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Sep-05-07

Chapter 1: Terrestrial Surface Carbon Fluxes 1. Introduction Carbon Pools: Carbon is stored on our planet in the following major pools: (1) as organic molecules in living and dead organisms found in the biosphere; (2) as the gas carbon dioxide in the atmosphere; (3) as organic matter in soils; (4) in the lithosphere as fossil fuels and sedimentary rock deposits such as limestone, dolomite and chalk; and (5) in the oceans as dissolved atmospheric carbon dioxide and as calcium carbonate shells in marine organisms. The table below provides estimated amounts in the major pools. Table 1. Estimated major stores of carbon on the Earth

Pool Amount in Billions of Metric Tons Atmosphere 578 (as of 1700) - 766 (as of 1999) Terrestrial Plants 540 to 610 Soil Organic matter 1500 to 1600 Ocean 38,000 to 40,000 Fossil Fuel Deposits 4000 Marine Sediments and Sedimentary Rocks 66,000,000 to 100,000,000

Global Carbon Cycle: Carbon is exchanged between the active pools due to various processes – photosynthesis and respiration between the land and the atmosphere, and diffusion between the ocean and the atmosphere. The global carbon cycle is shown in Fig. 1.

Figure 1. The global carbon cycle. Credits: http://earthobservatory.nasa.gov/Library/CarbonCycle/carbon_cycle4.html

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Atmospheric Carbon Dioxide: Accurate and direct measurements of the concentration of CO2 in the atmosphere began in 1957 at the South Pole and in 1958 at Mauna Loa, Hawaii. The Mauna Loa record is shown below in Fig. 2.

In 1958, the concentration of CO2 was about 315 ppmv, and the growth rate was about 0.6 ppmv/yr. This growth rate has generally been increasing since then; it averaged 0.83 ppmv/yr in the 1960s, 1.28 ppmv/yr during the 1970s, amd 1.53 ppmv/yr during the 1980s. The concentration in early 2006 was about 385 ppmv. Data from Mauna Loa are close to, but are not precisely the global mean value. The annual cycle in the Mauna Loa record is due to the seasonality of vegetation. In early spring, the concentration of CO2 is at its maximum, and as the plants green-up, the concentration drops, reaching a minimum value towards the end of the summer, and when leaves fall, it starts to build up again. This swing in the amplitude is most pronounced in the records from the northern high latitudes, where it can be as large as 15 ppmv.

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The atmospheric CO2 record prior to 1957 comes mainly from air bubbles in ice cores, which is reasonably accurate. Over the last 1000 years, CO2 concentration in the atmosphere has fluctuated at about +/- 10 ppmv around 280 ppmv. There are at least three arguments to be made for the case that the observed increase in atmospheric CO2 concentration is due to emissions related to human activity. (1) The rise in atmospheric CO2 concentration closely follows the increase in emissions related to fossil fuel burning. (2) The inter-hemispheric gradient in atmospheric CO2 concentration is growing in parallel with CO2 emissions. That is, there is more land mass in the Northern hemisphere, and therefore more human activity, and thus, higher emissions, which is reflected in the CO2 growth in the Northern hemisphere (compared to the SH). (3) Fossil fuels and biospheric carbon are low in Carbon 13 (an isotope). The ratio of carbon 13 to carbon 12 in the atmosphere has been decreasing. Figure 3, shown below, indicates that the concentration of CO2 has never been grater than 300 ppmv for the past 400,000 years.

Recommended reading: Angert et al. (2005), Drier Summers Cancel Out the CO2 Uptake Enhancement Induced by Warmer Spring, Proceedings of the National Academy of Sciences, Vol. 102, pp. 10823-10827. Buermann et al., (2007), The changing carbon cycle at Mauna Loa observatory, Proceedings of the National Academy of Sciences, Vol. 104, pp. 4249-4254. Terrestrial Carbon Processes: The terrestrial carbon cycle is a highly dynamic system that includes several storage pools, such as vegetation, soil, detritus, black carbon residue from fires, harvested products, etc., that can be characterized by their turnover time.

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Carbohydrate pools turn over on a daily basis, leaves can store carbon for several seasons, and carbon in living wood and soil pools may remain there for hundreds of years and millennia. Fire may return carbon to the atmosphere instantaneously and can produce long-lived black carbon. Any activity that changes the amount of biomass in vegetation and soil has potential to sequester carbon from, or release carbon to, the atmosphere. The terrestrial carbon cycle can be classified into the following fluxes (Fig.4): gross primary production (GPP), net primary production (NPP), net ecosystem production (NEP), and net biome production (NBP). About one-third of the total amount of CO2 in the atmosphere enters into green leaves every year. The amount that is fixed from the atmosphere, i.e., converted from CO2 to carbohydrates during photosynthesis, is called GPP, which is carbon assimilation by photosynthesis ignoring photorespiration. Terrestrial GPP has been estimated to be 120 Gt C/yr. Annual plant growth is the difference between photosynthesis and autotrophic respiration (Ra), and is referred to as net primary production (NPP). NPP is the fraction of GPP resulting in plant growth, and can be measured through sequential harvesting or by measuring plant biomass, provided turnover of all components (e.g., fine roots) is included. Global terrestrial NPP has been estimated to be 60 Gt C/yr, that is, about half of GPP is incorporated in new plant tissue. The other half is returned to the atmospheric as CO2 by autotrophic respiration, that is, respiration by plant tissues.

