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The canopy growth and transpiration modelof WAVES: Technical description andevaluation

P.G. Slavich, T.J. Hatton and W. R. Dawes

Technical Report No 3/98 (January 1998)

THE CANOPY GROWTH AND TRANSPIRATION MODEL OF WAVES: TECHNICAL

DESCRIPTION AND EVALUATION

P.G. Slavich1, T.J. Hatton2 and W. R. Dawes3

1 NSW Agriculture, Wollongbar Agricultural Institute, Bruxner Highway, Wollongbar, NSW, 2477

2 CSIRO Land and Water, Private Bag, PO Wembley, WA, 6014

3 CSIRO Land and Water, and CRC for Catchment Hydrology, GPO Box 1666, Canberra, ACT,

2601

Technical Report 3/98

January 1998

CSIRO Land and Water

SUMMARY

Groundwater recharge and discharge processes are affected by complex interactions between soil

properties, water table depth, soil salinity, vegetation characteristics and climatic conditions. Soil-

vegetation-atmosphere transfer (SVAT) models attempt to describe the dynamic nature of these

interactions and so increase our understanding of the sensitivity of the system to changes in

conditions. This paper describes the assumptions and governing equations of a vegetation growth

and transpiration model for use in hydrological studies, and evaluates the behaviour of the model in

relation to current understanding of the effects of environmental stress on ecophysiological

processes.

The vegetation growth model describes generic processes affecting carbon and water vapour

exchange at the canopy scale using daily climate data. It is designed to predict changes in leaf area,

root water uptake distribution and transpiration rates, as a component of a soil-vegetation-

atmosphere model (WAVES) which describes hydrological processes. Empirical relationships are

used to describe general ecophysiological processes. A new interpretation, based on stomatal and

mesophyll conductances for the transfer of carbon dioxide and water vapour, is established for the

integrated rate methodology of Wu et. al. (1994) for combining normalised (0-1) growth stress

indices for water and light availability, and temperature.

The modelled interactions between the growth and water use are demonstrated to be consistent with

current understanding of plant response to soil water stress and seasonal climatic conditions. The

modelled carbon assimilation and transpiration rates, water use efficiency (g C assimilated kg-1

H2,O transpired) and radiation efficiency (g C assimilated MJ-1 absorbed solar radiation) are

comparable with published values. Decreasing water availability is shown to increase water use

efficiency for leaf area index less than 2.0, decrease radiation efficiency and decrease the long term

equilibrium leaf area.

1 INTRODUCTION

Biophysical models of the soil-vegetation-atmosphere continuum can be used to increase our

understanding of the sensitivity of different vegetation types to changes in hydrological conditions

which affect groundwater recharge and discharge processes. SVAT models which consider soil

water and solute transport are sensitive to estimates of transpiration since it is usually a major

component of the surface water balance. However, transpiration interacts strongly with climate, soil

water availability and soil salinity through changes in leaf area, canopy conductance and root

distribution. Hence, to understand the plant-soil interactions which affect salinisation processes, soil

water and solute transport models need to be linked with a vegetation growth model which

describes canopy carbon and water vapour exchange processes, changes in leaf area and changes in

root water uptake.

Vegetation growth and water use models are driven by climatic data which are usually most

available as daily estimates such as total radiation, total rainfall, maximum temperature, minimum

temperature and average vapour pressure deficit. Hence, for a growth and water use model to be

widely applicable, it must be designed to give an adequate representation of water and carbon

transfer processes using daily climate data.

WAVES (Water Atmosphere Vegetation Energy and Solutes) is a SVAT model which uses an

efficient numerical solution to solve Richards’ equation for unsaturated water flow and the

convective dispersive equation for non-reactive solute movement (Dawes and Hatton, 1993; Dawes

and Short, 1993). Convergence and stability of the numerical solution can be guaranteed when the

Broadbridge and White (1988) model is used to describe soil hydraulic properties, greatly

facilitating application of the model across long time scales and wide ranges in soil water content.

Zhang et. al. (1996) described the assumptions used within WAVES to calculate the surface energy

balance of the over-story canopy layer, under-story and soil surface, and showed that simulated net

radiation, evapotranspiration and soil moisture content agreed well with those observed within the

First ISLSCP Field Experiment (FIFE) and Hydrologic Atmospheric Pilot Experiment and

Modelisation du Bilan Hydrique (HAPEX-MOBILHY).

The assumptions and algorithms used in the vegetation growth and transpiration sub-routines of the

WAVES model have been developed further and are described below. The aim of this work is to

describe the conceptual basis and assumptions of a vegetation growth and transpiration sub-model

which has been incorporated within WAVES and to evaluate the sub-model in relation to current

understanding of reduced soil water availability on canopy transfer processes. A central feature of

the model is the use of a common canopy conductance model to describe the effects of climatic

conditions and soil water availability on carbon and water vapour exchange. A general description

of the soil water and solute movement components of WAVES is also given.

1.1 Summary description of WAVES and explicit model assumptions.

WAVES is a system model of the soil-vegetation-atmosphere continuum, which accounts for the

major processes affecting vegetation growth and water use. It can incorporate saline soils underlain

by a fluctuating watertable, and surface flooding. The model requires inputs of daily climatic and

watertable data, parameters which characterise the vegetation type, and soil parameters which

describe the water holding capacity and hydraulic properties of soil layers. WAVES simulates the

daily carbon and water balance components, i.e. transpiration, soil evaporation, net flow to or from

the watertable; the profile distribution of soil water content and chloride concentration; production

of leaf, stem and root biomass and changes in root distribution.

Vegetation growth and transpiration are modelled at the canopy scale using a “big leaf” concept,

with parameters such as the maximum daily carbon assimilation rate at complete light interception,

the minimum soil matric and osmotic potential against which water uptake can occur, specific leaf

area, optimum growth temperature, light extinction coefficient, and mortality rates. The soil and

plant evaporation demands are modelled using the Penman-Monteith equation combined with

dynamic canopy conductance and surface soil resistance models. Incoming radiation is partitioned

between the canopy and soil surface using leaf area and a light extinction coefficient.

A dynamic canopy conductance model for carbon assimilation is used to derive the canopy

conductance for water vapour transfer. Normalised dynamic indices for soil water availability, light

availability and temperature modify canopy mesophyll and stomatal conductances in the canopy

assimilation model. The water availability index and carbon assimilation rate modify the rate of

change in canopy leaf area and root distribution.

Soil water and solute movement are modelled using a finite difference solution to the Richards’, and

convective dispersion equations, respectively. The forms of the soil moisture characteristic and

unsaturated hydraulic conductivity models can be selected by the user. The daily transpiration

predicted by the Penman-Monteith equation is extracted from the profile using weighting factors

determined by the modelled root density and a normalised weighted sum of the matric and osmotic

soil water potential of each layer. Water extraction is limited by the minimum matric and osmotic

water potential against which uptake is assumed to occur.

1.2 Explicit assumptions used in WAVES.

The explicit assumptions adopted in the model are summarised below.

(i) Light interception.

The canopy leaves are homogeneously distributed both vertically and horizontally.

(ii) Carbon assimilation.

The gross daily canopy assimilation rate is determined by mesophyll and stomatal conductances to

CO2 transfer between the atmosphere and the carboxylation site and the sun lit leaf area. The

stomatal conductance decreases as the plant available soil water decreases and leaf transpiration rate

increases. The mesophyll conductance decreases as the amount of absorbed photosynthetically

active radiation decreases, and increases or decreases with increasing temperature according to a

temperature optimum.

(iii) Transpiration.

The canopy is represented as a ‘big leaf’ to quantify sensible and latent energy exchange between

the canopy and the atmosphere.

(iv) Root growth and water uptake.

Decreasing soil water matric and osmotic potential reduce root growth and water uptake. There is a

minimum threshold matric and osmotic potential for root growth and water uptake. The soil water

uptake distribution with depth and the pattern of root growth is determined by the relative

distribution of the soil water availability and root density. Hence, root growth and water uptake is

highest at depths where soil water potential is highest and root density is greatest.

(v) Carbon allocation, respiration and mortality.

The proportion of assimilated carbon allocated to canopy growth decreases linearly with soil water

availability. Growth respiration rate is linearly related to the gross assimilation rate and maintenance

respiration rate is linearly related to the mass of carbon and doubles for a 10 degree increase in

average daily temperature. The rate of leaf, stem and root mortality is linearly related to carbon

mass.

(vi) Water and solute movement.

Soil water flow is isothermal and occurs through a non-swelling, non-hysteritic matrix. The solute is

non-reactive and excluded from uptake in significant quantity, e.g. sodium chloride.

2 DESCRIPTION OF WAVES COMPONENTS

2.1 Surface energy balance and light interception by canopy.

The amount of radiation intercepted by the canopy affects the energy available for both

photosynthesis and transpiration. The surface energy balance has four main components, i.e.

incoming short-wave radiation (0.3-3.0 µm) from the direct (sun) and diffuse sources (sky, clouds),

reflected outgoing short-wave radiation, incoming long-wave radiation (3.0-100 µm) emitted by the

atmosphere, and outgoing long-wave radiation emitted by the surface. The net total available

radiation is estimated from the sum of the net (incoming minus outgoing) short- and long-wave

radiation. Daily incoming short-wave (global) radiation is read as an input whilst net long-wave

radiation is calculated from air temperature and vapour pressure following Brustsaert (1982).

