Ph.D. DISSERTATION
MODELING PLANT-SOIL-ATMOSPHERE CARBON DIOXIDE EXCHANGE
USING OPTIMALITY PRINCIPLES
BY
KEVIN TU
B.A. University of California at Santa Cruz, 1992
DISSERTATION
Submitted to the University of New Hampshire
in Partial Fulfillment of
the Requirements for the Degree of
Doctor of Philosophy
In
Natural Resources
May, 2000
APPROVAL PAGE
TABLE OF CONTENTS
ACKNOWLEDGEMENTS………………………………………………………………….….…vi
LIST OF TABLES…………………………………………………………………………….….vii
LIST OF FIGURES………………………………………………………………………………viii
ABSTRACT……………………………………………………………………….…………….…x
CHAPTER
PAGE
INTRODUCTION……………………………………………………………………………...…..1
I. A REVIEW OF REMOTE SENSING MODELS……………………………………...…..……7
Satellite Observations and Plant Productivity……………………………………………...………7
Remote Sensing Models…………………………………………………………………..………10
Photosynthesis and Primary Productivity…………………………………….……..……10
Respiration……………………………………………………………………..……...….11
II. SEASONALITY AND OPTIMALITY OF CANOPY PHOTOSYNTHETIC
CAPACITY: THEORY AND EVALUATION OF A GENERALIZED MODEL……….……...13
Introduction……………………………………………………………………………….…….....13
Objectives…………………………………………………………………………………..……..17
Datasets……………………………………………………………………………………………17
Observations of Canopy Photosynthetic Capacity and Optimum Temperature………….19
Model Theory……..……………………………………………………………………………....23
Model Equations……..………………………………………………………………….……...…24
Canopy Quantum Yield…………………………………………………………..….…...26
Temperature and Moisture Modifiers……………………………………………….....…27
Time Constant for Acclimation…………………………………………………...……...30
Results and Discussion………………………………………………………………………..…..32
iii
Conclusions…………………………………………………………………………….………….49
Appendix……………………………………………………………………………….…….……51
III. MODELING CARBON EXCHANGE IN TERRESTRIAL ECOSYSTEMS
USING LIGHT ABSOPRTANCE AND OPTIMALITY THEORY………….…………….……55
Introduction…………………………………………………………………………………..……55
Datasets and Methods………………………………………………………………….……..…...60
Model Description..……………………………………….……………………………….……...62
Canopy Photosynthetic Capacity…..…………………………………………….….…....62
Canopy Photosynthesis…………....……………………………………………….…......67
Canopy Quantum Yield……………………………………………….…….…...68
Temperature Effects………………………………...…………………..……….68
Stomatal Limitations……………….……………………………………...…….69
Plant Water Stress………………….………………………………………….…69
Net Ecosystem Productivity……………….……………………………………...……...71
Plant Respiration……………….……………………………………….....…….71
Soil Heterotrophic Respiration.…….…………………………………...……….75
Soil Moisture……………….…………………………………………...…….…78
Soil Temperature………………...…………………………………..….…….…78
Results and Discussion………...……………….………………………………………..….….…79
Canopy Photosynthesis..………...……………………………………………….…….…79
Diurnal Variation..……...……………….……….……….…………..………….79
Functional Responses....………………………..……….….…….…..….……....81
Accuracy..………...…………………………………….…..…….……....……...83
Importance of Photoacclimation…………………………………..……..……....87
Generality of the Model…………………………………………..…..……….…88
Net Ecosystem Productivity……………………………..….…………….…….……......88
iv
Soil Temperature…...……………………………………………….….……..…88
Soil Moisture……………………………………………………….…….……...92
Soil Heterotropic Respiration……………………………………….….……..…92
Diurnal Variation…………………………………………………..…….……....92
Accuracy and Generality………………………………………….…….…….....96
Cumulative Carbon Exchange……………………………….……………...….….……..99
Conclusions..……………………………………………………….……………………..….…..105
SYMBOLS AND ABBREVITIONS……………………………………………………….…...109
REFERENCES………………………………………………………………………...………...112
v
ACKNOWLEDGEMENTS
vi
LIST OF TABLES
Table 2.1 Canopy Photosynthetic Capacity Site Characteristics…………….……………….….18
Table 2.2 Methods for Estimating Canopy Light Absorptance.……………………………….…21
Table 2.3 Relationship Between Canopy Photosynthetic Capacity and Light………..……….…44
Table 2.4 Tuned Time Constants of Acclimation……..………………………………………....48
Table 3.1 Net Ecosystem Productivity Site Characteristics……………………………………...58
Table 3.2 Canopy Photosynthesis Model Equations..…………………………………………….66
Table 3.3 Net Ecosystem Productivity Model Equations………………………………………...72
Table 3.4 Time Invariant Parameter Values……………………………………………………...85
Table 3.5 Comparison of With- and Without-Acclimation Model Predictions…………………..86
Table 3.6 Calibrated Site-Specific Model Parameters……………………………………………89
Table 3.7 Observed Soil Heterotrophic Respiration Models……………………………………..94
Table 3.8 Relationship Between Modeled and Observed NEE and GEE………………………...98
Table 3.9 Modeled and Observed Cumulative Fluxes………………………….…………….....103
vii
LIST OF FIGURES
Figure 1 Overview of Relationships Examined………………………………....……...….……....4
Figure 2.1 Climatological Distribution of Photosynthetic Capacity Study Sites..………………..20
Figure 2.2 Functional Relationships of the Photosynthetic Capacity Model …………………….25
Figure 2.3 Interrelationships Among Soil, Plant, and Atmospheric Moisture..………….……….29
Figure 2.4 Running Means of Light and Temperature.………………………………….……….33
Figure 2.5 Predicted Versus Observed Temperature Optima…………...…………………….….35
Figure 2.6 Seasonality of Predicted and Observed Plant Water Status…………………………..36
Figure 2.7 Seasonality of Predicted and Observed Canopy Photosynthetic Capacity..…….…….37
Figure 2.8 Predicted Versus Observed Canopy Photosynthetic Capacity..…..…………….…….39
Figure 2.9 Canopy Photosynthetic Capacity Versus Light Absorption.……………………….…43
Figure 2.10 Canopy Photosynthetic Capacity Versus Temperature.….………………………….46
Figure 2.11 Sensitivity of the Model to the Time Constant……….………….……………….….47
Figure A.1 NDVI and Canopy Light Interceptance and Absorptance……………………………52
Figure 3.1 Climatological Distribution of Study Sites………………………...………………….59
Figure 3.2 Net Ecosystem CO2 Exchange Measurements…...…………………….…….……….61
Figure 3.3 Model Flow and Organization…………………….………………………….……….63
Figure 3.4 Model Functional Relationships..…………………………………………….……….65
Figure 3.5 Overview of Moisture Calculations.………….……………………………………….70
Figure 3.6 Overview of Soil Heterotrophic Respiration Calculations…..……………….……….77
Figure 3.7 Diurnal Variation in Modeled and Observed Gross Ecosystem Exchange..………….80
Figure 3.8 Modeled and Observed Photosynthetic Light Response.……………………….…….82
Figure 3.9 Modeled Versus Observed Gross Ecosystem Exchange…………………….……….84
Figure 3.10 Seasonality of Modeled and Observed Soil Temperature..…………………………90
Figure 3.11 Seasonality of Modeled and Observed Soil Moisture.………………………………91
viii
Figure 3.12 Seasonality of Modeled and Observed Soil Heterotrophic Respiration..……………93
Figure 3.13 Diel Variation of Modeled and Observed Net CO2 Exchange………………………95
Figure 3.14 Modeled Versus Observed Net CO2 Exchange……………………...………………97
Figure 3.15 Time Course of Cumulative Carbon Fluxes..………………………………………100
Figure 3.16 Modeled Versus Observed Cumulative Carbon Fluxes……………………………101
Figure 3.17 Cumulative Ecosystem Respiration Versus Cumulative Photosynthesis…………..104
ix
ABSTRACT
The exchange of carbon dioxide (CO2) between terrestrial ecosystems and the atmosphere
plays a central role in the ecology of the biosphere and the climate system. A generalized model
of plant-soil-atmosphere CO2 exchange was described and evaluated using eddy covariance
measurements of net ecosystem exchange of CO2 (NEE) in arctic, boreal, temperate, and tropical
landscapes. The model requires no calibration and is based on theories of plant resource
optimization and plant-soil nutrient feedbacks and predicts canopy photosynthetic capacity
(Pcmax), canopy photosynthesis (Pc), plant respiration (Rp ), and soil heterotrophic respiration (RH)
The model can be applied globally using satellite-derived estimates of canopy light absorptance
(fAPAR), incident radiation (PAR), and air temperature (Tair). It provides the means by which to
relate satellite observations such as the Normalized Difference Vegetation Index (NDVI) to the
physiological status of vegetation and carbon exchange.
A unique aspect of the model is its use of a recursive filter for calculating photosynthetic
acclimation based on the integrated effect of environmental conditions. Good agreement was
found between modeled and observed Pcmax (r2=0.76), the latter derived from light response
curves fit to estimates of gross ecosystem exchange (GEE). Consistent with theories of resource
optimization, Pcmax varied strongly with time-averaged absorbed PAR and temperature.
Modeled Pcmax combined with a 'big-leaf' canopy model explained 74 to 85% of the
variability in GEE. The photo-acclimation model not only performed better than a traditional
time-invariant model and as good or better than calibrated site-specific models, it did not require
knowledge of vegetation type. The process of photo-acclimation appeared most important during
periods of greatest transition in plant physiological status (e.g. spring and fall).
Agreement between modeled and observed NEE (r2=0.66 to 0.81) was very similar to
that for GEE, implying little additional error was introduced by predictions of Rp and RH. Despite
excellent agreement between modeled and observed cumulative photosynthesis (r2=0.98) and
ecosystem respiration (Rp +RH) (r2=0.99), the agreement for NEE was not as good (r2=0.75), due
in part to NEE being the small difference between the two much larger fluxes of photosynthesis
and ecosystem respiration.
x
INTRODUCTION
Quantifying the exchange of carbon dioxide (CO2) between terrestrial ecosystems and the
atmosphere is central to understanding the ecology of the biosphere and its influence on global
biogeochemical cycles and the climate system. Photosynthetic fixation of CO2 provides the energy that
ultimately sustains the metabolism of all organisms and drives the exchange of materials and energy with
the atmosphere (Mooney et al. 1987). This fixation combined with the release of CO2 during respiration
by plants and soil microbes drives seasonal changes in the concentration of atmospheric CO2 (Keeling
1983). CO2 is an important greenhouse gas which influences both the physics and chemistry of the
atmosphere. Its current rise of about 1.8 ppmv per year (0.5%) may have profound effects on global
climate (IPCC). This in turn may adversely affect ecosystems of considerable environmental and
economic value (Costanza et al 1997).
The increase in CO2 during the last 150 years (Keeling 1986) from pre-industrial concentrations
around 280 ppmv to its current level of about 360 ppmv is largely due to anthropogenic activities such as
fossil fuel burning and deforestation (IPCC 1990). Spatial and temporal gradients in atmospheric CO2
concentrations (Tans et al. 1990, Fan et al. 1998),
13
C/12C isotope ratios (Ciais et al. 1995), and O2/N2
ratios (Bender et al. 1996, R. Keeling et al. 1996) suggest that terrestrial ecosystems at mid-latitudes of
the Northern Hemisphere sequester much of this CO2.
Eddy covariance measurements (Baldocchi et al. 1988) of net ecosystem CO2 exchange (NEE)
indicate that many tropical, temperate and boreal forests act as net CO2 sinks (Grace et al. 1996, Greco
and Baldocchi 1996, Goulden et al. 1996, Baldocchi et al. 1997, Hollinger et al. 1998) while others act as
net CO2 sources (Goulden et al. 1998, Lindroth et al. 1998). Biomass inventories suggest modest net
carbon uptake by forests (Kauppi et al. 1992, Birdsey et al. 1993, Kolchugina and Vinson 1993, Apps and
Kurz 1994, Dixon et al. 1994, Houghton 1996, Phillips et al. 1998), while field measurements (Goulden
et al. 1996), satellite observations (Myneni et al. 1997a), and modeling analyses (Randerson et al 1997)
indicate increased growing season length at northern latitudes -- consistent with the recent increase in
1
amplitude of the seasonal cycle of atmospheric CO2 (Keeling 1983).
Atmospheric CO2 monitoring and biomass inventories provide only indirect measures of net CO2
flux from ecosystems and vegetation. Theoretical and logistical considerations limit the use of eddy
covariance to select sites. These essentially “point measurements” may not be characteristic of entire
biomes (Keller et al. 1996, Houghton 1997). Alternative methods such as satellite remote sensing are
needed to better quantify the spatial and temporal patterns of ecosystem-atmosphere CO2 exchange at
regional to global scales.
Satellite remote sensing offers unequaled potential for synoptic monitoring of biosphere
functioning with global coverage, near-continuous data acquisition, and consistent instrumentation
(Hobbs and Mooney 1990, Matson and Ustin 1991). Satellite observations have proven useful for
monitoring inter-annual vegetation activity (Myneni et al. 1998), the effects of land use change (Skole
and Tucker 1993) and climate-biosphere interactions related to El Niño events (Myneni et al. 1996,
Anyamba and Eastman 1996). Direct measurement, however, of net ecosystem CO2 exchange is not
possible with satellite sensors. Satellites have the potential of providing information on the fraction of
incoming photosynthetically active radiation (PAR) absorbed by vegetation (FPAR) (Goward and
Huemmrich 1992), incident radiation (PAR) (Eck and Dye 1991), surface temperature (Vazquez et al.
1997), near-surface (Prihodko and Goward 1997) and tropospheric air temperature (Spencer and Christy
1990), and atmospheric humidity (Ottle et al. 1997).
Remote sensing of ecosystem-atmosphere CO2 exchange requires the use of models that relate
these variables to rates of photosynthesis and respiration. The challenge remains to develop models that
can provide estimates of land surface CO2 exchange comparable to those obtained by ground-based eddy
covariance (Baldocchi et al. 1996, Ruimy et al. 1996b). The principle limitation to meeting this challenge
is the inability to remotely sense the physiological status of plants and soil microbes. Current models
prescribe plant and soil characteristics from prior knowledge of the site in question or by applying
generalized biome-specific values using vegetation maps.
A growing body of evidence suggest that parameter estimation may be greatly facilitated and
2
simplified by exploiting the fact that plants generally adapt and acclimate to their local environment to the
extent that their physiological potential varies in parallel with the availability of resources (Figure 1).
Such behavior is often well explained by optimality theory. Optimality theory is widely used in plant
ecophysiology to generate and test hypotheses of plant form and function (Givnish 1986). As early as
1881, Greenhill employed optimality arguments to predict maximal tree height as a function of stem
diameter with an analytical solution expressing the trade-off between height growth and stem stability.
Observations have since confirmed Greenhill’s basic hypotheses (McMahon 1973) indicating the
potential of optimality theory to describe the behavior of real plants.
More recently, optimality theory has been used to advance theories of water (E) and nitrogen (N)
use in relation to leaf net CO2 assimilation (A) (Cowan 1977, Cowan and Farquhar 1977, Field 1983,
Field and Mooney 1986). Cowan (1977) predicted the optimal stomatal conductance (g) for a given rate
of photosynthesis (A) occurs when the marginal water cost of carbon gain (∂E/∂A) is constant and
transpirational water loss (E) is minimized. Although the absolute value of ∂E/∂A differs among plants,
observations indicate that ∂E/∂A does in fact remain relatively constant (Givnish 1986b). Further, A and g
generally vary in proportion to each other under unstressed conditions (e.g.Wong et al. 1979, Schulze and
Hall 1982) consistent with the maintenance of constant ∂E/∂A through stomatal regulation.
Optimality arguments have been criticized as being “teleonomic” because they assume a
purposeful behavior of a plant towards some goal (e.g. maximizing carbon gain) which is achieved
through some unspecified mechanism (Monod 1972). However, the assumption of maximizing carbon
gain is clearly valid because it bestows a competitive advantage for limited resources and increases
selective fitness (Mooney and Gulmon 1979). Furthermore, optimality assumptions often provide
practical solutions to complex problems, without which, a great deal more information would be required
to develop “objective” models with fewer unsubstantiated a priori arguments. Objective models such as
transport-resistance models (e.g. Thornley 1972) have been developed but are difficult to parameterize
such that simpler more “subjective” optimality models are often the best, if not only, model of choice.
3
Figure 1. Relationships among plant carbon gain (CO2 uptake), environmental limitations (light and
temperature), availability of resources (nitrogen and water), and satellite remote sensing that form the
basis of the optimality arguments explored in this study.
4
Recent advances in understanding how photosynthetic capacity varies within leaves and canopies
(Field 1983, Gutschick and Wiegel 1988, Farquhar 1989, Terashima and Hikosaka 1995) in relation to
light availability has led to generalized theories of acclimation and resource optimization. Field (1983)
predicted the optimal distribution of nitrogen among leaves that maximizes canopy photosynthesis occurs
when the marginal increase in A with respect to N (∂A/∂N) is constant throughout the canopy. This
implies that because light availability decreases exponentially with depth in a canopy so must potential
rates of photosynthesis (Pmax∝PAR) and by extension, so must leaf nitrogen (N∝PAR). Observations
support this hypothesis in that vertical profiles of photosynthetic capacity and nitrogen generally parallel
vertical gradients of light availability (e.g. Field 1983, Hirose and Werger 1987, DeJong and Doyle 1985,
Hollinger 1989, Ellsworth and Reich 1993). Sellers et al. (1992) demonstrated how such theories of light
acclimation and nitrogen distribution can be exploited to greatly simplify the integration of canopy
photosynthesis. Recent analyses suggest that these same principles can be further extended to the timedependence of photosynthetic capacity and can be exploited to simplify the prediction of Pmax over the
growing season (Takenaka 1989, Johnson et al. 1995, Haxeltine and Prentice 1996a).
Acclimation to the prevailing growth conditions allows plants to maintain optimal photosynthetic
and resources use efficiency (Arnon 1982, Anderson et al. 1995). This strategy maximizes evolutionary
fitness by ensuring optimal use of the environment and a competitive advantage for limited resources
(Bloom et al. 1985). Field (1991) summarized these concepts on the economy of resource use and carbon
gain first introduced by Mooney and Gulmon (1979) with the “functional convergence hypothesis”:
biochemical capacity for CO2 fixation should be curtailed whenever a limitation in the availability of any
resource prevents the efficient exploitation of additional capacity. That is, plants predictably function with
optimal efficiency in a given environment.
Other studies have shown that similar theories of acclimation and resource optimization applied
at the level of the whole plant can be used to predict maximum rates of net primary productivity (NPP)
and minimum rates of plant respiration (Rp ) (Dewar 1996). Further, numerous studies indicate there are
feedbacks between the nutrient status of plants and soils involving plant uptake, litterfall, and microbial
decomposition and mineralization (Vitousek 1982, Reed 1990, Woodward and Smith 1994). Eventual
5
accommodation between these processes provides simplifying constraints to the estimation of rates of
decomposition and soil respiration (RH).
These theories have the potential to greatly simplify parameter estimation in ecosystem models
and may prove to be particularly useful when applied with remote sensing observations. The overall
theme of this study is the application and evaluation of resource optimization constraints on the
estimation of canopy photosynthetic capacity, gross photosynthesis, and respiration by plants and soil
microbes within the framework of a generalized model of plant-soil-atmosphere CO2 exchange.
6
CHAPTER I
A REVIEW OF REMOTE SENSING MODELS
Satellite Observations and Plant Productivity
Kumar and Monteith (1981) first noted that the cumulative net CO2 uptake by a crop stand could
be estimated from above canopy measurements of visible (rVIS) and near-infrared (rNIR) reflectance in the
form of vegetation indices such as the normalized difference vegetation index:
NDVI=(rNIR-rVIS)/(rNIR+rVIS)
(1.1)
This extended previous studies relating crop growth with intercepted radiation (Warren-Wilson 1967,
Monteith 1972; 1977), radiation interception with canopy leaf area index (LAI) (Monsi and Saeki 1953),
and LAI with canopy reflectance and transmittance (Allen and Richardson 1968). Strong relationships
have since been demonstrated between NDVI and photosynthesis (Running et al. 1988), net primary
productivity (Box et al. 1989, Tucker et al. 1981, Tucker et al. 1985, Goward et al. 1985; 1987, Diallo et
al. 1991, Prince 1991b, Wylie et al. 1991, Lo Seen Chong et al. 1993), and net ecosystem CO2 exchange
(Tucker et al. 1986, Fung et al. 1987, Box et al. 1989). Further, a large body of empirical and theoretical
evidence supports the use of vegetation indices such as NDVI for the estimation of FPAR (Hipps et al.
1983, Asrar et al. 1984, Hatfield et al. 1984, Gallo et al. 1985, Sellers 1985, Baret and Olioso 1989,
Bartlett et al. 1990, Hall et al. 1990, Leon 1991, Wiegand 1991, Asrar et al. 1992, Demetriades-Shah
1992, Goward and Huemmrich 1992, Goward et al. 1994c, Law and Waring 1994, Myneni et al. 1994,
Strebel et al. 1994, Gamon et al. 1995, Hanan et al. 1996, Myneni et al. 1997b).
The underlying mechanism for these relationships is both biophysical and ecological in nature. In
theory, NDVI varies between 0 and 1 for vegetated surfaces, with desert values near zero and those for
tropical forests near one. Near-infrared reflectance is most sensitive to the amount of leaf area while
visible reflectance is most sensitive to chlorophyll content (Gates 1965, Knipling 1970, Gausman and
Allen 1973), therefore, vegetation indices can be used to gauge the relative amount of green
photosynthetically active vegetation (Goward 1989). Both NDVI and FPAR integrate the effects of the
7
leaf quantity (LAI) and leaf quality (chlorophyll) (Allen and Richardson 1968, Goward et al. 1994) such
that the relationship between the two is robust (Goward and Huemmrich 1992, Sellers 1985). On the other
hand, relationships between NDVI and biomass, LAI, or canopy chlorophyll or nitrogen content are
problematic (Plummer 1988, Wessman et al. 1988, Matson et al. 1994, Yoder and Waring 1994, Hall et
al. 1995).
