use of the root contact concept, an empirical leaf conductance model and pressure-volume curves in...

Plant and Soil 149: 1-26, 1993. © 1993 Kluwer Academic Publishers'. Printed in the Netherlands. PLSO 9554

Use of the root contact concept, an empirical leaf conductance model and pressure-volume curves in simulating crop water relations

C.R. JENSEN 1, H. SVENDSEN 1, M.N. ANDERSEN z and R. L(3SCH 3 Department of Agricultural Sciences, Section of Soil and Water and Plant Nutrition, The Royal

Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Copenhagen, Denmark, 2Department of Soil Physics, Soil Tillage and Irrigation, Danish Institute for Plant and Soil Science, Research Center Foulum, P.O. Box 25, DK-8830 Tjele, Denmark and 3Abteilung Geobotanik, Universitiit Diisseldorf, Gebiiude 26.12/UI, Universitiitsstr. 1, D-4000 Diisseldorf, Germany

Received 1 April 1992. Accepted in revised form 6 November 1992

Key words: barley, crop water relations, dynamic simulations, pressure-volume curves, root contact model, shaded and sunlit leaves, stomatal conductance model

Abstract

A simulation model "DanStress" was developed for studying the integrated effects of soil, crop and climatic conditions on water relations and water use of field grown cereal crops. The root zone was separated into 0.1 m deep layers of topsoil and subsoil. For each layer the water potential at the root surface was calculated by a single root model, and the uptake of water across the root was calculated by a root contact model. Crop transpiration was calculated by Monteith's combination equation for vapour flow. Crop conductance to water vapour transfer for use in Monteith's combination equation was scaled up from an empirical stomatal conductance model used on sunlit and shaded crop surfaces of different crop layers. In the model, transpirational water loss originates from root water uptake and changes in crop water storage. Crop water capacitance, used for describing the water storage, was derived from the slope of pressure-volume (PV) curves of the leaves. PV curves were also used for deriving crop water potential, osmotic potential, and turgor pressure. The model could simulate detailed diurnal soil-crop water relations during a 23-day-drying cycle with time steps of one hour.

During the grain filling period in spring barley (Hordeum distichum L.), grown in a sandy soil in the field, measured and predicted values of leaf water and osmotic potential, RWC, and leaf stomatal conductance were compared. Good agreement was obtained between measured and predicted values at different soil water deficits and climatic conditions. In the field, measured and predicted volumetric soil water contents (0) of topsoil and subsoil layers were also compared during a drying cycle. Predicted and measured 0-values as a function of soil water deficits were similar suggesting that the root contact model approach was valid.

From the investigation we concluded: (I) a model, which takes the degree of contact between root surface and soil water into account, can be used in sandy soil for calculation of root water uptake, so that the root conductance during soil water depletion only varies by the degree of contact; (II) crop conductance, used for calculation of crop transpiration, can be scaled up from an empirical single leaf stomatal conductance model controlled by the level of leaf water potential and micro- meteorological conditions; (III) PV curves are usable for describing crop water status including crop water storage.

2 Jensen et al.

Introduction

In North Western Europe with rainfalls varying in the growing season from 100 to 200mm, drought in agricultural crops generally occurs only on coarse textured sandy soils low in water holding capacity. On these soils root growth is most often restricted in the depth to about 60 to 80 cm with most roots in the upper 25 cm of the plough layer. The root distribution is uniform as these soils form few aggregates and large pores are lacking. By gravitational water flow and as roots remove water from the soil the water filled pores steadily drain until the point where they become discontinuous and flow is strongly hin- dered. At this stage only a limited part of the root system will be in contact with soil water (Jensen et al., 1989, 1990).

Mechanistic models have become a common tool for describing the dynamics of water flow and development of crop water deficit in order to get better insight into the behavior of the soil- plant-atmosphere continuum (e.g. Fernandez and McCree, 1991; Katerji et al., 1986; Molz, 1981; Stewart et al., 1985; Zur and Jones, 1981) and to schedule irrigation (Hanks and Nimah, 1988). Water movement in the liquid phase through the plant to the substomatal cavities can be described by the Ohm's law analogy where water moves along water potential gradients through a series of resistances connected with capacitances of water storages. In the substomatal cavities water evaporates and flow becomes proportional to the vapour pressure gradients and to stomatal conductance. The evaporated water originates from water which flows from the soil across the root cortex to the xylem system and from water storages within the plant. Radial water flow from the soil to the root surface can be described by the single root model of Cowan (1965) and Gardner (1960). In the single root model it is assumed that all root surfaces are in contact with soil water. However, as mentioned above, during depletion of soil water, evidence indicates that only a fraction of the root surface area is in contact with soil water. In a key study of Herkelrath et al. (1977) the term 'wetted fraction' of roots was introduced. In that study the effective conductance of a root segment was assumed to be proportional to the wetted frac-

tion of the surface area of the segment such that:

(1)

where q is the rate of flow through the root cortex membrane, Ors and 0s are the volumetric soil water content at the root surface and at saturation, respectively, Pr is the membrane conductance per unit length of root, ~0mr S is the soil water potential at the root surface and ~0 r is the water potential inside the root. By using this root contact concept, Herkelrath et al. (1977) found much better agreement between measured and calculated rates of water uptake than when using the Gardner (1960) model which does not take the degree of root contact into account. Further evidence supporting the notion that the extent of vapour gaps around roots will increase as soil water content decreases, so increasing soil-root interface resistance, has been obtained in experiments of Faiz and Weatherley (1978) and Jensen et al. (1989, 1990).

The purpose of the present study was to construct a simple mechanistic crop water relation model (named 'DanStress'). As test plant we used spring barley (Hordeum distichum L.) at the early grain filling stage of development. The model is based upon the idea that only roots in contact with soil water are effective in water uptake. It includes the following additions: (1) the root membrane conductance in contact with soil water is constant and independent of root water status and root depth; (2) the soil water matric potential at the root surface (~0mr~) is estimated iteratively by eq. (1) and the Cowan (1965) and Gardner (1960) steady state single root model describing radial water flow to the root surface using bulk soil matric potential (~bm) as a first estimate of qJmr~; (3) water flow across the roots is obtained from eq. (1) by substituting qJr by crop water potential assuming that the root resistance constitutes the major resistance to water flow in the plant; (4) the root zone is separated into topsoil and subsoil of several layers with different root densities, soil water potentials, hydraulic conductivities and capacitances. The vertical water flow between soil layers is calculated and dew and/or precipitation exceeding the crop interception capacity is added to the soil layer at the top. Field capacity is the

highest water content the soil can attain. The amount of water that cannot be stored in one layer drains into the next layer or out of the profile.

Otherwise, the model is based upon the assumption that transpiration from a dense crop can be obtained from Monteith's combination equation for water vapour flow in the atmosphere (Monteith, 1964). The crop conductance for use in Monteith 's combination equation is in the model scaled up from single leaf stomatal conductance controlled by the level of water potential and by micro-meteorological factors (L6sch et al., 1992).

In the model, change of crop water storage is calculated as the difference between root water absorption and transpirational water loss. The crop water content /potent ial curve describing crop water capacitance is estimated from pressure-volume (PV) curves of the leaves and used for calculation of crop water storage per ground area unit (Andersen et al., 1991). PV curves are also used for deriving crop water potential, osmotic potential, and turgor pressure.

The model calculates a series of steady state water flows on hourly intervals or less and recalculates storages at the end of each interval for use in the next interval.

At present the model does not take into account the processes of evaporation from the soil surface.

Materials and methods

Atmospheric water flow

The actual transpiration from a dense crop (qa) was calculated by Monteith 's combination equation (Monteith, 1964):

pCp(e, - %)ga + (RN - G)A q" = F'~E/A - y(1 + ga/gc) + A (2)

Cp = specific heat capacity of dry air; J g - ' °C-1 e a = air water vapour pressure; Pa e S = saturation water vapour pressure; Pa F~E = flow density of latent heat; J m -2 s -1

- 2 G = soil heat flux; W m

Simulating crop water relations 3

ga = boundary layer conductance to water yap- -1 our transfer; m s

gc = crop conductance to water vapour transfer; -1

m s qa = actual transpiration estimated from a

dense crop; g (water) m -2 (area) s -1 RN = net radiation; W m -2 A = first derivative of saturated vapour pres-

sure versus temperature; Pa °C -1 y = psychometric constant; Pa°C -1 1 = latent heat of evaporation; J g-1

- 3 p =a i r density; g m

Estimation of dew formation and dew evaporation was also undertaken by eq. (2) assuming the crop resistance to water vapour transfer (1/go) was equal to zero (Monteith and Unsworth, 1990 p. 193). The potential transpiration from a dense crop to the atmosphere ( q a p ) w a s calculated by Penman's combination equation (Penman, 1956):

A(RN - G) yf(U)(es - - Ca) + (3)

q a p - - A('y + A) A + ' y

f (U) =0.00263 (0.5 +0 .54 U a ) 86400 -1 1000; g (water) m -2 (area) Pa -1 s - l

qap = potential transpiration from a dense crop; g (water) m -2 (area) s -I

l U a = wind speed at 2 m height; m s

Assuming neutral conditions the boundary layer conductance (ga) was calculated using van Bavel's (1967) equation:

ga = ( K ] U a ) / ( l n [ Z a - d]/Zo) z (4)

K a = v o n Karman constant; 0.41 Z a = height of wind speed measurement; 2 m Z o = surface boundary roughness height; m

We assume d = 0.63 × crop height and Z o = 0.13 x crop height (Campbell, 1977).

Neutral conditions can be assumed without appreciable error in estimates of ga if high wind velocities ( > 2 m s -1) are prevailing (Luchiari and Riha, 1991) which is often the case in this region during the summer period.