The leaves within the canopy are assumed to be homogeneously distributed both vertically and

horizontally. Hence, the net total radiation passing through the canopy can be assumed to decrease

exponentially as leaf area increases, analogous to the Beer-Lambert law (Monteith, 1965), i.e.

( ) ( ) ( )Q Q k LAI Q k LAIl s c nl= − − − −1 α exp exp (1)

where Qs is the short wave radiant flux density at upper surface of the canopy (kJ m-2 d-1); Qnl is the

net outgoing long wave radiation at the upper surface of the canopy; Ql is the total net radiant flux

density below the canopy (kJ m-2 d-1); k is the daily average light extinction coefficient (m-2 soil m-2

leaf); LAI is the leaf area index of canopy (m-2 leaf m-2 soil); αc is the daily average albedo of the

leaf surface.

The light extinction coefficient incorporates effects of canopy architecture and leaf angle on the

average daily light interception. Hence, the total radiant flux intercepted (Qni), used in the Penman-

Monteith equation to estimate transpiration, is given by:

( ) ( )( ) ( )( )Q Q k LAI Q k LAInl s c nl= − − − − − −( exp exp1 1 1α (2)

The average daily photosynthetically active radiation (PAR), for sunlit leaves is assumed to be 50%

of net incoming radiation,

( )Q Qp s c= −1 2α (3)

where Qp is the daily average PAR at the top of the canopy (kJ m-2 leaf d-1).

2.2 Daily canopy carbon assimilation model.

A 'big leaf' daily conductance model for carbon dioxide and water vapour transfer can be derived

from a consideration of the effects of soil water potential, leaf transpiration rate, temperature and

light intensity on carbon fixation through effects on component transport conductances between the

atmosphere and the carboxylation site. The standard analysis for control of photosynthesis (Jones,

1983) is given as a resistance in series model, i.e.

AC C

r rga i

g m

=−+

(4)

where Ag is the CO2 assimilation rate, i.e. gross fixation minus photo-respiration; Ca is the

atmospheric CO2 concentration at the leaf surface; Ci is the internal CO2 concentration at the site of

carboxylation; rg is the gas phase diffusive resistance between the leaf surface and the surface of

mesophyll cells with the leaf via the stomatal aperture; and rm is a liquid phase biochemical

resistance for CO2 movement through the mesophyll cells to the carboxylation site. Expressing the

resistances (r) as conductances (g where g=1/r) this equation can also be expressed as:

ga i

g m

c a iA =C C1g

+1g

= g ( C - C )−

(5)

where gc is the combined (diffusive and mesophyll) conductance to CO2 exchange.

For a daily time step, it is assumed that the primary effect of reduced water availability or

excessively high leaf transpiration rates, is to reduce the gas phase conductance, and hence the

supply of CO2, through stomatal closure; and that the primary effect of reduced light and sub-

optimal temperature is to reduce the mesophyll conductance via effects on biochemical processes.

The biochemical activity associated with CO2 fixation is dependent on electron transport (Farquhar

et. al., 1980). The average daily light intensity is assumed to modify biochemical activity primarily

associated with the supply of electrons to the carboxylation cycle whereas temperature is assumed to

modify biochemical activity primarily associated with electron consumption. Hence, light and

temperature are assumed to independently modify the biochemical activity associated with

carboxylation and thus to have a multiplicative effect on the mesophyll conductance.

Normalised (0-1) stress indices are now introduced for soil water availability (XW) and leaf

evaporation rate (XE) which linearly scale the maximum gas phase conductance (ggmax); and light

(XL) and temperature (XT) normalised indices which linearly scale the maximum mesophyll

conductance (gmmax) when these factors are sub-optimal. At potential maximum assimilation, the

stress indices are equal to 1, and assimilation decreases as the stress factors decrease. Hence, the

combined diffusive and mesophyll CO2 conductance in Eqn. 5 can be expressed as,

c

g E W m L T

g =1

1g X X

+1

g X Xmax max

(6)

Normalising the combined CO2 conductance with the maximum CO2 conductance, assuming (Ca -

Ci) is constant as assimilation varies, gives an expression for the relative gross assimilation rate

(Rg);

gc

c

g

L T E W

R =g

g=

A

A=

1+W1

X X+

W

X Xmax max

(7)

where

W =g

gm

g

max

max

(8)

and hence

g gA = A Rmax (9)

Empirical parameters are used to define the normalising relationships between the water availability

index (XW) and the soil water and salt distribution; the leaf evaporation rate index (XE) and the

transpiration rate; the temperature index (XT) and the average daily temperature; and the light index

(XL) and the daily total radiation, and are described below. Briefly, XW is normalised using

minimum matric and osmotic soil water potential that the plant can transpire against; XE is

normalised using the potential maximum transpiration rate per unit sun-lit leaf area; XL is

normalised using the saturation photosynthetically active radiation flux; and XT is normalised using

a temperature optimum and temperature half optimum.

Because C4 plants tend to have higher maximum mesophyll conductances than C3 plants their

value of W and Amax also tend to be larger (Jones, 1983). The expected value of W would be 0.2

and 0.8 in C3 and C4 plants, respectively (Korner and Bauer,1979).

At the canopy scale carbon assimilation is linearly related to the proportion of radiation intercepted

(Monteith, 1972; Jarvis and Leverenz, 1982; McMurtrie and Wolf, 1983). Hence it is assumed for a

'big leaf' canopy that;

g gl

A = R A (1- ( k* LAI))D

43200max exp − (10)

where Ag is now the gross carbon assimilation rate per unit land area (kg C m-2 soil d-1); Amax is the

optimum assimilation rate (kg C m-2 soil per 12 hr day); Rg is the relative growth rate scaler (0-1); k

is the average daily light extinction coefficient for the canopy; LAI is the leaf area index; and Dl is

day length in seconds. The expression (1-exp(-k LAI)) represents the proportion of light intercepted

by the canopy.

The maximum potential assimilation rate represents that expected for non-stressed conditions, i.e. at

maximum light, and water availability and optimum temperature with complete canopy cover. It

represents gross assimilation less photo-respiration for a 12 hr day and is scaled proportionally for

seasonal changes in day length.

The maximum carbon assimilation per unit leaf area, calculated by the limit of Eqn. 10 divided by

LAI, as LAI approaches zero, is Amax k. This assimilation model is consistent with the premise that

canopy carbon assimilation is determined primarily by the photosynthetic rate of sunlit leaves, i.e.

Rg Amax k, and the sunlit leaf area, i.e. (1-exp(-k LAI))/k.

The average daily canopy conductance to CO2 can be estimated from the assimilation rate:

c

g

a 1 l

g =A R (1 ( k LAI))

C (1 a )D max exp− −

−(11)

where gc is the canopy conductance to CO2 (m s-1); Ca is the atmospheric concentration of CO2

(1.832×10-4 kg C m-3 at standard temperature and pressure), a1 is the ratio of CO2 at the

carboxylation site to the atmospheric concentration (Ci /Ca). This conductance includes effects of

both gaseous stomatal and liquid mesophyll conductances on CO2 exchange. However, only the

gaseous pathway contributes significantly to water vapour exchange. Using the resistors in series

equation and adjusting for the relative diffusion rates of CO2 and water vapour (1.6), gives the

canopy conductance ggw to water vapour as:

gw

W E

a 1 l

g =1.6 (1 / W +1) A X X (1 ( k LAI))

C (1 a )Dmax exp− −

−(12)

Equation (12) is an expression of a 'big leaf' daily conductance for water vapour transfer that is

derived from a similar 'big leaf' carbon assimilation model with explicit expressions for stresses

arising from variation in climatic and soil water conditions. It is used as the surface conductance

within the Penman-Monteith equation to simulate transpiration. The parameters which define the

limits of the conductance model are the maximum carbon assimilation rate of an unstressed

complete canopy (Amax, kg C m-2 d-1), the ratio of maximum mesophyll to maximum stomatal

conductance (W, dimensionless), the LAI, and the light extinction coefficient (k, m2 m-2).

The parameters which need to be set to calculate the environmental stress indices and, so define the

assimilation and transpiration rates under sub-optimal conditions, are summarised as follows;

XT - the temperatures for optimum and half optimum growth (C);

XL - photosynthetically active radiation flux for 'big leaf' light saturation (uE m-2 s-1);

XW - the minimum soil water matric and osmotic potential against which transpiration occurs (m);

XE - the minimum transpiration rate per unit sun-lit leaf area which induces stomatal closure and the

maximum proportion of daylight hours when stomatal response to transpiration occurs.

2.2.1 Light availability (XL).

A normalised index (0-1) of light availability (XL) is calculated as the ratio of the average PAR per

unit leaf area to the light saturation value of a unit leaf, i.e. estimated as:

Lp

psat lX =

Q 4600

Q D(13)

where Qpsat is the PAR (µmole m-2 leaf s-1) which gives maximum carbon assimilation; Qp daily

average PAR intercepted per unit leaf area of canopy; Dl is day length in seconds; assuming 1 kJ is

4600 µmoles of PAR.

2.2.2 Temperature (XT).

A normalised temperature stress factor (XT) which scales to 1 at the optimum growth rate

temperature (Topt) and 0.5 at the half optimum (Th) temperature is estimated empirically using a

symmetrical "bell" function, i.e.

