A Training Course on CO2 Eddy Flux Data Analysis and Modeling Parameter Estimation Katherine Owen John Tenhunen Xiangming Xiao Institute of Geography and Natural Resources, Chinese Academy of Sciences, Beijing, China Institute for the Study of Earth, Oceans and Space, University of New Hampshire, USA Department of Plant Ecology, University of Bayreuth, Germany The Institute of Geography and Natural Resources, CAS, July 25, 2006 !

Theory: What kind of parameters? Physiological Vcmax=average carboxylase capacity of the leaves alpha=average leaf light utilization efficiency Stomata live factor=percent of open stomates due to water stress Phenological LAI=leaf area index Length of active season for carbon uptake Other Soil Carbon

Theory: Why estimate parameters? Compare sites Look at changes in one site between years (ie, Dtemperature or storm damage) or over a year or season Parameterization for other scale models - regional, continental, global

Theory: Model Scales Globe Biome Region Complexity Landscape Eddy Covariance Tower Ecosystem Organism Organ Reproducibility Cell Molecule Atom

Theory: Model Concepts Top down overview of the system is formulated with no or few details of the parts problem: “black box” Bottom up individual parts of the system designed in detail problem: may not have enough information to describe all parts of the system Simplicity, Applicability Understanding, Predictive Power, Generality

Theory: What kind of models? Many, many bottom-up & top-down models exist (rectangular & non-rectangular hyperbola, PIXGRO, CSIRO Biosphere Model, Biome-BGC, PaSim, etc.) Different models may be suitable for different goals Different models may be suitable depending on availability of ancillary data (LAI, leaf angle, soil texture, etc.) Parameters can be estimated for different time periods (daily, weekly, monthly, etc.). Depends on data availability, goal of modelling, etc. We discuss 2 models in this presentation

Model 1: Empirical Top-Down Hyperbolic Light Response Model aka Rectangular Hyperbolic Model or Michaelis-Menten Equation a - radiation required for half maximal uptake rate, approximation of canopy light utilization efficiency b - maximum canopy CO2 uptake rate g - estimate of the average Reco occurring during the observation period b+g - canopy CO2 uptake capacity or the average estimate for the maximum GPP during the observation period NEE - un-gap filled half hourly net ecosystem exchange PPFD - half hourly photosynthetic photon flux density a, b, g - estimated for 10 day periods

Model 2: Bottom-up Physiological Carboxylase-based Process Model Input: Half-hourly flux and meteoroligical data understanding of ecosystem physiology and biogeochemistry Input: LAI European Beech Fagus sylvatica (Hainich, Germany) Carboxylation capacity, Light utilization efficiency, Vcuptake alpha 95% u* corrections Marginal distribuation sampling gap filling Short term exponential flux partitioning: NEE Reco & GPP (all methods according to Reichstein et al. 2005) 2002 Output: Physiological leaf parameters Vcuptake - average leaf carboxylation capacity at 25°C Vcmax alpha - average light utilization efficiency without photorespiration estimated for 10 day periods Site specific LAI & gap filled GPP & meteo data canopy model Vcmax is influenced by experimental errors in the measurement of NEE, assumptions made in the estimation of GPP, our inability to obtain detailed spatial estimates of LAI and associate these with variations in NEE, the lack of information on potential time dependent changes in LAI, particularly in conifer stands, and assumptions of the models, such as lack of acclimation along light gradients and non-occurrence of water stress. Hence, estimates of Vcmax from the inversions becomes a lumped parameter which we refer to as Vcuptake Ongoing canopy level physiological parameter fitting via model inversion LAI, SAI Sunlit (Photosynthesis model based on Farquhar & von Caemmerer) Phenology Shaded Leaf physiology 1 Canopy Layer Model simplification that retains basic physiological response of specific ecosystem types included in landcover descriptions

Model 2: Bottom-up Physiological Carboxylase-based Process Model At this point in time the model has no Hydrology Soil layer Snow affects Future predictions Ecosystem level only - no upscaling in this model One vegetation type (-> set physiological parameters) per site (conifer, deciduous, grassland or cropland)

