Dynamics of Water in Zea Mays L.Sensitivity Analysis of TROIKA ~

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ABSTRACTW ATER movement from the soil into roots, through

the plant, and out into the atmosphere in responseto the microclimate was simulated for field-grown maize(sweet corn) plants. Predicted leaf water potentials werecompared with field-measured values. A sensitivityanalysis of the simulation model was performed toindicate the required measurement accuracy for certainparameters.

Variations in internal plant (stem) resistance and leafarea significantly affected leaf water potentialpredictions. Root length and root permeability had lessdramatic effects. The model is relatively insensitive tochanges in root radius and leaf width.

emphasis on steady-state soil water. Molz and Remson(1971), Whisler et al. (1968) and Gardner (1964)conducted macroscopic studies of moisture removal fromthe root zone. They did not consider the effects of rootson the aerial portion of the crop. Nimah and Hanks(1973) developed a macroscopic model to predict watercontent profiles, evapotranspiration, water flow from orto the water table, root extraction, and root waterpotential under transient field conditions, but theirmodel does not predict leaf water potentials where manykey physiological processes occur. It does provide a"stem" water potential however. Taylor and Klepper(1978) presented a model to predict diurnal soil, root andplant water potentials. This model requires accurateinput rates of plant transpiration and root water uptakefrom each soil layer. Molz (1976) used transient radialflow models to study water movement to plant roots,again without considering the influence of the aerialportion of the crop on the water potential within the soil-plant-atmosphere system. Hillel et al. (1975) andBelmans et al. (1979) used a transient radial flow modelthat yielded plant water potentials necessary to maintaindifferent uptake rates.

The power of systems analysis is limited when theentire interacting system is not included within theanalysis, as in the case when a potential is forced to occurat a specific point in a system-e.g., when a waterpotential is assumed within the root xylem tissue or at theroot-soil interface. Federer (1979) simulated the soil-plant-atmosphere system for forest species to estimatetranspiration. Hansen (1975) combined Gardner's model(1960) for water flow to single roots, Monteith's model(1965) of the atmosphere, and internal cropconsiderations to simulate water transport in a growingcrop. Lambert and Penning de Vries (1973) simulatedthe entire soil-plant-atmosphere system. Thoughsomewhat simplified, the model did not force anypotentials or fluxes to be fixed within the system. Thispaper and its companion (Reicosky and Lambert, 1977)continue the efforts of Lambert and Penning de Vries(1973) to dynamically simulate water movement andpotentials throughout the soil-plant-atmosphere systems.

INTRODUCTIONAll physiological processes in a crop depend on water

status of the organ. Photosynthesis, cell expansion,translocation, etc., are all water-dependent and essentialto a healthy, growing and productive crop. Increases infood production efficiency may be possible when weunderstand more fully the dynamic behavior of water ingrowing plants.

Water potential gradients cause water to move fromthe surrounding soil to root surfaces, through the plantand out into the atmosphere. The transport processes aredynamic and the rates are transient. Steady state isseldom the case. Thus the microclimate variables are ofprime importance in driving the system. No two cropsystems behave alike due to differences in hydrauliccharacteristics of the soil, variations in rooting behavior,climatic differences, and inherent ~rop characteristics.

Many research workers have investigated waterrelations in plants. Considerable emphasis has beenplaced on evaluating flow and resistances to flow inspecific plant parts, e.g., roots (e.g., Busscher andFritton, 1978; Landsberg and Fowkes, 1978; Meyer etal., 1978; Shalhevet et al., 1976) and the (near) totalplant (e.g. Meyer and Ritchie, 1980; Hansen, 1974;Hailey et al., 1973). Several attempts to relate plant andsoil resistances have also been made (e.g. Burch, 1979;Ruckenbauer and Richter, 1980; Reicosky and Ritchie,1976).

Radial flow of water to a single root was used by Philip(1957) and Gardner (1960) to study water movement with

Article has been reviewed and approved for publication by the Soiland Water Div. of ASAE.

