Water withdrawal by plant roots

Jm#'nul ,)I Hl,=h,~l,~/,i, 17 (Iq72) 1t-S t) ,c* Ninth H~dlw~d Pubh,,'hmg Ctm~punl, Nill hl he rt'r~rqllJiJl ell h'/ p h l l l l l p l l r l l

WATER

l)r rrll~,lillllm

V~,llhOlJl Wlllll:n

WITHDRAWAL

r~ermP~,,,lllrl Irilrll lhe plJhh,,her

BY PLANT

ROOTS

R A F'E'DDESand P E" RI.J'T'E"MA In.~,tm~tc h~r L.a~d end H,"uh,r Manug,'ment R='~'¢,urt'h, I I't~,,emn.z,,er~,'The Nelh,,r/and.~

Ab~,lralq : As purl ol'a ,,ludy dealing wilh Ihe influence of some environmenlal c~mdillon!¢ on plan! gruwlh, waler wtlhdrawal pallcrn~ ol Red C'ahhage (Bru.~.wcu olcruc,'a L , ~.'.v. R~d~' H,'rl.~l)gruwn rm a ~,lll.'ky clay ~c,I are analyzed An analv,a,, c~l Ihe Iransporl re',,t~lanceI'~r liquid lt~w m fhe planf a,> well a'., an invesh. gallon on Ihe geomelry I'ach~r of Ihe roul syMem for red cabbage is presenled. The varmhun ol Ihe,,e I'aclor,.; wilh deplh i', d~.rtbed, and rool e~lraclicm rale'., al dilTerenl deplh,., are ~.JKulaled and compared wilh data oblained rrom waler balance .,,lud~e'~. The planl r¢,~tslanL.'e dula are m reascmable agreerrlenl wilh ext,~ling hlcralure Because ~1 a ricm homogeneou,., and p~=,~rrrw~l developmenl in Ihe early '~lagescff growlh, Ihe geomelry dala of Ihe mihal Rrowinj;, slage,= differ a I'aclor len Irom dala I'~und m hleralure Wilh ruol deveh~prrienl iricreas|nR wtlh deplh, geomelrv dala decrease h~ values ul,z,o reporled Ior of her crnps F'rr~m cah.ulalton'., tl i~ ',,hc~wn Ihal al mcrea,~ing drvin~ oul of Ihe '~o,I Ihe geomelrv rachJr i,J ,dighlly atTecled, bul Ihe plaril re~,iMance incre=.lse!~con,~iderahly 'The laller rest,,, lance, h¢~wever, decreases when Ihe evaporalir~n flux from IIie plaril incr¢uses 'T'ht,, phenomcn~|n is mainly cau,,ed by Ih¢ roof dP,Irtbuh, m it, Ihe ,~oil wHh deplh, resulling m a relaHvely higher waler uplak¢ Irom Ihe lup layers, a'~ compared wilh Ihe deeper layer,,, when Ihe evaporahori flux increa',,es.The ubfained re~,ull,~may al leasl parlly explain Ihu, apparenl noel Dareian behavlour orlhe flux ¢ff waler Ihrough Ihe planl% ,,omeltrne~ reporled in hlerafure. I. Introduction A n y reaso||abl¥ accurate m a t h e m a t i c a l des|.'ripl=on o f waler uptake by crops w i t h a non u n i f o r m root system, ,s c o r n p l i c a l e d T h e r e f o r e tt has been become ¢u,~lomary tc~ desert be, w a l e r I']uw I h r o u g h the ¢nlire sail plant-at rnos phere system w=th an electr,.'al a n a l o g (Van den H o n e r l , 1948). 'T'hts m~del assumes that the water flux q ( m ] r n - " s e c - = ) l h r o u g h the routed sod zone and the ruot-,'~tern-leal.slornata path is p r o p o r l i o n a l to Ihe total w a t e r head dHTerence Ah,~,. ( m ) and tnversely p r o p o r t i o n a l to the t o l a l resistance r (expre,,,sed in se~.'~nds) met in the syslem 'Thus, c o n s | d c r i n g a oned~mens..mul steady stale flow in a serie,~ parallel n e t w o r k , the h q m d flow e q u a t i o n ,s: q

--

I d I'

_

dh,,,,,,~

A dl

h~

h,,,o, ,.u,~=,. - h,.,,,~

_

r,.,,,l

r,,,,.I

- h,,,,,,,,,,,~ ....

h~,u - h,,,,,~ (m',~ec-

rplanl

/',~od

3t

"1" /"pI4nl

~)

(I)

1;"1

r

A

FE, DDE:S A N D

P

E". R I J T E ' M A

It ~hould be noled, that the res,slanL'e r (expressed Jn seconds) Io liquid ttow in the so,l-plant syslem m a I'uncl,,m o1' water head g,radlenls and shimld m,t he toni'used wllh the so-called dlffu.',don resmtam.'es r (see' m - i)which are lunctl~,ns t)l' waler vapour con~.'enirallons A lull dlseussmn on the various plant laL.'li>rs nnw.flved has heen gnven by Slalyer (Ig67) and Kra.mer (19¢~) Waler th,w lo Ihe roots has been described by models us deveh.,ped for example by Phdlp (1~'~7), Gardner (1~¢~(.)), Visser (1~¢~,-I), Cowan (1~5), Whmler etal (Iq6X), M,dzand Remson(Ig'7()) In the model or Gardnera smg.le rr,,I is taken to be a htdh~w infindively hmg cyhnder ,,1' uml'orm radius v=(m) with uniform waler absorbing properties Frl,m a soil which =s imllallv at uml'orm equdihrium waler L'onlenl, the rule of water uplake q~ per unit length ol ro,~t ( m ~ . m i se~.'-i)can he cal,.'ulated iI" waler Lander a head L.,,rad=ent Is flow=ng radially toward Ihe rool Under sleady slate ~.'on dlh,,rm (~;H/rtt =O) and in analogy ,.,I heal ilL,wing I'rom a distance v,(m) toward a hnear sink ,,I infinile length, one can wrHe'

,i;

=

~/'/~' [ / / m (

-

I''

..... , ..... , .... -- hrn(l',,,,,,I)] "

In(v /vl)

(

m2

.seL.-

- ,

)

(,")

where /~', the hydrauhe conducUvlty (rn sec- ~), is a I'unct.m of Ihe malric head hm(m). (In the. field (,1" hydrology F.'q. (2) is kn(,wn as Ihe sleady-slate flux t(,ward a well per unit lenL..-rth ,,1' well ) A dady flucluatlon in q~ will exist and Gardner (1~(-,8) thererore extended his model by assuming, a smus,',dal varlahon ¢~1"evaporal=on flux wilh time In the present study a ~',,nstant mean weekly q~ has been taken C,,wan and Mdlh,,rpe (IqhN) are rd' Ihe ,',pm,,n Ihat in dryin~..~, sod which shrinks there is water transpr, rttt, the r,,,,Is ~n the vapuur state when the :~lr gaps around Ihe ro,,Is are not larger than the radius or the ror, t In this sludy any p,,ssihle vapour Iransport has been lel'l out or ,.'rmslderauon 'The model or a single r,,,t can he e~tended to an entire (und'r, rm) root system (Gardner, 19f-,(): Gardner and Ehhg, Iq62). If/, Is the length ,,f root per unit volume ,,1' s,',l ( r e . m - ~) and :, is the rt,ohng deplh (m), the flux q. (m see-~) can be wrlllen as q, = I , ' : , , I ; ( m ' s e c

(t)

-~)

C'ombmat.~n ,,I _F,',qs (2) and (~) gjves q,

=

-

(h,,,,.

.... ~ -

h..o,,)/(b/k)(m

se~.'-')

(4)

where, h (m) is a parameler with whr~.'h the d=sta.nc¢ and geometry or the r,.',,~t syslem arc accorded h,r: ~') = [ I n ( t , : / l ' l ) ] / 2 1 T l , : '

r

(m)

(5)

WATER WI'THDRAWAL BY PLANT RI)OTS

]h

As can be observed by comparts~,n of Eq (4) wtlh the thlrd term of Eq (I),

/~/~ r,,,,,, =

In £q ('~) t t t s assumed that the mutual distance between the rue)Is ts sufficiently large tu a w , d mterl'erence and thal a steady-state prevails. In general h can be wr,tlen as h = B:,- J (~a) /'he final equation expressing the water flux Ihruugh the roots t~, the a t m o s p h e r e l s o b l a l n e d by ¢~mlb~nmglhe hl'lh t e r m ~ l ' E q ( I ) w l l h Eq (4) yielding

,I = ,I. = - (hi.,.,, - h,,.,.i)/(b/~ + tr, i) (In'see -~ )

(6)

A detailed analys=s of the tlnportance ,~1 the efl"~cls of r,,,.. ( = h / k ) and tr, ~ wtlh the aid of measured heads and flL.XCSwall be necessary, because a reduc l i o n 111 e v a p o r a l l o n f l u x rrluy c a u s e a s e r i o u s reductl~m 111 lhe product~m rate ~I' a ~.'r~p For such an analysts ~me needs I~, be informed ~,I~ the water withdrawal pallerns Ir~in lhe s.il by the r~,~Is, bolh wtlh depth and lime

2. Theory Fur a L.'ertarn pertud these patterns may be c)btamed by applymg the water c~mservali(m equallun on a g,ven volurne of soil (RIjlenta, lqt~'~; Rose and Sler n, lqh7) When e,~presstnL.,, fur the so,l surface lhe various terms ~i" lhe waler balance or c~mservatt~m equattun as deplh rate eqt.tvalenls, Ihe equullon may be W r l l l e n US

,, " ~,'()

£ = / - /, + 'l,J((), t) - qd((), t) - .