4 Jensen et al.

Crop interception of water

Dew and precipitation are intercepted by the crop. The interception capacity (Ic) of the crop is proport ional to the total crop area index (CAI):

I¢ = Ci. CAI (5)

-2 I c = crop interception capacity; g (water) m (ground area)

C i = interception capacity coefficient; g (water) m -2 (crop area)

C A I = c r o p area index; m 2 (crop area) m -2 (ground area)

As proposed by Jensen (1979) a C i value of 0.5 mm or 500g (water) m -z (crop area) was used. The water content stored for the following hourly time step (I~ t+l)) was calculated from the actual one as:

I~ t+~) = I s + (P + D - qap)3600 (6)

1~ t+l) = w a t e r stored in interception storage; g (water) m -2 (ground area)

P = precipitation; g (water) m -2 (area) s -1 D = dew; g (water) m -2 (area) s -1

When the interception storage (Is) was >0 transpiration and dew formation were calculated from eq. (2) assuming 1/g¢ = 0. Dew and precipitation exceeding the storage capacity of the canopy were allocated to the top soil layer.

Radiation in relation to crop area indices

After heading, the projected area index of the crop (CAI) consists of area contributions from both ears and leaves. The sunlit CAI (CAIsl) were computed from the total CAI according to Beer 's law (Monteith and Unsworth, 1990 p. 74; Ross, 1975 eq. 22):

CAIs, = (sin ~ /K) [1 .0 - e x p ( - K . CAI/s in qb)] (7)

K = C a n o p y light extinction coefficient = sun elevation angle

By summarizing ( - K . C A I ) downwards from the top of the canopy for the ear ( - K e . CAIn), the flag leaf i.e. leaf No 8 to emerge ( - K s •

CAI8), leaf No 7 ( - K 7 • CAIT) and for leaves of lower position ( - K 6 • CAI6) and by weighting K of the summarized layers with respect to CAI for the individual layers, the sunlit area of ears (CAIst_e), of ears and flag leaves (CAIsl_e_8), of ears, leaf Nos 8 and 7 (CAIsl_e_8_7) and of the total canopy (cmIsl_e_8_7_6) could be calculated from eq. (7). Thus, the ( - K . CAI) and K values for use in eq. (7) were calculated as:

( - K CAI)e = ( - K e • CAIn) ( - K CAI)e_8 = ( - K ~ . CAIe) - (K 8" CAIs) ( - K CAI)¢_8_7 = ( - K e • CAIn) - (K 8 • CAIs)

- ( K 7 • CAI7) ( - K CA~)e_~_~_6 = (-Ko" CAIo) - (K8" CAI~)

- ( K 7 • C A I ) - ( K 6 • C A I 6 )

and K as:

K e

Ke_ 8

Ke_8_ 7 =

Ke_8_7_6 = + +

K e

[(R e • CAIn) + (K 8 • CAIs ) ] / (CAI ~ + CAI8) [(K e • CAIn) + (K s • CAI8) + (K 7 • CAIT)] / (CAI e + CAI 8 + CAI7) [(K¢" c a I e ) + (K 8 • CAI8) (K~-CAIn) + (K6" CA16)]/(CAL CAI 8 + CAI 7 + CAI6)

and were used successively in eq. (7) to obtain a downwards integration of CAIs1.

The CAIsI of the individual layers CAI~_s~, CAI8_s1, CAI7_sl, and CAI6_sI were calculated by subtraction of the preceding integrated CAIsl value from the actual one, i.e.:

CAIe_sl = CAIn_s1 - 0 CAI8_sl = CAI~_8_sI - CAIe_s1 CAIv_sl = CAIe_8_7_sl - CAI~_8_sl CAI6_sl = C A I e _ 8 _ 7 _ 6 _ s l - Cmle_8_7_sl

Thus, by knowing the total area index of the individual layer, the shaded area index CAIsh of the layer could be calculated as:

CAIe_sh = CAI e - CAIe_sl CAI8_sh = CAI 8 - CAI8_sl CAI7_~h = CAI 7 - CAI7_~I

C A I 6 _ ~ , = C A I 6 - CAI6_s l

A similar downwards integrative procedure was used to calculate the net radiation which pene- trates the canopy. The net radiation (RN) at a horizontal level at the bottom of the ears (RN~), leaf No 8 (RNo_s), leaf No 7 (RN~_8_7), and leaf No 6 plus lower leaves (RNe_8_7_6) was obtained from:

RNcA r = RN a e x p ( - K CAI/sin ~) (8)

The reduced level of net radiation RNe, RN~_ 8, RNe_8_7, RNe_8_7_ 6 in the canopy was obtained by introducing ( - K CAI)e, ( - K CAI)e_8, ( - K CAI)~_8_7 and ( - K CAI)e_8_7_6 in eq. (8), respectively.


Parameterization of g and calculation of g,.

Stomatal conductance of sunlit (gsl) and shaded leaves (gsh) were computed by using an empirical simulation model (L6sch et al., 1992). The model was based on observed relationships between leaf stomatal conductance (g) and leaf water potential (01), irradiation (PAR), leaf temperature (t), and leaf-to-air water vapour concentration difference (AW) for leaves of different positions. For the flag leaves (leaf No 8) the model is given in Table 1, where g is the sum of adaxial and abaxial leaf conductance. The model was also used for leaf Nos 7 and 6. For leaf Nos 7, 6 and older leaves the coefficient b of the model (Table 1) was 3.8. The coefficient c was 18.6 in leaf No 7 and 17.2 in leaf No 6 and

Table 1. Empirical simulation model for calculation of leaf stomatal conductance (g) in flag leaves (leaf No 8) of barley plants, g is the sum of adaxial and abaxial conductance. The model was based on observed relationships between g and leaf water potential (6~), irradiation (PAR), leaf temperature (t), and leaf-to-air water vapour concentration difference (AW) when only one of the parameters varied, symbolized as g, , g*,PAR, g*,PAR.t and gO.PAR.t.aw, respectively. The model was also used for leaf Nos 7 and 6 with the following changes: Effect of AW and t on conductance was not taken into account; the coefficient b was 3.8 for leaf Nos 7 and 6 including older leaves. The coefficient c was 18.6 for leaf No 7 and 17.2 for leaf No 6 including older leaves (L6sch et al., 1992)

Relationship Algorithm

Leaf conductance versus 0~ below - 1 . 6 MPa (if ~b~ > - 1.6 MPa then by definition ~, = - 1.6 MPa)

Leaf conductance versus q~ and PAR

Maximal leaf conductance under otherwise non-limiting conditions versus temperature (t)

Reduction of maximal leaf conductance (R) (as calculated for the optimum temperature; top,) by low PAR and 6~

Leaf conductance versus 6~, PAR, and t below the opt imum temperature (top~)

Leaf conductance versus ~ , PAR and t above the optimum temperature (too,)

Leaf conductance versus 46, PAR, t and AW

g ~ = a - b . ( - ~ 0 a = 13 b = 2 . 8

g+,PAR = g J ( 1 . 0 + c" g , / P A R ) c = 23.285

gtemp . . . . = d + e • top, = f - h . t opt top, = 23.4 °C

R = g t e m p . . . . . - - g g , , e A R

g~,PAR,t : d + e • tleaf -- R d = 6.3 e = 0 . 1 6

g~.PAR., = f -- h ' tteaf - R f = 15.0 h = 0 . 2 1

gtO,PAR,t ,~XW = g ~ , P A R , t - - i " A W

i = 0.23

g = leaf stomatal conductance to water vapour transfer (mm s-~); ~ = bulk leaf water potential (MPa); PAR = photosynthetic active radiation (/.tmol photons m 2s 1, 400-700 nm); t = leaf temperature (°C); AW = leaf-to-air water vapour concentration difference (g m- 3).

6 Jensen et al.

older leaves indicating an adaption to shade. For leaves older than leaf No 8 changes in AW and leaf temperature were not taken into account (L6sch et al., 1992). As the stomatal responses to environmental factors for awns and flag leaves were similar (L6sch et al., 1992), the empirical stomatal model for the flag leaves was also applied to the ears with awns.

From several weighting possibilities (Rochette et al., 1991) crop conductance (go) for use in eq. (2) was calculated as:

gc = g~l + g~h (9)

where:

gsl = (CAIe_sl" ge_s,) + (CAI8_s," + (CAI7_s," gv_st) + (CAI6_ " g6_sl)

gsh = (CAIe_ n" ge_sh) + (CAI8_ h" g8_ h) + (CAI7_sh" gv_sh) + (CAI6_sh" g6_sh)

We assumed that RN during the day constituted 68% of global radiation (Fig. 3). This value is typical on clear days of July in this region (Hansen et al., 1981). PAR was assumed to constitute 50% of the level of global radiation (Ross, 1975). In order to obtain the mean irradiation level of a leaf or ear the horizontal RNcA I level at a given layer in the crop, eq. (8), was multiplied by K s in~ -1 (Monteith and Unsworth, 1990 p. 73) from which value the mean PAR value was derived. The mean PAR value was used in the empirical stomatal model (Table 1). For the shaded CAI of any layer the PAR level for use in the stomatal model was set to be 7.5% of the level of the sunlit CAI of the layer due to transmission of PAR (Jagtap and Jones, 1989; Monteith and Unsworth, 1990 p. 86).

Derivation of crop water relations and water storage from pressure-volume (PV) curves

The relative water content (RWC) of one m 2 area of the crop was at the end of each time step of one hour calculated as:

R W C = ( W a + q c - 3600)/Wp (10)

where

qc = net flow of water into the crop storage (see eq. 21; the factor 3600 converts from s to hr); g (water) m -z (area) s -1

W a = actual storage crop water content at the -2 beginning of a time step; g (water) m

(ground area) Wp = storage crol~ water content at full turgot ; g

(water) m- (ground area)

Thus, the sum (W, + qc" 3600) represents W a at the beginning of the next time step.

