Biogeosciences www.biogeosciences.net 1726-4170 1726-4189 4 5 2007 10.5194/bg-4-743-2007 http://www.biogeosciences.net/4/743/2007/ http://www.biogeosciences.net/4/743/2007/bg-4-743-2007.html http://www.biogeosciences.net/4/743/2007/bg-4-743-2007.pdf 743 758 2007-09-13 Characterizing ecosystem-atmosphere interactions from short to interannual time scales M. D. Mahecha miguel.mahecha@bgc-jena.mpg.de M. Reichstein H. Lange N. Carvalhais C. Bernhofer T. Grünwald D. Papale G. Seufert Max-Planck-Institut für Biogeochemie, P.O. Box 10 01 64, 07701 Jena, Germany Norsk Institutt for Skog og Landskap, P.O. Box 115, 1431 Aas, Norway Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal Institut für Hydrologie und Meteorologie, Technische Universität Dresden, 01062 Dresden, Germany DISAFRI, Università degli Studi della Tuscia, Via Camillo de Lellis, snc – 01100, Viterbo, Italy Climate Change Unit, European Commission – Joint Research Centre, Via E. Fermi 1, 21020 Ispra, Italy Characterizing ecosystem-atmosphere interactions in terms of carbon and water exchange on different time scales is considered a major challenge in terrestrial biogeochemical cycle research. The respective time series currently comprise an observation period of up to one decade. In this study, we explored whether the observation period is already sufficient to detect cross-relationships between the variables beyond the annual cycle, as they are expected from comparable studies in climatology. We investigated the potential of Singular System Analysis (SSA) to extract arbitrary kinds of oscillatory patterns. The method is completely data adaptive and performs an effective signal to noise separation. We found that most observations (Net Ecosystem Exchange, NEE, Gross Primary Productivity, GPP, Ecosystem Respiration, Reco, Vapor Pressure Deficit, VPD, Latent Heat, LE, Sensible Heat, H, Wind Speed, u, and Precipitation, P) were influenced significantly by low-frequency components (interannual variability). Furthermore, we extracted a set of nontrivial relationships and found clear seasonal hysteresis effects except for the interrelation of NEE with Global Radiation (Rg). SSA provides a new tool for the investigation of these phenomena explicitly on different time scales. Furthermore, we showed that SSA has great potential for eddy covariance data processing, since it can be applied as a novel gap filling approach relying on the temporal correlation structure of the time series structure only. Allen, M R. and Smith, L A.: Monte Carlo SSA: Detecting irregular oscillations in the presence of coloured noise, J. Climate, 9, 3373–3404, 1996. Aubinet, M., Grelle, A., Ibrom, A., Rannik, Ü., Moncrieff, J., Foken, T., Kowalski, A S., Martin, P H., Berbigier, P., Bernhofer, C., Clement, R., Elbers, J., Granier, A., Grünwald, T., Morgenstern, K., Pilegaard, K., Rebmann, C., Snijders, W., Valentini, R., and Vesala, T.: Estimates of the annual net carbon and water exchange of forests: the EUROFLUX methodology, Adv. Ecol. Res., 30, 113–175, 2000. Baldocchi, D.: Assessing the eddy covariance technique for evaluating carbon exchange rates of ecosystems: past, present and future, Global Change Biol., 9, 479–492, 2003. Broomhead, D S. and King, G P.: Extracting qualitative dynamics from experimental data, Physica D, 20, 217–236, 1986. Braswell, B H., Sacks, W J., Linder, E. and Schimel, D S.: Estimating diurnal to annual ecosystem parameters by synthesis of a carbon flux model