Stochastic transport theory for investigating the three-dimensional canopy structure from space measurements Dong Huang a, ⁎ , Yuri Knyazikhin a , Weile Wang a , Donald W. Deering b , Pauline Stenberg c , Nikolay Shabanov a , Bin Tan a , Ranga B. Myneni a a Department of Geography, Boston University, 675 Commonwealth Avenue, Boston, MA 02215, USA b NASA's Goddard Space Flight Center, Greenbelt, Maryland, 20771, USA c Department of Forest Ecology, University of Helsinki, FI-00014, Finland Received 19 December 2005; received in revised form 28 April 2006; accepted 4 May 2006 Abstract Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data. © 2007 Elsevier Inc. All rights reserved. Keywords: Stochastic radiative transfer; 3D canopy structure 1. Introduction The three-dimensional (3D) structure of vegetation canopies determines the spatial distribution of intercepted solar radiation which drives various physiological and physical processes integral to the functioning of plants. Thus, monitoring of the 3D canopy structure has long been one of the main goals of vegetation remote sensing from space (Castel et al., 2001; Diner et al., 1999; Justice et al., 1998; Ranson et al., 1997). The 3D radiative transfer theory provides the most logical linkage between satellite observations and the physics of processes operative in the generation of signals in optical remote sensing data (Davis & Knyazikhin, 2005; Knyazikhin et al., 2005a). Its direct use in operational data processing, however, is not feasible because of high computational costs. Therefore, the use of one-dimensional (1D) models is still the preferred option. The success of remote sensing of vegetation, thus, depends on being able to develop a radiative transfer approach for modeling the radiation regime of natural vegetation which is as realistic as the 3D model and as simple as the 1D model. At a given spatial location, the vegetation canopy should be treated as a realization of a 3D random field. Satellite-borne sensors measure the mean radiation field emanating from a satellite pixel. Available online at www.sciencedirect.com Remote Sensing of Environment 112 (2008) 35 – 50 www.elsevier.com/locate/rse ⁎ Corresponding author. Current affiliation: Environmental Sciences Depart- ment, Brookhaven National Laboratory, 75 Rutherford Dr., Upton, NY 11973. Tel.: +1 631 344 5818; fax: +1 631 344 2887. E-mail address: dhuang@bnl.gov (D. Huang). 0034-4257/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2006.05.026