modeling soil water movement with water uptake by roots

11
Plant and Soil 215: 7–17, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. 7 Modeling soil water movement with water uptake by roots Jinquan Wu 1 , Renduo Zhang 2, * and Shengxiang Gui 2 1 Department of Plant and Soil Sciences, Oklahoma State University, Stillwater, OK 74078, USA and 2 Department of Renewable Resources, University of Wyoming, Laramie, WY 82071-3354, USA Key words: modeling, plant water uptake, root zone, soil water Abstract Soil water movement with root water uptake is a key process for plant growth and transport of water and chemicals in the soil-plant system. In this study, a root water extraction model was developed to incorporate the effect of soil water deficit and plant root distributions on plant transpiration of annual crops. For several annual crops, normalized root density distribution functions were established to characterize the relative distributions of root density at different growth stages. The ratio of actual to potential cumulative transpiration was used to determine plant leaf area index under water stress from measurements of plant leaf area index at optimal soil water condition. The root water uptake model was implemented in a numerical model. The numerical model was applied to simulate soil water movement with root water uptake and simulation results were compared with field experimental data. The simulated soil matric potential, soil water content and cumulative evapotranspiration had reasonable agreement with the measured data. Potentially the numerical model implemented with the root water extraction model is a useful tool to study various problems related to flow transport with plant water uptake in variably saturated soils. Introduction Water uptake by plant roots greatly influences trans- port of water and chemicals in soil-plant systems. The transport process has critical effects on crop yields, as well as the quality and quantity of infiltration recharge to groundwater systems under croplands (Schmidhal- ter et al., 1994; Wallach, 1990). Enormous effort has been made to simulate soil water movement with water uptake by roots, using microscopic and macro- scopic approaches. The microscopic approach (Gard- ner, 1960) simulates water flow into individual roots. This method needs detailed information on the geo- metry of root systems, which is practically impossible to acquire. Most models simulating soil water move- ment with plant water uptake adopt a macroscopic approach, in which water extraction by plant roots is treated as a sink term distributed in the root zone. The sink term is incorporated into Richards’ equation that describes water movement in variably saturated soils (Jury et al., 1991). * FAX No: +1 307 7666403. E-mail: [email protected] Macroscopic models of root water uptake can be further divided into two groups. The first group con- tains water potential and hydraulic parameters inside plant roots (Hillel et al., 1976; Kramer and Boyer, 1995; Molz, 1981; Nimah and Hanks, 1973), which are difficult to quantify. In the second group, root wa- ter extraction rate is calculated from plant transpiration rate, rooting depth and soil water potential (Feddes et al., 1974, 1978; Gardner, 1983; Molz and Remson, 1970; Prasa, 1988; Raats, 1976). The parameters in the second group are relatively easy to obtain; therefore, the approach has been implemented into numerical models (Simunek et al., 1992; Vogel et al., 1996). However, the root water extraction models by Molz and Remson (1970) and Raats (1976) ignore the effect of soil water content on the distribution of root water uptake. For example, in Molz and Remson’s (1970) model, the root system always extracts 40% of the total transpiration from the top quarter of root zone, even if the top layer is desiccated by evapotranspira- tion. Feddes’ (Feddes et al., 1978) model takes into account the effect of soil water deficit on root wa- ter extraction by introducing a reduction coefficient dependent on soil water potential. Nevertheless, no

Upload: jinquan-wu

Post on 29-Jul-2016

214 views

Category:

Documents


1 download

TRANSCRIPT

Plant and Soil215: 7–17, 1999.© 1999Kluwer Academic Publishers. Printed in the Netherlands.

7

Modeling soil water movement with water uptake by roots

Jinquan Wu1, Renduo Zhang2,∗ and Shengxiang Gui2

1Department of Plant and Soil Sciences, Oklahoma State University, Stillwater, OK 74078, USA and2Department of Renewable Resources, University of Wyoming, Laramie, WY 82071-3354, USA

Key words:modeling, plant water uptake, root zone, soil water

Abstract

Soil water movement with root water uptake is a key process for plant growth and transport of water and chemicalsin the soil-plant system. In this study, a root water extraction model was developed to incorporate the effect ofsoil water deficit and plant root distributions on plant transpiration of annual crops. For several annual crops,normalized root density distribution functions were established to characterize the relative distributions of rootdensity at different growth stages. The ratio of actual to potential cumulative transpiration was used to determineplant leaf area index under water stress from measurements of plant leaf area index at optimal soil water condition.The root water uptake model was implemented in a numerical model. The numerical model was applied to simulatesoil water movement with root water uptake and simulation results were compared with field experimental data.The simulated soil matric potential, soil water content and cumulative evapotranspiration had reasonable agreementwith the measured data. Potentially the numerical model implemented with the root water extraction model is auseful tool to study various problems related to flow transport with plant water uptake in variably saturated soils.

