Agricultural and Forest Meteorology 113 (2002) 121–144 Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges W.J. Massman a,∗,X.Leeb a USDA/Forest Service, Rocky Mountain Research Station, 240 West Prospect, Fort Collins, CO 80526, USA b School of Forestry and Environmental Studies, Yale University, New Haven, CT 06511, USA Accepted 3 April 2002 Abstract This study derives from and extends the discussions of a US DOE sponsored workshop held on 30 and 31 May, 2000 in Boulder, CO concerning issues and uncertainties related to long-term eddy covariance measurements of carbon and energy exchanges. The workshop was organized in response to concerns raised at the 1999 annual AmeriFlux meeting about the lack of uniformity among sites when making spectral corrections to eddy covariance flux estimates and when correcting the eddy covariance CO2 fluxes for lack of energy balance closure. Ultimately, this lack of uniformity makes cross-site comparisons and global synthesis difficult and uncertain. The workshop had two primary goals: first, to highlight issues involved in the accuracy of long-term eddy covariance flux records; and second, to identify research areas and actions of high priority for addressing these issues. Topics covered at the workshop include different methods for making spectral corrections, the influence of 3D effects such as drainage and advection, underestimation of eddy covariance fluxes due to inability to measure low frequency contributions, coordinate systems, and nighttime flux measurements. In addition, this study also covers some new and potentially important issues, not raised at the workshop, involving density terms to trace gas eddy covariance fluxes (Webb et al., 1980). Wherever possible, this paper synthesizes these discussions and make recommendations concerning methodologies and research priorities. Published by Elsevier Science B.V. Keywords: Eddy covariance; Long-term flux records; Carbon balance 1. Introduction climate, air pollution, and CO2 concentrations (Wofsy and Hollinger, 1998). Because the eddy covariance The main scientific goals of the AmeriFlux network method directly measures the net flux of CO2,itis are to: (1) understand the factors and processes regu- the logical choice for attempting measurements of the lating CO2 exchange, including soil processes, vege- net CO2 exchange to and from terrestrial ecosystems. tation structure, physiology, and stage succession, and However, implementing the eddy covariance method (2) determine principal feedbacks that may affect the can vary significantly between sites. This is partic- future of the biosphere, such as responses to changes in ularly true for CO2 flux measurements which can be measured by either open- or closed-path systems ∗ Corresponding author. Fax: +1-970-498-1314. (e.g., Leuning and King, 1992; Suyker nad Verma, E-mail address: [email protected] (W.J. Massman). 1993). Although the greatest difference in eddy 0168-1923/02/$ – see front matter. Published by Elsevier Science B.V. PII: S0168-1923(02)00105-3 122 W.J. Massman, X. Lee / Agricultural and Forest Meteorology 113 (2002) 121–144 covariance instrumentation is likely to be between 2. Fundamental equations of eddy covariance open- and closed-path systems, there are also differ- ences between sonic anemometer designs, sampling 2.1. Summary frequencies, processing algorithms, the relative geo- metries of the instruments, and the degree of aerody- In this section, we present the fundamental equa- namic interference by the measurement platform. To tions of eddy covariance. However, because we wish further complicate the issue of cross-site, long-term to be as general as possible, all fluxes are expressed as comparisons of net CO2 exchange is the nearly uni- 3D vectors and the gradient operator, ∇, should be un- form inability to close the surface energy balance. derstood as independent of coordinate system. Wher- At most, if not nearly all, sites the energy available ever necessary and appropriate, a coordinate system to drive evaporation, sensible heat, photosynthesis, will be specified. The five fundamental equations, de- and canopy storage almost always exceeds sum of rived in Appendix B, detail the relationships between these other processes by 10–20%. Because sensible the various fluxes. Each equation is derived in a fully and latent heat fluxes are measured by eddy covari- consistent manner with the minimum number of as- ance, the concern naturally arises about whether the sumptions and wherever appropriate include heat and net CO2 flux is also underestimated and how or moisture effects. Here we present the results primarily if to correct for this. Without