I

(Tu)

/~t d :

O

where E, 7 arid I, are the fluxes (m.sec- i) ~I' evaporatwm, pr'eelpJlalw~n and intercepted preclp,lati,m at the soll surface (:.,) respecllvelv, and % ((), t) and % (•), t) lhe upward and d,~wnward flu~es thrt~ugh the phreallc surlace at a conslant water depth 1: =()), : ts lhe vertical cc~-~rdmale (rn) posHtve in upwarddtreclwm, O i s t h e wdumelrw nml,~lureeqmtent(m ~ r n - ' ) a n d t l h e per,~d ctmsldered (s). The inlegral of E,q (7a) over the time interval (t, - t, ) rl

.I fl

r~

x, + q , , ( u , t) - 'td(~), t)]d l

+

tl rt

:i

d:dt i' I Ik

has been used =n the cah.'ulalrons

(m)

17b)

R A. FEDDE.~ AND P. E' RIIrEMA

.~0

The tl(~w lhrou~,h Ih¢ r,,oln rs cah.'ulaled us Ihe mrasured Iolal Itow both Ihn~tnl..,h rc,~ls and non',, dlmnnu,,,hed wnlh Ih~ cah.'ulaled ~ . w thr~ugh lhe s~,l I_,snng Ih¢ ,,ubncrnpls r, u, d u n d s I',~r i~ll~ls, upward, down,,vard and ,,,,~nl respeclnvely, E'q ('7b) can t',~r every deplh : be wrnllen a,',. #,

I ,~

d : dt + II

II

II

(I

I# ,I

- j ,I,,(',l)dl

(m)

(~)

To ,,tmpltl'y calculalmns, tt wtll be cunvenzenl I~ use lime uverag, ed values al deplhs : fl

~I,(2) = (I, - I I ) . '

t"

q,l:)dl

(m".,ec -I )

('41

II

F'~lr Ihe '~,'aler uplake by Ihe r~l~,ls I', =d,1,/'d:(.sec-I), presst,m t.'., always vahd

l ',,<:,'>a': I1 II

II

Ihe I'~flhT,wml-.~, ~.'~



<,.,

l)

For Ihe ~.'alcuh.Ht~m ,fl' Ihe I.'r,lp reslsl;..Ince II In assumed Ih;.ll Ihe dlfferenl LIIrU)ulII,,; i~l W;.ller, C.~.ll'Llcled I'ronl Ihe '.,~,1 al lhe v;.Irt~us deplh.s :, flow Ill Ihe leaf Ilssue hV It(I,,,~' palhs wtm.'h are m u l u a l l y unl.'lll|llej..'led 'The ,~,ver'all re .st,,lan~.'e ~.';JII h~., c()tllpltl~.'d ,.s ht..'tl I;.tkttl~, tnl() a~.'~.'~tinl I h¢ varnous rest.',,I;.In~.'es nn e~..'h parl ill' lhe p;.llh,,,,,aY bb' rneal-i.~ ~ll' Ihe hllhl',,,vtrlls expres.,.,Ions. AI ,.ltw deplh : Ih¢ relalton t|l)ld. ~, -

hi- h,(:)

,~.(:)

= )', (:)

(11)

(~,ec- ' )

wher,: / 4 Is Ihe malrl~.' head In I1,: leave.'~, h,(z) Ihe IIl~lrIC he, d LII Ih~' ll,~,,I surl'uce ul deplh :. ,'r,(:) Ihe planl re,.,tslur,.'e (hI .,.,,ec) I~lr Wal~'r upl;.pk¢ Ir,,mt deplh : Inlegrull~irl ~lv~'r Ih~' llflul (rll,~,ltnl.,.) deplh ..'.. ytelds " i

i -Jig-

! qk

d

/,,(:)]d: = I )',(:),',,,,(:)d: / ql

(m')

(lla)

.%lmth.lr to E'.q ( I ) , I',lr Ih¢' vvl'u,de plunl sy.~lenl Ihe r~'lulu.ln holds (I;..Iktn.~,

WATEI~

WITHf.)RAWAL

BY P L A N T

R()(I[S

I1'7

for th¢ rn,,ment a as Ihe a v e r a g e ,,1' a over dL-pth 2)

/ll i ~"l

~l

(la)

(,pl W hcl'~

" I,pl

=

,.% I'pl

(In sec)

B e k ' a Ll~k'

t - [/,,-

]11 -- h n

I

(,pl

I,pl

h,(:)]d:

"()

~,,

and

,i I;(:)d: ~m¢ ~.'an Wrl[e

()

•-

[hi-

]/r('~)] d : = ',r,I

i

)',(2)d2

(rn:)

(Ib)

(I

F",qualizaln,}n ol Eq, (Ib) and Eq (I la) gnws: :q

,,,

I'

" I,pl

=

);(:)d:

()

t

I;(,:),','r,l(:)d:

ql

so Iha(

J J:(:)*'r '(:)d: ,-dl, :

II

--

( m . ,~ec )

---

(12)

11

'The average planl resmlanc¢ lhen I,,und t.. (f pl Ipl

=

( %eL' )

I n l h e c a l c u l a l , o n s f o r lhevart,m,~layers. following nuuncrical expres~,l,m

E,q (12) was appr~aL'hed byLhe

n=n

t'pl, n =

"=' -- ~ , n

(,see)

,'Jq. rl = I

where rr, ~ IS Iound as rr, u./n

(12a)

~

R

A, FEE)DES A N D P E RIJT'EMA

In an analo[,,~m,~ way as g~ven h~r (he d~r=vation or the planl re,~rslance, an tnle/:.,.raled as ~el] as := nuniertca[ expres,~.m I'~r Ihe ,~t] reslslance can be

developed S~

j )',1:)~ ,~

I~,,Ol]

--

o

(:')d: (m ~,ec)

.'t"

(1~)

};(:)d:

and n =n

Y' Jq.b./~,,

(see)

r,,.,, ,, -

(I ~a)

dq. ff=

I

where r,,...~ IS h~und a~ r,. d .,"//

3, Experimenl,,I procedure A~ part o1' a ,,,tudv de.'dtng, wnh the influence or ,,,ome environmental con d=lkms on plant growth, water wtlhdrawul patlerns or Red Ca hbal..,e ( Bro.~',~'lcu o/erlh'('(7 L ~' v. Rode Her/,~'/L plan(ed at ()(~., ().7S m", grlwvn on ,,,.Ircky ,.'lay s,~tl at Ihe L.",roundwater level e,~perimentul field Gee,~lmeramha~.'hf in The Nefher'land,,,, were analyzed The groundwater level wa,~ for each balance per.od kept :=l a ,.'tm~tanl deplh beh~w the ,~Jl ,~url'ace. For deluils concermng the clm,~lruclt~m ol Ihe experrmenlal field,. Ihe [y,~tmefers and the set up or lhe experiments, Ihc reader f,~ relerred Io F'edde,~ (Iq'71) 'The tn(egraled nef v~lume flux thrt)uL:,h Ihe c'on'qa,t phrcalic stirlace ( : = ( ) ) ~ w e r lhc Itme tnlerval ( l , - t = ) t,J

t t

/ ,/(0, t)dt= I [q,,(0, t)-q,j((),t)]dt

rl

(~')

Ii

wa,~ measured dtre¢ll.y wflh a lystmeler (Feddes, 1971) T'he amounl or mol,~lure M exlracled Irwin1 Ihe soil ahove Ihe phreulrc surlu*.'e ,qs defined by ,~1 = •

rr,=

rl

•

de

d/

(In)

18"1

~l

H

wa,s determined wtth the gamma radialton Irunsn.,~smn rne,thod In order 1o know Ihe relalmnshtp belween I~q~. c~unt rate and wel bulk

WATER WI'THDRAWAL BY PLANT R()()[S

~

derlsily, however, nn prtnctple a new calubratiun curve has hi he delermmed for each separale value o r d r y bulk den.~tty (Ryhiner and Pankov, 1969). The laller auth~r.s pr()pose I,~ use as dens,ly scale, not the mus.~ densH.es ~1' the vartuu.~ cornponenls ur the. sutl bul the den.~tltes or these compunent.~ expressed as an equivalent 'eleclrl)n' density ol water (/.i ~') 'Thi.~ resulted trl an equivalent water density. ,.~ = ().gp,~ + i~. + I ()Ii~,,

(k~, m- i)

(14)

where p,, is the dry bulk den.~dy oI' lh¢ mineral sad,/.)w lhe w~lume Iracti,}n ~1' water and i~,, Ihe dry bulk densrty i.i1' or~,anic mailer F'~)lh,wnn~.~ this method, Ihey ubtanned a ,single calnbralnc~n curve I'(~r different soils h)r each different type of m.'ves,s luhe. 'T'(~ correvl the measured data for non-pural lehsm and I'or devmt.ms in distance between the access tube,,,, Ihe pr(wedure described by Rtllema (19hq) was used An e~ample ~1' the ,,.,ml moisture retention curves cd" Ihe clay ,,,,1:),1as de lermtned at the lab~)rah~ry hlr a I'ew dry bulk densHtes is presented in F t.~, IA A rrl{.1 I r l,

hPurl

I~J?

hrn(I'n) . m

- l " -: I

e~

,

I

-

m

--

,

I

I

1--',-,

Ih

-

,,I

I

i

.

