Display of the earth taking into account atmospheric scattering

DisplayofTheEarthTakingintoAccountAtmosphericScatteringTomoyuki Nishitaakao SiraiFukuy ama UniversityHigashimura-cho, Fukuyama, 729-02 JapanKatsumi TadamuraEihachiro NakamaeHiroshima Prefectural UnivNanatsuka-cho, Shoubara City, 727 JapanAbstractA method to display the earth as viewed from outer space(oraspaceship)isprop osed.Theintentionofthepap erisapplicationtospaceightsimulators(e.g.,reentrythe atmosphere) and the simulation of surveys of the earth(comparisons with observations from weather satellites andweather simulations); it is not for geometric mo deling of ter-rains and/or clouds viewed from the ground, but for display-ing the earth including the surface of the sea viewed fromouter space taking into account particles (air molecules andaerosols) in the atmosphere and water molecules in the sea.The ma jor p oints of the algorithm prop osed here are theecientcalculationofopticallengthandskylight,withlookup tables taking advantage of the facts that the earthis spherical, and that sunlight is parallel.CR Categories and Sub ject Descriptors:I.3. 3 [Computer Graphics]:Picture/Image GenerationI.3. 7 [Computer Graphics]: Three-DimensionalGraphics and RealismKey Words:Earth, Atmospheric Scattering, OpticalLength, Sky light, Color of Water, Photo-realism,Radiative Transfer1INTRODUCTIONResearch on image synthesis of realistic 3-D mo dels is oneof the most p opular elds thesedays.Displays of naturalscenes such as mountains,trees, sea, cloudshave b een at-tractively rendered, and an image synthesis of the earth hasalso beendevelop ed.Images of theearthare widely usedin movies or TV commercials, e.g., the CG library of earthimages[6] was recently released for use in this eld.Theseimages,however,arefo cusedontocreateattractiveimages without any requirement of physical based accuracy.However, physically-based images are required for the studyof the simulation of surveys of the earth, such as observationfrom weather satellites in comparison to weather simulation,and ight simulators in space.The color of the earth whenviewed from spacevaries accordingto the relationship b e-tween the view direction and the p osition of the sun.In thefamous words of the astronaut, \the earth was blue". Whenwe observe the earth from relatively close to the atmosphere,the atmosphere surrounding the earth app ears as blue, andthe atmosphere near the b oundary of the shadow due to thesun app ears red (i.e., sunset). The color of clouds also variesaccording to the sun's p osition.These phenomena are opti-cal e ects caused by particles in the atmosphere, and cannotb e ignored.The color of the surface of the sea is not uni-form, such as navy blue; it has various colors which dep endon incident light to the sea and absorption/scattering e ectsdue to water molecules.This pap er prop oses an algorithm of physically-based im-age synthesis of the earth viewed from space.The metho dprop osed here has the following advantages:(1)Calculationofthesp ectrumearthviewedthroughtheatmosphere;earthisilluminatedbydirectsunlightandskylighta ectedbyatmosphericscattering. (2)Calculation of the sp ectrum of the atmosphere takingaccount of absorption/scattering due to particles in theatmosphere. (3)Calculationofthesp ectrumonsurfaceseatakingintoaccountradiativetransferofwatermolecules.The ma jor parts in 1) and 2) are concerned with the calcu-lation of optical length and sky light. For these calculations,numerical integrations taking into account atmospheric scat-tering are required, but they are e ectively solved by usingseveral (various) lo okup tables making go o d use of the factsthat the shap e of the earth is a sphere and that sunlight isa parallel light.For 3), we show that an analytical solutionis available instead of numerical integrations.Inthefollowingsections,basicideaoflightingmo del forrenderingthecolorof theearthtakingintoac-count atmospheric scattering, rendering the color of clouds,andsp ectrumcalculationof theseais describ ed.Finally,several examples are demonstrated in order to show the ef-fectiveness of the metho d prop osed here.2BASICIDEASIn order to render the earth, the following elements shouldb e taken into account:a geometric mo del of the earth, theatmosphere(airmolecules,aerosols),sea,clouds,andthesp ectrum of the sunlight.This pap er discusses rendering an algorithm of the earth,theatmosphere,sea,andcloudsviewedfromouterspaceorvariousp ositionswithintheatmosphere;followingoptical characteristics should b e considered:(1)The color of the atmosphere:the atmosphere containsair molecules and aerosols, and scattered sunlight fromthoseparticles reachesthe viewp oint;the intensityofthelightreachingviewp oinisobtainedbyinte-grating scatteredlight from every particle on the ray,and the light scattered from the atmosphere around theearth also reaches this viewp oint. (2)The color of the earth's surface:the earth is illumi-natedby b oth direct sunlight and sky light.Sunlightis absorb ed when light passes through the atmosphere,and sky light consists of light scattered by particles inthe air.On the way, passingthroughthe atmospherethe light is attenuated, and its sp ectrum changes.1