Appendix
Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Citation Index Appendix

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Appendix

Table A: The model equations of leaf CO2 assimilation rates and stomatal response. Equations are derived from Long (1991)a, Evans and Farquhar (1991)b, Sharkey (1985)c and Harley et al. (1992)d. Definitions of the symbols used are listed in Appendix II.  

A = (1 - G * / Ci) min{Wc, WJ, Wp} - Rd

(A.1)a

G * = (0.5Vomax · Kc · Oi) / (Vcmax · Ko )

(A.2)a

Oi = 210 [(0.047 - 0.0013087 T + 2.5603·10-5 T2 - 2.1441·10-7 T3 ) / 2.6934·10-2] At 25oC, Oi = Oa

(A.3)a

Ci = 0.7Ca [(1.674 - 0.061294T + 0.0011688 T2 - 8.8741·10-6 T3 ) / 0.73547] At 25oC, Ci= 0.7Ca

(A.4)a

KT = exp[E (Tk - 298) / (298 Tk ·R)]·(Tk / 298)0.5

(A.5)a

Wc = (Vcmax · Ci ) / [Ci + Kc ( 1 + Oi / Ko)]

(A.6)a

WJ = (J·Ci) / (4.5Ci + 10.5G *)

(A.7)a

J = {I2 + Jmax - [(I2 + Jmax)2 - 4q c·I2·Jmax]0.5} / 2q

(A.8)b

I2 = Io·(1 - f )·(1 - r) / 2

(A.9)b

Wp = 3TPU · (1 - G * / Ci )

(A.10)c

gs = g(0) + g(1)(A · RH / Ca)

(A.11)d

Table B: Canopy macroclimate and microclimate model equations derived from Long (1991) and Humphries et al. (1996).

DJ=365 hr = 24

Actot = ò ò Ac·dt

DJ=1 hr = 0

(B.1)

Ac = (Acsun · Isun ) + (Acshade · Ishade)

(where A is calculated as shown in Table A, and I is calculated as follows:)

(B.2)

Isun = Idir · (cost /cosq ) + Ishade

(B.3)

Idir = Is·a ((P/Po) / (cosq ))

(B.4)

cosq = sin(W )·sin(d ) + cos(W )·cos(d )·cos(15(t - tsn))

(B.5)

d = -23.5 cos (360 (DJ + 10) / 365)

(B.6)

Ishade = Idiff · e(-0.5F^0.7) + Iscat

(B.7)

Idiff =0.5 Is (1 - a ((P/Po) / (cosq ))) . cosq

(B.8)

Iscat = 0.07 Idir · (1.1 - 0.1l) e(-cosq )

(B.9)

lsun = 1 - e(-k·f/cos q ) / k

(B.10)

k = ((c 2 + tan2q )0.5cosq )/( c + 1.744)·(c + 1.183)-0.733

(B.11)

lshade = l - lsun

(B.12)

DJ=365 hr = 24

Etot = ò ò Ec ·dt

DJ=1 hr = 0

(B.13)

Ec = (Esun · lsun ) + (Eshade · lshade)

(B.14)

El = (s · F N + l · g · ga · D r va) / ( l · [s + g · (1 + ga / gc])

(B.15)

F N = Ja - Rlc

(B.16)

Ja = 2 Iabs ((1 - r - t ) / (1 - t )) · l

(B.17)

Rlc = ((4 · 5.67 · 10-8) (273 · T)3 · D T) · l

(B.18)

T = Tmean + Tran · Texc

(B.19)

Tmean = TYrmean + TYr · sin(2p (DJ - Dstart)/365)

(B.20)

Tran = TD + (TDmax - TD) · sin (2p · (DJ - Dstart)/365)

(B.21)

Texc = sin (2p · (hr - 10) / 24)

(B.22)

D T = Tcan-Tair =(F N((1/ga)+(1/gc))-l ·D r va) / (l ·[s + g .(1 + ga / gc)])

(B.23)

g = r · cp / l

(B.24)

ga = ((u*2 / u) · Lb) / ((u*2 / u) + Lb)

(B.25)

u*2 = u · k / [log (hms - d · hcan) / (hcan · z0)]

(B.26)

u = (u* / k ) / log (h)

(B.27)

Lb = (2.126 ·10-5 + 1.48 ·10-7 · Tair) / 0.004 Ö (Lw / u)

(B.28)

D r va = r 'v (1 - (RH / 100))

(B.29)

 Table C: (Table 2.1) Model equations to calculate leaf photorespiration and isoprene emission rates. Equation 2.10 is adapted from Thornley and Johnson (1990). Definitions of the symbols used are listed in Appendix II.