Figure 4. Schematic representation of the terrestrial carbon cycle. Arrows indicate fluxes; boxes indicate pools. The size of the boxes represents differences in carbon distribution in terrestrial ecosystems. CWD, coarse woody debris; Rh, heterotrophic respiration by soil organisms; PS, photosynthesis. Credits: Schulze et al. (2000), Managing forests after Kyoto, Science, 289:2058-2059.

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All the carbon fixed as NPP may be returned to the atmospheric CO2 pool through two processes: heterotrophic respiration (Rh) by decomposers (bacteria and fungi feeding on dead tissue) and herbivores; and combustion in natural or man-made fires. Most dead biomass enters the detritus and soil organic matter pools where it is respired at a rate that depends on the chemical composition of the dead tissue and on environmental conditions. Detritus and microbial biomass have a short turnover time (< 10 years). In contrast, soil organic carbon has decadal to centennial turnover times, because inert soil organic carbon is composed of molecules more or less resistant to further decomposition. Net ecosystem production, NEP, is the difference between NPP and heterotrophic respiration (Rh), which determines the amount of carbon lost or gained by the ecosystem without disturbances, such as harvests and fire. NEP can be estimated from measurements of CO2 fluxes over patches of land. Global NEP is estimated at about 10 Gt C/yr. Of these, annual NEP fluxes are in the range 0.7 to 5.9 tons C/ha/yr for tropical forests, 0.8 to 7.0 tons C/ha/yr for temperate forests, and up to 2.5 tons C/ha/yr for boreal forests. NEP is the most fundamental carbon flux for a natural forest ecosystem. Net biome production, NBP, is the carbon accumulated by the terrestrial biosphere when carbon losses from non-respiratory processes are taken into account, including fires, harvests/removals, erosion and export of dissolved organic carbon by rivers to the oceans. NBP is a small fraction of the initial uptake of CO2 from the atmosphere and can be positive or negative; at equilibrium it would be zero. NBP is the critical parameter to consider for long-term (decadal) carbon storage. NBP is estimated to have averaged 0.2 +/- 0.7 Gt C/yr during the 1980s and 1.4 +/- 0.7 Gt C/yr during the 1990s. Recommended reading: Schulze et al. (2000), Managing forests after Kyoto, Science, 289:2058-2059. Global Carbon Budget: The During the 1980s, carbon emissions totaled 5.4 +/- 0.3 Gt C/yr (Giga tons or 109 tons of carbon per year) from fossil-fuel burning and cement manufacture, and 1.7 (0.6 to 2.5) Gt C/yr from land-use changes. The net carbon flux into the oceans is estimated to be 1.9 +/- 0.5 Gt C/yr, and 0.2 +/- 0.7 Gt C/yr into the land. Because the atmospheric carbon increase is observed to be 3.3 +/- 0.1 Gt C/yr, there is still a 1.7 Gt C missing sink per year. For the 1990s, the estimates are somewhat similar, except for a larger land carbon sink. Many studies suggest 1 to 2 Gt of carbon sequestered in pools on land in temperate and boreal regions.

Table 2. Contemporary carbon budget for the 1980s and 1990s. Negative values denote flux from the atmosphere, that is ocean or land uptake. Credits: Schimel et al., (2001), Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems, Nature, 414:169-172.

1980s (Gt C/yr) 1990s (Gt C/yr) Emissions (fossil-fuel buring, cement manufacture) 5.4 +/- 0.3 6.3 +/- 0.4 Atmospheric increase 3.3 +/- 0.1 3.2 +/- 0.1 Ocean-atmosphere flux -1.9 +/- 0.5 -1.7 +/- 0.5 Land-atmosphere flux -0.2 +/- 0.7 -1.4 +/- 0.7 Emissions due to land-use change 1.7 (0.6 to 2.5) Assume 1.6 +/- 0.8 Residual terrestrial sink -1.9 (-3.8 to 0.3) -2 to -4

