Lecture 5. Multiple scattering as a source of radiation. Reflectance from surfaces. Remote sensing of ocean color.

Transcription

1 Lecture 5. Multiple scattering as a source of raiation. Reflectance from surfaces. Remote sensing of ocean color. 1. Direct an iffuse raiation. Multiple scattering. Single scattering approximation. 2. Reflectance from surfaces. 3. Applications of passive remote sensing using extinction an scattering: Remote sensing of ocean color. Require Reaing: S: Petty: 11 nto to Chapter Aitional reaing: NASA remote sensing of ocean color: Ocean color training material: 1. Direct an iffuse raiation. Multiple scattering. The solar raiation fiel is traitionally consiere as a sum of two istinctly ifferent components: irect an iffuse: ir if Direct raiation is a part of the raiation fiel that has survive the extinction passing through a layer with optical epth an it obeys the Beer-Bouguer-Lambert law see Lecture 4: ir exp / where is the incient intensity at a given wavelength at the top of a layer an is a cosine of the incient zenith angle = cos. 1

2 Diffuse raiation Diffuse raiation arises from the light that unergoes one scattering event single scattering or many multiple scattering. ncient light Thir orer scattering First orer scattering Secon orer scattering For single scattering P ks s [5.1] 4 where is the incient intensity in the irection efine by a soli angle. For multiple scattering integrating over all irections: P ks s 4 4 [5.2] NOTE: The above equation shows that the phase function reirects the incient intensity in the irection to the irection an the integral accounts for all possible scattering events within the 4 soli angle. Accoring to the Beer-Bouguer-Lambert law scattering raiance from path s can be expresse as ke s thus from Eq.[5.2] the scattering source function is P 4 4 [5.3] where = k s / k e is the single scattering albeo. 2

3 The scattering source function: 1 has units of intensity 2 plays the role of the Planck function in thermal raiative transfer but the scattering source function is more complex 3 epens on the raiation intensity in the incient irection ; fraction of raiation P which is scattere ; an fraction scattere into the new irection 4 The monochromatic raiative transfer equation for a plane-parallel atmosphere: expresses the net change in intensity ue to extinction an scattering along path z: = extinction + scattering A plane-parallel atmosphere Ztop = Z Z= * Using s = z/cos the raiative transfer equation can be written as z cos z z [5.4] k z e ntroucing the optical epth measure from the outer bounary ownwar as z z ke z z [5.5] an using ke z z an = cos we have ; ; ; [5.6] NOTE: Eq.[5.6] is calle the Schwarzchil s equation an alsocalle the ifferential form of the raiative transfer equation for the plane-parallel atmosphere. 3

4 4 Upwar or upwelling intensity is for 1 or 2 / ; Downwar or ownwelling intensity is for 1 or 2 / The raiative transfer equation [5.6] can be written for upwar an ownwar intensities: [5.7a] [5.7b] Solution of Eq.[5.7a] gives the upwar intensity in the plane-parallel atmosphere: exp 1 exp * * * [5.8a] Solution of Eq.[5.7b] gives the ownwar intensity in the plane-parallel atmosphere: exp 1 exp [5.8b] First-orer scattering: Observer Sun Ztop = Z Z= * o o

5 5 Direct solar raiation reaching the altitue z is / exp / exp o t e F z z k F z F where F is the solar constant at the top of the atmosphere. Scattering of the irect beam is the source of iffuse raiation see Eq.[5.1] / exp 4 P F [5.9] Assuming no surface reflection ark surface the upwelling intensity at the level Z or can be foun from Eq.[5.8a] as / ] / exp[ * [5.1] Substituting in the source function / ] / / exp[ 4 * P F [5.11] An observer i.e. a satellite sensor at Ztop or = measures *] 1 1 exp [1 4 o P F [5.12] f * <1 calle the single scattering approximation Eq.[5.12] simplifies to * 4 F P [5.13] Raiative transfer equation with multiple scattering: n the general case of multiple scattering / exp 4 ' ' ' ' ' ' F P P [4.14] Using the source function for scattering we can write the raiative transfer equation for iffuse raiation as an integro-ifferential equation:

6 ' ' exp / 4 P F P 4 4 [5.15] NOTE: To solve Eq.[5.15] one nees to know the scattering coefficient k s absorption coefficient k a an scattering phase function P as a function of wavelength in each atmospheric layer. NOTE: Various approximate an exact such as Discrete-orinate Aing-oubling Monte-Carlo etc. techniques have been evelope to solve the raiative transfer equation for iffuse raiation. Each technique requires a sophisticate numerical coe. There are a number of various numerical raiative transfer coes that are openly available to the scientific community. 2. Reflection from surfaces. Bi-irectional reflectance istribution function BRDF is introuce to characterize the angular epenence in the surface reflection an efine as the ratio of the reflecte intensity raiance to the raiation flux irraiance in the incient beam: R r r r r i i [5.16] i i i i where i cos i an i is the incient zenith angle i is the incient azimuthal angle an r cos r an r is the viewing zenith angle r is the viewing azimuthal angle. 6