The stomatal model given in Table 1 was obtained under long lasting clear weather conditions in 1986. Similar conditions prevailed in 1989 when we undertook PV analysis in mature barley leaves for leaf No 7 (the leaf below the flag leaf) (Jensen et al., 1992). The plants were fully watered or severely droughted. As only minor differences in water relations could be detected between leaf Nos 7 and 8 (the flag leaf) during the drying cycle, and as water relations of the ears seemingly were similar to those of the flag leaf (L6sch et al., 1992), we derived the crop water potential (~0), osmotic potential (qJ=) and turgor pressure (~Op) from the PVcurves, describing the ~0/RWC -1 relationship of leaf No 7, given in Figure 1. This could be done after having calculated changes of crop water storages by eq. (21) followed by calculation of crop RWC by eq. (10). Thus, storages changes were obtained from capacitance of the crop (dW,/d~0) via the PV curves. The PV curve of the fully watered crop was used when qJp was above zero. The PV curve of the droughted crop was used when further dehydration occurred. The way of describing PV curves as ~0 versus RWC -1 is detailed by Andersen et al. (1991).

Soil

The model was tested in South Jutland at the Governmental Research Station, Jyndevad. The soil is a coarse textured melt water sand. The topsoil (0-0 .4m depth) contains 78.7% coarse sand (0.2-2.0mm), 10% fine sand (0.02- 0,2mm), 3.8% silt (0.002-0.02), 4.1% clay (<0.002 mm), and 3.4% organic matter. The soil layer from 0.3 to 0,4 m depth is the ABh horizon and less well defined as it is enriched by material

0.0 | I I I

-0.5- I ' '

-1. O- ", "~ ,,,,y s t r e s s e d

'~ -1.5 \ ~ - fully watered .,~

- 2 . 5 l ~ ' ~ ' " "

-3.0" ~'~""~.

-&5 ", . . . . . . . . , . . . . . . . . . , . . . . . . . . . , . . . . . . . . . , . . . . . . . . 1.0 1.2 1.4 1.6 1.8 2.0

RWC -1

Fig. 1. Pressure-volume curves of the leaf below the flag leaf, used to characterize crop water relations. The curvi- linear lines indicate water potentials (¢) of fully watered ( ) and severely droughted plants (---) above the turgor loss points and the rectilinear line indicates the osmotic potential (¢~) as a function of inverse relative water content (RWC-~). The arrows show the zero turgor points. ~ = -1 .52 RWC a - 0 . 4 0 + 1.92 exp [ /3 (1 / (RWC-0 .15 ) - 1/ 0.85)]./3, sensitivity factor of elasticity, was -8.97 and -4.65 in fully watered and droughted plants, respectively. ~ = -1 .52 RWC ~ -0 .40 . (After Jensen et al., 1992; Fig. 1E)

washed out from the upper layers. The subsoil (0 .4-1.2 m depth) contains 86% coarse sand, 5% fine sand, 3% silt, 4% clay, 2% organic matter. The soil is classified as an Orthic Haplohumod, coarse sandy, siliceous, mesic according to the Soil Taxonomy System (Nielsen and M~berg, 1985) with a plant available water content of about 67 mm down to the rooting depth of about 0.6 m. The density of solids, the bulk density, and the volumetric water content at field capacity (0f.~) are given in Table 2.

S o i l m o i s t u r e r e t e n t i o n

The soil moisture retention curves obtained by pressure plate technique for the topsoil and subsoil are given in Figures 2A,D. Mathematical equations describing the curves were obtained by linear or polynomial regressions of ~n~ versus

S i m u l a t i n g c r o p w a t e r r e l a t i o n s 7

Table 2. Soil solid density, soil bulk density, and volumetric water contents at field capacity (0f~). (Modified after Han- sen, 1976)

Soil Soil solid Bulk Of density, density, mYm -3 g cm 3 g cm-3

Topsoil (0-0.4 m) 2.59 1.46 0.200 Subsoil (0.4-1.2 m) 2.59 1.44 0.092

Topsoil Subsoil

"~ -- -0.4. -0.4 "~ . -~ ",= -~ ,~ -0.8 ~-0.8

.o -1.2. -~-1.2

-1.6 I i i I ~ - 1 . 6 t i B 1 E

• ~, ~ "4" E E g -8 g -8- % %

-12 ~-12-

-16 , I , , ~ -16 i ,

-0.09 :)-0.09" --J" "E

E ~-0.12 A-0.12-

-0.15 . . . . . . 0.15 0.00 0.10 0.20 0.3 0.00 0.()3 0.()6 0.()9

19 (m 3 m "~) 0 (m 3 m ~)

Fig. 2. A-F A and D, soil water matric potential (qtm); B and E, logarithmic soil water hydraulic conductivity (k); C and F, soil water matric flux potential (M) of topsoil and subsoil, respectively, as a function of soil water content (0).

volumetric soil water content (0). By combining at least three regression curves the individual curves could be described mathematically.

S o i l w a t e r h y d r a u l i c c o n d u c t i v i t y ( k )

k of the topsoil and subsoil (Figs. 2B,E) was calculated directly from the soil moisture retention curve in accordance with the procedure of Campbell (1974). k at a water content (0) could be estimated by equation (11) from the saturation water content (0s) and the saturation hydraulic conductivity (ks) (Table 3):

8 Jensen et al.

Table 3. Constant used in eq. (11) 3 3

Soil b + s.e. 2 b + 3 k~, mrn s -~ 0s, m m

Topsoil (0-0.4 m) *3.69 +- 0.025 10.384 0.040 0.43 Subsoil (0.4-1.2 m) **3.34 -+ 0.086 9.682 0.258 0.44

*, In I//m = - 3 . 6 9 2 x I n 0 - 1 0 . 3 9 9 ; r = 0 . 9 9 9 , n = 32; for ~0 m < -0 .00125 MPa to Om > - 1 . 5 8 MPa. **, In tom = -3.341 x In 0 - 13.333; r = 0.994, n = 19; for tom < -0.0024 MPa to tom > -- 1.38 MPa.

k = k~(0/0~) 2b+3 (11)

A prerequisite for using eq. (11) is that the moisture retention curve when plotted on a log- log scale produces a straight line with the slope equal to - b for q~m and 0 values below the air entry water potential. This assumption was found to be correct for the coarse textured soil as evident from the data of the regression lines given in Table 3.

Soil water matric flux potential (M)

M combines k and 4'm into one parameter according to equation (12):

f qJm 4'm M = k d~0 m = ~ k A0m (12)

4'mo 4'mo

M was calculated as outlined by Shaykewich and Stroosnijder (1977); i.e., Aq, m ' k was summa-- rized from ~0 m values at or above field capacity (0too) until q~m of --160m. A~O m was -0 .1 m until q~, of - 2 m; --0.2 m until q'm of - 3 m; - 0 . 4 m until 0m of - 5 m etc. The M curves for the topsoil and subsoil, obtained by regressions as for the retention curves, are given in Figures 2C,F.

Root water uptake

Root water uptake per unit soil volume (qr) was calculated as:

Ors q r = Or - ~ s L(~Omrs - ~ ) (13)

L = root length density; m m -3 qr = root water uptake; g (water) m -3 (soil) S - 1

= crop water potential (used as estimation of ~0r); MPa

I~mrs = soil water matric potential at the root surface; MPa

Pr = root conductance per unit root length; g (water) m -1 (root) s -1 MPa 1

Ors = volumetric soil water content at the root surface; m 3 m -3

In eq. (13) bulk soil matric potential (qJm) was used as a first approximation of q~mrs, and volumetric bulk soil water content (0) as a first approximation of the soil water content at the root surface (Ors). In eq. (13) crop water potential (~) was used as an estimation of the interior root water potential (qJr) which was assumed to be independent of root depth. It is assumed that low root conductance is the main barrier to water transport in the liquid phase in the plant (Jensen et al., 1989). The effective root conductance per m root length (Preff.) was calculated as:

Pre,. = Pr-~s (14)

The soil profile was divided into discrete vertical 3 layers of 0.1 m depth with a volume of 0.1 m

per m 2 of soil area. Thus, root water uptake for a soil layer of one m 2 and 0.1 m deep equalled:

qrv, =qrV~ (15)

where

qrvi = root water uptake of soil layer i per unit area; g (water) m -2 (area) s -1

V i =vo lume of soil layer i of one m 2 of 0.1 m depth; 0.1 m 3 m -2 (area)

In order not to destroy the geometry of root distribution, when using the Cowan (1965) and Gardner (1960) single root model for radial water flow, we assumed all root surfaces to be wet and calculated the root water uptake per unit root length as:

q~ (16) Qr =L-

where


The total flow of soil water to the crop (%) was calculated as:

Q~ = root water uptake; g (water) m ~ (root) i = ( 2 0 ) s qp ~ q~vi

The steady state single root model of Cowan (1965) and Gardner (1960) reads:

2~" k- d~b~ ~bmrs (17) Q f - -

where

ln(rcy,/rroot)

rcy I = radius of the cylinder of soil through which water is moving; m

rroot = radius of the root; m

rcy I can be approximated by rcyl=( 'n ' -L) -1/2 (Gardner , 1960). The integral being:

f, o~" k "dOm = M b - M~ (18) mrs

where M b =ma t r i c flux potential of the bulk soil;

m m 2 S -1

M~s = matric flux potential at the root surface; mm 2 s -~

After rearrangement , Mr~ can be obtained from eq. (17) as:

In (rcyl/rroo0 • Q ~ Mr~ =Mb -- 27r (19)

A first estimation of Mrs could be calculated by using the first estimated value of Qr (eq. 16).