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Spatial Patterns of Carbon Uptake: Figure 5 shows the zonal distribution of terrestrial and oceanic carbon fluxes. These data were deduced from eight inverse models using different techniques and sets of atmospheric observations after accounting for fossil-fuel emissions. Results are shown for the 1980s (plain bars) and for 1990-1996 (hatched bars). Positive numbers are fluxes to the atmosphere. This figure represents our current understanding, that is, about 1 to 2 billion tons of carbon are somehow sequestered in sinks on land north of 30N. Elsewhere, the land is neutral, where sources nearly match sinks. The geographic distribution of the northerly land sink remains unknown. Figure 5. Zonal distribution of terrestrial and oceanic carbon fluxes. Credits: Heimann, M. (2001), Max-Planck Institute fuer Biogeochemi, Technical Report 2. Recommended reading: Schimel et al., (2001), Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems, Nature, 414:169-172. Rising CO2 Impacts on Ecosystems: Field experiments of elevated CO2 effects on aboveground biomass show, on average, a positive effect on biomass, ranging from -20% to +80%. Some early predictions of CO2 effects (C3 vs. C4 plants) are not generally supported, and it is necessary to consider the interactive effects of changes in CO2, temperature, and nitrogen. Dynamic global vegetation models involving transient changes show that biomes will not shift as intact entities. Significant changes in vegetation, especially in high latitudes, are likely over the next century, and changes in disturbance regimes will be most important. Based on forecast changes in land use, vegetation structure, and ecosystem physiology, the terrestrial biosphere will probably become a source rather than a sink for carbon over the next century. Because of land use change, the terrestrial biosphere of the 21st century will probably be further impoverished in species richness and substantially reorganized. More natural ecosystems will be in an early successional state or converted to production systems. The biosphere will be generally weedier and structurally simpler, with fewer areas in an ecologically complex old-growth state. Temperate crop production will probably increase

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slightly because of CO2 increases (5-7% for wheat for average field conditions), but crop production in the tropics may decline in some areas. Land use change will have the greatest effect on pastures and rangelands; due to a required >2% annual increase in crop production to meet the expanding human population, there will be increased incursion of cropland into rangelands. Recommended reading: Walker, B. and Steffen, W. (1997). An Overview of the Implications of Global Change for Natural and Managed Terrestrial Ecosystems, Conservation Ecology, Available at http://www.ecologyandsociety.org/vol1/iss2/art2/ Schroeter et al., (2005), Ecosystem service supply and vulnerability to global change in Europe, Science, Vol. 310, pp. 1333-1337. 2. Global NPP Modeling – The Production Efficiency Model A simple model to calculate vegetation net primary productivity (NPP) at coarse spatial and temporal resolutions is outlined here. This model is based on the algorithm used to produce MODIS NPP products (Heinsch et al., 2003, User’s Guide GPP and NPP (MOD17A2/A3) Products NASA MODIS Land Algorithm). A conservative relationship between absorbed photosynthetically active radiation (APAR) and net primary productivity (NPP) was first proposed by Monteith. APAR depends upon (a) the geographic and seasonal variability of day length and potential incident radiation, as modified by cloud cover and aerosols, and (b) the amount and geometry of displayed leaf material. This relation combines the meteorological constraint of available sunlight at a site with the ecological constraint of the amount of leaf-area capable of absorbing that solar energy. Such a combination avoids many of the complexities of carbon balance theory. The PAR conversion efficiency, ε, varies widely with different vegetation types. There are two principle sources of this variability. First, with any vegetation, some photosynthesis is immediately used for maintenance respiration. For the annual crop plants, these respiration costs were minimal, so ε was typically around 2 gC/MJ. Respiration costs, however, increase with the size of perennial plants. Published ε values for woody vegetation are much lower, from about 0.2 to 1.5 gC/MJ – this could be due to respiration of living cells in the sapwood of woody stems. The second source of variability in ε is attributed to suboptimal climatic conditions. Evergreen vegetation such as conifer trees or shrubs absorb PAR during the non-growing season, yet sub-freezing temperatures stop photosynthesis because leaf stomata are forced to close. Additionally, high vapor pressure deficits, > 2000Pa, have been shown to induce stomatal closure in many species, thereby reducing photosynthetic activity. These biome- and climate-induced ranges of ε must be taken into account in any global modeling of NPP. Daily Gross primary productivity: Daily GPP (kg C/m2/day) is calculated as, GPP=ε*APAR, where APAR=IPAR*FPAR. The fraction of photosynthetically active

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radiation absorbed by vegetation, FPAR (dimensionless), is typically a remote sensing product. The daily total PAR incident on the vegetation, IPAR, is estimated from daily total incident shortwave radiation, SWRad (MJ/m2/day) as, IPAR =0.45*SWRad. The efficiency parameter, ε (kg C/MJ), is estimated as ε=εmax*TMIN_scalar* VPD_scalar. The optimal efficiency parameter, εmax , is a biome dependent constant, derived an extensive set of observations. The two attenuation scalars, with values between 0 and 1, down-regulate εmax depending on the value of minimum temperature (TMIN) and vapor pressure deficit (VPD). They are modeled as a simple linear ramp functions and the lower and upper limits are biome dependent constants (Table 3). Table 3. Biome dependent constants for daily gross primary productivity (See Appendix 1)

Parameter Units Description εmax Kg C/MJ Maximum radiation conversion efficiency TMINmax deg C Daily minimum temperature at which ε=εmax (optimal VPD) TMINmin deg C Daily minimum temperature at which ε=0 (any VPD) VPDmax Pa Daylight average VPD at which ε=εmax (optimal TMIN) VPDmin Pa Daylight average VPD at which ε=0 (any TMIN)