( )( )

( )XT T

T TT

a opt

opt h

=−

−×

exp ln .

2

2 0 5 (14)

where Ta is the average daily temperature in ºC.

2.2.3 Soil water availability (Xw).

The availability of soil water for uptake is estimated from the total soil water potential, i.e. the sum

of the matric (ψ) and osmotic (π) potential of the soil water. The matric potential is calculated

directly from the moisture characteristic function, whilst the osmotic potential is calculated from the

sodium chloride concentration of the soil solution. This assumes the soil solution is chloride

dominated. The total soil water potential of each soil layer is normalised using the lowest soil water

matric potential against which the plant can transpire. A weighting factor adjusts for differential

effects of osmotic and matric potential on water availability. The lowest osmotic and matric

potential against which water can be transpired may differ due to soil hydraulic and root-soil contact

effects. Hence, for the i-th soil layer:

iWi osm i

lmin

X = 1-+ Wψ πψ (15)

where ψ is matric potential of soil water (m); π is osmotic potential of soil water (m); Wosm is an

osmotic potential weighting factor representing the ratio of the lowest matric potential (from dry

non-saline soil) to the lowest osmotic potential (from moist saline soil) against which transpiration

can occur, ψlmin is lowest soil water matric potential the plant can transpire against (m). Note that

XW is a normalised index and ranges from 0-1 only.

The soil water osmotic potential is estimated using:

i NaCl= -2 C RTπ (16)

where CNaCl is the molarity of sodium chloride in the soil water (mole kg-1); R is the universal gas

constant (0.8484 m mole-1 K-1); T is temperature in Kelvin.

The index of water availability to the plant is estimated as a the water uptake weighted average soil

water availability, i.e.

Wi=1nl

r W

i=1nl

r

X =W X

Wi i

i

∑∑

(17)

where Wri is a layer weighting factor; nl is number of soil layers in the potentially active root-zone.

The weight is assumed to be related simply to the relative amount of root carbon in the i-th layer,

i.e. Wri = Cri (kg C m-2).

Alternative approaches for averaging soil water availability could also be used. For example the

weighting factor could be calculated in relation to the relative layer thickness and the expected

relative water uptake distribution when water is non-limiting, i.e.

ir i iW = z U∆ (18)

where -zi is the thickness of the i-th soil layer (m); Ui is a weighting factor determined from the

water uptake distribution with non-limiting water availability. The Ui function accounts for the

understanding that water uptake tends to occur preferentially at shallow depths (Gardner, 1991) and

for many crop plants can be approximated by:

ii

U = 1z

z−

max

(19)

where zmax is the maximum depth of rooting and zi the distance to the mid point of the i-th layer.

Alternatively Ui could be represented as a exponential function (Raats, 1974; Hoffman and Van

Genuchten, 1983).

The value of ψlmin can be estimated from observations of minimum pre-dawn leaf water potential

measurements from water stressed plants. The value of Wosm may be estimated from minimum soil

water osmotic potential that the plant is assumed to be able to transpire against when the matric

potential is non-limiting.

2.2.4 Leaf evaporation rate (XE).

It is assumed that stomata closure at high vapour pressure deficit, sometimes referred to as the 'feed

forward' effect, is a response to the leaf transpiration rate rather than the vapour pressure deficit

directly (Mott and Parkhurst, 1991; Monteith, 1995). This effect usually occurs for only part of the

day, for example as partial stomatal closure near midday when the radiation, temperature and

vapour pressure deficit, and hence the atmospheric demand, are highest and is most pronounced

when soil water is non-limiting. Hence, at the daily scale XE would be expected to range from a

relatively high minimum value (XEmin) rather than from zero. If it is assumed that stomatal closure

to high transpiration rates occurs for a maximum of 25% of the daylight hours then XEmin would be

0.75. The notion that stomata close in response to the transpiration rate can be use to define XE by

setting a minimum or threshold daily transpiration rate per unit sun lit leaf area (Elmin ) below which

stomata are assumed to be insensitive to the transpiration rate, and hence XE=1, and an estimated

maximum daily transpiration rate per unit sun lit leaf area (Elmax) when XE= XEmin . The value of

Elmax can be estimated by setting XE = XEmin then determining the transpiration rate per unit sunlit

leaf area with (for given XW) for climatic conditions which extrapolate to the maximum evaporative

demand i.e. combinations of maximum temperature, vapour pressure deficit and solar radiation

which are expected to close stomata (eg. temperature 45 C, vpd 40 mbar and Q0=40 MJ m-2 d-1).

Assuming XE decreases linearly from 1 to XEmin as El increases from Elmin to Elmax gives:

EEmin

lmin lmaxl

lmin lmax EminX = (

1 X

E E)( E

E + E2

)+1+ X

2

−−

− (20)

where El is the daily transpiration per unit sun lit leaf area (Elmax > El > Elmin) for given XW, net

radiation and temperature, but assuming stomata are insensitive to the transpiration rate (i.e. with

XE=1). Note that if soil water availability reduces Elmax below Elmin then XE=1. The leaf

transpiration rates are expressed per unit sun lit leaf area because this is consistent with the

underlying assumption of the canopy carbon assimilation model.

Grantz and Meinzer (1990) showed that under field conditions instantaneous stomatal closure in

response to increasing vapour pressure deficit tends to be compensated for by stomatal opening in

response to increasing solar radiation so that within a daily cycle stomatal conductance is linearly

related to the ratio of solar radiation to vapour pressure deficit. This ratio represents the

climatological conductance (Monteith, 1965) which Dunin and Greenwood (1986) use to evaluate

the 'feed-forward' effect. Whilst this ratio may be useful to assess stomatal responses within a daily

cycle it is not a suitable index to quantify 'feed forward' effects when estimated from daily climatic

data as it is poorly related with transpiration rates across seasons.

2.3 Carbon allocation, respiration and biomass turnover.

The assimilated carbon is partitioned to leaves, roots and stems on a daily basis. The partitioning

coefficients depend on both genotype and environment. The amount of leaf, root and stem carbon

allocated is reduced by growth and maintenance respiration and mortality rates. The partitioning and

carbon loss assumptions are similar to that used by McMurtrie and Wolf (1983) and Running and

Coughlan (1988). Hence, the daily carbon increment for leaf, stem and root growth -C, when

Ag>CLRL is given by:

∆ L L L g L L L LC = n Y ( A C R )- C M− (21)

∆ (S,R) (S,R) (S,R) g L L (S,R) (S,R) (S,R) (S,R)C = n Y [( A - C R ) C R ] M C− − (22)

Where subscripts L, S and R refer to leaves, stems and roots respectively; C is carbon content of the

biomass, (kg C m-2); nL is the proportion of net canopy assimilation allocated to the canopy growth,

nS and nR are the proportions allocated to stem and root growth, respectively, of the remaining

assimilate dimensionless; Y are growth respiration coefficients which account for conversion of

assimilated carbon to biomass, dimensionless (a common value of 0.65 is assumed, Running and

Coughlan, 1988); R are maintenance respiration coefficients (kg C kg-1 C d-1) and M are mortality

coefficients (kg C kg-1 C d-1). Note that canopy maintenance respiration is subtracted before carbon

is allocated to stems or the roots and maintenance respiration is deducted before assimilate is used

for growth. The respiration coefficients are assumed to approximately double with a 10 ºC rise due

to increased respiration losses, i.e.

(L,S,R) 0(L,S,R)R = R (0.0693T)exp (23)

where R0(L,S,R) are the apparent leaf, stem and root maintenance respiration coefficients (kg C loss

kg-1 C biomass d-1); T is the daily temperature (degrees C).

The respiration of woody stems is proportional to the mass of live cambial cells and hence the

surface area of live stems rather than the total stem mass. For this reason the apparent maintenance

respiration coefficient for woody stems will be much smaller than the actual respiration coefficient

of the active cambial cell mass.

It is assumed that a functional equilibrium exists between the active size of the canopy needed to

supply assimilate and the active size of the root system needed to supply water (and nutrients) and

hence modify the assimilate allocation parameters (nL,nS and nR) as the water availability varies.

This is consistent with observations that water, salinity and nutrient stress tend to increase the

allocation of carbon to the roots relative to the above ground biomass (Cannell,1985). The

proportion of net carbon assimilation allocated for leaf growth is assumed to decrease linearly from

an assigned maximum (nlmax) to an assigned minimum (nlmin) as the water availability decreases, i.e.

L lmin lmax lmin Wn = n +( n n ) X− (24)

The carbon assimilation remaining after allocation to the canopy is allocated between the stem and

root system. The proportion of the remaining assimilation allocated for stem growth is assumed to

be a constant proportion (pls) of that allocated for leaf growth, i.e.

S ls Ln = p n (25)

This recognises that stem and canopy growth are closely linked and also forces the proportion of

assimilate allocated to stem growth to decrease as the water availability decreases. The remaining

carbon is allocated to root growth.

The daily changes in leaf, stem and root carbon may be positive (growing) or negative (senescence

or dying). The rate of carbon gain for each carbon sink depends on the difference between the rates

of carbon gain and loss. As the leaf carbon mass (and hence leaf area) increases, the rate of carbon

gain increases non-linearly whilst the rate of carbon loss increases linearly. The maximum leaf area

attained for a given level of environmental stress, occurs when the rate of leaf carbon gain and loss

are equal.