Via the M versus 0 curves of Figs. 2C,F a second estimation of Ors for use in eq. (13) could be obtained. Similarly, a second estimation of q~mrs could be obtained by converting Ors via the soil moisture retention curves (Figs. 2A,D). All Ors and ~mrs values based on the third iterative determinat ion of the values deviated by less than 0.01 per cent of the preceding ones and were used for the final calculation of qr by eq. (13). The relevance of the matric flux potential concept when calculating root water uptake, has earlier been pointed out (Raats and Gardner, 1971).

where

qp = total flow of water to the crop from layers with roots; g (water) m -2 (area) s -I

In the case at the end of a time step of one hour qp exceeded the capacity for plant water uptake, which was calculated as Wp - (W~ - q~ 3600), qp was in size equaled with W p - (W a - q , 3600), and the corrected q~i value of the n individual soil layers was calculated as:

q r v i c o r r e c t e d = q r v i _ u n c o r r e c t e d X

[Wp - (W, - q, 3600)]/qp . . . . . . . . . ted

W a is the actual crop water content at the beginning of a time step, and qa '3600 is the transpiration during a time step of one hour. The net water flow of water into the crop storage [qc; g (water) m -2 (area) s -j] is given by:

qc = q p - q~ (21)

Change of soil water content

Inflow into the first layer is from rainfall or dewfall exceeding the interception capacity of the crop (eq. 5). Field capacity is the highest water content the soil can attain. The amount of water that cannot be stored in one layer drains into the next layer or out of the profile. Water is only extracted from the layers by root water uptake (see above) and not from evaporation from the soil surface. At soil water contents below field capacity the vertical flow of water between two adjacent soil layers was obtained from Darcy's equation:

qi = - k ( l f l m ( i + l ) - I/Jmi -~ A I / t g ) / A Z " 106 (22)

where

qi = vertical water flow between soil layer i and layer ( i + 1) (the factor 106 converts from m 3 m -2 to g m-2); g (water)

--9 --I m - (area) s

10 Jensen et al.

%i ~Ona(i+ 1)

~ Z

=weigh ted hydraulic conductivity be- -1 tween two adjacent soil layers; m s

= soil water matric potential of layer i; m = soil water matric potential of layer (i +

1); m = soil water gravitational potential; m = soil layer thickness; m

As recommended by Haverkamp and Vauclin (1979) ~, was calculated as the geometric mean between two adjacent soil layers:

= rk k ~l/z (23) \ i 0+1)/

Haverkamp and Vauclin (1979) conclude that the geometric mean of two adjacent hydraulic conductivity values introduces the smallest weighting error of several methods tested against a quasi- analytical solution.

Change of water content due to vertical flow between the individual soil layers with a given filter area was calculated for layer 1, as:

qvl = ql (24)

where

q~l = change of soil water per unit area of layer; g (water) m -2 (area) s -1

and for each of the layers for i = 2 to ( n - 1 ) , where n is the total number of layers, as:

qvi = (q~-l) -- q~) (25)

0 for layer n is constant and equal to field capacity. Thus, the water content of a soil layer for the following hourly time step (0~ t+l)) could be calculated from root water uptake ( q r J , q~, and water content (0~) of the present time step:

01 t+l) = 0~ + (q, , i - qrv~) 10-6 3600/AZ (26)

If precipitation (P) and dew (D) exceeded the interception capacity (Ic) it was added to soil layer 1 so that:

0{ t+l) = 01 + (qvi -- qrvi + P + D) 10-6 3600/AZ (27)

Calculation of total root length in contact with soil water, weighted soil water potential and weighted effective root conductivity

Total root length in contact with soil water (Ltc), cm (root) cm -2 (soil surface area), was calculated from actual L i (cm cm -3) as:

Ltc = ~ L i 0rsi/0 s AZ 100 (28)

A weighted soil water matric potential of the rooting zone (~,,) was calculated using the following:

Li 0rsi/0~ Ifimi I~m ~- Z Li 0rsi/0s (29)

The weighted effective root conductance of the rooting zone (I~Fe~L) was calculated as:

Li 0rsi/0~ = (30) Preff. Pr ~ Li

Model language, test for convergence, and time step

The model was written in Turbo Pascal version 5.0. In order to test the model for convergence in respect to the time step used we included a time step function in the model by dividing flows on hourly basis (i.e., q~, qr~, qa) with different number of time steps. By testing the model with time steps from one hour to 10 min intervals, we found no significant divergence in 0 i and other parameters by including smaller time steps than one hour when the model was run on daily basis. Therefore, the time step of one hour was used in the present model.

Crop parameters, measurements and climatic conditions used in the presentation and field comparison of the model

In the presentation the model was run for a barley crop during the early part of the grain filling period from 25th June until the middle of July. We imposed a 23-day-drying cycle under climatic conditions corresponding to a typically clear day of the region (Fig. 3) (Hansen et al., 1981) resulting in a potential transpiration as


calculated by the Penman equation (eq. 3) of 4.6 mm day -~ (Fig. 5F). In practice the crop dry mass and its components would be changing as the crop grows. For convenience and in order to examine the dynamics of the water flow in the simplest framework we kept these parameters fixed in the presentation run.

Also, we compared simulated and field measured values of leaf ~, ~b, RWC, and leaf stomatal conductance (g) for diurnal observations obtained in 1986 and 1987. Conductance was measured with a Ll1600 steady state porometer (LiCor Inc., Lincoln, Nebr., USA). The adaxial and abaxial leaf surfaces were measured separately and summed to give the whole- leaf conductance. After the porometric measurement, the leaf was enclosed in a polyethylene bag, and then rapidly cut and transferred to a pressure chamber for measurement of qJ. Imme- diately upon the qJ determination the leaves were frozen in liquid nitrogen, later thawed and ~0, determined by thermocouple hygrometry. Other whole leaves were used for determination of RWC after floating on distilled water for 4 hours under dim light. Further details of these measurements and observations are given in the description of the field experiments by Jensen et al. (1992) and L6sch et al. (1992).

Crop area indices (CAI) components, root densities of 6-7 soil layers, and crop water content at full turgor (Wv) used in the presentation run and in the comparison of simulated and

measured values are given in Table 4 and are from the same field experiments (Andersen et al., 1992a,b). The average CAI of ears (9 .2cm 2 per ear) was obtained from projected area measurements of ears with awns still attached. A similar value was found by Thorne (1965) in two varieties of field grown Hordeum distichum L. From ear area times average number of ears per unit area (651 ears m 2) a CAI e value of 0.6 was obtained. Since, for morphological reasons the effective transpiring area of the ears including awns was not fully taken into account by the projected area measurements, the CAI e value of 0.6 is only to be regarded as a best estimate. Crop height was 0.89 ( + 0 . 0 3 ) m as determined from the ground to the awn tip in fully watered plants just after heading.

The simulation was always run with 12 soil layers (1.2 m depth). The 5-6 lower layers were without roots. Root conductance (Pr) was set as 9.17 10 3 mg (water) m -I (root) s i MPa- l . The root radius was 0.072 (_+0.014) mm as determined from microscopy of 8 field grown barley root samples in 0.1 m deep layers from 0-0.4 m depth. In order to avoid interference from few thick main roots (Seaton et al., 1977) only the radii of laterals were determined. Within each sample 20 measurements of root radius were undertaken. No significant differences in radii were found with depth.

According to Monteith and Unsworth (1990 p.

Table 4. Crop area index (CAI; for significance of index see text below eq. 7), root densities (L, cm cm -3) of 0.1 m deep layers (index 1--7 indicate increasing soil layer depth), and potential storage crop water content (W w gm 2) used in the model presentation and in the field comparison of the model. Rooting depths were 0.6 and 0.7 m in the model presentation and in the field comparison, respectively

Model presentation Field comparison 1986 Field comparison 1987

A; 26 June B; 3 July C; 16 July A; 25 June 13; 2 July C; 7 July

CAI c 0.6 0.6 0,6 (1.6 0.6 11.6 0.6 CAI s 0.4 (I.25 0,25 0.25 0.4 0.4 0.4 CAI 7 1.3 0.65 0.65 0.65 1.4 1.5 1.2 CAI~ 2.7 1.50 1.50 0.10 1.6 1.6 0.8 CAI~,~,~ 5.0 3.0 3.0 1.6 4.0 4. i 3.0 Lt (cm cm 3) 8.7 8.0 11.7 9.2 6.9 7.0 8.0 L, 5.0 4,0 6.8 5.8 3.5 3.5 3.8 L~ 2.8 2.7 3.3 3.3 2.6 3.0 3.2 L 4 0.47 0.4 0.5 0.4 1.1 1.1 0.82 L s (I.27 0.2 0.3 0.25 0.6 0.6 (/.68 L~ 0.1 0.1 0.2 0.15 0.1 0.15 0.2 L 7 - 0.01 0.01 0.01 0.01 0.1 0.1 Wp (g m 2) 3000 1400 190/) 1700 2900 3300 3300

12 Jensen et al.

77) the light extinction coefficient (K) of the erect ears was set to 0.2. K of the leaves was calculated by eq. (8) from radiation and CAI values obtained as mid-day values by L6sch et al. (1992) and the K value was 0.6, which is close to the value given by Monteith and Unsworth (1990) for barley.

In the simulations, the drying cycle was initiated at 24.00 hr and the soil water content was set at field capacity (Table 2). The actual storage water content of the crop (W,) at this time was set to equal Wp.

For the presentation run, the following climatic conditions were used: Air water vapour pressure (%) was 1.3 kPa throughout the day and night period. Windspeed varied from 0.8 to 2.1 m s -1, air temperature from 12.5 to 19°C, net radiation from - 7 2 to 4 9 1 W m -2 and global radiation from 0 to 7 2 3 W m 2 (Fig. 3). All climatic data refer to conditions 2 m above the ground. The soil heat flux varied from - 7 to 49 W m -2 (Fig. 3). For the field comparison, the

i i i 1 i I 1 i 1 i i i i i i i i i i i i i i

o 20 1"---

ci / \ E / \

16 / \

~, _ J \ -'-" 12 - ' t g J - - temperature E

- o 8 wind speed

03 I::).

4 -o

O ' V , l . . . . . . . . . . . . . . . . . . . . . . . . . . . . I l t l t l --- global radiation

E 8 0 0 net radiation

\ x 600 /

400 /

-,= / x 6 200 / x

0

~" -200 . . . . . . . . . . . . . . . . . . . . . . 0 3 6 9 12 15 18 21 24

Time (hours)

Fig. 3. Diurnal variations in temperature, wind speed, radiation and soil heat flux used in the model presentation during the 23-day-drying cycle.

main climatic conditions are given in Figs. 11 and 12 and were obtained from a climatic station situated about 500 m from the experimental field and measured 2 m above well watered short grass.