Model 2: Bottom-up Physiological Carboxylase-based Process Model: Main Equations Radiation - Duncan et al. (1967) / Chen et al. (1999) The fractions of the hemisphere that visible from upper and lower leaf surfaces are calculated. Photosynthesis - Farquhar & von Caemmerer (1982). Rubisco enzyme reaction limited by the regeneration of RuBP (at low light or high internal CO2 concentrations) or by Rubisco activity and CO2/O2 concentration (at saturated light or low internal CO2 concentrations) with the leaf temperature is calculated iteratively using energy balance.

Research Goals using the 2 models 1. Demonstrate relationships between empirical & physiological parameters from the 2 models 2. Examine patterns in CO2 uptake/loss vs. climate, LAI, canopy & leaf physiology 3. Identify “functional ecosystem types” 4. Simplify physiological parameters for use in continental scales Attempt to reduce the physiological-based model to the level of simple empirical descriptions, while maintaining response to factors like remotely sensed LAI, fertilization, management, and canopy water use so the parameters could be used in a continental scale model. Owen et al. 2006, Global Change Biology, submitted 4 Research Goals 1 2 3. We also aim to identify functional ecosystem groups, such as deciduous forests or grassland and so on, where the relationships in goal #1 are similar for each site that can be identified in the group. 4

Using the 2 models to compare parameters 18 European sites at half-hourly time step: Model 1: Empirical Hyperbolic Light Response Model Model 2: Physiological Carboxylase-based Process Model fit for Vcuptake2* and alpha (2 parameter fit) with seasonal LAI variation fit for Vcuptake1* with alpha = f (Vcuptake ) (1 parameter fit) with constant LAI at maximum estimated at site ****Goal: reduce number of parameters Formation of relationships according to “ecosystem functional type“ for Europe Comparison of European relationships with 17 North American / Asian sites Model 1 Model 2: We have 2 approaches to the Physiological model. First 2para. But, one of our goals is to reduce the number of parameters, because spatial variation of parameters are difficult to describe at continental scales. Therefore, we tested two simplifying assumptions: 1) eliminating seasonal variation in LAI and assuming LAI equal to the observed maximum, and 2) assuming alpha to be proportional to Vcmax. I will refer to the derived values as Vcuptake2* when alpha and Vcmax are independent, and as Vcuptake1* when alpha depends on Vcmax. In the case of Vcuptake2*, LAI will change over the season, except for coniferous forests. In the case of Vcuptake1*, LAI is always constant at the observed seasonal maximum. Relationships Comparisons NA/Asia

Data Analysis Pine Forests Duke Pine, North Carolina, USA Turkey Point, Ontario, Canada Loobos, Netherlands Hyytiälä, Finland Sodankylä, Finland Dense Coniferous Forests Harvard Hemlock, Massachusetts, USA Howland, Maine, USA Campbell River, British Columbia, USA Tharandt, Germany Mixed Forests Vielsalm, Belgium Deciduous Forests Duke Hardwood, North Carolina, USA Takayama, Japan Collelongo, Italy Harvard, Massachusetts, USA Hesse, France Hainich, Germany Soroe, Denmark Petsikko, Finland Wetlands Rzecin, Poland Kaamanen, Finland Tundra Upad, Alaska, USA Barrow, Alaska, USA Grasslands Duke Field, North Carolina, USA Canaan Valley, West Virginia, USA Oensingen Intensive, Switzerland Fort Peck, Montana, USA Lethbridge, Alberta, Canada Grillenburg, Germany Jokioinen, Finland Croplands Bondville, Illinois, USA Mead, Nebraska, USA Gebesee, Germany Lonzee, Belgium Klingenberg, Germany 35 Eddy Covariance Sites in temperate and boreal ecosystems around the Northern Hemisphere, consisting of different vegetation types were chosen for the analysis and shown on the map as red dots. The vegetation types include Pine, dense coniferous, mixed, deciduous forests, wetlands, tundra, grasslands and croplands. Years that included water stress were not included in the analysis presented today. Another study with the effects of water stress is planned.

