, cm ; C (h), , cm 3 g cm - 3 g d - 1, , cm ; E (t), cm g d - 1 ; hl (t) 1 h (z, t) h 2. ], d - 1 ; T p ; L nrd (z ) h (L, t) = hl (t) t > 0 (4)

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1 T ransactions of the CSA E V o l. 20 N o. 4 July ( ) : : : ; ; ; ; : S152. 7; S : A : (2004) [ 9 - ] [ 1 ] [ 2-7 ] [ 2 8 ] W u [ 9 ] ; D irk sen C (h) 5h 5t = 5 K (h) ( 5h - 1) - S (z t) (1) 5z 5z [ 10 ] Hom aee [ 5 ] M u sters Bou ten [ 7 ] h (z 0) = h 0 (z ) 0 z L (2) ; Coelho O r [ 11 ] M u sters Bou ten [ 7 ] V rugt [ 12 ] - K (h) ( 5h 5z - 1) = - E (t) t > 0 (3) z = 0 h (L t) = hl (t) t > 0 (4) [ 13 ; ] [ ] Zuo Zhang [ 16 ] h cm ; C (h) cm - 1 ; K (h) cm g d - 1 ; S (z t) cm 3 g cm - 3 g d - 1 ; L cm L L r L r cm ; E (t) cm g d - 1 ; hl (t) cm ; z cm ; t d [ ] S (z t) [ ] S (z t) = Χ(h)S m ax (z ) = Χ(h) T p L r L nrd (z ) (5) Y (z ) - L nrd (z ) = (6) 1 L r L r Y (z ) dz 0-0 h (z t) h 1 Θ h (z t) - h 2 Χ(h) = 1 - h 1 < h (z t) < h 2 h 1 - h 2 : : : 863 (2001AA ) ; : (1965- ) Em ail: qiangzuo@cau. edu. cn 1 h (z t) h 2 [ ] [ 2 8 S m ax ] d - 1 ; T p cm g d - 1 [ 9 ; L nrd (z ) ] ; Y (z ) cm g cm - 3 ; Χ(h) (7)

2 [ 7 ] h 1 h 2 Χ(h) cm h (z t) h 2 Χ(h) h (z t) h 1 Χ(h) = 0; Θ T p L r Η 3 (z 2T ) ; 2T Η(z 1. 2 L nrd (z ) (5) S (z T ) = T 1 T S (z t) d t 0 T pl nrd (z ) L r Χ[h (z 0) ] + Χ[h (z T ) ] 2 (8) SNA P SCAN 1236 ( A GFA ) (8) W inrh IZO ( R egen t L nrd (z ) In strum en ts ) : Η(z 0) Η(z T ) ; [ ] S (z 0 T ) ; L nrd (z ) ; 0 2T T p L r L nrd (z ) L nrd (z ) (5) 0 2T ; (1) (4) 2T Χ D irk sen [ 10 ] 2T ) Η 3 (z 2T ) Η(z T ) Η(z 2T ) Hom aee [ 5 ] : [ 21 Χ ] h Χ(h) Χ(h) h 1. 3 ( ) [ 8 ] 45 cm 10 PV C M u sters Bou ten [ 7 ] (7) g cm cm cm Χ(h) h 1 h 2 M u sters Bou ten [ 7 ] h 1 = cm h 2 = - 64 cm Θ h 1 h cm 4 2 [ 7 ] 450 Θ : hm - 2 ( ) 3 cm : Y (z ) ( (5) ) Θ Θ 3 : R 3 (S S E ) d S S E ; W 1 6 d Θ S S E Θ R 50% ; W 2 6 d Θ 70% R W 1 ( ) 13 : 3 ; 5 10 ( 6 d R W 1 2 ) 5 W 2 3 ( ) Θ d 1 (t = 0 T ) Η(z 0) Η(z T ) 0 T S (z T ) [15 16 ] h 0 T T p L r Y (z ) : PV C PV C 4 cm 25 cm 20 cm 1) E: R W 1 3 (8) 0 T (

3 4 : 3 ) R W cm E g d - 1 E = cm d - 1 ( 2. 0 m 3. 0 m ) 2) T p: E T R R E T E ( ) T p 3) : van Genuch ten [ 22 ] 5 d ΗS = cm 3 cm - 3 Ηr = cm 3 cm - 3 ; Α= : 1 6 ) cm - 1 n = m = mm m = 1-1gn 4) K (h) : van Genuch ten [ 22 ] K S = cm d cm (FW cm : 0 70 cm 70 cm 3 1 T able 1 So il hydraulic param eters in the field experim ent gcm K S gcm g d - 1 ΗS gcm 3 g cm - 3 Ηrgcm 3 g cm - 3 Αgcm - 1 n : 3 Θ= 4 10 cm 15 cm (5) ( 15 cm 2) W : 1 ) E: [ M icro lysim eter (M L s) ] M L s [14 ] ( : Sarto riu s W eender L andstrasse ; : ) 0 15 kg : 7 kg 0. 2 g; 7 kg 0. 5 g 2) T p : Penm an E T p [ 24 ] E p [ 25 ] T p = E T p - E p : Θ 1 W 1 W 2 W 2 F ig. 1 M easured so il w ater content p rofiles fo r treatm ent W 1 and W 2 and the sim ulated one fo r treatm ent W 2 in the co lum n experim ent W ( 1) ( 2) (7) Θ : Θ= (7) Θ