Technical contribution No. 1435, SC Agricultural ExperimentStation. Published by permission of the Director.

The authors are: JERRY R. LAMBERT, Professor, AgriculturalEngineering Dept., Clemson University, Clemson, SC; and DONALDC. REICOSKY, Soil Scientist, USDA.ARS, Morris, MN.

1984- TRANSACTIONS of the ASAE @ 1984 American Society of Agricultural Engineers 0001-2351/84/2701-0117$02.00 117

OBJECTIVESWater movement and potentials directly affect the

growth processes of a crop. As we try to optimize the netresult of these processes and the associated economics,knowledge of the plant-water status is vital. Therefore,our objective is to quantify the dynamic response ofmaize to different soil water levels and the environmentto determine soil water "treatments" that improvegrowth and yield. The specific objective of this paper is toperform a sensitivity analysis of six selected plantparameters as they affect leaf water potential simulated

by the modified model TROIKA to determine thedesired observation accuracy of these parameters.

THE MODELTROIKA is a model developed by Lambert and

Penning de Vries (1971, 1973) to simulate watermovement from soil, through the root, stem and leafsystem of a bean-like plant which has a single horizontalleaf, and then out into the atmosphere. AlthoughoriginalIy developed to describe a bean plant, the modelwas modified and extended to describe maize. Thegeneral model form is schematized in Fig. 1 and outlinedbelow. The specific changes resulting in this version aredescribed.

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(WSUPRT)Fig. 2-System dynamics flow chart of TROIKA. (a) Water flowthrough soil. (b) Water flow through plant. (c) Heat flow through leaf.(a)

1984- TRANSACTIONS of the ASAE118

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Conceptually, TROIKA is based on a complete butsimplified treatment of water movement from the bulksoil, through unsaturated soil to the root surface,through the root and stem to the leaves, and thenthrough the cuticle or stomates and boundary layer intothe free atmosphere. Water storage is present in leaves,roots, and in each thin annular cylinder of soil coaxialwith the root, and is a level or state variable in systemdynamics terminology. Flow between each serial pair oflevels depends on the applicable potential difference andthe conductivity. Each level is an integral ofa net fluxrate, which is dependent on system parameters,environmental variables and functional relations as wellas potential differences. A continuous, dynamic flowsystem results.

Water and heat movement in the soil-plant-atmosphere system, as conceptualized in TROIKA, isflow charted in detail in Fig. 2. As indicatedschematically by arrows, water moves radially from theoutermost annular cylinder or shell of soil throughsuccessive shells and into the root xylem. The radius ofsoil surrounding the root is determined from the soilvolume occupied by roots and the length of roots whichare active in water uptake. While unsaturatedconductivity of soil is used to calculate flow of waterbetween shells of soil, flow from the first soil shell intothe root zylem is based on the PERmeability of the RooT(PERRT). Water flow from inside the root xylem to themesophyll cells is caused by the difference between theTotal Water PoTential of the RooT and Total WaterPoTential of the LEaves (TWPTRT and TWPTLE)across the RESistance in the STem (RESST) or internalplant resistance, even though we find a lack of data toconfirm or disprove this simple assumption. We definestem resistance to be the total resistance from the rootxylem to the substomatal cavity. Thus, it includesresistance to flow within the root xylem, in the stem andpetiole xylem tissue, and across all tissue between thevein xylem and the substomatal cavity or the epidermaltissue. From the mesophyll tissue water moves into theatmosphere a<:ross a combined cuticular resistance andstomatal resistance, hereafter referred to as leafresistance (RSUBL) in series with the boundary layerresistance (RSUBW).