g (lower line), b+g (upper line) (mmol CO2 m-2 s-1) Daily GPP (g C m-2 day-1) Day of Year g (lower line), b+g (upper line) (mmol CO2 m-2 s-1) Figure 1, Owen et al. Reduced CO2 uptake during winter at coniferous forest sites is influenced by continentality (Tharandt) and latitude influences on growing season length (Hyytiälä and Sodankylä). The Loobos maritime coniferous site remains active throughout the year. There is a general decrease in annual GPP for deciduous forest sites from south to north in response to growing season length. All modeled forest canopies had similar CO2 uptake capacity at mid-season, with coniferous stands fixing ca. 10 and deciduous stands ca. 15 g C m-2 day-1. The uptake of CO2 by wetlands, crops and grasslands is quite variable with responses to season length, nutrient availability (cf. compare wetlands with the fertilized grassland Oensingen), and management measures (crop rotation schemes and harvests). Maximum CO2 uptake capacity = 5 g C m-2 day-1 in wetlands, = 10 g C m-2 day-1 at the non-fertilized grassland site in Grillenburg and lightly fertilized site at Jokioinen, and = 15 g C m-2 day-1 or greater at the crop sites and the heavily fertilized meadow in Oensingen. There are unexpected peaks in GPP for Vielsalm and Rzecin. Calm nights and/or missing data may result in very few, but enough and adequate NEE data that happen to be large and not representative for the window period that will then exaggerate values of GPP and Reco. Arrows indicate harvests or mowing

GPP (g C m-2 day-1) b+g (mmol CO2 m-2 s-1) Figure 2, Owen et al. Daily GPP is correlated with the maximum rate of canopy CO2 uptake, (b+g), (r2 between 0.68 and 0.96) for all ecosystem types and the slopes of the regressions are similar across types. Nevertheless, there are some periods, for example late in the season at Hyytiälä, Loobos and Tharandt, where the apparent relationship shifts. This shift depends on the relative length of time the canopy performs under high or low light conditions, which changes over the course of a season. Such shifts contribute to the scatter and reduce the r2 values of the correlations. Other differences stem from the comparison between the estimates of a, b and g obtained using ungap-filled NEE data and the gap-filled daily GPP data. Given the simplicity of the hyperbolic light response model, the inversion solutions are obtained in a dependable fashion with few difficulties arising in the statistical fitting of light response curves.

g (mmol CO2 m-2 s-1) Rref (mmol CO2 m-2 s-1) Figure 3, Owen et al. The 10-day average Rref, the reference ecosystem respiration at 15 °C in the Lloyd and Taylor equation, and g, an estimate of the average ecosystem respiration, for different functional ecosystem types are strongly related with r2 values between 0.55 and 0.9. g is derived from light responses and is dependent on observations during both daytime periods (with generally higher data quality) and nighttime periods (when atmospheric stability can complicate flux measurements). Rref similarly provides an estimate of seasonal changes in ecosystem respiratory capacity based on the evaluation of temperature response. Thus, the parameters provide a consistent picture of seasonal influences on Reco. The lowest r2 values are for coniferous stands which suggest that daytime observations may have different effects during winter and summer due to changing light quality, day length, temperature acclimation phenomena, temperature gradients within the dense stands, or due to the quality of the eddy data.

a (mmol CO2)/(mmol photon) b+g (mmol CO2 m-2 s-1) Figure 4, Owen et al. Strong seasonal changes in the parameter a accompanies changes in g and (b + g). These changes are important since one goal is to reduce the number of parameters that require description in spatial modelling at large scales. a may be described as a linear function of canopy CO2 uptake capacity in the case of deciduous forests, wetlands, grasslands and croplands, e.g., summer active ecosystems. But there is considerable scatter in the relationships, and a tendency toward a curvilinear relationship may in fact occur with an initial rapid increase in (b + g) followed by a saturation in a at values near 0.05. The interpretation of these relationships is difficult as it could be a physiological response. Especially in the case of coniferous forests, a seems to be sensitive to factors other than those influencing canopy maximum CO2 uptake capacity (b + g), such as light quality, cold stress influence, or acclimation, but the values of a fall within observations for other ecosystem types.

