Abstract
Energy balance closure is the main indicator of the quality of energy flux measurements obtained by the eddy covariance technique. Many researchers use a simple linear regression model between energy balance components to evaluate closure. However, these studies typically fail to verify the appropriateness of the statistical assumptions of regression analysis, which can lead to erroneous conclusions if the model is not satisfactory. Thus, the aim of this study was to calibrate and validate simple and robust with bootstrap and cross-validation linear regression models to verify the efficiency of energy balance closure in the Amazon ecosystem. Measurements of net radiation and latent, sensible, and ground heat fluxes were made from January to December 2008 in a tropical rain forest area in South West Amazonia in an experimental site belonging to the network of flux towers of the Large-Scale Biosphere-Atmosphere Experiment in Amazonia (LBA). The results demonstrated that simple linear regression models are not appropriate for analyzing energy balance closure. However, robust linear regression models with bootstrap and cross-validation improved the fit to the data. Despite the better fit, there was an increase in energy balance closure residuals suggesting that the eddy covariance technique is underestimating the values of energy fluxes in Amazon forest areas more than what were reported in previous researches.
Similar content being viewed by others
References
Aguiar RG, Von Randow C, Priante Filho N, Manzi AO, Aguiar LJG, Cardoso FL (2006) Fluxos de massa e energia em uma floresta tropical no sudeste da Amazônia. Rev Bras Meteorol 21:248–257
Alterra Green World Research. Alteddy 3.4. Wageningen, 2013. www.climatexchange.nl/projects/alteddy. Accessed 29 Mar 2013
Andreae MO, Artaxo P, Brandão C, Carswell FE, Ciccioli P, Costa AL, Culf AD, Esteves JL, Gash JHC, Grace J, Kabat P, Lelieveld J, Malhi Y, Manzi AO, Meixner FX, Nobre AD, Nobre C, Ruivo MLP, Silva-Dias MA, Stefani P, Valentini R, Jouanne J, Waterloo MJ (2002) Biogeochemical cycling of carbon, water, energy, trace gases, and aerosols in Amazonia: the LBA-EUSTACH experiments. J Geophys Res 107:33–31
Araújo AC, Nobre AD, Kruijt B, Elbers JA, Dallarosa R, Stefani P, Randow C, Manzi AO, Culf AD, Gash JHC, Valentini R, Kabat P (2002) Comparative measurements of carbon dioxide fluxes from two nearby towers in a central Amazonian rainforest: the Manaus LBA site. J Geophys Res 107:58-1–58-20. https://doi.org/10.1029/2001JD000676
Aubinet M, Grelle A, Ibrom A, Rannik Ü, Moncrieff J, Foken T, Kowalski AS, Martin PH, Berbigier P, Bernhofer C, Clement RC, Elbers J, Granier A, Grünwald T, Morgenstern K, Pilegaard K, Rebmann C, Snijders W, Valentini R, Vesala T (2000) Estimates of the annual net carbon and water exchange of forests: the EUROFLUX methodology. Adv Ecol Res 30:113–175
Aubinet M, Chermanne B, Vandenhaute M, Longdoz B, Yernaux M, Laitat E (2001) Long term carbon dioxide exchange above a mixed forest in the Belgian Ardennes. Agric For Meteorol 108:293–315
Baldocchi DD (2003) Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Glob Chang Biol 9:479–492
Baldocchi DD, Hincks BB, Meyers TP (1988) Measuring biosphere-atmosphere exchanges of biologically related gases with micrometeorological methods. Ecology 69:1331–1340
Barr AG, Morgenstern K, Black TA, Mccaughey JH, Nesic Z (2006) Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of the CO2 flux. Agric For Meteorol 140:322–337. https://doi.org/10.1016/j.agrformet.2006.08.007
Callegari-Jacques S (2003) Bioestatística: princípios e aplicações. ARTMED, São Paulo
Castellví F, Snyder RL, Baldocchi DD (2008) Surface energy-balance closure over rangeland grass using the eddy covariance method and surface renewal analysis. Agric For Meteorol 148:82–93. https://doi.org/10.1016/j.agrformet.2008.02.012
Cava D, Contini D, Donateo A, Martano P (2008) Analysis of short-term closure of the surface energy balance above short vegetation. Agric For Meteorol 148:1147–1160. https://doi.org/10.1016/j.agrformet.2007.09.003
Chatterjee S, Hadi AS (2006) Regression analysis by example. Wiley, New Jersey
Chernick MR, Friis RH (2003) Introductory biostatistics for the health sciences: modern applications including bootstrap. Wiley, New Jersey
