1740 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 6, JUNE 2008 McCART: Monte Carlo Code for Atmospheric Radiative Transfer Vanni Nardino, Fabrizio Martelli, Piero Bruscaglioni, Giovanni Zaccanti, Samuele Del Bianco, Donatella Guzzi, Paolo Marcoionni, and Ivan Pippi Abstract—McCART is a numerical procedure to solve the radiative transfer equation for light propagation through the atmosphere from visible to near-infrared wavelengths. The pro- cedure has been developed to study the effect of the atmosphere in the remote sensing of the Earth, using aerospace imaging spectrometers. The simulation is run for a reference layered plane nonabsorbing atmosphere and a plane ground with uniform re- flectance. For a given distribution of ground reflectance and for a specific profile of scattering and absorption properties of the atmosphere, the spectral response of the sensor is obtained in a short time from the results of the Monte Carlo simulation by using scaling relationships and symmetry properties. The procedure also includes an accurate analysis of the adjacency and trapping effects due to multiple scattering of photons coming from neighboring pixels. McCART can generate synthetic images of the Earth’s surface for arbitrary viewing conditions. The results can be used to establish the limits of applicability of approximate algorithms for the processing and analysis of hyperspectral images acquired by imaging spectrometers. In addition, the algorithm can be used to develop procedures for atmospheric correction for the accurate retrieval of the spectral ground reflectance. Index Terms—Aerosols, atmospheric propagation, multilayered media, remote sensing, scattering. I. I NTRODUCTION M EASUREMENTS of remote sensing of the Earth at visible and near-infrared wavelengths are greatly influ- enced by the turbidity of the atmosphere. Scattering and absorp- tion by aerosol and gases highly complicate light propagation compared with the idealized case of a perfectly transparent at- mosphere. As a consequence, the relationship between the mea- sured signal and the physical parameters of interest becomes very complicated, and the relevant information can be retrieved only if a suitable inversion procedure is available. The first step in developing a reliable inversion procedure is the availability of an efficient solver of the forward problem, i.e., an algorithm that, given the characteristics of the light source and of the re- ceiver and the optical properties of the ground and of the atmo- sphere, enables us to determine the response of the receiver. Light propagation through turbid media is described by the radiative transfer equation (RTE) [1]–[3]. Several radiative transfer codes are used to find solutions of the RTE. These Manuscript received July 3, 2007; revised November 19, 2007. V. Nardino, F. Martelli, P. Bruscaglioni, and G. Zaccanti are with the Di- partimento di Fisica, Università degli Studi di Firenze, 50019 Sesto Fiorentino, Italy. S. Del Bianco, D. Guzzi, P. Marcoionni, and I. Pippi are with the Istituto di Fisica Applicata “Nello Carrara,” Consiglio Nazionale delle Ricerche, 50019 Sesto Fiorentino, Italy (e-mail: I.Pippi@ifac.cnr.it). Digital Object Identifier 10.1109/TGRS.2008.916464 codes are based on an explicit solution of the RTE or on a Monte Carlo (MC) approach to the radiative transfer problem. The first ones are currently used in atmospheric radiation appli- cations like MODTRAN4 [4], [5] which uses the DISORT [6] radiative transfer code as a subroutine for the implementation of the azimuth dependence of multiple scattering, 6S which solves the RTE in an iterative way using successive orders of scattering [7], COMANCHE [8] which uses an analytical formulation of the upwelling radiance, SHARM-3-D [9], [10] which uses the method of spherical harmonics [11]–[13], and SHDOM which uses the spherical harmonics discrete ordinate method [14], [15]. These codes use different levels of sophistication when modeling complex effects, like radiation trapping between the ground and atmosphere, and neighboring pixel adjacency ef- fects. For example, MODTRAN uses a single spatially homog- eneous spectral reflectance to model the surface surrounding the imaged pixel. Both MODTRAN and 6S are used by several model-based methods (ATREM [16], [17], FLAASH [18], and ATCOR [19]) to generate lookup tables for atmospheric-effect correction. Similarly, McCART uses MODTRAN to generate molecular absorption profiles. Models based on an MC approach [20]–[23] solve the RTE, using probabilistic modeling of the associated radiative transfer processes. These methods are flexible, and their self- consistency may be predicted by examining the variance be- tween estimates made from subsets of the simulation. The main goal of this paper is to describe a methodology based on MC simulations, the McCART procedure, which, making use of scaling relations that greatly reduce the compu- tation time, enables us to evaluate in a reasonable time the spec- tral at-sensor radiance for a specific distribution of reflectance of the Earth’s surface. The McCART procedure has been de- veloped to evaluate the effect of a user-defined atmosphere on aerospace multispectral and hyperspectral images of the Earth. The direct problem is solved: the procedure is able to obtain the at-sensor radiance, given the spectral surface reflectance distribution [Lambertian or characterized by a bidirectional reflectance distribution function (BRDF)]. The model, described in Section II, is based on a numer- ical MC simulation carried out for a nonabsorbing reference atmosphere with layered plane-parallel structure and for a non- absorbing plane Earth surface. Taking advantage of the transla- tional symmetry of the problem and of the weak dependence of the at-sensor radiance on the viewing direction, a large number of useful trajectories are drawn and stored in a reasonable time 0196-2892/$25.00 © 2008 IEEE