## 1. Introduction

[2] Estimating vertical carbon dioxide (CO_{2}) source/sink distributions and net fluxes within and above forested canopies continues to be a critical research problem in biosphere-atmosphere exchange processes [*Wofsy et al.*, 1993], contemporary ecological research [*Baldocchi and Harley*, 1995], and an active research problem in micrometeorology [*Katul et al.*, 1997, 2001; *Warland and Thurtell*, 2000; *Siqueira et al.*, 2000; *Leuning*, 2000]. Establishing the relationship between source strength and concentration profiles is essential for such problems and provides practical methodology for long-term field studies currently underway [*Kaiser*, 1998; *Falge et al.*, 2001a, 2001b]. In fact, the main method in such problems is to use the fluid mechanics principles. Historically, research effort was devoted to deriving such functional relationships by linking local turbulent fluxes to mean local concentration gradient via an effective turbulent diffusivity (K-Theory). Over the past 30 years, theoretical considerations and experiments have demonstrated that scalar and momentum fluxes within many canopies do not obey K-Theory [*Deardorff*, 1972, 1978; *Corrsin*, 1974; *Shaw*, 1977; *Sreenivasan et al.*, 1982; *Denmead and Bradley*, 1985; *Finnigan*, 1985; *Raupach*, 1988; *Wilson*, 1989]. Alternative descriptions have been developed in consequence. These include higher-order closure models [*Wilson and Shaw*, 1977; *Finnigan and Raupach*, 1987], large-eddy simulation [*Shaw and Schumann*, 1992], wavelet analysis [*Collineau and Brunet*, 1993] and Lagrangian dispersion models [*Raupach*, 1989a, 1989b; *Raupach et al.*, 1992; *Denmead*, 1995]. The first three approaches require rapid measurement of instantaneous scalar concentrations. The inverse Lagrangian dispersion model developed by *Raupach* [1989b], however, permits the identification of scalar sources and sinks in the canopy space from measurements of mean concentration profiles which are usually much easier to obtain. It was suggested by *Raupach* [1988, 1989a, 1989b] that Lagrangian transport approaches are better than their Eulerian counterpart in giving the ability to overcome flux-gradient closure model limitations [*Corrsin*, 1974; *Deardorff*, 1978; *Sreenivasan et al.*, 1982; *Wilson*, 1988].

[3] *Raupach* [1988, 1989a, 1989b] proposed the “Localized Near Field” (LNF) theory of dispersion in plant canopies, which showed that the scalar concentration profile within the canopy is the result of contributions from both local and distant sources. The LNF theory coupled with the distribution of vertical profiles of the standard deviation of wind speed (σ_{w}(*z*)) and the Lagrangian timescales (*T*_{L}(*z*)) within the canopy, so that expressions between source strength and mean concentration profile can be derived and solved. Up to the present, a number of authors [*Raupach et al.*, 1992; *Denmead and Raupach*, 1993; *Denmead*, 1995; *Katul et al.*, 1997; *Massman and Weil*, 1999; *Leuning et al.*, 2000; *Leuning*, 2000] used this approach, which with good agreement reported between modeled turbulent fluxes and those measured above the canopy. However, all the studies depend on the eddy covariance measurement to determine the friction velocity and the atmospheric stability parameter, which limited the method to be used widely. *Wang et al.* [2005] used the method to simulate the water vapor source/sink strength and evapotranspiration only using the gradient measurement of microclimate parameters, which produced good agreement between modeled evapotranspiration and those measured by the open-path eddy covariance measurement system.

[4] The object of this study is to investigate the inverse Lagrangian dispersion analysis method developed by *Raupach* [1988, 1989a, 1989b] for broadleaved Koreanpine forest in Changbai Mountain, China, for estimating both CO_{2} source/sink distribution and CO_{2} flux from 17 to 22 June 2003, only using the gradient measurement of microclimate parameters. The calculated CO_{2} flux results are compared with the results measured by the open-path eddy covariance measurement system mounted on the tower above the canopy. The daily variation of CO_{2} flux source/sink distribution within the canopy and the relationship between CO_{2} flux and photosynthetically active radiation are also discussed.