Daily Leaf Maintenance Respiration: Leaf maintenance respiration (Leaf_MR, kg C/day) is calculated as

Leaf_MR = Leaf_Mass*leaf_mr_base*Q10_mr [(Tavg - 20.0) / 10.0] where leaf_mr_base is the maintenance respiration of leaves per unit leaf mass (kg C/kg C/day) at 20°C, which is a biome dependent constant (Table 4), and Tavg is the average daily temperature (°C). Leaf mass (kg) is calculated as LAI/SLA, where LAI, the leaf area index (m2 leaf per m2 ground area), is obtained from remote sensing and the specific leaf area (SLA, projected leaf area per kg leaf C) is a biome dependent constant (Table 4). Daily Fine Root Maintenance Respiration: The maintenance respiration of the fine root mass (Froot_MR, kg C/day) is calculated as

Froot_MR = Fine_Root_Mass*froot_mr_base*Q10_mr [(Tavg - 20.0) / 10.0] where froot_mr_base is the maintenance respiration per unit of fine roots (kg C/kg C/day) at 20°C, which is a biome dependent constant (Table 4). Fine root mass (Fine_Root_Mass, kg) is estimated as Leaf_Mass * froot_leaf_ratio, where froot_leaf_ratio is the ratio of fine root to leaf mass (unitless), also a biome dependent constant (Table 4). Table 4. Biome dependent constants for daily maintenance respiration (See Appendix 1)

Parameter Units Description SLA m2/kg C Projected leaf area per unit mass of leaf carbon froot_leaf_ratio none Ratio of fine root carbon to leaf carbon leaf_mr_base kg C/kg C/day Maintenance respiration per unit leaf carbon per day at 20 C froot_mr_base kg C/kg C/day Maintenance respiration per unit fine root carbon per day at 20 C Q10_mr none Exponent shape parameter controlling respiration as a function of

temperatrure

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Daily Intermediate Net Primary Productivity: An intermediate NPP (kg C/day) can be calculated (GPP – Leaf_MR - Froot_MR). However, this product does not include the maintenance respiration associated with live wood (Livewood_MR), nor does it include growth respiration (GR). Annual Live Wood Maintenance Respiration: Annual maximum leaf mass, the maximum value of daily leaf mass, is the primary input for both live wood maintenance respiration (Livewood_MR). To account for Livewood_MR, it is assumed that the amount of live woody tissue is (1) constant throughout the year and (2) related to annual maximum leaf mass. This approach relies on empirical studies relating the annual growth of leaves to the annual growth of other plant tissues. Leaf longevity is required to estimate annual leaf growth for evergreen forests, but it is assumed to be less than one year for deciduous forests, which replace all foliage annually. Thus, it is assumed that there is no litterfall in deciduous forests until after maximum annual leaf mass has been attained. The mass of livewood (Livewood_Mass, kg C) is calculated as ann_leaf_mass_max* livewood_leaf_ratio, where ann_leaf_mass_max is the annual maximum leaf mass (kg C) obtained from the daily Leaf_Mass calculation. The livewood_leaf_ratio is the ratio of live wood mass to leaf mass (unitless), and is a biome dependent constant (Table 5). The associated maintenance respiration (Livewood_MR, kg C/day) is calculated as Livewood_Mass*livewood_mr_base*annsum_mrindex, where livewood_mr_base (kg C /kg C/day) is the maintenance respiration per unit of live wood carbon per day, a biome dependent constant (Table 5), and annsum_mrindex is the annual sum of the maintenance respiration term Q10_mr [(Tavg-20.0)/10.0].

Annual Leaf Growth Respiration: This quantity (Leaf_GR, kg C/yr) is calculated as ann_leaf_mass_max*ann_turnover_proportion*leaf_gr_base, where leaf_gr_base is the base growth respiration (kg C/kg C) for leaves and ann_turnover_proportion is the annual proportion of leaves that turnover (per year) which indicates the proportion of newly grown leaves each year, both of which are biome dependent constants (Table 5). Annual Fine Root Growth Respiration: Growth respiration for fine roots (Froot_GR, kg C/yr) is calculated as Leaf_GR*froot_leaf_gr_ratio, where froot_leaf_gr_ratio is the ratio of fine root growth respiration to leaf growth respiration (unitless), which is a biome dependent constant (Table 5). Annual Live Wood Growth Respiration: Growth respiration of livewood (Livewood_GR, kg C/yr) can be calculated as Leaf_GR*livewood_leaf_gr_ratio, where the biome dependent constant (Table 5) livewood_leaf_gr_ratio is the ratio of livewood leaf growth respiration (unitless). Annual Dead Wood Growth Respiration: Deadwood growth respiration (Deadwood_GR, kg C/day) is calculated as Leaf_GR*deadwood_leaf_gr_ratio, where the biome dependent constant (Table 5) deadwood_leaf_gr_ratio is the ratio of deadwood to leaf growth respiration (unitless).