I

I --

~ I),:l

:

n I I,i

=

1'44 I*q rn } I

--el>,:l

""' 11 ) i' (I

':,L _

:

I ~Jl

,4,..14

I

,

II )

',~1.) I( I 40 ':'(.t e.~(.) vilhJrrlPIIll hllll wl31.PI (ilrll.Prli L) ( Ill I w{]lpr m ] ¢,(tll )

IL)

11 I,.' Pl:llJIViJIPlll

e

I

I

n

J I I WUIPI

I

--I n

--,,e

n

I ~

I~__1,_

I 4

1 '=.~

('le,.rl,,ll y

=lh

•

_,

17

P (I(3~I,,q

IH

m

I )

F'tg I A) Relalnon bclween malrtc head and volumelrtc sr.I walerconlenl. B) Equtvalenl waler dens.ly Bolh h~r clay al Ihree dry bulk den,~thcsand a ,,,ampl.ng deplh q,l' 0 ,-I'~ I~ 0 ~,0 m (after F'eddes, Iq'/I).

With the gamma Iranm,sMon melhud the dry bulk density is nncorpuraled ,n the obtained data and when ll,j is known one can determ,ne h,.. directly rromthemeasurcmentswtlhthea'dofFrg IB The graph represenlsJn l'ael the .same relaltonship a.s Fig. I A, except that the vartable,n Fig I B is the equivalent waler den,~.ly p*, in,~lead or Ihe m~tsture conlenl H

40

R A FE'DDES A N D P. E, RIJ'TIEMA TABLE (,"alculoilon of ihe wdier wlfi'Idrowdl p.'ifierri oi' r~'d ¢~b~age orl cl.'iv for ,' = O ai I rrl heinw qi.iol

:

p*(/,)

fin)

{kh:'lTi -:l)

p*(t..,)

/'~*

p*(tv)-IP°(t'.O

( ,.', f ) =

= q(O,t) ÷

= JM~

(kR.nrl -:~)

(kp,. rrl :l)

(ram)

0 0 0 (I (I

~7~ 14'~q) 1~2~ ~()l) 'T7%

Ih 2 1~14

IbiS,

1~14

-()1

I '<7 ~

I ~4~

f '~9

(m)

2 ,J8

221 00"

2,4 '~

I ~6 20

2,,41

1,41 10

I q~

,4 2 ,.' I 2~ It4

I h7

21 1~,4 I '~ ,4q

I th

I0 90 6. tl

21 llh

l '~7 1

I ~ 1,4

I '~~,4

Iq

0 hT'~ (1 h~(1 O,h2~

(Iq7

46

O ~'7~ 0 ~ ",( ) q) ~2'~ 0 ~(X)

(man dav -I)

Ih I

0 7S(1 11 '72 '~ l) '7(X)

- h.,

Jt

(rnm .week -n )

I IX.)O (),9~0 09.% 09(X)

ql,,,.n(:, t)

['J411

'~1 Ih2'7

IhlO

I(,18

17

(14'~ 0 4(1 () ~'~

I '70R

I hgg

1701

I L)

() 10

I 7tlf~

071 0 hi)

0,47 S

q) 2~ () ~0 0 IS 0 I(1 0 L)", 0.(10

I hh2

I '7(1,4 I hSq

1'70'~

I hhO

I,.1

0 %) q) I~

24

0 "~~ (),~

22

0 t0

O2 0 I

,4 ~1~ ~ I~ 2 't4 2 (tq I ~X I 2,4 0 ~h

(),'74 () ~1

0 27

0 2O 0 It)

19 I hl)~

I h(12

I hi)4

01

() 2~ 0 2,4

1%~

1%4

l ~f,

04

l) 17

* All value,, nn IPu!, columrl frurn fig I * * A l l value.,, in IhP, c o l u m n horn fig. 2.

WATER W I T H D R A W A L

-~` tl = . J u l y 18 a n d t~,. = July 2~, 1%7

~url'ace q(O, t ) = I 2 m m . w e e k

J(-hm)

J( - h,r, ) --I

~

J,,

(m)

(mm.dav

1 ' 71)

,4 h~

,M ~11

t, 1

lq O0

9

IO-:' Ill- '

,4f, Oh

1.72

I0-~

2N Oh

,J 2~

i0-,~

I 2 ~,') 9 18

I O~

2 711 8 2(.)

l. '~1') 0 71 0,42

I qO

1 60

'~ 41)

q,,,.,(,.',t) ( r r l m . d a v -i)

I)

I11-"**

7~

(mm.d,'IV

q,,,,,,(:, t ) I)

( m r r i . d a v -~)

0 02

2 -Ih

0 ()~ 0 I)7

2,40 2 ~,4

012

221

(1 20

I q'~

(1 ~1)

I h",

0,40

I 27

(1,4 7

1) 8'+

0,4~

0,48

l) ~0

l) 2 ;

0 ~I

l) I)')

0 ~(1

11 IX)

00t

8~4"7

0 Oh

'77'+

0 ON

~21)

q,,,,,(:, t)

I11 :j I() -~

I(} ?

I0-'

18 ~

'7 2'~ I~

'7

d m, ,, q,,,,,,,

'-Jq, = Pr d-

( n l n l ' d a v -I)

(d:iv i)

O Oh

O ()i)I 2

O Oh

O I)IH 2

O I+

O (X)2h

O 'Id)

(1 (H')hO

() 1~

O(K)Ph

0 ~N

(1 (Xl'7h

0,41

0 0082

1) 2",

1) (M)",(.)

0 14

0 (X)28

() (l~

(I O1)I 8

i) 18

I 0 -u

I 0 -u

~JJ

BY P L A N T RI)DT'S

i) ,4~

0,4 7 0 48 O47

0 '+,4

42

r . A. F'EDDE~ A N D P. E RIJ'TEMA

'The relatlun between hydraulic conducllvtty and matrtc head as derived rrom measurernenL,~ ~n tl~e laboratory as well us rrom field measurements is given in F'Ig. '2 hVdl"{3ull{

({)l'}l'llJ( Ilvlly

1(:)e' - - _

[

I I {.);' ~ " " ' "

1L

k(m

,jI)

(rl'lrri

i h,ly I

-' i(.)v

t

I"',, °

i.'l('lV I )

-

i

I , ,:

l

1( )'~ -

•

~'1

il)lO

1(')11 ' I(')1~1(], '

° ~

-[ I( )t

i * •

i llPh'i (, ilhllo{l • r(lil[ ZIIIIP ~

" ° ~ "" . -

h.]lu ~r q.lh ~r y ~

I . i(')l

I'li'~l, .1() II

, .l() I rrli.lIl II

F'I~ 2

-, i(.) '~

~l .r() :~ hPild

_~,1(

)1

I

-I 1() 4 .i() j

hrr I (rrl)

RelallOri befwt'en l'igdrauh,.' L'ondu~.'ilviiy arid mafrl~." l'ie0d l'or L'l.'ly (.',fler Fedde~, l q T l )

4, A n a l y s i s

The total vertical flux q,,,,,,i (:, t) at each depth is known by addmg the data o1' the Eqs (8') and (8") 'T'he vertical flux through the sod q,, (:, I) can he calculated rrom Darcy's law as q . , ( : , l ) = - I ~ ( V k , , + I) (m sec l ) (15) where/, is in re.see- ~, kr. is malr,." head and h R is gra.vitalronal head ,n m water ~.'olumn (Vk N= I ) and also inlegrated over the lime tnterva.I (t, - t I ). 'T'o stniphl'y the calculation.,,, slmlla.r to Eq (9), lime averaged values at depths : were taken bolh I'or q,,,,,i (:, l) and q., (:, t) In Table I an example, ur the cah.'ulaltl.~n ol' waler extraclJun by roots al depths : rs given for red cabbage on ~.'lay I'cmr lhe permd July 18 through July 2% 1 ~ 7 'The mean matrix." head in th,s permd rs g,ven in Fig. "~A, the lime averaged curnulaltve withdrawal pallerns ol b(~th crop and sod (q,,,,,i), sod unly (q,,) and crop only (q,) are presented in Fig. 3B, while Ihe lime a v e r a g e d e x l r a e l i u n r a l e a l d e p t h s : , T , ( z ) , i s g l v e n t n Fig tC Prom Figs 3B and .~C' it rollows that the effeclive rootmg depths can be round as the depths

WATE, R WITHDRAWAL

BY PLANT

RIiIi'T,~

,,-1'~

whcrL-.' IhL-." (.'umLilaLivc w i t h d r a w a l J'unL'[ilm (if' iutul f l o w and ,,;oil I-]uw inter~.'epl In ihn~ paper the m a x i m u m

r o o f i n g d e p t h (:~,,,,) is luken to be the

el-Teclnve rooinng, depth :~li plu'~ ~() rain F'r~lrn F'ng, .tC it can be .,.,een thai For fl v'iiTi'i I

(rrll

It)ll

I--

I )1.-tl.)

C

A

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kill

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%

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.

.

.

l()

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.

I~, i_'II q (:)(I()I~

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i

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I

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qlH

l',. ~

lh

(HI

q),-I

qlL-I

I; ~

Ill

z* I rn)

,riflli I)(ll)

,Nil lq) rn', n ) I

'~'"",:,,~, ~<',,

,

i7.,

.

,',j

,/=

.hJly

;"i

- AiIrJu',I

J ., . , , _ / . . -

I, (.)'.", I

(.)4

-,

Ill ) I

I)ld

,

[

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2{ I

Ill

ii.~i

[

I

i

I',.'

