HETEROFOR 1.0: a spatially explicit model for exploring the response of structurally complex forests to uncertain future conditions – Part 1: Carbon fluxes and tree dimensional growth
Jonard, Mathieu; André, Frédéric; de Coligny, Françoiset al.
2020 • In Geoscientific Model Development, 13, p. 905-935
[en] Given the multiple abiotic and biotic stressors resulting from global changes, management systems and practices must be adapted in order to maintain and reinforce the resilience of forests. Among others, the transformation of monocultures into uneven-aged and mixed stands is an avenue to improve forest resilience. To explore the forest response to these new silvicultural practices under a changing environment, one needs models combining a process-based approach with a detailed spatial representation, which is quite rare.
We therefore decided to develop our own model (HETEROFOR for HETEROgeneous FORest) according to a spatially explicit approach, describing individual tree growth based on resource sharing (light, water and nutrients). HETEROFOR was progressively elaborated within Capsis (Computer-Aided Projection for Strategies in Silviculture), a collaborative modelling platform devoted to tree growth and stand dynamics.
This paper describes the carbon-related processes of HETEROFOR (photosynthesis, respiration, carbon allocation and tree dimensional growth) and evaluates the model performances for three broadleaved stands with different species compositions (Wallonia, Belgium). This first evaluation showed that HETEROFOR predicts well individual radial growth (Pearson's correlation of 0.83 and 0.63 for the European beech and sessile oak, respectively) and is able to reproduce size–growth relationships. We also noticed that the net to gross primary production (npp to gpp) ratio option for describing maintenance respiration provides better results than the temperature-dependent routine, while the process-based (Farquhar model) and empirical (radiation use efficiency) approaches perform similarly for photosynthesis. To illustrate how the model can be used to predict climate change impacts on forest ecosystems, we simulated the growth dynamics of the mixed stand driven by three IPCC climate scenarios. According to these simulations, the tree growth trends will be governed by the CO2 fertilization effect, with the increase in vegetation period length and the increase in water stress also playing a role but offsetting each other.
Disciplines :
Environmental sciences & ecology
Author, co-author :
Jonard, Mathieu; Université Catholique de Louvain - UCL
André, Frédéric; Université Catholique de Louvain - UCL
de Coligny, François; Université de Montpellier
de Wergifosse, Louis; Université Catholique de Louvain - UCL
Beudez, Nicolas; Université de Montpellier
Davi, Hendrik; INRAE - Institut National de la Recherche Pour l'Agriculture, l'Alimentation et l'Environnement
Ligot, Gauthier ; Université de Liège - ULiège > Département GxABT > Laboratoire de Foresterie des régions trop. et subtropicales
Ponette, Quentin; Université Catholique de Louvain - UCL
Vincke, Caroline; Université Catholique de Louvain - UCL
Language :
English
Title :
HETEROFOR 1.0: a spatially explicit model for exploring the response of structurally complex forests to uncertain future conditions – Part 1: Carbon fluxes and tree dimensional growth
Aber, J., Neilson, R. P., McNulty, S., Lenihan, J. M., Bachelet, D., and Drapek, R. J.: Forest processes and global environmental change: predicting the effects of individual and multiple stressors, Bioscience, 51, 735-751, 2001.
André, F., Jonard, M., and Ponette, Q.: Precipitation water storage capacity in a temperate mixed oak-beech canopy, Hydrol. Process., 22, 4130-4141, 2008a.
André, F., Jonard, M., and Ponette, Q.: Influence of species and rain event characteristics on stemflow volume in a temperate mixed oak-beech stand, Hydrol. Process., 22, 4455-4466, 2008b.
André, F., Jonard, M., and Ponette, Q.: Biomass and nutrient content of sessile oak (Quercus petraea (Matt.) Liebl.) and beech (Fagus sylvatica L.) stem and branches in a mixed stand in southern Belgium, Sci. Total Environ., 408, 2285-2294, 2010.
André, F., Jonard, M., Jonard, F., and Ponette, Q.: Spatial and temporal patterns of throughfall volume in a deciduous mixedspecies stand, J. Hydrol., 400, 244-255, 2011.
Anlauf, R. and Liu, Y. P.: Simulation of simple one-dimensional transport processes, in: Models for Processes in the Soil: Programs and Exercises, edited by: Richter, J., Catena Verlag, Cremlingen-Desdedt, Germany, 1990.