Determination of the water loss from the leaves hasbeen simplified in this version of the model (Fig. 2b).The boundary layer resistance (RSUBW) remainsessentially unchanged, but the leaf resistance (RSUBL)no longer includes the detailed calculations of water andCO2 movement into and out of the guard cells, whichwere present in the original version of the model(Penning de Vries, 1972). Instead, experimental data oncombined stomatal and cuticular resistance as a functionof leaf water potential have been used directly. Amaximum resistance of80 s/cm represents the <:uticularresistance, since the stomates are then closed. Thestomates are assumed to be closed in darkness and to beas open as allowed by water potential considerations at0.1 cal/cm2/min radiation. Experimental data were alsoused to determine leaf water potential from relative watercontent of the leaf (Reicosky and Lambert, 1977).

The vapor concentration within the substomatal cavityis assumed to be that of saturation, and, therefore, isdependent on leaf temperature. The Initial LeafTemperature (TU) is assumed equal to initial (in this

1984- TRANSACTIONS of the ASAE

study, pre-dawn) air temperature and a dynamic heatbalance on the leaves is based on incoming short waveradiation, latent heat of evaporation, convection,reflection and reradiation (Fig. 2c). Long wave radiationfrom the leaf is calculated using the method of Idso andJackson (1969).

The concepts were quantified by programming inCSMP (Continuous System Modelling Program) allrelationships here described (Lambert and Penning deVries, 1971).

VALIDATIONMaize (sweet corn) grown at Florence, South Carolina,

during 1972 on Varina sandy loam (Reicosky et al.,1975) was used to validate the modified model TROIKA,as reported elsewhere (Reicosky and Lambert, 1977).Certain parameters were obtained from the literature;other pai"ameters and variables were observedexperimentally. Initial values of twoparameters-PERmeability of the RooT (PERRT) andRESistance of the STem (RESST)-were first estimatedfrom House and Findlay (1966) and Nobel (1974, p.406), respectively, and then adjusted so that predictedand observed leaf water potentials agreed more closely.

SENSITIVITY ANALYSIS

A sensitivity analysis of a model indicates the responseof the predicted variables to variations in the values ofthe parameters of the model. Thus, we can determine thedesired observation accuracy of these parameters.

Six parameters were selected for this sensitivityanalysis from about 20 included in the model. Selectionof the parameters was based on their strategic position inthe flow charts (Figs. 1 and 2) and by intuition. Theparameters not included in the sensitivity analysis wereeither interrelated (e.g. root length, root volume, andnumber of assumed soil shells); previously investigated(e.g. weighting factor for determining effectiveconductivity between two adjacent shells (de Wit and vanKeulen, 1972); handbook constants (e.g. diffusivecoefft<:ient of heat in air); or initial conditions, whichcould only have an effect during the early times of asimulation (e.g. Initial Leaf Temperature, TLI). The sixselected parameters covered those easily observed (leafwidth) and those more difficult (stem resistance),average values (root radius) and single values (leaf area),and parameters expected to have the same short-termeffect but possibly different long-term effects throughfeedback (root length and root permeability).

The heat balance is based on exposed leaf area withtranspiration from shaded leaves assumed negligible.The actual leaf area per plant is used until the Leaf AreaIndex (LAI) exceeds 1.0. If a leaf area greater thanground area per plant were used, the incoming radiationintercepted by the plant would exceed the radiationactually available to the plant. Therefore Leaf AreaIndex is limited to LAI = 1 and is one limitation of themodel.

Observed Leaf Water Potential (OLWP) measuredwith a pressure chamber throughout the day and thepredicted Total Water PoTential of the LEaf (TWPTLE)were compared based on:

1. measured average Leaf WiDTh (WDTL),2. measured LEaf ARea (ARLE), limited to LAI = 1,3. maize root RADIUS (RADIUS) data from

Newman (1973),

TABLE 1. PARAMETER VALUES USED IN THE MODELTO SIMULATE MAIZE LEAF WATER POTENTIAL

ON JULIAN DAY 153.

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House and Findlay (1966) and adjusted to obtain betteragreement between predicted and observed leaf waterpotential.

The base line yalues of these six parameters are givenin Table 1. Julian day 153, 1 June 1972 was chosen forthe sensitivity analysis. Observed microclimate data usedin the model are shown in Fig. 3 along with the observedand simulated leaf water potentials for the irrigated andnon-irrigated treatments described by Reicosky andLambert (1977).