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I

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q H_':I

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lqdl.~l

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'H'I Ill .If~l q..l(:)( Ilil'lm ', i )

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IJ

Ib

J I)

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F t~, ~,. Pruliles ol A) mafrnc h~ad, B) hn|e avera~,ed ,.'unnJlallve waler v, nll'ldrawal of bnlh crop arid .~od r./i,,l,Li, ul ,~od llnlv ~,J,~,aarid of rool~ only q,,,,i, and C) Inrne averaged exlrudnon rale }-r hir red cabha~e on clay rnr Ihe period July IH IhrouL.,,h July 2% I~Jh7, Dt waler wHhdrawul pallern,~ ror Ihe olher pernod~ nndaculed (alter Fedde,i, Iq71)

,4,4

R A FF, DDES A N D P E RIITEMA

Ihe period nn que.~lwm the maximum exlracln~m rate oc~.'urs at a d~plh o1' () ~,() t~ (),I,~ m heh~w surlac~' A.s said hel'~re, Ihe exlra~.'lion pallerns ~1 Ihe varz~u.s peru.~d.s (Fig tB and .tE)) wtll be used h~ [:,,tw.~ a qtlanlllullVt:' analysts ol Ihe rrlagntlude and vurra II()n ol' tile renJslan~.'es I,,,,ll and rpl wJlh [itll~' F(~r Iht.s purp(,se ()tie qarl divide h~r ea~.'h periled lhe ro~l z~me in a nulnber ~fl' layL:r,~, say ~1' '~l) mm Ihl~.'l,,ness and apply E.q (6) 1o eaL'h layer sepuralely In Ihls way I'q>r ea~.'h period a numbez ~fl' equations q.'an be evah.laled wllh knm~,n values ~1 Aql(:), h.,(:) ai|d I/~(:),From whl~.'h I h e l h r e e u n k n q ~ . n varlablCShl,.., a h(z)and rr,l(:)have I~ be s~dved F~r a ~.'rop hke grass wHh a r~)ol system whi~.'h d~es nol ~.'hange hu) mu~.'h wHh lime, it ~.'an be assumed thai /1(,) and t'r,l(:) ar~.~ ~.'~mslanl wHh Itine (Rillema. I~;f,'~) 'This d~e.s sol h~ld, h~wever, I~>r a ~.'ahbal:,,e~.'r~p where Ihe ro~fl ~,y.'.,lenl ~.'hanges with deplh and Ilrne (,see ah,~ Ra~'Jlz, lq7()) Therelore ~me can exp¢~.'l Ihal For ea~.'h period Ihere inu,sr he a I'un~.'li~ma] relall~mnhlp ol'h and rr, n wilh deplh As a first ;Ippr~,a~.'ln, I,~r ea~.'h pernod an exp, menllal varialton ~fl b, rr, i and Ihe r~u~t mass I1' wllh depth w'a:~ adopled Wllh the deplh below ~ i l surl'aue : ' (m) laken posllnv¢ d~wn~ards, nr I'ollows Ihal b(:~) = h((t)exp(~t:*)

(Its)

r~,n

(17)

) = ~ (())exp(.~:*)

I1'(:*) = II"(())exp(-.~t-*)

(IN)

To delermtne ~t it is a,ssuined Ihat IJ'(:*IT1,1 N ) = l l ( ) [ Jl'(1)) and, as slated ¢arfier, :,*..~, = :,~a=+() ()s T'he value ~1 : ~.... us ~,blatned b~Hh I'r,m~ measure ments ~ l ' r o o l m g deplh nn Ihe field and I'r~un F'q:.*n tB and 3E) 'Thn,s pr,wedure was laken, because a delernHnaln~m ~1' r ~ l ma.~n tn ~.'lay .sod n.,, hardly D~s snble N~w, suhSlllUll~tl o1' E'q (16) alld (17) nnl~, E'q (6) leads For every, layer al deplh :'~ h~. h, - h,,(z*)

a q ' ( z ~ ) = -l~(())exp(~t,:*),'/;(z ~') + rr,~(())exp(,~,: )

(~a)

Rearrangtng tl I~ a .stmpler form t:,tve,s: - [h,,(:*)/,t/.1/' ( : * ) ] ~.-.~p( - ~. #l) = _ [hl/dq r( , ) ] e.l(p( - ,j~:') .-I- h(())//; (:*) I' =

~-Ii

+ u , ~ , + a.

- ~r,~(O)

(~h) k I

"t"

(6c)

Appficalu.m of Eq (6c) t~ Ihree ~r nmre layers al deplh.s :~, wtlh m~.'rernents ol' ().()~; nl leads to u .s~lult~m ~1 Ihe w~r,ables Ig, b(I)) and ~d()) Be-

WATER

WITIIDRAWAL

BY P L A N I

RIN)(S

,-I~

l.'alJ'.,C ~I' Ullcerlalnty oI' nlalrlC head'., and l]uxe.s in the h~p layer. ~.'ah.'ulalion'., were sl;Jrled at () 12'+ nl bel lhe as.~Ltmcd exp~mcnlial variati~m ol',,r, i with deplh, r+,i increased l ~ Fast at the L.'realer depths+ ,At thL'se depth.,, the r~ul ma~,+ decrease',, hut Y*+LIn.F.. +, r~l.'., +.ire ab, o l~rmcd. [..+,iVll1~.,. a relaltvelv lart..,,e a~.'tlX,lly and pern,eahtlitv Due lu htt.,.h /, value.,., ii, Ihe:,e re~.,,ton~, lhe .',,~tl re'.+t,.+tan~.'e(h//~) will be h~w and pus~thle tncurre~.'l c.+.,lllnale.~ ~t' h will tw *~1'mittc, n irnp~>rtam.'e S~il r,:'~t,.,laric~' is rel,:.tttvely I,~vw us c~mtpared wtlh plartt re.~t,,tam.'e T'he rever,,e hr~ld.'., I~, the t~p layers When the ,.,(~ll t.~+ dry, /~ will he ,.,mall :ind in c~m,part',+on wlll'l Pr,I the ',,~nl re'.,l,.+lanee (b,'/+,) be. e(m';e'., relatively larL.',,e 'T Fit'., t.s l he IEa,M)n that v,'r(mt.,, +;+,limale;, ~I' l'r,l have l()r dry l~)p laver,., e,nlv a ',Iu~hl tnfluent.'e on lhe hHal ru-stl,,tant.'e ol lhe ,,,~)tl-plant "~V ",I e , T l .

Keeptit~, tht:, In tritnd, in a .,.,et.',~rid alten'ipl an tleruttve pr(,:edure wu~ l~dh~v,'ed, taking lhe lq value,., and h value,, ~hta,ned v+.ilh lhe flr'.,l appioat.'h us a hast.,, This yielded/'r,I value,+ Ihr~ui.,h which ',,rm~,~th curves were drawn. F'r~rrl the ~.'urve'.i, correcled rl, t values ,,,,.'ele read and used t~+~delertrilrie new h ~,alues :trtd vt~.'~ vel',a Tht', prueedttre wa.,., repealed .,,everal lime.'., T'he variatt,m ~1 rr, I and h v,,ilh depth du,in~, II,e vari~us period.~ i,'+ ,.,h~wr, tn F'l~..,, ,4 It t.~ ~,een thai durmL.., the hrsl Ihree week,.+ ~1 ~..,r,~,lh Ihere t',, an al,n,~l,I exp~menllal telall~mship ~1 rr, I wllh deplh A l l e r Ihls periled, II'IE /"pl dala hehw,/ O..i+', m in~.'rea:,e lel,,,,, la~,l a.'., a resillt ol Ihe deveh~pment ~l new r~l~l'., 1 he depth a,td exlelll t~l blatll.'htl,bTM, ~l Ihe rool.~ ,,, nt.t.'ely nmr'ked t'W lhe h t..'u,ve,,, In the lir!~,l ;i I~ ,-I week,+ rt~,,~t dex, eh~pnlern wa.s rutl'ler poul After lht,, periled, h~w+,ev~'r, lh~' deptli I*~ which r,..~,H.~were ¢xtendtnl?, t.'han+..,ed tn l e ~ than a m~mlh i rom (1 ~l'~ h~ l) ~(I m W i l h aid ,~1 Ihe curve:+ I~r rr, I arid h in Fig, ,J root extru~.'lion rule.'., al dll' 141111 ll-,,,Ii,h3r,i+ ~ llilq,,' I )(.}(.)

II l"

II I <''

1~il.]y,,)

Ir 17

fll~ll

qll,,lij/ile'

II

I

"--"

l

I.t44

IllJrl3lTl~'ler

"~

ll(,~)(r"rl)

I

-----

-------:

4

----'~' JtllyJllllp4~II i111"Iy d - hlly II

,I

IH

hJly IH ==% (

I1"~1

q.)l~ ,leldh

FI~ ,4

JqJly ~==l AII4JU'JI ~= AIII,~IJ'j I ~t t~

I z '+
VarlLiIiq~n In planl rc',,,i,,ILIri*.(' ~.lrid r(~(tl d T d d n L c ~1 ~ m , , e c t . i l i v c

perl,~cl,, ( a l l c r

param~:h=r w i I h d c p l h

Fcclde,,,

I'-A71)

h)r a numhur

r

,40

A FF,I[)L)E,'.~ A N D P E, RI,JI-E,'MA

lerent deplhs were ¢ak'ulaled lur the various perl~d.~ and con]pared wllh d;.ila ~hlamed I n , n Ihe waler halunc'e ,>ludies The result.,., I',~r Ihe lu,,t 4 weeks are shown ~n F'l~. '~ E~cepl for Ihe upper ~od layer, thecalculaled values compare well w,th Ihe e.~per,rnenlal dala It has already been p~finled out that the 'experirne;itar data In the lop layer were <)blamed hy means ol i

,.'l+-'r~lh z (rrl) ()()()1-

\.