Baker, D. L. and Don Scott, H.: A limited tutorial on using finite differences in soil physics problems, available at: http://www.aquarien.com/findif/Findifa4.html (last access: 29 February 2020), 1998.
Ball, J. T., Woodrow, I. E., and Berry, J. A.: A model predicting stomatal conductance and its contribution to the control of photosynthetis under different environmental conditions, in: Progress in Photosynthesis Research, edited by: Biggins, J., vol. 4, 221-224, 1987.
Berger, U., Piou, C., Schiffers, K., and Grimm, V.: Competition among plants: concepts, individual-based modelling approaches, and a proposal for a future research strategy, Perspect. Plant Ecol., 9, 121-135, 2008.
Boisvenue, C. and Running, S. W.: Impacts of climate change on natural forest productivity-evidence since the middle of the 20th century, Glob. Change Biol., 12, 862-882, 2006.
Bontemps, J. D., Hervé, J. C., Leban, J. M., and Dhôte, J. F.: Nitrogen footprint in a long-term observation of forest growth over the twentieth century., Trees, 25, 237-251, 2011.
Bosc, A.: EMILION, a tree functional-structural model: presentation and first application to the analysis of branch carbon balance, Ann. Forest Sci., 57, 555-569, 2000.
Bravo, F., Fabrika, M., Ammer, C., Barreiro, S., Bielak, K., Coll, L., Fonseca, T., Kangur, A., Löf, M., Merganicova, K., Pach, M., Pretzsch, H., Stojanovic, D., Schuler, L., Peric, S., Rötzer, T., del Rio, M., Dodan, M., and Bravo-Oviedo, A.: Modelling approaches for mixed forests dynamics prognosis, Research gaps and opportunities, Forest Syst., 28, eR002, doi:10.5424/fs/2019281-14342, 2019.
Campioli, M., Vincke, C., Jonard, M., Kint, V., Demarée, G., and Ponette, Q.: Current status and predicted impact of climate change on forest production and biogeochemistry in the temperate oceanic European zone: review and prospects for Belgium as a case study, J. Forest Res., 17, 1-18, 2012.
Cantarello, E., Newton, A. C., Martin, P. A., Evans, P. M., Gosal, A., and Lucash, M. S.: Quantifying resilience of multiple ecosystem services and biodiversity in a temperate forest landscape, Ecol. Evol., 7, 9661-9675, 2017.
Carl, C., Biber, P., Veste, M., Landgraf, D., and Pretzsch, H.: Key drivers of competition and growth partitioning among Robinia pseudoacacia L. trees, Forest Ecol. Manage., 430, 86-93, 2018.
Charlton, S. R. and Parkhurst, D. L.: Modules based on the geochemical model PHREEQC for use in scripting and programming languages, Comput. Geosci., 37, 1653-1663, 2011.
Cichota, R., Elias, E. A., and van Lier, Q. D. J.: Testing a finitedifference model for soil heat transfer by comparing numerical and analytical solutions, Environ. Model. Softw., 19, 495-506, 2004.
Collalti, A., Trotta, C., Keenan, T. F., Ibrom, A., Bond-Lamberty, B., Grote, R., Vicca, S., Reyer, C. P. O., Migliavacca, M., Veroustraete, F., Anav, A., Campioli, M., Scoccimarro, E., Šigut, L., Grieco, E., Cescatti, A., and Matteucci G.: Thinning can reduce losses in carbon use efficiency and carbon stocks in managed forests under warmer climate, J. Adv. Model. Earth Sy., 10, 2427-2452, 2018.
Collalti, A. and Prentice, I. C.: Is NPP proportional to GPP? Waring's hypothesis 20 years on, Tree Physiol. 39, 1473-1483, 2019.
Collins, M., Knutti, R., Arblaster, J., Dufresne, J. L., Fichefet, T., Friedlingstein, P., Gao, X., Gutowski, W. J., Johns, T., Krinner, G., Shongwe, M., Tebaldi, C., Weaver, A. J., and Wehner, M.: Long-term Climate Change: Projections, Commitments and Irreversibility, in: Climate Change 2013: The Physical Science Basis, Contribution ofWorking Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G. K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P. M., Cambridge University Press, Cambridge, UK, New York, NY, USA, 2013.
Courbaud, B., de Coligny, F., and Cordonnier, T.: Simulating radiation distribution in a heterogeneous Norway spruce forest on a slope, Agr. Forest Meteorol., 116, 1-18, 2003.