Sellers (1985) elaborated on the work of Monteith (1977) to show that for a range of canopy
structures, photosynthetic capacity should be near-linearly related to NDVI because the response of both
canopy photosynthesis and NDVI saturate with respect to LAI. This result provides a biophysical
constraint on the observed correlation between NDVI and carbon gain and implies that NDVI should be
near-linearly related to the change in photosynthesis (P) with respect to the change in incident
photosynthetically active radiation (NDVI ∝ ∂P/∂PAR) (Sellers 1987). A bare soil surface will exhibit no
“photosynthetic” sensitivity to a change in PAR while a fully vegetated surface will exhibit strong
sensitivity (Verma et al. 1993). Verma et al. (1993) tested this hypothesis using canopy scale
measurements of CO2 exchange and aircraft based measurements of canopy reflectance and found general
agreement between the simple ratio (SR = rNIR/rVIS) and ∂P/∂PAR for a tallgrass prairie (note SR =
[NDVI+1]/[1-NDVI]). This is consistent with the ecological interpretation that plant investment in light
energy capture (i.e. NDVI) parallels changes in the capacity to utilize light for photosynthesis (i.e.
∂P/∂PAR) (Field 1991).
Field (1991) argues that all plants face the similar challenge of maximizing carbon gain and
resource use efficiency in their respective environments and that natural selection has favored individuals
who regulate investment in leaf area, chlorophyll, and light energy capture in general, to levels that
maximize net primary productivity. Accordingly, chronic stress typically causes parallel reductions in leaf
area and carbon gain such that NDVI or FPAR generally integrate the effects of low nutrient availability
and soil drought (e.g. Squire et al. 1986). The overall effect is conservative variation between the amount
of radiation absorbed (APAR) and NPP (Field 1991). The intrinsic link between absorbed radiation and
photosynthesis combined with the fact that NDVI can be obtained from satellite sensors underlies the use
of NDVI as a general global index of plant carbon gain (Sellers 1985, Field et al. 1994).
8
Monteith (1977) observed conservative variation in the relationship between NPP and APAR for
crops grown under ideal conditions. Studies have since shown that this relationship varies with vegetation
type and environmental conditions (Sivakumar and Virmani 1984, Russell et al. 1989, Prince 1991a,
Ruimy et al. 1994). It is affected by numerous factors such as temperature (Jarvis and Leverenz 1983,
Squire et al. 1984, Olioso 1987, Mohamed et al. 1988), water availability (Green et al. 1985, Linder 1985,
Munchow 1985, Byrne et al. 1986, Squire et al. 1986), nutrition (Green 1987, Steven and DemetriadesShah 1987), soils (Allen and Scott 1980), canopy architecture (Heath and Hebblethwaite 1985),
phenological development (Jarvis and Leverenz 1983, Marshall and Willey 1983, Gosse et al. 1986,
Green 1987, Olioso 1987, Garcia et al. 1988, Russell and Ellis 1988, Tollenaar and Bruulsema 1988),
photosynthetic pathway (Bonhomme et al. 1982), and ozone exposure (Unsworth et al. 1984).
The ratio of NPP to APAR also varies as a function of age and growth form (Penning de Vries
1972, Hunt 1994, Ruimy et al. 1996b, Goetz and Prince 1998a, 1998b). As plants age and accumulate dry
matter, NPP generally decreases as maintenance respiratory costs increase (Hunt 1994). Further, different
species and plant functional types generally have different respiratory costs owing to different allocation
strategies among roots, shoots, and leaves (e.g. Ruimy et al. 1996b).
The sensitivity of the NPP/APAR ratio to these various conditions is consistent with the
hypothesis that APAR is intrinsically related to potential gross phtosynthesis (photosynthetic capacity)
rather than actual photosynthesis or NPP (Sellers 1985; 1987, Field 1991, Prince 1991a, Ruimy et al.
1996b, Goetz and Prince 1998a). Accordingly, relationships between net ecosystem CO2 exchange and
APAR or NDVI are typically site specific and seasonally variable (Bartlett et al. 1990, Whiting et al.
1992, Cihlar et al. 1992, Whiting 1994, Ogunjemiyo et al. 1997). Bartlett et al. (1990) concluded that
quantitative assessment of ecosystem-atmosphere CO2
exchange using spectral reflectance requires
knowledge on plant and soil responses to environmental factors which can reduce photosynthesis below
its maximum unstressed rate and decouple photosynthesis from plant and soil respiration.
9
Remote Sensing Models
Photosynthesis and Primary Productivity. Numerous models have been developed that relate
spectral reflectance to canopy photosynthesis (Pc), net primary productivity (NPP), and net ecosystem
CO2 exchange (NEE) under various environmental conditions. These models range in complexity from
empirically based “Production Efficiency Models” (PEM) (Prince 1991a) to more detailed biochemically
based models (e.g. Sellers et al. 1996). Both types of models are difficult to validate at regional to global
scales. However, gas exchange measurements at the ecosystem level are becoming more common
(Baldocchi et al. 1996). These datasets have proven useful for testing ecosystem models driven by remote
sensing observations (Gao 1994, Waring et al. 1995, Ruimy et al. 1996b, Colello et al. 1998).
Production efficiency models (Heimann and Keeling 1989, Potter 1993, Ruimy et al. 1994,
Maisongrande et al. 1995 Prince and Goward 1995, Waring et al. 1995) are based on process based
growth models used extensively in agriculture and forestry (Monteith 1972; 1977, Gallagher and Biscoe
1978, Warren-Wilson 1981, Jarvis and Leverenz 1983, Steven et al. 1983, Gallo et al. 1985, Linder 1985,
Charles-Edwards et al. 1986, Landsberg 1986, Kirschbaum et al. 1994, Landsberg and Waring
1997).These models operate in a multiplicative manner:
NPP = ε n ∑ APAR fT fD fW...
(1.2)
where ε n is the dry matter:radiation quotient (∆NPP/∆APAR), APAR is the absorbed photosynthetically
active radiation, and fT ,fD, and fW are multipliers (0<fx<1) that account for the effects of various
environmental factors such as air temperature, leaf-to-air vapor pressure difference, soil water, and so on.
The dry matter:radiation quotient is equivalent to the so-called radiation use efficiency or light use
efficiency (LUE) despite the fact that efficiencies range in value from 0 to 1. Recent applications have
replaced ε n with ε g, the dry-matter yield of APAR in gross primary production (GPP), because of
significant variation in the ratio of respiration to gross production (Prince 1991a), although several recent
analyses suggest that respiration is a conservative fraction (~0.5) of GPP (Ryan 1991, Gifford 1994,
Waring et al. 1998).
10
One drawback to PEMs is that they operate at a daily or longer time step which precludes their
use for evaluating diurnal variations in gas exchange or their incorporation into high temporal resolution
general circulation models (GCM) (e.g. Sellers et al. 1996). An additional limitation to PEMs is that they
must be calibrated for wide range of species or ecosystems representative of global vegetation. Numerous
parameters for many ecosystems are unknown and must be arbitrarily prescribed.
Models based on the instantaneous response of photosynthesis to environmental conditions
(Goward and Dye 1987, Running et al.1989, Lüdeke et al. 1991, Hunt et al. 1996), including those based
on the biochemistry of photosynthesis (Gao 1994, Warnant et al. 1994, Myneni et al. 1995, Sellers et al.
1996, Colello et al. 1998), represent carbon gain and respiration in a more physiologically realistic
manner. Biochemically based models of photosynthesis (e.g. Farquhar et al. 1980, Collatz et al. 1991;
1992) theoretically apply to all plants with similar photosynthetic pathways (i.e. C3 or C4). In their
simplest and most generalized form, models that couple stomatal conductance with photosynthesis (e.g.
Collatz et al. 1991, 1992) require only a few critical parameters, such as the carboxylation capacity (Vcmax)
of ribulose bisphosphate carboxylase-oxygenase (Rubisco), the quantum yield at limiting light levels (α),
and Topt , the temperature optimum for photosynthesis. Carboxylation capacity and the quantum yield
define the initial slope and the light-saturated rate or asymptote of the photosynthetic light response curve.
In simpler treatments, the carboxylation capacity may be represented by the light-saturated rate of
photosynthesis, Pmax. Estimation of Pmax. α, and Topt , is recognized as the major constraint to the global
application of process-based models of photosynthesis (Wullschleger 1993, Warnant et al. 1994, Hanan
1997, Dang et al. 1998, Colello et al. 1998).
Respiration. Respiration, both above and below ground is difficult to estimate with remote
sensing models. Plant respiration is typically subsumed within the dry matter:radiation quotient (ε n),
estimated as a fraction of GPP (Goward and Dye 1987, Landsberg and Waring 1997), or modeled based
on vegetation type (Ruimy et al. 1996a). Prince and Goward (1995) used an empirical relationship
between biomass and maintenance respiration following Hunt (1994), where biomass was estimated from
satellite-derived visible reflectance (rVIS). As noted by Prince and Goward (1995), this approach requires
further evaluation.
11
Soil heterotrophic respiration is similarly difficult to estimate given the inability to remotely
sense soil conditions. Most models that predict net ecosystem CO2 exchange (NEE) or its equivalent, net
ecosystem productivity (NEP = NPP - RH) estimate soil heterotrophic respiration using a standard “Q10"
type function (Fung et al. 1987, Ludeke et al. 1991, Knorr and Heimann 1995, Maisongrande et al. 1995):
RH = Rref Q10(T-Tref)/10
(1.3)
where RH is the respiration rate, Rref is the respiration rate at the reference temperature Tref, T is the
ambient temperature, and Q10 is the ratio of the rate at Tref to that at Tref ±10 degrees (Jones 1983).
Recognizing that Rref is site specific but lacking satellite-based methods for sensing soil conditions, Rref is
typically estimated with the constraint that annual soil respiration equals annual NPP (NEP = 0). This
assumption precludes the detection of carbon sequestration and is not consistent with recent findings
indicating that many ecosystems act as net carbon sinks (e.g. Goulden et al. 1996, Grace et al. 1996,
Greco and Baldocchi 1996, Hollinger et al. 1999) and others act as net carbon sources (e.g. Goulden et al.
1998, Lindroth et al. 1998). Models that do not assume annual zero net carbon exchange (e.g. Potter et al.
1993, Hunt et al. 1996) explicitly model soil respiration using simplified versions of the CENTURY
model (Parton et al. 1987) or use functions calibrated to specific sites (Veroustraete et al. 1996, Gao 1994,
Colello et al. 1998). Application of either approach requires parameters that cannot be remotely sensed
such as the carbon and nitrogen content of the soil and litter as well as soil texture, temperature, and
moisture.
12
CHAPTER II
SEASONALITY AND OPTIMALITY OF CANOPY PHOTOSYNTHETIC CAPACITY:
THEORY AND EVALUATION OF A GENERALIZED MODEL
Introduction
The exchange of carbon dioxide (CO2) between terrestrial ecosystems and the atmosphere is
central to the ecology of the biosphere and its influence on global biogeochemical cycles and the climate
system. Photosynthetic fixation removes ~15% of the CO2 in the atmosphere each year (Williams et al.
1997) and combined with the release of CO2 during respiration by plants and soil microbes,
photosynthesis drives seasonal changes in atmospheric CO2 concentrations (Keeling 1983). However,
seasonal and interannual variations in net terrestrial uptake (photosynthesis minus respiration) is uncertain
and difficult to quantify.
Spatial and temporal gradients in atmospheric CO2 concentrations (Tans et al. 1990, Fan et al.
1998),
13
C/12C isotope ratios (Ciais et al. 1995), and O2/N2 ratios (Bender et al. 1996, R. Keeling et al.
1996) provide indirect evidence for a strong terrestrial sink at mid-latitudes of the Northern Hemisphere.
Direct measurement of net ecosystem CO2 exchange (NEE) by eddy covariance (Baldocchi et al. 1988)
generally support these findings and indicate that many tropical, temperate and boreal forests act as net
CO2 sinks (Grace et al. 1996, Greco and Baldocchi 1996, Goulden et al. 1996, Baldocchi et al. 1997,
Hollinger et al. 1998) while others act as net CO2 sources (Goulden et al. 1998, Lindroth et al. 1998).
Biomass inventories suggest modest net carbon uptake by forests (Kauppi et al. 1992, Birdsey et al. 1993,
Kolchugina and Vinson 1993, Apps and Kurz 1994, Dixon et al. 1994, Houghton 1996, Phillips et al.
1998), while field measurements (Goulden et al. 1996), satellite observations (Myneni et al. 1997a), and
modeling analyses (Randerson et al 1997) indicate increased growing season length at northern latitudes - consistent with the recent increase in amplitude of the seasonal cycle of atmospheric CO2 (Keeling
1983).
13
Atmospheric CO2 monitoring and biomass inventories provide only indirect measures of net CO2
flux from ecosystems and vegetation while theoretical and logistical considerations limit the use of eddy
covariance to select locations. Satellite remote sensing, on the other hand, offers unequaled potential for
synoptic monitoring of biosphere functioning with global coverage, near-continuous data acquisition, and
consistent instrumentation (Hobbs and Mooney 1990, Matson and Ustin 1991).
Although satellite observations have proven useful for monitoring inter-annual vegetation activity
(Myneni et al. 1998), the effects of land use change (Skole and Tucker 1993) and climate-biosphere
interactions related to El Niño events (Myneni et al. 1996, Anyamba and Eastman 1996), direct
measurement of net ecosystem CO2 exchange is not possible. Recent advances have made it possible to
derive estimates of many surface characteristics crucial to terrestrial ecosystem functioning including
incident photosynthetically active radiation (PAR) (Eck and Dye 1991), the fraction of incoming PAR
absorbed by vegetation (FPAR) (Goward and Huemmrich 1992), surface temperature (Vazquez et al.
1997), near-surface air temperature (Prihodko and Goward 1997), atmospheric humidity (Ottle et al.
1997), and functional vegetation type (Nemani et al. 1997).
The challenge remains to develop models that can relate these variables to estimates of net
ecosystem CO2 exchange comparable to those obtained by ground-based eddy covariance (Baldocchi et
al. 1996, Ruimy et al. 1996b). With respect to photosynthesis, the principle limitation to meeting this
challenge is the inability to remotely sense the physiological status of plants. Photosynthetic capacity
(Pmax) and its optimum temperature (Topt ) are typically prescribed in ecosystem models solely on the basis
of ecosystem type. This approach not only relies on the accuracy of global ecosystem classifications, of
which intercomparisons have revealed large discrepancies (Defries and Townsend 1994), but also
assumes seasonally invariant physiological status despite the long recognized physiological plasticity of
most plants (Larcher 1969, Bjorkman 1981, Pearcy and Sims 1994).
Seasonal variation in photosynthetic capacity of leaves is well established (e.g. Heinicke and
Childers 1937, Saeki and Nomoto 1958, Bourdeau 1959, Davis et al. 1963, Helms 1965, Shiroya et al.
1966, Gordon and Larson 1968, Connor et al. 1971, Logan 1971, Hanson et al. 1994, Garcia-Plazoalo et
14
al. 1997, Murthy et al. 1997, Tezara et al. 1998), as is the seasonal variation in the photosynthetic
temperature optimum (Schulze et al. 1976, Berry and Bjorkman 1980, Hikosaka 1997). Variation in
photosynthetic capacity results from shifts in foliar biochemistry and anatomy that occur in response to a
change in growth conditions (e.g. Woledge 1971, Boardman 1977, Berry and Bjorkman 1982, Leverenz
and Jarvis 1980, Bjorkman 1981, Badger et al. 1982, Oquist and Martin 1986, Anderson and Osmond
1987, Sims and Pearcy 1992, Sims et al. 1998). These responses involve changes in either leaf thickness,
affecting the quantity of photosynthetic tissue per unit leaf area, or photosynthetic enzyme concentration,
affecting the photosynthetic capacity per unit leaf volume (Pearcy and Sims 1994, Sims et al. 1998).
Temperature optima are thought to shift due to reduced enzyme activity at lower temperatures,
the relative amount of various enzymes, each with a characteristic temperature optimum, and nitrogen
partitioning between chlorophyll and ribulose bisphosphate carboxlyase-oxygenase (Rubisco) (Hikosaka
1997). At the canopy scale, the variation in Pmax and Topt are less understood but crucial to the
understanding and prediction of terrestrial photosynthesis.
A growing body of evidence indicates that parameter estimation may be greatly facilitated and
simplified by exploiting the fact that plants generally adapt and acclimate to their local environment to the
extent that their physiological potential varies in parallel with the availability of resources. Such behavior
is often well explained by optimality theory. Field (1983) hypothesized that the optimal distribution of
nitrogen among leaves is that which maximizes canopy photosynthesis and occurs when the marginal
increase in A with respect to N is constant throughout the canopy (∂A/∂N=λ). This implies that because
light availability decreases exponentially with depth in a canopy so must potential rates of both
photosynthesis (Pmax∝PAR) and nitrogen (N∝PAR).
Observations support this hypothesis in that vertical profiles of photosynthetic capacity and
nitrogen generally parallel vertical gradients of light availability (e.g. Field 1983, Hirose and Werger
1987, DeJong and Doyle 1985, Hollinger 1989, Ellsworth and Reich 1993). Subsequent studies have
employed theories of resource optimization to describe and predict the depth-distribution of nitrogen and
15
photosynthetic capacity that results from spatial variation in light availability within natural canopies
(Hirose et al. 1988, Terashima and Evans 1988, Pons et al. 1989, Schieving et al. 1992, Evans 1993,
Hikosaka and Terashima 1995, Sands 1995, Hollinger 1996, Dang et al. 1997).
Based on these observations, Sellers et al. (1992) demonstrated that theories of acclimation can be
exploited to simplify the integration of canopy photosynthesis. Recognizing that these same principles
can be further extended to the time-dependence of photosynthetic capacity, Haxeltine and Prentice (1996)
predicted seasonal patterns of canopy photosynthetic capacity that result from similar, albeit temporal,
variations in light availability that occur throughout the growing season.
A drawback to optimality arguments is that they can be criticized as ‘teleonomic’ because they
assume a purposeful behavior of a plant towards some goal (e.g. maximizing carbon gain) that is achieved
through unspecified or unknown mechanisms (Monod 1972). For example, optimal photosynthetic
capacity can be estimated as the value which provides maximum net assimilation (P - Rd) in a given light
environment (Takenaka 1989, Johnson et al. 1995, Haxeltine and Prentice 1996a). Both leaf respiration
(Merino et al. 1982) and photosynthetic capacity (Field and Mooney 1986) increase with leaf nitrogen,
however respiration generally increases linearly while capacity increases non-linearly and eventually
saturates. While maximizing carbon gain clearly bestows a competitive advantage for limited resources
and increases selective fitness (Mooney and Gulmon 1979), assuming carbon gain is maximized without
considering the limitations related to how it is maximized can only be approximately correct.
A better approach would be to include, in addition to the leaf respiration costs already considered,
the costs of such factors as leaf construction and nutrient allocation (Mooney and Gulmon 1979,
Hollinger 1996). Chen et al. (1993) proposed “coordination theory” as an alternative approach which
indirectly addresses such costs associated with resource allocation. In contrast to simpler optimality
models that are constrained by the condition of maximizing carbon gain without considering the “costs”
associated with the underlying mechanisms (i.e. allocation), the coordination approach is constrained by a
more mechanistic and less teleonomic criterion of maximizing resource use efficiency. Coordination
theory is consistent with source-sink approaches inherent to more “objective” transport-resistance models
16
(e.g. Thornley 1972). Moreover, coordination theory greatly simplifies the estimation of photosynthetic
capacity and holds promise for application with satellite data because the key variable is the absorbed
irradiance or specifically, the absorbed photosynthetically-active radiation (APAR) -- the product of
incident PAR and the fractional canopy light absorptance (fAPAR), both of which can be determined
globally from satellite observations (e.g. Myneni 1997b, Prince et al. 1998).
Objectives
Coordination theory has been used to describe and predict the depth-distribution of nitrogen and
photosynthetic capacity that results from spatial variation of light availability within a canopy (Chen et al.
1993), but it has not been used to explain or predict seasonal patterns of photosynthetic capacity at the
canopy scale that result from temporal variations in light availability that occur throughout the growing
season. The overall goals were to: (1) develop a simple generalized model suitable for application at
canopy to global scales based on coordination theory and driven by light, temperature and fAPAR; (2) test
the model at contrasting sites from a wide range of environments, and (3) evaluate the controls on canopy
photosynthetic capacity as they relate to seasonality and theories of plant resource optimization.
Observations of canopy photosynthetic capacity were derived from estimates of maximum gross
ecosystem CO2 exchange (GEE). Gross ecosystem CO2 exchange was derived from eddy covariance
measurements of net ecosystem CO2 exchange (NEE) made in arctic, boreal, temperate, and tropical
environments. A unique aspect of the model is its use of a recursive filter for calculating photosynthetic
acclimation based on the integrated effect of environmental conditions. The sensitivity of modeled
photosynthetic capacity to variation in the filter time constant was examined and site-specific time
constants were inferred for each site by fitting the model predictions to the observations.
Datasets
The model was evaluated at ten sites covering a wide range of vegetation and climatological
characteristics (Table 2.1). Ecosystems represented were arctic tundra, boreal forest, boreal wetland,
17
Table 2.1. Site Characteristics
Site
Description
Peak LAIe
MAT
(°C)
Annual
Rainfal (mm)
Year
Source
Location
Happy Valley
arctic tundra
1.0
-2.2
275
1994
Alaska, USA
(69°09′N, 148°58′W)
NSA-OBS
boreal forest, (old
black spruce)
2.7
-1.5
317
1996
Manitoba, Canada
(55°54′N, 98°30′W)
NSA-FEN
boreal fen
1.4
-1.6
317
1996
Manitoba, Canada
(55°54′N, 98°24′W)
SSA-OBS
boreal forest, (old
black spruce)
2.4
0.8
421
1996
Saskatchewan, Canada
(53°54′N, 105°7′W)
Howland Forest
temperate coniferous
forest
4.7
6.3
1040
1996
Maine, USA
(45°15′N,68°54′W)
Hollinger et al. 1999
Harvard Forest
temperate deciduous
forest
3.4
7.6
1117
1992
Massachusetts, USA
(42°32′N,72°11′W)
Wofsy et al. 1993
Konza Prairie
temperate C3/C4
grassland
2.8
14.0
840
1987
Kansas, USA
(39°03′N,96°32′W)
Verma et al. 1992
Ponca City
temperate crop
(winter wheat)
5.2
15.0
835
1997
Oklahoma, USA
(36°46′N, 97°08′W)
Verma, unpublished???
HAPEX-Sahel
tropical C3/C4
savannah
1.4
27.7
554
1992
Niger, West Africa
13°33′N,2°31′E)
Hanan et al. 1997
ABRACOS
tropical rain forest
4.0
24.2
>2000
1992
Rondonia, Brazil
(10°5′S,61°57′W)
Grace et al. 1996
2
-2
Vourlitis and Oechel
1996
Goulden et al. 1997
Lafleur et al. 1997
Jarvis et al. 1997
Peak LAIe refers to the seasonal maximum effective LAI, the one-sided leaf area index (m m ) without adjustment for leaf clumping (see Chen
et al. 1997).