2.4 Leaf area expansion and canopy growth.

Carbon allocated to leaves is assumed to increase leaf area by an amount determined by the specific

leaf area (Sla m2 kg-1 leaf C), i.e.

LAI = S Cla L (26)

Hence, the canopy leaf area growth rate is given by:

dLAI

dt= S [ A R (1- ( k LAI))D / 43200 R LAI / S ] n Y - M LAIla g l L la L L Lmax exp − − (27)

The direct dependence of the canopy leaf area growth rate on the specific leaf area (Sla) is consistent

with the observation of Lambers and Porter (1992) that species with high specific leaf area also tend

to have higher relative growth rates.

2.5 Root growth and water uptake.

The carbon allocated to the root system (-Cr) is distributed amongst soil layers using the same

weighting function used for the soil water availability index, i.e.

∆ ∆i

i i

i i

r rr W

i=1nl

r W

C = CW X

W X∑(28)

where subscript i refers to the i-th soil layer, -Cr (kg C m-2 d-1) is the daily total root carbon growth

increment; Wri is the layer weighting factor (Eqn. 17); XW is the normalised water availability. The

same soil layer weighting coefficients used to distribute carbon root growth with depth are used to

distribute the daily transpiration, estimated from the Penman-Monteith equation, as root uptake

from soil layers. Hence, root growth, water uptake and the root-zone water availability index are

linked.

If -Cr is negative, i.e. roots are dying, then proportionally more roots are assumed to die in the layers

with the least available soil water. A negligible minimum root carbon is maintained at all depths to

ensure root continuity.

2.6 Transpiration

Transpiration from the canopy is calculated using the 'big leaf' form of the Penman-Monteith

equation (Monteith, 1973) which combines radiation and aerodynamic terms for sensible and latent

heat transfer, i.e.

λρ

γE =

Q + D c ( e - e) / r

+ (1+ r / r )n l p s a

s a

∆∆

(29)

where λE is the water vapour flux density (MJ m-2 d-1); λ is the latent heat of vaporisation of water

(MJ kg-1); Qn is the net total radiation intercepted by the canopy (MJ m-2 d-1); ρ is the density of air

(kg m-3); Cp is the specific heat of air, constant 0.00101 (MJ kg-1 C-1); e is the water vapour pressure

above boundary layer (mbar); es is the saturation water vapour pressure (mbar); γ is the

psychometric constant (mbar C-1); ∆ is the slope of the saturation vapour pressure curve (mbar C-1);

rs is the canopy resistance to water vapour (s m-1) (i.e. 1/ggw from Eqn. 12) ; ra is the aerodynamic or

boundary layer resistance (s m-1); Dl is day length in seconds.

Many of the variables in this equation are temperature (T ºC) dependent, i.e. latent heat of

vaporisation, air density, saturation vapour pressure, psychometric constant and the slope of the

saturation vapour pressure curve. These variables are estimated using the following empirical

relationships (Murray,1967):

λ = 2.501- 0.0024T (30)

se = 6.1078 (17.269T

237.16+T)exp (31)

γ = 0.646+.0006T (32)

ρ = 1.292 -0.00428T (33)

The slope of the saturation vapour pressure curve is estimated from Eqn. (31) as the difference

between es(T+0.5) and es(T-0.5).

2.7 Atmospheric-vegetation coupling to vapour pressure deficit.

The effects of transpiration on the vapour pressure deficit at the canopy surface is accounted for

using the atmospheric decoupling coefficient (Ac) of Jarvis and McNaughton (1986). When an

evaporating surface is strongly coupled to the surrounding atmosphere the boundary layer resistance

becomes small relative to the surface resistance, so that the evaporation is determined mainly by the

surface resistance and the vapour pressure deficit (Ac®0). However, when the boundary layer

resistance is large relative to the surface resistance, then evaporation is determined mainly by

radiation and temperature (Ac®1). The decoupling coefficient scales the vapour pressure deficit

operating at the canopy surface from the atmospheric vapour pressure deficit and potential

evaporation driven by radiation. Hence:

c c eq c aD = D +(1- ) DΩ Ω (34)

where Da is vapour pressure deficit of the atmosphere (mbar); Dc is the operational vapour pressure

deficit of across canopy surface (mbar), and:

eqn s

p

D =Q r

( +1) C

γεε ρ

(35)

cs a

=+1

+1+ r / rΩ

εε

(36)

where γ is the psychometric constant; ε is ∆/γ; rs is the resistance of the evaporating surface.

2.8 Soil surface resistance to evaporation.

The soil resistance is determined by the method of Choudhury and Monteith (1988). Soil

evaporation from soil which is wetter than air dry is assumed to occur with zero surface resistance.

As a drying front develops then soil evaporation is assumed to occur isothermally by water vapour

diffusion from the next soil layer which is wetter than air dry. The soil resistance for this phases of

evaporation is determined by the soil porosity and path length for diffusion, i.e. for ">"0,

( )r

p Dsoilm

=−τ " " 0 (37)

where τ is a tortuosity term, set at 2; " is the distance to the first node which has a water content

greater than the air dry water content; p is the soil porosity (m3 m-3); Dm is the molecular diffusion

coefficient for water vapour, 2.5×10-5 m2 s-1. The depth term "0 represents the depth of soil in which

pressure changes are responsible for mass flow of air and is set at 0.03m. When " is less than "0 the

soil resistance is assumed to be zero.

2.9 Canopy interception of rainfall

Interception of rainfall and subsequent evaporation can be an significant water balance component.

Sharma (1984) showed that evaporation of intercepted rainfall from a wet Eucalyptus canopy was 5

times larger than the potential transpiration during wet winter months in SW Western Australia.

Canopy interception (Rainintc) is assumed to be directly proportional to the leaf area index, i.e.

intc intcRain = f LAI (38)

where fintc is the rainfall interception coefficient (m LAI-1 d-1). The daily rainfall is reduced for

interception by each canopy layer and any surface litter. Also the average canopy radiation is also

reduced by the energy requirement to evaporate all of the intercepted water. Stem flow is not

considered.

2.10 Saturated and unsaturated soil water movement.

Soil water movement is modelled using a numerical solution to Richards’ equation for unsaturated

flow in one dimension with water extraction by roots expressed as a sink (S), i.e.

∂∂

∂∂

∂∂

−

θ ψt

= -z

K - Kz

S (39)

To reduce non-linearity with respect to time and distance the Richard 's equation is expressed using

the Kirchhoff transformation (U, m2 d-1) on the RHS (see for example, Ross and Bristow, 1990), i.e.

∂∂

−∂∂

−∂∂

−

θt

=z

KU

zS (40)

where θ is soil water content (m3 m-3); K is unsaturated hydraulic conductivity (m d-1), and:

U = K( ) d D dψ ψ θ θψ θ

−∞∫ ∫= ( )0

(41)

The boundary conditions used to solve this equation are set daily according to climatic and soil, and

watertable conditions. A flux boundary condition is used at the surface for parts of the day when

there is rainfall or flooding and when the surface soil water potential is greater than an assumed

minimum value (ψmin), where:

minψ ψ ψ= ( + ) / 2lmin smin (42)

This changes to a potential boundary condition when the soil surface has a water potential less than

the ψmin. The values of ψsmin is set as the lowest matric potential on the soil hydraulic properties

table (see below). If a watertable is present then a constant potential boundary condition is

maintained at the depth of the watertable. Otherwise the flux boundary condition is maintained at

the base node.

2.11 Soil hydraulic properties.

WAVES reads soil hydraulic properties from a table generated by an external program. In this way,

the user can choose which relationships between ψ, θ and K they want to use, along with their

derivatives with respect to ψ, and the Kirchhoff transform. Three commonly used soil hydraulic

models are the Campbell model (1985), van Genuchten model (1980), and the Broadridge-White

model (1988).

2.11.1 The Campbell method (C).

Campbell (1985) used a power function to describe the moisture characteristic and models of Childs

and Collis-George (1950) to relate this to the unsaturated hydraulic conductivity, i.e.

For ψ < ψe, θ=θs; K(ψ) = Ks.

For ψ ≥ ψe:

θθ

ψψ

= ( )s

-b

e

(43)

K( ) = K ( )s

2+3/ beψ

ψψ (44)

where θs is saturated water content; ψe is the air entry or bubbling potential; ψ is the matric

potential, is Ks the saturated hydraulic conductivity.

2.11.2 The van Genuchten method (VG).

van Genuchten (1980) presented a continuous inverse power function to describe the moisture

characteristic and combined this with Mualem's (1976) unsaturated hydraulic conductivity model:

Θ = [1+ ( ) ]-mnα ψ (45)

K( )= Ks 1 - ( ) [1+ ( ) ]

[1+ ( ) ]

2n-1 -mn

m/ 2nψ

αψ αψαψ

(46)

where Θ is the relative saturation, i.e.

Θ =-

-r

s r

θ θθ θ

(47)

and θr is the residual water content; α and n are fitting parameters, and m=1-1/n.

2.11.3 The Broadbridge and White method (BW).

Broadbridge and White (1988) derived a moisture characteristic based on physically realistic

functional forms relating water content to diffusivity (D(θ)) and hydraulic conductivity (K(θ)), i.e.

