
J. Jpn. Soc. Soil Phys.
BC tNo. 3+, p. -3 .1 ,**,





*ῌ*ῌ*ῌ *Soil water movement under micro-irrigation using a perforated tube
Shinpei NAKAGAWA*, Katsuyuki SOMA*, Jun’ichi KASHIWAGI* and Shinji SUZUKI**Graduate School of Agriculture, Hokkaido University
Abstract
E#ects of di#erent initial moisture conditions on the formation of wetted soil volume under
micro-irrigation were investigated in a layered soil having a plow layer and a subsoil layer withmacropores.

Water was applied at a constant rate of +** cm- min-+ for 1,* minutes using aperforated tube covered with vinyl mulch. Water application e$ciency was also evaluated fromsoil water storage and inﬁltration loss caused by bypass ﬂow
In the case of initially dry condition, the wetting front was spread in an elliptical shape with the
major axis in the downward direction. In the case of wet condition, however, the horizontal
boundary between the plow layer having high saturated hydraulic conductivity and the subsoil
layer having low one a#ected inﬁltration. Water reached to the boundary ﬂowed horizontally andinﬁltrated into the plow layer from the bottom. The amount of water inﬁltrated vertically was
more than that of horizontally inﬁltration in an imaginary main root zone. Inﬁltration loss beyond
the root zone due to bypass ﬂow was accounted for 23῍ in dry condition and 1/῍ in wet condition
for 1,* min respectively.

After 1* min irrigation, the rate of storage was unchanged in both thedry and the wet conditions. In view of water application e$ciency, irrigation period exceedingabout 1* minutes is inadequate
Key words : Micro irrigation, Perforated tube ,Wetted soil volume, Bypass ﬂow, Water application
e$ciency.: efc  hi+BC jk ;<K+    lmn2o+&pq! rstu"vwt x῍ 



.

: Bresler, et al =+31+@\] "!  "#$% &'()*+%, yz! - yz % {|Kefc "#$},! ~&'(,-.)*&/01234! 5 6

}f+ K#3:  ! OP- >?  +7- 89&+-: )* ;<K.$,3+,$.: ,Q,! o2=! >?@ ABC;< =BDE0! FGBC%R YZ  >? [1-\] K,3_

@ H IJKLM$/012! /NAOP1! %&`+abq!  "->?&OP._

QRSTUMR2$.:-.: VWX YZ  >? [1.

GKc "-\] K^#3_ &`+ab: \] "

 ! G ¡A¢£&¤-)*

&w,$uq! ¥¡¦§u.$¨.R2$.:/0.$

Warrick, +31.@ Aefc

cdc

=Philip, +31+ ;=Brandt, et al., +31+ ;Lafolie, et al., +323 ; gR! +33,@ "#$cd12$K.3

© %ª"#$«%QR\]¬%/­&®: ¯ °* O±O±²!±YZ³ ´*0ῌ2/23 µ"¶· 3 ;¸ 3 ¹# : ῌ! ! )*! º»$! ῌ¼%

E+} d 3+ ¼ ¢,**,£

40

ῌ+Fig. +



a¹b^-ºG

»cQR+

Imaginary root zone at the experimental soil proﬁle.



Z[?4E+}> A#zlm     A=~> / Z@ -CD& Z[ E%+} !"

# $% & '+** cm- AB

FG  O  H } /* cm- AB ()*+,- ./!0 ~= , I<JEZ@  K

)*1 23 45

LK32.+ kPa OFG  B #67 8 9 :!;<+* cm B . cm I<JZ@  CD& Z[

=>?@  A&",-B 

=GK 0.1 kPa OICD&

%C D>-E FGHI #Z[ '"  CD ICD& Z[     '" 45  JK 

E DS#$ D   UM!)*+,-!LMN>?"  O (H } & Z[)*N=L

PQR+=S#I$8%$TU&'V WXY8

!0! v O DP

:(JKE MN>D?"Z,    ,+ 

N> '"  O  H }Z[Q F{R1

Z[)\* ])$^+_`aGbc]def

$K¤ TM¥

S ( -¡ ¢+321£E X U¦M'" ,, 

#$§)*+,-^+^ghi,4-jklm'" 0¨ I#© VWX§MN ª

E./0123X+ 4n8op56¨#«¬G­YW®¯Z°

q Ap+ Ap, 8 ,A =- 7r8s jk±[²³´I# VW0 µ + ¶lm9: t=udGv w; Z[Z[dGv xyz{fv<=A|B >61/ cm I#]^YW , #!_ ,* cm ³´VW'" 