Introduction

Water uptake by plant roots greatly influences trans-port of water and chemicals in soil-plant systems. Thetransport process has critical effects on crop yields, aswell as the quality and quantity of infiltration rechargeto groundwater systems under croplands (Schmidhal-ter et al., 1994; Wallach, 1990). Enormous efforthas been made to simulate soil water movement withwater uptake by roots, using microscopic and macro-scopic approaches. The microscopic approach (Gard-ner, 1960) simulates water flow into individual roots.This method needs detailed information on the geo-metry of root systems, which is practically impossibleto acquire. Most models simulating soil water move-ment with plant water uptake adopt a macroscopicapproach, in which water extraction by plant roots istreated as a sink term distributed in the root zone. Thesink term is incorporated into Richards’ equation thatdescribes water movement in variably saturated soils(Jury et al., 1991).

∗ FAX No: +1 307 7666403. E-mail: [email protected]

Macroscopic models of root water uptake can befurther divided into two groups. The first group con-tains water potential and hydraulic parameters insideplant roots (Hillel et al., 1976; Kramer and Boyer,1995; Molz, 1981; Nimah and Hanks, 1973), whichare difficult to quantify. In the second group, root wa-ter extraction rate is calculated from plant transpirationrate, rooting depth and soil water potential (Feddes etal., 1974, 1978; Gardner, 1983; Molz and Remson,1970; Prasa, 1988; Raats, 1976). The parameters in thesecond group are relatively easy to obtain; therefore,the approach has been implemented into numericalmodels (Simunek et al., 1992; Vogel et al., 1996).However, the root water extraction models by Molzand Remson (1970) and Raats (1976) ignore the effectof soil water content on the distribution of root wateruptake. For example, in Molz and Remson’s (1970)model, the root system always extracts 40% of thetotal transpiration from the top quarter of root zone,even if the top layer is desiccated by evapotranspira-tion. Feddes’ (Feddes et al., 1978) model takes intoaccount the effect of soil water deficit on root wa-ter extraction by introducing a reduction coefficientdependent on soil water potential. Nevertheless, no

8

consideration is given to the variation of the maximumroot water extraction rate (the root water extractionrate under no soil water stress) with depth in the rootzone. Prasad (1988) modified Feddes’ model to allowvariation of the maximum root water extraction ratewith depth using a linear function to represent the rootdensity distribution. As pointed out by Prasad him-self (Prasad, 1988), however, discrepancy still existedbetween observed and simulated water depletions us-ing the linear model of maximal root water extractiondistribution. A nonlinear distribution function basedon root density distributions would conceivably bringbetter agreement between observed and simulated res-ults. Another problem associated with the currentlyexisting models simulating soil water movement withroot water uptake is the lack of consideration to thegrowth of roots and shoots of annual crops, especiallywhen periodic soil water stress is involved.

The first objective of this study was to developa root water uptake model for annual crops by in-troducing a normalized distribution function of rootdensity, which characterizes the relative distributionof root density at various growth stages. The effect ofsoil water tress on the development of plant canopywas simulated using the ratio of actual to potentialcumulative transpiration. The second objective was toimplement the root water uptake model in a numericalmodel. The numerical model was used to simulate soilwater movement with root water uptake and simula-tion results were compared with data measured in afield.

Material and methods

Root uptake function

Water extraction by plant roots of annual crops isdependent on the evaporation potentiality of the at-mosphere, the plant canopy and the water content androot density in the root zone. Under optimal soil wa-ter condition, for most annual crops with relativelynarrow row spacing, the distribution of root water ex-traction is determined by the root density distribution.By assuming that the specific water extraction rate isproportional to root density under optimal soil watercondition, the maximal specific water extraction rateSmax (cm3 d−1 cm−3 or d−1) may be expressed asfollows (Feddes et al., 1978; Prasad, 1988):

Smax(z) = crLd(z) (1)

whereLd (z) is the root length density (cm cm−3); zdepth from the soil surface (cm); andcr a proportionalconstant (cm2 d−1).