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RESULTS AND DISCUSSION

Both the Observed Leaf Water Potential (OLWP) andthat predicted (TWPTLE) using the base line parametersin Table 1 are shown in Figs. 4-13 for comparison. Eachparameter is increased and decreased by appropriatemultiples of the measured or estimated values so that theeffects of variation of the particular parameter can beevaluated.

WiDTh of the Leaf (WDTL) (Fig. 4) is not verysignificant in predicting leaf water potentials throughouta day in the irrigated treatment. The spread of the curveswas even narrower for the non-irrigated treatment (datanot shown). The role of leaf width, taken to be theaverage width of the upper maize leaves, in the model isto determine the thickness of the laminar boundary layeradjacent to the leaf across which water must diffuse to

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TIME, HoursFig. 5-Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for three different LEaf AReas(ARLE) In the Irrigated treatment.

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TIME, Hours

Fig. 4-Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for three different values of LeafWIDTh (WDTL) In the irrigated treatment.

120 1984- TRANSACTIONS of the ASAE

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Fig. 6-Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for three different LEaf AReas(ARLE) In the non. Irrigated treatment.

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get to the free atmosphere. The equation used is DL =0.34 WDTL/WS (Monteith, 1965) where DL is thediffusion length and WS is wind speed. The boundarylayer resistance is in series with the paralleled stomataland cuticular resistances. Therefore, as long as theboundary layer resistance is relatively low, the totalresistance to water diffusion from within the leaf to thefree atmosphere is not significantly affected by avariation in leaf width (this occurs when wind speed isrelatively high). The implication is that relatively crudeleaf width measurements will suffice for use in TROIKA.

LEaf ARea (ARLE) should be determined withconsiderable more accuracy than that required for leafwidth. As can be seen in Fig. 5, a 4-bar differenceresulted from halving or doubling the base line leaf area(1548 cm2) for the irrigated treatment under theenvironment used for this sensitivity analysis. On thenon-irrigated treatment at lower soil moisture, however,a different pattern occurs, as shown in Fig. 6. Althoughhalving leaf area resulted in a 3- to 4-bar increase in leafwater potential from mid-morning to mid-afternoon,doubling the leaf area did not decrease the predicted leafwater potential nearly as much. The implication is thatoverestimation of leaf area is not as critical asunderestimation in the non-irrigated treatment. Eavisand Taylor (1979) found daily transpiration rates ofsoybeans to almost double when leaf area was doubledunder high soil water content.

Leaf area per plant directly affects the amount ofradiation absorbed by the leaves of the plant, most ofwhich is used to evaporate water, creating higher flowrates through the plant. For this analysis, an effectiveleaf area equal to the ground area of 1548 cm2/plant wasused although irrigated plants had about 4600 cm2 ofleaves/plant and non-irrigated plants had about 2250cm2/plant. The assumption is that shaded leaves do nottranspire significant amounts of water, since most of theenergy used to evaporate water during transpirationcomes from radiation.

TROIKA is not very sensitive to root radius per se, asshown in Fig. 7 for the irrigated treatment. In theexperimentally significant range, even doubling theradius has little effect on the predicted leaf waterpotential. Any effect was due to the alteration of root

1984- TRANSACTIONS of the ASAE 121

surface area and of the surface areas of the shellinterfaces, since the shell thickness does not change.

Convergence of radial flow toward the root changes- asroot diameter changes. As flowing water convergestoward a line sink, velocity increases and potentialgradient increases. Thus the larger the root, the lesspotential drop is necessary.

For the non-irrigated treatment, with dryer soil,variation in the root radius had a different pattern ofeffect, as in Fig. 8. According to model implications anincrease in root radius gives the root access to morewater. Thus, for the non-irrigated treatment, wheretransmission of water in the soil toward the root is moreof an impediment than in the irrigated treatment, anincrease in root radius from the base line (0.03 cm)results in a relatively higher predicted leaf waterpotential than for the irrigated treatment. Similarly adecrease to 0.01-cm radius has relatively greater effectfor the irrigated treatment because the higher uptakerate causes more effect due to convergence of flow towardthe root. The insensitivity of leaf water potential to rootradius is corroborated by Williams (1976) who predicted

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Fig. IO-Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for five different root lengths(ROOTL) In the non-Irrigated treatment.