with eddy covariance net ecosystem exchange observations, Global Change Biol., 11, 335–355, 2005. Cao, L.: Practical method for determining the minimum embedding dimension of a scalar time series, Physica D, 110, 43–50, 1997. Ciais, P., Reichstein, M., Viovy, N., Granier, A., Ogée, J., Allard, V., Buchmann, N., Aubinet, M., Bernhofer, C., Carrara, A., Chevallier, F., Noblet, N D., Friend, A., Friedlingstein, P., Grünwald, T., Heinesch, B., Keronen, P., Knohl, A., Krinner, G., Loustau, D., Manca, G., Matteucci, G., Miglietta, F., Ourcival, J M., Pilegaard, K., Rambal, S., Seufert, G., Soussana, J F., Sanz, M J., Schulze, E D., Vesala, T., and Valentini, R.: Europe-wide reduction in primary productivity caused by the heat and drought in 2003, Nature, 437, 529–533, 2005. Coifman, R R., Lafon, S., Lee, A B., Maggioni, M., Nadler, B., Warner, F., and Zucker, S W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proceedings of the National Academy of Sciences, 102, 7426–7431, 2005. Diks, C. and Mudelsee, M.: Redundancies in the Earth's climatological time series, Phys. Lett. A, 275, 407–414, 2000. Dunn, A L., Barford, C C., Wofsy, S C., Goulden, M L., and Daube, B C.: A long-term record of carbon exchange in a boreal black spruce forest: means, responses to interannual variability, and decadal trends, Global Change Biol., 13, 577–590, 2007. Falge, E., Baldocchi, D., Olson, R J., Anthoni, P., Aubinet, M., Bernhofer, C., Burba, G., Ceulemans, R., Clement, R., Dolman, H., Granier, A., Gross, P., Grünwald, T., Hollinger, D., Jensen, N.-O., Katul, G., Keronen, P., Kowalski, A. nad Ta~Lai, C., Law, B E., Meyers, T., Moncrieff, J., Moors, E., Munger, J W., Pilegaard, K., Rannik, Ü., Rebmann, C., Suyker, A., Tenhunen, J., Tu, K., Verma, S., Vesala, T., Wilson, K., and S., W.: Gap filling strategies for long term energy flux data sets, Agric. Forest Meteorol., 107, 71–77, 2001. Foken, T. and Wichura, B.: Tools for quality assessment of surface-based flux measurements, Agric. Forest Meteorol., 78, 83–105, 1996. Fujita, D., Ishizawa, M., Maksyutov, S., Thornton, P E., Saeki, T., Nakazawa, T..: Inter-annual variability of the atmospheric carbon dioxide concentrations as simulated with global terrestrial biosphere models and an atmospheric transport model, Tellus B, 55, 530–546, 2003. Ghil, M. and Vautard, R.: Interdecadal oscillations and the warming trend in global temperature time series, Nature, 350, 324–327, 1991. Ghil, M., Allen, M R., Dettinger, M D., Ide, K., Kondrashov, D., Mann, M E., Robertson, A W., Saunders, A., Tian, Y., Varadi, F., and Yiou, P.: Advanced spectral methods for climatic time series, Rev. Geophys., 40, 1–25, 2002. Golyandina, N., Osipov, E.: The "Caterpillar"-SSA method for analysis of time series with missing values, J. Stat. Plan. Infer., 137, 2642–2653, 2007. Golyandina, N. and Stepanov, D.: SSA-based approaches to analysis and forecast of multidimensional time series, in: Proceedings of the 5th St. Petersburg Workshop on Simulation, pp. 293–298, St. Petersburg State University, St. Petersburg, 2005. Golyandina, N., Nekrutkin, V., and Zhigljavsky, A.: Analysis of Time Series Structure: SSA and related techniques, no 90 in Monographs on Statistics and Applied Probability, Chapman & Hall/CRC, Boca Raton, 2001. Goulden, M L., Munger, J W., Fan, S M., Daube, B C., and Wofsy, S C.: Exchange of Carbon Dioxide by a Deciduous Forest: Response to interannual Climate Variability, Science, 271, 1576–1578, 