0 Z[I#!¸%E`^#·7\!

JK : F ¼,Y )ῌ+Table +
Depth

HorizonTexture

cm
*ῌ+1
+1ῌ.*
.*ῌ/3
/3ῌ10

st+N67

Soil physical properties at experimental ﬁeld

cm cm

Dry bulk
densityg cmg-

Saturated hydraulicconductivity*
cm sg+

Unsaturated hydraulicconductivity at g,.3 kPa
cmg+*41*40*
*40*
*40*

*403
*4*+4*+4*3

340+*g-·,4*+*g+4.+*g-·+4++*g242+*g.·-4-+*g.4++*g.·04++*g.

+4-+*g/-41+*g1/4.+*g1
¸

ῌ,

H»¥

Porosity
-

Ap+
Ap,
,A
,AC

41

L
L
CL
SL

g-

* Geomean·standard deviation  -** cm 






  
 #$%&'( !")*+,-#$%.

/  0 + #$%&'(1! 23456789:;<  / ==>?@; ABC .* cm >C // cm 
DEFG#$%&'(HIJ K
E #$%&'(LGMAB -*cm :NOP/QR CS#$%&'( )*+,-#$%. / T)U$VWXF V(YZ[\G,]^/ _  AB[\ `ab!cFGde de"#$#^/ ;f + AB$
#5 /* cm- ming+ !Khij +** cm- ming+ 

Fig. ,

j k%L &l'mn*+ok% ,¹º

Water retention curves of the surface
soils.

p. Lhrg+ 5(9:GF?G qrst
+** cm-ming+ u0 Lh rg+v w:x!yKk%L

st+N673 + 1! MY z{ +** cm- ming+ deN| }JL s85.L" Y()234~FG*!" 1,*st9 / cm {)*+,-#$%.

5g.3.+kPa J);g..3 kPa 23J)L , *9: Ap+ =;;G{<5!y 01= 3.0+*g- cm sg+  =
x> L = Ap, ; ,A ¡K g..3 kPa +N,#-!

L5 {< ?%>¢@1 01

;ABx23J);G  J)= Ap, 5 +..+*g- ,A 5 2.2+*g. cm

st. J) 23J)stsg+ =A£¤9K 9B : X ¥¦§¨©

J)stABj{?@/4501K

AB Ap+ 4 / mm BC5ª«L w_GABde23 w 9 / cm  )*+,-#$%.

54g..3 kPa Kz5j

5´E9:

_0 , FµDG~FG Ap+ ¶ , ;;Gg32.+ kPa _F- 
-++* mm D%BCx¬_:GF _ Ap, ,A ­®¯ *° ;±²9:>Cm³J

#5!y Hg..3 kPa !yF
#$%.

)*+,-

-!{#5F;5I Ap,,,A >¢7J1 +N,#Lg..3

YZ ¹῎º » 3+ ¼ ,**,

42kPa 





32.+ kPa



ῑ Ap+  *.+* Ap, *.*0 ,A  *.*. cm- cm - UVW +/  Ap+  Ap, 



[\]^

_

x%789: +/ yz

x%{C_`ahvw l |} Ap+ -, 

 !"#$%&'( )*+,-./-&01234ST`ahvw c#def ge`a%BsS _`ah=>ῒ?@%ABC DE  !"#$FGH

B1

'



4IJ%KC 5678 L4MNC

O - %P ./QRST  5678
UVW +* X%YZ[\]^' c#defge`ah

78

i~E lEyz

 ge`a%=C_`ah 78 vw

 56789:;< +,* X%+\@ C%789:

D ῍<YZ Quu6? s%ῌ'_`a%b

%%H' U/I (ijkCB )*J L4MN%oBC QRST O l X 56784I1%ge`a%m. u6ST O / %P QRST 

no&p<qrsS< Utῐ4

1,* Xc#def .a YZ[\( )%ABC1c#d_`a% .* cm ῏EYZ[*23 ( )*23H'ῒ?4I1\]^789:CB< DE%=Cu6%<' lC 0* X% // cm+ kPa y-P Utῐ4n

 c#d῏E ( )* MN~
E'4I <'D%3 MNW '1¡<'D¢E H<£¤c#d_`a% +* cm ῏Ex]^ +/ cm %ABC¥1¦( )*23 4I L§%¨B
f1( )*2w .b ,* cm ῏E.c // cm ©ª23 c#d

 .* cm ῏E.dUtῐ41,* 

X1( )* 23«<
DE%=Cu6¬­  c#def /a %A®'( )*JQRST ¯°YZ[
ῌFig. -

5678 J O ¶·789:4I8¸x[H
Advance of wetting front (numbers in
the lines show minutes after the startof irrigation, dashed lines show theboundary of the horizons).