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Annual Net Primary Productivity: This is calculated as the annual sum of daily intermediate NPP minus the annual live wood maintenance respiration and annual growth respiration of leaves, fine roots, live and dead wood. Table 5. Biome dependent constants for annual maintenance and growth respiration (See Appendix 1)

Parameter Units Description livewood_leaf_ratio none Ratio of live wood carbon to annual maximum leaf carbon livewood_mr_base kg C/kg C/day Maintenace respiration per unit live wood carbon per day at

20C ann_turnover_proportion per year Annual proportion of leaves that turn over, or proportion of

newly grown leaves each year leaf_gr_base kg C/kg C Respiration cost to grow a unit of leaf carbon froot_leaf_gr_ratio none Ratio of fine root to leaf annual growth respiration livewood_leaf_gr_ratio none Ratio of live wood to leaf annual growth respiration deadwood_leaf_gr_ratio none Ratio of dead wood to leaf annual growth respiration

Recommended reading: (1) Potter, C. S., J. T. Randerson, C. B. Field, P. A. Matson, P. M. Vitousek, H. A. Mooney, and S. A. Klooster, Terrestrial ecosystem production: A process model based on global satellite and surface data, Global Biogeochem. Cycles, 7, 811 – 842, 1993. 3. Modeling Canopy Photosynthesis We describe in this section a model of instantaneous canopy photosynthesis. The simplest of such models is the one employed by the Common Land Model (CLM). Canopy photosynthesis is modeled as, sun Asun Lsun + Asha Lsha, where Lsun and Lsha are the sunlit and shaded leaf area indices (dimensionless; see Section 3.C in Chapter 3 – Radiation Fluxes) and, Asun and Asha are the photosynthetic rates of sunlit and shaded leaves (µ mol CO2/m2/s) – these are obtained from a leaf photosynthesis model driven with average absorbed photosynthetically active radiation (PAR) for sunlit and shaded leaves. This separation of leaf area into sunlit and shaded leaves is important because photosynthesis is a nonlinear function of absorbed PAR. If one wishes to more realistically calculate canopy photosynthesis, in view of the fact that light decreases exponentially in a canopy of leaves, then the following formulation may be employed. As a first approximation, assume that the canopy consists of green planar leaves only. Consider leaf elements of orientation ΩL at depth L(z) in the canopy. Here L is the leaf area index (one-sided green leaf area per unit ground area) acumulated from the top of the canopy downwards to depth z. Let Q(ΩL,L) denote the PAR flux density absorbed by leaf surfaces (µ mol E/m2 leaf area/s). The corresponding canopy gross photosynthetic rate, per unit ground area, is

!

GPP = dL1

2"0

LAI

# d$L

2"

# gLA[Q($L ,L)] ,

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where LAI is the canopy leaf area index and gL is the probability density of leaf normal orientation. The leaf photosynthetic rate, A, is a function of PAR absorbed by the leaves, and is evaluated with a model to be detailed elsewhere. Leaf Normal Orientation: Let

ΩL ≡ (θL, ! L) ≡ (µL, ! L), µL ∈ (0,1), ! L ∈ (0,2π), be the normal to the upper face of a leaf element. If this normal is in the lower hemisphere, the lower face may be treated as the upper face, i.e., the definition of the upper face of a leaf element is the face the normal to which is in the upper hemisphere. Hence, the space of leaf normal orientation is always 2π steradians. Further, let (1/2π) Lg (ΩL) be the probability density function of leaf normal orientation,

!

1

2"d#L

2" +

$ gL(#L) =1.

If

!

µLand

L! are assumed independent, then

!

1

2"gL (#L ) = g L(µL)

1

2"hL($L) ,

where

!

g L(µL)and (1/2π) )(h LL ! are the probability density functions of leaf normal inclination and azimuth, respectively, and

!

dµLg L(µL) =1,0

1

"

!

1

2"d#LhL(#L)

0

2"

$ =1.

The simplest model of leaf normal orientation distribution is constant leaf normal inclination and uniform distribution of azimuths,

!

1

2"gL (#L ) =

1

2"$(µL %µL

*) .

The following example model distribution functions for leaf normal inclination are widely used: (1) planophile – mostly horizontal leaves, (2) erectophile – mostly erect leaves, (3) plagiophile – mostly leaves at 45 degrees, (4) extremophile – mostly horizontal and vertical leaves, (5) uniform – all inclinations equally probable, and (6) spherical – leaf normals distributed as on a sphere. These distributions can be expressed as,

Planophile:

!

g L("L ) sin "L =2

#(1+ cos 2"L) ,

Erectophile:

!

g L("L ) sin "L =2

#(1$ cos 2"L) ,

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Plagiophile:

!

g L("L ) sin "L =2

#(1$ cos 4"L) ,

Extremophile:

!

g L("L ) sin "L =2

#(1+ cos 4"L) ,

Uniform:

!

g L("L ) = 2/! , Spherical:

!

g L("L ) = sin L

! , and are plotted below in Fig. 6.