Fig. 9-Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for five different root lengths(ROOTL) In the Irrigated treatment.

water potential within :t 1 bar for a range of -SO to+ 100% of the base line root length value. This finding issignificant from an experimental standpoint. Rootlengths are difficult and laborious to obtain. Thisindicated range will aid in determining experimentalprocedures necessary to obtain data satisfactory for usein simulation of water flow in the soil-plant-atmospheresystem. Caution must be exercised, however, when usingdryer soils.

Root permeability (PERRT) effects on simulated leafwater potential shown in Fig. 11 are very similar to thoseof root length shown in Fig. 9. Since an increase in eitherparameter causes a linear increase in the rate of waterflowing into the root, the similar effects are notcontradictory. We expected that the nonlinearconductivity effects of decreased water in the shell, e.g.immediately surrounding a shorter root length, wouldcause at least slightly different long-term results than adecreased root permeability. Evidently, under the moistconditions used for this analysis, the decreased soil watercontent near the root had essentially no effect on waterflow to the root. The root permeability effects were very

water potential difference between root and bulk soilusing the models of Gardner (1960) and Cowan (1965).

An overestimate of root length caused less error thanan underestimate when trying to predict leaf waterpotentials using TROIKA (Fig. 9) for the irrigatedtreatment. Only when we used unrealistically low valuesof root length (32.87 m) did the simulation show asignificant effect on leaf water potentials. For dryer soil,however, varying the root length yielded different results,as indicated in Fig. 10. An increased root lengthsignificantly increased leaf water potential since waterflux was slower in the dryer soil. Thus, an increase inroot length results in increased uptake rates and,consequently, increased leaf water potentials. Eavis andTaylor (1979) found root length to have no significanteffect on transpiration of soybean. Williams (1976)found lower matric potential differences betwen the rootsurface and bulk soil under moist conditions than underdry conditions, but did not estimate plant waterpotentials.

Under the simulated moist conditions the watersupplied to the root is sufficient to maintain the leaf

cn'-<UmJ«i=zWt-

~a:w

f;t:~U-

~~

Fig. II-Comparison of observed leaf water potentials and thosepredicted by the model TROIKA for five different values of rootpermeability (PERRT) In the irrigated treatment.

Fig. 12-Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for five different values of stemresistance (RESST) In the Irrigated treatment.

122 1984- TRANSACTIONS of the ASAE

and hydration levels. Considerable literature exists toindicate that plant resistance is variable (Jones, 1978)but an equal volume of literature shows plant resistanceto be constant (Hailey et al., 1973). We suspect thatsmall variations may exist due to shrinking and swellingof the hydraulic openings, but that most variationsreported are a<:tually due to poor measurement ormodeling techniques or to failure to include capacitanceeffects in the system. Jones (1978), for example,combines soil and plant resistances and capacitancessuch that changes in soil re~istance would be indicated asa variable plant resistance.

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~(I:ill

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Fig. 13--'Comparlson of observed leaf water potentials and thosepredicted by the model TROIKA for five different values of stemresistance (RESST) In the non-Irrigated treatment.

SUMMARY

The results of this sensitivity analysis of TROIKA-amodel for simulating water flow through soil, into andthrough the p.\ant and into the atmosphere-indicatestem resistance to be of vita.\ importance in calculatingleaf water potential. Leaf areashou.\dbe determined withan accuracy of 5 to 10% to keep simulated leaf waterpotentials within a bar of the observed leaf waterpotential. Root length and root permeability havesimilar, less dramatic effects. The model is relativelyinsensitive to changes in root radius and leaf width.