Culf AD, Fisch G, Malhi Y, Nobre CA (1997) The influence of the atmospheric boundary layer on carbon dioxide concentrations over a tropical forest. Agric For Meteorol 85:149–158
Culf AD, Foken T, Gash JHC (2004) The energy balance closure problem. In: Kabat P et al (eds) Vegetation, water, humans and the climate: a new perspective on an interactive system. Springer, Berlin, pp 159–166
Cunha US, Machado SA, Figueiredo Filho A (2002) Uso de análise exploratória de dados e de regressão robusta na avaliação do crescimento de espécies comerciais de terra firme da Amazônia. Rev Arvore 26:391–402
da Rocha HR, Goulden ML, Miller SD, Menton MC, Pinto LDVO, Freitas HC, Figueira AMS (2004) Seasonality of water and heat fluxes over a tropical Forest in eastern Amazonia. Ecol Appl 14:S22–S32
Draper NR, Smith H (1998) Applied regression analysis. Wiley, New York
Estatcamp (2013) Action 2.5. www.portalaction.com.br. Accessed 25 Mar 2013
Flachaire E (1999) A better way to bootstrap pairs. Econ Lett 64:257–262
Foken T (2008) The energy balance closure problem: an overview. Ecol Appl 18:1351–1367
Foken T, Wimmer F, Mauder M, Thomas C, Liebethal C (2006) Some aspects of the energy balance closure problem. Atmos Chem Phys 6:4395–4402
Franssen HJH, Stöckli R, Lehner I, Rotenberg E, Seneviratne SI (2010) Energy balance closure of eddy-covariance data: a multisite analysis for European FLUXNET stations. Agric For Meteorol 150:1553–1567. https://doi.org/10.1016/j.agrformet.2010.08.005
Giloni A, Simonoff JS, Sengupta B (2006) Robust weighted LAD regression. Comput Stat Data An 50:3124–3140. https://doi.org/10.1016/j.csda.2005.06.005
Henderson AR (2005) The bootstrap: a technique for data-driven statistics. Using computer-intensive analyses to explore experimental data. Clin Chim Acta 359:1–326. https://doi.org/10.1016/j.cccn.2005.04.002
Heusinkveld BG, Jacobs AFG, Holtslag AAM, Berkowicz SM (2004) Surface energy balance closure in an arid region: role of soil heat flux. Agric For Meteorol 122:21–37. https://doi.org/10.1016/j.agrformet.2003.09.005
Hodnett MG, Oyama MD, Tomasella J, Marques Filho AO (1996) Comparisons of long-term soil water storage behaviour under pasture and forest in three areas of Amazonia. In: Gash JHC, Nobre CA, Roberts JM, Victoria RL (eds) Amazonian deforestation and climate. Wiley, Chichester, pp 57–77
Hollander M, Wolfe DA (1999) Nonparametric statistical methods. Wiley, New York
Kohsiek W, Liebethal C, Foken T, Vogt R, Oncley SP, Bernhofer C, Debruin HAR (2007) The energy balance experiment EBEX-2000. Part III: behaviour and quality of the radiation measurements. Bound-Layer Meteorol 123:55–75. https://doi.org/10.1007/s10546-006-9135-8
Lee X (1998) On micrometeorological observations of surface-air exchange over tall vegetation. Agric For Meteorol 91:39–49
Leuning R, Gorsel E, Massman WJ, Isaac PR (2012) Reflections on the surface energy imbalance problem. Agric For Meteorol 156:65–74. https://doi.org/10.1016/j.agrformet.2011.12.002
Li Z, Yu G, Wen X, Zhang L, Ren C, Fu Y (2005) Energy balance closure at ChinaFlux sites. Sci China Ser D 48:51–62
Mathworks (2012) Matlab. www.mathworks.com. Accessed 22 Apr 2013
Mauder M, Jegede OO, Okogbue EC, Wimmer F, Foken T (2007) Surface energy flux measurements at a tropical site in West-Africa during the transition from dry to wet season. Theor Appl Climatol 89:171–183. https://doi.org/10.1007/s00704-006-0252-6
Meyers TP, Hollinger SE (2004) An assessment of storage terms in the surface energy balance of maize and soybean. Agric For Meteorol 125:105–115. https://doi.org/10.1016/j.agrformet.2004.03.001
Microsoft (2010) Excel. http://office.microsoft.com/en-us/excel. Accessed 22 Apr 2013
Minitab (2016) Minitab 17. www.minitab.com/pt-BR/default.aspx. Accessed 22 Nov 2016
Moncrieff JB, Massheder JM, Bruin H, Elbers J, Friborg T, Heusinveld B, Kabat P, Scott S, Soegaard H, Verhoef A (1997) A system to measure surface fluxes of momentum, sensible heat, water vapour and carbon dioxide. J Hydrol 188-189:589–611
Montgomery DC, Runger GC (2003) Estatística aplicada e probabilidade para engenheiros. LTC, Rio de Janeiro