Dagnelie, P., Palm, R., Rondeux, J., and Thill, A.: Tables de cubage des arbres et des peuplements forestiers, Les Presses Agronomiques de Gembloux, Gembloux, Belgique, 1999.
Damesin, C., Ceschia, E., Le Goff, N., Ottorini, J. M., and Dufrêne, E.: Stem and branch respiration of beech: from tree measurements to estimations at the stand level, New Phytol., 153, 159-172, 2002.
Davi, H., Dufrêne, E., Francois, C., LeMaire, G., Loustau, D., Bosc, A., Rambal, S., Granier, A., and Moors, E.: Sensitivity of water and carbon fluxes to climate changes from 1960 to 2100 in European forest ecosystems, Agr. Forest Meteorol., 141, 35-56, 2006.
Davi, H., Cailleret, M., Restoux, G., Amm, A., Pichot, C., and Fady, B.: Disentangling the factors driving tree reproduction, Ecosphere, 7, e01389, https://doi.org/10.1002/ecs2.1389, 2016.
del Río, M., Bravo-Oviedo, A., Ruiz-Peinado, R., and Condés, S.: Tree allometry variation in response to intra-and inter-specific competitions, Trees, 33, 121-138, 2019.
deWergifosse, L., André, F., Beudez, N., de Coligny, F., Goosse, H., Jonard, F., Ponette, Q., Titeux, H., Vincke, C., and Jonard, M.: HETEROFOR 1.0: a spatially explicit model for exploring the response of structurally complex forests to uncertain future conditions. II. Phenology and water cycle, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2019-201, in review, 2019.
de Wergifosse, L., André, F., Goosse, H., Caluwaerts, S., De Cruz, L., De Troch, R., and Van Schaeybroeck, B.: CO2 fertilization, water deficit and vegetation period drive the response of mixed broadleaved forests to a changing climate in Wallonia, Ann. Forest Sci., in review, 2020.
Dufour-Kowalski, S., Courbaud, B., Dreyfus, P., Meredieu, C., and de Coligny, F.: Capsis: an open software framework and community for forest growth modelling, Ann. Forest Sci., 69, 221-233, 2012.
Dufrêne, E., Davi, H., Franis, C., Le Maire, G., Le Dantec, V., and Granier, A.: Modelling carbon and water cycles in a beech forest: Part I: Model description and uncertainty analysis on modelled NEE, Ecol. Model., 185, 407-436, 2005.
Duursma, R. A. and Medlyn, B. E.: MAESPA: a model to study interactions between water limitation, environmental drivers and vegetation function at tree and stand levels, with an example application to [CO2]-drought interactions, Geosci. Model Dev., 5, 919-940, https://doi.org/10.5194/gmd-5-919-2012, 2012.
Ennos, R., Cottrell, J., Hall, J., and O'Brien, D.: Is the introduction of novel exotic forest tree species a rational response to rapid environmental change?-A British perspective, Forest Ecol. Manag., 432, 718-728, 2019.
Epron, D., Le Dantec, V., Dufrêne, E., and Granier, A.: Seasonal dynamics of soil carbon efflux and simulated rhizosphere respiration in a beech forest, Tree Physiol., 21, 145-152, 2001.
Farquhar, G. D., von Caemmerer, S., and Berry, J. A.: A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species, Planta, 149, 78-80, 1980.
Fernandez-Martinez, M., Vicca, S., Janssens, I. A., Sardans, J., Luyssaert, S., Campioli, M., Chapin III, F. S., Ciais, P., Malhi, Y., Obersteiner, M., Papale, D., Piao, S. L., Reichstein, M., Rodà, F., and Peñuelas, J.: Nutrient availability as the key regulator of global forest carbon balance. Nat. Clim. Change, 4, 471-476, 2014.
Forrester, D. I. and Albrecht, A. T.: Light absorption and light-use efficiency in mixtures of Abies alba and Picea abies along a productivity gradient, Forest Ecol. Manag., 328, 94-102, 2014.
Genet, H., Bréda, N., and Dufrêne, E.: Age-related variation in carbon allocation at tree and stand scales in beech (Fagus sylvatica L.) and sessile oak (Quercus petraea (Matt.) Liebl.) using a chronosequence approach, Tree Physiol., 30, 177-192, 2010.