I i

_

(li()

__

__

•' ,,,_ '

"-~

_L_

'

"~'-•#

i

I.~ ;.'I~


i _

~(~

-

-

~

i = #-

--

"

-

I

-_ I

'~'i,

'L

/''

,,

_,

''" --

I

{I':~(

NI

"s.-

,"/" m

(.1~()

~-'~,

i

--',

-

l--

T i_•

•

_l

-I

--

.0

-

_

,

~-

_l M/I

I

__

,

,

,

I I

()hi, () 7 U

~() I

,.+

'I

i

+-;' ilh I,lr, l e d II WIJ I P'F I i~111211( --h l ] y I I ~L-'I - - '

II

-,hliy

l

I

i

i

;.'

d

b

15

fL'l

l (I

,.'

,4

,hJly

L'~ i

l

J

h

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"~l:~A IJ{~ll 'll

,

I

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:.1

A,,qu,,l I :, .~D... ~ , '~' -I

]

fill h 1.11 {lllrl

_

,,

i

~Jl.P

Yr ~

h I) I(.) I.~t~y

Fl~; % (." ~rr pari',,ori o f lime ,J vcraL.,,~.'d r~~f e~.lra~,.llon rale,., I'~r red eahhagecul~,.'u a ed with IIle rr, i a d d h curve,, ol FiR ,-I w l l h rale5 ~blalnc-d I'r,un waler bal,'.m¢~¢ .sludle,~ over h~,ur ,'l~n,;e~.'llllve wc'¢k,, (al'lc'r F'eddv,~, 1~-~71)

e,xlrapolalton Due l • ,+mall am~unl,~ or rain, lhe malrlc head,,+ in lhe h.~p layer may be L.'hanglnj:, l'rum time t~ tln]e, probably re,~ullint2, in err~rs Figure '~ ,,,hows lhu[ waler uplake hy lhe r~,H,~ in a h~p layer ~I" say ()()~iI) I(1 m is about ne~l,pible. 'TABLF

2

Re,,iJll,, ol I I1~ ¢;Ih.'Lllal IOrl,,~ orl the mean plunl resl.~lanL'~' (t [,i ). ffle~ rl ,~()11 re~,l~,lanL'e (t ,,q,ii =/)/'~() arid mean r~,_~l d/,,lanee p a r a m e l e r (/~) L irl~'

I 2 1 ,4 % f) 7

P~'rl{id

June 21 f • 27 June 2'7 Io July ,4 h d y 4 h~ II July II h~ IX July IN Io 2'~ July iS ll~ A u g . ; ,.1 AIJ~.~, 2 Ill Aug.; 9

t pl

r hllll

dav,~)

(day,,)

(rrlm)

27 lhO IX 2t)O ~l Xf~O 11 ,41() ,41 2.~1) t'7 '4qO }h 140

;,7 2,-10 11 210 t~,421) 21 4~0 IO.l'~O '7 920 ~ ,49()

2,4 ? I') X 110 %,4 2 '7 I h I ?

WATER WITHDRAWAL BY PLANT R(.)()T'S

47

'The average plant resistaw]ce over the whole rool,lng depth, as well as the average sod resmtance aver this depth were calculul,ed rrom l,he data oh l,alned using the E'.qs (12a) and (I ~,a) The results i,l' these cah.'ulatK, ns I',,r

rnl, r..,,,i and b are presenled in Table 2 .';;. Discussion

It] I,leral.ure the p,',lenllal is ol'l,en expressed per urn[ volume, the]] rn~ has the dln]enslun uf I~,r cxa.mple bar .day .cm -I (eqmvalenl, w,l,h I(.)I'-)days)and h the dzmensKm ,-,1' bar (equivalent, with about I ( ) l q m ) [.Islng these con version factors, 'Table 3 was composed, presenting a number or rrd and b values ror d=fferent crops and different sods as presented =n hl,eral,ure The rr, I data for cabbage (T'able '2) are in Ihe same order or rnagn,l,ude as the data menUoned in 'Table ~, The h data ol' the inH,al [:,.rowing stage (lines I-3, Table 2) differ a I'ach~r ten Irom the b values reported ah,,ve 'T'his 'TaBLe, ~1

Dala on planl resislanee (rp~) and rlu)l dlslanee parameler (b) as eMracled rrom hleralure m

Source

Crop

Soll

d¢pll'= (m)

rpl ( I0 ',j days)

b (mm)

-

I12

04

0 2S 0.28 O.24

I0 4 I0 f, 10.'2

4.4 U7 S.'.)

0 ~0

10.0

22

O 40

I0.1

I I

r¢)ollng

Gardner arid

Birdsh,q Trelod Very fine sand hne .sandy loam clay Loamy sand RHlema (l~')h'~) Grass ,,Heky clay pea I Rulema and Ryhmer (Iqf,h) Summer wheal Coarse sand Endr~,di and C',.parse sand RJilema (Iqhq) Pnlaloes E.hhg ( 19(1t)

,s ma,nly caused by the non-homol::,eneous and poor root, development in h o r i z o n t a l d l r e c h o n in Ih¢ early sttagcs of growl,h

I.Inder Ihes¢ c o n d d i o n s

lhe concentral.,on or rools bel,ween the access l,ubes used ror l,he moJsl,ure measuremenls, was m fact not represent,rag l,he average root, concentra.l,mn in the sod. When root, development increases wuh hme, b values (hnes 4-7,

Table 2) decrease h, values also reporl,ed ror other crops The given dal,a h:',r red cabbage demonsl,rale l,hat poss=ble elTecls of h,w mal,rp." heads (high m a i n e sucuons) m l,he sod on the evaporaUon flux m the early stages of

TABLI

F xarnple ~1 th~ c a l c u l a h o n o f ~ a n d tpn fur Ihe p¢rnod of Augu,,I ~ Io ~, u,~nrng I'or each layer ug d r p l h , * Ih~ -I,8()m 'wel')arldar h '';

--/t,,.H

/1

h

(hi)

(m)

( r a m . d a y ')

(m)

().O(X) 1) 1)2'~ 0 0~0 0.O7% () I ()q.) (I I ?~ l) I '~q.) q) I 7'~ () ?()() l) 73'~ () 2'~0 (1 27~ 0 llH) l) t?~ 0 1",(~ 0 ;7~ (1,4(X) 0.4 ?", () ,4',0 () 4 7", 1) ~(X) O ')?'~ (),~'~1) l) '~ 7~ 0 hlX) l) h?%

O h~(I {),h7~ () 7(X) 0 72~ O 7')0 () 77'~

h = r,,,Hi

( I O ' days)

rpl

( I0'~ day,,)

l) OI I!)

l) (IX I

t 17

OOI tN

OO1

O 217

21)

2(I ?

;,q)l

0 I)lhl

() 07

0,41'~

lq

19,4

? 7?

0 01~?

l) I ~,

() 781

(~7

(-¢7,~1

? ,4t

11()??;

0 ~'~

I 121

120

121 I

2 17

()()?h()

() 1'7

I.,421

18~

IXh.,4

I ql

0();1()

l) ~1

I h,4~

~tl)

2tl t~

I 70

(t01h7

(,),67

I X2(-~

2~

2 % F{

I ~1

0 0-1.40

1) Xh

I 9",",

Y70

'77,.) (J

I ;~

0 0",40

I 07

I ~XI

~XO

?X~ (')

I. I 7

0 Oh t 7

I 20

20?R

?q')

207 ()

I OI

l) ()'7'~,4

I ~1

2 l)2q

tO7

tO9,1)

0 ~1

0 ()~cA()

I X%

? 079

121

12 t I

I) 70

O IOhq)

? tf~

2 22('~

147

t,4q 2

0 ht

0 12'7()

t 10

~ ~)qX

417

41q,h

O 14')0

4 '4(1

I 179

8h*)

I,JflX.4

A~¢L~rdlrlg h, Eq. I ~la

0 X242

-'~q~l~duw,

sor,,,,i;=

= 7481 d a v s a n d h = ' ? 4 . ~ l XO

A¢¢ordnnp, Io E,q 12a' rpl. r, -

6 ~)(')g14 O fl247

( I()'L dav,,)

(') ()1 ?t)l)

h,,,,, = - I XO-~ =OOt,4

r,,,,,n,.-

}-rpl

; 72

(i '~,4 ?X X~ +

q ~'J)

A

7Xgh II

7XOhtl days, '~o rr, i . . . . XO

ORTO day,,

n) A l l value,, nn I h N c o l u m n I r o m F'ug 2 :;) A l l w~luc,~ nn Ihn,~ c o l u m n h)r ca(.'h layer al d e p l h : * f i o m F'ng 4

L = Z~4mm.

q h

4 h and rpi value4 of Fig 4 wnlh an a~4urried dnslrihulnun o f Ihe rrialrn~.' head ol Ihe ~oil wllli d~pih (h .,~l a,,MJmed hl,+,~.r = - II) rn

-- (/Ill,~lr -- ~141dl)

(hi)

~+ q),()l

+~rl+ol4

( ITIITl'da V I)

~

qli) %

"~nl.lIJl,,

(ITUTI,day- I )

A

qH} 4 ~p

~

L'~(InqllJl,,, "7~

()O 4

PrOol,,'r r'l

(toni)

(ITInl)

A

qHI 4

~¢l'nq.Jl,,

qnl.)ol4 (++)

#r,)ol,, 1:',)

qliJ,~l,,( ++',)

l ()(11

h 3H

O()h~,

() ++277

~?'~

11127

0 +qX

h (++

()i)t~'7'4

O Ifv4()

1%

1~'714,-I

O ll44

h 4g

00177 ~

I1 08Nh

~14%

~,44h'~

l) 10'7

'7 28

O t)l L)'7,-I

O O~ ~ 7

4 211

;,4q80

1) ()h'~

7 47

i) (')l)f~24

() O~12

1~O

.1'7'~(10

O q)~8

'7 H 1

(1 (11)4~(1

l) (1~ I1)

24q

}HH'~ I

1) 1)2'~

X ()~

11 01) t,44

00174

~X 7

,-I01 h t

0 1171

14 ~0

0 (X)I~ I

(I Olh?