Soil moisture content affects the sensitivity of leafwater potential to variations in aJI system parameterswhich we studied. Other environmental variab.\es willalso affect the sensitivity of leaf water potentials tovariations in the system parameters.

Studies of soil-plant-atmosphere water relationssometimes include exploration of root systems inaddition to measurements above ground. This sensitivityanalysis indicates that root radius can be rough.\yestimated and that care should be taken not tounderestimate root length (or density), by retrieving allroots.

ReferencesI. Belmans, c., J. Feyen and D. Hillel. 1979. An attempt at

experimental validation of macroscopic-scale models of soil moistureextraction by roots. Soil Science 127:174-186.

2. Burch, G. J. 1979. Soil and plant resistances to waterabsorption by plant root systems. Aust. J. Agric. Res. 30:279-292.

3. Busscher, W. J. and D. D. Fritton. 1978. Simulated flowthrough the root xylem. Soil Science 125(1):1-6.

4. Cowan, I. R. 1965. Transport of water in the soil-plant-atmosphere system. J. Appl. Ecol. 2:221-239.

5. Eavis, B. W. and H. M. Taylor. 1979. Transpiration ofsoybeans as related to leaf area, root length, and soil water content.Agron. J. 71:441-445.

6. Federer, C. A. 1979. A soil-plant-atmosphere model fortranspiration and availability of soil water. Water Res. Research15(3):555-562.

7. Gardner, W. R. 1960. Dynamic aspects of water availability toplants. Soil Science 89:63-67.

8. Gardner, W. R. 1964. Relation of root distribution to wateruptake and availability. Agron. J. 56:41-45.

9. Hailey, J. L., E. A. Hiler, W. R. Jordan and C. H. M. vanBavel. 1973. Resistance to water flow in Vigna sinensis L. (Endl.) athigh rates of transpiration. Crop Sci. 13:264-267.

10. Hansen, G. K. 1974. Resistance to water transport in soil andyoung wheat plants. Acta Agric. Scand. 24:37-48.

II. Hillel, D., C. G. E. M. van Beek and H. Talpaz. 1975.Microscopic-scale model of soil water uptake and salt movement toplant roots. Soil Sci. 120:385-399.

12. House, C. R. and N. Findlay. 1966. Water transport in isolatedmaize roots. J. Exp. Bot. 17:344-354.

13. Idso, S. B. and R. D. Jackson. 1969. Thermal radiation fromthe atmosphere. J. Geoph. Res. 74:5397-5402.

14. Jones, H. G. 1978. Modeling diurnal trends of leaf potential intranspiring wheat. J. Appl. Ecol. 15:613-626.

similar to root length effects for the non-irrigatedtreatment (data not shown) also.

Fig. 12 shows the extreme sensitivity of predicted leafwater potential to stem resistance (RESST). While ourstem resistance involves some simplifying assumptions, itis similar in concept to the connection resistancearbitrarily defined by Meyer and Ritchie (1980) or tofrictional resistance between culm and leaf, found to beof major importance by Ruckenbauer and Richter(1980). Halving or doubling this parameter causedvariations of 3 to 4 bars water potential away from thebase line leaf water potential. Most of the potential dropoccurs within the plant under conditions of moist soiland relatively high transpiration rates (Lambert andPenning de Vries, 1973). This fact is hinted at by resultsof the sensitivity analysis of root length, pointed out morestrongly by results from the stem resistance analysis,indicated by the simulated values of leaf and root waterpotentials, and supported by the literature (Reicosky andRitchie, 1976; Newman, 1973; and Molz, 1976). Thus, itshoul.d not be surprising that leaf water potential, ascalculated by the model, is particularly sensitive to thestem resistance parameter.