1996. Granier, A., Reichstein, M., Brédaa, N., Janssens, I A., Falge, E., Ciais, P., Grünwald, T., Aubinet, M., Berbigier, P., Bernhofer, C., Buchmann, N., Facini, O., Grassi, G., Heinesch, B., Ilvesniemi, H., Keronen, P., Knohl, A., Köstner, B., Lagergren, F., Lindroth, A., Longdoz, B., Loustau, D., Mateus, J., Montagnani, L., Nyst, C., Moorsu, E., Papale, D., Peiffer, M., Pilegaard, K., Pita, G., Pumpanen, J., Rambal, S., Rebmann, C., Rodrigues, A., Seufert, G., Tenhunen, J., Vesala, T., and Wang, Q.: Evidence for soil water control on carbon and water dynamics in European forests during the extremely dry year: 2003, Agric. Forest Meteorol., 143, 123–145, 2007. Grünwald, T. and Bernhofer, C.: A decade of carbon, water and energy flux measurement of an old spruce forest at the Anchor Station Tharandt, Tellus B, 59, 387-396, 2007. Hanson, P J., Amthor, J S., Wullschleger, S D., Wilson, K B., Grant, R E., Hartley, A., Hui, D., Hunt, E R., Johnson, D W., Kimball, J S., King, A W., Luo, Y., McNulty, S G., Sun, G., Thornton, P E., Wang, S., Williams, M. Baldocchi, D D. and Cushman, R M.: Oak forest carbon and water simulations: Model intercomparisons and evaluations against independent data, Ecol. Monogr., 74, 443–489, 2004. Hsieh, W.: Nonlinear multivariate and time series analysis by neural network methods, Rev. Geophys., 42, 1–25, 2004. Hsieh, W. and Hamilton, K.: Nonlinear singular spectrum analysis of the tropical stratospheric wind, Q. J. R. Meteorol. Soc., 129, 2367–2382, 2001. Hsieh, W. and Wu, A.: Nonlinear multichannel singular spectrum analysis of the tropical Pacific climate variability using a neural network approach, J. Geophys. Res., 107(C7), 3076, doi:10.1029/2001JC000957, 2001. Jevrejeva, S., Grinsted, A., Moore, J C., and Holgate, S.: Nonlinear trends and multiyear cycles in sea level records, J. Geophys. Res., 111, C09012, doi:10.1029/2005JC003229, 2006. Katul, G., Lai, C.-T., Schäfer, K., Vidakovic, B., J., A., Ellsworth, D., and Oren, R.: Multiscape analysis of vegetation surface fluxes: from seconds to years, Adv. Water Resour., 24, 1119–1132, 2001. Kondrashov, D. and Ghil, M.: Spatio-temporal filling of missing data in geophysical data sets, Nonlin. Processes Geophys., 13, 151–159, 2006. Kondrashov, D. and Ghil, M.: Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets", Nonlin. Processes Geophys., 14, 3–4, 2007. % %http://direct.sref.org/1607-7946/npg/2007-14-3SRef-ID: 1607-7946/npg/2007-14-3. Kramer, M A.: Nonlinear principal component analysis using autoassociative neural networks, AIChE Journal, 37, 233–243, 1991. Lange, H. and Bernhardt, K.: Long-term components and regional synchronization of river runoffs, in: Hydrology: Science and Practice for the 21st Century, edited by Butler, A., British Hydrological Society, London, 165–170, 2004. Law, B E., Falge, E., Gu, L., Baldocchi, D., Bakwin, P., Berbigier, P Davis, K J., Dolman, H., Falk, M., Fuentes, J., Goldstein, A H., Granier, A., Grelle, A., Hollinger, D., Janssens, I., Jarvis, P., Jensen, N. O Katul, G., Malhi, Y., Matteucci, G., Monson, R., Munger, J., Oechel, W., Olson, R., Pilegaard, K., Paw, U. K T., Thorgeirsson, H., Valentini, R., Verma, S., Vesala, T., Wilson, K., and Wofsy, S.: Carbon dioxide and water vapor exchange of terrestrial vegetation in response to environment, Agric. Forest Meteorol., 113, 97–120, 2002. Moffat, A., Papale, D., Reichstein, M., Barr, A G., Braswell, B H., Churkina, G., Desai, A R., Falge, E., Gove, J