Genet, A., Wernsdörfer, H., Jonard, M., Pretzsch, H., Rauch, M., Ponette, Q., Nys, C., Legout, A., Ranger, J., Vallet P., and Saint-André, L.: Ontogeny partly explains the apparent heterogeneity of published biomass equations for Fagus sylvatica in central Europe, Forest Ecol. Manag., 261, 1188-1202, 2011.
Giot, O., Termonia, P., Degrauwe, D., De Troch, R., Caluwaerts, S., Smet, G., Berckmans, J., Deckmyn, A., De Cruz, L., De Meutter, P., Duerinckx, A., Gerard, L., Hamdi, R., Van den Bergh, J., Van Ginderachter, M., and Van Schaeybroeck, B.: Validation of the ALARO-0 model within the EURO-CORDEX framework, Geosci. Model Dev., 9, 1143-1152, https://doi.org/10.5194/gmd-9-1143-2016, 2016.
Greene, D., Messier, C., Asselin, H., and Fortin, M.: The effect of light availability and basal area on cone production in Abies balsamea and Picea glauca, Can. J. Bot., 80, 370-377, 2002.
Grote, R. and Pretzsch, H.: A model for individual tree development based on physiological processes, Plant Biol., 4, 167-180, 2002.
Haxeltine, A. and Prentice, I. C.: A general model for the light use efficiency of primary production by terrestrial ecosystems, Funct. Ecol., 10, 551-561, 1996.
Helmisaari, H. S., Derome, J., Nöjd, P., and Kukkola, M.: Fine root biomass in relation to site and stand characteristics in Norway spruce and Scots pine stands, Tree Physiol., 27, 1493-1504, 2007.
Henry, H. A. L. and Aarssen, L. W.: The interpretation of stem diameter-height allometry in trees: biomechanical constraints, neighbour effects, or biased regressions?, Ecol. Lett., 2, 89-97, 1999.
Hounzandji, A. P., Jonard, M., Nys, C., Saint-André, L., and Ponette, Q.: Improving the robustness of biomass functions: from empirical to functional approaches, Ann. Forest Sci., 72, 795-810, 2015.
Janssen, P. H. M. and Heuberger, P. S. C.: Calibration of processoriented models, Ecol. Model., 83, 55-66, 1995.
Jonard, M., André, F., and Ponette, Q.: Modeling leaf dispersal in mixed hardwood forests using a ballistic approach, Ecology, 87, 2306-2318, 2006.
Jonard, M., André, F., Jonard, F., Mouton, N., Procès, P., and Ponette, Q.: Soil carbon dioxide efflux in pure and mixed stands of oak and beech, Ann. Forest Sci., 64, 141-150, 2007.
Jonard, M., André, F., and Ponette, Q.: Tree species mediated effects on leaf litter dynamics in pure and mixed stands of oak and beech, Can. J. Forest Res., 38, 528-538, 2008.
Jonard, F., André, F., Ponette, Q., Vincke, C., and Jonard, M.: Sap flux density and stomatal conductance of European beech and sessile oak trees in pure and mixed stands during the summer drought of 2003, J. Hydrol., 409, 371-381, 2011.
Jonard, M., Fürst, A., Verstraeten, A., Thimonier, A., Timmermann, V., Potocic, N., Waldner, P., Benham, S., Hansen, K., Merila, P., Ponette, Q., De La Cruz, A. C., Roskams, P., Nicolas, M., Croisé, L., Ingerslev, M., Matteuci, G., Decinti, B., Bascietto, M., and Rautio, P.: Tree mineral nutrition is deteriorating in Europe, Global Change Biol., 21, 418-430, 2015.
Jonard, M., André, F., and de Wergifosse, L.: Code of HETEROFOR 1.0, https://doi.org/10.5281/zenodo.3591348, 2019.
Jonard, M., André, F., and de Wergifosse, L.: Installer of HETEROFOR 1.0, http://amap-dev.cirad.fr/projects/capsis/files, last access: 29 February 2020.
Jucker, T., Bouriaud, O., and Coomes, D. A.: Crown plasticity enables trees to optimize canopy packing in mixed-species forest, Funct. Ecol., 29, 1078-1086, 2015.
Kersten, M. S.: Laboratory research for the determination of the thermal properties of soils, University of Minnesota, Engineering Experiment Station, 1949.
Le Moguédec, G. and Dhôte, J. F.: Fagacées: a tree-centered growth and yield model for sessile oak (Quercus petraea L.) and common beech (Fagus sylvatica L.), Ann. Forest Sci., 69, 257-269, 2012.