Vcuptake2* (mmol CO2 m-2 leaf area s-1) b+g (mmol CO2 m-2 s-1) Figure 5, Owen et al. General seasonal trends are recognizable in the relationships between (b + g) and Vcuptake2* for different functional ecosystem types. LAI was allowed to change over the course of the year except for coniferous forests so only sites with the best estimates of LAI were used. The change in importance of limiting and high light conditions during individual periods, the imposition of defined temperature response curves based on previous cuvette gas exchange experimentation that are not ideal for describing overall gas exchange of the canopy, or time dependent change in measurement errors may cause the sensitivity in parameter estimates. The slope of the relationships are similar for all ecosystem types except pine forests. The differences in pine forests could suggest that different functional types exist among coniferous stands. However, inaccurate values of LAI may also contribute, since understory components were not always included in LAI estimates.

Vcuptake2* (mmol CO2 m-2 leaf area s-1) alpha (mmol CO2)/(mmol photon) Alpha = MINIMUM [ Vcuptake2* * 0.0008 , 0.06 ] Figure 6, Owen et al. In the interest of reducing the number of model parameters, the relationship of light utilization efficiency, alpha, was studied with respect to possible dependency on canopy CO2 uptake capacity, Vcuptake2*, both from the physiological model, using stands where the seasonal changes in LAI are best known. As with the hyperbolic light response model, substantial variation in alpha could be explained with a linear dependency on Vcuptake2*, but the general impression is that alpha increases rapidly to values near 0.06 and is then limited. In addition, unexplained variations in alpha occur which may depend on real changes in processes or on the model inversion procedures. Numerous regressions, including the rectangular hyperbolic, polynomial and logarithmic regression, were fitted to these data and had a maximum r2 value of 0.35. All regressions saturated at values close to 0.06. For the polynomial regression, only the linear and quadratic term were found to be significant and justify a non-linear approximation. For simplification we interpreted this scatter as the linear solid line.

(mmol CO2 m-2 leaf area s-1) (mmol CO2)/(mmol photon) Vcuptake1* (mmol CO2)/(mmol photon) Alpha Vcuptake2* Day of Year Figure 7, Owen et al. Here is the comparison between seasonally changing LAI and constant annual maximum LAI and between 1 and 2 parameter fits on summer active ecosystems for the Hesse beech forest in 2002 and Grillenburg grassland in 2004. The arrows show dates of grass cutting in Grillenburg. Using a constant LAI in Grillenburg or in Hesse led to an underestimate in the parameter values for only very short periods during initial increases in LAI with leaf expansion in spring and after each cut of the grassland sites and during the senescence period in fall. As LAI increases above ca. 3 or 4, no further influence on the parameter values occurs, considering either the 2-parameter or 1-parameter model inversions. Having alpha dependent on Vcuptake also had a very small influence; e.g., seasonal changes in Vcuptake obtained for either the 2-parameter or 1-parameter model were quite similar.

Vcuptake1* (mmol CO2 m-2 leaf area s-1) Daily GPP (g C m-2 day-1) Day of Year Vcuptake1* (mmol CO2 m-2 leaf area s-1) Figure 8, Owen et al. Only few of the sites have quantified seasonal changes in LAI, we obtained parameter estimates for Vcuptake1 (with alpha dependent on Vcuptake) with a constant LAI value of the year at the maximum annual value. Here are those values of Vcuptake1* , which a robust indicator of the canopy CO2 uptake capacity from the physiological model (solid line) superimposed on the daily observations of GPP (open circles). Vcuptake1* more poorly follows the seasonal trend in GPP as compared with (b + g) from Fig 1. While (b + g) directly reflects maximum CO2 uptake rates during each ten day period, Vcuptake1* is the activity required at 25 °C to allow the observed maximum rates. If high rates are required at low temperatures during winter, cf. Loobos pine forest, Vcuptake1* may increase, because temperature dependencies used in the model inversions currently remain constant over the course of the year. Additional problems will occur if the maximum LAI does not account for all CO2 sinks within the ecosystem, such as moss or lichen layers, loss of needles during autumn in certain pine sites, or stem photosynthesis.