ψ λ λ( )= -(1- )

- C [C - ]

[C -1]-1Θ

ΘΘ

ΘΘ

ln (48)

K( )= Ks (C -1)

C -

2

ΘΘ

Θ(49)

where λ is a flow weighted average soil water potential, termed the macroscopic capillary length,

and C is a parameter related to the time to ponding of rainfall.

The Broadbridge-White model parameter λ generally increases with clay and silt content. It ranges

from several centimetres in coarse sands to several metres in some clays. The C parameter is realted

to soil structure, but also tends to increase as clay content increases. It ranges from 1.01 in

structureless sands to 2 in structured clays.

2.12 Numerical stability of finite difference solution of Richards’ equation.

The numerical methods used to solve Richards’ equation can guarantee numerical convergence and

stability when the Broadbridge-White model of soil hydraulic properties is used (Short et. al.

(1995)). There are two reasons for this. Firstly, the soil water diffusivity remains finite when the soil

is either very wet or very dry. Secondly, the soil water relationships are monotonic in accordance

with Richards (1931). A useful property of the soil model is that the equation and solution can be

scaled to be independent of λ and C. Short et al. (1995) used this feature to establish that numerical

convergence is guaranteed with all soils at all rainfall rates when the distance between solution

nodes was less than approximately λ.

2.13 Solute movement.

The solute in WAVES is assumed to be sodium chloride. Further, we assume that this salt is

conservative, i.e. it is not adsorbed by the soil matrix, is not taken up by plants or removed through

evaporation, and does not affect the soil hydraulic properties. The convective-dispersive equation

for conservative solutes is:

∂∂

∂∂

∂∂

( C)

t= -

z(qC - D

C

z)

θθ (50)

where C is the solute concentration of the soil water (kg m-3); q is the vertical water flux m3 m-2 d-1;

D is the solute dispersion coefficient (m2 d-1).

The solute dispersion coefficient for each layer is estimated using:

i 0 ii

i

yD = D +q

Dθ βθ

(51)

where D0 is the diffusion coefficient of NaCl in water, 0.001 m2 d-1; β is a tortuosity term, set at 0.5,

qi is the water flux, θi is water content, and Dy is the soil dispersivity, set at 0.02 m d-1.

2.14 Flow diagram of model.

The relationships between model components are in Fig. 1. An important feature of WAVES is how

the soil water availability feeds back on canopy growth rate through reducing both the assimilation

and transpiration rates, and to the proportion of carbon allocated for canopy growth. The soil water

availability index (XW) also feeds back on the distribution of root growth and water uptake. The root

growth, soil water and solute movement feed-back on XW.

2.15 Summary of data requirements and parameters.

(a) Site

1 Latitude (+/- N/S degrees)

2 Slope (degrees)

3 Aspect (degrees clockwise from north)

(b) Climate and hydrological data - daily totals or averages

1 Maximum daily temperature (C)

2 Minimum daily temperature (C)

3 Vapour pressure deficit (mbar)

4 Rainfall (m)

5 Duration of rainfall (d)

6 Incoming short-wave radiation (kJ m-2 d-1)

7 Depth of flood (if present)

8 Daily watertable depth (m)

(c) Soil properties - per horizon

1 Saturated hydraulic conductivity (m d-1)

2 Moisture characteristic parameters (S and C for BW model)

3 Saturated water content (kg m3)

4 Residual water content (kg m3)

5 1 minus the albedo of the surface soil (1-Is).

(d) Initial soil condition - per depth node

1 Matric potential (m)

2 Concentration of NaCl in soil water (kg L-1)

(e) Vegetation parameters - for each vegetation layer

1 1 minus the canopy albedo (1-Ic).

2 Rainfall interception coefficient (fint, m LAI-1d-1)

3 Light extinction coefficient (k, LAI-1)

4 Maximum carbon assimilation rate (Amax, kg C m-2 d-1)

5 C02 ratio parameter (a1= Ci/Ca)

6 Minimum soil water matric potential for water uptake (`lmin, m)

7 Ratio of maximum mesophyll to stomatal conductance (W)

8 Stem allocation parameter (pls)

9 Temperature when growth rate is half optimum (C)

10 Temperature when growth rate is optimum (C)

11 Saturation PAR light intensity of sunlit leaves (Qpsat, TE m2 s-1)

12 Maximum rooting depth (zmax, m)

13 Specific leaf area (Sla, m2 (kg C)-1)

14-16 Leaf, stem and root maintenance respiration coefficients (RL, RS, RR, kg kg-1 d-1)

17-19 Leaf, stem and root mortality coefficients (ML, MS, MR, kg kg -1 d-1)

20 Maximum proportion of assimilate allocated to canopy (nlmax)

21 Minimum proportion of assimilate allocated to canopy (nlmin)

22 Osmotic potential weighting factor (Wosm, dimensionless)

23 Aerodynamic resistance (ra, s m-1)

(f) Initial vegetation data

1 Initial leaf carbon (kg m2)

2 Initial stem carbon (kg m2)

3 Initial root carbon per depth node (kg m2)

3 EVALUATION OF MODELLED INTERACTIONS BETWEEN GROWTH,

WATER USE AND CLIMATIC CONDITIONS .

The interactions between leaf area, carbon assimilation, transpiration and water stress predicted by

the model were evaluated in relation to the current understanding of plant water relations. In

WAVES, the climatic data drives both transpiration and assimilation rates which are linked through

the canopy conductance model. A similar approach has been used in other SVAT models (Leuning

et. al. (1991); Running and Gower, 1991; McMurtrie et. al.,1992). This allows the effects of

environmental conditions on leaf area development and stomatal functioning, and hence

assimilation and transpiration, to be represented. This contrasts with other SVAT models which

assume an empirical relation between relative dry matter production and the ratio of transpiration to

potential transpiration (Nimah and Hanks, 1973; Cardon and Letey, 1992).

3.1 Evaluation of interactions between water stress, assimilation, transpiration, water use

efficiency and radiation efficiency for wheat.

The canopy conductance model was used to evaluate the relationships between leaf area, carbon

assimilation, transpiration and water stress using vegetation parameters representative of wheat

(Table 1). The vegetation parameters were estimated from the canopy carbon and water vapour

exchange study of Whitfield and Smith (1989) and Whitfield (1990). The water use efficiency

(WUE) was estimated as the amount of gross carbon assimilation (Ag) per unit of water transpired

per day (g C Kg-1 water d-1). The canopy radiation efficiency was calculated as the amount of carbon

assimilated per unit of total short-wave radiation absorbed per day (g C MJ-1 d-1). The climatic

variables were set to represent clear summer conditions for the wheat belt of SE Australia. The leaf

transpiration rate scaler (XE) was fixed at 1, i.e. no 'feed forward' effect was modelled.

Both assimilation (Fig. 2) and transpiration rates (Fig. 3) increased non-linearly with increases in

water availability and LAI. The canopy conductance to water vapour (Fig. 4) increases non-linearly

with the LAI and is most sensitive to water availability at high LAI. The WUE (Fig. 5) varied across

a range consistent with literature values summarised by Larcher (1980). At low LAI the modelled

water use efficiency increased as soil water availability decreased which is consistent with a wide

range of studies (Sinclair et. al., 1975; Fischer and Turner, 1978; Shalhevet and Hsiao, 1986;

Monteith and Elston, 1993). At high LAI the WUE decreased with increasing in water stress. The

WUE of the unstressed canopy (XW =1) was very sensitive to LAI up to a value of 2. The modelled

relation between radiation efficiency and water stress (Fig. 6) indicates that the radiation efficiency

decreases with decreasing water availability and is independent of LAI.

These modelled responses for wheat are consistent with the field study of Whitfield (1990) who

measured carbon and water vapour exchange of wheat canopies at maximum leaf area development

(LAI 6-8) and which were irrigated weekly or were rainfed. The measured carbon assimilation rates,

transpiration rates and radiation efficiency values of the weekly irrigated plots were 23.5 g C m-2 d-1,

9.7 mm d-1 and 0.82 g C MJ-1 and of the rainfed plots were 14.9 g C m-2 d-1, 4.7 mm d-1 and 0.62 g

C MJ-1, respectively. The measured values for the weekly irrigated plots agree well with modelled

values if the water availability is assumed to be close to 1 and as do those for the rainfed plots if the

water availability is close to 0.2.

3.2 Annual variation in assimilation, transpiration, water use efficiency and radiation

efficiency.

Average monthly temperature, vapour pressure deficit and radiation for Deniliquin NSW (Fig. 7)

were used to demonstrate the effect of seasonal variation in climatic conditions on assimilation and

transpiration rates for a constant LAI of 1 and a range of soil water availability. The vegetation

parameters representing Eucalyptus spp. were used (Table 2). The maximum gross assimilation rate

was set similar to the maximum observed by Denmead et. al., (1993).

The seasonal pattern in assimilation (Fig. 8) and transpiration (Fig. 9) closely follows the seasonal

climatic conditions and is consistent with the general growth cycle of the region. The water use

efficiency for a constant LAI and water availability (Fig. 10) was predicted to be relatively constant

throughout the year with peak values during spring. The modelled WUE values are comparable to

values measured using micro-meterological techniques on Eucalyptus canopies which range from

1.4-2.6 g C /kg H2O (Denmead et. al., 1993)). This seasonal behaviour contrasts to that modelled by

Monteith (1993) who suggested that the WUE would increase as the vapour pressure deficit

decreases. However, Monteith (1993) did not consider the effects of temperature and radiation on

the mesophyll conductance, and hence assimilation.