244

412i)h

(] ()~(J

X 4q

0 ()tl 11 ?

0 0 I 4h

tlh

4214 4

0 0 I L.I

8 h8

0 (1t)1111,1

l) I)144

'~114

,.I AI)u)4

11 (lit-)

X X1

11 01)24'7

L) OI,4q

1(11

,4 lX,4q

L) OlX

8 49

(I O(12q I

0 ()14 '~

2'+4

4,.Ir,S S

00I X

I?

0 ()1)2X3

0 q)l 41

241

,4 '~ 1(,7

O OI 7

q ~,.I

0 (X)2h4

l) OI '~2

2~-V~

4'~qO~

(I OIh

t'7

l) 1111221

0 I)l 12

290

4tPmO

001,4

9 46

0 01110q

l) lil)~,-I

1~4

4 71 Ih

(1 00'7

0 h() ]

() ,40,4 0 ~47 0.21..+ O. I~,.I O I hq 0 14X l) I ~N q) IOq l) ()40 (11172 0 O44 O11~7 ()1)~1 0 O0 7

() 8242

4-

4qt t

+

6~()N1,4

+

#.ml,(.',~) = E v . ~ p -

:4"the h and rr,~ dala are holdnng Ior layer,, o 1 ' 0 0 I m Ihnckne,,s, 40 J'~",',,i',i. n,~ relerrm/,; Io fhe flu~ I h r o u g h aycr~ uf 0.01 rn Ihlcknt'4s

~()

R A FEDDE,SAND P E RIITE'MA

I?,ruwlh, will start ut a lower malr~c head(hi~,her n l a l n c s u c t m n s ) t h a n in {he later ~laL;,es rfl" growth In F'l~:,, f~ the h values ~'~1"Table.,,; 2 and "~ arc plolted at.;ain.st the reciprocal ~1' the' etTectivc m o h n g depth ,.',,, It is see)) thai as a crude approx=mati('m (see also Eq ~a) ror crops with a .h~m)oL.,.ene,~us r()cfl d~,,;tr~bulion the empirical relat~m h = 1)(l(ll "~ ;',~-.~

(I~-))

w=lh b~lh h and : =n m, h~dds. The Ihree deviating poml,s or red c~hhal~,e reler h) the n,m hom~}?..,.eneous and p ~ r tool development in the hel:?jnmn~. r~r Ihe It.rowing?, slu~,e (lines I - 1,, Table 2) The accuracy or Ihe calculal~on ~1 lhe overall resl.,,lance,,; ~1 planl and soil ~,, largely dependent on the accuracy ~~1"the delerm~nat~on or,.,Iq, (Eqs ri~,l

illhh3rliP

iliJr~.l,q-iPl~r

12a

LI ( n ' l r r l )

mT

m Lq'~ I-

_ej_i

I --I

,H

i i I1,)

-

I

I

11•IFP,~)

•

I|llJ '~5

( HiIlerrll

I

llLlll,lhle=j I Ill'~ I iJrlill31~e

(I fll"h I~dl l]lllJ l,~ijtelTlr4,1%Ifll4~ (Fpl.ldp~l 11,,ill 1

Ih 1,4

I

I I

I

1,"

-

d,l I

-i

Ill _

,-

i

~

__

_

! +,

( ) L,.,,."'-

I

I

2 r'~,e ii)rcH ¢31 q~f ~'lfPI I I v P

]

j

I 4 5 rq)r, dlrlC:] f.l~a~.l(~'t zptlf(rlrll )

Fl~., h. Empirical rclall,)n I')elwc'en IhL= tool dl~,lance paramc'fc'r (h) urid Ihe re~.'~pmcal of Ih¢.~ ¢'ReCllVCr¢.~l|ng depfh ,h,rr -I h - I 1,. I0 It,~-I (T'lie dc'vlallng enL'lrcled red cabbage pomf5 are due In nq)n hqm-iuk,~nc'~u,~r,,H rlcveh~prrienl in h~)r~z~)nlaldireclion m fhe be' ~;inritng eft' Ihe. ~.~,rnwmg,,la~ )

and I.'ta). Moreover the dislr=huti~n in dq, with deplh is i m p u r l a n t in the determ,nallon of the final resistances For example in con,secutlv¢ dry perlod,~ Ihe water uptake =n the lop layers =s about zer
WATER

WITHLIRAWAL,

ROI.)T~

I

r.

lip

¢'i l~l

q"'J ,'~ P I t+'l

~,.~

r

"'P +.'?~

q" I

'=i'

I

u~.

BY P L A N T

I"

,.=r~

+++1

~! '.'?

~, ;+I ':"-'

,

ri

~

P,g '~'

i~i l.t-+ u+,.~

-~' -

I

,

,.p fi

.-Iq'l

I

='3 ¢.,I

I-, '~"

,.~

-fl

I;'

,'~, l

"~:,, F' -,":' r

,

I

--,

i'~

~b

i.-',

"~

I-,

--

i

,,, ~_,, '-'P' I-,

,~

.'~

ixl

r+'l

,'~ --

r

-

I

I

i,,

irb rl

,'+'1 q" I rl f'l

--

is'l

~-)

q.) ,4.

I;i

,-, ,

I',

~:,

,,J+.~

,"t

q~

",i!, 2 ,2 '2

•T,, 'T

,-

Ap

-~

[]

-

r=,~ ,','+ ,,,",

~

I

r+',

tel

I

I

.~l

,%~,

FI A

FE, fII-)ES A N D

P E, RIITE, MA

Thin lealure may be illuMraled by Ihe I~dh~v, mg cal,.'ulalton,,.,, ,~1' wht~.'h Table ,-I ts presenled us an example I'~r the period ol August 2 to 4.~. T'he pr(wedtire ts I~ slarl with a l.'erlain asnumed dis{ribulmn of Ihe inatrt~.' head (h..,,,~) with deplh, vtelding via Fit.'. 2, /~ a,s I'uncUun ul" deplh I.Ising lurLher for every layer at deplh : * , b and rr, I value,~ uf Ft~.~. ,-I For Ihls pert(~d, and pulltnj?, a certain rnatnc head at lhe evap~rattnL.,. ,sHes ~,Hhm the leaven,., (in Table ,-I /h=.,I = - I ( ) m ) one ~.'an calculate h~r each layer .,Iq ........ by applytng Eq (h), alter whtt.'h hy hHaltztnL.,, these data q,u,,.,(=.,)(whp.'h ix the evap~raIron I-1LIX Irom Ihe ur~p. E.'~.,~) r~ h~und Multiplp.'aLtun I'~r each layer or 3q,.,,,,, wilh r...u,~ and r~ re.~peellvely, and using, the Eqs I '~a and 12a ~Hher r.,.,~ (and thus h) and ~r,~ dala are c~rr]puled In 'Table S a number ~1 q,,,...( :.. ), h and ~r,~ data a.J'e cah.'ululed I'~~r Ihree dttTerent a.ssumed dtslributi~m~ ~H' the muir,,, head wilh depth (~ee FtL~, '1), namely 'wet', ' m e d m n r and 'dry', Ior dtlTerenl assumed values ~1'/h~,,~ Fr~.n Table ~, ~t can he concluded thai a( tncrea.'.,ing drvtng, out ~1' Ihe s~tl ~r,~ tn~.'reases A prauhcal example ~1 Ihe elTecl or Ihe averat..,e malrtc head ~1' z" (n',)

lipid

//

1)()(.)

II

'w~'

~11~)

li ',i. v' I

'i~,~,i,,~=,'

/

/

i

I

( I,JI )

I

/

m

/

I I

/'

I

II ~11

I I

]

/ (i qll

1-

/

/

I1%1

I I

/

I I

/ /'- /

./

I

I) 7()

( It'll )11 ) '~ , ,

I 111 I

t

ILl I I

I I

II

#

I 2

/

/I

/

Y

I.lhl

/,

I

,/ /

/

_

___ I

i II.) I

II.) ~ I'1 ~ 'TI I m

I

3

4 i d--

Fi~., 7

Assumed

dtslrthuu~m

q~l' m u l N r

head w H h d~.'plh h}r a ' w e l ' ' d r y ' :,all miH,dlJr¢ ,,l~g¢

a 'medium'

,Hid LI

WATER WITHDRAWAL BY PLANT RI)I)TS

.~,1~

Ih¢ soil in the root zone on Ihe value o1' Ihe avcrag, e plant resi,stanc'e van be derived From the dala I'or polaloes prc,senled by Endr(~dt and Rilterna ( l % q ) The author,s g,lve lhc relutI~n

rh= f ( - h z ) = l ' [ E ' p ( , r , , ÷ h / [ ) - h , , , , , , ]

(sea i n - ' )

('21))

where r h t.',; the ttnl+ avera~,ed dtl-Tu,~r(m resn,+tam.'e I~+ walcr vap~Lir ¢~I lhe canopy ,'.;urlacc' and ~F, is the' tirnc' aw'rat:,ed pv, lenlial evaporation Hux 111 lhe cah.'ulaltons lhc' authurs used a cl~tlslunl value (~I' I() 3()() days l'~r t'r,n 'The data presented in F'I~, X ~,.'leurly dcm(~nslrale u d~:vtuti~m belwec'n lhe p~linls l~r a dry and a wel r,~ol z~ne, tndt~.'alin~, lhal rr, n For lhe wel condilu>ns ts uboul lh¢ hull oI' lhe value u.sed tn lhe cah.'ulalt
I

ii.) ~

--l,l

"/]

t~

I

,. +'m__

--

--__

__

": 'I'"

.',,".'I

;,:,,. II

)1

-/ t

_ _

e

h 4

• dry ii WPI

,I I

I

I

i

'dill 'dill

I I H lq+ )

I

I

4

h

I ,,..I

A I i ~b t~ IL) ~

htl ' (rn) I I

I ,?