Fiso = (s s · Min {Wisoco, Wisop, Visomax}·103 ) / 5

(2.1)

Wisoco = h · FPYR

(2.2)

h = Exp[(0.1368 T) - 8.335)]

(2.3)

FPYR = (2Vc + 3Vpr) - Rd

(2.4)

Vc = Min {Wc, WJ, Wp}

(2.5)

Wc = (Vcmax · Ci) / [Ci + Kc · (1 + Oi / Ko)]

(2.6) (A.6)

Ci = 0.7Ca·[(1.674 - 0.061294T + 0.0011688T2 - 8.8741·10-6T3)/ 0.73547] At 25oC, Ci = 0.7Ca

(2.7) (A.4)

Oi = 210[(0.047 - 0.0013087T + 2.5603·10-5T2 - 2.1441·10-7T3 )/ 2.6934·10-2] At 25oC, Oi = Oa

(2.8) (A.3)

KT = exp[E (Tk - 298) / (298 Tk ·R)]·(Tk / 298)0.5

(2.9) (A.5)

WJ = (J·Ci) / (4.5Ci + 10.5G *)

(2.10) (A.7)

J = [I2 + Jmax - ((I2 + Jmax)2 - 4q c ·I2 · Jmax)0.5] / (2 · q c)

(2.11) (A.8)

I2 = I · (1 - r) · (1 - t ) / 2

(2.12) (A.9)

G * = (0.5Vomax ·Kc·Oi) / (Vcmax·Ko )

(2.13) (A.2)

Wp =3TPU / [(1 - G *) / Ci]

(2.14) (A.10)

Vpr = (G * / Ci) · Min {Wc, WJ, Wop}

(2.15)

Wop = (3·TPU) / (G * / Ci)

(2.16)

Wisop = h ·[(Vc + 1.5Vpr) - Rd ] · [(Oi + Vc) / (Ci + Vpr+ Rd)]

(2.17)

Visomax = [niso · exp (Eiso / RT)] / [1 + exp(D S / R - D H / RT )]

(2.18)

Table D: (Table 3.1) Equations used to scale up the leaf isoprene emission model (Table 2.1, Table D) to the canopy level.

DJ=365 hr = 24

F'isotot = ò ò F'isoc·dt

DJ=1 hr = 0

(3.1)

F'isoc = S (F'isocsun · Isun ) + (F'isocshade · Ishade)

(where I is calculated as in Table B, Appendix I)

(3.2)

F'iso = Fiso · v

(where Fiso is calculated as shown in Table 2.1, p.42 and Table C, in Appendix II)

(3.3)

v = (0.5 sin (2p ((DJ-DJsv)/365)))) + 0.5

(3.4)

Table E: (Table 4.1) Model equations to simulate the effects of acute ozone exposure on rates of photosynthesis.

t

F'O3eff = ò ( [O3] · gz ) - FO3(0) . dt

0

(4.2)

gz = 1.62 gs / 1.67

(4.3)

gs = g(0) + g(1) · (A · RH / Ca)

(4.5) (A.11)

D Vcmax = Kz · F'O3eff

(4.7)

[O3] = [O3]Pk - [O3]B · sin (2p · (Hr - HrPk) / 16) · 12) / 24) + [O3]B

(4.8)

Table F: (Table 5.1) Equations of the model to simulate the effects of chronic ozone exposure on wheat photosynthesis and productivity.

t

F'O3tot = ò ( [O3] · gz ) . dt

0

(5.1)

[O3] = [O3]max sin (p (h-8) / 16)

(5.2)

gz = gs / 1.67

(5.3)

D Vcmax =Kz · F'O3eff

(5.4)

t

F'O3eff = ò ( [O3] · gz ) - FO3(0) . dt

0

(5.5)

 

[O3] = [O3]mean + O3]ran · [O3]exc

(5.6)

[O3]mean = [O3]avYr + [O3]ranYr · sin (2p · (DJ - DJO3start)/365)

(5.7)

[O3]ran = [O3]ranD + ([O3]ranDmax - [O3]ranDav · sin (2p · (DJ - DJO3start)/365)

(5.8)

[O3]exc = sin (2p · (Hr - HrO3peak -6 ) / 24)

(5.9)

t

lcan = [ ò ( Ta ) - Tb · dt ] / 12

0

(5.10)

Y = 0.7 · WT

(5.11)

t

WT = ò ((0.65 · A) - RG) - RM) · dt

0

(5.12)

RG = 0.65 · a · A

(5.13)

RM = b · WT · 2(T/10)

(5.14)

APPENDIX II

Definition of symbols

Symbol definitions are cited by Long (1991)a, Evans and Farquhar (1991)b, Harley et al. (1992)c, Thornley and Johnson (1990)d, Humphries et al. (1996)e and Porter (1984)f. Values of symbols are given, unless specified otherwise within individual chapters or calculated within model simulations.