The dominant process in the whole plant water re-lations is the root absorption of large quantity of waterfrom the soil and the water translocation through theplant, as well as eventual loss to the atmosphere aswater vapor. In annual crop plants, a vast majority ofthe absorbed water is lost to transpiration (Hopkins,1999). Hence, the water extraction rate from the wholeroot zone under optimal soil water conditions may beapproximated by the potential transpiration rate (Tp,cm d−1), i.e.

Tp =∫ Lr

O

Smax(z)dz (2)

whereLr is the rooting depth (cm). Substituting Equa-tion (1) into Equation (2) yields:

Tp = cr∫ Lr

O

Ld(z)dz (3)

then

cr = Tp∫ LrO Ld(z)dz

(4)

Combining Equation (1) and Equation (4) gives:

Smax(z) = TpLd(z)∫ LrO Ld(z)dz

(5)

Equation (5) can be rewritten as:

Smax(z) = Tp

LrLrd(z) (6)

whereLrd (z) is a dimensionless function representingthe relative distribution of root density:

Lrd(z) = Ld(z)

1Lr

∫ LrOLd(z)dz

(7)

The relative root density distribution is a functionof Lr , which varies with growth stages, and can betransformed to a function with a normalized depth by:

Lrd(z) = Lnrd(zr ) = Ld(zr )∫ 1OLd(zr )dzr

(8)

whereLnrd (zr ) is the normalized distribution functionof relative root density, andzr (= z/Lr ) is the nor-malized depth ranging from 0 to 1. SinceLnrd (zr ) is

9

independent of rooting depth it can be used to char-acterize root density distributions at different growthstages with a single function.

Combining Equation (6) and Equation (8), weobtain:

Smax(z) = TpLnrd(zr)

Lr(9)

For root uptake under water stress, a water stressresponse coefficient (Feddes et al., 1978) is used todetermine the specific water extraction rate:

S = α(h)Smax = α(h)TpLnrd(zr )Lr

(10)

whereα(h) is the water response function dependenton soil matric potentialh and plant species.

Under specific conditions, the general plant waterextraction model (Equation (10)) can be reduced tosome existing models. For example, if the variationof root density with depth is small, we have:

Lnrd(zr ) = LdO1Lr

∫ LOLdOdz

≈ 1 (11)

whereLd0 is a constant root density (cm cm−3) andEquation (10) is reduced to the model of Feddes etal. (1978). If the root density distribution is a linearfunction of depth with a zero density at the bottom ofthe root zone, Equation (8) becomes:

Lnrd(zr ) = αr (Lr − z)1Lr

∫ LO αr(Lr − z)dz

= 2(1− z/Lr)

(12)

whereαr is a root distribution coefficient (cm cm−3 cm−1).Substituting Equation (12) into Equation (10) yields:

S = 2α(h)Tp

Lr(1− z/Lr) (13)

which is the same as Prasad’s (1988) model. As shownbellow, in generalLnrd is a nonlinear function ofzr (=z/Lr ) and can be determined from root density data.

Potential transpiration and rooting depth

The potential transpiration rate (Tp) is the maximumpossible water uptake by roots and calculated using thepotential evapotranspiration (ETp) from both plant and

soil surface, and the potential evaporation (Ep) fromthe soil surface:

Tp = ETp − Ep (14)

The potential evapotranspiration rateETp (cm d−1)can be evaluated using a modified Penman equation(Monteith, 1965). The potential evaporation rateEp(cm d−1) from the soil surface is computed fromanother modified Penman equation (Ritchie, 1972):

Ep = δ

(δ + γ )LRnexp(−0.39A) (15)

whereδ is the slope of the saturation vapor pressurecurve;Rn the net solar radiation flux (W m−2); L thelatent heat of vaporization of water per unit mass (Jkg−1); γ the psychrometer constant (mbar◦K−1); andA is the leaf area index.