Finally, we tested the model in the field by comparing simulated and measured soil water contents in relation to soil water deficit of the soil profile (0-0.8 m depth). The deficits for the rooted soil layers were calculated as: E (0 co . - 0~), and are given below in mm water. The comparison was done for the period 26.6.86- 30.7.86. The soil water content was measured with the neutron moderation method at 0.1, 0.3, 0.5, and 0.7 m depth twice a week as detailed by Andersen et al. (1992a). Fifty measured observations at each depth from 10 different plots selected by random were compared with simulated values. The simulation was run with crop characteristics as an average of those stated for the 3 and 16 July 1986 in Table 4. The root densities used in the simulation were representa- tive for the whole testing period (Andersen et al., 1992a; Fig. 7). The climatic data used were the same as those used for the presentation run, and they represent reasonably well the climate of the simulated period.

R e s u l t s

Simplification of crop water status modeling

In the model we regarded the crop in respect to water status as being a 'big leaf' and derived crop water status parameters from PV curves of the 'middle positioned' leaf No 7 (the leaf below the flag leaf) (Fig. 1). However, on clear days diurnal observations indicated that leaf water potential increased with lower leaf position (L6sch et al., 1992). Typically, mid-day leaf water potential increased 0.05 to 0.2 MPa in leaf No 7 as compared with leaf No 8 (the flag leaf) and 0.1 to 0.3MPa in leaf No 6 as compared with leaf No 7. Thus, water status parameters derived from PV curves of leaf No 7 must only be regarded as an estimate of mean crop water relations. Due to the inelastic leaf tissue of barley (Jensen et al., 1992) the above differences in leaf water potential were only reflected in

minor differences in RWC between leaves and organs; e.g. for leaf No 8, 7, 6, and ear plus stem mid-day RWC values were 0.91-+ 0.01, 0.92 + 0.01, 0.93 + 0.02 and 0.92--- 0.01 s.e. (n = 4), respectively, as determined on a clear day. Similarly small RWC differences were found between leaf No 8 and 7 during five diurnal field observations of RWC when the values ranged from 0.88 to 0.99 in the cloudy year 1987. The above results showing limited decrease of leaf water potential with crop height indicate, that low root conductance was the main barrier to water transport. This justifies, that the root water potential was equated with crop water potential in the root water uptake model (eq. 13).

Model presentation

Figures 4A-C show diurnal shaded and sunlit CAI, crop conductance (gc), and transpiration, respectively, in a well watered crop. Around mid-day, sunlit and shaded CAI made up 26 and 74%, respectively, of total CAl. During the middle of the day conductance from sunlit and shaded CAI contributed 46 and 54%, respectively, to gc of 12-13 mm s- ' . The shaded contribu- tion was almost exclusively from leaf No 7 and 6 (including older leaves, if present). The rate of transpiration calculated by Monteith's combination equation (eq. 2) made up 84% of the transpiration calculated by Penman's equation (eq. 3) (Fig. 4C). The influence of dew fall on transpiration was taken into account by letting the crop evaporate with 1/go--0 in eq. (2) until the dew had disappeared in the morning. A further comparison between transpiration calculated by Monteith's and Penman's equations is given in mm day-~ in Figure 5F.

In order to present simulated effects of soil water depletion on crop water relations, predicted results are given below for the barley crop in the grain filling period during a 23-day-drying cycle. Fig. 5A shows the soil water content of the topsoil and subsoil layers with different root densities. The water content of the layer just below the soil surface with high root density decreased especially rapidly during time. The resulting decrease in the weighted soil water potential (@m; eq. 29) which takes into account


5.0

4.0

_ 3.0 , <

o 2.0

1.0

0.0 'raO

E E (D 0 c -

O

c-

O O

- - shaded

-- - sun l i t

f \

. . . . sunlit + shaded - - shaded; - -- sunlit

15 B

/ " ~ , , 10 ,, \

5 t - %

I I I I I I I I I I I I I I 1 | 1 1 1 I I I I I I I

= 150 C

E 120

E 90 c -

.o 60

~. 30 or)

.~ 0 i -

-30 ,,, . . . . . . , , , . . . . . . . . . . .

0 4 8 12 16 20 24

Time (hours) Fig. 4. A-C A, diurnal variation in sunlit and shaded crop area indices (CAI); B, diurnal crop conductance (g. CAI) to water vapour transfer from shaded and sunlit CAI; C, diurnal variation in transpiration as calculated by Monteith's (actual eq. 2) or Penman's equation (potential eq. 3) where negative transpiration indicates dew formation. The simulation was run at a soil water content at field capacity.

the degree of root contact with soil water, is shown in Figure 5B. Figure 5B also shows diurnal changes in crop water potential (¢) indicating that in the beginning of the drying cycle the crop rehydrates during the night. Dur- ing the first 17 days of the drying cycle, the mid-day potential difference between crop and 'soil water potential was about 1.8-2.0 MPa. At the end of the drying cycle it decreased to about

14 Jensen et al.

0.20

0.16

~ 0.08

0.04

0.00

0.004 ~E '~ 0.003

0.002

o.001 0.000

-:- 7O

E 60 N 5o o ~- 40 t~

,I,,,o

o 30

~ 20 r - o

t l l l l l l l l l t l l t l l l l l l l l l

~ , , _ - ~ topsoil: . . . . . 1 A

subsoil: "- - - ~

, . . . . . . . . . . . . lllt I l l l l t l l l l l l l l l t l l t I

100 ~,,,,,,,,,,,,,,,,,,,,,,,,1 0 5 10 15 20 25

0

-1

-2

0 - 3

~ -4

-5

0,8

0.6

0.4 - - crop cond. E . . . . boundary layer cond. ] -'m>. 5

, , , ~N t I t i " ' ~ , n i - . l t~1 ,~, ,,.~t ~,,,,.~ ~,,,1 I ,,,'1 ,,,llt~, I I,,,~1 ,,llt~;,I I' E 4 , , ,11: ,LI , ,ll: ,I,,I,, ,11: I,,,I , I,,,I , I,,,I I , I , , , I , I , , I , I , , , I , I , , , I , I , , , 3 ,I I, ,,I, I, , ,I I, ,,,I I, ,,,,I I , , , ,,,I I, ,,,11 ,,11 , ,,,11, , , ,U, , , , ,ll, , ,,11, , , , ,11, -~

F- 0

I I I I I I I t I t I I t I

" \ " \ B

. . . . soil water potential - - crop water potential

F

\

~ .

Penman . . . . M0nteith

] l ] l l l l l I I l | l I I I t l l l I I I

0 5 10 15 20 25

Time (days) Time (days) Fig. 5. A-F Water relations during 23-day-drying cycle. A, volumetric soil water content (0) of six 0.1 m deep soil layers (depth increases with size of layer No.); B, water potential of the crop (tO) and weighted soil water matric potential (@m); C, weighted effective root conductance (tSre,); D, relative crop water content (RWC); E, crop and boundary layer conductance to water vapour transfer; F, transpiration as calculated by Monteith's (eq. 2) and Penman's equations (eq. 3).

1.1 MPa. The soil water matric potential at the root surface (@mrs) only slightly decreased below @m of the bulk soil (Figs. 6A-C) . In the subsoil with low root density, minor diurnal oscillations with an amplitude of about 0.3 to 1.6 kPa could be ascertained (Fig. 6C). Hence, the decrease of the weighted effective root conductances (/3refr.;

eq. 30), which takes the degree of root contact into account (Fig. 5C), was the main reason for decreased root water uptake.

In order to elucidate the effect of the size of the In (rcyl/rroot) relationship in eq. (17) on the calculated ~O,,rs value we ran the model with twice the root radius (Loot) value used in the


¢O 13-

v

.¢0

O) O

¢10

0,0

-0,5

-1.0

-1.5

-2,0

-2.5

-0.07

-0,14

-0.21

-0.28

-0,35

-0,005

-0.010

-0.015

-ii layer 0 - 0.1 m

l I l l I I l I I I I I I I I

layer 0.2 - 0.3 m IIlll . . . . . . . . . i ! i i i i i i i i

C

layer 0.5 - 0.6 m -0.020 . . . . . . . . . . . . . . .

0 4 8 12 16 Time (days)

Fig. 6. A-C Soil water matric potential of the bulk soil (tOm) and at the root surface (~m~s) at three depths during the drying cycle. Figs. A and B are topsoil and Fig. C is subsoil. Root densities are given in Table 4 (model presentation).

presentation; i.e., rroot was increased from 0.0072 cm to 0.0144 cm. This resulted in only an insignificant increase in ~0mr S (at most <0.4 kPa), and as a whole the results of the simulation were only insignificantly influenced.

When the rate of diurnal transpiration essen- tially exceeded that of root water uptake at about day 12 in the drying cycle (Fig. 7A), a progressive decrease of RWC (Fig. 5D), crop water potential (Fig. 5B), and gc (Fig. 5E)

occurred. The latter resulted in the decrease of transpiration (Fig. 5F), as the conductance values were used in Monteith 's combination equation (eq. 2). From Fig. 5E, it is also clear that boundary layer conductance (g,) was large compared with go.

It should be noted that the transpiration flow at any given instant is balanced by the flow from root water uptake and from water storage. The reference level for the balance is the inner space of the xylem vascular tissue. The tissue is hydrat- ing if the flow to the storage is positive and dehydrating if it is negative. Flow of transpiration, water uptake (Fig. 7A) and accumulated storage water (E qc in eq. 21; Fig. 7B) showed,

160

140

120

"E 1 O0

8o

60

40

20

0

_ o.oi E ~ -o.21

~ -0.4 2

. , -0.6 ~ ~, -0.8"

-~ .1.0 ~

-~ -1.22

- 1 , 4 : o

< -1.6:

4.8:

- - transpiration

-- --- uptake

A

B

O 5 10 15 20 25

Time (days)

Fig. 7. A,B A, flow of transpiration and root water uptake; B, accumulated storage water during the drying cycle.

