or by the e1evation ang1e of radar antenna，does not occur in the
cases

of

short−range

4）The
the

radar

radar

antennaradars．

beam
needwidths

not

be

so

need

not

be

so

sma11because

of

short

range，andgreat．

1．10 Although there may be a prob1em of cost in setting up a system ofradar net，we consider that such system is desirab1e because the communication
system is not expensive，and the radars also are not so expensive from the fo1一
一

2

一

A

System10WingComposedaCentra1Computer

not

be

and

Weather

Radars＿M．Sugawara勿α2．

of

their

short

are

the

integrated

reaSOnS：

1）

Radars

2）As

need

the

fina1data

have

powerfu1because

range．

fromtheradarsotherduringtheintegration．Therefore，therather1arge

noises．

wi11cance1each
mayof

va1ue，theradarnoisesapparatus

3）Because of the short range，the radar beam widths need not be so sma11．
4）As we use the data from radarsl after calibration with rainfa11te1emeters，

the radar apparatus may have some drift or nuctuations of low cyc1es whose
periods are much1onger than the time interva1of ca1ibration．
5）Each apparatus of the system，such as radars，integrators，etc．，must be
made by the same speci丘cations，and the production cost per unit may become
1OWer．

2．Resu1ts

of

O11r

Experiments

2．1 The irst tria1was to comect the computer with the radar directly．
Using the ana1og−to−digita1converter，it was tried to convert the radar signa1
it。。1fi・t・digit・f…bt・i・i㎎th・di・t・ib・ti…f・・d・…h・i・t…ity・・p・1・・
coordinate meshes in digita1forms．Then we can transform them into the pre−cipitation

with

the

rain−

fa11te1emeters（M．Sugawara功αZ．，1968≡M．Sugawara，1968）．After

distribution

on

po1ar

coordinate

meshesafter

ca1ibration

some

suc−

cessfu1experiments，a conc1usion that it wou1d be better to integrate the radar
signa1at the radar site before the transmission to computer was obtained，and
an apparatus was made for the test of that possibi1ity（M．Sugawara，1968）．
2．2

The

1）The

radar

radar

which

was

was

made

used

for

our

severa1year

experiment

before

and

had

was

many

too

weak

o1d

for

points．

recon・

StruCtiOn．

2）The

wave1ength

1onger
our

radar

was

made

is3cm，being

at

not

for

the

detection

suitab1e

irst

for

rainfal1measurementsofartiicia1rainfal1and

antenna

which

its

requirewave1engths．

3）It

is

importantradarantematorotatetheradarrotates10times

perminute．

s1ow1yforourpurpose，but

4）Our radar is situated at the center of a sma11p1ain surrounded by moun−tains in a11directions as shown in Fig．2．It is the worst situation for rainfa11

meaSurement．

5）In our new system with integrators，the noise leve1becomes1ow by in−tegration，but our radar apparatus is made to cut off the radar signa1under

origina1noise1eve1．Therefore，we cannot
may become usefu1in our new system．
2．3

The

out1ineoftheana1ogutilizedevices

with

the

gates

and

weak

radar

integrators

signa1which
is

as

fo1−

1OWS：

which
not

1）The radar range of60km is divided into20sections by gate circuits
open for20μsec successive1y．The irst section nearest to the radar isusedbecause

2）

Each

of

of

noises．

disso1ved

radar signa1s through the gates is integrated by the
incomp1ete integrator（the1inear fi1ter of first−degree1ag system）of time con−stant of0．1second，during which the radar antema rotates by6．in azimuth．
3）Each integrator is samp1ed and he1d simu1taneous1y at the interva1of0．1
second，in other words at the interva1of6o in azimutha1ang1e。
一3