Rooting depth and leaf area index have a great ef-fect on evapotranspiration. The development of plantroots and leaves are influenced by the available soilwater in the root zone. Therefore, the relationshipsbetween leaf area index or rooting depth and growthstages differ in different soil water regimes. Signific-ant reductions in leaf area index are observed underwater stress (Mayaki et al., 1976). The growth curvesof rooting depth and leaf area index under optimal soilwater condition are employed as the reference growthcurves. In analogy to yield-water relationship of al-falfa (Heichel, 1983; Tanner and Sinclare, 1983), thefollowing equation is proposed for characterizing thedevelopment of plant leaves under water stress:

A(t) =∫ tO Ta(t)dt∫ tOTp(t)dt

Ap(t) (16)

whereA is the leaf area index under water stress;Apthe leaf area index under optimal water condition;t thetime after planting (d), and the numerator and denom-inator of the right-hand side are the cumulative actualand potential transpiration, respectively. The leaf areaindex under optimal soil water condition can be ob-tained from experimental observations (Gardner et al.,1985; Heichel, 1983; Jordan, 1983). The actual tran-spiration rate is evaluated from the water extractionrate by:

Ta(t) =∫ Lr

O

S(z, t)dz (17)

For most species of annual crops, drought has muchless effect on the development of root systems than on

10

canopy development. In an experiment on the growthof soybeans at Manhattan, Kansas, Mayaki et al.(1976) observed that the height and leaf area index ofirrigated soybeans almost doubled those of nonirrig-ated soybeans, while the rooting depths of the irrigatedand nonirrigated soybean plants were virtually thesame. Therefore, for annual crops with water stresseswithin a certain extent, measured growth curves ofrooting depth under optimal soil water condition maybe used directly in simulations.

The growth of plant height, leaf area and rootingdepth can typically be described by a sigmoid growthfunction comprising four growth periods (Gardner etal., 1985). The growth in the early period is rep-resented by an exponential growth rate; followingis a linear growth period with a relatively constantgrowth rate; after the linear growth period the increasein growth becomes progressively less until the lastgrowth period, the steady state, is reached. The fol-lowing equation is proposed to describe the sigmoidalgrowth dynamics of plant height and rooting depth:

H(tnm) = Hm{ l + agag[l + agexp(−bgtnm)] −

l

ag}(18)

HereH represents plant height or rooting depth (cm);Hm the maximal plant height or rooting depth (cm);andag andbg are dimensionless coefficients depend-ent on growth rates at different growth stages; andtnmis a normalized time defined as:

tnm = (t − tp)/Tg (19)

in which t is time after an arbitrary beginning date(day); tp planting time from the beginning date (day);andTg the total length of a growth season (day). Aprobability density function is modified to simulate thevariation of leaf area index with growth time:

Ap(tnm) = Amexp[−dg(tnm − cg)2] − exp(−dgc2

g)

1− exp(−dgc2g)

(20)

where Am is the maximal leaf area index;cg thenormalized peak time when leaf area index is at itsmaximum value; anddg a dimensionless coefficientdependent on growth and senescence rate of leaves.For a specific crop,Am, cg anddg can be determinedby fitting leaf area index data measured under optimalsoil water condition (i.e. under no soil water stress forthe whole growth period).

Water flow equations

From a macroscopic point of view, Richards’ equa-tion combined with a root-extraction sink term canbe used to describe soil water movement with plantwater uptake. For densely populated crops with a re-latively uniform horizontal distribution of root waterextraction, the following one-dimensional model isemployed to simulate movement of soil water in avertical profile under rainfall and irrigation infiltrationand evapotranspiration (Vogel et al., 1996):

∂θ

∂t= ∂

∂z[K(θ)(∂h

∂z− 1)] − S (21)

Here h is soil matric potential (cm);t time (day);K soil hydraulic conductivity (cm d−1); θ volumet-ric soil water content (cm3 cm−3); z the Cartesiancoordinate originating from soil surface and positivedownward (cm); andS the sink term representing thewater extraction rate by plant roots per bulk volumeof soil (d−1) (Equation (10)). The initial and boundaryconditions are expressed by:

h(z, t) |t=0= h0(z)

−K(θ)(∂h∂z− l) |z=0= q0

h(z, t) |z=D= 0 (22)

whereh0(z) is the initial distribution of matric poten-tial in the profile;D the depth to the water table (cm);q0 either the net rainfall intensity or the actual soil sur-face evaporation rate. The actual evaporation from thesoil surface is evaluated based on the potential evapor-ation rate calculated using Equation (15) and the watercontent at soil surface (Wu et al., 1996):

Es = Ep θ0− θaθf − θa , θa < θ0 ≤ θf

Es = 0, θ0 < θa;Es = Ep, θ0 > θf (23)

whereEs is the actual evaporation rate from soil sur-face;θ0 water content at soil surface;θa air-dry watercontent of the top soil; andθf field capacity of thetop soil. If rainfall intensity is so high that pondingoccurs at soil surface, or flood irrigation is appliedover a field, the upper boundary is changed from theflux-type boundary into a pressure-type boundary:

h(z, t) |z=0= 0 (24)

The flow equations were solved numerically by modi-fying HYDRUS (Vogel et al., 1996), a code for sim-ulating one-dimensional water flow, solute transport

11

Figure 1. Vertical and horizontal layout of tensiometers and access tube for the neutron probe.

and heat movement in variably saturated media. Inthe numerical model, the sink term was implementedbased on the root water extraction model developed inthis paper.