16 Jensen et al.

as expected from the above findings, strong diurnal oscillations. During daytime, transpiration exceeded water uptake causing negative storage flow and tissue dehydration. The reverse occurred during nighttime. These accumulated storage water oscillations correspond to the above mentioned changes in crop RWC (Fig. 5D). From Figures 7B and 5F, it is clear that an essential part of the transpirational water loss comes from changes in crop water storage; e.g., at day 1 and 13 in the drying cycle 0.4 and 1 .0mmday -~ (Fig. 7B), respectively, of the transpirational water loss of 3.9 and 3.0 mm day -~ (Fig. 5F) come from dehydration of the crop.

In Figure 8A, diurnal changes in crop water potential (q0, osmotic potential (tp=), and turgor pressure (qJv) are shown during the first 14 days of the drying cycle under climatic conditions as specified above, i.e. high evaporative demands. The simulations indicate large changes in ~Op during the diurnal cycle in the beginning of the drying cycle due to decrease of crop storage water content resulting in low turgor potential during the middle of the day. Under less severe evaporative demands (about 2/3rd of the level in Fig. 8A), in the simulation obtained by reducing the radiation level to half the level of that given in Figure 3, less dehydration of the crop and less

decrease of crop storage water content occurred, resulting in medium ~bp values prevailing during the middle of the day, as shown in Figure 8B.

We also modeled the effects of four levels of evaporative demand, obtained by running the simulation at radiation intensities equal to 100, 80, 60, and 40% of that given in Figure 3. This resulted for the three latter in mid-day transpiration levels at field capacity being about 88, 74 and 57%, respectively, of the level at full intensi- ty (Fig. 9A). The transpiration showed a threshold like nature; e.g. at the highest evaporative demand the transpiration decreased markedly when the mean soil matric water potential was below about -0 .5 MPa (Fig. 9A) or when cm roots per cm 2 soil area in contact with soil water (Ltc; eq. 28) decreased below 25 (Fig. 9C). Decreasing the evaporative demands meant that lower mean soil water potentials could prevail or less root contact was needed at a given transpiration rate. Higher crop water potentials at low evaporative demands resulted in more open stomata at low soil water potentials (Fig. 9B) and at low root contact (Fig. 9D).

As the simulated potential difference across the plant tended to be constant (Fig. 5B) our results indicated that Preff. o r the length of roots in contact with soil water governed root water uptake. This is clear from Figure ]0, which

0 . 0 -

-0.5 -

.~ - 1 . 0 -

- 1 . 5 -

o -2 .0 -

-2.5 -

-3.0 - A

-3.5 -

-4.0 J J i i i | i w i | i i v i

0 5 10

Time (days)

-%,- ~,- - v . - , f \ r , ,~., , - k z ' N , , - v ° , j - , j " N f ' \ t

- - - turgor pressure B - - water potent ial

-- - osmot ic potential

! 1 ! i ! i i | | i i |

5 10

Time (days)

Fig. 8. A,B Diurnal changes of crop turgor pressure (%), crop water potential (t~) and crop osmotic potential (~) during the first 14 days of the drying cycle. In B the evaporative demands were reduced to a level about 2/3rd of that in A by halving the radiation level given in Figure 3.


E

E v

t - O

J , _

Q .

t -

L . -

t--

150 I I I

IX.

v

¢u

c cD

0

(D

Q. o

(.9

100

50

0

-1.0

-1.5

-2.0

-2.5

-3.0

-3.5

-4.0

-4.5

A

l

i A(,'7 , , [

B

•/.,/, "/ . /

I II I

-2.0 -1.5 -1,0 -0.5 Mean soil water pot.(MPa)

C

I

D / _ q l I n I o

~d

. - f L f ' ~

. . z ~ - , j

[ I ! I I I I

0 10 20 30 40

Root contact (cm root cm2area) Fig. 9, A-D Mid-day values of transpiration and crop water potential as a function of simple mean soil water potential of layers 1-6 or of root contact, i.e., length of wetted roots in contact with soil water (L,c; eq. 28) of layers 1-6. The curves marked as ( ), (---), (---) and (-.--) indicate the relationships at decreasing evaporative demands obtained by applying in the simulations 100, 80, 60, and 40%, respectively, of the radiation level given in Figure 3.

shows that mid-day values of root water uptake were proportional to Preff.' However, due to change of water storage, the transpiration/fireff. relationship had a threshold-like nature. The small peak in transpiration at a Preff. value of about 0 .0013mgm-~s- lMPa -1 is due to the shift of PV curve under drought conditions (Fig. 1).

Comparisons of measured and simulated results

In order to verify the model behavior, we compared simulated and measured diurnal values of water potential, osmotic potential, RWC, and single leaf stomatal conductance of sunlit leaves.

In 1986, the comparison was made at high temperatures and net radiation levels and at soil water deficits of 54, 10 and 41 mm, respectively (Figs. 11A-C). In 1987 the comparison was made at low soil water deficit and at lower temperatures and levels of radiation than in 1986 (Figs. 12A-C). At 25.6.1987 and 2.7.1987 no conductance measurements were undertaken. The crop water characteristics used in the simulations are given in Table 4.

The comparison showed that the water potential of the flag leaf (leaf No 8) could be predicted to a high degree as only minor deviations occurred between measured and predicted results even though the water potential ranged

18 Jensen et al.

140

E

E l

. m

o

v "

2O

O0

8O ~ I

6o

40"

20"

0 0.000 0.001

/ /

/

J

----transpiration

- - uptake

! !

O. 02 0.003 0,004 0,005 p,,.(mg m-' s" MPa)

Fig. 10. Mid-day values of root water uptake and transpiration as a function of weighted effective root conductance (t~reff) during the 23-day-drying cycle.

from close to zero to - 3 . 5 M P a (Figs. 11 and 12). Also the osmotic potential of the flag leaf could be predicted to a high degree; although in 1986 (Fig. 11), the measured osmotic potentials tended to be lower than the simulated ones, probably due to osmotic adjustment occurring during the day. In 1987, in young flag leaves, measured osmotic potentials were higher than predicted (Fig. 12A). The simulated osmotic values are based on old leaves. This discrepancy is due to the fact that in young leaves, the measured osmotic potential at full turgot was found to be about -1 .1 MPa and decreased to about -1 .9 MPa within 14 days (Jensen et al., 1992).

Measured and simulated values of flag leaf stomatal conductance agreed reasonably. How- ever, in 1987 (a wet and cloudy year causing a high CAI value), the measured flag leaf conductance values were higher than the simulated ones (Fig. 12C). However, the measured values were between simulated values with and without correction for leaf-to-air water vapour concentration difference (~W).

In the rooted layers, measured 0 values at 0-0.2 m and 0.4-0.6 m depths were slightly higher than predicted; at 0 .2-0 .4m, measured and predicted values were similar (Fig. 13). How-

ever, for both topsoil and subsoil we found that the slope, i.e. the change of soil water content with change in mm deficit was similar for measured and simulated values of rooted layers. In the nearly rootless soil layer at 0.6-0.8 m depth the measured values were about 10% lower than predicted which is due to a slightly more roughly textured soil deeper in the subsoil (Nielsen and MOberg, 1985). This we have not taken into account in the model.

In the field we estimated weekly transpiration from neutron probe soil water determination (Andersen et al. 1992b; Figs. 1 and 2). During the clear weather period of June and July 1986 the transpiration of fully irrigated plants was about 3.9 mm day- ~. The transpiration gradually decreased to about 1.0 to 0.5 mm day ~ at a soil water deficit of about 50 mm. This agrees with the simulated transpiration obtained with the Monteith equation on typically clear days (Fig. 5F), and with the fact that measured and simulated 0-values as a function of soil water deficit were similar (Fig. 13) indicating that the model can predict transpiration of a crop during soil water depletion.

Discussion

The water potential at the root surface (~bmrs) was calculated by the Cowan (1965) and Gardner (1960) single root model (eq. 17) assuming that the whole root surface was in contact with soil water. Even though this assumption is not fulfil- led during soil water depletion when decrease in root contact occurs as formulated in eq. (1), reasonable estimates of Omr~ may be obtained as: (I) in the radial flow zones towards the root surface with and without soil water contact tangential exchange of water is likely to occur; (II) decrease of 'root density' due to lack of contact only slightly influences the qJmr~ calculation, because in the radial single root model (eq. 17) root density is used for calculation of the logarithmic relationship of radii, ln(rcy~/rroot); e.g., if the root density (L) is decreased from 3.0 to 1.5 cm cm 3 due to lack of contact and when rroot = 0.0072 cm, then the In (rcyJrroot) relationship would increase only from 3.81 to 4.16. Also, by running the model at similar conditions as at


30 O -,..-%

~- 20 "T

E 10

0

o,__ 500 ¢8 o_ 400 .~." 300 E 200 ~ 100

z 0 rr"

-100 - 0 . 5

IX.

-1 .5

o ~ -2.5

~ - 3 . 5

- - - 4 . 5 IX.

-2.5 o cy. -3.5 E

o -4.5 "T

~. 8 E ~, 6 c--

o

~ 2 c- o

u 0

A; 26 June 1986 54 mm deficit

! | i i I

- - T~

l--7-T i t - - RN

I I t I I

I I I I I

! 0

j_~ -- leaf 8 ---leaf 7

I/1 \

8 16

B; 3 July 1986 0 mm deficit

i ! i i 1

-- RN - - e a

C; 16 July 1986 41 mm deficit ~ ' Ta' ' ' '

I I I I - r -

t 240 8 16

Time (hours) 240

oo t O _(3

i

8 16 24

Fig. I1. A - C Field comparisons of predicted (curves) and measured (points) water potential, osmotic potential and stomatal conductance of sunlit single leaves on 26.6.1986, 3.7.1986, and 16.7.1986. In A (O) indicates leaf No 8 (flag leaf) and ( + ) leaf No 7. In B and C different symbols indicate flag leaves from different plots. The comparisons were made at 54, 10, and 41 mm soil water deficit after the simulations had run for 18, 3, and 21 days, respectively. Diurnal observed climatic conditions (T, , air temperature; U,,, wind speed; e~, water vapour pressure; RN, net radiation) are given in the upper part of the figure.