MAT is the mean annual air temperature (°C).
18
temperate coniferous forest, temperate deciduous forest, temperate C3/C4 grassland, temperate crop,
tropical C3/C4 savannah, and tropical forest (Figure 2.1). Net ecosystem exchange (NEE) of CO2 was
measured at each site by eddy covariance (Baldocchi et al. 1988) and gross ecosystem exchange (GEE)
and maximum gross ecosystem exchange at saturating light and non-limiting temperature and moisture
(GEEmax) were estimated as described below. Meteorological variables and canopy leaf area index (LAI)
and/or canopy light interceptance was also measured at each site. Light (PAR) absorbed by the green leaf
area fraction of the canopy (fAPAR) was determined from measurements of green leaf area index (LAI),
light transmittance through the canopy, or above-canopy light reflectance, depending on the site (Table
2.2). Details are provided in the Appendix.
Gaps in field measurements invariably occur for various reasons including instrument
malfunction, power failure, and system calibration (Wofsy et al. 1993). However, the present model
requires a continuous time series of data to adequately characterize the running means. The three required
variables for the model, incident PAR, air temperature (Tair), and canopy light absorptance (fAPAR), were
filled using various techniques (Appendix). Briefly, gaps in Tair were filled by simulating diel variations in
temperature as a function of time, using daily minimum (Tmin) and maximum (Tmax) temperatures. For
gaps on days without reliable measurements of Tmin and Tmax, their mean values from the nearest 10 days
(5 prior and 5 after) were used. Gaps in incident PAR were filled by attenuating the top-of-theatmosphere PAR flux density (Itoa) by an atmospheric transmittance (βa) inferred from the diel
temperature amplitude following Glassy and Running (1994).
Observations of Canopy Photosynthetic Capacity and Optimum Temperature
It is not possible to directly measure gross ecosystem exchange (GEE) nor the maximum
exchange during optimal growth conditions (i.e. canopy photosynthetic capacity) using the eddy
covariance technique. However, GEE is often derived from the sum of NEE and ecosystem respiration
(Reco) estimated from nighttime NEE adjusted to daytime temperatures (Kim and Verma 1990, Verma et
19
ArticAlpine
Tundra
Cold
Temperate
Taiga
0
nd
odla
Wo
S hr ub la
10
Temperate
Forest
nd
ru b
Woodland
T ho rn sc
Desert
20
Temperate
Rainforest
Semidesrt
Mean Annual Temperature ( °C)
-10
Warm
Temperate
Tropical
Tropical
Seasonal
Forest
Tropical
Rainforest
30
0
1000
2000
3000
4000
Mean Annual Precipitation (mm)
Figure 2.1. Distribution of study sites with respect to mean annual temperature and precipitation.
20
Table 2.2. Methods used to derive fAPAR at each site.
Site
Description
Steps taken to estimate fAPAR
Site Measurement
Happy Valley
arctic tundra
NDVI
NDVI→fAPAR
NSA-OBS
boreal forest
NDVI
NDVI→fAPAR
NSA-FEN
boreal fen
rVIS & rSW
(rVIS & rSW )→NDVI→fAPAR
SSA-OBS
boreal forest
LAIe
LAIe →fIPAR→NDVI→fAPAR
Howland
temperate coniferous forest
NDVI
NDVI→fAPAR
Harvard Forest
temperate deciduous forest
fIPAR (subtracted 0.04 for PARreflected)
None (assumed fAPAR=fIPAR)
Konza Prairie
temperate C3/C4 grassland
NDVI
NDVI→fAPAR
Ponca City
temperate crop, (winter wheat)
rVIS & rSW
(rVIS & rSW )→NDVI→fAPAR
HAPEX-Sahel
tropical C3/C4 savanna
fAPAR (from Hanan et al. 1997)
None
ABRACOS
tropical rainforest
LAIe (assumed)
LAIe →fIPAR→NDVI→fAPAR
21
al. 1993, Goulden et al. 1996, 1997):
GEE = NEE - Reco
(2.1)
Reco = NEEnight 2(Tair-Tnight)/10
(2.2)
where
and NEEnight and Tnight are the average nighttime values of net ecosystem CO2 exchange and air
temperature, respectively, during the previous night. Consistent with studies of leaf level gas exchange,
canopy photosynthetic capacity (GEEmax) is expressed as a positive value, in contrast to conventional
micrometorological notation. Eddy covariance measurements are not reliable during periods of low
turbulent mixing between the atmosphere and the surface (Wofsy et al. 1993). Thus, fluxes of net
ecosystem CO2 exchange were not used when the friction velocity (u() was below 0.15 m s-1 (Wofsy et al.
1993) -- or, if u( was not available (e.g. NSA-FEN) -- when the windspeed (U) was less than 0.5 m s-1
(Lafleur et al. 1997). At the tropical forest site (ABRACOS), fluxes were rejected if the absolute value of
the storage flux exceeded 10 µmol m-2 s-1 following Grace et al. (1996).
GEEmax was inferred from GEE by fitting a rectangular hyperbola to the GEE estimates plotted as
a function of incident PAR (I) (Ruimy et al. 1996):
GEE=GEE∞I /(K+I)
(2.3)
where K is the PAR level when GEE equals half GEE∞, and re-evaluating the fitted light response model
at a light level (I sat ) known to be saturating (Frolking et al. 1998):
GEEmax= GEE∞ I sat /(K+I sat )
(2.4)
As the goal was to examine canopy acclimation to variable light levels throughout the growing season, it
would be inappropriate to presume the value of I sat . Light saturation was simply taken as the maximum
light level for each day the light response curve was fit. Thus, values of GEEmax derived in this fashion
should represent a reasonable estimate of the maximum GEE achieved on any given day. Curves were fit
at daily intervals to allow the distinction of days with clear skies and optimal growth conditions from
those with stressful and/or cloudy conditions. GEEmax was determined only on those days when light
22
alone explained more than 90% of the variation in GEE (r2>0.9), that is when other factors did not appear
to have a confounding affect on the photosynthetic light response. Finally, afternoon fluxes consistently
had a lower response than pre-noon fluxes. This response may be due in part to afternoon temperature and
VPD effects on photosynthesis. Thus, only pre-noon fluxes were used for curve fitting. Inclusion of
afternoon fluxes simply reduced the number of days with acceptable r2 values.
This curve fitting approach was selected over other methods because it was simple, easy to apply,
and easy to interpret the results. GEEmax could have been inferred from the value of photosynthetic
capacity used in a model of gross canopy photosynthesis calibrated to provide the best fit to the
observations. However, any process that is not accurately represented in the model will affect the final
estimate of photosynthetic capacity. Predictions may thus fit observations for the wrong reasons, leading
to errors in tuned parameters (Mäkelä and Valentine, in press).
The optimum temperature for photosynthesis during the growing season at each site was
determined from visual estimation of the time-averaged temperature corresponding to the seasonal
maximum photosynthetic capacity (GEEmax) on a plot of GEEmax versus temperature (not shown).
Model Theory
Coordination theory involves a balance between complementary processes, such as root and shoot
activity or carbon and nitrogen supply, achieved through various means of coordination (e.g. allocation).
Applied to photosynthesis, this theory implies that through time, leaves balance investment in N between
the ability for electron transport (Wj) and carboxylation (Wc) -- each of which potentially limits
photosynthesis (P≈
≈ min[Wj, Wc]). Coordinated investment that results in co-limitation between Wj and Wc
minimizes the overinvestment of resources in either rate.
If rates of electron transport and carboxylation are co-limiting, the supply of RuBP by electron
transport exactly equals its demand by Rubisco such that the production of unusable RuBP is minimized.
Resource allocation that balances limitation by electron transport and carboxylation also minimizes
photoinhibition or damage due to the harvesting of excess unusable photons at saturating light levels
23
(Anderson and Osmond 1987, Osmond 1994). The notion of co-limitation is consistent with the
functional convergence hypothesis (Field 1991) in that leaves and or canopies will adjust to the mean
growth conditions so that no one factor -- physiological (i.e. Wj, Wc) or environmental (light, temperature,
water, nitrogen, CO2) -- is more limiting than any another.
Observations of leaf level gas exchange are in general agreement with this functional
convergence and coordination theory. Co-limitation between electron transport and carboxylation has
been observed for many leaves (Evans 1989) and their respective capacities (Jmax and Vcmax) are strongly
correlated (Wullschleger 1993). Sun leaves have higher photosynthetic capacities than shade leaves
(Boardman 1977, Bjorkman 1981), consistent with minimizing photoinhibition and maintaining colimitation between electron transport and carboxylation at different levels of light availability.
Additionally, both leaf nitrogen content and maximum stomatal conductance exhibit linear non-saturating
relationships with photosynthetic capacity, reflecting regulated investment in nitrogen and the potential
influx of CO2 to useable levels (Cowan and Farquhar 1977, Ehleringer and Bjorkman 1977, Wong 1979,
Field and Mooney 1986).
Functional convergence and coordination theory imply that since, on average, no one factor limits
photosynthesis, the average conditions should be representative of the optimal conditions. That is, the
average irradiance should equal the optimal irradiance ( I =Iopt ) and the average temperature should equal
the optimal temperature ( T =Topt ). It follows that as the average conditions change throughout a growing
season, the biochemical capacity for photosynthesis and its temperature optimum will shift as well.
Mathematically, co-limitation implies that Pmax is given by the point of intersection between the average
rates of light limited ( Wj = α I ) and light saturated ( Wc =Pmax) photosynthesis (Figure 2.2a).
Model Equations
Assuming canopy photosynthetic capacity (Pcmax) varies with light availability such that colimitation is maintained between the light limited (αI) and light saturated rates (Pcmax), Pcmax may be
24
1.0
Pmax
αI
Photosynthesis →
0.8
0.6
(a)
fT
(b)
0.4
0.2
Iopt
Topt
0.0
Absorbed Irradiance →
Temperature →
0.10
0.8
0.08
α (mol mol-1 )
1.0
0.6
(c)
fD
0.4
0.2
C4
0.06
(d)
C3
0.04
0.02
0.0
0.00
0
1
2
3
4
5
6
-20
VPD (kPa)
0
20
40
60
Temperature (°C)
Relative Pmax
1.0
0.8
0.6
(e)
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
fW
Figure 2.2. Model relationships between photosynthesis and light (a), relative photosynthesis and
temperature (b), relative photosynthesis and VPD (c), quantum yield and temperature (d), and relative
photosynthetic capacity and relative plant water status (e).
25
expressed as the product of the time-averaged quantum yield (α , µmol µmol-1) and the time-averaged
PAR absorbed by the canopy ( I , µmol m-2 s-1):
Pcmax= α I
(2.5)
In practice, Equation 2.5 can be applied using measurements of incident radiation (PAR), air temperature,
and canopy light absorptance (fAPAR). In this study, PAR, air temperature, and fAPAR were determined at
each site (Appendix). It should be noted that an analogous expression to Equation 2.5 could be derived for
carboxylation capacity (Vcmax) using the biochemical model of Farquhar et al. (1980) as modified by
Collatz et al. (1991, 1992) by setting Wj = Wc :
Vcmax,C3 = α C3 I ( ci + K m )/( ci +2 Γ )
(2.6a)
Vcmax,C4 = α C4 I
(2.6b)
where α C3, α C4, ci , and Γ are described below and K m is the effective half-saturation constant given
by:
K m = K c (1+ O / K o )
(2.7)
i
where K c and K o are Michaelis-Menten constants and O i is the time-averaged oxygen concentration in
the leaf. To avoid potential difficulties associated with the inference of such parameter values from
calibrated models, as discussed above, Vcmax was not estimated or examined. Rather, the remainder of this
chapter deals with estimates of photosynthetic capacity (GEEmax), as derived from light response curves
for gross ecosystem CO2 exchange (GEE).
Canopy Quantum Yield
Canopy quantum yield is assumed to equal that of individual leaves and is determined differently
for C3 and C4 plants (Figure 2.2d) due to their respective sensitivities to CO2 concentration within the leaf
(ci) (Ehleringer and Bjorkman 1978):
α = (fC3 α C3 + (1-fC3) α C4
(2.8)
26
where fC3 is the C3 fraction. Assuming the time-averaged ratio of internal to atmospheric CO2
c
concentration ( cai ) is 0.7 for C3 plants, and the optimal leaf temperature equals the running mean daytime
air temperature ( T , see below), the time-averaged quantum yield may be expressed (Collatz et al. 1991,
1992):
α C3 = 0.08 [( ci - Γ )/( ci +2 Γ )] (fTopt fW)
(2.9a)
α C4 = 0.06 (fTopt fW)
(2.9b)
where fTopt and fW are empirical temperature and moisture stress modifiers (see below) that account for
non-CO2 related effects (e.g. Baker et al. 1988) that reduce the quantum yield below its unstressed value,
ci is the time-averaged leaf internal CO2 mole fraction (mol mol-1) equal to
ci
ca
c a , and Γ is the time-
averaged CO2 compensation point (mol mol-1):
Γ = 0.5 O /( S Pa )
(2.10)
i
where O i is the average partial pressure of oxygen in the leaf (20900 Pa), Pa is the average atmospheric
pressure (Pa), and S is the time-averaged specificity of Rubisco for CO2 relative to O2:
S = 2600 • 0.57
( T − 25)/10
(2.11)
Temperature and Moisture Modifiers
Photosynthetic capacity generally increases with increasing temperature as a result of faster
reaction rates at higher temperatures (Woodward and Smith 1994). As temperatures rise and fall
throughout a growing season, the acclimating plant will thus exhibit a rise and fall of photosynthetic
capacity (Pcmax), concurrent with a rise and fall of the temperature optimum (e.g. Schulze et al. 1976).
There is, however, a temperature beyond which any further increase causes lower rates of photosynthesis
at saturating light levels (Woodward and Smith 1994). Optimality theory predicts this threshold
temperature reflects genotypic adaptation, that is, optimal photosynthetic efficiency is achieved through
adaptation to the local thermal climate. In contrast, seasonal shifts in the optimum temperature reflect
27
acclimation or phenotypic plasticity in a given climate. Assuming genotypic adaptation to the local
thermal climate, the threshold temperature (Topt ) was assumed equal to T at the time of the seasonal
maximum canopy light absorptance (fAPAR) (Potter et al. 1993). If fAPAR does not vary (e.g. evergreen
vegetation), Topt was set equal to the annual maximum T , assuming the greatest photosynthetic capacity
that can occur does occur in a given location. The running mean daytime air temperature ( T ) was
calculated using Equation 13 (see below) and half-hourly (or hourly) air temperature (°C) for periods
when light levels were greater than zero (PAR>0).The photosynthetic temperature response (fTopt ) thus
determines the relative upper limit to photosynthetic capacity at a given temperature (Figure 2.2b):
f Topt =1.1814/([1+exp(.2[Topt -10- T ])][1+exp(.3[ T -10-Topt ])])
(2.12)
The form of this equation is taken from Potter et al. (1993). It was assumed that temperature effects on the
quantum yield (Baker et al. 1988) parallels those on photosynthesis (Equation 2.9).
Photosynthetic capacity is reduced during times of low leaf water potential (Sharkey and Badger
1982, Von Caemmerer and Farquhar 1984, Sharkey and Seeman 1989) and it was assumed that such
effects caused parallel reductions in quantum yield, consistent with known reductions in photochemical
efficiency during drought stress (Bjorkman et al. 1984, Demmig-Adams et al. 1988, Werner et al. 1999).
While neither soil water content nor plant moisture status were explicitly modeled, it was assumed that
the relative change in LAI reflects long-term changes in plant water status and hence soil moisture (Grier
and Running 1977, Squire et al. 1986). Short-term variation in plant water status (which occurs faster than
variations in LAI) was inferred from the moisture status of the atmosphere (Figure 2.3). It was assumed
that persistent atmospheric drought was consistent with low leaf water potential (Sellin 1999) which was
consistent with persistent stomatal closure (Graham and Running 1984).
Atmospheric moisture status may be a reasonable indicator of plant moisture status due to
feedback between stomatal conductance, transpiration, and leaf-to-air vapor pressure deficit (VPD). High
VPD is consistent with low leaf water status because of VPD- and temperature-related inhibition of
stomatal conductance. For example, high atmospheric VPD and high leaf temperatures induce low
28
Figure 2.3. Interrelationships among soil, plant, and atmospheric moisture status.
29
stomatal conductance (g), through VPD and temperature stress, leading to low rates of transpiration (E
where E=gVPD). For a given increase in VPD, there is a linear increase in transpiration while there is
often an exponential decrease in stomatal conductance (Figure 2.2c):
fD = 1/(1+exp[1.3(VPD-3)])
(2.13)
where VPD (kPa) is the instantaneous (e.g. half-hourly or hourly) value. This relationship is based on
measurements of stomatal conductance in tropical, temperate, and boreal ecosystems on crops, grasses,
shrubs, and deciduous and evergreen trees (Aber & Federer 1992, Fan et al. 1995, Jarvis et al. 1976,
Schulze and Hall 1982, Hollinger 1992, Hollinger et al. 1994, Kim and Verma 1991, Korner 1994,
Leuning 1995, Monson and Grant 1989, Reich et al. 1990, Schulze et al. 1976, Smith and Goltz 1994,
Whitehead et al. 1981). It is consistent with other relationships in the literature (e.g. Lohammer et al.
1980, Leuning 1995, Jacobs et al. 1996) with the exception that in Equation 10, there is little effect when
VPD<1 kPa, (e.g. Korner 1994).
The calculation of relative plant water status (fW) from atmospheric moisture status requires
consideration of the two following caveats. First, it is assumed that persistent stomatal closure occurs only
when leaf water potential is very low, that is, leaf water potential should be related to time-averaged
(rather than instantaneous) stomatal conductance. Second, feedback between plant moisture status,
transpiration, and atmospheric moisture is likely to be realized only during midday hours
(1000<Hr<1400) when physiological activity is near its daily peak and the canopy and atmospheric
boundary layers are convective and well mixed (Monteith 1995). Given these constraints, relative plant
water status (fW) was calculated as the running mean of midday relative stomatal conductance (fD):
fW = f D,midday
(2.14)
Calculation of the running mean is described below.
Time Constant for Acclimation
Models of acclimation can be structured “objectively” (e.g. Thornley 1998) such that a change in
30
environmental conditions causes a physiologically realistic imbalance in one or more state conditions and
eventually, a new steady state is reached. Alternatively, optimality models assume a new steady state is
reached instantaneously, which is computationally simpler but physiologically unrealistic (Thornley
1991). The objective approach is realistic but impractical to apply at regional to global scales given the
many parameters required. On the other hand, optimality assumptions may be unrealistic but suitable for
global application. As a compromise, the optimality approach is used here with time-averaged
environmental light and temperature conditions so as to minimize the influence of their short-term
variations. One approach to averaging environmental factors suitable for this purpose is with recursive
low pass filters of the form:
X = ω X i-1 + (1-ω)Xi
(2.15)
where X is the filtered value of variable X, X i-1 is the previous filtered value, Xi is the value of variable
X at time i, and ω is the weighting factor which depends upon the time interval between measurements
(∆t) and the time constant (τ):
ω=exp(-∆t/τ)
(2.16)
Using the instantaneous-optimality approach with time-averaged variables should provide reasonable
agreement with more accurate models of acclimation. As such, the problem reduces to determining the
appropriate time constant for photosynthetic acclimation.
As noted by Cowan (1986), optimal photosynthetic acclimation could only be achieved if protein
degradation and synthesis were so rapid that enzyme activities could vary precisely with external factors
that affect light harvesting and carboxylation such as light, temperature, plant water status, humidity, and
CO2. Acclimation is more likely to occur over a period of a several days (Cowan 1986, Field 1991,
Pearcy and Sims 1994, Thornley 1998). During this time materials and nutrients such as nitrogen can be
reallocated in response to the prevailing growth conditions.
Canopy acclimation encompasses both leaf level changes in foliar biochemistry and anatomy and
canopy level morphological changes in the amount of leaves and their orientation, inclination, and
31
distribution. The time constant discussed here primarily reflects changes in canopy physiology, as
changes in canopy morphology were assumed to be captured by changes in canopy light absorptance
(fAPAR) (Squire et al. 1986, Field 1991). The synthesis and reorganization of pigments, membranes and
enzymes generally occur on the order of days while changes in leaf development and display occur over a
period of days to weeks or longer (Pearcy 1994). The time scale for full acclimation ultimately depends
on the rate of leaf turnover, which can be quite slow in some woody species (Kamaluddin and Grace
1992).
As a first approximation and in line with results from an ‘objective’ transport-resistance model
initialized for a non-growing leaf on a non-growing plant (Thornley 1998), the time constant for
acclimation was assumed to be five days. It should be noted that this value is also consistent with the
typical residence time of weather fronts in many regions. Vegetation may have adapted to this natural
periodicity by maintaining a common level of physiological plasticity.
Results and Discussion
Seasonal variation of the calculated 5-day running means of temperature ( T ) and irradiance ( I )
along with estimated fAPAR for each site is shown in Figure 2.4. These variables were combined with
predictions of relative photosynthetic capacity as a function of temperature (fTopt ) and predicted genotypic
temperature optima (Figure 2.5) along with relative plant water status (Figure 2.6) to calculate canopy
photosynthetic capacities at each site using Equations 2.5, 2.8, and 2.9 to 2.15 (Figure 2.7 and 2.8).