Field experiment

To show the application of the numerical model withthe root water extraction model, we used a data setfrom a two-year field experiment. The experiment wasconducted at an experiment station in Henan provinceof northern China beginning in April 1988. The aver-age annual precipitation was 66 cm and the averageannual water surface evaporation from an E-601 evap-oration pan (equivalent to the US Weather Bureau

(USWB) class A pan) was 123 cm. The precipitationusually concentrated in a rainy season from May toOctober. The average groundwater depth at the stationwas 3.69 m in the non-raining season and the averagefluctuation range of the water table was 1.99 m. Thefluctuation was mainly caused by infiltration rechargefrom rainfall and irrigation, pumping of groundwaterfrom the phreatic aquifer and leakage from an irriga-tion channel. The soil profile of the experiment fieldcomprised two layers: the texture of the upper layerfrom 0 to 2.0 m was sandy loam and of the lowerlayer from 2.0 to the maximum sampling depth 3.5m fine sand. The plant rotation in the field includedsummer maize (Zea maysL.) (from early June to late

12

Table 1. Soil hydraulic parameters in the two main layers of the experimental plot

Depth Soil type Ks θs θr α n

(m) (cm d−1) (cm3 cm−3) (cm3 cm−3) (cm−1)

0–2.0 Sandy loam 73.50 0.445 0.076 0.0070 3.12

2.0–3.5 Fine sand 384.7 0.356 0.010 0.0091 5.59

Ks : saturated hydraulic conductivity;θs andθr : saturated and residual water content;α andn: coefficients in the van Genuchten (1980) equation.

September) and winter wheat (Triticum aestivumL.)(from early October to early June of next year).

Twelve tensiometers were installed near an obser-vation well in the field, at the depths of 0.1, 0.2, 0.3,0.4, 0.6, 0.8, 1.0, 1.2, 1.5, 2.0, 2.5 and 3.0 m. The ten-siometers were arranged in two rows 0.60 m apart. Aneutron-probe access tube, 3.5-m deep, was placed inthe center between the tensiometers. The vertical andhorizonal layout of the access tube and tensiometersis shown in Figure 1. Measurements of matric po-tential and water content were taken every five daysduring the two-year experiment. Additional measure-ments were conducted after irrigation and relativelylarge rainfall events. The operation of tensiometerswas interrupted by freezing in the winters (from themiddle of November to the end of March).

Soil samples were taken from the spoils of the in-stallation holes of the tensiometers and neutron-probeaccess tube. The hydraulic conductivity and retentionfunctions of the two main layers, the sandy loam andfine sand, were determined from laboratory experi-ments of the soil samples. The closed-form functionsof Van Genuchten (1980) were used to fit the experi-mental data, and the fitted parameters are summarizedin Table 1.

Results

Based on various data sets of root density observa-tions (Merrill, 1992; Merrill et al., 1987; Rowse et al.,1978; Stibbe and Hadas, 1977; Upchurch and Ritchie,1984; Vos and Groenwold, 1987), we analyzed thenormalized relative root density distributions of wheat,maize, cotton and beans (field bean and broad bean).In the analysis, we normalized the observed root dens-ity distributions using Equation (8) and then pooledtogether the normalized root distribution data at differ-ent growth stages for each crop (Figures 2 (a–d)). Asshown in Figure 2, the normalized relative root densitydistributions at different growth stages are quite sim-ilar, which indicate the feasibility of using a single

normalized root density function for the whole growthseason of each crop. A third-order polynomial equa-tion was utilized to fit the pooled data of each crop asfollows:

Lnrd(zr ) = R0+ R1zr + R2z2r + R3z

3r (25)

whereRi (i = 0, 1, 2, 3) are the polynomial coeffi-cients. The fitted polynomial coefficients and coeffi-cients of determination (r2) are listed in Table 2 forthe crops.