20 Jensen et al.

30 O

~- 20 " 7

E 10

0 O • --- 500 a~

~ - 400 9." 300 E 200

100

z 0

-100

o 0.95

" " 0.90

0.85 D.. ~; -0.5

O - 1 . 5

(1)

-2.5

~ -1.5 O

E -2.0

o -2.5 "7 ¢/) E 8 E o 6 r- ~ 4 o

"o 2 O

° 0

A; 25 June 1987 i i i i i

- - T . U.

f r ~

I I I I I - - RN . . . . ea

' L ' + + + ' ~ ' ; "

+

I ::i: I l I I

+-H-+ +H=I=+ +

+ +

I I I I + ' ,

0 8 16

B; 2 July 1987 i i i i i

- - Ta U,

- - RN . . . . ea

+

+ + +

I I I i I

+ + +

I I I i I

C; 7 July 1987 i i ! i i

22 8 16

Time (hours)

- - J ~ J T- " - - RN - - - - - e ,

i I i i t

I I I i I

!4 0 24 0 24

I I I t I 0 +~w)

c~,~ o+- (-Aw)

8 16

Fig. 12. A-C Field comparisons of predicted (curves) and measured (points) RWC, water potential, osmotic potential and stomatal conductance of sunlit flag leaves on 25.6.1987, 2.7.1987 and 7.7.1987. The comparisons were made at 5 to 10 mm soil water deficit. In C the conductance is shown with (+AW) and without (-AW) correction for leaf-to-air water vapour concentration difference in the leaf stomatal conductance model (Table 1). Legend otherwise as for Figure 11.


0.16

0.12 e3

E 0.08

0.04

0.00

0.16

0.12 g

0.08 0

0.04

0.00

I I I ! I I I ! I I

0 - 0 . 2 m

O

D

b

0.2 - 0.4 rn

I I I I I I ! ! I !

I I I I I I I I I

0 . 4 - 0.6 m

X ',x, X .yg,

x

0.6 - 0.8 m

15 25 35 45 55 65

Deficit (mm) Fig. 13. Field comparison of predicted (curves) arid measured (points) soil water contents (0) at 0-0.2, 0.2-0.4, 0.4-0.6, and 0.6-0.8 m depth as a function of soil water deficit of the whole rooted profile.

! I I I ! I I ! ! !

5 25 35 45 55 65

Deficit (mm)

the presentation, except that rroot was doubled in size, the latter rationale (II) was confirmed, as only an insignificant increase in the ~mrs value took place as a result of the change in the root radius.

During the drying cycle, our simulated results showed only an insignificant decrease in $~rs as compared to that in the bulk soil (Sin) (Fig. 6) indicating that soil resistance to water flow did not limit water uptake, as also concluded by others (Gardner, 1991; Jensen et al., 1989). As the driving force (the potential difference) was maintained during most part of the drying cycle (Fig. 5B), our results suggest that water uptake decreased due to a reduction in effective root conductance (Preff.) (Fig. 5C). This caused a low rate of water supply to the plants (Fig. 7A), and

in turn it resulted in dehydration (Fig. 5D) and stomatal closure (Fig. 5E).

The suitability of modeling root water uptake by using the contact concept was seemingly confirmed by the fact that simulated and measured values of soil water content agreed well for rooted soil layers (0-0.7 m depth) (Fig. 13). In all cases the slopes of the 0/deficit relationships were similar. Due to low k values the slopes are a result of root water uptake and thus mainly dependent on the absolute root length which was thoroughly determined for the different soil layers. However, at 0-0 .2m and 0.4-0.6m depths, the measured absolute 0 levels were slightly higher than predicted. This discrepancy is probably due to an incorrect characterization of the soil in respect to soil water retention, as

22 Jensen et al.

we only used an average retention curve for describing the topsoil and subsoil, respectively (Figs. 2A,D). For a complete description of the soil, two slightly differing curves for the topsoil and subsoil would have been necessary (Hansen, 1976). That poor contact between roots and soil may have a significant effect on root water uptake is also confirmed by results of Faiz and Weatherley (1978) and Jensen et al. (1989), as mentioned in the Introduction. Furthermore, recent results of Moreshet et al. (1990) showed that in soybean the hydraulic conductance of the root system was proportional to the root weight. These results were obtained by reducing the root system by radially slicing through the soil to remove the lower part of the roots from pot- grown plants. Fernandez and McCree (1991) used the root contact concept of Herkelrath et al. (1977) successfully when simulating plant water relations. Also, a more complex root-soil contact model has recently been developed (Veen et al. 1992) indicating that for root densities normally encountered in agricultural crops (L < 5 cm cm -3) the reduction in water uptake at limiting supply of water is approximately proportional to the degree of root-soil contact, as found when using the Herkelrath et al. (1977) root contact model (Fig. 10).

In our model we used a constant conductance per m of wetted root length of 9.1710-3mg (water) m -t (root) s -t MPa -1 influenced only by the degree of contact. This value gave sensible results when running the model. However, the value is an order of magnitude less than the conductance reported by Herkelrath et al. (1977) obtained in pot grown wheat seedlings. The deviation may be due to the fact that we considered field-grown plants at a more mature stage, viz. the grain filling stage. Also, we included the conductance of the whole radial and axial water flow system across the root membranes and xylem system of roots, stems and leaves, as we equated the internal root water potential with that of the leaves or the crop (eq. 13), making the assumption that the major resistance to water transport in the plant is the radial one across the root membranes (Jensen et al., 1989; Moreshet et al., 1990). However, the conductance value used in the simulation is quite similar to conductances obtained for the whole plant in

field experiments by Zur et al. (1982) on fine sand with soybean under wet conditions. Zur et al. found conductances ranging from 8.3 10 -3 to 2.8 10 -2 mg (water) m -z (root) s -1MPa -1.

Stomatal closure occurred when root length in contact with soil water was below about 20- 30cm (root) cm -2 soil (area) (Figs. 9C,D). However, by reducing the evaporative demands the root water uptake could proceed with fewer roots in contact with soil water or at lower soil water potentials due to a smaller reduction in crop water potential, less stomatal closure, and hence less decrease in transpiration (Figs. 9A,B). This picture is in accordance with classi- cal findings of Denmead and Shaw (1962).

A key point in the above simulation was the use of the empirical stomatal conductance model (Table 1) which is further described by L6sch et al. (1992). In this model the effects of changes in both leaf water potential and micro-meteorological factors on conductance were taken into account. As mentioned by L6sch et al. (1992) the examples from days in 1986 (Fig. 11) show that the stomatal model, compiled from stepwise regression calculations for the single parameter that influence stomatal conductance, worked as a whole and was able to predict various types of diurnal courses. The data for 1987 (Fig. 12C) served as an independent test of the stomatal model predictions, and the model also predicted stomatal opening and closure including closure during the day. Variable adaptation to lower light conditions during the cloudy growing season of 1987 may have caused the slightly higher measured than predicted conductance that year. These aspects and the similarities of the present stomatal model with other modeling approaches (e.g., Jarvis, 1976) are further discussed by L6sch et al. (1992). As in the present model, it is common for most of these models to describe the multifactorial dependence of stomatal apertures on the environment as being additive. This has the advantage that the empirical quantification of the single dependencies can be easily extended to a yet more causal quantitative description if knowledge about the functional dependency of the stomatal response to a particular factor is increased.

During the middle of the day in fully watered plants the crop conductance was about

13 mm s -~ (Fig. 4B). This value is similar to crop conductance values found in a non-senescent wheat crop in England (Fowler and Unsworth, 1979) and it is also within the range given for field grown crops by Ben-Asher et al. (1989) (5 to 30 mm s -~) and by Monteith and Unsworth (1990 p. 252) (10mms -l) and in field grown maize by Rochette et al. (1991) (10-20 mm s-I). Also we found that transpiration calculated by Monteith's equation (eq. 2) at high soil water content made up 84% of transpiration calculated by eq. 3, which is the version of Penman's equation most often used for calculating potential transpiration in this region. This may indicate that evaporation from the soil may contrib- ute 16% to the potential transpiration (often termed evapotranspiration) which is a larger magnitude of soil evaporation than found by others in irrigated wheat (Luchiari and Riha, 1991). However, transpiration as calculated by Monteith's equation (eq. 2) is based on temperatures and water vapour saturation differences (% - ca) measured at the reference height, while crop conductance values for use in Monteith's equation are based on leaf-to-air water vapour pressure concentration differences (AW) and temperatures at the crop surfaces. In the stomatal model (Table 1), we equate AW with (G - e,) and leaf temperature with air temperature both measured at the reference height. Thus, errors may occur when calculating g~ from eq. (9), as the conditions at the crop surfaces may be different from those at the reference height (Jensen et al., 1990a). Also, low levels of boundary layer conductance will increase the differences between the two sites (e.g. Adams et al., 1991). Furthermore, in the stomatal model we did not take into account that AW and crop temperature may vary within the crop. More humid conditions are expected in lower crop layers. In the field experiment we could not detect any difference between AW measured at the flag leaf and at the leaf below (No 7) (L6sch et al., 1992; Fig. 5) indicating that a major part of the crop was well enclosed into the crop gross boundary layer. Calculation of crop temperature and (e~- e~) at the crop surface from values at the reference height has recently been performed by Adams et al. (1991) for use in different evapotranspiration models. They found that


modeling of stomatal conductance in pinegrass could be improved by using (e S- ca) values estimated at the leaf surfaces.