7 Two extreme types of the surface reflection: specular reflectance an iffuse reflectance. Specular reflectance is the reflectance from a perfectly smooth surface e.g. a mirror: Angle of incience =Angle of reflectance Reflection is generally specular when the "roughness" of the surface is smaller than the wavelength of raiation. n the solar spectrum about.4 to 2 m reflection is therefore specular on smooth surfaces such as still water. Practically all real surfaces are not smooth an the surface reflection epens on the incient angle an the angle of reflection. Reflectance from such surfaces is referre to as iffuse reflectance. Special case of iffuse reflection: Lambertian reflection. A surface calle the Lambert surface if it obeys the Lambert s Law which states that the iffusely reflecte light is isotropic an unpolarize i.e. natural light inepenently of the state of polarization an the angle of the incience light. Reflection from the Lambertian surface is isotropic: R R [5.17] r where RL is the Lambert reflectance also calle surface albeo. r i i L 7

8 n general the surface reflectance albeo is a function of wavelength. Examples of representative surface albeo at ~ 55 nm wavelength: fresh snow/ice =.8-.9 eserts= soil/vegetation= ocean=.5 Figure 5.1 Examples of spectral reflectances albeo of various surfaces. NOTE: Each surface type has a specific spectral fingerprint that is the surface reflectance has a specific epenence on the wavelength. This plays a central role in the remote sensing of lan an ocean surfaces. 8

9 The principle of interaction: The resulting intensity emerging from the surface of the layer is a superposition of reflecte an transmitte intensities. NOTE: Eqs.[5.12]-[5.13] for the first orer scattering were erive for non-reflecting surfaces calle black surfaces. The principle of interaction enables the incorporation of raiances reflecte from the surfaces. Consier an atmospheric layer that can reflect an transmit the incient raiation. Reflection R an transmission T functions of iffuse raiation are efine as reflecte R transmitte T where is the incient intensity in the irection. [5.18] [5.19] f the atmopsheric layer illumitate by many sources of raiation from below an above with k of the k-th source below an j of the j-th source above then the intensity emerging from the layer in the irection is R j j j T k k k j k [5.2] 9

10 NOTE: See an example for the case of two layers in S Applications of passive remote sensing using extinction an scattering: Remote sensing of ocean color see also Lab 4 Remote sensing of ocean color provies information on the abunance of phytoplankton chlorophyll an the concentration of issolve an particulate material in surface ocean waters. mportance: biological prouctivity in the oceans the oceans take up about 1/3 of CO2 two major mechanism: solubility pump an biological pump the latter is controlle by phytoplankton biomass marine optical properties the interaction of wins an currents with ocean biology effects of human activities on the oceanic environment. Ocean color is referre to the wavelength epenence of the water-leaving raiances at the ocean surface. Ocean color is the result of scattering an absorption by chlorophyll pigments as well as issolve an particulate matter in the surface ocean water. Principles of ocean color retrievals: Phytoplankton has a specific absorbing spectrum => its concentration can be retrieve if the spectral water-leaving raiances are measure. Nee for accurate atmospheric correction: Water-leaving raiances can be as low as a few percent of the TOA top-of-theatmosphere raiances measure by satellite sensors => it is critical to quantify an correctly remove the contribution from the atmosphere to the TOA raiances. Satellite sensors use for ocean color: see more info at CZCS Coastal Zone Color Scanner flown on the NMBUS-7 satellite: ata available for

11 SeaWiFS Sea-viewing Wie Fiel-of-View Scanner launche onboar Orbview-2 satellite: ata from 1997 MODS Moerate Resolution maging Spectroraiometer launche on Terra an Aqua satellites: ata from 1999 for Terra an from une 22 for Aqua Table 5.1 MODS SeaWiFS an CZCS channels an their central wavelengths use for ocean color retrievals. nm MODS SeaWiFS CZCS Concept of an ocean color retrieval algorithm retrieval of the chlorophyll concentration: CZCS SeaWiFS an MODS algorithms use the normalize water-leaving raiance [ w ] N efine as where T is the iffuse transmittance; w is the raiance reflecte by water. [ ] T w w N [5.21] The normalize water-leaving raiance is approximately the raiance that woul exit the ocean in the absence of the atmosphere with the sun in the zenith. Assuming the Lambertian surface reflectance associate with the raiance [ w ] N can be efine as [ R w ] N [ w ] N F 11

12 an Eq. [5.21] becomes R [ R ] T w w N Figure 5.2 Normalize water-leaving reflectance ratio as a function of pigment chrolophyll a concentration Goron et al f the ratio [ R 443] /[ R 55] is known the pigment concentration C can w N w N be approximate as log C 1.2log 1 r.5log1 r 2.8log1 r where r.5[ R w 443] /[ R 55] N w N NOTE: Retrievals of ocean color are strongly affecte by atmospheric conitions. No retrievals in the presence of clous an heavy aerosol plumes i.e. large optical epth. NOTE: Ocean color -like algorithms are also wiely use for characterizing lake rivers an other water boies. 12

13 mportance of accurate sensor calibration an atmospheric correction: Figure 5.3 Example of water leaving raiances an TOA raiances as a function of wavelength The atmosphere is 8-9% of the total top-of-atmosphere signal in blue-green wavelengths 4-6 nm ~1% error in instrument calibration or atmospheric moel leas to ~1% error inwatr leaving raiances w NOTE: Water leaving raiances are low at ~8-9 nm calle ark ocean so that raiances measure by channels locate in this spectral region are affecte by atmosphere only -> use for atmospheric correction 13

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