The numerical model solving Equations (21)–(24)was used to simulate soil water distributions and ac-tual evapotranspiration loss from the monitored fieldduring the corn-growth season of 1988. The crop wasplanted on June 10 after a pre-seeding irrigation andharvested on September 21 immediately after matur-ity. Rooting depth data from a maize field with soilproperties similar to our simulated field were usedto determine the parameters of root growth in Equa-tion (18). Data of plant height and leaf area indexunder optimal soil moisture condition were obtainedfrom an irrigation experiment plot near the monitoredfield. Growth parameters of rooting depth and plantheight were determined by fitting Equation (18) tothe observed data (Table 3). Fitting Equation (20) tothe observed leaf area index data yieldedAm = 4.44,cg = 0.624 anddg = 2.053 (r2 = 0.986). The rootdistribution parameters used in the simulation were de-termined from minirhizotron-observation and washed-soil-sample data (Merrill et al., 1987; Upchurch andRitchie, 1984).

The potential evapotranspiration and potential soilsurface evaporation were calculated from the met-eorological data observed at the experimental station(Figure 3). Observed rainfall data and irrigation re-cords were used for the simulation. It was assumedthat no soil surface evaporation occurred during therainfall or irrigation periods. The simulation beganfrom the day of planting, and the observed distributionof matric potential on that day was used as the initialprofile. In the simulation, the lower boundary changed

13

Figure 2. Normalized relative root density distribution functions for (a) wheat, (b) maize, (c) cotton, and (d) beans. The circles are lumped dataof normalized relative root density based on various sources in the literature.

Table 2. Polynomial coefficients inLnrd (zr ) for different crops

Crop Reference R0 R1 R2 R3 r2

Wheat Vos and Groenwold, 1987; Merrill, 1992 2.21−3.72 3.46 −1.87 0.959

Maize Upchurch and Ritchie, 1984; Merrill et al., 1987 2.15−1.67 −2.36 1.88 0.973

Cotton Stibbe and Hadas, 1977 1.46−0.18 −0.62 −0.66 0.943

Beans Rowse et al., 1978; Vos and Groenwold, 1987 1.44−0.14 −0.61 −0.69 0.948

with time according to the variation of groundwaterdepth measured through the observation well.

The simulated cumulative evapotranspiration wascompared with the cumulative evapotranspiration(CET) from the monitored field. The CET in the fieldwas estimated from the measurements of water content

and matric potential based on the following root zonewater balance equation:

CET(t) = W0 −W(t) +∑

I (t) −∑

qd(t)

(26)

14

Figure 3. Potential evapotranspiration and potential soil surface evaporation. The evapotranspiration was calculated with a modified Penmanequation using daily meteorological data observed at an irrigation experiment station in Henan province of northern China. The potentialsoil surface evaporation was calculated using Equation (15). The noisy fluctuation of the calculated daily values was smoothed out through aleast-square optimization procedure.

Table 3. Growth parameters of rooting depth and plantheight

Component part Hm (m) ag bg r2

Rooting depth 1.487 5.372 6.105 0.997

Plant height 1.654 25.98 9.174 0.999

where∑

I(t) is cumulative infiltration from rainfalland irrigation (mm);W0 initial water storage in the soilprofile (mm); W(t) water storage (mm); and

∑qd (t)

cumulative deep percolation (mm) at timet. The cu-mulative rainfall and irrigation were calculated fromthe rainfall data and irrigation records; the water stor-age was calculated from the neutron-probe measure-ments of soil water content; and the deep percolationwas determined from soil water flux at the depth of1.75 m. The soil water flux at 1.75 m was calculatedfrom the matric potentials measured by tensiometersinstalled at the depths of 1.5 and 2.0 m.

Figure 4 compares the cumulative evapotranspira-tion determined from measured soil matric potentialand soil water content with the simulation results. Thesimulated CET matched the measured CET with the

maximum deviation about 10% when taking into ac-count the effect of water stress on the development ofplant canopy. The simulated CET without consideringthe water-stress effect on the growth of plant leavesand stems significantly overestimated the cumulativeevapotranspiration loss by more than 25%.