In the non-irrigated treatment, leaf water potentialwas affected less by variations in stem resistance (Fig.13). This finding is logical because in dryer soil, morewater potential decrease occurs in the soil, because oflower conductivity, water flux rate is decreased, andtherefore less water potential decrease occurs across thestem. Changes in stem resistance cause smaller effectsthan would the same change when higher flux ratesoccur. Stem resistance is not easily measuredexperimentally. Values are generally determined fromroot and leaf water potential measurements under knowntranspiration rates. These measurements are timeconsuming. However, if advances are to continue inquantitative evaluation of water movement throughplants, this analysis indicates that more data are neededon stem resistance than those in the literature. Therelationship of species, age, stem diameter and length,and physiological conditions to stem resistance are allimportant.

The present version of TROIKA assumes constantstem resistance and root permeability over all flow rates

1231984- TRANSACTIONS of the ASAE

15. Lambert, J. R. and F. W. T. Penning de Vries. 1971. TheModel TROIKA: Listing. Agric. Engr. Res. Ser. No. 16, S.C. Agric.Expt. Sta., Clemson.

16. Lambert, J. R. and F. W. T. Penning de Vries. 1973.Dynamics of Water in the soil-plant-atmosphere system: A Modelnamed TROIKA. pp. 257-273 in Hadas, A. et al., eds. EcologicalStudies: Analysis and Synthesis, V. 4. Springer-Verlag, Berlin.

17. Landsberg, J. J. and N. D. Fowkes. 1978. Water movementthrough plant roots. Ann. Bot. 42:493-508.

18. Meyer, W. S., E. L. Greacen and A. M. Alston. 1978.Resistance to water flow in the seminal roots of wheat. J. Exp. Bot.29(113):1451-1461.

19. ,Meyer, W. S. andJ. T. Ritchie. 1980. Resistance to water flowin the sorghum plant. Plant Physiol. 65:33-39,

20. Molz, F. J. and 1. Remson. 1971. Application of an extraction-term model to the study of moisture flow to plant roots. Agron. J.63:62-77.

21. Molz, F. J. 1976. Water transport in the soil-root system:Transient analsysis. Water Res. Research 12:805-808.

22. Monteith, J. L. 1965. Evaporation and e.vironment. Symp.Soc. Exp. BioI. 29:205-234.

23. Newman, E. 1. 1973. Permeability to water of the roots of fiveherbaceous species. New Phytol, 72:547-555,

24. Nimah, M. N. and R. J. Hanks. 1973. Model for estimating soilwater, plant and atmosphere interrelations. 1. Description andsensitivity. SSSA Proc. 37:522-527.

25. Nobel, P. S. 1974. Introduction to Biophysical PlantPhysiology. W. H. Freeman & Co., San Francisco.

26, Penning de Vries, F. W. T. 1972, A model for simulatingtranspiration of leaves with special attention: ) stomatal functioning. J.Appl. Ecol. 9:57-77.

27. Philip, J. R. 1957. The physical principles of water movementduring the irrigation cycle. Proc. 3rd. Int. Congo Irrig. Drainage8:125-128.

28. Reicosky, D, C., R. B. Campbell and C, W. Doty. 1975.Diurnal fluctuation of leaf.water potential of corn as influenced by soilmatric potential and microclimate. Agron. J. 67:380-385.

29. Reicosky, D. C, andJ. R. Lambert. 1977. Dynamics of water inthe soil-plant-atmosphere system: Comparison of field measured andsimulated corn leaf water potential. SSSAJ 42:221-228.

30. Reicosky, D. C. and J, T. Ritchie. 1976. Relative importance ofsoil resistance and plant resistance in root water absorption. SSSAJ40:293-297.

31. Ruckenbauer, P. and H. Richter. 1980. Frictional resistances towater transport in water-cultured wheat plants. Phyton 20:37-45.

32. Shalhevet, J., E. V. Maas, G. J. Hoffman and G. Ogata. 1976.Salinity and the hydraulic conductance of roots. Physiol. Plant.38:224-232.

33. Taylor, H. M. and B. Klepper. 1978, The role of rootingcharacteristics in the supply of water to plants. Adv. Agron. 30:99-128.

34. Whisler, F. D., A. Klute and R. J. Millington. 1968. Analysisof steady state evapotranspiration from a soil column. SSSAJ32:167-174.