Rochette et al. (1991) tested six different methods of scaling up leaf stomatal conductance to crop conductance (g~) in field grown maize. The weighting procedure given in eq. (9), where stomatal conductances of shaded and sunlit leaf area are summarized, gave better estimates of gc than more simple methods obtained by only considering g of sunlit leaves from the top of the crop. However, Rochette et al. (199!) found that the weighted g~ value was often too high (opposite to our findings) and recommend a "shelter" factor correcting go. Rochette et al. (1991) also point out that leaf distribution should be considered when calculating PAR at the leaf surface. They improved the modeling of gc by using a spherical leaf angle distribution, so that a more correct PAR value at the leaf surface was obtained for use in the stomatal model. This aspect we took into account in the present model by multiplying the horizontal PAR value by Ksin ~-~ giving mean radiation levels at crop surfaces.

A problem similar to the weighting procedure when scaling up gc is the determination of the CA1 of awns and ears. In this study we simply measured the projected area of ears with awns still attached, and used the stomatal model (Table 1) for calculating the g CA1 value. However, using the projected area underesti- mates CAI especially of awns. Biscoe et al. (1973) found that 73% of ear transpiration may originate from awns and that transpiration was proportional to awn area as calculated from single awn area. They also found a low g value of awns as compared to flag leaves. Therefore investigations are needed on ear conductance and area in order to determine contributions from both lemma and awns to g~. Such investigations should also comprise age effects, because over time ears become mature and transpire less.

As envisaged above, inclusion of crop water capacitance and water storage flow is needed when simulating diurnal fluctuations of plant water status. Furthermore, accurate estimations of tissue elasticity are important in order to elaborate plant water relations under drought stress (Jensen et al., 1992). These aspects were

24 Jensen et al.

t a k e n in to account by using PV curves for de- sc r ib ing W R W C re la t ionsh ips dur ing the dry ing cycle , resu l t ing in good a g r e e m e n t b e t w e e n pre- d i c t ed and m e a s u r e d va lues of d iu rna l changes in the c rop w a t e r r e l a t ion p a r a m e t e r s ~O, ~0= and, R W C (Figs . 11, 12). A l s o , the good a g r e e m e n t b e t w e e n the p r e d i c t e d and m e a s u r e d changes in t hese p a r a m e t e r s p r o b a b l y conf i rms the s to rage flow given in F igu re 7B. T h e r e f o r e , we find tha t P V curves are useful for m o d e l i n g d iurna l fluc- t u a t i o n s of p l an t wa te r s tatus .

Conclusion

F r o m the inves t iga t ion we conc luded : ( I ) O n sandy soils a m o d e l which t akes the deg ree of con tac t b e t w e e n roo t surface and soil wa te r into accoun t , can be used for ca lcu la t ion of roo t w a t e r u p t a k e , so tha t the roo t conduc t ance du r ing soil w a t e r d e p l e t i o n only var ies by the

d e g r e e of con tac t ; ( I I ) c rop c o n d u c t a n c e used for ca lcu la t ion o f c rop t r ansp i r a t i on can be sca led up f rom an empi r i ca l single leaf s t oma ta l conduct - ance m o d e l c o n t r o l l e d by the level o f c rop wa te r p o t e n t i a l and m i c r o - m e t e o r o l o g i c a l factors ; ( I I I ) p r e s s u r e - v o l u m e curves are useful for descr ib ing c rop w a t e r s ta tus inc luding c rop wa te r s to rage .

Acknowledgements

W e are gra te fu l to the D a n i s h Ve te r ina ry and A g r i c u l t u r a l R e s e a r c h Counc i l (P ro j ec t Nos 13-

3514, 13-3689, and 13-3870) for g ran ts suppor t - ing this work . We are also gra tefu l to the D a n i s h R e s e a r c h Service for P lant and Soil Science for t echn ica l s u p p o r t and field facil i t ies. We t h a n k P ro fe s so r , D r H E Jensen , D r I E H e n s o n , D r C P e t e r s e n and L e c t u r e r S H a n s e n for he lpfu l sugges t ions and c o m m e n t s on the manuscr ip t . A l s o , we t h a n k the r e fe rees for e n c o u r a g e m e n t and he lpfu l sugges t ions . T h e typewr i t ing of Mrs E Brush is g ra te fu l ly a cknowledged .

References

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covered forest clear cut. Agric. For. Meteorol. 56, 173- 193.

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Andersen M N, Jensen C R and L6sch R 1992b The interaction effects of potassium application and drought in field-grown barley. II. Nutrient relations, tissue water content and morphological development. Acta Agric. Scand., Sect. B, Soil and Plant Sci. 42, 45-56.

Bavel C H M van 1967 Changes in canopy resistance to alfalfa induced by water depletion. Agric. Meteorol. 4, 165-176.

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Campbell G S 1977 An Introduction to Environmental Biophysics. Springer-Verlag, New York.

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Simulat ing crop water relations 25

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Main symbols

CAI =projected crop area index; m 2 (crop area) m 2 (ground area)

Cp = specific heat capacity of dry air; J g l °C J D =dew;g(wa te r ) m : (area) s t e,, -w a t e r vapour pressure; Pa e~ = saturation water vapour pressure; Pa F~r ~ = flux density of latent heat; J m 2 s G - so i l heat flux; Wm 2 g = leaf stomatal conductance; mms g~, -boundary layer conductance to water vapour trans-

fer; ms-~ or mms 1103 g~ = crop conductance to water vapour transfer; m s ~ or

mm s ~ 103 I t = crop interception capacity; g (water) m ~ (ground

area) I = water stored in interception storage; g (water) m -'

(ground area) k, = soil water hydraulic conductivity of layer (i); mm s

or m s ~ 10 3

2 6 Simulat ing crop water relations

k~ = s a t u r a t e d soil wa te r hydrau l ic conduc t iv i ty ; m m s ' or m s t 10

K = canopy l ight ex t inc t ion coeff icient

K, = yon K a r m a n cons tan t ; 0.41 L = roo t l eng th dens i ty ; m m- 3 or cm cm ~ 10 ̀ 4

L,,. = to ta l root length in con tac t wi th soil wa te r ; cm (root) cm-2 (soil surface area)

M b = ma t r i c flux p o t e n t i a l of the bu lk soil; m m 2 s t

M ~ = mat r ic flux p o t e n t i a l at the roo t surface; m m 2 s

P = p r ec ip i t a t i on ra te ; g (water) m -2 (area) s -~

P A R = p h o t o s y n t h e t i c act ive r ad ia t ion (400-700 nm); /~mol p h o t o n s m 2 s l

q . = t r ansp i r a t i on e s t i m a t e d f rom a dense crop; g (water) m z (area) s - I

q~o = p o t e n t i a l t r ansp i r a t i on f rom a dense crop; g (water) m 2 (area) s~ '

q¢ = net flow of w a t e r in to the c rop s to rage ; g (water) m 2

(area) s '

ql = v e r t i c a l w a t e r flow b e t w e e n soil l aye r i and layer (i + 1); g (water ) m 2 (area) s ~

qp = to ta l flow of w a t e r to the c rop f rom soil layers wi th roots ; g (water) m -2 (area) s

% = roo t w a t e r u p t a k e f rom soil layer i; g (water) m -s (soi l) s 1

qr~ = roo t w a t e r u p t a k e f rom soil layer i pe r uni t a rea ; g (water) m 2 (area) s l

q~i = change of soil w a t e r pe r uni t a r ea of l ayer i; g (water) m -2 (area) s -I

Qr = roo t w a t e r u p t a k e ; g (water) m ~ ( root) s

roy t = rad ius of the cy l inder of soil t h rough which w a t e r is mov ing ; m

too, = r a d i u s of the roo t ; m

R N = ne t r ad ia t ion ; W m -z

R W C = re la t ive c rop w a t e r con ten t

U~ = w i n d speed at he igh t Z . ; m s -~

V = v o l u m e of soil l aye r i of one m z of 0 . l m dep th ; 0.1 m 3 m 2 (area)

W, = ac tua l s to rage c rop wa te r con ten t ; g (water) m 2

(g round area)

Wp = s to rage crop wa te r con ten t at full tu rgor ; g (water) m z (g round area)

Z , = he igh t of wind speed m e a s u r e m e n t ; 2 m

Zo = surface b o u n d a r y roughness he igh t ; m

A = first de r iva t ive of s a t u r a t e d v a p o u r p ressure versus

t e m p e r a t u r e ; Pa °C

2tW = l e a f - t o - a i r wa te r v a p o u r c o n c e n t r a t i o n d i f fe rence ; g

(water) m-3 (air)

AZ = soil l ayer th ickness ; 0.1 m

3' = psychomet r i c cons tan t ; Pa ° C -

A = la ten t hea t of evapo ra t i on ; J g

= sun e leva t ion angle

~O = crop wa te r po ten t i a l ; m or M P a 10 2

+g = soil w a t e r g rav i t a t iona l po ten t i a l ; m or M P a 10 -2

tO L = leaf w a t e r po ten t i a l ; m or M P a 1 0 -2

tO~. = bu lk soil wa te r mat r ic po ten t i a l ; m or M P a 10 2

t#.,o = bu lk soil w a t e r mat r ic po t en t i a l at or above field capac i ty ; m or M P a 1 0 -2

~ . = w e i g h t e d soil w a t e r mat r ic po ten t i a l ; m or M P a 10 -~'

q~r = w a t e r po t en t i a l ins ide the root ; m or M P a 10 2

~0., S = soil w a t e r ma t r i c po t en t i a l at the roo t surface; m or M P a 10 -2

p = air dens i ty ; g m -3

Or = roo t conduc tance pe r uni t roo t l eng th ; g (water) m (root) s 1 M P a

tSreff. = w e i g h t e d ef fec t ive root conduc t ance pe r uni t root

l eng th ; g (water) m -t ( root ) s -~ M P a 0 = vo lume t r i c b u l k soil w a t e r con ten t ; m 3 m -3

0 t o = v o l u m e t r i c soil w a t e r con ten t at field capac i ty ; m 3 m 3

0~, = vo lume t r i c soil w a t e r con ten t at the roo t sur face ; m3m 3

0 S = vo lume t r i c s a tu ra t ion soil wa te r con ten t ; m 3 m- 3

Section editor: B E Clothier

use of the root contact concept, an empirical leaf conductance model and pressure-volume curves in...

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