0 15 30 45 60 75 900.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

(b)

(c)

(e)

(d)

(a)

Lea

f N

orm

al I

ncl

inat

ion

Dis

trib

uti

on

Fu

nct

ion

Leaf Inclination in Degrees

0 15 30 45 60 75 90

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 6. The )( Lg ! for (a) planophile (mostly horizontall leaves), (b) erectrophile (mostly vertical leaves), (c) plagiophile (leaves inclined mostly at about 45 degrees), (d) extremophile (mostly horizontal and vertical leaves) and (e) uniform (all inclinations equally probable) distributions. Radiation Incident on Leaves: Let γ be the fraction of direct sunlight in light (PAR) incident on the canopy. Thus, PARdir = γ PAR, and PARdif = (1- γ) PAR. Here, PARdir and PARdif are the direct and diffuse PAR flux density, per unit ground area, incident on the leaf canopy. The direct PAR flux density, per unit leaf area, absorbed by the leaf surfaces of orientation ΩL located at depth L(z) inside the canopy is

!

Qdir ("L ,L) = (1#$L )

%PAR

|µo ||"o •"L | exp #

G("o)L(z)

|µo |

&

' (

)

* + ,

where ωL is the leaf albedo for PAR, µo is cos(θo), θo is the solar zenith angle, Ωo is the solid angle of direct sun light, and the G function is the projection of unit leaf area on the plane perpendicular to Ωo, that is,

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!

G("o) =1

2#d"L

2# +

$ gL ("L ) |"L •"o |.

The G function is equal to 0.5 if the leaves are assumed to be uniformly distributed. The diffuse PAR flux density, per unit leaf area, absorbed by the leaf surfaces of orientation ΩL located at depth L(z) inside the canopy is

!

Qdif ("L ,L) = (1#$L )

(1# %)PAR

&d"d

2& #

' |"d •"L | exp #G("d )L(z)

|µd |

(

) *

+

, - ,

where the integration is over all downward directions in sky hemisphere (2π−). This formulation can be generalized the case of needles in coniferous canopies (which modifies the G function) and to a stand of trees (which modifies the expression in the exponents). Recommended reading: (1) Gutschick, V.P., Joining leaf photosynthesis models and canopy photon transport models. In: R.B. Myneni and J. Ross (ed.), Photon-Vegetation Interactions, Spring-Verlag, pages 501-535, (1991). (2) Thornley, J.H.M., (2002). Instantaneous canopy photosynthesis: Analytical expressions for sun and shade leaves based on exponential light decay down the canopy and an acclimated non-rectangular hyperbola for leaf photosynthesis, Annals of Botany, 89: 451-458. 4. Modeling leaf Photosynthesis The simplest leaf photosynthesis model is a response function of steady-state leaf photosynthetic rate, A, to absorbed PAR, Q. A three-parameter equation is generally used to predict leaf photosynthetic rate,

!

A = {Q" + Amax

# [(Q" # Amax)2 # 4Q"$A

max](1/ 2)} /(2$) .

The three parameters are (1) the asymptote at high irradiances Amax or the light-saturated rate; (2) initial slope or initial quantum yield,

!

" = dA /dQ as

!

Q" 0 (0.05 mol CO2/mol PAR); it may be assumed to be a universal constant; (3) angularity

!

" which can vary between 0 (the rectangular hyperbola) and 1. The inverse of α is quantum requirement. This is approximately 19 absorbed quanta per CO2 fixed for C4 leaves, and varies between 15 and 22 for C3 leaves, depending on temperature. The response function parameters depend on the leaf’s physiological and developmental stage. In general, there is a strong variation of photosynthetic capacity, Amax, with depth in the canopy and this needs to be parameterized. This is done using depth profiles of specific leaf mass (leaf mass per unit leaf area). The three parameters are estimated from measurements of leaf photosynthesis at levels of incident PAR irradiance. In such instances Q refers to PAR flux density incident on the leaf surface, and not absorbed PAR. This requires appropriate