ῌ.
Fig. .

QRST

U/I

\( )*23 c#d +* cm ῏E


/b

 +2 X%YZ[\]^  / cm

A&±x]^

' +/ cm

lE²E



23 lEyX , `a 56³<'&p%78_`a%vw % ,. X%
 -/ cm %ABC´µJ O+,

&01¦(¶·4I min

Matric potential distributions at several times (mim) during the irrigation (dry condition).

12 : ¤¥stu23( ¼44$9 <% B

ῌ/Fig. />@NB4%Lº*%043

c*m»6º min

Matric potential distributions at several times (mim) during the irrigation (wet condition).



,* cm /c 

 +   I', < !E" +/ cm 

)( 

!"#$%&cm $() c .c $

Y && ,A I ,AC  /3.* cm  /d $'() Ap+ %

I&)qr

9:$" 0* 0

$*+, -0* -$./, kPa 0"123stu"'9 +* cm & 4%56+78&

cm +$(NB$;, % ,AC ${&

0!9:; <=>$9?@ABCD2
 %E FGHIJ9:$; KL%=MNB$OP QR; <S? TU ;%V WXH Y ?@KL$'()#$T
ZH[I

)( \]^_=MNB

9,>@NB#$TZ& `;a#I;b)c - [ 4%KL$'()>@N

B$de<?

  9 , f   +** cm-

min/+ ghi& OPhiTZ&

YIFj

<



,A I ,AC 2%#SV,* cm S? n [IopIFj

 =M

NBOP Ap+ I Ap, qrstu
cm k$

$'()dIve+*

& I|b  Ap,  +1.* cm 2%u&) ,A ${& Ap, I ,A Ib IFj

;b

>@








#& t ¡$1<%

¢%2£Y ¤¥stu$9b)hi%¦§¨2&u'©6(ª2Fjstu%#$ +* cm 

$«

¬

­®HI&) ¦§¨2stu %#$;b-/ cm #$ .* cm ¯+[ hiw  %lm$Z|;};bn >@NBc /b $'()  $%#$  $x(yz{6%f?

& ^_

" !$#b)%

 -/ cm  Ap, "%!

+  %NBI$$'()%#?@Y $'() Ap,&& ,AC %lm ,A 9,f([I  ? n--kI;[I c . / Ap+ I Ap,  %lm Ap, d:f(

$'()  //I~G

Y Ap,  [$&) >@NBOPyz'9?@%

)I&

c +
<*%V Darcy °$x:I&) ±²

³! . ¯+)¢%2 . <%1$9b)A  ¢%I%lmD($9, Ap, &)Fj OP A¢% +! +320 2£YOS? n  #9,2%#$PI,-$£Y[I| .´H . ¡$

& IFj¯+ ) P µz2¶/·I& ix '9 iy

Z|(Y $ =MNBOP Ap, I ,A  .* cm >@A $k;qr2;b

[

 ¸

X Y ·!¢%2Hc0a ) P $'¹ X ·$&)µ q #/0  » 3+ ¼ 3,**,444

ῌῌ0Fig. 0. P 

L

N

Matric potential gradient and axis of
coordinate at area P for a grid system.

 i iix cosqῌῌ11m$ jkl
#m 3F+F4

Fig. 1

Relationship between hydraulic conductivity and matric potential (Lines
indicate van Genuchten’s model).

ῌ

iy sinq   

  ! ῌ"! q #$

  % !  q !&'/01p1{1 ()*+,-./01

F 1m$!   5! 
pp
q tan2+3iyῌix42 ῍q῍῍,,5- q  q p 6% 7 8-9--1m$20.1 kPa ?

ῌ: ;<= , D 1 1m$ jk#m!