35. Williams, J. 1976. Dependence of root water potential on rootradius and density. J. Exp. Bot. 27(96):121-124.

APPENDIXDICTIONARY OF VARIABLES

AFACAREA(I)ARLEASWRAVCGRCND(I)

Absorption factor for short wave radiation, dimensionlessArea of inner surface of i'. soil shell, cm'/cm rootArea of leaves, cm'Absorbed short wave radiation, cal/cm'minActual vapor concentration differential, g/mJAverage conductivity of soil shells i and i-I, cm/min

COND(I) Conductivity of i'. soil shell, cm/minDESC Desorption curve for Varina sandy loam, water content vs

soil water matric potentialDH Diffusive constant for heat in air, cm'/sDIST(I) Distance from root surface to center of i'. soil shell, cmDL Diffusive length of boundary layer, cmDRESAH Diffusive resistance of boundary layer to heat, s/cmDW Diffusive constant for water, cm'/sEHL Evaporative heat loss, cal/cm'minEL Emissivity of leaf, dimensionlessES Emissivity of sky, dimensionlessFLR(I) Flow rate of water from the i'. soil shell, cmJ/min cm rootFRWLS Fraction of water in leaf when saturated, dimensionlessFRWRS Fraction of water in root when saturated, dimensionlessFWC(I) Fractional water content of i'. soil shell, cmJ/cmJHCLE Heat content of leaves, cal/cm'LWR Long wave radiation from the leaf, cal/cm'/minOLWP Observed leaf water potential, barsPERRT Permeability of root, cmJ/cm' s bar. Defined to be

between the root surface and the root xylemRADIUS Effective radius of root, cmRESST Stem resistance, bar s/cm', Defined to be between root

xylem and leaf mesophyll tissueRH Relative humidity of free atmosphere, %RHTBL Table of relative humidity by time of dayROOTL Root length, cmRSUBL Diffusive resistance of stomates and cuticle to water, s/cmRSUBW Diffusive resistance of boundary layer to water, s/cmRWCLE Relative water content of leaves, "I.RWCRT Relative water content of root, "I.SBC Stefan-Boltzmann constant cal/cm' °C' minSHL Sensible heat loss, cal/cm' minSPHL Specific heat of leaf, cal/cmJ °CSTORES RSUBL vs leaf water potential functionSVC Saturation vapor concentration vs temperature functionSVCA Saturation vapor concentration of atmosphere, g/m'SVCL Saturation vapor concentration of leaves, g/mJSWR Incoming short wave radiation, cal/cm' minSWRTB Table of SWR by time of dayTA Temperature of air, °CT A TB Table of air temperature by time of dayTCKNS Thickness of leaf, cmTCKNSS Thickness of leaf when saturated, cmTDRES Total diffusion resistance between substomatal cavity and

free atmosphere, s/cmTIMH Time, hTL Temperature of leaf, °CTLI Initial leaf temperature, °CTLA YER(I)Thickness of i'. soil shell, cmTWPLLE Leaf water potential vs relative water content functionTWPTLE Total water potential of leaves, barsTWPTRT Total water potential of root, barsVOLUI) Volume of i'. soil shell, cmJ/cm rootVOLRT Volume of root, cmJVOLW(I) Volume of water in the i'. shell of soil, cmJ/cm rootW Weighting factor for averaging conductivity of adjacent

soil shells, dimensionlessWCLE Water content of leaves, mg/cm'WCLS Water content of leaves when saturated, mg/cm'WCRT Water content of root, mgWDTL Width of leaf, cmWLOSS Rate of water loss from leaves, mg/cm' minWP(I) Water potential of i" soil shell, barsWS Wind speed, cm/sWSTB Table of wind speed by time of dayWSUPLE Water supplied to leaves, mg/minWSUPRT Water supplied to the total root, mg/minWVCA Water vapor =ncentration of atmosphere, g/mJWVCL Water vapor concentration of leaf, g/mJ

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