Predicted genotypic temperature optima show a strong relationship with observed values but with
a relatively large offset (Figure 2.5). Much of this offset may stem from the difficulty in determining the
observed temperature optima (visually estimated). With the exception of the winter wheat site, the boreal
and temperate forest sites achieved peak photosynthetic capacity around 18-20EC, while the non-forest
and tropical sites peak between 25-30EC. Unlike the non-forest sites, the predicted temperature optima for
the forest sites consistently exceeded those observed by 3-5 EC. This overestimation at the forest sites
32
-40
160
170
180
190
Day of Year
200
-1
210
1000
500
0
-500
-1000
60
40
1
I
f
APAR
20
0
0
T
-20
-40
100
150
200
250
Day of Year
Fraction PAR Absorbed (fAPAR)
1500
Predicted Optimal Temperature (°C)
Boreal Fen
NSA-FEN, Manitoba
-1
350
300
Temperate Coniferous Forest
Howland, Maine
1000
500
0
-500
-1000
60
f
APAR
40
1
I
20
0
0
T
-20
-40
0
-1
50 100 150 200 250 300 350 400
Day of Year
Fraction PAR Absorbed (fAPAR)
1500
-500
-1000
1
I
f
APAR
20
0
0
T
-20
-40
0
Fraction PAR Absorbed (fAPAR)
0
40
-1
50 100 150 200 250 300 350
Day of Year
Boreal Forest
SSA-OBS, Saskatchewan
1500
1000
500
0
-500
-1000
60
40
I
1
f
APAR
20
T
0
0
-20
-40
50
100 150 200 250 300
Day of Year
Fraction PAR Absorbed (fAPAR)
-20
500
60
-1
350
Temperate Deciduous Forest
Harvard Forest, Massachusetts
1500
1000
500
0
-500
-1000
60
f
APAR
40
1
I
20
0
0
T
-20
-40
0
Fraction PAR Absorbed (fAPAR)
0
APAR
1000
Predicted Optimal Temperature (°C)
f
1500
Predicted Optimal Temperature (°C)
0
Boreal Forest
NSA-OBS, Manitoba
Predicted Optimal Temperature (°C)
-1000
I
20
Predicted Optimal Irradiance (µmol m-2 s-1)
-500
1
T
Predicted Optimal Irradiance (µmol m-2 s-1)
0
40
Predicted Optimal Irradiance (µmol m-2 s-1)
500
60
Fraction PAR Absorbed (fAPAR)
1000
Predicted Optimal Temperature (°C)
1500
Predicted Optimal Temperature (°C)
Predicted Optimal Irradiance (µmol m-2 s-1)
Predicted Optimal Irradiance (µmol m-2 s-1)
Predicted Optimal Irradiance (µmol m-2 s-1)
Arctic Tundra
Happy Valley, Alaska
-1
50 100 150 200 250 300 350 400
Day of Year
Figure 2.4. Temporal variation of 5-day running means of temperature ( T ) and irradiance ( I ) and
estimated canopy light absorptance (fAPAR).
33
f
APAR
0
0
-20
-40
-1
120140160180200220240260280300320
Day of Year
Tropical C3/C4 Savanna
Niger, West Africa
1000
500
0
-500
-1000
60
I
40
1
T
f
APAR
20
0
0
-20
-40
230
240
250 260 270 280
Day of Year
-1
290
Fraction PAR Absorbed (fAPAR )
1500
500
0
-500
-1000
I
40
20
1
f
APAR
0
0
T
-20
-40
0
50
100
150
Day of Year
200
Fraction PAR Absorbed (fAPAR)
20
1000
60
-1
250
Tropical Rainforest
Rondonia, Brazil
1500
1000
500
0
-500
-1000
60
20
34
f
APAR
1
T
0
0
-20
-40
130
Figure 2.4. Continued.
I
40
140
150
160
Day of Year
170
-1
180
Fraction PAR Absorbed (fAPAR)
T
1500
Predicted Optimal Temperature (°C)
-1000
1
Winter Wheat Crop
Ponca City, Oklahoma
Predicted Optimal Temperature (°C)
-500
40
Predicted Optimal Irradiance (µmol m-2 s-1)
0
I
Predicted Optimal Irradiance (µmol m-2 s-1)
500
60
Fraction PAR Absorbed (fAPAR)
1000
Predicted Optimal Temperature (°C)
1500
Predicted Optimal Temperature (°C)
Predicted Optimal Irradiance (µmol m-2 s-1)
Predicted Optimal Irradiance (µmol m-2 s-1)
Temperate C3 /C4 Grassland
Konza Prairie, Kansas
Figure 2.5. Relationship between predicted and observed genotypic temperature optima. Observed
genotypic temperature optima were estimated as the time-averaged temperature (T ) concurrent with the
seasonal peak gross ecosystem CO2 exchange (GEEmax). Predicted optima (Topt , see text) were derived
from the time-averaged temperature concurrent with the seasonal peak light absorptance (fAPAR).
35
0
-0.5
0.8
fW
-1
0.6
Pre-Dawn Leaf
Water Potential
-1.5
0.4
Konza Prairie
150
200
250
-2
300
Observed Pre-Dawn Leaf Water Potential (kPa)
Predicted Relative Plant Water Status (fW )
1
Day of Year
Figure 2.6. Predicted relative plant water status (fW) and observed pre-dawn leaf water potential
(observations from Verma et al. 1992).
36
Happy Valley, Alaska
10
8
6
4
2
160
170
180
Day of Year
190
200
20
Boreal Fen
NSA-FEN, Manitoba
18
16
14
12
10
8
6
4
2
0
100
200
Day of Year
Temperate Coniferous Forest
Howland, Maine
30
20
10
0
100
200
Day of Year
Boreal Forest
NSA-OBS, Manitoba
25
20
15
10
5
0
0
100
200
Day of Year
300
200
Day of Year
300
25
Boreal Forest
SSA-OBS,
Saskatchewan
20
15
10
5
0
0
300
40
0
30
210
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
0
150
0
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
-2 s-1)
12
Canopy Photosynthetic Capacity (µmol m
Arctic Tundra
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
14
100
40
Temperate Deciduous Forest
Harvard Forest,
Massachusetts
30
20
10
0
300
0
100
200
Day of Year
300
Figure 2.7. Temporal variation in predicted and observed canopy photosynthetic capacity by site.
37
40
30
20
10
0
100
200
Day of Year
Tropical C3/C4 Savanna
Niger, West Africa
15
10
5
0
220
230
240
250
260
Day of Year
Winter Wheat
270
280
Ponca City, Oklahoma
40
30
20
10
0
0
25
20
50
300
-2 s-1)
0
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
-2 -1
Canopy Photosynthetic Capacity (µmol m s )
Temperate C 3/C4 Grassland
Konza Prairie, Kansas
Canopy Photosynthetic Capacity (µmol m
-2 s-1)
Canopy Photosynthetic Capacity (µmol m
50
290
100
200
Day of Year
300
40
Tropical Rainforest
Rondonia, Brazil
30
20
10
0
120
Figure 2.7. Continued.
38
130
140
150
Day of Year
160
170
180
Figure 2.8. Relationship between predicted and observed canopy photosynthetic capacity.
39
may have been in part due to the rough estimation of the timing of peak seasonal photosynthetic activity.
At the evergreen sites (NSA-OBS, SSA-OBS, Howland), fAPAR was assumed constant and thus provided
no clear indication of seasonal peak leaf display. In contrast, at the non-forest sites, the seasonal peak in
fAPAR was relatively distinct (Figure 2.4), providing a clear indication of the timing of peak activity and
better agreement between the predicted and observations peaks in photosynthetic capacity with respect to
temperature (Figure 2.5)
The magnitude and seasonal variation in predicted plant water stress (fW) was similar to the
pattern of observed pre-dawn leaf water potential measured at the Konza Prairie site (Figure 2.6) with a
few exceptions. The decrease in predicted plant water status near JD 165 did not coincide with a similar
drop in observed pre-dawn leaf water potential. (The lack of measurements around JD 235 precludes a
similar conclusion.) Additionally, around JD 210 both predictions and observations indicated a sharp
decline in plant water status, but the predictions remained at low water status longer than the
observations. Changes in pre-dawn leaf water potential appear to be less dynamic than time-averaged
changes in atmospheric VPD. Despite these discrepancies, the overall agreement is encouraging,
particularly considering the simplicity of the approach, and supports the notion that the time-averaged
midday moisture status of the atmosphere may be a reasonable and useful index of vegetation moisture
status.
The seasonal pattern and magnitude of the predicted canopy photosynthetic capacities were
similar to those observed (Figure 2.7). Notable exceptions were found at the northern boreal forest (NSAOBS) and boreal fen, and the winter wheat and tropical rainforest. Discrepancies at the northern old black
spruce (NSA-OBS) site were likely due to the uncertainty and errors in fAPAR estimates. Reported LAI e
estimates ranged from 2.4 (Dang et al. 1997) to 2.7 (Chen et al. 1997) and NDVI ranged from 0.40 (K.
Czajkowski, personal communication) to 0.70 (Dang et al. 1997). Overestimation at NSA-OBS and
underestimation at NSA-FEN are not surprising given the potential errors in fAPAR. Using the lower range
of fAPAR at NSA-OBS (~0.4) provided excellent agreement between the predictions and observations (data
not shown).The fAPAR estimates for the boreal fen were questionable, given that they were derived from
40
reflected PAR and shortwave radiation (Appendix) and the relationship used to relate fAPAR to NDVI
(Equation A4) was derived for vascular plants. The non-vascular component of the fen may have a much
different spectral response than vascular plants (Bubier et al. 1997).
Despite a clear overestimation of fAPAR during the early period of canopy development prior to
JD 50 at the winter wheat site (Figure 2.4) as compared to field measurements of LAI (S. Verma,
unpublished, data not shown), estimates of canopy photosynthetic capacity (Figure 2.7) agreed well with
observations. This is likely the result of large temperature constraints (low fTopt ) during this time period. In
contrast, after JD 50, estimates of fAPAR agree well with estimates derived from direct LAI measurements
(data not shown), yet the model overestimates photosynthetic capacity during canopy senescence (Figure
2.7). Agreement was found after adjusting the temperature response function (fTopt ) so that relative
photosynthetic capacity declined more sharply at temperatures above the genotypic optimum. This
empirical a priori modification to the temperature response function was not used in the final model
predictions. This result indicates that site-specific responses may deviate from the highly generalized
function represented by Equation 2.13, although the latter may be adequate for global applications. It is
not clear why the model overestimated capacities at the tropical forest site. Overall, the predicted
photosynthetic capacities were close in both magnitude and seasonality with the observations, providing
justification for the use of Equation 2.5.
The relationship between predicted and observed capacities is shown in Figure 2.8. Predicted
photosynthetic capacity varied in a positive linear fashion with observed GEEmax. It should be noted that
even if maximum rates of GEE can be derived from eddy covariance measurements of NEE, there is no
way to know if the seasonal variation in maximum GEE is due to seasonal variation in stress (which
reduces GEE below its potential maximum) or seasonal variation in the potential maximum itself. No
attempt is made here to distinguish between these two conditions. Nevertheless, the overall agreement
suggests that canopies acclimate to the prevailing light availability and regulate investment in
photosynthetic capacitiy to levels in tune with multiple environmental constraints (e.g. light, temperature,
and water).
41
Consistent with theories of resource optimization and photo-acclimation, canopy photosynthetic
capacity exhibited a strong positive linear relationship with the time-averaged absorbed PAR, particularly
when the latter was constrained during times of sub-optimal temperature and water status (Figure 2.9).
Temperature and moisture constrained time-averaged absorbed PAR was calculated using site
measurements of incident PAR and fAPAR and temperature (fTopt ) and plant water status (fW) constraints.
The solid line in Figure 2.9 is a linear regression forced through the origin, the slope of which equals the
average quantum yield (mol CO2 mol-1 photon absorbed) across the sites. This value (0.051) is similar to
maximal quantum yields exhibited by individual leaves (Ehleringer and Bjorkman 1978, Collatz et al.
1998). The strength of this relationship (r2=0.75) supports the contention that the time-averaged radiation
is a good general index of photosynthetic capacity. This result also implies that canopies maximize light
utilization and regulate investment in photosynthetic capacity to levels in tune with light availability.
Temperature and moisture constraints account for a significant amount of the seasonal variability
in canopy photosynthetic capacity. This undoubtedly stemmed from the fact much of the variability is not
related to changes in fAPAR. Sites with evergreen vegetation and persistent leaf display absorb, but do not
utilize absorbed radiation during winter periods. Similarly, vegetation in environments with occasional
drought during the growing season (e.g. Konza Prairie) may maintain leaf area, albeit in reduced amounts,
throughout drought periods. While canopies may be absorbing radiation during such periods, they may
not be utilizing the absorbed radiation (Waring and Landsberg 1998). The application of temperature and
moisture constraints on mean absorbed PAR ( APAR ), accounted for an additional 29% of the variance in
canopy photosynthetic capacity (Table 2.3). Daily maximum PAR (PAR max) and mean incident PAR
( PAR ) both accounted for a similar amount of the variability (r2=0.26 and 0.29, respectively), while mean
absorbed PAR (APAR ) accounted for an additional 17% over mean incident ( PAR ). Constrained mean
absorbed PAR ( APAR fTopt fW) accounted for significantly more of the variability in GEE (29%) than any
other measure.
Consistent with the previous studies showing increasing photosynthetic capacity with increasing
42
Figure 2.9. Relationship between observed photosynthetic capacity and time-averaged absorbed radiation.
The latter was calculated as the product of canopy light absorptance (fAPAR) and the 5-day running mean
of incident PAR ( I ). This product was then constrained during times of sub-optimal temperature (fTopt )
and moisture (fW).
43
Table 2.3. Proportion of variation in GEEmax accounted for by different measures of light availability;
maximum incident PAR (PAR max), mean incident PAR ( PAR ), mean absorbed PAR ( APAR ), and mean
absorbed PAR with moisture and temperature constraints ( APAR fWfTopt ).
Definition
r2
Additional variance explained
PARmax
maximum incident PAR
0.26
---
PAR
mean incident PAR
0.29
0.03
APAR
mean absorbed PAR
0.46
0.17
APAR fW fTopt
mean utilizable absorbed
0.75
0.29
44
temperature at the leaf (Woodward and Smith 1994) and canopy scale (Hollinger et al. 1999), observed
rates of canopy photosynthetic capacity (GEEmax) exhibited a strong positive exponential relationship with
temperature (Figure 2.10). The strength of this relationship across a wide range of ecosystems from the
arctic to the tropics underscores the important control by temperature on the seasonal variability of
canopy photosynthetic capacity. While the data do not provide direct evidence for temperature
acclimation, it is consistent with the hypothesis that plants acclimate to recent growth temperatures. The
poor relationship between canopy photosynthetic capacity and temperature at the tropical sites (Figure
2.10) is likely due to the small temperature range observed during the measurement periods at these sites.
Model predictions of canopy photosynthetic capacity (Pcmax) for the coniferous forest site
(Howland, 1997), calculated using half-hourly Tair and PAR and a range of time constants (1, 5, 10, 20,
30, 60, and 120 days), is shown in Figure 2.11. For each run, the model was initialized using data from
1996. The model predictions appear relatively insensitive to changes in the time constant between 1 and
10 days. Lower values (1 day) were unrealistically sensitive to short-term variations in light and
temperature while higher values (>10) introduced a large and unrealistic phase lag to the timing of the
capacities. Given the relative insensitivity of the predictions to the time constant around 5 days and the
unrealistic phase lag introduced at values greater than 10 days, the use of a 5-day time constant appeared
reasonable.
To provide an indication of the actual time constants for photosynthetic acclimation of the
different canopies, time constants were varied at each site until the sum of squared residuals between the
predicted and observed capacities was minimized (Table 2.4). At the temperate sites, the tuned time
constants were similar to the 5-day value used in the model. Tune time constants were generally greater at
the boreal and tropical sites. In the tropics the environment is so constant that the actual value used is
likely to be of little consequence to the predictions. The time constant had to be increased by a factor of
12 at the tropical rainforest site to induce a 2.3 µmol m-2 s-1 difference in predicted capacity. Caution
should be used when interpreting this result as the length of the time constant (58 days) is longer than the
45
measurement period (~50 days). Similarly, at the tropical savanna site, the fitted time constant is more
Figure 2.10. Relationship between observed canopy photosynthetic capacity and temperature. To facilitate
comparison among sites, photosynthetic capacities (GEEmax) and time-averaged temperatures (T ) from
each site were normalized to the seasonal maximum GEEmax and to T concurrent with the seasonal
maximum GEEmax, respectively.
46
Figure 2.11. Sensitivity of model predictions to variation in the time constant for acclimation. The numbers on each
curve indicate the time constant (in days) used in the calculation.
47
Table 2.4. Tuned time constants for acclimation of canopy photosynthetic capacity to light and
temperature. Tuning was done by minimizing the sum of squared differences between predicted and
observed (GEEmax) values over the full measurement period. ∆RMSE is the change in the root mean
square error as a result of model tuning (RMSEafter - RMSEbefore). The percentage change is given in
parentheses. Note that the nominal value of the time constant is 5 days.
Site
Tuned Time Constant (days)
)RMSE (µmol m-2 s-1)
Arctic Tundra
7
-0.01 (0.4 %)
Boreal Forest (NSA-OBS)
13
-4.70 (70%)
Boreal Fen
9
-0.09 (3%)
Boreal Forest (SSA-OBS)
3
-6.90 (62%)
Temperate Coniferous Forest
7
-0.13 (3%)
Temperate Deciduous Forest
4
-0.01 (0.1%)
Temperate C3/C4 Grassland
8
-1.50 (3%)
Temperate Crop (Winter Wheat)
21
-0.39 (4%)
Tropical C3/C4 Savanna
13
-0.04 (2%)
Tropical Rainforest
58
-2.30 (33%)
48
than double the nominal 5-day value. However, this greater time constant improves the model fit by less
than 0.1 µmol m-2 s-1.
In contrast, the boreal forest northern old-black spruce site appeared much more sensitive to the
time constant. For the identical increase (from 5 to 13 days), as the tropical savanna site, the predicted
capacities changed by a much larger 4.7 µmol m-2 s-1 (a 70% decrease in error). Interestingly, the largest
change as a result of allowing the time constant to change was observed at the southern old black spruce
site. Decreasing the value from 5 to 2 decreased the RMSE by a relatively large 6.9 µmol m-2 s-1 or 62%.
The reason for this is unclear and may be the result of other errors in the model or the data (fAPAR, for
example).
These results are consistent with the constancy of tropical environments, more variable conditions
(typical 5-day periodicity of weather fronts) in the temperate region, and a short growing season in the
boreal zone characterized by a fast transition from winter to summer conditions (see Figure 2.4). In such
an environment, maintenance of a high photosynthetic capacity (less physiological plasticity) would allow
a plant to take advantage of favorable growth conditions as soon as they occur. Overall, however, it is
difficult to separate the errors in fAPAR (or in the predicted temperature response) from the errors in the
time constant. Further, the tuning process had minimal effect on the model predictions for most sites
(<4%), providing confidence in the 5-day time constant used in the model.
Conclusions
A generalized uncalibrated model of canopy photosynthetic capacity based on principles of
resource optimization and driven by variables accessible via remote sensing (fAPAR, PAR, Tair) was
described and evaluated in a wide range of ecosystems from arctic, boreal, temperate, and tropical
environments. A unique aspect of the model is its use of a recursive filter for calculating photosynthetic
acclimation based on the integrated effect of environmental conditions. This filtering method was found
to be robust as the modeled photosynthetic capacity was relatively insensitive to value of the time
49
constant. A value of 5-days appears reasonable for most sites. Greater time constants provided better fits
in the tropics and the boreal region, owing to constancy of environmental conditions in the tropics and
potentially less physiological plasticity in the boreal region.
A strong positive linear relationship was found between modeled and observed canopy
photosynthetic capacities and the predicted photosynthetic capacities were in close agreement with both
the magnitude and seasonality of the observations. In addition, a strong linear relationship was found
between modeled and observed genotypic temperature optima. Consistent with theories of resource
optimization and photo-acclimation, canopy photosynthetic capacity exhibits a strong positive linear
relationship with the temperature and moisture constrained time-averaged absorbed PAR. Temperature
and moisture constraints accounted for a significant amount of the seasonal variability in canopy
photosynthetic capacity as well. This undoubtedly stemmed from the fact much of the variability is not
related to changes in fAPAR. Consistent with the previous studies showing increasing photosynthetic
capacity with increasing temperature at the leaf and canopy scales, observed rates of canopy
photosynthetic capacity exhibited a strong positive exponential relationship with temperature. The
strength of this relationship underscores the importance of temperature to the seasonal variability of
canopy photosynthetic capacity.
These results provide justification for the hypothesis that canopies acclimate to the prevailing
light availability and regulate investment in photosynthetic capacity to levels in tune with multiple
environmental constraints. Further, the model presented here provides the means by which to relate
satellite NDVI to the physiological status of vegetation and provides justification for the use of NDVI as a
global general index of potential carbon gain.
50
APPENDIX
Gaps in Tair data were filled by simulating diel variations in temperature as a function of time,
using measured Tminand Tmax (Landsberg 1986):
Filled Tair = 0.5(Tmin + Tmax) + 0.5(Tmax - Tmin)cos(2B(Hr - 12)/24)
(A1)
For gaps on days without measurements of Tmin and Tmax, their mean values from the nearest 10 days (5
prior and 5 after) were used. Gaps in incident PAR data were filled by attenuating the top-of-theatmosphere PAR flux density (Itoa) by an atmospheric transmittance (βa)
Filled PAR = Itoa βa
(A2)
where atmospheric transmittance was estimated from the diel temperature amplitude (∆T=Tmax-Tmin)
following Glassy and Running (1994):
βa = m(1-exp[-0.003 ∆T2.4])
(A3)
where m was an empirical coefficient (0<m<1) used to provide the best fit (OLS) between measured and
predicted PAR (m was generally greater than 0.95 and r2 values were generally 0.73, except for Harvard
Forest where m=0.68 and r2=0.40). Values of Itoa were determined as described by Brock (1981), based on
latitude and the position of the sun. This gap filling approach, while not as accurate as using
measurements from nearby weather stations, was practical and provided reasonable and consistent results.
Light (PAR) absorbed by the green leaf area fraction of the canopy (fAPAR) was determined in
various ways among the sites as summarized in Table 2.2. At the HAPEX-Sahel site, fAPAR was
determined by a combination of measurements and modeling (Hanan et al. 1997) and at the Harvard
Forest site, fAPAR was assumed to equal the fraction intercepted, assuming all leaves present in the canopy
were green. For all the other sites, except NSA-FEN and the winter wheat site (see below), fAPAR was
derived from above-canopy estimates of NDVI using the following relationship (Figure A1):
fAPAR=1/(1+exp[6(0.64-NDVI)])
(A4)
(r2=0.87, n=133). Equation A4 was derived using measurements of light interceptance
51
Fraction Intercepted PAR (fIPAR)
1.0
(a)
Crop
Tree
Shrub
Grass
Fitted
0.8
0.6
0.4
0.2
r 2=0.75
0.0
0.0
0.2
0.4
0.6
0.8
1.0
NDVI
Fraction Absorbed PAR (fAPAR)
1.0
(b)
Crop
Tree
Shrub
Grass
Fitted
0.8
0.6
0.4
0.2
r2=0.87
0.0
0.0
0.2
0.4
0.6
0.8
1.0
NDVI
Figure A1. Relationship between canopy light interceptance (fIPAR) and NDVI (a) and canopy
light absorptance (fAPAR) and NDVI (b). Canopy light interceptance refers to PAR interceptance
by the entire canopy (green + nongreen components) whereas canopy light absorptance refers to
PAR absorptance by the green leaf fraction.