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modification to the Q term in models of canopy photosynthesis (Section 3). It should be noted that water and mineral nutrition stresses are common in nature, that is, the rule rather than exception. This simple model does not account for such details. Collatz et al. (1991 and 1992) developed models for C3 and C4 leaf photosynthesis that are now widely used. The CLM also uses these models. Given light flux density per unit leaf area incident on a leaf, the models calculate the corresponding leaf photosynthetic rate, per unit leaf area, as the minimum of three potential capacities – (1) JE which describes the light-photosynthesis response, (2) JC which is the Rubisco-limited rate, and (3) JS which is the capacity for the export or utilization of the products of photosynthesis. All three capacities have units of µ mol CO2/m2 leaf area/s and depend on environmental temperature (T) and the ratio of kinetic parameters describing the partitioning of RuBP to the carboxylase or oxygenase reactions of Rubisco (τ, dimensionless). The capacities JE and JC also depend on environmental relative humidity (hs). And, the capacity JE depends linearly on the light flux density incident on the leaf (Q) and the intrinsic quantum efficiency for CO2 uptake (α, dimensionless). An excellent description of these models and their use is given in the CLM Technical Document. Rubisco: Carbon is essential to life. All of our molecular machines are built around a central scaffolding of organic carbon. Unfortunately, carbon in the earth and atmosphere is locked in highly oxidized forms, such as carbonate minerals and carbon dioxide gas. In order to be useful, this oxidized carbon must be "fixed" into more organic forms, rich in carbon-carbon bonds and decorated with hydrogen atoms. Powered by the energy of sunlight, plants perform this central task of carbon fixation. Inside plant cells, the enzyme ribulose bisphosphate carboxylase/oxygenase (rubisco) forms the bridge between life and the lifeless, creating organic carbon from the inorganic carbon dioxide in the air. Rubisco takes carbon dioxide and attaches it to ribulose bisphosphate, a short sugar chain with five carbon atoms. Rubisco then clips the lengthened chain into two identical phosphoglycerate pieces, each with three carbon atoms. Phosphoglycerates are familiar molecules in the cell, and many pathways are available to use it. Most of the phosphoglycerate made by rubisco is recycled to build more ribulose bisphosphate, which is needed to feed the carbon-fixing cycle. But one out of every six molecules is skimmed off and used to make sucrose (table sugar) to feed the rest of the plant, or stored away in the form of starch for later use. In spite of its central role, rubisco is remarkably inefficient. As enzymes go, it is painfully slow. Typical enzymes can process a thousand molecules per second, but rubisco fixes only about three carbon dioxide molecules per second. Plant cells compensate for this slow rate by building lots of the enzyme. Chloroplasts are filled with rubisco, which comprises half of the protein. This makes rubisco the most plentiful single enzyme on the Earth. Rubisco also shows an embarrassing lack of specificity. Unfortunately, oxygen molecules and carbon dioxide molecules are similar in shape and chemical properties. In proteins that bind oxygen, like myoglobin, carbon dioxide is easily excluded because carbon

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dioxide is slightly larger. But in rubisco, an oxygen molecule can bind comfortably in the site designed to bind to carbon dioxide. Rubisco then attaches the oxygen to the sugar chain, forming a faulty oxygenated product. The plant cell must then perform a costly series of salvage reactions to correct the mistake. Recommended reading: (1) Collatz, G.J., Ball, J.T., Grivet, C., and Berry, J.A. 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis, and transpiration: A model that includes a laminar boundary layer. Agric. For. Meteorol. 54:107-136. (2) Collatz, G.J., Ribas-Carbo, M., and Berry, J.A. 1992. Coupled photosynthesis-stomatal conductance model for leaves of C plants. Aust. J. Plant Physiol. 19:519-538. (3) Gu, L. et al., (2003), Response of a deciduous forest to the Mount Pinatubo eruption: Enhanced photosynthesis. Science, 299: 2035-2038 5. Modeling Heterotrophic Respiration Respiration from litter and soil carbon pools represents a major carbon efflux from the ecosystems. It is primarily regulated by soil temperature and soil moisture. For given soil moisture conditions, and provided there is enough decomposable material, an increase in soil temperature almost invariably leads to an increase in microbial respiration rates due to increased activity of soil micro-organisms, although optimal temperatures for microbial activity are believed to reached between 35 and 45 degrees C. The dependency of microbial soil respiration rates on soil moisture is, however, not straightforward. Low soil moisture values (and the resulting high absolute values of soil matric potential) are known to constrain microbial activity and resulting microbial soil respiration. On the other hand, when the soils are saturated, then the lack of availability of oxygen to microbes restricts microbial activity and respiration rates. After climate, the primary control on litter and soil organic matter decomposition rates is exerted by litter quality which is usually expressed in terms of C:N or lignin:N ratios but these effects are not included in this simple model. We shall describe the heterotrophic respiration module developed as part of the Canadian Terrestrial Ecosystem Model in this section. This model has a daily time step and can be used in climate models. The following is based on Arora (2003). Heterotrophic respiration, Rh, is estimated as the sum of respiration from the litter (CD) and soil carbon (CH) pools, Rh = RhD + RhH . Respiration from the litter (RhD) and soil carbon (RhH) pools is estimated using specified respiration rates at 15C, the amount of carbon in these pools, a temperature dependent Q10 function (given below), and a soil moisture dependent factor.

!

RhD = "DCD f15(Q10) fD (#) ,

!

RhH = "HCH f15(Q10) f H (#) , where CD and CH are the amounts of carbon in litter (debris) and soil carbon (humus) pools (kg C/m2), and βD and βH are the specified vegetation-dependent respiration rates

16

(kg C/kg C/day) for the litter and soil carbon pools. The function f15(Q10) is a temperature dependent function given by

!

Q10(T"15)/10 where T in degrees C is the litter (TD) or soil

carbon (TH) temperature. The litter pool represents combined litter from the mortality of leaf, stem, and root components. Litter temperature is therefore modeled as the weighted average of soil temperature of the top layer and root temperature. Assuming the profiles of soil organic carbon and root distribution are fairly similar, the temperature of the soil carbon pool may be modeled as that of root temperature. The Q10 value used in the above equation is estimated as a function of temperature using the following expression

!