The form of the relationship between the quantity of incident radiation and the gross canopy

assimilation (Ag/Q0) was also evaluated using the Eucalyptus parameters (Table 1). The annual

form of the Ag/Q0 relationship was constructed using LAI=1 and climate data from (Fig. 7). The

modelled seasonal variation in the Ag/Q0 relationship (Fig. 11) approached a linear form. This is in

general agreement with the review of Ruimy et.al. (1996) which concluded that at a daily scale,

canopy assimilation tends to be linearly related to the quantity of absorbed radiation. For this

evaluation absorbed radiation and incident radiation are linearly related (i.e. Qab=Q0 (1-exp(-k LAI))

or for k=0.4, LAI=1 then Qab=Q0 0.329).

3.3 Long term water availability and equilibrium leaf area.

The model was used to evaluate the effect of long term water availability on the equilibrium leaf

area. The equilibrium leaf area is that for which the assimilate allocated to the canopy for growth

just balances the canopy respiration and leaf mortality rates. Vegetation parameters were set to

represent a Eucalyptus spp (Table 1) whilst average annual temperature (17.5 C) and radiation (17.5

MJ d-1) were used to set the normalised temperature index (XT) and light availability index (XL).

The water availability was varied from 0-1 and the equilibrium LAI estimated when the carbon

available for leaf growth was equal to that required for respiration and leaf replacement (Fig. 12).

The relationship between the equilibrium leaf area and soil water availability was calculated using a

range of leaf partitioning parameters (nL) which were kept constant as the water availability was

decreased. The analysis illustrates the equilibrium leaf area is very sensitive to the leaf partitioning

coefficient (nL). If water stress causes a decrease in the leaf carbon partitioning coefficient then the

equilibrium leaf area will decrease even more rapidly with water availability and approach a linear

relationship.

3.4 Evaluation against lucerne growth and water use lysimeter study.

The aim of this section is to evaluate canopy growth and evapotranspiration modelled using

WAVES against that measured in a lysimeter study of irrigated lucerne grown above a shallow

watertable. The Whitfield studies (Whitfield et al. 1986a; Whitfield et al., 1986b; Wright et al.,

1986) of carbon assimilation and evapotranspiration of irrigated lucerne were also used to guide

parameterisation of the growth model.

3.4.1 The lucerne lysimeter study.

The full experimental details of the lysimeter study are described by Smith et. al. (1996) and are

summarised below. The lucerne was grown in a weighing lysimeter (1.2×1.45 m, 1.5m deep) for 3

years (1990-1993). A non-saline (EC 0.1 dS/m) watertable was maintained at 0.6 m until March

1991 when it was dropped to 1 m. The watertable was raised to 0.6 m again in October 1991 then

dropped to 1 m in January 1992. On the 4 March 1992 a saline (EC=16 dS/m) watertable was

introduced and maintained at a depth of 1 m until the end of the 1992/93 season. The lysimeter was

sprinkler irrigated when the soil water deficit reached 80 mm. The soil in the lysimeter was

classified as a Hanwood loam and had sandy loam (60% sand, 10 % silt and 30 % clay) to 0.25 m

and a light brown clay to (35% sand, 5% silt, 50% clay and 10% calcium carbonate) from 0.25 to

1.5 m.

3.4.2 Model calibration.

WAVES requires both soil and vegetation parameters to be set. The soil parameters describe the

water holding capacity, moisture characteristic and saturated hydraulic conductivity of each soil

layer. The vegetation parameters include those of the conductance model describe above as well as

allocation, respiration and mortality coefficients.

(a) Soil hydraulic parameters.

The soil hydraulic parameters used for the simulation are shown in Table 2. The saturated field

water content was set from soil moisture monitoring observations made with a neutron moisture

meter. This data indicated a relatively large gradient in saturated water content with depth. Four

layers were needed to accommodate these gradients. The moisture characteristic parameters of the

Broadbridge and White (1988) model (C, λ) were set according to the texture profile description

and the observed saturated water content profile. The saturated hydraulic conductivity was set to

accommodate observed infiltration rates and upflow rates.

(b) Vegetation parameters.

The Whitfield studies (Whitfield et.al. 1986a; Whitfield et. al., 1986b; Wright et. al. ,1986) of

carbon assimilation and evapotranspiration of irrigated lucerne were used to guide parameterisation

of the conductance model (Table 3). The soil water availability was normalised assuming maximum

salinity for water uptake was 35 dS/m (or approximately -140 m of osmotic potential) based on the

study of Bernstein and Francois (1973). The carbon allocation parameters were calibrated i.e. set by

running the model and comparing modelled leaf area index with that expected from the field study.

No parameters were adjusted to fit the measured and modelled evapotranspiration rates. The model

was run without any leaf mortality until the LAI exceeded 3, approximately the time to flowering.

No 'feed forward' effect was assumed.

3.4.3 WAVES simulation results for lucerne.

There was excellent agreement between measured and modelled evapotranspiration rates in

1990/91, and 1992/3, whilst that for 1991/92 was slightly under predicted (Table 4). The measured

and modelled daily evapotranspiration and LAI for the 1991/92 irrigation season show similar

temporal trends and generally agreed well (Figs. 13(a) and (b). The initial rate of increase in LAI

was similar to that modelled. However, near the end of the cutting cycle the modelled rates were

slightly greater than those measured. This is likely to be associated with the effects of flowering on

the assimilation rate and allocation pattern which are not accounted for in the model assumptions.

The modelled evapotranspiration rates were slightly lower than those measured, possibly due to

advective effects not considered by the model. It is evident that both the climatic conditions and

leaf area are important in determining the evapotranspiration rate. The modelled daily variation in

upflow from the water table was in reasonable agreement with that measured (Fig. 14 ). This result

was obtained without direct calibration. The upflow was closely related to the evapotranspiration.

The general agreement between observations and several modelled processes gives reasonable

confidence that the basic assumptions adopted within the WAVES model give a adequate prediction

of growth and water use under shallow watertable conditions.

3.5 Sensitivity analysis of canopy growth to model parameters.

A sensitivity analysis was conducted to highlight the effect of parameter uncertainty on the

simulated daily change in canopy LAI and the equilibrium LAI for the range of soil water

availability. The change in LAI per unit LAI (- LAI/LAI) for a fully sunlit leaf (i.e. LAI*=1 (see

below) and XL=1) was calculated for the water availability index varying from 0.1 to 1 (in 0.05

increments) whilst vegetation parameters (Table 5) were either increased 10% or decreased 10%

from values considered representative of Eucalyptus largiflorens. The parameters considered were

evaluated using:

∆LAI

LAI= (

k A R S

LAIR )Y (( n n ) X + n ) M

g la

* L L lmax lmin w lmin Lmax − − − (52)

where LAI* is the LAI per unit of sunlit LAI (LAI*³1; LAI* approaches 1 as the LAI approaches low

values equivalent to a single leaf), i.e.

*LAI =LAI k

1 ( k LAI)− −exp(53)

The change in LAI* at equilibrium (LAI*eq i.e. for - LAI=0) was also calculated for the same range

of XW and parameter adjustment. The average squared deviation of both ∆LAI/LAI and LAI *eq was

calculated between predicted values using the representative parameter (yr) and its adjusted value

(ya, i.e. y-10% or y+10%) across the range of XW, i.e.

DEV =( y y )

ni=1

n

a r2∑ −

(54)

where n is the number of XW.

The results (Table 5) show that the maximum canopy assimilation rate, the specific leaf area and

light extinction coefficient are the most influential parameters and are also equally influential. This

is also obvious from inspection of Eqn. 52. Hence they may be treated as a lumped parameter. The

growth respiration coefficient also has a similar influence and could also be lumped with the above

parameters. Hence only one of these parameters can be calibrated. The others should be set close to

expected or measured values. Representing all the parameters explicitly in the model is desirable as

this will result in a narrower calibration range for the most uncertain parameter. The next most

influential parameters are the day length, the maximum proportion of assimilate allocated for

canopy growth and the leaf mortality rate. The latter has a larger influence on the LAI*eq than the

daily growth rate and hence would be better calibrated using a long time series. The other

parameters have relatively small effects.

4 DISCUSSION

The normalised CO2 conductance equation has similar form as the growth rate model proposed by

Wu et. al. (1994), termed integrated rate methodology (IRM). The ratio of the maximum mesophyll

to gas phase conductance (W) of the canopy conductance model is analogous to the weighting

parameter of water relative to light in the growth rate model of the IRM equation. Here the equation

is used to combine conductances whilst Wu et. al. (1994) used it to combine single function growth

rates. Hence, the value of W and the IRM weighting coefficients would be expected to have

different values.