Oncley SP, Foken T, Vogt R, Kohsiek W, Debruin HAR, Bernhofer C, Christen A, Gorsel E, Grantz D, Feigenwinter C, Lehner I, Liebethal C, Liu H, Mauder M, Pitacco A, Ribeiro L, Weidinger T (2007) The energy balance experiment EBEX-2000. Part I: overview and energy balance. Bound-Layer Meteorol 123:1–28. https://doi.org/10.1007/s10546-007-9161-1
Pereira AR, Angelocci LR, Sentelhas PC (2002) Agrometeorologia: fundamentos e aplicações práticas. Agropecuária, Guaíba
Rawlings JO, Pantula SG, Dickey DA (1998) Applied regression analysis: a research tool. Springer, New York
Richardson AD, Hollinger DY (2005) Statistical modeling of ecosystem respiration using eddy covariance data: maximum likelihood parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models. Agric For Meteorol 131:191–208. https://doi.org/10.1016/j.agrformet.2007.09.001
Rummel U, Ammann C, Gut A, Meixner FX, Andreae MO (2002) Eddy covariance measurements of nitric oxide flux within an Amazonian rain forest. J Geophys Res 107:17-1–17-9. https://doi.org/10.1029/2001JD000520
Savin NE, White KJ (1977) The Durbin-Watson test for serial correlation with extreme sample sizes or many regressors. Econometrica 45:1989–1996 http://www.jstor.org/discover/10.2307/1914122?uid=3737664&uid=2&uid=4&sid=21102486228281. Accessed 23 Apr 2013
S-Plus (1998) S-Plus 4 guide to Statistics. http://www.mathsoft.com. Accessed 08 Aug 2012
Stoy PC, Mauder M, Foken T, Marcolla B, Boegh E, Ibrom A, Arain MA, Arneth A, Aurela M, Bernhofer C, Cescatti A, Dellwik E, Duce P, Gianelle D, Van Gorsel E, Kiely G, Knohl A, Margolis H, Mccaughey H, Merbold L, Montagnani L, Papale D, Reichstein M, Saunders M, Serrano-Ortiz P, Sottocornola M, Spano D, Vaccari F, Varlagin A (2013) A data-driven analysis of energy balance closure across FLUXNET research sites: the role of landscape scale heterogeneity. Agric For Meteorol 171–172:137–152. https://doi.org/10.1016/j.agrformet.2012.11.004
Tukey JW (1977) Exploratory data analysis. Eddison-Wesley, Massachusetts
Twine TE, Kustas WP, Norman JM, Cook DR, Houser PR, Meyers TP, Prueger JH, Starks PJ, Wesely ML (2000) Correcting eddy-covariance flux underestimates over a grassland. Agric For Meteorol 103:279–300
Vieira S (2006) Análise de variância: (Anova). Atlas, São Paulo
Vittinghoff E, Shiboski SC, Glidden DV, Mcculloch CE (2004) Regression methods in biostatistics: linear, logistic, survival, and repeated measures models. Springer, New York
von Randow C, Manzi AO, Kruijt B, Oliveira PJ, Zanchi FB, Silva RL, Hodnett MG, Gash JHC, Elbers JA, Waterloo MJ, Cardoso FL, Kabat P (2004) Comparative measurements and seasonal variations in energy and carbon exchange over forest and pasture in South West Amazonia. Theor Appl Climatol 78:1–22. https://doi.org/10.1007/s00704-004-0041-z
von Randow C, Kruijt B, Holtslag AAM, Oliveira MB (2008) Exploring eddy-covariance and large-aperture scintillometer measurements in an Amazonian rain forest. Agric For Meteorol 148:680–690. https://doi.org/10.1016/j.agrformet.2007.11.011
Vourlitis GL, Nogueira JS, Lobo FA, Sendall KM, De Paulo SR, Dias CAA, Pinto OB Jr, Andrade NLR (2008) Energy balance and canopy conductance of a tropical semi-deciduous forest of the southern Amazon basin. Water Resour Res 44:1–14. https://doi.org/10.1029/2006WR005526
Wilson K, Goldstein A, Falge E, Aubinet M, Baldocchi D, Berbigier P, Bernhofer C, Ceulemans R, Dolman H, Field C, Grelle A, Ibrom A, Law BE, Kowalski A, Meyers T, Moncrieff J, Monson R, Oechel W, Tenhunen J, Verma S, Valentini R (2002) Energy balance closure at FLUXNET sites. Agric For Meteorol 113:223–243
Acknowledgements
This work is part of the Large Scale Biosphere-Atmosphere Experiment in Amazonia (LBA) and was supported by Brazilian Foundation for the Coordination of Improvement of Higher Education Personnel (CAPES/PRODOUTORAL). The authors wish to acknowledge the students from LBA/Rondonia for data collection. Thanks are due to Chico Mendes Institute for Biodiversity Conservation (ICMBio), Biological Reserve of Jaru (REBIO Jaru), and their staffs for support during the field work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aguiar, R.G., De Musis, C.R., Aguiar, L.J.G. et al. Energy balance closure in the Southwest Amazon forest site—a statistical approach. Theor Appl Climatol 136, 1209–1219 (2019). https://doi.org/10.1007/s00704-018-2548-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-018-2548-8