52
the green leaf fraction.
senescence (in non-evergreen canopies). The canopies included annual grassland (Gamon et al. 1995),
saltmarsh grassland (Bartlett et al. 1992), corn and cotton (Weigand et al. 1991), fallow shrub (Hanan et
al. 1997), and evergreen and deciduous shrubs (Gamon et al. 1995). Reflected PAR (PAR reflected) at the
top of the canopy was assumed to be 4% if not otherwise cited.
NDVI was either measured at the site above the canopy from helicopter and corrected for
atmospheric effects (Konza Prairie: Verma et al. 1993, NSA-OBS: Dang et al. 1997), from a boom
extension (Howland: Ranson et al. 1994), or by a hand-held radiometer (Happy Valley: McMichael et al.
1999). At SSA-OBS and ABRACOS, NDVI was estimated from total (green + non-green) canopy
interceptance (fIPAR) which in turn was derived from effective LAI (LAI e) measurements made with the
LiCor LAI-2000 Plant Canopy Analyzer:
fIPAR=1-exp(-kLAIe)
(A5)
where k=0.5 (the light extinction coefficient) and LAI e is the effective leaf area index defined as the onesided LAI without adjustment for leaf clumping (Chen et al. 1997). NDVI was then estimated by
inverting the relationship between total (green + non-green) interceptance (fIPAR) and NDVI (Figure A1):
NDVI=0.56-ln([1/fIPAR]-1)/7.3
(A6)
(r2=0.80, n=266). This relationship was determined using measurements of total PAR interceptance by
green and non-green canopy fractions (1-PAR below/PAR above-PAR reflected) made in number of canopies
including grassland (Demetriades-Shah et al. 1992), fallow grass (Hanan et al. 1997), corn and cotton
(Wiegand et al. 1991), millet (Hanan et al. 1997), fallow shrub (Hanan et al. 1997), deciduous shrub (Law
and Waring 1994), deciduous forest (Waring et al. 1994, Dang et al. 1997), evergreen shrub (Law and
Waring 1994, Goward et al. 1994), and coniferous forest (Goward et al. 1994, Ranson et al. 1994, Waring
et al. 1994, Dang et al. 1997).
At the NSA-FEN and Ponca City winter wheat sites, NDVI was estimated from measurements of
PAR (rVIS) and shortwave radiation (rSW) reflected by the canopy. Near infrared reflectance (rNIR) was
determined by combining rVIS and rSW: rNIR=2rSW - rVIS. This assumes that half of the incident radiation is
53
in the visible wavelengths and the half is in near-infrared wavelengths such that rSW is the average of rVIS
and rNIR. NDVI was then calulated as: NDVI=(rNIR - rVIS)/(rNIR + rVIS) and fAPAR was then determined with
Equation A4.
At each site, time-averaged midday fAPAR was determined by fitting (OLS) a 5th-order Fourier
series to the instantaneous midday (1000<Hr<1400) measurements of fAPAR following Sellers et al.
(1995):
5
fAPAR =
∑ (a
0
+ an cos[ nt r ]+ bn sin[ nt r ])
(A7)
n
where a0, an, and bn are fitted coefficients and tr is time in radians. The seasonal variation in fAPAR, T , and
I is shown in Figure 2.4.
54
CHAPTER III
MODELING CARBON EXCHANGE IN TERRESTRIAL ECOSYSTEMS USING
LIGHT ABSORPTANCE AND OPTIMALITY THEORY
Introduction
The exchange of carbon dioxide (CO2) between terrestrial ecosystems and the atmosphere plays a
central role in the ecology of the biosphere and the climate system. CO2 is an important greenhouse gas
which influences both the physics and chemistry of the atmosphere. Thus, its current rise of about 1.8
ppmv per year (0.5%) may have profound effects on global climate (IPCC 1990). Roughly 15% of the
atmospheric carbon pool is assimilated by plants each year (Williams et al. 1997). This fixation of CO2
provides the energy that ultimately sustains the metabolism of all organisms and drives the exchange of
materials and energy with the atmosphere (Mooney et al. 1987). A fraction of this fixed carbon is respired
by plants and soil microorganisms back to atmosphere while the remainder is stored in plant biomass and
soils. Quantifying the net balance between photosynthetic fixation and respiratory loss is critical to
understanding how the climate system affects ecosystem processes which, in turn, feedback to regulate
atmospheric CO2 levels (Hollinger et al. 1999).
Studies based on atmospheric flask samples and transport models (Tans et al. 1990, Ciais et al.
1995, Keeling et al. 1996, Fan et al. 1998) provide only indirect measures of surface CO2 exchange. Eddy
covariance measurements, aside from theoretical and logistical constraints, provide only point
measurements. Ecosystem models driven by remote sensing observations, on the other hand, offer the
potential for synoptic monitoring of global ecosystem functioning (e.g. Sellers et al. 1996). However,
aside from a few exceptions (e.g. Prince and Goward 1995), the application of ecosystem models with
remote sensing data is limited by the paucity of regional ecological databases (Leuning et al. 1995,
Williams et al. 1998). More importantly, satellite observations currently provide little information on the
55
physical or biological status of soils. Satellite-driven models thus have no consistent means of assessing
carbon loss through soil heterotrophic respiration.
Most models that predict net ecosystem CO2 exchange (NEE) or its equivalent, net ecosystem
productivity (NEP = NPP - RH) estimate soil heterotrophic respiration using standard temperature
dependent functions (Fung et al. 1987, Ludeke et al. 1991, Knorr and Heimann 1995, Maisongrande et al.
1995). Such functions are typically parameterized with the constraint that annual soil respiration equals
annual NPP (ΣNEP = 0). The few exceptions to this approach (Potter et al. 1993, Hunt et al. 1996)
explicitly model soil respiration using simplified soil carbon cycle models (e.g. Parton et al. 1987) or use
functions calibrated to specific sites (Veroustraete et al. 1996, Gao 1994, Colello et al. 1998). Application
of either approach requires parameters that cannot be remotely sensed such as the carbon and nitrogen
content of the soil and litter in addition to soil texture, temperature, and moisture.
Plant respiration is similarly difficult to predict. It is typically subsumed within the dry
matter:radiation quotient (ε n) (Prince 1991), estimated as a fraction of GPP (Goward and Dye 1987,
Landsberg and Waring 1997), or modeled based on vegetation type (Ruimy et al. 1996a). A promising
approach involves remotely sensing aboveground biomass and relating this to rates of maintenance
respiration (e.g. Prince and Goward 1995).
Recent studies have shown that theories of resource optimization applied to plant canopies can
provide suitable constraints to estimate canopy photosynthetic capacity (e.g. Johnson et al. 1995,
Haxeltine and Prentice 1996). Such theories have a sound theoretical basis in that acclimation to the
prevailing growth conditions allows plants to maintain optimal photosynthetic and resources use
efficiency (Arnon 1982, Anderson et al. 1995). This strategy maximizes evolutionary fitness by ensuring
optimal use of the environment and a competitive advantage when resources are limited (Bloom et al.
1985).
Estimates of canopy photosynthetic capacity, in turn, may be used to estimate the rate of whole
plant respiration consistent with maximizing daily net primary productivity (e.g. Dewar 1996). Further,
56
numerous studies indicate the presence of feedbacks between the nutrient status of plants and soils
involving plant uptake, litterfall, and subsequent microbial decomposition and mineralization (Vitousek
1982, Reed 1990, Woodward and Smith 1994). Eventual accommodation among these processes provides
a link between canopy physiological status and soil metabolism. These interrelationships provide the
framework for a potential link between remotely sensed variables, such as canopy light interceptance
(FPAR), and ecosystem metabolism.
Utilizing theories of acclimation and resource optimization, a generalized model of plant-soilatmosphere CO2 exchange, OPTICAL (OPTImal CALibration), is described and evaluated using eddy
covariance measurements of net ecosystem CO2 exchange (NEE) at eight sites from boreal, temperate,
and tropical environments. The model requires three variables, light, temperature, and canopy light
absorptance. These variables are used in novel ways to constrain estimates of soil temperature and plant
and soil moisture status. Canopy photosynthetic capacity is prescribed by assuming plants optimize both
photosynthetic efficiency and carbon gain for a given level of light availability (Cowan 1986, Farquhar
1989, Takenaka 1989, Field 1991, Chen et al. 1993). Photosynthetic acclimation throughout the growing
season is incorporated through a unique method of integrating the canopy response to recent changes in
light and temperature. The importance of photo-acclimation was examined by running the model using
both temporally dynamic and temporally static photosynthetic capacities. The generality of the model was
also examined by comparison with simple statistical models calibrated at each site. Rates of whole plant
respiration were estimated by solving for the optimal rate that maximized daily NPP and which was
consistent with the prescribed rate of canopy photosynthetic capacity. Soil heterotrophic respiration was
constrained using empirical relationships from the literature among leaf level photosynthetic capacity,
litter decomposition, and soil organic carbon.
57
Table 3.1. Site Characteristics
Site
Description
Peak LAIe
MAT
(°C)
Annual
Rainfal (mm)
Year
Location
Source
Goulden et al. 1997
NSA-OBS
boreal forest, (old
black spruce)
2.7
-1.5
317
1996
Manitoba, Canada
(55°54NN, 98°30NW)
NSA-FEN
boreal fen
1.4
-1.6
317
1996
Manitoba, Canada
(55°54NN, 98°24NW)
SSA-OBS
boreal forest, (old
black spruce)
2.4
0.8
421
1996
Saskatchewan, Canada
(53°54NN, 105°7NW)
Howland Forest
temperate coniferous
forest
4.7
6.3
1040
1996
Maine, USA
(45°15NN,68°54NW)
Hollinger et al. 1999
Harvard Forest
temperate deciduous
forest
3.4
7.6
1117
1992
Massachusetts, USA
(42°32NN,72°11NW)
Wofsy et al. 1993
Konza Prairie
temperate C3/C4
grassland
2.8
14.0
840
1987
Kansas, USA
(39°03NN,96°32NW)
Verma et al. 1992
HAPEX-Sahel
tropical C3/C4
savannah
1.4
27.7
554
1992
Niger, West Africa
13°33NN,2°31NE)
Hanan et al. 1997
Lafleur et al. 1997
Jarvis et al. 1997
Rondonia, Brazil
Grace et al. 1996
(10°5NS,61°57NW)
2 -2
Peak LAIe refers to the seasonal maximum effective LAI, the one-sided leaf area index (m m ) without adjustment for leaf clumping (see Chen et al. 1997).
MAT is the mean annual air temperature (EC).
ABRACOS
tropical rain forest
4.0
24.2
>2000
58
1992
ArticAlpine
Tundra
Cold
Temperate
Taiga
0
Temperate
Forest
Temperate
Rainforest
Woodland
rub
Thorn sc
Desert
20
and
odl
Wo
Shrubland
10
Semidesrt
Mean Annual Temperature ( °C)
-10
Warm
Temperate
Tropical
Tropical
Seasonal
Forest
Tropical
Rainforest
30
0
1000
2000
3000
4000
Mean Annual Precipitation (mm)
Figure 3.1. Distribution of study sites with respect to mean annual temperature and precipitation.
59
Datasets and Methods
The model was applied in eight ecosystems (Table 3.1) from contrasting environments. These
sites included two boreal forests, a sub-boreal coniferous forest, a temperate mixed deciduous forest, a
temperate C3/C4 grassland, a tropical C3/C4 savannah, and a tropical forest (Figure 3.1). Seasonal variation
in NEE for each site is shown in Figure 3.2. Measurements of incident photosynthetically active radiation
(PAR) and air temperature (Tair) were made at each site. Measurements of canopy light absorptance
(fAPAR) and methods for filling data gaps in light and temperature are described in Chapter II. Estimates of
gross ecosystem CO2 exchange (GEE) were derived from eddy covariance measurements of net
ecosystem CO2 exchange (NEE) for each site, as described in Chapter II.
Data at all sites except NSA-FEN was used only if the friction velocity (u() exceeded 0.15 m s-1
and PAR>0 µmol m-2 s-1. At fen site, u( was not available so data was used only if the windspeed (U)
exceeded 0.5 m s-1. Further, at the ABRACOS site, all data for which the absolute value of the storage
flux (Fstorage ) exceeded 10 µmol m-2 s-1 was not used (Grace et al. 1996). It should be noted that, in
contrast to the typical micrometeorological sign convention, a positive CO2 flux indicates uptake by the
ecosystem.
The importance of photo-acclimation to the overall prediction of canopy photosynthesis
throughout the growing season was examined by running the model using both temporally dynamic and
temporally-static photosynthetic capacities. Time-invariant capacities and temperature optima were
assigned to each site based on the values for the corresponding vegetation type in the SiB2 model (Sellers
et al. 1996) as summarized in Table 3.4. As Vmax0 represents the maximum carboxylation rate of a leaf at
the top of the canopy, this value was scaled to a whole-canopy rate using Equation 3.18. Photosynthetic
capacity (Pcmax) was derived from canopy Vmax (Vcmax) by inverting the biochemical model of
photosynthesis (Collatz et al. 1991, 1992):
Pcmax,C3 = Vcmax(ci-Γ)/(ci+Kc[1+Oi/Ko])
(3.1)
Pcmax,C4 = Vcmax
(3.2)
60
Figure 3.2. Measured net ecosystem exchange (NEE).
61
where ci is the CO2 concentration (µmol mol-1) inside the leaf (~0.7ca), Γ is the CO2 compensation point
(µmol mol-1), Oi is O2 concentration (20900 Pa) inside the leaf and Kc and Ko are Michaelis-Menten
constants (Collatz et al. 1991, 1992):
Kc = (30)2.1( T
-25)/10
Ko = (30000)1.2( T
(3.3)
-25)/10
(3.4)
Model Description
The model is described in three parts as related to: (1) canopy photosynthetic capacity, canopy
photosynthesis, (2) and net ecosystem productivity (Figure 3.3). The last section is further divided into
sections describing soil heterotrophic respiration and plant respiration.
Canopy Photosynthetic Capacity
Seasonal variation in photosynthetic capacity of leaves is well established (e.g. Heinicke and
Childers 1937, Saeki and Nomoto 1958, Bourdeau 1959, Davis et al. 1963, Helms 1965, Shiroya et al.
1966, Gordon and Larson 1968, Connor et al. 1971, Logan 1971, Hanson et al. 1994, Garcia-Plazoalo et
al. 1997, Murthy et al. 1997, Tezara et al. 1998), as is that of the photosynthetic temperature optimum
(Schulze et al. 1976, Berry and Bjorkman 1980, Hikosaka 1997). Variation in both result from shifts in
foliar biochemistry and anatomy that occur in response to a change in growth conditions (e.g. Woledge
1971, Boardman 1977, Berry and Bjorkman 1982, Leverenz and Jarvis 1980, Bjorkman 1981, Badger et
al. 1982, Oquist and Martin 1986, Anderson and Osmond 1987, Sims and Pearcy 1992, Sims et al. 1998).
Further, it is well established that vertical profiles of photosynthetic capacity and nitrogen
generally parallel vertical gradients of light availability (e.g. Field 1983, Hirose and Werger 1987, DeJong
and Doyle 1985, Hollinger 1989, Ellsworth and Reich 1993). Theories of resource optimization have been
used to describe and predict the depth-distribution of nitrogen and photosynthetic capacity that results
from spatial variation in light availability within natural canopies (Field 1983, Hirose and Werger 1987,
62
OptiCal
fAPAR
Tair
PAR
I
Tdew
fW
Pcmax
1.
fTopt
VPD
fSW
Tsoil
fD
fT
Pc
2.
NPP
3.
RH
NEP
Rplant
Figure 3.3. Model flow and organization. The circles represent model inputs and the rectangles
represent the end products of the three sub-models for canopy photosynthetic capacity (1), canopy
photosynthesis (2), and net ecosystem productivity (3).
63
Hirose et al. 1988, Terashima and Evans 1988, Pons et al. 1989, Schieving et al. 1992, Sellers et al. 1992,
Evans 1993, Hikosaka and Terashima 1995, Sands 1995, Hollinger 1996, Dang et al. 1997). These
theories have recently been used to predict seasonal patterns of canopy photosynthetic capacity that result
from similar, albeit temporal, variations in light availability that occur throughout a growing season
(Haxeltine and Prentice 1996).
Theories of plant functional convergence (Field 1991) and coordination (Chen et al. 1993)
applied to photosynthesis imply that leaves balance investment in N between the ability for electron
transport, Wj, and carboxylation Wc in such a way that results in the co-limitation between Wj and Wc Such
resource allocation minimizes photoinhibition or damage due to the harvesting of excess unusable
photons at saturating light levels (Anderson and Osmond 1987, Osmond 1994) and ensures that no one
factor, physiological (i.e..Wj, Wc) or environmental (light, temperature, water, nitrogen, CO2) is more
limiting than any another.
Observations of leaf level gas exchange are in general agreement with this theory. Co-limitation
between Wj and Wc has been observed for many leaves (Evans 1989) and their respective capacities (Jmax
and Vcmax) are strongly correlated (Wullschleger 1993). Sun leaves have higher photosynthetic capacities
than shade leaves (Boardman 1977, Bjorkman 1981), consistent with minimizing photoinhibition and
maintaining co-limitation between Wj and Wc at different levels of light availability. Both leaf nitrogen
content
and
maximum
stomatal
conductance
exhibit
linear
non-saturating
relationships
with
photosynthetic capacity, reflecting regulated investment in nitrogen and the potential influx of CO2 to
useable levels (Cowan and Farquhar 1977, Ehleringer and Bjorkman 1977, Wong 1979, Field and
Mooney 1986).
The overall result is that Pmax can be approximated by the point of intersection between the light
limited (P≈ α I ) and light saturated (Pmax) rates (Figure 3.4a). At the canopy scale this may be written:
Pcmax = α I
(3.5)
64
1.0
Pmax
αI
Photosynthesis →
0.8
0.6
(a)
fT
(b)
0.4
0.2
Iopt
Topt
0.0
Absorbed Irradiance →
Temperature →
0.10
0.8
0.08
α (mol mol-1 )
1.0
0.6
(c)
fD
0.4
0.2
C4
0.06
(d)
C3
0.04
0.02
0.0
0.00
0
1
2
3
4
5
6
-20
VPD (kPa)
0
20
40
60
Temperature (°C)
Relative Pmax
1.0
0.8
0.6
(e)
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
fW
Figure 3.4. Figure 2.2. Model relationships between photosynthesis and light (a), relative photosynthesis
and temperature (b), relative photosynthesis and VPD (c), quantum yield and temperature (d), and relative
photosynthetic capacity and relative plant water status (e).
65
Table 3.2. Canopy photosynthesis model equations and parameters.
No.
Equation or Parameter
Definition
(1)
S = 2600(0.57(T-25)/10)
specificity of Rubisco for CO2 relative to O2
(2)
Γ = Oi/(2SP)
CO2 compensation point (µmol mol -1)
(3)
" C3 = 0.08 (0.7ca -Γ)/(0.7ca +2Γ) fW fTopt
maximum C3 quantum yield (mol mol-1)
(4)
" C4 = 0.06 fW fTopt
maximum C4 quantum yield (mol mol-1)
(5)
" = (fC3)" C3 + (1- fC3)" C4
optimal quantum yield (mol mol-1)
(6)
I = PAR fAPAR
canopy absorbed PAR (µmol m-2 s-1)
(7)
Pcmax = α Ι
canopy photosynthetic capacity (µmol m-2 s-1)
(8)
P(I)=("I+Pcmax -(("I+Pcmax )2-4"IPcmax 2)0.5)/(22)
canopy light response (µmol m-2 s-1)
(9)
Pc =P(I) fT fD
canopy photosynthesis (µmol m-2 s-1)
(10)
fTopt = 1.1814/(1+exp[0.2(Topt-10- T )])(1+exp(0.3( T -10- Topt)])
temperature dependence of photosynthetic capacity
(11)
fT = 1.1814/(1+exp[0.2( T -10-Tair )])(1+exp(0.3(Tair -10- T )])
temperature dependence of photosynthesis (-)
(12)
fD=1/(1+exp[1.3(VPD-3)])
VPD dependence of photosynthesis (-)
(13)
fW =(T)fWi-1+(1-T)fD if Hr=1300 else fW =fWi-1
plant water stress function (-)
(14)
Ι =(T) Ι
running mean incident PAR (µmol m-2 s-1)
(15)
T =(T) T
(16)
T=exp(-)t/J)
+(1-T)I
i-1
if I>0 else = Ι
+(1-T)Tair
i-1
i-1
if PAR>0 else T = T
running mean daytime temperature (EC)
i-1
running mean weighting coefficient
66
where Pcmax is the canopy photosynthetic capacity, α is the canopy quantum yield and I is the timeaveraged irradiance absorbed by the green fraction of the canopy (Table 3.2). This method provides the
means to predict both the magnitude of photosynthetic capacity and its seasonal variation simply from the
time-series of light, temperature, and fAPAR. This approach was previously applied and tested at the same
sites used here (Chapter II).
Canopy Photosynthesis
Actual rates of canopy photosynthesis were calculated by reducing canopy photosynthetic
capacity as a result of environmental constraints (Table 3.2):
Pc = Pc(I) fT fD
(3.6)
where Pc(I) is the unstressed rate of photosynthesis at a given irradiance (Table 3.2) and fT and fD are
empirical constraints related to the effects of air temperature and moisture (Figure 3.4). Equation 3.6 is
based on the 'big-leaf' concept (e.g. Sellers et al. 1992). If all leaves optimally acclimate then every leaf in
a canopy should photosynthesize in concert and the transition from light-limitation to light-saturation will
occur simultaneously among all leaves (Farquhar 1989, Field 1991, Terashima and Hikosaka 1995).
Under these conditions, canopy photosynthesis can be modeled as the rate of an individual leaf but with
the leaf area of an entire canopy.
Big-leaf assumptions are likely to breakdown given the instantaneous variations in sunlight that
typically occur in a canopy as a result of diurnal changes in solar elevation and cloud cover, particularly
with respect to gaps in the canopy (Terashima and Hikosaka 1995, DePury and Farquhar 1997). In
addition to the fact that canopies are not evenly illuminated at instantaneous timescales, leaves may not
fully acclimation to their local light environments. Under such conditions the non-linear nature of light
response curves can invalidate big leaf approximations (Wang et al. 1998).
Multi-layer models are not subject to these potential problems but their complexity makes their
application difficult. As noted by Raupach and Finnigan (1988), single-layer models are incorrect but
useful, whereas multi-layer models are correct but often difficult to employ. As a compromise between
67
these two extremes, DePury and Farquhar (1998) and Wang et al. (1998) have extended the two-layer
“sun-shade” model of Norman (1979) to include aspects of optimal nitrogen distribution (Field 1983) and
coupling between stomatal conductance and photosynthesis (Ball 1988).