一Reportofthe

Nationa1Research

RoingoUge■

Centerfor．

oDisasterPrevention，No．5，March1971■

CChousutOge
・KKOkeZO㎞yOmO

ノ

ZO060，o

oo

ム0Km

も

1739

白．

ト

▲

砕

坂

20K

、
■

o

o

、

設

C

●

172

o

▲

o

200

oo
へ

伽一

■

〃
■

思

θ

o

●

200

o

『

♂罵

o

o

■

q

600

■

o

■

、

●
■

600
じ

●

o、

1∞0

■

＾

1700

0﹄

か
、

●

ooo

＼
＼

o

ルロ

心

■

N

η
η

Fig．2．

4）The integrated radar signa1s heIdtransmission．In our case they are recorded

in ana1og memories are sent out forin a magnetic tape recorder for the

reproduction at the computer．
5）Thus，we can obtain the1oca1integral of radar signa1s on po1ar coordi−

natemeshes，where〃＝3km

and∠θ＝6。．Sma11er

meshesof〃＝1．5to2km

and〃＝2．to3o were wanted，but we cou1d not get them because of expense．
2．4 The data recorded on ana1og magnetic tapes are reproduced and tumed
into digits which are summed up on po1ar coordinate meshes for some time in−terva1s，usua11y of ten minutes．Then we get a map of radar echo distribution
indigita1forms．
2．5 Distribution of radar echo intensity is transformed into rainfa11distribu−
tion in a digita1computer．
2．5．1 The丘rst correction is the compensation of radar echo intensity weak−ened by mountains．We assume that the effect of mountain shadow decreases
exponentia11y with distance．Therefore，we mu1tip1y the echo density by thecompensation

factor．
λ＝1＋oΣ眺exp｛一α（プー71）｝，γ包くγ

whereαisadecreasingcoe茄cient，6a

constant，卵the−4

一intensityofgroundecho

A

Systema

mountainofComposedofawhich1ies

Centra1Computer

at

the

and

Weatherdistanceれfrom

Radars＿M．Sugawaraθ〜1、

theradar，and7thedistanceof the point which1ies behind the mountain．The constantsαand o are so deter−
mined by tria1s as to give the good自na1resu1ts．
The corrected echo intensity on the mesh domain where the ground echo
exists must be corrected again by e1iminating the ground echo．
2．5．2 Then the corrected radar echo must be tumed into rainfa11．The re−1ation between rainfa11intensity R（γ）and radar echo intensity P（κ）is given as

1…（1）一／［1…（・）・・1・・1・州／1…／・1…（・）／…〃1・

where7isthem

thedistance

from

the

case

of

neg1igib1e

in

our

2．5．3

our

systemIn

weradar，β，A，B，C，D
the

use

radar

of3−cmthe1ntegra11og

constants，and

D

amOng

wave1ength．

P（γ）1nsteadof1og

P（7），so

there

appears a prob1em of puttmg P（7）and R（プ）1nstead of P（プ）and R（ヅ）m theabove radar equation，because both of the1ogarithmic and exponentia1functionsare

not1inear．
There exists

a1so

a

more

di冊cu1t

prob1eminoursystem

in

which

the

weak

radar signals be1ow the noise1eve1are cut off previously．If the weak radar
signa1is nuctuating above and be1ow the noise1eve1during the integration in−terva1，the integra1va1ue with the cut−off signa1must become greater than the
integra1of origina1signa1． Even the noise itse1f cannot cance1each other in
this

case．

Therefore，if we put the integra1of the cut−off signa1into the radar equa−tion without correction，we wi11get far greater va1ues than the actua1when thesigna1s are weak and the distance is1arge or the damping effect of the rain is
1arge．

2．5．4

The

correction

for

the

bias

of

this

type

must

be

statistica1，and

itisrather reasonab1e to add the statistica1correction to the radar equation which
has also a statistica1origin in its main part．As we use the radar equation on
po1ar coordinate meshes，we put integerタinstead of distanceκ，where6corre−
sponds to the6−th radia1interva1． Thus the radar equation tums into the fo1−
1owingform，where

Po

is

the

noise1eve1．

1…（1）一古［1・・つ1）・λ（1・・1・・）・・昌／鮒1

As

this

formulagives

much1arger

rainfa11than

actua1when

the

radar

signa1

P（ゴ）is smal1and the second and third terms of the formu1a are1arge，we must
mu1tip1y correction factors F and G to the second and third terms，respectively．

