## 1. Introduction

[2] Long-term measurements of net ecosystem exchange (NEE) are now routinely employed to estimate ecosystem carbon budgets using eddy covariance (EC), yet the large error in the measurement of ecosystem respiration (*R*_{E}) under nighttime conditions remains an unresolved problem that must be confronted [*Baldocchi et al.*, 1996; *Goulden et al.*, 1996; *Law et al.*, 1999a, 1999b; *Lindroth et al.*, 1998; *Moncrieff et al.*, 1996; *Schmid et al.*, 2000; *Valentini et al.*, 2000; *Wofsy et al.*, 1993]. Often, nocturnal conditions are dominated by vertical subsidence, lack of steadiness in mean atmospheric conditions, and intermittent turbulent transport often initiated by transients such as passage of clouds [*Cava et al.*, 2004]. When viewed from the one-dimensional vertically integrated scalar continuity equation, these factors contribute to increased “decoupling” between the desired *R*_{E} quantity and the CO_{2} flux above the canopy, the latter being the observed quantity by EC methods. Furthermore, these nocturnal conditions tend to amplify the limitations of the EC instrument configurations for measuring the turbulent flux. For example, separation distance between gas analyzers and anemometers, volume averaging by anemometers across some path length, and finite sampling periods that may be too short to resolve intermittency (and other low-frequency contributions) contribute to a reduction in the measured turbulent flux by EC systems [*De Bruin et al.*, 1993; *Kaimal and Finnigan*, 1994; *Kaimal and Gaynor*, 1991; *Leuning and Judd*, 1996; *Massman*, 2000; *Moncrieff et al.*, 1996].

[3] In this study, we argue that these theoretical and sampling reasons necessitate exploring other micrometeorological methods that are sensitive to different set of assumptions and approximations to constrain or independently verify nighttime *R*_{E} estimates derived from EC.

[4] An independent approach to estimating *R*_{E} is to utilize a functional relationship between aboveground mean CO_{2} sources, , or turbulent fluxes, , and a relatively simpler quantity to measure such as mean CO_{2} concentration profiles, , within the canopy volume, where *t* is time, *z* is the height from the forest floor and the overbar denotes the temporal and spatial averaging operator. This framework is not new and dates back to *Woodwell and Dykeman* [1966]. The basic premise is that and can be related to using the temporally and horizontally averaged one-dimensional continuity equation for a planar homogeneous flow, given by

which, upon vertical integration, yields

where *h* is the mean canopy height, and *R*_{E} is defined as

where is the forest floor efflux. In equation (2), (which can be measured by EC) represents *R*_{E} when = 0. A primitive approach to compute in equation (1) can be formulated on the basis of measurement using first-order closure principles (or K-theory) by assuming that

where *K*_{t} is the eddy diffusivity.

[5] Over the past 30 years, however, theoretical developments and many laboratory and field experiments have demonstrated that scalar and momentum fluxes within many canopies do not always obey K-Theory [*Corrsin*, 1974; *Deardorff*, 1972, 1978; *Denmead and Bradley*, 1985; *Finnigan*, 1985; *Raupach*, 1988; *Shaw*, 1977; *Sreenivasan et al.*, 1982; *Wilson*, 1989]. To alleviate K-Theory limitations, other theoretical and practical methods were developed without resorting to a local eddy diffusivity approximation [*Katul and Albertson*, 1999; *Raupach*, 1988, 1989a, 1989b; *Siqueira and Katul*, 2002].

[6] For example, *Lai et al.* [2002a] used the Localized Near Field (LNF) theory to relate to and demonstrated some success in estimating the two components of *R*_{E} (i.e., and ) over a 1-year period for near neutral and mildly stable flows. However, they pointed out a drawback of their method, titled Constrained Source Optimization (CSO), in that it was incapable of resolving the effects of local thermal stratification at a particular *z* within the canopy except through a Lagrangian integral timescale. Previous Lagrangian methods attempted to correct the Lagrangian timescale via a uniform multiplier derived from Monin-Obukhov similarity theory [*Hsieh et al.*, 2003; *Leuning*, 2000]. Several basic issues within Lagrangian models remain subject to debate outside the stability effects – most notable is that almost all Lagrangian models assume a vertically uniform timescale [*Lai et al.*, 2002a]. This assumption cannot be reconciled with a uniform mixing length scale inside the canopy [*Katul et al.*, 2004].

[7] On the other hand, *Siqueira et al.* [2002, 2003], and *Siqueira and Katul* [2002] developed Eulerian closure models that are capable of accounting for local thermal stratification within the canopy volume if mean air temperature profile measurements are available.

[8] This study combines the two approaches by revising the CSO method of *Lai et al.* [2002a] to include local thermal stratification within the canopy volume using higher-order closure principles. We tested this modified CSO method over a 3-year period at a maturing southeastern pine forest using independent measurements of and . The study period includes a mild drought (2001), a severe drought (2002), and a very wet year (2003) so that widest ranges of hydrologic and climatic conditions at this site are sampled. Improvements over *R*_{E} estimation from EC measurements using standard friction velocity *u** thresholds are discussed within the context of annual carbon balances.