The principle variables in sun/shade models are fairly conservative such that they can be applied
without considerable complexity beyond that of big-leaf models (DePury and Farquhar 1998). Assuming
there is always an equal amount of leaf area exposed normal to sunlight (spherical leaf angle distribution),
only a few key variables are required (Norman 1979). In more complex treatments (DePury and Farquhar
1998, Wang et al. 1998) several leaf and canopy optical properties must be specified including scattering,
reflectance, and extinction coefficients to direct and diffuse PAR. These parameters are fairly
conservative among most plants (Sellers et al. 1996) such that they should not impose significant
constraints to the global application of sun/shade models.
Despite these recent advances, sun/shade models -- like big-leaf models-- still require an
empirical curvature parameter describing the non-linear response of photosynthesis (or electron transport)
to absorbed irradiance. Further, contrary to criticisms, many studies have found that big-leaf models are
adequate for describing instantaneous ecosystem scale photosynthesis (Amthor et al. 1994, Lloyd et al.
1995, Hanan et al. 1998, Hollinger et al. 1999). Given the relative simplicity and proven success of bigleaf models, in addition to the inability to prescribe the canopy light response from first principles without
detailed knowledge of foliar biochemistry (e.g. Kull and Kruijt et al. 1998), the big-leaf approach was
used here.
Canopy Quantum Yield. Canopy quantum yield was assumed to equal that of individual leaves
and was determined differently for C3 and C4 plants (Ehleringer and Bjorkman 1978, Collatz et al. 1998)
(Figure 3.4d). Maximum canopy quantum yield was constrained as was photosynthetic capacity (Table
3.2). This assumes the efficiency of electron transport is inhibited similarly to carboxylation capacity (i.e.
Pcmax).
Temperature Effects. The temperature to which the vegetation is adapted (Topt ) was assumed
equal to the mean daytime air temperature, T , calculated as the 5-day running mean (Table 3.2) at the
68
time of the seasonal maximum light absorptance (fAPAR). For those sites where fAPAR did not vary (e.g sites
with evergreen vegetation), it was assumed that the plants were adapted to their local thermal climate
such that Topt was set equal to the annual maximum T .
In this fashion, Topt represents a genotypic temperature optimum and characterizes a temperature
response function (fTopt , see Table 3.2) which defines the upper limit to capacity for photosynthesis at a
given temperature. The genotypic temperature optimum was distinguished from the phenotypic
temperature optimum which changed with the mean daytime air temperature (T ). This temperature of
acclimation due to phenotypic plasticity characterized a temperature response function (fT , see Table 3.2)
which defined the upper limit to actual photosynthesis at a given temperature. Thus, although a plant may
be acclimated to the recent daytime air temperature (T ) and thus operating near its phenotypic optimum
for most of the day, its capacity for photosynthesis may be relatively low if the phenotypic optimum was
below or above the genotypic optimum (Topt ).
Stomatal Limitations. The response of photosynthesis to VPD-related effects (fD, see Table 3.2),
was described in Chapter II. Briefly, stomatal closure was induced above a VPD of 1 kPa with an
exponential decline in stomatal conductance between 1 and 6 kPa (Figure 3.4c). This relative stomatal
conductance function, fD, was applied directly to photosynthesis because it was assumed that
photosynthesis varied linearly with stomatal conductance. This assumption is strictly valid only during
non-stressful conditions (Wong et al. 1979) but was employed because it is both simple and robust.
Plant Water Stress. The moisture status of the plant (fW ) was assumed to affect photosynthetic
capacity directly (Figure 3.4e and Table 3.2) and was represented by the 5-day running mean of relative
midday stomatal conductance:
fW = f D ,midday
(3.7)
This assumes that persistent atmospheric drought occurs concurrently with persistent stomatal closure
which only occurs when the plant is water stressed (Figure 3.5). This may be valid as long as there is
feedback between transpiration and VPD. High VPD can induce low stomatal conductance (g) (Figure
69
Figure 3.5. Interrelationships among soil, plant, and atmospheric moisture status.
70
3.4c), leading to low rates of transpiration (E where E=gVPD). For a given increase in VPD, there is a
linear increase in transpiration while there can be an exponential decrease in stomatal conductance
(Figure 3.4c). Such accommodation between plant and atmospheric moisture is likely to occur only
during midday hours when the canopy and atmospheric boundary layers are convective and well mixed
(Monteith 1995). For further description of this parameterization, see Chapter II.
Net Ecosystem Productivity
Net ecosystem productivity (NEP) was calculated as the difference between CO2 uptake by
canopy gross photosynthesis (Pc) and CO2 loss by plant (Rp ) and soil heterotrophic respiration (RH)
(Figure 3.3):
NEP = Pc - Rp - RH
(3.8)
Canopy gross photosynthesis was described above and plant and soil respiration are described below. The
calculation of soil temperature and moisture and their respective effects on soil respiration are described
below as well. Equations related to prediction of net ecosystem productivity are summarized in Table 3.3.
Plant Respiration. Dewar (1996) extended the concept of photosynthetic nitrogen use efficiency
(Field 1983) to the whole plant and proposed that for a given APAR, net primary productivity (NPP) has
a maximum value with respect to plant nitrogen content. Nitrogen (N) is a strong determinant of both
photosynthetic capacity (e.g. Field and Mooney 1986, Evans 1989) and maintenance respiration (Jones et
al. 1978, Merino et al. 1982, McCree 1983, Waring et al. 1985, Irving and Silsbury 1987, Ryan 1991,
Ryan 1995). The majority of plant nitrogen resides in proteins of which the replacement and repair
accounts for approximately 60% of total maintenance respiration (Penning de Vries 1975).
As the nitrogen content of a canopy (Nc) increases, both the capacity for photosynthesis and the
intrinsic rate of maintenance respiration increase. The optimum canopy nitrogen content is that which
provides the maximum net carbon gain or net primary productivity (NPP), or the greatest difference
between photosynthesis and respiration. In economic terms, the return on nitrogen investments
theoretically diminishes for a leaf with increasing nitrogen invested (Field 1991) and there exists a point
71
Table 3.3. Net ecosystem productivity model equations and parameters.
No.
Equation or Parameter
Definition
(1)
NEP = Pc - Rp - RH
net ecosystem producitivy (µmol m-2 s-1)
(2)
RT = 2(Tair - T
temperature dependence of maintenance respiration
(3)
Rg = (1-Yg)
)/10
/(1+exp[0.3(Tair -10- T )])
t24
∫
daily growth respiration (µmol m-2 d-1)
(Pc -Rm,inst) dt
0
t24
∫
(4)
Rm =
(5)
Rp,inst ≈ Rp,inst = (Rg+Rm )/t24
instantaneous maintenance respiration (µmol m-2 s-1)
(6)
Amax = Acmax (1- τ PAR )/ k PAR
maximum leaf assimilation rate (µmol m-2 s-1)
(7)
Acmax = Pcmax - (0.11Pcmax )2(Tair - T
(8)
τ PAR = 1-fIPAR
canopy PAR transmittance (-)
(9)
SOC = ln(Amax /50)/ln(0.999927)
soil organic carbon (g m-2)
(10)
L.0.1 SOC
litter carbon (g m-2)
(11)
JSOC,20 = (0.12775) 2.4(20-26)/10
soil carbon turnover time at 20°C (years)
(12)
JL,20 = 12exp(-0.095Amax )
litter turnover time at 20°C (years)
(13)
RH,20 = fc,max 0.00264 (0.55LJL,20-1 +0.55SOCJSOC,20-1)
soil heterotrophic respiration at 20°C (µmol m-2 s-1)
(14)
A20 = RH,20/exp(-308.56/[20+46.02])
Lloyd and Taylor coefficient
(15)
RH = fSW A20exp(-308.56/[Tsoil+46.02])/(1+exp[Tsoil-40])
soil heterotrophic respiration (µmol m-2 s-1)
(16)
fSW = fW fAPAR′
soil moisture stress function (-)
(17)
fAPAR′ = fAPAR/(fAPAR,max fTopt) if JD<JD@ fAPAR,max else fAPAR′=1
normalized fAPAR (-)
(0.34 Pcmax td/t24) RTfW dt
daily maintenance respiration (µmol m-2 d-1)
0
(18)
(19)
)/10
maximum canopy assimilation rate (µmol m-2 s-1)
Tsoil = (fc fSW )Tmin + (1-fc fSW )Tmax
if Tair >0EC
Tsoil = 0.1[(fc fSW )Tmax + (1-fc fSW )Tmin]
if Tair <0EC
time-averaged soil temperature (°C)
Tsoil = Tsoil +0.5(Tmax -Tmin)(1- fc fSW )cos(2π[t-1600]/2400)
soil temperature (°C)
72
(optimal N) where further increase in N will provide no further increase in net assimilation (∂A/∂N=0).
This argument can be applied to canopy nitrogen (Nc) and whole plant NPP, that is, there exists a point
(optimal Nc) where further increase in Nc will provide no further increase in net carbon gain
(∂NPP/∂Nc=0). The critical assumption here is that canopy nitrogen varies in proportion with whole plant
nitrogen. This appears to be a reasonable assumption for most plants (Dewar 1996). An analogous
argument can be made by replacing Nc with canopy photosynthetic capacity (Pcmax) because Nc varies in
proportion with Pcmax. As such, optimal Pcmax is that which satisfies the constraint, ∂NPP/∂Pcmax=0.
Expressing instantaneous rates of both canopy gross photosynthesis (Pc) and maintenance
respiration (Rm,inst) as functions of Pcmax:
Pc = (αI + Pcmax - [{αI + Pcmax)2 - 4αI Pcmaxθ]0.5)/(2θ)
(3.9)
Rm,inst = rPcmax
(3.10)
Where θ is an empirical curvature parameter (0.9), I is the absorbed irradiance (I = fAPAR PAR), and r is
the ratio of maintenance respiration to Pcmax, net primary productivity may be expressed:
t24
t24
0
0
NPP = Yg ( ∫ (αI+Pcmax - [(αI+Pcmax)2 - 4αI Pcmaxθ]0.5)/(2θ) dt - ∫ rPcmax dt)
(3.11)
where Yg is the proportion of assimilate not lost as growth respiration and td is daylength (s).
Differentiation of the Equation 3.11 with respect to Pcmax and setting ∂NPP/∂Pcmax=0 (the optimality
constraint) results in an expression with two unknowns, Pcmax and r. Thus, for every value of Pcmax there
exists a unique value of r which satisfies the condition ∂NPP/∂Pcmax=0. Given the complexity of
differentiating Equation 3.11, numerical integration was performed with the constraint that NPP is
maximized for a given Pcmax by allowing r to vary. Assuming a sinusoidal variation in PAR over the
course of a day with average irradiance equal to 71% of the maximum irradiance (Running and Coughlan
1988), the following relationship was found:
r = 0.34 td/t24
(3.12)
73
where t24 is the time in one day (86400s). Thus, for an average day with 12 hours of sunlight (td=12), the
optimal instantaneous maintenance respiration rate is 0.17Pcmax, or 17% of canopy photosynthetic
capacity.
The optimal instantaneous maintenance respiration rate, Rm,inst, was adjusted for the effects of
temperature and plant water status. The temperature effect (RT ) was represented by an exponential
function with a Q10 of 2 and an upper temperature limit 10°C above the photosynthetic temperature
optimum ( T ):
RT = 2(Tair- T
)/10
/(1+exp[0.3(Tair-10- T )])
(3.13)
In addition, it was assumed that respiration, along with all physiological activity, decreased during
periods of water stress, the latter represented by fW. In summary, instantaneous maintenance respiration
(Rm,inst) was determined as:
Rm,inst = (0.34 Pcmax td/t24) RT fW
(3.14)
Growth respiration (Rg) was estimated as a fraction (1-Yg) of the difference between daily total
photosynthesis and maintenance respiration (Jarvis and Leverenz 1983):
t24
Rg = (1-Yg) ∫
(Pc-Rm,inst) dt
(3.15)
0
Thus, growth respiration could only be calculated at a daily time step (Rg cannot be calculated correctly at
using Equation 3.15 when Pc is zero at night), although photosynthesis and maintenance respiration could
be calculated at an instantaneous time step. In order to estimate an instantaneous rate of whole plant
respiration (Rp,inst) consistent with the time interval of eddy covariance measurements, an average
instantaneous rate ( Rp,inst ) was determined by summing instantaneous Pc and Rm,inst over the whole day,
solving for Rg using Equation 3.15, and dividing by the time in one day:
Rp,inst ≈ Rp,inst = (Rg+Rm)/t24
(3.16)
For lack of a better method, the instantaneous rate of whole plant respiration was thus held constant over
the entire day with a new value calculated each day.
74
Soil Heterotrophic Respiration. Woodward and Smith (1994) provide evidence indicating that
rates of plant nitrogen uptake are not only indicative of leaf photosynthetic capacity, but also reflect levels
of soil nitrogen availability and soil fertility in general. As leaf level net assimilation capacity (Amax)
decreases, plants increasingly rely on organic sources of nitrogen and soil organic carbon content
generally increase. This is consistent with decreased nitrogen mineralization rates and increased soil
carbon turnover times as a result of low microbial productivity in low productivity ecosystems (Vitousek
1982). If accommodation between plant and soil metabolism eventually occurs, Amax should provide an
indication of soil organic carbon (SOC) content (Woodward and Smith 1994):
SOC = ln(Amax/50)/ln(0.999927)
(3.17)
where Amax and SOC have units of µmol CO2 m-2 s-1 and gC m-2, respectively. Assuming that Equation
3.17 is based on measurements of sunlit leaves near the top of the canopy, Amax was estimated by
assuming an optimal distribution of photosynthetic capacity with depth in a canopy (Sellers et al. 1992).
That is, vertical gradients of Amax parallel vertical gradients of light transmittance such that the whole
canopy assimilation capacity Acmax can be related to the capacity of a sunlit leaf at the top of the canopy
(Sellers et al. 1992):
Amax = Acmax(1- τ PAR )/ kPAR
(3.18)
where τ PAR is the time-averaged whole canopy PAR transmittance (note τ PAR = 1-fIPAR) and kPAR is the
time-averaged PAR extinction coefficient (~0.5). Canopy net assimilation capacity, Acmax, was calculated
as:
Acmax = Pcmax - (0.11Pcmax)2(Tair- T
)/10
(3.19)
where 0.11 is the fraction of photosynthetic capacity respired as dark respiration (Enriquez et al. 1996).
Based on results from the CENTURY model, Schimel et al. (1994) predicted small variations in
the relative distribution of soil carbon among microbial, litter (L), and slow and active pools across a wide
range of biomes types and mean annual temperatures and soil textures:
L≈0.1 SOC
(3.20)
75
Additionally, data presented by Woodward and Smith (1994) was used to relate leaf photosynthetic
capacity to leaf litter turnover times (years) at a reference temperature of 20°C:
τL,20 = 12exp(-0.095Amax)
(3.21)
It was assumed that total litter (leaf + root) has half the nitrogen concentration as leaf litter alone. Using
data from Woodward and Smith (1994) relating leaf litter turnover times to C:N ratios indicates that
doubling C:N has the effect of increasing turnover times by 66%.
Assuming a constant turnover time for SOC (τSOC =0.12775 years) at a reference temperature of
26°C and an exponential temperature dependence with a Q10 of 2.4 following Hunt et al. (1996), the
turnover time (years) adjusted to 20°C was estimated as:
τSOC ,20 = (0.12775) 2.4(20-26)/10
(3.22)
Combining gives the rate of soil heterotrophic respiration (µmol m-2 s-1) at 20EC:
RH,20 = fc,max 0.00264 (0.55LτL,20-1 +0.55SOCτSOC,20-1)
(3.23)
where 0.00264 converts to µmol m-2 s-1, 0.55 is the proportion of decomposed C evolved as CO2, and fc,max
is the seasonal maximum fractional vegetation cover (assumed equal to fIPAR/0.962, where 0.962 is the
maximum fIPAR value of the NDVI/fIPAR relationship described in the Appendix, Chapter II). Vegetation
cover was included because unvegetated soil was assumed to have too little moisture and/or nutrients to
support either plant growth or significant microbial activity. Under ambient conditions, RH was adjusted
for temperature and moisture effects assuming a temperature dependence described by Lloyd and Taylor
(1996) and moisture limitations equal to plant moisture limitations (fSW, see below):
RH = fSWA20exp(-308.56/[Tsoil+46.02])/(1+exp[Tsoil-40])
(3.24)
where fSW is the soil moisture stress function (see below) and A20 is the Lloyd and Taylor (1996)
coefficient:
A20 = RH,20/exp(-308.56/[20+46.02])
(3.25)
A schematic representation of the soil heterotrophic respiration calculation is shown in Figure 3.6.
76
Plant N-Uptake
N Mineralization
CO
Soil
2
Plant litter
Plant N-Uptake
CO2Litter
Litter
.55
N Mineralization
Assuming:
kL = f(Litter N, Tsoil, SW)
kSoilC = f(Tsoil ,SW)
Soil C <=> Amax
Litter <=> Soil C
And:
Litter N <=> Amax
Then:
CO2Litter + CO2SoilC = f(Amax,Tsoil,SW)
Soil C
.55
Passive C
Figure 3.6. Carbon and nitrogen interactions between plants and soil assumed in the simplified
soil heterotrophic respiration model.
77
Soil Moisture. While neither soil water content nor plant moisture status was explicitly modeled,
it was assumed that a relative change in the canopy leaf area index (LAI) reflected a long-term, timeaveraged change in plant water status and hence soil moisture availability (Figure 3.5). Long-term
changes in soil moisture availability were assumed related to the relative change in transpiring leaf area
(fAPAR) assuming plants maintain a balance between transpirational demand and soil moisture availability.
In addition, it was assumed that short-term changes in plant water status that occurred faster than changes
in LAI could be inferred from the moisture status of the atmosphere (Equation 3.7 and see Chapter II).
Thus, at any moment in time, soil moisture availability may be reflected by either changes in plant water
status or by changes in fAPAR. The soil moisture stress function (fSW) was thus calculated as the product of
short-term (fW) and long-term (fAPAR′) effects:
fSW = fW fAPAR′
(3.26)
where fAPAR′ is the current fAPAR value relative to its seasonal maximum:
fAPAR′ = fAPAR/(fAPAR,max fTopt )
(3.27)
Because it is unlikely that a plant will exhibit soil water stress prior to the seasonal peak leaf display,
represented by fAPAR,max, fAPAR′ was set to unity before fAPAR,max occurred. Finally, in order to deduce
changes in soil moisture from changes in leaf area, the confounding effects of temperature must first be
removed. Towards this end, fAPAR was normalized to fTopt (Table 3.2) which represented temperature
limitations above and below the genotypic temperature optimum (Topt ).
Soil Temperature. Soil temperature was assumed to track, on average, local air temperature. This
implies that sites with persistently high air temperatures have high soil temperatures (and visa versa).
Complicating the picture, the presence of a canopy covering the soil surface will shade and insulate the
soil, effectively slowing the rise and fall of soil temperature and increasing its tendency towards the daily
minimum air temperature (Tmin), rather than the maximum. Conversely, in the absence of canopy cover
the soil surface temperatures will rise with under direct sunlight and will tend towards the daily maximum
air temperature (Tmax). Soil moisture will have similar effects as canopy cover, slowing temperature
78
changes with a tendency towards the minimum air temperature as the soil approaches field capacity.
Thus, the time-averaged soil temperature may be expressed as somewhere between the two extremes of
the Tmin and Tmax:
Tsoil = (fcfSW)Tmin + (1-fcfSW)Tmax
if Tair>0EC
(3.28)
where Tsoil is the daily average near-surface soil temperature (EC), and fc is the fractional vegetation cover
(fc≈fIPAR see above). Below 0°C, the situation is reversed because of the change in the sign convention,
that is, soil temperature is assumed to track Tmax rather than Tmin:
Tsoil = 0.1[(fcfSW)Tmax + (1-fcfSW)Tmin]
if Tair<0°C
(3.29)
Initial results indicated that wintertime soil temperatures were not strongly influenced by changes in air
temperature so Tsoil was multiplied by 0.1. Presumably, this factor accounts for insulation by snow or ice
which dampen temperature fluctuations. Diel variations in soil temperature, which can be large in the
absence of vegetation cover and when soil moisture is low, was introduced by assuming the daily time
course followed a cosine function:
Tsoil = Tsoil +0.5(Tmax-Tmin)(1- fcfSW)cos(2π[t-1600]/2400)
(3.30)
where t is the time (noon=1200).
Results and Discussion
Application and evaluation of the canopy photosynthetic capacity routine is presented and
discussed in Chapter II.
Canopy Photosynthesis
Diurnal Variation. Diurnal variation in modeled and observed canopy photosynthesis, assumed
here to be equivalent to gross ecosystem exchange (GEE), is shown in Figure 3.7 for three 1-week periods
during early, middle, and late times of the measurement periods at each site. Overall, model predictions
79
Boreal Forest (NSA-OBS)
Boreal Fen
Boreal Forest (SSA-OBS)
Temperate Coniferous Forest
Temperate Deciduous Forest
Temperate C3/C4 Grassland
Tropical C3/C4 Savanna
Tropical Rainforest
Figure 3.7. Modeled (lines) and observed (symbols) gross ecosystem exchange of CO2 (GEE)
during early, middle and late periods of the measurement periods at each site.
80
agree well with the observations. However, the model overestimated on Julian Days (JD) 207 and 208 at
the boreal northern old black spruce site (NSA-OBS) and underestimated on several days including JD
209 at the temperate coniferous forest, JDs 156, 203, 204, 206, and 210 at temperate deciduous forest,
during most of the early period at the temperate grassland site, most of the late period at the tropical
savanna, and JD 133 at the tropical rainforest. These discrepancies are indicative of problems with either
fAPAR estimation, temperature and PAR gap filling, the derivation of GEE from NEE or model
parameterization (e.g. big-leaf approximation, temperature and VPD response functions, and estimates of
Pcmax or Topt etc.). Separation of these various effects is difficult. However, underestimations during the
early period in the temperate grassland and during the late period at tropical savanna site are consistent
with the underestimations of Pcmax during these times (see Chapter II) implying errors in parameter
estimation.
Functional Responses. Predicted and observed photosynthesis is plotted with respect to incident
PAR in Figure 3.8. For each site, all the data from each 1-week period (early, middle, late) were pooled
together. For all but northern boreal forest (NSA-OBS) and the tropical savanna, the big-leaf model
appeared to provide good predictions of the canopy light response, as the residuals generally exhibited a
weak relationship with incident PAR at most sites (r2<0.1, P>0.05, data not shown). The discrepancies at
the boreal forest and tropical savanna likely stem from errors at the Pcmax level which, in turn, could result
from errors in fAPAR.
