On the relative magnitudes of

photosynthesis, respiration, growth and carbon storage

in vegetationMarcel van Oijen (CEH-Edinburgh)

Carbon fluxes in vegetation

PRm Rg

R

ρ = R/P is often ~0.5• Gifford (1995): ρ f(Temp.)• Cheng et al. (2000): ρ f(CO2)

Physiological explanation ?• Monteith (1981)

Mathematical explanation !• Law of conservation of mass …

Vegetation biomass

Carbon fluxes in vegetation

PRm Rg

R

Vegetation biomass

Carbon fluxes in vegetation

PRm Rg

R

Reserves StructureG

NPP = P – Rg – Rm

= G + SRg = G (1-Yg) / Yg

G (1-¾) / ¾= G / 3

S = P-Rm-Rg-G

ρ = (Rg + Rm) / Pα = S / P

Rm / P =Rg / P =G / P =S / P =

Carbon fluxes in vegetation

PRm Rg

R

Reserves StructureG

NPP = P – Rg – Rm

= G + SRg = G (1-Yg) / Yg

G (1-¾) / ¾= G / 3

S = P-Rm-Rg-G

ρ = (Rg + Rm) / Pα = S / P

Rm / P = (4ρ+α-1) / 3Rg / P = (1-ρ-α) / 3G / P = 1-ρ-αS / P = α

Knowing two parameters, ρ and α,fully determines P : Rg : Rm : S : G

Carbon fluxes in vegetation

Rm / P = (4ρ+α-1) / 3Rg / P = (1-ρ-α) / 3G / P = 1-ρ-αS / P = α

ρ = 1/2

α = 1/4

Vertical bar represents

P = Rm + Rg + G + S

Carbon fluxes in vegetation

Rm / P = (4ρ+α-1) / 3Rg / P = (1-ρ-α) / 3G / P = 1-ρ-αS / P = α

Rm = 5/12

Rg = 1/12

G = 1/4

S = 1/4

ρ = 1/2

α = 1/4

Carbon fluxes in vegetation

Rm / P = (4ρ+α-1) / 3Rg / P = (1-ρ-α) / 3G / P = 1-ρ-αS / P = α

0

1

3/43/16 1

RgRm

S

G

α = 1/4

ρ Excluded becauseρ < (1-α)

Excluded becauseρ > (1-α)/4

Carbon fluxes in vegetation

0

1

1/8 1/21/4 1

G

RmRg G

S

RmRg

α = 0 α = 1/2

ρ

0 10

1

3/43/16 1

RgRm

S

G

α = 1/41

Carbon fluxes in vegetation

Rm / P = (4ρ+α-1) / 3Rg / P = (1-ρ-α) / 3G / P = 1-ρ-αS / P = α

ρ < (1-α)

ρ > (1-α)/4

Constraints on the respiration ratio ρ

Constraints on the storage ratio α

(1-4ρ) < α < (1-ρ)

Measurements of R & P in grassland

0

25

50

75

0 50 100 150 200 250 300 350Time (d)

Respiration (R, g CO2 m-2 d-1)Photosynthesis (P, g CO2 m-2 d-1) = P

º = R

Wageningen rhizolab(Ad Schapendonk)

Measurements of R & P in grassland

0

25

50

75

0 50 100 150 200 250 300 350Time (d)

Respiration (R, g CO2 m-2 d-1)Photosynthesis (P, g CO2 m-2 d-1) = P

º = R

-1

0

1

2

0 50 100 150 200 250 300 350

Time (d)

R:P (=ρ)S:P (=α)

`

º = R/P=ρ = S/P=α

Rg = Rm Net remobilisation of reserves: 3-11 d after each cut

Discussion

• Conservation of mass strongly constrains C-fluxes• Eqs are valid over any period & any spatial scale (with P>0)• Eqs are valid for any environmental conditions little impact

of temperature and CO2

• In periods of net remobilisation (α<0), eqs still valid but then ρ can be >1

• Long-term value of α must be >0 (otherwise reserves depleted) fluxes most constrained over longer periods (Monteith, 1981)

• Steady-state growth would require α = constant (~0.2?) to maintain homeostasis

• Eqs tool for:• Analysis of incomplete data sets• Checking internal consistency of models