Figure 8, Owen et al. The Vcuptake1* parameter is sensitive to nitrogen availability and management as seen for the non-fertilized Grillenburg and heavily fertilized Oensingen meadows. Finally, Vcuptake1* is a ‘property’ of the canopy, independent of meteorological conditions, and thus contains more generality than a, b and g. General patterns in seasonal change in Vcuptake1* can support and guide further efforts to bridge flux network observations and simulation modelling at large scales.

GPP (g C m-2 day-1) b+g (mmol CO2 m-2 s-1) Figure 9, Owen et al. Additional sites from North America and Asia were analyzed to determine whether the CO2 uptake characteristics and the relationships of the "functional ecosystem types" are applicable to other temperate and boreal zones . This figure shows the relationships for the results between daily GPP from flux partitioning and (b + g) for European, North American and Asian sites for ten day periods for different functional ecosystem types. The comparison demonstrates that the relationships for European sites are valid for the other temperate and boreal sites examined in the Northern Hemisphere. r2 values and slopes are vary similar to Fig 2. Among coniferous sites, Loobos, Duke Pine, Tharandt and Howland exhibited large annual changes in the apparent relationship of (b + g) to GPP. A different relationship seems to apply below and above daily GPP values of ca. 3 g C m-2 day-1. Further detailed study must be carried out to explain these characteristics which appear to be an integral component of conifer ecosystem gas exchange.

Figure 10, Owen et al. Here are the relationships and linear regressions for the results between daily GPP and Vcuptake1*, which is a robust indicator of the canopy CO2 uptake capacity from the physiological model, using constant annual maximum LAI for European, North American and Asian sites. Broad agreement is once again found at all sites within the indicated categories. Dense conifer forests appear to have two phases of response, with a separation in the correlation between Vcuptake1* and GPP at ca. 2 to 3 g C m-2 day-1. Some pine stands seem to exhibit similar behavior to those stands classified as dense conifers, e.g., Turkey Point, but the remaining pine stands exhibit larger Vcuptake1*, suggesting that a separate functional type between dense conifers and pine forests may be justified. Whether a clean separation of these groups by species type, influence of understory, or LAI is possible remains unclear. Vcuptake1* (mmol CO2 m-2 leaf area s-1) GPP (g C m-2 day-1)

Figure 10, Owen et al. The predicted relationships are similar independent of global region. The relatively wet Alaskan tundra sites fit well to the European wetland relationship. Drier tundra sites appeared to exhibit a different behavior, but we need more data to make final conclusions. The mixed deciduous forest sites at Harvard Forest and Takayama were extremely similar to the European beech forest sites. The relationship obtained for C3 crops fits both the North American legumes and the European grain and root crops. A comparison of common management practices of similar ecosystems in different climate zones, or a comparison of different ecosystems under similar climates, would help to separate the influences of climate and management on important crop and grassland species. Regardless, these results support the basic idea that Vcuptake1* is a robust indicator of the canopy CO2 uptake capacity useful in simulations at large scales.

Conclusions Close correlation between the 2 models Relationships exhibit 6 “functional groups” for sites modeled around Northern Hemisphere Relationships differ for dense coniferous and pine forests Poor quality or lack of LAI data is a problem Possibility of Vcuptake1* and MODIS LAI being used in future in continental scale models Incorporating seasonal changes in physiology in the model is still a challenge

Future Work Assess parameters from water stressed sites Obtain more eddy covariance data from other ecosystem types, i.e., tropical

Thank you for your attention! Acknowledgements The project investigators and research staff who provided data CarboEurope, Fluxnet, AsiaFlux, AmeriFlux, Fluxnet-Canada, and individual flux stations Thank you for your attention!