H., Heimann, M., Hollinger, D Y. Hui, D., Jarvis, A J., Kattge, J., Noormets, A., Richardson, A D. Stauch, V J.: Gap filling methods intercomparison, Agric. Forest Meteorol., in press, 2007. Nakai, Y., Kitamura, K., and Abe, S.: Year-long carbon dioxide exchange above a broadleaf deciduous forest in Sapporo, Northern Japan, Tellus B, 55, 305–312, 2003. Palu\v s, M.: Detecting nonlinearity in multivariate time series, Phys. Lett. A, 213, 138–147, 1996. Palu\v s, M. and Novotná, D.: Enhanced Monte Carlo SSA and the case of climate oscillations, Phys. Lett. A, 248, 191–202, 1998. Palu\v s, M. and Novotná, D.: Quasi-biennial oscillations extracted from the monthly NAO index and temperature records are phase-synchronized, Nonlin. Processes Geophys., 13, 287–296, 2006. Papale, D. and Valentini, R.: A new assessment of European forests carbon exchanges by eddy fluxes and artificial neural network spatialization, Global Change Biol., 9, 525–535, 2003. Papale, D., Reichstein, M., Aubinet, M., Canfora, E., Bernhofer, C., Kutsch, W., Longdoz, B., Rambal, S., Valentini, R., Vesala, T., and Yakir, D.: Towards a standardized processing of Net Ecosystem Exchange measured with eddy covariance technique: algorithms and uncertainty estimation, Biogeosciences, 3, 571–583, 2006.% %http://direct.sref.org/1726-4189/bg/2006-3-571SRef-ID: 1726-4189/bg/2006-3-571. Peters, O., Hertlein, C., and Christensen, K.: A Complexity View of Rainfall, Physical Review Letters, 88, 018 701–1–018 701–4, 2002. Plaut, G. and Vautard, R.: Spells of low-frequency oscillations and weather regimes in the Northern Hemisphere, J. Atmos. Sci., 51, 210–236, 1994. Plaut, G. and Vautard, R.: interannual and interdecadal variability in 335 years of Central England temperatures, Science, 268, 710–713, 1995. Reichstein, M., Falge, E., Baldocchi, D., Papale, D., Valentini, R., Aubinet, M., Berbigier, P., Bernhofer, C., Buchmann, N., Gilmanov, T., Granier, A., Grünwald, T., Havr�nkov�, K., Janous, D., Knohl, A., Laurila, T., Lohila, A., Loustau, D., Matteucci, G., Meyers, T., Miglietta, F., Ourcival, J.-M., Rambal, S., Rotenberg, E., Sanz, M., Seufert, G., Vaccari, F., Vesala, T., and Yakir, D.: On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm, Global Change Biol., 11, 1–16, 2005. Reichstein, M., Ciais, P., Papale, D., Valentini, R., Running, S., Viovy, N., Cramer, W., Granier, A., Ogé, J., Allard, V., Aubinet, M., Bernhofer, C., Buchmann, N., Carrara, A., Grünwald, T., Heinesch, B., Keronen, P., Knohl, A., Loustau, D., Manca, G., Matteucci, G., Miglietta, F., Ourcival, J M., Pilegaard, K., Rambal, S., Schaphoff, S., Seufert, G., Soussana, J.-F., Sanz, M.-J., Schulze, E D., Vesala, T., and Heimann, M.: A combined eddy covariance, remote sensing and modeling view on the 2003 European summer heatwave, Global Change Biol., 13, 634–651, 2007. Richardson, A D., Braswell, B H., Hollinger, D Y., Burman, P., Davidson, E A., Evans, R S., Flanagan, L B., Munger, J W., Savage, K., Urbanski, S P., and Wofsy, S C.: Comparing simple respiration models for eddy flux and dynamic chamber data, Agric. Forest Meteorol., 141, 219–234, 2006. Richardson, A D., Hollinger, D Y., Aber, J D., Ollinger, S V., and Braswell, B H.: Environmental variation is directly responsible for short- but not long-term variation in forest-atmosphere carbon exchange, Global Change Biol., 13, 788–803, 2007. Richardson, A D. and Hollinger, D Y..: A method to estimate the additional uncertainty in gap-filled NEE resulting