1…（1）一古［1・・争；）・阯（1・・1・・）…昌鮒1

The

correction

factors

・一い

are

given

as

0g争…）十ん卵）戸5：∵

Reportofthe

National

ResearchCenter。bse「ved
50 mm hfor

DisasterPrevention，No． 5，March1971

・一ド）10gP（ク）

㌫二1）

●

■

〃）＝1／（α十わゴ），

●

20

●

●

whereん，α，ろare■constants．Mean−

●
●

10

ing

●

●

■■

●●

●

●

5

●

■

●

一

■■

一

●

讐

■

●

・

the

function1（ゴ）may

ab1y

a

simplearithmic

●

The

forms

correction●＾

factorsastosu1ts，but

2

5

Fig．3．BeforeCol⊂ulαted

are

of

the

determined

obtainbygood

ina1re−

10

20

10

20
5r

50mm

h

2．5．5

calibration（Kakezakoyama）．

Observed

0neoftainedbyremainsti11many

1a

shown

is

the

distancetheresu1ts

ob−

above

corrected

formu−

the
in

the

rainfa11va1ues

mm h
mmlh

there

ambiguities．

between50）．

constants●Col⊂u一1and一trials，so

2

prob−

of1og−

function（〃1ogク十B

●

●

be

approximation

●

■

●

of

Fig．3．The

observed

corre1ation

andbecomesestimated

bad，whi1e

from

the

radar

increases．

Without

the

above

correction，how−ever，thereisscarce1yatspots．

●
■

20

●

tion

distant

any

corre1a−●

between

ra−

dar

2．5．6

signa1andprecipitation

may

iuctuatewith

part1y●■The

re1ation

●

10

■

●

●

●■

一

■

・・

5

■

●

●

・

・

●

1l

．．

2

variation●●■

drops，and

●一

…

●

乏

5

Fig．4．After

0

10

20

Co［culαted

that

50mmlh

be

20

50

There

may

be

these

corrections

a1so

local
we

part1y

of

These

from

the

f1uctuationsofthe趾ctua−ofradar，etc．

can

be

corrected

thevariestime．These

withdetermined

by

the

rain

from

power

mu1tip1ying

derivedcalibration（Kakezakoyama）．

After

can

time

distribution

tion

by

Co［culo1ofcorrection

factorva1uescomparingrainfa11with

the

the

observa−tiOn．

iuctuation

which

get

betters1ight1ycanbecorrected

by1oca1factor．

asin

resu1ts

shown

Fig．4．

2．5．7More important method to obtain better resu1ts must be the repeatedcalibration with short time intervals．For examp1e，if we repeat the ca1ibration
at15−minute interva1s，then we get hour1y precipitation as the sum of four ca1i−
brated va1ues．We wi11get better results than in the case when we ca1ibrate
one

time

per

hour．

Unfortunately

we

can

use

hour1yprecipitation

data

on1y，and

therefore，in−stead of using the precipitation data of15mimtes，we sum up the successive
four ca1ibrated hour1y data and compare the sum with the observed precipita−
tion
we

of

four

hours．The

consider

them

2．5．8

0ne

from

the

radar

to

be

reasondata

resu1tsshow

not

su価cient

why

the

is

the

betterfor

corre1ation

estimate

corre1ation

as

shown

in

Fig．5，but

use．

of

is

not

good

is

that

area1precipitation

−6一

on

the

va1ue

po1ar

derivedcooridinate

A

SystemComposedofaCentra1Computer

andObserved

20

mmlh
1●

●●■

10

Radars＿M． Sugawara勿α1．

Weathermeshdomains

from

the

and

va1ue

cipitation

which

by

gauge

■

a

rain

is

of

di伍erent

point

is
at

a

point・

Unfortunately

measurethepre−measuredwecannotarea1precipita−tion direct1y to compare withthe radar data．
Instead ofarea1precipitation we can use