Term

Value

Units

Definition and Source

A

µmol m-2 s-1

Net leaf rate of CO2 uptake per unit leaf area.a

Ac

µmol m-2 s-1

Net canopy rate of CO2 uptake per unit ground area.e

Actot

g m-2 yr-1

Ac integrated over the course of a year.e

Acsun

µmol m-2 s-1

Net leaf rate of CO2 uptake per unit area sunlit leaves.e

Acshade

µmol m-2 s-1

Net leaf rate of CO2 uptake per unit shaded leaves.e

a

0.34

dimensionless

Growth respiration coefficient.f

b

0.002

day-1

Maintenance respiration coefficient.f

Ca

µmol mol-1

Atmospheric concentration of CO2.a

Ci

µmol mol-1

Intercellular concentration of CO2.a

cp

1010

J Kg-1 K-1

Specific heat capacity of dry air.e

DJ

d

Julian date.a

DJO3start

75

Julian day

Day of ozone start cycle.

DJTstart

130

Julian day

Day of temperature start cycle.

DJs

130, 115, 310

d

Start day of annual temperature cycle.

DJsv

130, 115, 310

d

Start day of seasonal vegetation cover.

d

0.77

dimensionless

Zero plane displacement.e

E

Kc (65 800),

Ko (1400),

Rd (66 405),

Vcmax(68 000),

Vomax(37 530),

Jmax (28 000)

J mol-1

Activation energy.a

Eiso

125 125

J mol-1

Activation energy of Visomax.

El

mmol m-2 s-1

Evapo/transpiration rate at sunlit/shaded leaves in a canopy layer.e

Ec

mmol m-2 s-1

Instantaneous canopy evapo/transpiration rate.e

Etot

mmol m-2 yr-1

Ec integrated over the course of a year.e

Fiso

nmol m-2 s-1

Rate of isoprene emission from a leaf.

F'isotot

Kg km-2

Amount isoprene emitted in one year

F'O3eff

mmol m-2

Effective ozone dose.

FO3(0)

nmol m-2 s-1

Threshold flux of ozone entering the leaf.

F'O3tot

mmol m-2

Ozone uptake.

FPYR

mmolC m-2 s-1

Rate of pyruvate formation from RubP carboxylation and RubP oxygenation.

f

0.23

dimensionless

Fraction of light not absorbed by functional photosynthetic pigments.a

ga

mmol m-2 s-1

Leaf boundary layer conductance.e

gc

mmol m-2 s-1

Canopy conductance to CO2.e

gs

mmol m-2 s-1

Stomatal conductance to water.c

gz

mmol m-2 s-1

Stomatal conductance to ozone. (Laisk et al., 1989.)

g(0)

81.1 at Ca = 350 72.8 at Ca = 650 µmol m-2 s-1

dimensionless

Minimum stomatal conductance to water when A = 0 at light compensation point.c

g(1)

9.58 at Ca = 350 8.92 at Ca = 650 µmol m-2 s-1

dimensionless

Empirical coefficient of stomatal conductance sensitivity to A, Ca, and RH.c

D H

208 680

J mol-1

Change in enthalpy.d

hcan

5, 1

m

Height of canopy.e

hms

2

m

Windspeed measurement height.e

h

2

m

Height of canopy layer above ground.e

HrO3peak

16

hr

Hour at which [O3] reaches a peak.

HrT

14

hr

Hour at which Temperature reaches peak.