Q10 = exp[2.04(1"T /Topt )] where T in degrees C is the litter or soil carbon temperature. The function fH(ψ) represents the effect of soil moisture on microbial respiration rates from the soil carbon pool via soil matric potential ψ. Being a suction pressure soil matric potential is usually expressed as a negative value, but its absolute values are considered in the following text. Optimum soil moisture conditions are assumed to occur when soil matric potential lies between 0.04 and 0.06 MPa. Between 0.06 and 100 MPa the value of fH(ψ) is assumed to decrease linearly with the logarithm of matric potential, and when the soil matric potential is greater than 100 MPa, then microbial respiration is assumed to cease. Between 0.04 MPa and saturation matric potential (ψsat), the value of fH(ψ) is also assumed to decrease linearly with the logarithm of matric potential, and at saturation matric potential microbial respiration rate is assumed to be half of that when the soil moisture is optimum. Formally, the corresponding expression is,

!

f H (") =

1# 0.5log(0.04) # log"

log(0.04) # log"sat

, 0.04 >" $"sat

1, 0.06 $" $ 0.04

1#log" # log(0.06)

log(100) # log(0.06), 100.0 $" > 0.06

%

&

' '

(

' '

and fH(ψ) = 0 if ψ > 100. The soil matric potential is expressed as a function of soil moisture following

!

"(#) ="sat(# /#

sat)$c where ψsat and θsat (saturated soil mmoisture

content) and c are parameters related to soil type. The soil moisture factor for litter decomposition ([fD(ψ)] is similar to that for soil carbon [fH(ψ)] with the difference that soil moisture content of only top soil layer is used and litter decomposition rates are assumed not be constrained by high moisture content (and low absolute values of soil matric potential). The daily values of respiratory fluxes from the litter and soil organic matter pools are thus estimated on the basis of soil temperature and moisture for the three soil layers simulated by the land surface scheme and passed to the heterotrophic respiration sub-module. Recommended reading: (1) Arora, V.K., (2003). Simulating energy and carbon fluxes over winter wheat using coupled land surface and terrestrial ecosystem models, Agricultural and Forest Meteorology, 118(1-2), 21-47.

17

(2) Knorr, W. et al., (2005). Long-term sensitivity of soil carbon turnover to warming. Nature, 433: 298-301. Appendix 1. Example values for the constants in the production efficiency model

Biome class Parameter name ENF EBF DNF DBF MF WL WGL CSL OSL GL CL εmax 0.000908 0.0011 0.00110 0.0011 0.0010 0.00086 0.00076 0.00066 0.00066 0.0006 0.00076 Tmin_start 8.31 9.09 10.44 7.94 8.50 10.24 11.39 8.61 8.80 12.02 12.02 Tmin_stop -8.00 -8.00 -8.00 -8.00 -8.00 -8.00 -8.00 -8.00 -8.00 -8.00 -8.00 VPD_start 3100 3600 3100 3600 3600 5000 5000 4100 4100 5000 4100 VPD_stop 610 1100 610 1100 1100 1100 1100 970 970 1000 930 sla 16.1 20.3 28.0 32.2 21.5 30.0 30.0 18.0 12.0 40.0 40.0 q10_mr 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 froot_leaf_ratio 1.3 1.1 1.3 1.1 1.2 1.5 1.8 1.4 1.4 1.0 2.0 livewood_leaf_ratio 0.081 0.162 0.152 0.203 0.132 0.107 0.051 0.079 0.040 0.000 0.000 leaf_mr_base 0.00653 0.00604 0.00805 0.00778 0.00677 0.00824 0.00869 0.00519 0.00714 0.00908 0.0098 froot_mr_base 0.00519 0.00519 0.00519 0.00519 0.00519 0.00519 0.00519 0.00519 0.00519 0.00519 0.00619 livewood_mr_base 0.00322 0.00397 0.00297 0.00371 0.00372 0.00212 0.00100 0.00436 0.00218 0.00000 0.00000 leaf_gr_base 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 froot_leaf_gr_ratio 1.3 1.1 1.3 1.1 1.1 1.5 1.8 1.0 1.5 2.0 2.0 livewood_leaf_gr_ratio 0.16 0.20 0.15 0.19 0.19 0.11 0.05 0.22 0.11 0.0 0.0 deadwood_leaf_gr_ratio 1.6 1.1 1.5 1.6 1.8 1.0 0.5 0.0 0.0 0.0 0.0 ann_turnover_fraction 0.25 0.50 1.0 1.0 0.5 0.25 0.25 0.25 0.25 1.0 1.0

ENF = evergreen needleleaf forest, EBF = evergreen broadleaf forest, DNF = deciduous needleleaf forest, DBF = deciduous broadleaf forest, MF = mixed forest, WL = woodland, WGL = wooded grassland, CSL = closed shrubland, OSL = open shrubland, GL = grassland, CL = cropland