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Radiative transfer in mountains: Application to the Tibetan PlateauK. N. Liou,1Wei-Liang Lee,1and Alex Hall1Received 26 August 2007; revised 20 October 2007; accepted 5 November 2007; published 7 December 2007.[1] We developed a 3D Monte Carlo photon tracingprogram for the transfer of radiation in inhomogeneous andirregular terrain to calculate broadband solar and thermalinfrared fluxes. We selected an area of 100  100 km2in theTibetan Plateau centered at Lhasa city and used the albedoand surface temperature from MODIS/Terra for this study.We showed that anomalies of surface solar fluxes withreference to a flat surface can be as large as 600 W/m2,depending on time of day, mountain configuration, andalbedo. Surface temperature is the dominating factor indetermining anomalies of the surface infrared fluxdistribution relative to a flat surface with values as highas 70 W/m2at cold mountain surfaces. The average surfacesolar flux over regional domains of 100  100 km2and50  50 km2comprising intense topography can deviate fromthe smoothed surface conventionally assumed in climatemodels and GCMs by 10–50 W/m2. Citation: Liou, K. N.,W.-L. Lee, and A. Hall (2007), Radiative transfer in mountains:Application to the Tibetan Plateau, Geophys. Res. Lett., 34,L23809, doi:10.1029/2007GL031762.1. Introduction[2] The energy emitted by the sun that is available at thetop of the Earth’s atmosphere (TOA) is a function of threesets of factors that include latitude, solar hour angle, and theEarth’s position relative to the sun and can be preciselycalculated [Liou, 2002]. The solar flux received by thesurface involves the attenuation of solar beam by scatteringand absorption caused by atmospheric gases, aerosols, andcloud particles. The last comprises terrain characteristicsincluding elevation, slope, orientation, and surface albedo.In mountainous terrain, the direct and diffuse solar fluxesreaching a sloping surface can be reflected to space and/orto other surfaces that cannot be fully accounted for by theconventional plane-parallel radiative transfer approach for aflat surface. For low solar elevation angles, the curvature ofthe Earth can also pose limitations on the use of theconventional plane-parallel radiative transfer approach foratmospheric calculations, but this issue is secondary com-pared to intense topographic effects. The problem of radi-ative transfer in mountains is three-dimensional in natureand it is indeed intricate. Evaluation of the solar fluxavailable at mountain surfaces by means of an accurateanalytic solution w ith appropriate boundary conditionsimposed appears to be very difficult, if not impossible.[3] Nevertheless, a variety of models of varying sophis-tication and complexity have been developed to computesolar flux components in ru gged terrain [e.g., Duguay,1993]. The direct incident beam is generally computed byintroducing a cosine correction of the local zenith angle andconsidering the shadow caused by topography [e.g., Olyphant,1986]. Diffuse radiation has been modeled as being propor-tional to the area of sky dome visible to the target surface[e.g., Dozier and Frew, 1990]. Factors contributing to terrain-reflected flux, particularly significant over snow surfaces[Dozier, 1980], have generally not been considered expli-citly, but are approximated by assuming a first-order reflec-tio n betw een surrounding terrain and the target surface .Miesch et al. [1999] used a Monte Carlo approach to computethe radiance reaching the satellite-borne sensor over a simple2D rugged terrain to demonstrate its importance in remotesensing application. Moreover, Chen et al. [2006] developeda 3D Monte Carlo radiative transfer model that calculatessolar flux components exactly given a realistic distribution ofscatterers and absorbers in the atmosphere and provided thefirst definitive assessment of the relative importance of theflux components in a clear-sky atmosph ere.[4] It is clear that significant progress has been made onthe understanding and quantification of solar flux transfer inintense topography. However, the the rmal infrared (IR)radiation emitted from mountains with an inhomogeneoussurface temperature distribution has not been studied tounderstand its significance in surface energy balance. IRradiative transfer involving mountainous surfaces dependson their temperatures, which are related to elevation, and theamount of absorbing and emitting gases above. At the sametime, emissions and reflections between nonblack moun-tains can also take place. To the best of our understandingthermal IR radiative transfer in mountains remains anuncharted research subject.[5] We investigate the effect of mountains on the transferof broadband solar and thermal infrared fluxes and attemptto understand the underlying physical processes. For thetra nsfer of so lar r adiation, we follow the Monte Carloapproach developed by Chen et al. [2006] to trace photonsemitted by the sun, a point source, and evaluate theirinteractions with the atmospheres (without clouds) and theunderlying mountains with known topography and albedo.Moreover, we develop an innovative Monte Carlo approachinvolving the transfer of emitted thermal IR radiation frommountains and its interactions with the absorbing andemitting atmosphere above. These are discussed in Section2. In Section 3, we apply the 3D solar and thermal IRradiative transfer to the Tibetan Plateau and use the snowand albedo data available from MODIS to conduct surfaceradiation analysis. Conclusions are given in Section 4.2. Spectral 3D Radiative Transfer in Mountains[6] The Monte Carlo method appears to be the bestapproach for the intricate radiative transfer problem involv-GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L23809, doi:10.1029/2007GL031762, 2007ClickHereforFullArticle1Department of Atmospheric and Oceanic Sciences and Joint Institutefor Regional Earth System Science and Engineering, University ofCalifornia, Los Angeles, California, USA.Copyright 2007 by the American Geophysical Union.0094-8276/07/2007GL031762$05.00L23809 1of6ing complex 3D topography because photons can be tracedexactly in any irregular and inhomogeneous space config-uration. In the present Monte Carlo approach, the domain ofstudy in the atmosphere is discretized in terms of finitecubic cells such that each can undergo absorption, scattering,and emission. Photons entering TOA are defined by unitirradiance and its direction is determined by the sun’sposition. The optical path


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