As examples, Figure 5 compares the simulated andobserved soil suction head (the absolute value of soilmatric potential) and soil water content 5 days afteran irrigation event, and Figure 6 compares the res-ults 10 days after the irrigation event. The simulatedsoil suction head and soil water content match theobserved data with average relative deviations of 10and 15%, respectively, on the 5th day. On the 10thday, the average relative deviations between simulatedand observed results are 15 and 20% for soil suctionhead and soil water content, respectively. In the sim-ulation, the soil near the surface (to a depth about25 cm) dried very quickly. The high suction valuesnear the soil surface obtained from the numerical sim-ulations were supported by the field observation. Inthe filed experiment, the operation of the tensiometersnear the soil surface broke down because of fast wa-ter loss from the tensiometers into the desiccated soilabout two weeks after the irrigation. The simulation

15

Figure 4. Comparison of simulated cumulative evapotranspiration with that calculated from measured soil matric potential and soil watercontent. The solid line represents the simulation result by considering the water stress effect on plant height and leaf area index development,whereas the dashed line without considering the water stress effect. The dots represent the calculated cumulative evapotranspiration from themeasured data at different growth stages.

Figure 5. Comparison of simulated and measured (a) suction head (the absolute value of soil matric potential) and (b) water content 5 daysafter an irrigation event.

results also show the discontinuity in the water contentdistributions attributable to the change in soil texture.

Summary

A water extraction model incorporating the effect ofwater stress and root density distribution was de-

veloped to simulate root water uptake by plants. Underspecific conditions, the general plant water extractionmodel can be reduced to some existing models, suchas the model of Feddes et al. (1978) and Prasad’s(1988) model. A nonlinear function of normalizedroot density distribution was proposed to character-ize the relative distribution of root density at differ-ent growth stages. Observed root density data from

16

Figure 6. Comparison of simulated and measured (a) suction head (the absolute value of soil matric potential) and (b) water content 10 daysafter an irrigation event.

various sources were analyzed to determine the nor-malized root density functions for annual crops ofwheat, maize, cotton and beans. Plant height and leafarea index under water-stress conditions were simu-lated by modifying the reference growth curves underoptimal soil water conditions with the ratio of actualto potential transpiration. A one-dimensional numer-ical model was developed and the water extractionmodel was implemented to simulate soil water move-ment with plant water uptake. Numerically simulatedresults were compared with data from a field exper-iment, which serves as an example to illustrate theapplication of the numerical model and the root wa-ter uptake model. The measured soil matric potentialand soil water content were used to evaluate actualevapotranspiration from the field. Comparison of thesimulated cumulative actual evapotranspiration withthat calculated from the measured soil matric potentialand soil water content exhibited good accordance withthe maximum deviation about 10%, as the effect ofwater stress on the growth of plant leaves and stemswas considered. In this example, the simulated soilmatric potential and soil water content were compar-able with the measured data with an average deviationbetween 10 and 20%. The numerical model with theroot water extraction model can be applied for vari-ous practical problems, such as to simulate infiltrationrecharge to groundwater in croplands and to guideirrigation schedules. Combined with chemical trans-port processes, the models can be used to evaluate theeffect of agrochemicals on groundwater quality.

Acknowledgements

The authors thank Dr M B Kirkham and anotheranonymous reviewer for their critical review of themanuscript.

References

Feddes R A, Bresler E and Neuman S P 1974 Field test of a modifiednumerical model forwater uptake by root systems. Water Res.Res. 10, 1199–1206.

Feddes R A, Kowalik P J and Zaradny H 1978 Water uptake by plantroots.In Simulation of Field Water Use and Crop Yield. Eds RAFeddes, PJ Kowalik and H Zaradny. pp 16–30. John Wiley &Sons, Inc., New York.

Gardner W R 1960 Dynamic aspects of water availability to plants.Soil Sci. 89, 63–73.

Gardner W R 1983 Soil properties and efficient water use: A review.In Limitations to Efficient Water Use in Crop Production. EdsHM Taylor, WR Jordan and TR Sinclair. pp 45–64. SSSA, 677South Segoe Road, Madison.

Gardner F P, Pearce R B and Mitchell R L 1985 Physiology of cropplants. The Iowa State University Press, Ames, Iowa 50010.

Heichel G H 1983 Alfalfa.In Crop-water Relations. Eds ID Teareand MM Peet. pp 127–155. John Wiley & Sons, Inc., New York.

Hillel D, Talpaz H and Van Keulen H 1976 A macroscopic-scalemodel of water uptake by a nonuniform root system and of waterand salt movement in the soil profile. Soil Sci. 121, 242–255.

Hopkins W G 1999 Water relations of the whole plant.In Introduc-tion to Plant Physiology. Ed. WG Hopkins. pp 37–59. John Wiley& Sons, Inc., New York.