~

I e.,

i

I

k'l IL)

I J

llJ I ( l'~,~l )

Ftk; X Relalton belwcen Ihe dlHu,,,ion r~.sl,slan++.'c, ol Ihe ~.'r~+p+,.';.qh~pyth und Ihe p o l e n h q l waler head rn Ihe leave',,+hi rb for peH;Afc~'sk.;ruwn in u wel and in a dry ',,otl dertved (From

Eridrudt and Rillen'la, I~-J¢~.~)

~,.~

R A f, EDI-)ES AN[') P. E. RIITEMA

Ihr()ugh the roots h) lhe almo.,,;phere When q,,,,,,.,(:,) us nncrea,.ang, lhe g.ra dnenl -(lh-h,,,,,n) nncrea.,.,e.',; relat)velv more )n lhe upper lhan nn (he deeper layer.,., (')I the .,,;od Thus wdl re.,,ull )n d)ITerenl pattern.,., (.)r waler uplake a( varn(")u,~ e v a p o r a t i o n rale,,;. In the lasl Iwo colunm.~ ()I Table 4 lhe way ()I' c()mpulull()n ()i' the relalive walei uptake [q,,,,,~.,(z)/'q,,,,,,.,(z..)] for [he ca,~e meul)oned lq,,,,,,..("..) = () 82 ram. day- ~] i~ ~h()wn In F'n~, 9A Ihe dl,~lribuln()n ()1 Ihm relative water uptake with deplh I.'.; compared wilh (he c:~se where ~,,,,,..(:..)= S.ol r a m . d a y ) In F,g (-)B and A d(-'l)l h ~(l'r))

B

W@l'

' rrlp(.111J rrl '

I. . . . I_i

t-,4,,l-

/'

,

,,I~----' ....

)'

I- ~

'

( )()t.)

(.)2q)

(.) l')( )

,'/ II /

/

,.,o., ,-,,., d,,v' '~.'-_'_--':-_' I ',

q)4()

I-

IICIy I

rrlm

"/, , ' /

I

,

,.~,h, .,,,., ,,,,~'

,'/ i"'':'" <.,~,,.,L'7 t'"", '~ b'/ , I

,-----

)-

'

i:)(')[

~

I

'

.......

I ,~ " q.',',, ,'. . . .

"

' ....

?

- '/ I I ~ ) , ~ _ ~ . ' , p

i

(t~q)

~

', "

-

H.)()

()11()

q ) L'I)

( ) ,.I~ )

l~) rrlr"rl ("l(av I

;.

( ) L')(.)

....

T', ,-~,~_v'

( )id( )

l()I)

qlz) r@l(111v~,

~'l@l)t It zl~ (rrt) ( ) ( )('),-

~.

.

.

'l.lr V ' . . .

.

,,,,.,-

~

t-- -h---.

=

I

l'~'"~I

I) a()-

~

I

.

.

.

.

.

.

ii I l~.l~(J

rl)lllb (z,:, r lll=ll 'i

.

.

/

.

s j,f,F ,..,, "

p ,,, "

~---"

w(Jl~-,l

' 7 - - - - ~'" '":. . . . .

~P

-

i

• ~'" ~,~' , , ~ , / I,,,' ~ . . . . • ' ~ /

q)('H1----

Ii .-y/ " ~ ( ) l~l()lll~

I

/'

- • - '4 F4 l~Irrl l i l l y I:l ( Z , , ) rq),,l',~

21'7mmdoy

I

i

i I (]~)()

I

1 ()4()

I

J ( 11")( )

I

I I )1~()

I

l II11)

I

12(1 q (z)

I Phllll/P

WI'II@I'

l.lpll'll(e

(I (Z,,)

l(.d',

Fig O

Relallve waler uplake by Ih~ roofs fi)r Ih~ ca~e~ prenenled in FIR '7 Ior varinus Cvapor.',llq)n l~ux¢i Lilruw,l,,(J,,)

WATER W I T H D R A W A L

BY PLANT RI)()'T,";

")h

0C relative water uptake,s For the cases ol'the 'medium' and the 'dry' sltuat.')n ()1' Fig 7 I'or various values ul" q,,,,,,~(:,,) (see al,.,() 'T'a,hle 5) are presented F'r.m these fig,ures it =,,., clearly ,,~een that at higher evaporation I-]u)ce,.; more waler is taken I'r.m the upper sod layer,,;, as c
q ( z ,+} E rt.Jl.~|.p

4 rl)ll

+'---I

I-

-

I

7-- I--

'Wt"l

i

/~n

'

~ lllJn'l i

/

-

i '

, ',.I,v'

t-/ /

/I /

!

1

/

I

--~

~/

---I-

'

/I

--

,/

I

i-

,

i

(.)

._1~1 ILl

L~('I

I(.)

,-I(l

~)()

~()

7()

I~l)

q4)

I(I(.I

,, -1

--

t,~ I

I -

--,~

,.', '

-- 1--

-

-

-

L I

.

I

.

.

.

.

I __

I~:~)

' - ( hh,.,ur - FI,,,,II ) ( m )

i

t t t

| ~-__

IL~() 1"4(') 14q)

,'J ti

.J

I1(I

I

.

.

~

.

i

I

I .

.

_~l_

.

.

.

.

I

I

Fl~.~. 10 Relall(~n!., belwet'n Ihe evaporall(~rl flux or Ihe c r o p q.,,,,,,(:,) and Ihe waler head ddTercnce,s hel w , ~ n I he leal' and I he I,,¢)11 - (h,+,,,-h,,,,.) a,, ,. ~.llculaled Ior ~ ' w e l ' , a 'rnediurr=' and a ' d r y ' nlolslute '.,lage o1' Ihe '.,o=1 lur variolJ'S valu¢',,, ol h~,.,,,=, ~,l'.)wm~ Ihe ,,o ,..'ailed 'nqm D a r c m n b e h a v . ) u r ' ol Ih¢' w~,Her flux I h r . u ~ h plank,

'~

R. A F-E.I)DES AN[) P E. RIITEMA

p~,~iltve v a l u e s ol Ihe g r a d n e n l I-)art'mr~ b e h a w o u r ' a constant,

The data show

nn fact Ihe s o c a l l e d

'ram

a s Ihe ral¢~ e v a p ~ r , _ l i o n flux o v e r h e a d g r a d n e n l rs n o l

a resulL w h i c h ts a l s o r e p ~ r l e d by v a r i o u s o t h e r a u t h o r s ( T i n k h n

and Weatherly,

1~6fl, It.)flS, B a r s s , IqT()) I h e

m a y at leasl p a r l l v t ' x p l a t n Ihe a p p a r e n t w a t e r flux t h r o u g h

results obtained

'non-Darcnan

m Ihls s t u d y

behav,mr'

ol Ihe

p l a n t s nrt l e r m s o f b o t h s p a c u l l r o o t d r s l r l b t l t i ~ r l ir! t h e

,,~nl a n d d t s l r i b u l t o r l ~d' t h e m a l r t t ' h e a d tn Ihe r~lol z ~ n e