Letort, V., Cournède, P. H., Mathieu, A., de Reffye, P., and Constant, T.: Parametric identification of a functional-structural tree growth model and application to beech trees (Fagus sylvatica), Funct. Plant Biol., 35, 951-963, 2008.
Ligot, G., Balandier, P., Courbaud, B., Jonard, M., and Kneeshaw, D.: Managing understory light to maintain a mixture of species with different shade tolerance, Forest Ecol. Manag., 327, 189-200, 2014.
Lindner, M., Maroschek, M., Netherer, S., Kremer, A., Barbati, A., Garcia-Gonzalo, J., Seidl, R., Delzon, S., Corona, P., Kolström, M., Lexer, M. J., and Marchetti, M.: Climate change impacts, adaptive capacity, and vulnerability of European forest ecosystems, Forest Ecol. Manag., 259, 698-709, 2010.
Lindner, M., Fitzgerald, J. B., Zimmermann, N. E., Reyer, C., Delzon, S., van der Maaten, E., Schelhaas, M.-J. Lasch, P., Eggers, J., van der Maaten-Theunissen, M., Suckow, F., Psomas, A., Poulter, B., and Hanewinkel, M.: Climate change and European forests: What do we know, what are the uncertainties, and what are the implications for forest management? J. Environ. Manage., 146, 69-83, 2014.
Lines, E. R., Zavala, M. A., Purves, D. W., and Coomes, D. A.: Predictable changes in aboveground allometry of trees along gradients of temperature, aridity and competition, Glob. Ecol. Biogeogr., 21, 1017-1028, 2012.
Mäkelä, A.: Implications of the pipe model theory on dry matter partitioning and height growth in trees, J. Theor. Biol., 123, 103-120, 1986.
Mäkelä, A. and Valentine, H. T.: The ratio of NPP to GPP: evidence of change over the course of stand development, Tree Physiol., 21, 1015-1030, 2001.
Manion, P. D.: Tree Disease Concepts, Prentice-Hall, Englewood Cliffs, NJ, 402 pp., 1981.
Maraun, D. andWidmann, M.: Statistical downscaling and bias correction for climate research, Cambridge University Press, Cambridge, 2018.
Mellert, K. H. and Göttlein, A.: Comparison of new foliar nutrient thresholds derived from van den Burg's literature compilation with established central European references, Eur. J. Forest Res., 131, 1461-1472, 2012.
Messier, C., Puettmann, K., Chazdon, R., Andersson, K. P., Angers, V. A., Brotons, L., Filotas, E., Tittler, R., Parrrott, L., and Levin, S. A.: From management to stewardship: viewing forests as complex adaptative systems in an uncertain world, Conserv. Lett., 8, 368-377, 2015.
Monteith, J. L.: Climate and the efficiency of crop production in Britain, Philos. Trans. Royal Soc. B, 281, 277-294, 1977.
Morales, P., Hickler, T., Rowell, D. P., Smith, B., and Sykes, M. T.: Changes in European ecosystem productivity and carbon balance driven by regional climate model output, Global Change Biol., 13, 108-122, 2007.
Oliver, T. H., Heard, M. S., Isaac, N. J. B., Roy, D. B., Procter, D., Eigenbrod, F., Freckleton, R., Hector, A., Orme, C. D. L., Petchey, O. L., Proeniv V., Raffaelli, D., Suttle, K. B., Mace, G. M., Martín López, B., Woodcock, B. A., and Bullock, J. M.: Biodiversity and resilience of ecosystem functions, Trends Ecol Evol., 30, 673-684, 2015.
Penning de Vries, F. W. T.: The cost of maintenance processes in plant cells, Ann. Bot., 39, 77-92, 1975.
Pretzsch, H.: Canopy space filling and tree crown morphology in mixed-species stands compared with monocultures, Forest Ecol. Manag., 327, 251-264, 2014.
Pretzsch, H., Forrester, D. I., and Rötzer, T.: Representation of species mixing in forest growth models, A review and perspective, Ecol. Model., 313, 276-292, 2015.
R Core Team: R: A language and environment for statistical computing, 2013.
Reyer, C., Lasch-Born, P., Suckow, F., Gutsch, M., Murawski, A., and Pilz, T.: Projections of regional changes in forest net primary productivity for different tree species in Europe driven by climate change and carbon dioxide, Ann. Forest Sci., 71, 211-225, 2014.