The assimilation model predicts a non-linear relationship between the normalised carbon

assimilation rate and soil water availability or leaf conductance to water vapour which is consistent

with observed relationships. This is illustrated (Fig. 15) using data from West et. al. (1986, Fig. 2)

measured on cow pea at a range of salinity stress. After normalising the assimilation rate and leaf

conductance to water vapour against their maximum observed values the relationship falls close to a

line for W=0.2 for optimal light, temperature and non-limiting vapour pressure deficit (i.e. XL =1;

XT =1;XE =1). Note that under sub-optimal light or temperature there is relatively little effect of low

soil water availability (or leaf water vapour conductance) on the assimilation rate.

The term (1+1/W )/(1-a1) of the daily canopy conductance model in Eqn. 12, which relates the water

vapour conductance to the maximum assimilation rate of a non stressed leaf, can be related to the

slope term of the instantaneous stomatal conductance models presented by Ball et. al. (1987) and

Leuning (1995). Under non-limiting environmental conditions and assuming that a1 is 0.5, the above

term becomes 15 and 5.6 for C3 ( i.e. W=0.2) and C4 (W=0.8) species, respectively. Whilst these

values are of similar order to those reported by Ball et. al. (1987) and Leuning (1995), a direct

comparison is not appropriate because the 'feed forward' effect to vapour pressure deficit in this

carbon assimilation conductance model is represented as being dependent on the leaf transpiration

rate rather as an effect of vapour pressure deficit and average daily assimilation is considered rather

than instantaneous values. It should be noted that at a daily scale the 'feed forward' response has a

second order effect on carbon and water vapour exchange in most field environments, particularly if

soil water is limiting.

The model is designed to predict changes in leaf area and transpiration in relation to variation in

climatic conditions and soil water availability with a daily time step. Hence the vegetation

parameters which show diurnal variation, eg assimilation and stomatal conductance, should be

understood as representing average daily values at the canopy scale. A central feature of the

modelling approach is to describe both the transfer of carbon and water vapour using a common

canopy conductance model.

The assumption that leaf fall is a proportion of the total leaf mass is equivalent to assigning a leaf

half life of 0.693/Ml. In some species leaf litter rates may increase with both leaf area and with

seasonal variation in the canopy growth rate. Catastrophic leaf drop events associated with acute

water stress, frost, herbivory or waterlogging may also occur and are not represented in the model.

Indexes describing these processes may be required for some applications.

An ecophysiological approach has been taken in constructing the model in that it explicitly

considers the surface energy balance, daily stresses on stomatal functioning, carbon allocation,

respiration and mortality rates. The stress indices for water, light and temperature are scaled

empirically and normalised to ensure the modelled responses are bounded within known limits. The

water and salt stress mechanisms such as root hormonal signals on stomatal activity or leaf osmotic

adjustment are not explicitly represented. The model simply uses lumped stress parameters within

general response functions describing stomatal conductance and carbon assimilation. The

physiological aspects of the model may be classified as "top-down" or as lumped parameter models

(Jarvis, 1993). Hence, the model behaviour with a particular parameterisation needs to be compared

with known field behaviour under known conditions to check that the parameterisation provides an

acceptable description of the major water and carbon transfer processes. Once appropriately

calibrated, the model is better suited to evaluating the sensitivity of vegetation growth to a change in

hydrological conditions rather than as a solely predictive tool. Nor is the model a tool to increase

understanding of physiological mechanisms, but rather to provide an understanding of

ecophysiological interactions of vegetation with climate and soil conditions.

When the model is being calibrated, the primary emphasis should be given to matching observed

leaf areas and transpiration rates, across a known range of water availability, with modelled values.

The model evaluation showed that, for given climatic conditions, transpiration rates are most

sensitive to the leaf area only when the LAI is relatively low. For a given leaf area the canopy

growth is sensitive to the assimilation rate and the leaf partitioning coefficient, whilst the canopy

conductance, and hence transpiration rate, is sensitive only to the assimilation rate.

The calibration of partitioning parameters which affect stem and root growth are secondary and may

not even affect the modelled water use. The pattern of root water uptake does not depend on the

absolute mass of root carbon present in a particular layer but on the relative distribution of both root

carbon and water availability. This assumption, and the strong coupling between root and canopy

growth, reduces the sensitivity of the modelled water uptake distribution to the absolute root mass.

Because of sampling difficulties, it is often impossible to quantitatively verify modelled root

growth. However, root observation chambers and natural isotope studies can provide semi-

quantitative data on patterns of growth and water extraction, and hence an approach to evaluate the

root growth assumptions.

The modelling approach means that a relatively large number of vegetation parameters must be set

to run a simulation. Some parameters which are expressed explicitly within the model may be

considered constants and set at values representative of ecotypes and only adjusted if specific

information is available. Temperature and light saturation values were estimated for a range of

species types from Versteeg and Keulen (1986) and Larcher (1980). Respiration coefficients (R0)

for crop plants vary from 0.0036-0.0095 kg C kg-1 C d-1 and are approximately 0.00084 kg C kg-1 C

d-1 for evergreen trees (estimated from Larcher, 1980).

Other parameters must be set from field observations and measurements made on the specific

vegetation type. These include specific leaf area, light extinction coefficient, minimum soil water

potential, and leaf mortality coefficients.

A key group of parameters, to which the model is most sensitive, may to be set by calibrating their

value using inverse modelling i.e. adjusting their value within an acceptable parameter range to fit

observed field behaviour of canopy growth and transpiration rates . These parameters include the

maximum carbon assimilation rate and the leaf partitioning coefficients. The maximum carbon

assimilation rates, summarised for a range of species ecotypes in Larcher (1980), tend to be higher

in grasses and crop plants than evergreen trees and dry sclerophyll vegetation. Versteeg and Keulen

(1986) also suggest maximum leaf assimilation rates (Table 7) which may be used to estimate

starting values for maximum full canopy assimilation rates for calibration.

5 CONCLUSIONS

The model attempts to represent the first order effects of daily soil water availability, light

availability and temperature on transfers of carbon dioxide and water vapour between the canopy

and the atmosphere, and on carbon allocation processes within the plant. It is concluded that the

modelled interactions between the growth and water use are consistent with current understanding

of plant response to soil water stress and seasonal climatic conditions. The modelled carbon

assimilation and transpiration rates, water use efficiency and radiation efficiency are comparable

with measured values.

The model behaviour is consistent with the notion that canopies both reduce their leaf area in water

limited environments and increases their leaf area in well watered environments so as to maximise

the carbon assimilated per unit of water transpired. The good agreement between observations and

several modelled processes for different vegetation types, and the modelled consistency with

ecological theory, gives reasonable confidence that the assumptions of the 'big leaf' conductance

models are soundly based for evaluating interactions between vegetation and hydrological

processes.

Table 1 Climatic conditions and vegetation parameters used to evaluate model interactions.

(i) Climatic variables

average temperature 25 0C

total incoming radiation 30000 kJ m-2 d-1

vapour pressure deficit 20 mbar

(ii) Vegetation parameters Wheat Eucalyptus

canopy albedo (Ic) 0.1 0.1

specific leaf area (Sla, m2 kg-1 leaf C) 14 12

light extinction coefficient (k, m2 soil m-2 leaf) 0.45 0.4

maximum carbon assimilation rate (Amax, kg C m-2 d-1) 0.027 0.015

optimum growth temperature (0C) 25 25

temperature at half maximum growth (0C) 10 10

ratio of maximum mesophyll

to stomatal conductance (W) 0.2 0.2

CO2 ratio parameter (a1=Ci/Ca) 0.6 0.6

saturation PAR (Qpsat, TE m-2 s-1) 1200 1800

aerodynamic resistance (ra, s m-1) 50 20

Table 2 Soil hydraulic parameters (Broadbridge and White, 1988) for Hanwood loam in

lysimeter.

Depth (m) Ks (m/d) θs θr C λ (m)

0-0.1 0.07 0.30 0.12 1.01 0.2

0.1-0.3 0.05 0.35 0.20 1.05 0.3

0.3-0.6 0.02 0.45 0.20 1.05 0.4

0.6-1.5 0.02 0.38 0.15 1.05 0.3

Table 3 Vegetation parameters used in lucerne simulation. (S) is set as a constant

representative value; (W) based on field studies of Whitfield, (M) set from

observation or measurement by Smith et. al. (1996) , © manually calibrated, (E)

estimated from Dirksen (1985), (B) estimated from Bernstein and Francois (1973).

1 1 minus the canopy albedo (1-Ic). 0.1(S)

2 Rainfall interception coefficient (fint, m LAI-1d-1) 0.001(S)

3 Light extinction coefficient (k, LAI-1) 0.59 (M)

4 Maximum carbon assimilation rate (Amax, kg C m-2 d-1) 0.024 (W)

5 C02 ratio parameter (a1= Ci/Ca) 0.6 (S)

6 Minimum soil water matric potential for water uptake (`lmin, m) -150 (E)

7 Ratio of maximum mesophyll to stomatal conductance (W) 0.2 (S)

8 Stem allocation parameter (pls) 0.7 (C)

9 Temperature when growth rate is half optimum (deg C) 25 (S)

10 Temperature when growth rate is optimum (deg C) 10 (S)

11 Saturation PAR light intensity of sunlit leaves (Qpsat, TE m2 s-1) 1200 (S)

12 Maximum rooting depth (zmax, m) 1.0 (M)

13 Specific leaf area (Sla, m2 (kg C)-1) 54 (W)

14 Leaf maintenance respiration coefficients (R0L, kg kg-1 d-1) 0.002 (S)

15 Stem maintenance respiration coefficients (R0S,, kg kg-1 d-1) 0.002 (S)

16 Root maintenance respiration coefficients (R0R, kg kg-1 d-1) 0.002 (S)

17 Leaf mortality coefficients (ML kg kg -1 d-1) 0.022 (W)

18 Stem mortality coefficients (MS, kg kg -1 d-1) -

19 Root mortality coefficients (MR, kg kg -1 d-1) 0.03 (S)

20 Maximum proportion of assimilate allocated to canopy (nlmax) 0.35 (C)

21 Minimum proportion of assimilate allocated to canopy (nlmin) 0.2 (S)

22 Osmotic potential weighting factor (Wosm, dimensionless) 1 (B)

23 Aerodynamic resistance (ra, s m-1) 30 (S)

Table 4 Measured and modelled seasonal evapotranspiration (ET) and upflow from a shallow

water table for lucerne lysimeter study.