Despite differences in canopy architecture, the identical parameterization of the big-leaf model at
all sites provided reasonable predictions. For example, the coniferous canopy (Howland) has a relatively
high total one-sided leaf area index (~6, Hollinger et al. 1999) with small needle-leaves that presumably
scatter light to a greater extent than the more vertically-oriented leaves of the temperate C3/C4 grassland
canopy (LAI~3), which allow greater light penetration deep in the canopy at high sun angles. However,
consistent with the near-linear response of the grassland canopy, the model overestimated at low light
levels and underestimated at high light levels. Knowledge of basic architectural characteristics as related
to broad functional vegetation types (e.g. Nemani and Running 1997) may improve the estimation of
81
Figure 3.8 Predicted and observed photosynthetic light response. Only data from the early,
middle, and late periods of the growing season (see Figure 3.4) are shown.
82
canopy light absorptance (e.g. Myneni et al. 1997) as well as the integration of whole canopy
photosynthesis using sun/shade models with functional-group-specific radiation transfer coefficients.
Interestingly, the initial slope of the photosynthetic light response at the grassland was lower as
compared to that of the coniferous forest (Figure 3.8). Yet, the maximum photosynthetic rates were higher
at the grassland site. There may be trade-offs, related to either canopy architecture or physiology, such
that the ability to achieve high photosynthetic rates at high light intensities correlates with lower
photosynthetic efficiency at low light intensities. The lower initial slope at the C3/C4 grassland site may
have also resulted from higher leaf temperatures which can effectively decrease C3 quantum efficiencies.
This effect would not have been captured by the model because leaf temperatures were assumed equal to
air temperatures.
Variation in canopy photosynthesis with respect to temperature and VPD appeared to be well
predicted by the model based on the fact that the variation in residuals (observed GEE - predicted GEE)
appeared to be independent of variations in these factors -- as indicated by low coefficients of
determination for regressions between residuals and Tair and VPD (r2<0.1 for all sites, P>0.05, data not
shown). Apparently, the unexplained variation in GEE was unrelated to variations in temperature and
VPD and may have been due to inherent variability of the eddy covariance measurements. Models,
calibrated or uncalibrated, across all levels of complexity, generally do not explain more than 80% of the
variability in half-hourly eddy covariance measurements (e.g. Amthor et al. 1994, Goulden et al. 1997).
Accuracy. Consistent with the time series (Figure 3.7) and light response plots (Figure 3.8) there
was good overall correspondence between the modeled and observed gross ecosystem exchange (Figure
3.9) for all sites. As expected from the over-predictions of canopy photosynthetic capacity found at the
northern boreal forest site (NSA-OBS) (Figure 2.7), the slope of the relationship between modeled and
observed GEE is greater than one. At all other sites, the slopes were less than one suggesting a systematic
under-estimation of the highest fluxes. Among all sites, the model explained from 74 to 85% of the
variability in gross ecosystem exchange.
83
25
15
Boreal Forest (NSA-OBS)
y=1.08x+0.43
2
r =0.80
20
Boreal Fen
y=0.69x+0.42
2
r =0.82
10
15
10
5
5
0
0
-5
-5
-5
0
5
10
15
20
25
-5
25
5
10
15
35
Boreal Forest (SSA-OBS)
y=0.87x+0.72
20
Predicted GEE (µmol m-2 s-1)
0
Temperate Coniferous Forest
y=0.83x+0.73
30
2
2
r =0.74
r =0.80
25
15
20
10
15
10
5
5
0
0
-5
-5
-5
0
5
10
15
20
25
-5
35
0
5
10
15
20
25
30
35
50
Temperate Deciduous Forest
y=0.75x+0.66
r2=0.76
30
25
Temperate C3/C4 Grassland
y=0.79x+2.97
r 2=0.85
40
30
20
15
20
10
10
5
0
0
-5
-5
0
5
10
15
20
25
30
35
0
20
10
20
30
40
50
35
Tropical C3/C4 Savanna
y=0.85x
r 2=0.83
Tropical Rainforest
y=0.84x+2.39
r 2=0.74
30
25
20
10
15
10
5
0
0
-5
0
10
20
-5
0
5
10
15
20
25
30
35
Observed GEE (µmol m-2 s-1 )
Figure 3.9. Relationship between model predictions and field observations of gross ecosystem
exchange of CO2.
84
Table 3.4. Time-invariant parameter values (taken from SiB2, Sellers et al. 1996a) used for ‘without
acclimation’ model predictions. Vmax0 is the maximum Rubisco capacity of a sun leaf at the top of the
canopy (µmol m-2 s-1). T low and T high are temperatures at which photosynthesis is at 50% of its maximum.
Site
SiB2 Land Cover Type
Vmax0
Tlow
Thigh
Boreal Forest (NSA-OBS)
Needleleaf-evergreen trees
60
5
30
Boreal Fen
Dwarf trees and shrubs
60
5
30
Boreal Forest (SSA-OBS)
Needleleaf-evergreen trees
60
5
30
Temperate Coniferous Forest
Needleleaf-evergreen trees
60
5
30
Temperate Deciduous Forest
Broadleaf-deciduous trees
100
10
38
Temperate C3/C4 Grassland
C4 grassland
30
15
40
Tropical C3/C4 Savanna
C4 groundcover & tall vegetation
30
15
40
Tropical Rainforest
Broadleaf-evergreen trees
100
15
40
85
Table 3.5. Comparison of model predictions made with and without acclimation.
With Acclimation
b
r2
1.08
0.43
0.80
Boreal Fen
0.69
0.42
Boreal Forest (SSA-OBS)
0.87
3Error (tC ha-1)
Without Acclimation
3Error (tC ha-1)
m
b
r2
-1.1 (23.1%)
1.13
0.49
0.72
-1.49 (31.1%)
0.82
0.32 (11.5%)
0.73
0.47
0.68
-0.08 (2.8%)
0.72
0.74
-0.32 (4.6%)
0.91
0.89
0.70
-0.94 (14.2%)
0.83
0.73
0.80
-0.01 (0.1%)
0.87
1.27
0.69
-1.34 (20.3%)
0.75
0.66
0.76
0.16 (3.3%)
0.90
0.47
0.72
-0.27 (5.8%)
Temperate C3/C4 Grassland
0.79
2.97
0.85
-0.03 (1.6%)
0.48
2.88
0.77
0.48 (31.1%)
Tropical C3/C4 Savanna
0.85
0.00
0.83
0.08 (9.5%)
1.00
0.00
0.83
-0.03 (4.5%)
0.84
2.39
0.74
-0.11 (11.2%)
0.83
2.17
0.74
-0.04 (7.9%)
Site
m
Boreal Forest (NSA-OBS)
Temperate Coniferous
Forest
Temperate Deciduous
Forest
Tropical Rainforest
-1
The cumulative error (tC ha ) is the sum of residuals (3(Oi-P i)).
The percentage error (100*3(Oi-P i)/3Oi*) is given in parentheses.
The variables m and b relate predicted values to those observed (P<0.05) such that Predicted=mObserved+b
86
Importance of Photoacclimation. Parameter values used in the model runs without
photosynthetic acclimation are summarized in Table 3.4. The results of the model runs using these values
as well as those produced with the acclimation routine are shown in Table 3.5. It should be noted that
variation in the amount of leaf area though the growing season will cause the canopy capacity to vary,
even though the leaf level rates remain constant. This may be considered a form of (morphological)
acclimation if in fact plants regulate the amount of leaf area in tune with favorable growth conditions
(Field 1991). Thus, the without-acclimation runs should be interpreted as being as close as possible to
every thing else being equal except for variation in physiological status through time.
The performance of the model with and without acclimation as compared to the observed gross
ecosystem exchange is summarized in Table 3.5. Overall, the model with acclimation provided better
predictions, as indicated by higher r2 values and smaller cumulative errors. Acclimation appeared to
account for an additional 0 to 14% of the variability in gross ecosystem exchange. However, the slopes
were generally closer to unity for the model without acclimation. Nevertheless, these differences were
generally modest and, as such, may imply that photosynthetic acclimation is not crucial for accurate
prediction of photosynthesis over the growing season. Further, the model runs without acclimation
incorporate a certain degree of seasonal variation in canopy photosynthetic potential through variation in
leaf area index (fAPAR). Changes in the amount of leaf area may thus be more important to the prediction
of canopy photosynthesis than changes in physiological status of the leaves. However, visual inspection
of the seasonal time course of predictions and observations (not shown) suggests that the model runs
without acclimation did not accurately capture the timing of spring increases and fall declines in gross
ecosystem exchange as well as the model with acclimation. Acclimation may provide the greatest benefit
during the periods of greatest transition in physiological status, such as spring and fall or during onset and
senescence.
The results also imply that canopy photosynthesis can be predicted equally well without any prior
knowledge of vegetation type. At a minimum, all that is required is fAPAR, incident PAR, and air
87
temperature. This provides support for the acclimation model and these three variables as being
representative of the fundamental processes which control variation in photosynthesis throughout the
growing season and among sites with contrasting vegetation and climate.
Generality of the Model. As noted by Aber et al. (1996) and Goulden et al. (1997), most of the
variability in gross ecosystem exchange at a particular site can be explained by relatively simple models
fit to the observations. Such models thus provide a benchmark against which the relative accuracy or
generality of other more sophisticated models may be assessed. Parameter values and overall variance
explained by fitting such simple models at each site is summarized in Table 3.6.
The r2 values of the simple calibrated models (Table 3.6) are very similar to those of the model
without acclimation (Table 3.5). This is consistent with the fact that both models did not incorporate any
form of acclimation. The OPTICAL model (with acclimation) accounted for up to 19% more of the
variance in gross ecosystem exchange than the fitted site-specific models. Across all sites the OPTICAL
model thus did nearly as well or better than the site-specific models, supporting the notion that the
OPTICAL model is a good general model of canopy photosynthesis. Surprisingly, a “global” regression
model, based solely on light and temperature, explained 62% of the variation in GEE across all sites. At
each site, however, the r2 values for the OPTICAL model exceeded those of the global regression model.
Net Ecosystem Productivity
Soil Temperature. Seasonal variation in predicted and observed soil temperature is shown in
Figure 3.10. Overall, model predictions of the near-surface soil temperature agree reasonably well with
the observations taken near 10 cm depth. The magnitude of the predicted soil temperatures also agree
closely with observations at all sites except Harvard Forest where the model underestimates in early
summer and is consistently low thereafter. This cause of this underestimation is not clear. It appears to be
unrelated to concurrent changes in ambient or mean daytime air temperature or fAPAR.
The seasonality of soil temperature and much of its variability was accounted for by the model
88
Table 3.6. Fitted parameter values for site-specific statistical models.
Site
GEE4
K
Topt
r2
NSA-OBS
14.6
149
19.7
0.76
NSA-FEN
10.2
247
21.6
0.63
SSA-OBS
17.3
210
17.8
0.70
Howland
26.0
206
22.6
0.79
Harvard Forest
33.0
346
23.5
0.77
FIFE
"=0.024 mol mol-1, k=0.18 kPa-1
25.0
0.69
HAPEX-Sahel
28.9
1502
25.7
0.82
ABRACOS
30.7
543
27.3
0.77
All Sites
19.6
253
22.5
0.62
GEE was modeled using a rectangular hyperbola constrained at low and high temperatures:
GEE = GEE4I/(K+I) C f(T)
where I is incident PAR, GEE4 is the asymptote (µmol m-2 s-1), and K is the light level at half GEE4 (µmol m-2 s-1).
The temperatere modifier f(T) was calculated as:
f(T) = 1/([1+exp(0.2[Topt -10-Tair])][1+exp(.3[Tair-10-Topt ])])
where Topt is the optimal temperature (EC). The temperate grassland site was best modeled with a linear light
response and by adding a VPD response:
GEE = "I C f(T) C f(VPD)
where " has units of mol mol-1 and f(VPD)=1-kVPD with the constant k in units of kPa-1. For all other sites, VPD
generally explained only a small amount of the variation (<1%) in GEE and was not included.
89
30
20
2
r =0.95
Boreal Forest
(NSA-OBS)
15
2
Boreal Fen
25
r =0.84
20
Measured
10
15
10
5
5
0
0
Midday Soil Temperature at 10 cm Depth (°C)
Observed
-5
-5
0
50
100
150
200
250
300
350
25
100
2
r =0.90
Boreal Forest
(SSA-OBS)
20
20
15
15
10
10
5
5
0
0
-5
-5
-10
-10
50
100
150
200
250
300
350
30
25
150
200
250
300
350
25
2
r =0.94
Temperate
Coniferous Forest
0
100
200
300
400
40
r2=0.82
Temperate
Deciduous Forest
35
20
Temperate Grassland
r2=0.40
30
15
25
10
20
5
15
0
-5
0
100
200
300
400
10
100
150
200
250
300
50
2
r =0.26
Tropical Savanna
40
30
20
10
220
230
240
250
260
270
280
290
Day of Year
Figure 3.10. Seasonal variation of modeled (line) and observed (symbols) midday soil
temperature at 10 centimeter depth.
90
350
35
1.0
0.9
Observed
30
0.8
0.7
25
20
0.5
0.4
Modeled
15
0.3
0.2
10
Temperate Grassland
0.1
5
0.0
100
120
140
160
180
200
220
240
260
280
300
Day of Year
100
1.0
Modeled
90
0.9
80
0.8
70
0.7
Observed
60
0.6
50
0.5
40
0.4
30
0.3
20
0.2
Tropical Savanna
10
Modeled Soil Moisture Stress Function
Observed Percent Extractable Soil Water
0.6
0.1
0
0.0
220
230
240
250
260
270
280
290
Day of Year
Figure 3.11. Seasonal variation of modeled soil moisture stress function (a value of 1 equals no
stress) and observed soil moisture. The observations are represented by smooth curves fit to the
data to facilitate comparison with the model predictions throughout the growing season.
91
(r2>0.8) except at the sites without complete annual temperature and fAPAR measurements. For example, at
the temperate grassland and the tropical savanna sites, only 40 and 26 percent, respectively, of the
variation in soil temperature was accounted for by the model. This suggests that the model captures
seasonal changes much better than short-term changes and points to the significance of cold periods to the
overall r2 values.
Soil Moisture. The predicted soil water stress function (fSW) is shown for the temperate grassland
and the tropical savanna sites in Figure 3.11. Also shown are the measurements of extractable soil
moisture at these two sites. Seasonal changes in soil moisture appear strongly related to changes in fSW,
supporting the hypothesis that plant leaf area display, represented by fAPAR, and time-averaged midday
stomatal conductance, represented by fW, are related to soil moisture availability.
Soil Heterotrophic Respiration. Seasonal variation in predicted and observed soil heterotrophic
respiration is shown in Figure 3.12. The observations were derived from simple temperature dependant
models of total (root + microbial) soil respiration obtained from the literature (Table 3.7). These models
were fit to either chamber or sub-canopy eddy covariance measurements with the exception of the tropical
savanna site, where no measurements were made. At this site, a soil heterotrophic respiration model was
calibrated concurrently with a plant respiration model to nighttime above-canopy eddy flux measurements
Considerable debate exists over the accuracy of both chamber and sub-canopy eddy covariance
measurements (Goulden et al. 1996, Lavigne et al. 1997). It is not clear which provides more reasonable
measurements at each site thus both are presented when possible. Model predictions agree well with the
sub-canopy eddy covariance observations at the temperate coniferous forest (Hollinger et al. 1999) and
the temperate deciduous forest (Moore et al. 1996) but generally underestimate chamber measurements by
a factor of two. Excluding the tropical savanna, the model captured the seasonality of soil heterotrophic
respiration well (Figure 3.12).
Diurnal Variation. Diurnal variation in predicted and observed net ecosystem exchange (NEE) for
three 1-week periods during early, middle, and late times of the measurement periods at each site is
shown in Figure 3.13. Similar to the results for gross ecosystem exchange (Figure 3.7), model predictions
92
4
2
Boreal Forest (NSA-OBS)
Boreal Forest (SSA-OBS)
3
Chamber
Midday Soil Heterotrophic Respiration (µmol m-2 s-1)
2
1
Modeled
1
Modeled
Chamber
0
0
0
100
200
300
0
3
100
200
300
10
Temperate
8 Deciduous Forest
Temperate Coniferous Forest
2
6
Modeled
4
1
2
Eddy Flux
0
0
100
Chamber
200
Modeled
Eddy Flux
0
300
0
100
200
300
3
7
Temperate
C3/C4
Grassland
6
5
Tropical C3/C4 Savanna
2
4
Calibrated
Chamber
3
1
2
Modeled
1
Modeled
0
0
0
100
200
300
0
100
200
300
Day of Year
Figure 3.12. Time series of predicted and observed midday soil heterotrophic respiration.
Observations represent temperature dependent models fitted to either chamber or sub-canopy
eddy covariance measurements (Table 3.6). Soil heterotrophic respiration was assumed to be 60%
of the total CO2 flux (roots + heterotrophs).
93
Table 3.7. Models used for observed soil heterotrophic respiration in Figure 3.11. Models were fit to measurements of total soil CO2 efflux (roots
+ heterotrophs) as determined with chambers or by sub-canopy eddy covariance. Soil heterotrophic respiration (RH) was assumed 60% of total soil
CO2 efflux (Schimel et al. 1994)
Site
Model
Method
Source
Boreal Forest (NSA-OBS)
RH=0.6 (0.6 exp[0.119 Tsoil])
Chamber
Lavigne et al.1997
Boreal Forest (SSA-OBS)
if 140<JD<195 then RH=0.6(0.8+0.0218[JD-140])2.35(Tsoil-15)/10
if 195<JD<230 then RH=0.6(2+0.0143[JD-195])2.35(Tsoil-15)/10
if 230<JD<270 then RH=0.6(1.5+0.0175[JD-230])2.35(Tsoil-15)/10
if JD>270 then RH=0.6(0.8)2.35(Tsoil-15)/10
Chamber
Lavigne et al.1997
Temperate Coniferous Forest
RH=0.6(3(Tsoil-10)/10)
Eddy Covariance
Hollinger et al. 1999
Temperate Deciduous Forest
RH=0.6(0.488 exp[0.1372 Tsoil])
RH=0.6(2.31[0.0669 Tsoil-0.4074])
Chamber
Eddy Covariance
Davidson et al. 1999
Moore et al. 1996
Temperate C3/C4 Grassland
RH= 0.6(0.135+0.054LAI) SW exp(0.069[Tsoil-25])
Chamber
Norman et al. 1987
Tropical C3/C4 Savanna
RH=0.6(1.194 f(Tsoil)f(SW))
f(Tsoil)=exp(0.059[Tsoil-20])/(1+exp[0.507(Tsoil-35.8)])
f(SW)=(SW-0.01)/(0.12-0.01)
Calibrated Model
Hanan et al. 1997
94
Figure 3.13. Modeled (lines) and measured (symbols) net ecosystem exchange of CO2 (NEE)
during early, middle, and late periods of the growing season.
95
of daytime net ecosystem exchange agree well with observations on most days. The overall patterns of
modeled and observed NEE are very similar to the patterns for GEE (Figure 3.7) suggesting little
additional error was introduced by the model predictions of plant and soil heterotrophic respiration. For
example, the mid-season overestimation of NEE at the northern boreal forest during JDs 207 and 208 is
not unlike the overestimation of GEE on these same days (Figure 3.7) which presumably stemmed from
overestimation in canopy photosynthetic capacity (Figure 2.7). Similarly, the model underestimation of
NEE during the early period at the temperate grassland site (Figure 3.13), was consistent with the
underestimation of GEE during this time (Figure 3.7), which in turn was consistent with the
underestimation in canopy photosynthetic capacity (Figure 2.7). This pattern is repeated for most of the
other days at the other sites.
Across the wide range of sites represented, predicted and observed rates of nighttime net
ecosystem exchange agree well except perhaps during the middle period at the temperate deciduous forest
and during the middle and late periods at the tropical savanna. The overestimation of nighttime ecosystem
respiration at the deciduous forest may be due to an overestimation of plant respiration. Given that
nighttime ecosystem respiration is the sum of plant and soil heterotrophic respiration and model
predictions of latter appear too low as compared to chamber measurements (Figure 3.12), an
overestimation could only result from an overestimation in plant respiration. Similarly, the overestimation
of nighttime ecosystem respiration at the savanna site during the middle and late periods (Figure 3.13)
may also stem from an overestimation of plant respiration given that model predictions of soil
heterotrophic respiration appear too low (Figure 3.12).
Accuracy and Generality. Consistent with the time series plots (Figure 3.13), there was good
overall correspondence between the modeled and observed rates of net ecosystem exchange for all sites
(Figure 3.14). The correspondence is also very similar to that shown in Figure 3.9 for gross ecosystem
exchange. As expected from the over-predictions of canopy photosynthetic capacity found at the northern
boreal forest site (Figure 2.7), the slope of the relationship between modeled and observed NEE is greater
96
20
15
10
Boreal Forest (NSA-OBS)
y=1.09x+0.27
r2=0.72
Boreal Fen
y=0.58x
r2 =0.70
10
5
5
0
0
-5
-10
-10
Predicted NEE (µmol m-2 s-1)
20
15
10
-5
-5
0
5
10
15
20
Boreal Forest (SSA-OBS)
y=0.81x+0.27
r2=0.70
5
0
-5
-10
-10
30
25
20
15
10
5
0
-5
-10
-15
-5
15
10
5
10
15
20
0
5
10
30
Temperate Coniferous Forest
25
y=0.83x+0.12
20
2
15 r =0.73
10
5
0
-5
-10
-15
-20
-20
-10
0
10
20
40
Temperate Deciduous Forest
y=0.66x-0.22
r2=0.66
30
20
30
Temperate C 3 /C 4 Grassland
y=0.79x+1.27
r2=0.81
10
0
-10
-10
20
0
-5
0
10
20
30
-20
-20
30
Tropical C 3 /C 4 Savanna
y=0.80x-1.38
r2=0.80
20
-10
0
10
20
30
40
Tropical Rainforest
y=0.92x+0.51
r2=0.77
10
5
0
0
-10
-5
-10
-10
-5
0
5
10
15
20
-20
-20
-10
0
10
20
30
Observed NEE (µmol m-2 s-1)
Figure 3.14. Relationship between predicted and observed net ecosystem exchange of CO2
(NEE).