some understanding as a summary and as background for later discussions. of and ability to compensate for these differences, Eq. (1) shows the relationship between the turbulent cross-site comparisons and global scale synthesis are T 3D temperature flux, v a , and the measured 3D sonic difficult and uncertain at best. In an effort to address T virtual temperature flux, v s , the measured turbulent these site-to-site differences in flux systems and data p 3D pressure flux, v a, and the 3D vapor covariance, processing, the National Institute for Global Environ- v ρ . [Note here throughout this paper, we use the mental Change (NIGEC) sponsored an AmeriFlux v term covariance to mean that part of the turbulent flux workshop on 30 and 31 May, 2000 in Boulder, CO exclusive of the WPL term (Webb et al., 1989 and to address eddy covariance flux corrections and un- Appendix B). The complete fluxes (or those turbulent certainties in long-term studies of carbon and energy fluxes that include the WPL term) are denoted with a exchanges. The purpose of this paper is to synthe- ρ F size, and where necessary extend, the discussions and superscript F, e.g., v v .] conclusions of the workshop. Wherever possible, this T T α¯ ( +¯χ ) ρ paper also provides recommendations on methodolo- v a = 1 v s − v 1 v v v T¯ 1 + δ λ¯ T¯ 1 + δ λ¯ ρ¯ gies and priorities for future research. a oc v s oc v d The remainder of this paper is divided into five β¯ ( +¯χ ) p + v 2 v v a sections. The next section discusses the fundamental ¯ p¯ (1) 1 + δocλv a equations of eddy covariance. Section 3 discusses the flux loss due to physical limitations of instrumentation, where v is the 3D turbulent (fluctuating) velocity; ¯ such as line averaging effects, sensor separation, data α¯ v = 0.32µv/(1 + 1.32χ¯v); βv = 0.32χ¯v/(1 + ¯ ¯ processing, and related issues that cause spectral atten- 1.32χ¯v); λv = βv(1 +¯χv); χ¯v the volume mixing ra- uation of the flux. 2D and 3D effects, such as drainage tio or mole fraction for water vapor (=¯pv/p¯d); p¯v the and advection, are examined in Section 4. Section 5 mean vapor pressure; p¯d the mean partial pressure of discusses coordinate systems and Section 6 focuses dry air (i.e., ambient air devoid of water vapor); p¯a the specifically on night time flux issues. The paper closes mean ambient pressure (=¯pd +¯pv); µv (=md/mv) with two appendices. Appendix A lists the workshop is the ratio the molecular mass of dry air, md,to participants, speakers, and organizing committee. the molecular mass of water vapor, mv; ρ¯d the mean ¯ Appendix B provides a detailed discussion and deriva- ambient dry air density; Ts the mean temperature ¯ tion of the fundamental equations of eddy covariance. measured by sonic thermometry; Ta the mean ambi- These equations are developed in three dimensions ent temperature and δoc = 1 for an open-path sensor and include the WPL terms associated with fluxes of and δoc = 0 for a closed-path sensor. We use the δoc temperature and water vapor (Webb et al., 1980). notation to unify the mathematical development for W.J. Massman, X. Lee / Agricultural and Forest Meteorology 113 (2002) 121–144 123 ρ −¯ω ρ both the open- and closed-path systems. Note here v c cv d (Webb et al., 1980; Paw U et al., 2000, that Eq. (1) assumes that the cross-wind correction Appendix B). [We note here that for Eq. (6),we ¯ to Ts (Kaimal and Gaynor, 1991) is included in the have dropped a small correction term to Sc related to sonic signal processing software and as such it does the stoichiometry of photosynthesis and respiration not explicitly appear in Eq. (1) (see Appendix B). ρ (Appendix B).] The turbulent dry air flux, v d is Eqs. (2) and (3) are the turbulent water vapor and given as CO2 fluxes including the WPL terms as developed in vT vp Appendix B and adapted from Paw U et al. (1989) and vρ =−ρ ¯ (1 +¯χ ) δ a − a −µ vρ (7) d d v oc ¯ p¯ v v Webb et al. (1980): Ta a F Although not all issues raised by these equations were v ρ = (1 +¯χv)v ρ v v discussed at the workshop, it is important for the pur- T p +¯ρ ( +¯χ ) δ v a − v a poses of the workshop and this paper to discuss some v 1 v oc ¯ p¯ (2) Ta a of the implications of these equations to the practice of eddy covariance. T p ρ F = ρ +¯ρ ( +¯χ ) δ v a − v a 2.2. Some implications v c v c c 1 v oc ¯ p¯ Ta a +¯ω µ ρ The equation of mass conservation, Eq. (6),isthe c vv v (3) basis for long-term studies of the CO2 budget. The where ρ¯c is the mean ambient CO2 density, ω¯ c traditional method of obtaining (an approximate) CO2 (=¯ρc/ρ¯d) the mean mass mixing ratio for CO2 and ρ¯v budget over a 24 h period, usually involves the vertical the mean ambient water vapor density.