 ῍ "5- q ! ῌ ">  &'Y  5-1m$

5- ? . P @ABC 3D +, H+, H,, V+,V,4 ;EFGH I=' J;EF!GKLM Y N

GK X’ N!OP 3D 0 3b44

U

=I

=' _hijkl!no' 
1m$! van Genuchten 3+32*4 "U5+

+  Ap, 1!J=wx.!z{hijkl!a|¡¢6 8£s!D 2, 3 Y

X’ N

X NIEQ! q’, X’ N

 H+}H/, V+}V/ D + Y7 ¤¥/0

! ix’

 

1_7BC ¦hijkl§ix ix cosqR+cr7῎

iy sinqR1 !1,-  q’ ST7U5 ix’ &?

z{hijkl H+ ! ,.* ¨©

GK X’Y L

 3H/4 U5Xª«¬­ 5-

1¥® . P @A7BC

¯\lU56-/0 3H+4 hijkl¬­ IU ? !qGz{hij

V()BC

WX&' 
D + YZ[\]O^_`a= 
 . cd?-:.!Jefb
 gkl¯\lG 3V+4¯\lU51 1. /cm -. 3V,4 !Y  0* ¨©+°_I ¯\lU5-±= hijk

fhijkl! 1m$l¬­²?s®³I ¯\lU5 -/ cm 

U5no  p!EQqGr! * Q-´c 3V/4  1¥®qGpIUst -; Iuv wx.yz{hij

 D 3 µ¶_BC ¤¥1_kl| *}+2*~d  3*},1*~EQ§+chijkl7!Ys7 gf1m$ . cjk

|hijkl

 U5o  3H+, H,4 U5¹º¬­  +,* ¸I

1·²U5 ,* ¸ : ,- #P 4 1>XU

ῌ28&(#)*+



45

cAde hiTU

Fig. 2Matrix ﬂow passing the horizonal and vertical boundaries of the major root zone (drycondition).

Fig. 3Matrix ﬂow passing the horizonal and vertical boundaries of the major root zone (wetcondition).

ῌ38&(#)*+

  Ap+  Ap,

 

"#$% &'(#)*+

H-, H., H/ 
H, !

cAde x`TU/ _`ab klT4m% abno
?1>WX p4,- q V+  V, j.
r1>WXstu v64w%Q x,- ./01234 +/ cm 5678 V+, V,,`TUyz &{('(#V- 9:;<=/0 ,* >?4@A4BC4DE

9 A|RSTU4no+ 9A|4}~% FG78 V., V/ HIDE% JKL/ JKL/0@lT41>WX%QP v

0!56 V/ MN#OPQ 1* >?4



RSTU

4
V1>TU1>WXY3 Z [\ ]9 ^ - _`abcAde/0f/g4 hiTU 123j.3




)*=

 p4RSTU4&{(#)*+

123WX H, stu 6-. 

:;[\/0,- #PQ#yAB» C 3+ ¼ #,**,$46

῍ῌ,
Table ,

8Bn)¸@¹Hirizontal, vertical and total amount of water lost beyond the major zone

Initial moisture
condition

Applied
water
cm-

HI

VI

cm

cm

1,5***
1,5***

+
+52/,

+5/*2
052++

Dry
Wet

-

VIῌHI

S

-

Pm

cm

cm

05/21
35*.,

0-53*.
/.5,3/-+5/3+.

Pm/Applied
water

-

*.23
*.1/

HI ; Horizonal inﬁltration, VI ; Vertical inﬁltration, S ; Storage water, Pm ; Bypass ﬂow

 

  !" #+33.$ %& '()*+,-0.

/ 123' 456 78 3

29:;<()=>?@A38B()
*+,-C

.

IC

0/JK,L +* cm %

DE'F6 G ., /

9H +*

B

 MN-OPQCR/AS 4D3T<
K,L;<F ,* cm BUD123'V/6 ()*+,-C 0DE'78()*+,-F

0DE'/W

16 R;<XYZ%'F[\]'()
=>^/126 ;<_/12K,L/`]'aFb+* cm6 K,L/`]'a
Zb-/ cm6

ῌῌ+*Fig. +*

ZF .* cm c d14DCe*L!"fg] :AMN-OP
Q#hF$i%2 9 #G /b$6

%jkl

%/0º¦#h

Cumulative water storage of the major
root zone during the irrigation (solidline shows cumulative amount ofapplied water).

m'5Ce*L!l&]''(FE'V/6 n)CopqL!/e*L!*DE'/ 0/ MN-OPQc9

1  'jkCr+,5jk#12(c2i e*L!