97
Table 3.8. Relationships between predicted and observed NEE shown in Figure 3.13. The slope (m) and
intercept (b) relate predicted NEE to observed NEE: Predicted=mObserved+b. The slope of the
relationship between predicted and observed GEE is provided for comparison. The statistical NEE model
was identical to the GEE model (Table 3.6) with the exception that an ecosystem respiration constant was
subtracted from GEE.
Statistical NEE
Modeled NEE
GEE
r2
r2
intercept
slope
slope
Boreal Forest (NSA-OBS)
0.71
0.72
0.33
1.09
1.08
Boreal Fen
0.62
0.70
0.01
0.58
0.69
Boreal Forest (SSA-OBS)
0.68
0.69
0.34
0.82
0.87
Temperate Coniferous Forest
0.70
0.73
0.12
0.83
0.83
Temperate Deciduous Forest
0.69
0.66
-0.22
0.66
0.75
Temperate C3/C4 Grassland
0.74
0.81
1.27
0.79
0.79
Tropical C3/C4 Savanna
0.81
0.80
-1.38
0.80
0.85
Tropical Rainforest
0.80
0.77
0.51
0.92
0.84
Site
98
than one. At all other sites, the slopes were less than one and offsets were small, suggesting a systematic
underestimation of the highest fluxes.
Across all sites, the model accounted for 66 to 81% of the variability in net ecosystem exchange.
These results are summarized in Table 3.8 along with the r2 values for simple models calibrated to
measurements from each site. The r2 values of the simple calibrated models are very similar to those of
the OPTICAL model (Table 3.8). The fact that the model can provide predictions of net ecosystem
exchange comparable to site-calibrated models supports the notion that the OPTICAL model is a good
generalized model of net ecosystem exchange.
The slopes of the relationship between modeled and observed NEE are generally lower than the
regression slopes relation modeled and observed GEE (Table 3.8). A NEE-slope closer to unity than a
GEE-slope implies an improvement in model performance by the addition of plant and soil respiration
predictions. Such an improvement could only occur as a result of compensating errors in the estimation of
ecosystem respiration (plant + soil respiration). This only occurred at the tropical rainforest site and
implies that ecosystem respiration was overestimated, counteracting an underestimation in gross
ecosystem exchange (Table 3.8).
Cumulative Carbon Exchange
The time course of predicted and observed cumulative gross ecosystem exchange, net ecosystem
exchange, and ecosystem respiration over the measurement period at each site is shown in Figure 3.15. In
general, the agreement between the magnitude of the predictions and observations is very good, with
notable discrepancies (e.g. temperate deciduous forest and tropical savanna) as previously discussed. At
all sites, the model appears to track the temporal pattern of carbon exchange very well. In terms of both
magnitude and seasonality, the best predictions are consistently for cumulative gross ecosystem exchange.
Of the three component fluxes, gross ecosystem exchange involves the least number of assumptions and
is the most directly related to fAPAR (Field 1991). It should be noted that there are really only two
component fluxes predicted by the model as net ecosystem exchange is simply predicted as the difference
99
8
4
Boreal Forest (NSA-OBS)
6
4
ΣGEE
Uptake
Σ NEE
-2
Loss
0
-1
ΣResp
-4
-1
50
100
150
200
250
300
ΣResp
-2
-6
Cumulative Carbon Exchange (tons C ha )
ΣNEE
1
0
350
8
-3
100
150
200
250
8
Boreal Forest
(SSA-OBS)
ΣGEE
4
300
350
ΣGEE
Temperate
Coniferous Forest
6
4
ΣNEE
2
ΣNEE
2
0
0
-2
-2
ΣResp
-4
ΣResp
-4
-6
-6
50
100
150
200
250
6
4
ΣGEE
2
2
6
Boreal Fen
3
300
350
2
100
200
2
ΣGEE
Temperate
Deciduous Forest
0
1
ΣResp
0
400
ΣGEE
Temperate C3/C4
Grassland
ΣNEE
300
ΣNEE
0
-2
ΣResp
-4
-6
0
100
200
300
400
-1
140 160 180 200 220 240 260 280 300
2
1
Tropical C3/C4 Savanna
Tropical Rainforest
ΣGEE
ΣNEE
0
1
ΣGEE
ΣResp
ΣNEE
0
ΣResp
-1
230
240
250
260
270
280
290
-1
120
130
140
150
160
170
180
Day of Year
Figure 3.15. Time course of predicted (dotted line) and observed (solid line) cumulative net
ecosystem exchange (NEE), gross ecosystem exchange (GEE), and ecosystem respiration (Resp).
100
Modeled (tons C ha-1 )
8
7
6
5
4
3
2
1
0
Modeled (tons C ha -1)
8
7
6
5
4
3
2
1
0
Gross Photosynthetsis
(a)
y=x
2
r =0.98
RMSE=0.43 tC ha-1
-1
MAE=0.27 tC ha
0
2
3
4
5
6
7
8
Ecosystem Respiration
(b)
Boreal Forest (NSA-OBS)
Boreal Fen
Boreal Forest (SSA-OBS)
Temperate Coniferous Forest
Temperate Deciduous Forest
Temperate C3/C4 Grassland
Tropical C3/C4 Savanna
Tropical Rainforest
1:1 line
y=x
2
r =0.99
-1
RMSE=0.39 tC ha
-1
MAE=0.31 tC ha
0
3
Modeled (tons C ha-1 )
1
1
2
3
4
5
6
7
8
-1
Observed
(tons C ha )
Net CO
Exchange
2
(c)
2
y=x
2
r =0.75
RMSE=0.42 tC ha-1
-1
MAE=0.32 tC ha
1
0
0
1
2
Observed (tons C ha-1)
3
Figure 3.16. Relationship between cumulative predicted and observed gross photosynthesis (a),
ecosystem respiration (b), and net CO2 exchange (c).
101
between gross ecosystem exchange and ecosystem respiration and any error in ecosystem respiration
translates directly into an error in net ecosystem exchange.
The final cumulative values at the end of the measurement period at each site (cumulative values
do not necessarily equal annual totals) for each of the component fluxes are shown in Table 3.9 and
plotted in Figure 3.16. Despite excellent agreement between model predictions of gross carbon fixation
(Figure 3.16a) and ecosystem respiration (Figure 3.16b) across all sites (r2>0.98, slopes=1, intercepts=0,
P>0.05), the agreement for net carbon exchange is not as good. The regression slope between modeled
and observed NEE was, however, not significantly different from one (Figure 3.16c). The modest errors
in gross photosynthesis and ecosystem respiration are in fact large relative to the magnitude of net
ecosystem exchange. As net ecosystem exchange is the small difference between two large fluxes (gross
photosynthesis and ecosystem respiration), it is inherently difficult to predict. Nevertheless, across a range
of sites, the OPTICAL model should thus provide reasonable estimates of gross and net ecosystem
exchange.
The model predictions as shown in Figures 3.14 and 3.16 suggest good overall agreement with
the observations, particularly with respect to r2 values and regression statistics. However, as evident from
Figure 3.15 and Table 3.9, regression analysis may mask important discrepancies relevant to carbon
exchange. For example, the tropical savanna site has a slope of 0.80 (Figure 3.14) similar to that at the
southern boreal forest (0.81), temperate coniferous forest (0.83), and temperate grassland (0.79) but has a
much greater cumulative error -- 0.31 tons C ha-1 or a 97% error, versus <10% error for the other sites.
Although the magnitude of the fluxes at the savanna are relatively small and thus inherently more difficult
to predict, regression analysis did not reveal the relatively large errors between model predictions and
observations. On the other hand, cumulative totals can agree for the wrong reasons, as the cumulative
totals could indicate exact agreement but the regression slope could be zero. Models which aim to
accurately predict net ecosystem carbon exchange, should thus consider both the cumulative error in
addition to regression statistics.
Inherent in the model is a link between ecosystem respiration and canopy photosynthetic
102
Table 3.9. Summary of modeled and observed cumulative fluxes.
NEE (tons C ha-1)
Site
GEE (tons C ha-1)
Resp (tons C ha-1)
Observed
Modeled
Observed
Modeled
Observed
Modeled
Boreal Forest (NSA-OBS)
0.81
1.31
4.84
5.94
4.03
4.63
Boreal Fen
0.86
0.48
2.78
2.46
1.92
1.98
Boreal Forest (SSA-OBS)
2.21
2.25
6.86
7.18
4.65
4.93
Temperate Coniferous Forest
2.21
1.87
6.69
6.78
4.48
4.91
Temperate Deciduous Forest
1.26
0.38
4.79
4.61
3.53
4.23
Temperate C3/C4 Grassland
0.86
0.80
1.49
1.51
0.62
0.71
Tropical C3/C4 Savanna
0.32
0.006
0.75
0.70
0.43
0.69
Tropical Rainforest
0.32
0.35
0.97
1.08
0.64
0.73
103
Ecosystem Respiration (tons C ha-1 )
6
Ecosystem Respiration
vs. Gross Photosynthesis
5
Boreal Forest (NSA-OBS)
Boreal Fen
Boreal Forest (SSA-OBS)
Temperate Coniferous Forest
Temperate Deciduous Forest
Temperate C3/C4 Grassland
Tropical C3/C4 Savanna
Tropical Rainforest
Regression
4
3
2
y=0.73x
r2=0.98
1
0
0
1
2
3
4
5
6
7
8
Gross Photosynthesis (tons C ha -1)
Figure 3.17. Relationship between ecosystem respiration and canopy photosynthesis.
104
capacity (Rp ∝P cmax, RH∝Pcmax), the latter of which is, over time, instrinsically related to gross ecosystem
exchange (Field 1991). There is thus an inherent connection in the model between gross ecosystem
exchange and ecosystem respiration. This implies a connection not only between plant carbon
assimilation and respiration but between plant productivity and soil microbial productivity (Raich and
Schlesinger 1992). The data in Table 3.9 support such a relationship, albeit between ecosystem respiration
and gross photosynthesis (Figure 3.17). Cumulative ecosystem respiration is, on average, 73% of
cumulative gross primary productivity. Across sites, such a relationship may be valid but individual sites
clearly do not lie on the 73% line (Figure 3.17). The observations presented in Figure 3.17 merely support
the notion that ecosystem respiration generally covaries with gross primary productivity -- not that every
site is accumulating carbon.
Conclusion
A generalized model of plant-soil-atmosphere CO2 exchange was described and evaluated using
half-hourly and hourly eddy covariance measurements of ecosystem CO2 exchange in boreal, temperate,
and tropical landscapes.
Canopy photosynthesis was calculated using a 'big-leaf' approach appeared to provide good
predictions of canopy gross photosynthesis as there was good overall correspondence between the
modeled and observed gross ecosystem exchange for all sites. Despite differences in canopy architecture,
the identical parameterization of the big-leaf model at all sites provided reasonable predictions.
Apparently, the unexplained variation in canopy gross photosynthesis was unrelated to variations in
temperature and VPD and may have been due to inherent variability of the eddy covariance
measurements. There appear, however, to be a systematic under-estimation of the highest fluxes. Among
all sites, the model explained from 74 to 85% of the variability in gross ecosystem exchange.
The model with photosynthetic acclimation provided better predictions, as indicated by higher r2
values and smaller cumulative errors than the model without acclimation. Acclimation appeared to
account for an additional 0 to 14% of the variability in gross ecosystem exchange. These differences in
105
the model predictions, however, were generally modest and, as such, may imply that photosynthetic
acclimation is not crucial for accurate prediction of photosynthesis over the growing season. However,
visual inspection of the seasonal time course of predictions and observations suggests that the model runs
without acclimation did not capture the timing of spring increases and fall declines in gross ecosystem
exchange as well as the model with acclimation. Acclimation may provide the greatest benefit during the
periods of greatest transition in physiological status, such as in the spring and fall during onset and
senescence.
The results also imply that canopy photosynthesis can be predicted well without any prior
knowledge of vegetation type. At a minimum, all that is required is fAPAR, incident PAR, and air
temperature. This provides support for the acclimation model and the three driving variables as being
representative of the fundamental processes which control variation in photosynthesis throughout the
growing season and among sites with contrasting vegetation and climate. The model with acclimation
accounted for up to 19% more of the variance in gross ecosystem exchange as compared to calibrated
site-specific models. Across all sites the model thus did nearly as well or better than the site-specific
models, supporting the notion that the acclimation model is a good general model of canopy
photosynthesis.
Similar to the results for gross ecosystem exchange, model predictions of daytime net ecosystem
exchange agree well with observations on most days. The overall patterns of modeled and observed net
ecosystem exchange was very similar to the patterns for gross ecosystem exchange suggesting little
additional error was introduced by the model predictions of plant and soil heterotrophic respiration.
Predicted and observed rates of nighttime net ecosystem exchange agreed well and there was good overall
correspondence between the modeled and observed rates of net ecosystem exchange, similar to that found
for gross ecosystem exchange. At most sites, the regression slopes relating predictions to observations
were less than one and offsets were small, suggesting a systematic underestimation of the highest fluxes.
Across all sites, the model accounted for 66 to 81% of the variability in net ecosystem exchange. The r2
values of calibrated site-specific models of net ecosystem exchange were very similar to those of the
106
OPTICAL model
supporting the notion that the OPTICAL model is a good generalized model of net
ecosystem exchange.
In general, the agreement between the predictions and observations of cumulative gross
ecosystem exchange, net ecosystem exchange, and ecosystem respiration over the measurement period at
each site was very good. At all sites, the model appears to track the temporal pattern of carbon exchange
very well. In terms of both magnitude and seasonality, the best predictions are consistently for cumulative
gross ecosystem exchange. Of the three component fluxes, gross ecosystem exchange involves the least
number of assumptions and is the most directly related to fAPAR. Despite excellent agreement between
model predictions of gross carbon fixation and ecosystem respiration across all sites (r2>0.98, slopes=1,
intercepts=0, P>0.05), the agreement for net carbon exchange was not as good. The modest errors in
gross photosynthesis and ecosystem respiration are in fact large relative to the magnitude of net
ecosystem exchange. As net ecosystem exchange is the small difference between two large fluxes (gross
photosynthesis and ecosystem respiration), it is inherently difficult to predict. Nevertheless, across a range
of sites, the OPTICAL model should thus provide reasonable estimates of gross and net ecosystem
exchange.
Inherent in the model is a link between ecosystem respiration and canopy photosynthetic
capacity (Rp ∝P cmax, RH∝Pcmax) the latter of which is, over time, instrinsically related to gross ecosystem
exchange. The observations support such a relationship, albeit between ecosystem respiration and gross
photosynthesis. Cumulative ecosystem respiration was, on average, 73% of cumulative gross primary
productivity (r2=0.98, P>0.05). Across sites, such a relationship may be valid but individual sites clearly
do not all lie on the regression line. The observations merely support the notion that ecosystem respiration
generally covaries with gross primary productivity -- not that every site was accumulating carbon.
The model, as described here, can be applied using satellite derived fAPAR (Myneni et al. 1997,
Nemani and Running 1997), Tair (Prince et al. 1998), and incident PAR (Dye 1992). fAPAR can be derived
from satellite NDVI using, for example, the approach of Myneni which requires knowledge of the
functional vegetation type. The latter may be determined with the approach described by Nemani and
107
Running. This dependence on vegetation type does not nullify the advantage of the classificationindependent OPTICAL model. Consistent with the OPTICAL model, the classification approach of Nemani
and Running is a based entirely on remote sensing observations. More importantly, the use a vegetation
classification for the estimation of parameters in a NDVI-driven fAPAR model is justified because the
parameters relating to canopy architecture do not change significantly over time. Further, the use of a
vegetation classification to prescribe canopy optical characteristics does not preclude the use of a
temporally dynamic model of plant and soil physiological characteristics which are known to vary
significantly through time and between members of the same functional group.
108
SYMBOLS AND ABREVIAITIONS
Symbol
A
Acmax
Amax
A20
a0
an
APAR
bn
ca
ci
ci
ca
E
fAPAR
fAPAR′
fAPAR,max
fIPAR
fc,max
fD
f D , midday
fIPAR
Fstorage
fT
fTopt
fW
fSW
g
GEE
GEE∞
GEEmax
GPP
I
Iopt
I sat
Itoa
JD
Jmax
k
kPAR
K
Kc
Km
Ko
L
LAI
Definition
leaf net assimilation (µmol m-2 s-1)
maximum canopy net assimilation (µmol m-2 s-1)
maximum leaf net assimilation (µmol m-2 s-1)
Lloyd and Taylor coefficient
Fourier coefficient
Fourier coefficient
absorbed PAR (µmol m-2 s-1) (overbar denotes time-average)
Fourier coefficient
atmospheric CO2 concentration (µmol mol-1) (overbar denotes time-average)
CO2 concentration in the leaf (µmol mol-1) (overbar denotes time-average)
ratio of ci to ca (-) (overbar denotes time-average)
rate of transpiration (mol H2O m-2 s-1)
fraction of incident PAR absorbed by the green fraction of the canopy (-)
normalized fAPAR
annual maximum fAPAR
fraction of incident PAR intercepted by the canopy (-)
maximum fractional vegetation cover (-)
relative stomatal conductance at ambient VPD (-)
time-avereraged relative stomatal conductance at midday VPD (-)
fraction of incident PAR intercepted by the canopy (-)
storage flux (µmol m-2 s-1)
relative photosynthesis at the ambient air temperature (-)
relative photosynthetic capacity at the optimal temperature (-)
relative photosynthetic capacity at a given plant moisture status (-)
soil water stress function (-)
stomatal conductance (mmol H2O m-2 s-1)
gross ecosystem CO2 exchange (µmol m-2 s-1)
Michaelis-Menten asymptote for maximum GEE (µmol m-2 s-1)
maximum gross ecosystem CO2 exchange (µmol m-2 s-1)
gross primary productivity (µmol m-2 s-1)
incident PAR (µmol m-2 s-1) (overbar denotes time-average)
optimal incident PAR (µmol m-2 s-1)
saturating incident PAR (µmol m-2 s-1)
incident PAR at the top of the atmosphere (µmol m-2 s-1)
Julian Day (January 1 = JD 1)
electron transport capacity (µmol e- m-2 s-1)
PAR extinction coefficient (-)
time-averaged PAR extinction coefficient (~0.5)
Michaelis-Menten half-saturation constant
Michaelis-Menten constant (overbar denotes time-average)
Michaelis-Menten constant (overbar denotes time-average)
Michaelis-Menten constant (overbar denotes time-average)
litter carbon (g m-2)
total one-sided leaf area index (m2 m-2)
109
LAIe
m
N
Nc
NDVI
NEE
NEEnight
NEP
NPP
Oi
P
Pa
PAR
PAR above
PAR below
PAR max
PAR reflected
Pc
Pc(I)
Pcmax
Pmax
r
Reco
Rg
RH
RH,20
Rm
Rm,inst
rNIR
Rp
Rp,inst
rSW
RuBP
Rubisco
RT
rVIS
S
SOC
SR
t
t24
T
Tair
td
Tmax
Tmin
Tnight
Topt
Tsoil
effective LAI, one-sided leaf area index without correction for clumping (m2 m-2)
fitting parameter
leaf nitrogen concentration (mg g-1)
canopy nitrogen concentration (mg g-1)
Normalized Difference Vegetation Index (-)
net ecosystem CO2 exchange (µmol m-2 s-1)
nighttime net ecosystem CO2 exchange (µmol m-2 s-1)
net ecosystem productivity (µmol m-2 s-1)
net primary productivity (µmol m-2 s-1)
oxygen concentration in the leaf (Pa) (overbar denotes time-average)
rate of photosynthesis (µmol m-2 s-1)
time-averaged atmospheric pressure (Pa) (overbar denotes time-average)
photosynthetically active radiation (µmol m-2 s-1) (overbar denotes time-average)
PAR above the canopy (µmol m-2 s-1)
PAR below the canopy (µmol m-2 s-1)
daily maximum incident PAR above the canopy (µmol m-2 s-1)
PAR reflected by the canopy (µmol m-2 s-1)
canopy photosynthesis (µmol m-2 s-1)
unstressed rate of photosynthesis at a given irradiance (µmol m-2 s-1)
canopy photosynthetic capacity (µmol m-2 s-1)
photosynthetic capacity (µmol m-2 s-1)
ratio of maintenance respiration to Pcmax (-)
ecosystem respiration (µmol m-2 s-1)
growth respiration (µmol m-2 d-1)
soil heterotrophic respiration (µmol m-2 s-1)
soil heterotrophic respiration (µmol m-2 s-1) at a reference temperature of 20°C
maintenance respiration (µmol m-2 d-1)
instantaneous plant maintenance respiration (µmol m-2 s-1)
near-infrared reflectance (-)
plant respiration (µmol m-2 s-1)
instantaneous plant respiration (µmol m-2 s-1) (overbar denotes time-average)
shortwave reflectance (-)
ribulose bisphosphate
ribulose bisphosphate carboxylase-oxygenase
temperature dependence of maintenance respiration (-)
visible reflectance (-)
time-averaged specificity of Rubisco for CO2 relative to O2
soil organic carbon (gC m-2)
Simple Ratio
time (hours)
time in one day (86400 s)
time-averaged air temperature (°C)
air temperature (°C)
daylength (s)
daily maximum air temperature (°C)
daily minimum air temperature (°C)
nighttime air temperature (°C)
genotypic temperature optimum (°C)
predicted near-surface soil temperature (°C) (overbar denotes time-average)
110
tr
U
u(
Vmax
Vcmax
Vmax0
VPD
Wc
Wj
time in radians
wind speed (m s-1)
friction velocity (m s-1)
carboxylation capacity (µmol m-2 s-1)
canopy carboxylation capacity (µmol m-2 s-1)
maximum carboxylation rate of a leaf the top of the canopy (µmol m-2 s-1)
saturation vapor pressure deficit (kPa)
rate of carboxylation (µmol m-2 s-1)
rate of electron transport (µmol m-2 s-1)
X
Xi
X i-1
Yg
α
βa
∆t
∆T
εg
εn
τ
τL,20
τSOC
τSOC ,20
filtered value of variable X
previous filtered value of variable X
τ PAR
Γ
θ
ω
Xi is the value of variable X at time i
proportion of assimilate not lost as growth respiration (-)
canopy quantum yield (mol mol-1) (overbar denotes time-average)
atmospheric transmittance
time interval (days)
diel temperature amplitude (°C)
dry matter:radiation quotient for GPP (gC MJ-1)
dry matter:radiation quotient for NPP (gC MJ-1)
time constant (days)
leaf litter turnover times (years) at a reference temperature of 20°C
SOC turnover time (years) at a reference temperature of 26°C
SOC turnover time (years) at a reference temperature of 20°C
time-averaged canopy PAR transmittance (-)
CO2 compensation point (mol mol-1) (overbar denotes time-average)
curvature parameter (0.9)
weighting coefficient (-)
111
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