from long gaps in the CO2 flux record, Agric. Forest Meteorol., in press, doi:10.1016/j.agrformet.2007.06.004, 2007a. Richardson, A. D., Mahecha, M. D., Falge, E., Kattge, J., Moffat, A., Papale, D., Reichstein, M., Stauch, V. J., Braswell, B. H., Churkina, G., Kruijt, B., and Hollinger, D. Y.: Statistical properties of random CO2 flux measurement uncertainty inferred from model residuals, Agric. Forest Meteorol., in press, 2007b. Saigusa, N., Yamamoto, S., Murayama, S., and Kondo, H.: Inter-annual variability of carbon budget components in an AsiaFlux forest site estimated by long-term flux measurements, Agric. Forest Meteorol., 134, 4–-16, 2005. Seneviratne, S I., Koster, R D., Guo, Z., Dirmeyer, P A., Kowalczyk, E., Lawrence, D., Liu, P., Lu, C.-H., Mocko, D., Oleson, K W., and Verseghy, D.: Soil Moisture Memory in AGCM Simulations: Analysis of Global Land-Atmosphere Coupling Experiment (GLACE) Data. J. Hydrometeor., 7, 1090–1112, 2006. Schneider, T.: Comment on "Spatio-temporal filling of missing points in geophysical data sets" by D. Kondrashov and M. Ghil, Nonlin. Processes Geophys., 13, 151–159, 2006, Nonlin. Processes Geophys., 14, 1–2, 2007. Shun, T. and Duffy, C.: Low-frequency oscillations in precipitation, temperature, and runoff on a west facing mountain front: A hydrogeologic interpretation, Water Resour. Res., 35, 191–201, 1999. Siqueira, M B., G G. Katul, D A. Sampson, Stoy, P C., Juang, J.-Y., McCarthy, H R. and Oren, R.: Multi-scale model inter-comparisons of CO2 and H2O exchange rates in a maturing southeastern U.S. pine forest, Global Change Biol., 12, 1189–1207, 2006. Stoy, P C., Katul, G G., Siqueira, M. B S., Juang, J.-Y., McCarthy, H R., Kim, H.-S.,Oishi, A C., and Oren, R.: Variability in net ecosystem exchange from hourly to inter-annual time scales at adjacent pine and hardwood forests: a wavelet analysis, Tree Physiol., 25, 887–902, 2005. Stoy, P C., Katul, G G., Siqueira, M. B S., Juang, J.-Y., Novick, K A., Joshua, M., Uebelherr, and Oren, R.: An evaluation of models for partitioning eddy covariance-measured net ecosystem exchange into photosynthesis and respiration, Agric. Forest Meteorol., 141, 2–18, 2006. Takens, F.: Detecting strange attractors in turbulence, in: Lecture Notes in Dynamical Systems and Turbulence edited by Rand, D A., and Young, L.-S., Lecture Notes in Mathematics, 898, 366–381, Springer, 1981. Tenenbaum, J B., de~Silva, V., and Langford, J C.: A global geometric framework for nonlinear dimensionality reduction, Science, 290, 2319–2323, 2000. Tessier, Y., Lovejoy, S., Hubert, P., Schertzer, D., and Pecknold, S.: Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions, J. Geophys. Res., 101(D21), 26 427–26 440, 1996. Torrence, C., and Compo, G P..: A Practical Guide to Wavelet Analysis, B. Am. Meteorol. Soc. 61–79, 1998. Vautard, R. and Ghil, M.: Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35, 395–424, 1989. Vautard R., Yiou P., and Ghil M.: Singular spectrum analysis: a toolkit for short noisy chaotic signals, Physica D, 58, 95–126, 1992. von Storch, H. and Zwiers, F.: Statistical Analysis in Climate Research, Cambridge University Press, Cambridge, 1999. Wilson, K. and Baldocchi, D.: Seasonal and interannual variability of energy fluxes temperate deciduous forest in North America, Agric. Forest Meteorol., 100, 1–18, 2000. Yiou P., Sornette, D., and Ghil M.: Data-adaptive wavelets and multi-scale singular-spectrum analysis, Physica D, 142, 254–290, 2000.