4 W 1 W 2 F ig. 4 M easured so il w ater content distributions F ig. 2 M easured roo t length density distributions fo r treatm ent W 1 and W 2 in the co lum n experim ent 4 W 1 fo r treatm ent W 1 in the co lum n experim ent 6 Θ Θ= F ig. 3 Comparisons betw een the m easured and the FW sim ulated so il w ater content distributions fo r P lo t 6 in the field experim ent 6 2 ( L nrd (z ) ( W 1) W ( 4) W 1 L nrd (z ) 5 : ( ) (8) : (8) ; 5 W 1 L nrd (z ) F ig. 5 Comparisons betw een the m easured and the estim ated no rm alized relative roo t length density distributions fo r treatm ent W 1 in the co lum n experim ent ) L nrd (z ) cm F ig. 6 M easured so il w ater content distributions L nrd (z ) fo r P lo t 6 in the field experim ent : 0 10 cm L nrd (z )

5 4 : 5 Y ield [M ]. Ed. Feddes R A Kow alik P J and Zaradny H 7 6 John W iley & Sons Inc N ew Yo rk [9 ] W u J Q Zhang R D Gui S X. M odeling so il w ater F ig. 7 Comparisons betw een the m easured and the estim ated no rm alized relative roo t length density distributions movem ent w ith w ater up take by roo ts[j ] : P lant and So il fo r P lo t 6 in the field experim ent [10 ] D irk sen C Koo l J B Koo revaar P et al. H YSWA SOR2 Sim ulation model of hysteretic w ater and so lute transpo rt in roo t zone. In W ater flow and so lute transpo rt in so ils [M ]. Ed. R u sso D and D agan G. Sp ringer V erlag [11 ] Coelho F E O r D. A param etric model fo r tw o2 dim ensional w ater up take intensity by co rn roo ts under drip irrigation [J ]. So il Sci Soc Am J : ( ) [12 ] V rugt J A van W ijk M T Hopm ans J W et al. O ne2 tw o2 and th ree2dim ensional roo t w ater up take functions fo r transient modeling[j ]. W ater R esour R es : [13 ]. [J ] : [14 ]. M icro lysim eter [J ] : [ 15 ]. [J ] (2): [16 ] Zuo Q Zhang R. E stim ating roo t2w ater2up take using an inverse m ethod [J ]. So il Science ( 9): [17 ] Ro se D A. T he descrip tion of the grow th of roo t system [J ]. P lant and So il : [ 18 ]. [J ] [ 19 ]. - [J ] (3): [20 ] Eph rath J E Silberbush M Berliner P R. Calibration of m in irh izo tron readings again st roo t length den sity data [ ] [1 ] Gardner W R. M odeling w ater up take by roo ts[j ]. Irrig Sci : [2 ] P rasad R. A linear roo t w ater up take model [ J ]. J H ydro logy : [3 ]. - - [22 ] V an Genuch ten M T H. A clo sed fo rm equation fo r [M ]. : [4 ]. [J ]. So il Sci Soc Am J : [M ]. : [5 ] Hom aee M. Roo t w ater up take under non2unifo rm tran sien t salin ity and w ater stress [ D ]. W agen ingen A gricu ltu ral U n iversity the N etherland [6 ]. - [M ]. : [7 ] M usters P A D Bouten W. A m ethod fo r identifying op tim um strategies of m easuring so il w ater contents fo r calibrating a roo t w ater up take model [J ] : J H ydro logy [8 ] Feddes R A Kow alik P J Zarandy H. W ater up take by p lant roo ts In Sim ulation of F ield W ater U se and C rop obtained from so il co res[j ]. P lant and So il : [21 ] Feddes R A Kow alik P J Ko linska2m alinka K et al. Sim ulation of field w ater up take p lants using a so il w ater dependen t roo t ex traction function [ J ] : J H ydro logy p redicting the hydraulic conductivity of unsaturated so ils [23 ] Evett S R W arrick A W M ath ias A D. W all m aterial and capp ing effects on M icro lysim eter tem peratu re and evapo ration[j ]. So il Sci Soc Am J : [24 ] M onteith J L. Evapo ration and environm ent [A ]. P roc

6 Symp Soc Exp B io l[c ] : [25 ] R itch ie J T. A model fo r p redicting evapo ration from a row crop w ith incomp lete cover[j ]. W ater R esour R es : Abstract: Estimating normalized root length den sity d istr ibution of win ter wheat using m easured so il water con ten t prof iles Zuo Q ia ng M e ng Le i W a ng D ong (Colleg e of R esou rces and E nv ironm ent and K ey L aboratory of P lant2s oil Interactions M inistry of E d ucation Ch ina A g ricu ltu ral U niversity B eij ing Ch ina) It is very difficu lt even no t im po ssib le to m easu re roo t den sity tim ely and accu rately especially in the field. How ever it is an essen t ia l p a ram eter fo r roo t study. In th is study an app roach to est im a t ing the no rm alized roo t length den sity distribu tion w as p ropo sed w h ich w as based on tw o m easu red so il w ater con ten t p rofiles and the inverse m ethod to estim ate the average roo t2w ater2up take rate. T he app roach w as also u sed to estim ate the no rm alized roo t length den sity distribu tion s of w in ter w heat grow n in so il co lum n s and in the field. T he resu lts show ed that the app roach w as reliab le to estim ate the no rm alized distribu tion s of relative roo t length den sity com pared w ith the m easu red valueṡ T herefo re the estim ated effective roo t den sity param eter can be p rovided fo r roo t2w ater2up take m odels and so il w ater flow can be sim u lated con tinuou sly even w ithou t any m easu red roo t den sity info rm ation. Key words: no rm alized roo t den sity; roo t2w ater2up take rate; so il w ater; inverse m ethod