References Bar,,,,, H. D , Iq71) (."lmlr~lled erivnronmetil ,,,llJdtc'., ~1 IIie etTe¢l~; c~l vormble :llrno'.,lnliL'rtt' walcr ,.,I,.lllJ~:, (11' Zl-'tJ ,~..lal,.~,' L and ~lher ,,,pt'cte,, S v m p /in planl re,,,pc, n,.,c ,,Ire,,,, ¢~n pli,,h~ ,,Vrllh~.~M,.,, Iron,.,pirafion atifl w,alur Io l.'Jlrrlall¢ laclor,.,, I.Ipp,.,ala, Sweden, I.Prlt',,,c,~. Parr., (m prq-,,,,) ("~,.,,~,.111, I R , I*-~fl'~ 'T'rari,,,p~rl ~1 Wal~'r in Ihu ,.a~tl pI,Jnl almq=,,plicr¢ ,.,y,.,Ic-tn .I ,.Ipp/ E, ol Z 221 C'l~v,,,an, .I R and M i l l h o r p c , F / , 1¢68. Planl I'a~.lor,, influencing Ih~;' wafer ,,fall.I,, ~d planl In,,,,ue,, In tl',zt~./ [h'ht'tt~ a m / P h m t G/mi'th (Ed "1" T' KL~zh',,.,,.'~,kn) V~II I (.'haplcu t~ Acacl Prc,.,~, New "l'orl,., pp. I ~17-1qI Endrq~dt, (._1 and R~jlemu, P E , I~¢pd~ (."alculalton ul ev,,p~lran,.,pirul,m Irom polah~¢"., Nr'th .I ,4j..r.' S o . 17. ,-I 281-2t~ ~-) T'echri Bull I(."W t~-~ Fedd~',,, r . A , It)'71. Walt'r, h~'al and crop urowlh Thc',,~,, (.'orimluntt'alton Agtt~. I.tniv Wageritnp.cri '71 - I 2, pp I N,4 Gardner, W R , It)~~) S~il waler relali~ms in ar.J and semi arnd ¢on¢lih.n,, In' Plaril walerrelali~m,,h~p,.,triaridand;,errit artdt'¢mdili~m,, I.~ne,,¢o. Parn,~.Rev ~ l ' R e , J , p p t7 Gardner, W R , 1'+¢~8 A v a l l a b t h l y arid mc.',,:.uremenl ~1 ~,~~1 waler In 'T' T' Kozh~w,,ki ( [ O ) , JJ'tttl,r D~./lCitv and P/dill Gtolvth V~I I (.'[larllt'r ", Acad Pr~',,,, New Yl~rk, 1(17-1 t~ G a r d n e r , W R and Ehhg, C' F , I'#t',2 Sq~lTle oh,,t'rvallorl,, orl II'1¢" m~wc'menf of ,.~aler Io planl r~ol,,, ,,.I,erou J 54 ,4'~1-,-I'~ (3ardner, W. R arid Ehhg, C F' , I~¢~t 'T'hc irlt]ut-rlL'¢ ~[ ,~oll walcr ori Irorl,,pnrol,m IW planl,, J ¢.;~.ophv~'. R~'~'. 08:'~71q-'~72,4 H~merl, ]" H Van I')cn, Iq,..18 Waler Iran~.,porl irl planl'., a,., a ¢ah'nary pr(~ce,,'., Z)t,,' Far,~dm, S,c .t I .If~- I ~ ~1 Kramer, P. J . It)hq Plait/ a m / S m l |l.'ott.r Rt,lathm.~htp.~ .4 Mod,'/n Svnth~'~l~. M¢(qraw Hill Book Comp. N~'w York 'T~ronh~ /imd~ri, pp ,.182 Molz, F J and Rern!,~m, J , ItA'Tl) F'xlrLlt'l~orl lerm rn~dt:ls of '~oll mon,,lure w,e by Iron ,..plrtrig pl;.Irlll, II'dh'r Re'~mtr~'c.~' R,'~' O, '~ I 14fl-I I'~t~ Phihp. I R , Iq'~7 The phv:,r~.al principle,,~[ soil waler rrioverricnl during Ihe trrngal,m ~.vcle 'Trarls Ird (."origr Irilern. Corrtm hr Drain , Uueslion 8, 12%1'~,-I R,.twtlz, E' , Iqtd.A The dependence u[ gn~wlh r01e and Iran,.,plralion role ~m Ihe planl and ,,~nl phV,,w.',l paramt'ler~ tinder conlrolk'd c~mdil,)ns S m l S,~ I10, l' 172-18t Riilern;.I, P F' , Iqt~'~ Arl arlalv,,~,, ol m'lual ev.'~p~han,,plrah~n ,4grt~ Re~'. R¢'p 6.~9. pp 1117 Pl.ldo¢, Wagerimgen RiiIt'mo, P E , I~~ c) The t:alculolron ~1" non parall,~h,,m ~1 gamma access luhe'~, usmg ,,od ,,amphng dalo. J Hi,tirol. t~: 2(It~-212 Ft'¢hn. Bull I(."W t~7. R/lie/no, P. E en Rvhmer, A. H , It~t~h. De b,,slrrielers in N/derland (111) A,~['wclt'n van

WATER

WITHDRAWAL

BY P L A N T

~7

RI)IIT,'.;

verdarrlpmg en re,~ullalerl van verdampmgslmderzoek. Ver~,l. Meded HwJrol C'l~rrult 'T'N(114(IqhR):Nt~14q Meded IC'W ION R~,~e, C W. and Slern, W R , Iqh7 r)elerlTiinallon ol wllhdrawal ol waler I'rolrl ,..,iHI I'W rap rl=ol,~ a ~, a lurl~Hori ol deplh and lime. ,4u.~lt ,1 Sod R,..~ 5 I I - I q Ryhmer, A H, and Pankow, J , Iq6q Sod irloi,~lure rnea,,ureirlerH by IIle ganlma Iran,, ffil,,411)ri melhod .1 Ht'dr, d t). Iq,4-2(.14 Feelin Bull I C W h 6 Slalver. R, (.) , 1967 Plant wah.r RHurmHdIlp~ ELoetmtental Botany An Ink'rn Serte,, ~iI Monographs Vifl II L . n d o n a n d New York Acad, Prev,,,pp 16h. l"mkhn, R, and Wealherlv. P E . I~-~66 ( )ri lhe relal[~m,Jup helweerl Iran,.ptralttm rule and lear waler polenlml New P h v t o l , 65, ,.t ~.1)~-'~17 'T'lnklln, R and Wealherly, P. E,, ll#d4 The ei-Tecl ol l l a i P , p i r a l l o n rale ~n Ihe leal wak'r poleril~al of normal and ~,,od tooled planl,, New Phl,hd 07, ~ 6()'~-61 '~ Vl,,~cr, W

(." , IC)h,4 M o l b l l l l e

r e q u i r e m e r l l , . , ~1 cr,~p,., .'lnd r a l e o l inol,~llJre d e p k ' l i , m o l

Ihe '~.d T'echn Bull IC'W 12 Whi,,ler, F D , Klule, A . arid M i l h r i g h m , R J , ILH-d'I Arlalv,~l,,, ol ,,,leadv ,dale e~'ar,,., Iran,,plrallon Irt~m a '.,oll c{flllmn Proc Sml,.~','t Sou .4m,'r 3Z Ih7-17,4.

Lisl

of u~d symbols

'The l e t t e r s a , p , H , ~,~x are also used I~,r any gnven c o n s t a n t

Some ol'lhe

s y m b o l s used m a rew c o n s e c u l w e e q u a l l t m s l a l h n g oul,~lde the rnaln hne ol a r g u m e n t are defined in the l e x t only (3tven are SI iJiiil,~ Values ~1' physical p r ~ p e r t l e s a p p l y h) c o n d t l t o n s c~l' 2 9 t K a n d / o r

I I)1 t bar.

Sy t u b a l

I n l e r pr~.tal ton

LI ntis

Eh m e n s . in

,4

A r ea

m '

L,"

h

Root d,stance parameler

m

L,

I l l ~' irl - ? set' - I

L, t

vulume

in..,,eL.' ~

C t-

r

Function

-

g

A c c e l e r a h o n d u e to gravity

m sec- "

L, t - ~'

m

L,

m

L,

defined by Eq ('~) E

Aclual evaporallUn

flux,

w ~ l u m e flux E~

Potenl,ul evaporaHon

(,/=q

h..,,,1

flux.

NI t)

'Total ¢nerbw oI' water ex-

pressed per umt welghl, lhus eqmvulent with head (h,,.,,i = 'i',,,,,,d,q)

h v It m

Equwalents or grav,lat.onal head resp

Iq,~i ,

- I

m a t r w head

E'.quwalents ~1" w a l e r head at the

'i8

R A F,E',r)DESAND P E". RIIT'E,MA

Syrnb,,I

InterprelaUon

hll)Ol 1,,ull,

e v a p o r a t m g surfaces wtlhln the leaves, at the r*~ol surfaces

h,,Ol i

A',A',

I

/I.!

resp, tn the sod LJnsalurated resp. saturated hydrauhc c(mductiwly express

q, r h

rr, i, r,,o,i t

I' 2

m

L

L , I -I L'"

L,

.I.; ~'/ d : d t In

q! ~ q,~

Dimens=on

ed per unH we,ghl m sec-i Length of routs per uml vulume of so.l rn mAm(~unl ~d' water exlracled per un.l ul horl,,~mlal area f r o m the soil ah~we lhe gr(~undwaler lable rn

,~1 =

q,J, qu

Units

II

Volume flux of waler passtn.t.,, through a urn[ h(~rizor]lal area per uml l~me Downward resp upward flus ~I waler through a phrealtc surlace at c~mslanl depth Flux uf water lhrough lhe roots resp lhe sod Rule uf water uptake per unil length ul rool D,ffus,un res,slam.'e ol water vaporer dependent un waler head eqmvulent in Ihe leaf tissues Resistances to hqutd flow tn the planl resp Ihesod 'T'tme Volume Verlical dlslance I'r(m] reference level, as mdJcaled in lex[ Depth below lhe surface

m ~ m - .'.see- ~ L . l - r

re.see ~

L [-~

m sec -~

L [-i

m ~.rn - ' . s e e - ~ L."'I- i

see m -v

I L -~

sec sec m

L

m

m

t

L, ~

WATER WITHDRAWAL

BY PI ANT ROOTS

Symbol

Inlerprelalt~m

l.Jnil.',,

"I Z,,

Rq.Jttng deplh Vertical dmtance between Ihe gr~mndwaler table and Ihe

m

s~il sul face Re,~t,dam.'es to hqutd flow In

m

lhe plant (,',rt = :.,rpt) resp the sod (;.,..,,,, = :,~,,,...) V,Ldume ol water per umt ~.'olun'le ~*l' .',,Ol] i|1 bulk

rn 'see

~

Din]en.,,Ion

L,' [

m ~, in - ~

V I , I' 2

Radii

m

L,

P

kg' in -

M L. -~

p÷

E)en.,,ilV E'qutvalenl 'elevtrtm' denstly ~tl' waler Bulk densily of dry mineral

kg' m-

M

P,J, tt,~, ]~',..,

m a i l e r resp water (p,, =g~N 2~) Waler uptake by r,tot,,

kt.', i n -

M L-~

( 1~ = dq,/'d: )

'.,e¢ - i

l

m see-

L,,l -I

L-

MH], O f g ; | l l l C

/,/,

tP hll,.I I

Flux ~t preclpllall~m r e n p tnlercepled prec~ptlalu.ln, vtflurne T'~dal waler D d e n l l a l expressed a s ¢ r l e r g v p e r Unll m a s ~

,1,,,,,,,,

,I k g - ' 'Tolal ener'L.W ~fl' ~aler expre',,.',;ed per u n i t volume I h t l s equivaler~t Wll h pre.'.,sure bar

L,"' l - '*

M

L,-I'l

(G,,,,,, = It'/',,,,,,, ) Gradient (V = C,',~: or V = d / d : , a'~ defined tn the [ext)

in-i

L,- i