Rodríguez-Calcerrada, J., Martin-St. Paul, N. K., Lempereur, M., Ourcival, J. M., del Carmen del Rey, M., Joffre, R., and Rambal, S.: Stem CO2 efflux and its contribution to ecosystem CO2 efflux decrease with drought in a Mediterranean forest stand, Agr. Forest Meteorol., 195-196, 61-72, 2014.
Rodríguez-Calcerrada, J., López, R., Salomón, R., Gordaliza, G. G., Valbuena-Carabaña, M., Oleksyn, J., and Gil, L.: Stem CO2 efflux in six co-occurring tree species: underlying factors and ecological implications, Plant Cell Environ., 38, 1104-1115, 2015.
Rötzer, T., Liao, Y., Goergen, K., Schüler, G., and Pretzsch, H.: Modelling the impact of climate change on the productivity and water-use efficiency of a central European beech forest, Clim. Res., 58, 81-95, 2013.
Ryan, M. G.: Effects of climate change on plant respiration, Ecol. Appl., 1, 157-167, 1991.
Ryan, M. G. and Yoder, B. J.: Hydraulic limits to tree height and tree growth. What keeps trees from growing beyond a certain height? BioScience, 47, 235-242, 1997.
Schäfer, K. V. R., Oren, R., and Tenhunen, J. D.: The effect of tree height on crown level stomatal conductance, Plant Cell Environ., 23, 365-375, 2000.
Schwalm, C. R. and Ek, A. R.: A process-based model of forest ecosystems driven by meteorology, Ecol. Model., 179, 317-348, 2004.
Simioni, G., Marie, G., and Huc, R.: Influence of vegetation spatial structure on growth and water fluxes of a mixed forest: Results from the NOTG 3D model, Ecol. Model., 328, 119-135, 2016.
Teh, C. B. S.: Introduction to mathematical modeling of crop growth. How the equations are derived and assembled into a computer program, Brown Walker Press, Boca Raton, Florida, USA, 2006.
Tetens, O.: Uber einige meteorologische Begriffe, Z. Geophys., 6, 297-309, 1930.
Thompson, I., Mackey, B., McNulty, S., and Mosseler, A.: Forest resilience, biodiversity, and climate change. A synthesis of the biodiversity/resilience/stability relationship in forest ecosystems. Secretariat of the Convention on Biological Diversity, Montreal, Technical Series no. 43, 2009.
Thurm, E. A., Biber, P., and Pretzsch, H.: Stem growth is favored at expenses of root growth in mixed stands and humid conditions for Douglas-fir (Pseudotsuga menziesii) and European beech (Fagus sylvatica), Trees-Struct. Funct., 31, 349-365, 2017.
Trouvé, R., Bontemps, J. D., Seynave, I., Collet, C., and Lebourgeois, F.: Stand density, tree social status and water stress influence allocation in height and diameter growth of Quercus petraea (Liebl.), Tree Physiol., 35, 1035-1046, 2015.
Van Wijk, W. R. and De Vries, D. A.: Periodic temperature variations in a homogenous soil, in: Physics of Plant Environment, edited by: VanWijk, W. R., North Holland Publishing Company, Amsterdam, 1963.
Villar, R., Held, A. A., and Merino, J.: Dark leaf respiration in light and darkness of an evergreen and a deciduous plant species, Plant Physiol., 107, 421-427, 1995.
Voldoire, A., Sanchez-Gomez, E., Salas y Mélia, D., Decharme, B., Cassou, C., Sénési, S., Valcke, S., Beau, I., Alias, A., Chevallier, M., Déqué, M., Deshayes, J., Douville, H., Fernandez, E., Madec, G., Maisonnave, E., Moine, M. P., Planton, S., Saint-Martin, D., Szopa, S., Tyteca, S., Alkama, R., Belamari, S., Braun, A., Coquart, L., and Chauvin, F.: The CNRM-CM5.1 global climate model: description and basic evaluation, Clim. Dynam., 40, 2091-2121, 2013.
Vose, J. M. and Bolstad, P. V.: Challenges to modelling NPP in diverse eastern deciduous forests: species-level comparisons of foliar respiration responses to temperature and nitrogen, Ecol. Model., 122, 165-174, 1999.
Yamori, W., Hikosaka, K., and Way, D. A.: Temperature response of photosynthesis in C3, C4, and CAM plants: temperature acclimation and temperature adaptation, Photosynth. Res., 119, 101-117, 2013.