I

µmol m-2 s-1

Photon flux. a

I0

µmol m-2 s-1

Irradiance incident on leaf surface.b

I2

µmol m-2 s-1

Irradiance absorbed by photosystem II.b

Iabs

µmol m-2 s-1

Photon flux absorbed by either sunlit or shaded leaves within a canopy.e

Idir

m mol m-2 s-1

Photon flux in direct beam solar radiation.a

Idiff

m mol m-2 s-1

Diffuse photon flux.a

Is

2600

m mol m-2 s-1

Solar constant. Photon flux in a plane perpendicular to the solar beam above the atmosphere.a

Iscat

m mol m-2 s-1

Direct beam radiation scattered by surfaces within the canopy.a

Ishade

m mol m-2 s-1

Mean I for shaded leaves within the canopya

Isun

m mol m-2 s-1

Mean I for sunlit leaves within the canopy.a

J

µmol m-2 s-1

Potential rate of electron transport.a

Ja

µmol m-2 s-1

Total solar radiation absorbed by either sunlit or shaded leaves within a canopy layer.e

Jmax

220

µmol m-2 s-1

Light saturated rate of potential rate of electron transport.c

Kc

460

µmol mol-1

Michaelis constant for CO2.a

Ko

330

mmol mol-1

Michaelis constant for O2.a

KT

K

Temperature correction.a

Kz

0.09245, 0.009

dimensionless

Empirical coefficient of sensitivity of Vcmax to F'O3eff.

Lw

0.04

m

Leaf width in the direction of the wind.e

l

4.6, 8

m2 m-2

Leaf area index.e

lshade

m2 m-2

Leaf area index of shaded leavese

lsun

m2 m-2

Leaf area index of sunlit leavese

niso

1.45 x 1021

dimensionless

Empirical constant.

[O3]ranDav

10

µmol mol-1

Average daily range of [O3].

Determined for Sibton data (DOE, 1994).

[O3]ranDmax

12

µmol mol-1

Maximum daily range of [O3].

Determined for Sibton data (DOE, 1994).

[O3]ranYr

14

µmol mol-1

Annual range of [O3].

Determined for Sibton data (DOE, 1994).

[O3]ranYrav

15

µmol mol-1

Average annual range of [O3].

Determined for Sibton data (DOE, 1994).

Oa

210

mmol mol-1

Atmospheric concentration of oxygen.a

Oi

mmol mol-1

Intercellular concentration of oxygen.a

P

kPa

Atmospheric pressure.a

P0

101.324

kPa

Standard atmospheric pressure at sea level.a

r

0.2

dimensionless

Leaf reflectance.b

R

8.314

J K-1 mol-1

Gas constant.a,d

Rd

1.1

µmol m-2 s-1

Rate of dark respiration.a

RG

µmol m-2 s-1

Growth respiration.

RH

%

Relative humidity.a

RM

g m-2 d-1

Maintenance respiration.

D S

670

J K-1 mol-1

Change in entropy.d

s

kPa K-1

Slope of saturated water vapour pressure

change with respect to temperature.e

T

oC

Leaf temperature.a

Tair

oC

Ambient air temperature.e

Tcan

oC

Air temperature within canopy.e

TD

5, 5, 0.3

oC

Mean amplitude of daily temperature.

TDmax

5, 5, 0.3

oC

Maximum amplitude of daily temperature.

Tk

K

Absolute temperature

Tmean

10, 12, 26.6

oC

Annual mean air temperature.

TYr

6, 12, 0.3

oC

Amplitude of annual temperature.

TPU

23

µmol m-2 s-1

Triose phosphate utilisation.b

u

m s-1

Windspeed at a given height.e

u*

m s-1

Windspeed.e

v

0-1

dimensionless

Coefficient of seasonal vegetation cover.

Vc

µmol m-2 s-1

Carboxylation velocity.a

Vcmax

98

µmol m-2 s-1

Maximum RubP saturated rate of carboxylation.a

Visomax

µmol m-2 s-1

Maximum capacity of isoprene synthase activity.

Vo

mmol m-2 s-1

Oxygenation velocitya

Vomax

0.21Vcmax

mmol m-2 s-1

Maximum RubP saturated rate of

oxygenation.a

Vpr

mmol m-2 s-1

Velocity of photorespiration.

Wc

µmol m-2 s-1

RubP saturated rate of carboxylaytion.a

WJ

µmol m-2 s-1

RubP limited rate of carboxylation.a

Wisoco

µmol m-2 s-1

Pyruvate limited rate of isoprene synthase activity.

Wp

µmol m-2 s-1

Phosphorylation limited rate of

carboxylation.a

Wisop

µmol m-2 s-1

Phosphorylation limited rate of isoprene

synthase activity.

Wop

mmol m-2 s-1

Phosphorylation limited rate of

photorespiration.a

WT

Kg m-2

Total dry weight.

Y

Kg m-2

Yield, above ground biomass.

a

0.75

dimensionless

Atmospheric transmittance.a

g