6 /st

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. , ῌta6 e*L! 'n)6

QySzEpzPvzPhzPm

]' g1 ¡¢£¤DCῌ

VVD6 Q ;  #cm-$6 S ;%/0 #cm-$6¥<¦aC + cm- /=1 §AS

Ep ; {"| #cm-$6 P ; n) #cm-$ D6 1m}

  0/Jt;n>Fa 9

 v, h, m C~%%taopqL!6 J?¨123 4 32d1

aopqL!

ta/an)@C6 ¥<¦e*L! 'n).

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1,*

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CFA 6 ,QQ 9.2341'/3:©ªAS 6 1,*

23'V/6 51 6]'n)

*L! 'n)C¡¢05 23῍6 (:opqL!C Darcy r:/16 )05D 1/῍ J« 6 iqL726 826]'Fe*L!/12!¯1qL n)626]'qB 'e'¬/­®

G +* 8B/0#hg] 4°±

Li 672C82F

 1*+,.** cm,62F +,0** cm, DE' 6 /0CAS ¡¢0C 1*²³6 ¡¢ῌ()0/J´v

CµZ²³J¶·´v1

hi : NBC-O5+9t MD 

   !"#$ % 

 +** cm- min&+

'

(

47

%%) (  NBC-OVW0=>@P M0=

G!OH1L"#yOk NBC-'(  VWI)*+,-./0123  

% b 59t\JK ZM&

456789-:;<+)LOk ;byOk')*J=>;?0:;%  @A BCDE;?%
kPaG

 

ΐ

 F&.3.+

 F&..3 kPaG HI

<)J

LO A <J MONOO Ap

KLM)NBC-OPQRῐ ῕ ῔ ῑ=>;?0O 1,* A)ST "# UO !VW QRX./0
ῒ:; 1* A))Y)J

Brandt, A., E. Bresler, N. Diner, I. Ben-Asher, J. Heller;and D. Goldberg. (+31+) : Inﬁltration from a trick-? 1*  =>;?0  le source, +. Mathematical models. Soil Sci. Soc.

M Z [

\]^

Am. Proc. -/ : 01/ῌ02,.

_`a b VW) X./0

Bresler, E., J. Heller, N. Diner, I. Ben-Asher, A. Brandt

!0cde VW)BC-b

and D. Goldberg. (+31+) : Inﬁltration from a trick-"f +* cm # )J X./02$g

le source, ,. Experimental data and theoreticalY) 1* hcPei%f23j)J

P % )NBC-O

Ok'VW BC-

predictions. Soil Sci. Soc. Am. Proc. -/ : 02-ῌ023.
Lafolie, F., R. Guennelon and M. Th. van Genuchten.

l&RmOn

(+323) : Analysis of water ﬂow under trickle irri- 0 X./0o'p'l(qp)*

gation. +. Theory and numerical solution. Soil

J A )r+QR 0s pe *+,-[,3-

 .U# '5+9t /034?% b  QRYupv)J

Sci. Soc. Am. J. /- : +-+*ῌ+-+2.

>  F+321G : P X QMNR
ST U  // F3G : ,3ῌ-/¡HVWῌ¢£XY F+320G : ,¤¥^¦+Z+§¨© ª«¬­ -1ῌ-3¡.ῌ ῎ ῍ ῏U[®¯°\±]²³B F+33.G : Z±^´µMZwx)NBC-OP5+³¶ 5+9t  Uµ_§·

9t OkVW0=  Oy1

Philip, J. R. (+31+) : General theorem on steady in- wxVW QR0i

ﬁltration from surface sources with application%f2pz{s p2  "f)

to point and line sources. Soil Sci. Soc. Am. Proc.

34c|-}BC-b5?6

-/ : 201ῌ21+.

QRO*  wxVW 7~p
8f90s :<b? ,Z Ap+

Ap, ;;0=> <;0;O="fs`=aῌ¸b"ῌ>VW F+33,G : 0ccqMDῌJE*dT¹e& M&+ 00 : -3ῌ./¡

van Genuchten, M. Th (+32*) : A closed-form equa-./0b3Oy1  % tion for predicting the hydraulic conductivity of4b  BC-Di%2[>?
P )QR @c|AB[,3  A Darcy C4
M=D

P*+,-[,3O

<  UEb F VW ./0
J

!b?



 1* A))Y)unsaturated soils. Soil Sci. Soc. Am. J. .. : 23,ῌ232¡
Warrick, A. W. (+31.) : Time dependent linearized inﬁltration, +. Point sources. Soil Sci. Soc. Am. Proc.
-2 : -2-ῌ-20.
º»f¼g : ,**+ f 1 ¼ ,- gº+f¼g : ,**, f / ¼ +0 g