Jordan W R 1983 Cotton.In Crop-Water Relations. Eds. ID Teareand MM Peet. pp 213–253. John Wiley & Sons, Inc., New York.

Jury W A, Gardner W R and Gardner W H 1991 Soil physics. JohnWiley & Sons, Inc., New York. 328 p.

Kramer P J and Boyer J S 1995 The absorption of water and rootand stem pressures.In Water Relations of Plants and Soils. EdsPJ Kramer and JS Boyer. pp 167–200. Academic Press, Inc., SanDiego.

17

Mayaki W C, Teare I D and Stone L R 1976 Top and root growth ofirrigated and nonirrigated soybeans. Crop Sci. 16, 92–94.

Merrill S D 1992 Pressurized-wall minirhizotron for field observa-tion of root growth dynamics. Agron. J. 84, 755–758.

Merrill S D, Doering E J and Reichman G A 1987 Application of aminirhizotron with flexible, pressurized walls to a study of cornroot growth, Minirhizotron Observation Tubes: Methods andapplications for measuring rhizosphere dynamics. ASA specialpublication. ASA, 677 Segoe Road, Madison. 50, 131–143.

Molz F J 1981 Models of water transport in the soil-plant system: Areview. Water Res. Res. 17, 1245–1260.

Molz F J and Remson I 1970 Extraction term models of soil mois-ture use by transpiring plants. Water Res. Res. 6, 1346–1356.

Monteith J L 1965 Evaporation and environment. Proc. Symp. Soc.Exp. Biol. 19, 205–234.

Nimah M N and Hanks R J 1973 Model for estimating soil wa-ter, plant and atmospheric interrelations: I. Description andSensitivity. Soil Sci. Soc. Am. Proc. 37, 522–532.

Prasad R 1988 A linear root water uptake model. J. Hydrol. 99, 297–306.

Raats P A C 1976 Analytical solutions of a simplified flow equation.Trans. ASAE. 19, 683–689.

Ritchie J T 1972 A model for predicting evaporation from a rowcrop with incomplete cover. Water Res. Res. 8, 1204–1213.

Rowse H R, Stone D A and Gerwitz A 1978 Simulation of thewater distribution in soil, II. The model for cropped soil and itscomparison with experiment. Plant Soil. 49, 533–550.

Schmidhalter U, Selim H M and Oertli J J 1994 Measuring andmodeling root water uptake based on chloride discrimination ina silt loam soil affected by groundwater. Soil Sci. 158, 97–105.

Simunek J, Vogel T and Van Genuchten M Th 1992 The SWMS_2Dcode for simulating water flow and solute transport in two-dimensional variably saturated media, V.1.1, Research ReportNo. 126, U.S. Salinity Lab, ARS USDA, Riverside.

Stibbe E and Hadas A 1977 Response of dryland cotton plantgrowth, soil-water uptake and lint yield to two extreme types oftillage. Agron. J. 69, 447–451.

Tanner C B and Sinclair T R 1983 Efficient water use in crop pro-duction: Research or re-search?In Limitations to Efficient WaterUse in Crop Production. Eds HM Taylor, WR Jordan and TRSinclair. pp 1–27. SSSA, 677 South Segoe Road, Madison.

Upchurch D R and Ritchie J T 1984 Battery-operated color videocamera for root observations in minirhizotrons. Agron. J. 76,1015–1017.

Van Genuchten M Th 1980 A closed-form equation for predictingthe hydraulic conductivity of unsaturated soils. Soil Sci. Soc.Am. J. 44, 892–897.

Vogel T, K Huang, R Zhang and Van Genuchten M Th 1992The HYDRUS code for simulating one-dimensional water flow,solute transport and heat movement in variably saturated media,V.5.0, Research Report No. 140, U.S. Salinity Lab, ARS USDA,Riverside.

Vos J and Groenwold J 1987 The relation between root growthalong observation tubes and in bulk soil. Minirhizotron Observa-tion Tubes: Methods and applications for measuring rhizospheredynamics. ASA special publication. ASA, 677 Segoe Road,Madison 50, 39–49.

Wallach R 1990 Soil water distribution in a nonuniformly irrigatedfield with root extraction. J. Hydrol. 119, 137–150.

Wu J, Zhang R and Yang J 1996 Analysis of rainfall-rechargerelationships. J. Hydrol. 177, 143–160.

Section editor: BE Clothier