2

the

sum

of

point

precipitationsof severa1 rain gauges， andthe sum is compared with the
●●●

O．5

sum

of

●●●

in

Cα1cu一αted
Cdcu

0．5

Fig． 5

1

2

Average

5

10

2．6

20

Thoughtheina1re−su1ts shown in Fig．6are notsatisfactory，it may be said

for4hours（Kakezakoyama）．

that

Observed
20

va1uesFig．6．

mmlh

O．2

corresponding

derived from the radar data．
0ne of the resu1ts is shown

in

mmlh

our

methodisconsideration

conditionsofpromising，

of

our

many

bad

experiments．

10
11己efere11ces

●

・・
■

1）Sugawara，M．，Katsuyama，Y．
andthe

Yasosl］ima，H．（1968）：

possibi1ity

processing

tion

of

of

echoesOntherea1−timeradar

precipita・bydigita1computer．

Rψ0〃ψ伽肋ガ0〃α1肋θα肋■C刎伽／oプ肋αs伽〃ωθ〃o〃，・■●

No．1，1−13．

（InJapanese）．
●

0n

methodofflood

forecasting

us−

a

ing

a

digitalcomputer

con・

with

weatherradar．

■●●

O．5

2）Sugawara，M．（1968）：
●●
●
o
．●
■

Col cu−ot ed
ColcL

0．2

＾

O．5

F

Fig． 6．Averageandfor4hours

o1

2
of

【

two

5

10

（

20 o

nectedmmlhaτ加σsθゲルα1oμ〃D妙壬α1Co刎ク〃〃∫

spots（Kakezakoyama

伽月タ〃olo馴，Vo1．

1，Pub1ication

Chausutoge）．

No．80，IASH，

161＿169．
3︶

Kess1er，E．and

Wi1k，K．E．（1968）：Radarmeasurementof

precipitationforhydrological4︶

purposes．肋ρoγねo〃W〃0／〃D〃oゾθc姑，No．5，WMO．

5︶

Sugawara，M．（1969a）： On a method of precipitation measurement by combining
radars and a computer． W1〃〃。Soク舳62，13，No．1，34−55。（In Japanese）

Sugawara，M．（1969b）：On

digita1processing舳∂Co〃701，8，No．12，129−136．

（In

of

radar

precipitation

weatherechoes．地αs〃θ榊〃Japanese）（Manuscript

7

received27March1970）

Reportofthe

Nationa1ResearchCenterfor

DisasterPrevention，No．5，March1971

多数のレーダと中央の計算機による地域雨量測定法

菅原正巳・勝山ヨシ子・大村一夫
国立防災科学技術セソター第3研究部
現在，地域雨量を直凄測定する唯一の方法はレーダ利用であろうが，困ったことに，レーダエコーの濃さと雨量強度との関係は，雨滴分布で左右される．それを，雨量テレメータの観測値で補正するために，

レーダ，テレメータ，計算機の組合せの方式がまず考えられた．そうするとレーダから計算機までの情柵伝送が問題になる．レーダ后号は非常な高周波で，そのf云送には費用がかかる．］方，大雨とか洪水は，

せいぜい15分単位ですむ程度のきわめて低周波現象である．それにメガヘルツ級のレーダ信号が必要であるとすれば，どこかにむだがあるに違いない．そこでレー列言号をレーダの所で積分することを考えた．

ゲート回路と積分回路からなるアナログ機構により，極座標メッシュ上で，レーダ信号の局所的平均値を作り，アナログホールドし，順次送り出していく．

この際，ア1／テナをゆっくり回転させれば，伝送密度を十分に落とすことができて，普通の電話線にのせることができる．伝送費用は安くなるし，積分によりレーダ信号中の雑音のレベルが落ちるから，レーダをあまり高級にしなくても，精度が得られる．したがって，多数レーダを配置し，それを中央の計算機で支配するシステムを組むことができる．

われわれが行なった実験では，既存の設備を使わざるを得なかったから，ア：／テナの回転速度を落とすこともできず，極座標メッシュも〃＝3km，〃＝6。とあまり小さくできなかったが，それにもかかわらず，昭和44年6月〜7月に行なった実験結果はかなり良好であった．
レーダ信号の区分的積分値は，現地（人吉）でデータレコーダにアナログ記録され，東京に持ち帰って
A−D変換され，計算機に入れられた．

概座標メッシュ上に数値化されたレーダ信号は，まずグラソドエコーの補正が施され，次に雨量に変換された．われわれのレーダでは，あるレベル以下のレーダ信号が切り拾ててあるが，それから生じたと思

われるかたよりが1このとき補正された．この補正をしても，結果（図3）はあまりよくない．そこで，各時間ごとに全地点に共通な補正係数，各地点ごとに全時問を通じて共通な補正係数を定めて，これを‡卦
けると，結果はいくらかよくなる（図4）．15分ごとに補正をすれば，結果はよくなると思われるが、その資料がないので，1時間ごとの補正をして，4時間の和にして比較したのが図5で，結果はかなりよくなる．元来，レーダで測る雨量は地域雨量であるから，これを地点雨量と比較するのが無理であろう．そこでf可地点かの合言十にして比較したものが図6で，結果はさらによくなる．

これらの点からみて，レーダ，テレメータ，計算機の組合せ方式は，十分有望であると思われる．

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