90/91

Measured

90/91

Modelled

91/92

Measured

91/92

Modelled

92/93

Measured

92/93

Modelled

ET mm 1483 1518 1535 1292 1012 1011

Upflow mm 808 690 748 797 251 327

Table 5 Mean deviation of the canopy growth rate (∆LAI/LAI) and the LAI*eq when

parameters are adjusted -10% or +10% from their representative values (yr) for

Eucalyptus largiflorens and for soil water availability (XW) varying from 0.1 to 1.

Parameter (yr)

DEV

∆LAI/LAI

(-10%)(*10-7)

DEV

∆LAI/LAI

(+10%)(*10-7)

DEV LAI *eq

(-10%) (*10-2)

DEV LAI *eq

(+10%)(*10-2)

Amax (0.01) 2.24 2.24 2.12 2.12

Sla (12) 2.24 2.24 2.12 2.12

k (0.4) 2.24 2.24 2.12 2.12

Y L(0.65) 2.09 2.09 2.04 2.00

nlmax (0.3) 1.11 1.11 0.986 0.961

nlmin (0.2) 0.26 0.26 0.246 0.243

ML (0.003) 0.90 0.90 2.20 1.52

Dl (43200) 1.58 1.11 1.38 0.98

W (0.2) 0.0184 0.0157 0.017 0.015

Top (25) 0.374 0.365 0.354 0.345

Th (10) 0.013 0.019 0.012 0.018

R0L (0.001) 0.0056 0.0056 0.0125 0.0122

Table 6 Suggested temperature optimum (Top ,ºC), half optimum temperature (Th ,ºC),

maximum leaf assimilation rate (Almax, kg C m-2 leaf 12hr-1), and light saturation

PAR (Qpsat , µmole m-2 leaf s-1 ). (Estimated from Versteeg and van Keulen, 1986;

and Larcher, 1980).

Plant type TTop Th Almax Qpsat

C3 from temperate

climates

C3 from warm climates

C4 from warm climates

C4 adapted to lower

temperature

17

27

30

25

7

15

17

14

0.013

0.016

0.029

0.029

1200

1800

1800

1800

Table 7 List of symbols used in Section 3.

Ag carbon assimilation rate per unit land area (kg C m-2 soil d-1)

Amax maximum potential assimilation rate (kg C m-2 soil per 12 hr day)

Ca atmospheric concentration of carbon dioxide (set at 1.832×10-4 kg C m-3 at standard

temperature and pressure)

Ci CO2 concentration internal to the site of carboxylation

CL carbon content of the leaf mass (kg C m-2)

CR carbon content of the root mass (kg C m-2)

CS carbon content of the stem mass (kg C m-2)

CNaCl molarity of sodium chloride in the soil water (mole kg-1)

Cp specific heat of air, constant 0.00101 (MJ kg-1 C-1)

Dl day length in seconds

LAI leaf area index of canopy (m-2 leaf m-2 soil)

ML.S,R mortality coefficients for leaves, stems and roots, respectively.

R universal gas constant (0.8484 m mole-1 K-1)

Rg normalised carbon assimilation rate

Qni total net radiant flux intercepted used in the Penman-Monteith equation

Ql downward total radiant flux density below the canopy (kJ m-2 d-1)

Qnl net long wave radiation above the canopy (MJ m-2 d-1)

Qp daily average PAR absorbed by the sunlit leaf area of the canopy (kJ m-2 leaf d-1)

Qpsat Photosynthetically active radiation (µmole m-2 leaf s-1) which gives maximum carbon

assimilation

Qu downward radiant flux density at upper surface of the canopy (kJ m-2 d-1)

R0(L,S,R) apparent leaf, stem and root maintenance respiration coefficients (kg C loss kg-1 C biomass

d-1)

RL.S.R are maintenance respiration coefficients for leaves, stems and roots, respectively.(kg C kg-1

C d-1)

Sla specific leaf area ( m2 kg-1 leaf C)

Ta average daily temperature (C)

Th temperature at half the maximum growth rate (C)

Top optimum growth rate temperature (C)

U weighting function for root water uptake under maximum water availability

W ratio of maximum mesophyll conductance to maximum stomatal conductance

Wosm soil osmotic potential weighting factor

Wri weighting factor for soil water availability of ith layer

WUE water use efficiency (g C assimilated kg-1 H20 transpired)

XL normalised light availability (0-1)

XT normalised temperature modifier for light availability (0-1)

XS normalised salt stress index of potential root-zone

XW normalised availability of soil water in the potential root-zone (0-1)

YL,S,R growth respiration coefficients for leaf, stem and roots ( 0.65 is assumed), respectively.

e water vapour pressure above canopy boundary layer (mbar)

es saturation water vapour pressure (mbar)

gc combined conductance to CO2 exchange (m s-1)

ggw canopy conductance to water vapour (m s-1)

gg gas phase conductance between the leaf surface and the surface of mesophyll cells within

the leaf (m s-1)

gm liquid phase conductance for CO2 movement through the mesophyll cell to the

carboxylation site (m s-1)

k daily average light extinction coefficient (m-2 soil m-2 leaf)

nL proportion of net canopy assimilation allocated to the leaves

nS,R proportion of the assimilate remaining after canopy allocation, which is allocated to stems

and roots, respectively.

nlmax maximum proportion of net canopy assimilation allocated to leaves when XW= 1

nlmin minimum proportion of net canopy assimilation allocated to leaves when XW = 0

pls weighting coefficient for stem allocation

ra aerodynamic or boundary layer resistance (s m-1)

rg gas phase resistance between the leaf surface and the surface of mesophyll cells within the

leaf (s m-1)

rm liquid phase resistance for CO2 movement through the mesophyll cell to the carboxylation

site (s m-1)

rs canopy resistance to water vapour (1/ggw) (s m-1)

zmax the maximum depth of rooting

α albedo coefficient of canopy.

ρ density of air (kg m-3)

λ latent heat of vaporisation of water (MJ kg-1)

ψ matric potential of soil water (m)

ψlmin lowest soil water matric potential the plant can transpire against (m)

π osmotic potential of soil water (m)

πt threshold osmotic water potential for toxicity effects on leaf mortality

λE water vapour flux density (MJ m-2 d-1)

γ psychometric constant (mbar C-1)

∆ slope of the saturation vapour pressure curve (mbar C-1)

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Figure 1 Flow diagram showing feed back relationships operating within model. XL, XT andXW are normalised light, temperature and water stress factors; Cr is root carbon;subscript I refers to a soil layer; LAI is leaf area index; k is the light extinctioncoefficient; WT is watertable depth if present.

Modelling Growth and Transpiration in WAVES

Figure 2 Simulated carbon assimilation (Ag) of wheat for varying soil water availability andleaf area index (LAI).

Figure 3 Simulated transpiration of wheat for varying soil water availability (XW) and leafarea index (LAI).

Figure 4 Simulated canopy conductance of wheat for varying soil water availability (XW)and leaf area index (LAI).

Figure 5 Simulated water use efficiency (g C assimilated per kg of water transpired) ofwheat for varying soil water availability (XW) and leaf area index (LAI).

Figure 6 Simulated radiation efficiency of wheat with varying soil water availability (XW).

Figure 7 Monthly variation in average daily maximum temperature, minimum temperature,vapour pressure deficit and solar radiation for Deniliquin, NSW Australia.

Figure 8 Simulated seasonal variation in carbon assimilation of Eucalyptus spp. atDeniliquin at a range of soil water availability and LAI of 1.

Figure 9 Simulated seasonal variation in transpiration rates of Eucalyptus spp. forDeniliquin at a range of soil water availability and LAI of 1.

Figure 10 Simulated seasonal variation in water use efficiency of Eucalyptus spp. atDeniliquin for a range of soil water availability and LAI of 1.

Figure 11 Modelled annual form of the Ag/Q0 relationship for Eucalyptus canopy at LAI=1.

Figure 12 Simulated equilibrium leaf area of Eucalyptus spp. with varying soil wateravailability XW and leaf carbon allocation coefficient (nL).

Figure 13 Simulated and measured evapotranspiration (a) and leaf area index (b) for lucerne.

Figure 14 Simulated and measured upflow from the watertable under lucerne.

Figure 15 Non-linear relationship between normalised assimilation rate and normalised soilwater availability (or normalised leaf conductance to water vapour). Points aremeasured values from West et al. (1986) for cowpeas.

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