表观反射率(反射率、反照率)的计算

1、表观反射率（反射率、反照率）的计算第一步、分别计算各个波段每个像元的辐射亮度L 值：L=Gain*DN+Bias或者LmaxLmin* (QCAL QCALmin ) L minLQCALminQCALmax式中， QcaL 为某一像元的DN 值，即 QCAL=DN 。 QCALmax 为像元可以取的最大值255 。 QCALmin 为像元可以取的最小值。如果卫星数据来自LPGS(The level 1 productgeneration system)，则 QCAL=1(Landsat-7数据属于此类型)。如果卫星数据来自美国的NLAPS ( National Landsat Archive

2、 Production System )，则 QCALmin=0 (Ldsat-5的 TM 数据属于此类型)。根 据 以 上 情 况 ， 对 于Landsat-7来 说 ， 可 以 改 写 为 (QCALmin=1)：LLmaxLmin * (DN1) Lmin254对于 Landsat-5 来说，可以改写为 (QCALmin=0)：LLmaxLmin * DNL min255表 1Iandsa-7 ETM+ 各个反射波段的Lmax 和 Lmin 值Table1ThevaluesofLmmax andLminforreflecting bands ofLandsat-7ETM+(W m-2-s

3、r-1 m-1)波段2000年 7月 1日之前2000年 7月 1日之后Band低 Gain高 Gain低 Gain高 GainLminLmaxLminLmaxLminLmaxLminLmax1-6.2297.5-6.2194.3-6.2293.7-6.2191.62-6.0303.4-6.0202.4-6.4300.9-6.4196.53-4.5235.5-4.5158.6-5.0234.4-5.0152.94-4.5235.5-4.5157.5-5.1241.1-5.1157.45-1.047.7-1.031.76-1.047.57-1.031.067-0.3516.6-0.3510.93

4、2-0.3516.54-0.3510.8表 2 Landsat-5 TM 各反射波段的LmaxTable 2 The values of Lmax and Lmin for reflecting bands of波段1984/03/01 至 2003/05/04和 Lmin 值Landsat-5 TM (W m-2-sr-1 m-1)2003/05/04 之后BandLminLmaxLminLmax1-1.52152.10-1.52193.02-2.84296.81-2.84365.03-1.17204.30-1.17264.04-1.51206.20-1.51221.05-0.3727.19

5、-0.3730.27-0.1514.38-0.1516.5为了使传感器的辐射分辨率达到最大，而又不使其达到饱和，根据地表类型( 非沙漠和冰面的陆地、沙漠、冰与雪、水体、海冰、火山等6 大类型 )和太阳高度角状况来确定采用高增益参数或是低增益参数。一般低增益的动态范围比高增益大1.5 倍，因此当地表亮度较大时，用低增益参数 ; 其它情况用高增益参数。在非沙漠和冰面的陆地地表类型中，ETM+ 的 1 一 3和 5,7 波段采用高增益参数，4 波段在太阳高度角低于45 度（天顶角 45 度）时也用高增益参数，反之则用低增益参数。详见文献(NASA Landsat Project ScienceOff

6、ice , 1998b ) 。第二步、计算各波段反射率（反照率、反射率） ：LD2iESUN(i为第 i波段）Cos( )式中， p 为人气层顶 (TOA) 表观反射率 (无量纲 )， 为常量 ( 球面度 str)，L 为大气层顶进人卫星传感器的光谱辐射亮度 (W m-2-sr-1m-1) ，D 为日地之间距离 (天文单位 ),ESUN 为大气层顶的平均太阳光谱辐照度 (W m-2-sr-1m-1), 为太阳的天顶角 ( =90?- ， 为太阳高度角， Cos( )也可以这样计算： Cos( )=Sin *Sin +Cos *Cos *Cosh, 式中 甲为地理纬度， 为太阳赤纬， h 为太阳

7、的时角。太阳赤纬是太阳光与地球赤道平面的夹角)。也可以是：TE sun(L()(1 0.0167sin 2 (D 93.5) )2) cos s365其中 , s 为太阳天顶角,D 为儒略历 (Julian)日期 , 这两个参数可由数据头文件读出。 L ( ) 为入瞳辐亮度 ,Esun为外大气层太阳辐照度。上式成立的条件是假设在大气层顶，有一个朗勃特(Laribcitian) 反射面。太阳光以天顶角 人射到该面，该表面的辐照度为E = ESUN*Cos( )/D 2(吕斯哗， 1981)。该表面的辐射出射度 M= L( 吕斯骤， 1981)。根据 Lanbertian 反射率定义，大气层顶的表

8、观反射率P 等于M 和 E 的比值，即iMLD 2(i 为第 i 波段）EESUNCos( )表 3 随时间变化的日地距离（天文单位）Table 3 Earth-Sun distance at different time (Astonomical units)日数距离日数日数日数日数日数日数日数日数daydaydaydaydaydaydaydaydayday10.9832740.99451521.01402271.01283050.9925150.9836910.99931661.01582421.00923190.9892320.98531061.00331821.01672581.005

9、73350.9860460.98781211.00761961.01652741.00113490.9843600.99091351.01092131.01492880.99723650.9830表 4 Landsat-7和 Landsat-5 的大气层顶平均太阳光谱辐照度ESUN(W m-2-sr-1m-1 )TahlP 4 Mean solar spectral iwadiance at the atmosphemic top for Landsat-7 and Landsat-5波段 Band123457Landsat-7 ESUN1969184015511044225.782.07La

10、ndsat-5 ESUN195718261554103621580.67两步合为一步计算如下：iD 2Lma xLmin(QCALQCAL min )Lmin(i为第 i波段）ESUNCos( )QCAL maxQCAL min对于 Landsat-7 上试简化为：iD 2LmaxL min(QCAL1)LminESUN Cos( )254对于 Landsat-5上试简化为：iD 2LmaxLminQCALLminESUNCos( )255其中， QCAL 为图像灰度值DN。反照率的计算：TM1 TM4波段所对应的宽波段反照率可表示为4i(i 为 TM 第 i个波段的反射率）1Table 1.

11、 Characteristics of the Enhanced Thematic Mapper Plus (ETM+)bands.BandSpatialLowerUpperBandwidthBitsGainOffsetresolutionlimitlimit(nm)per(m)( m) ( m)pixel128.500.450.52708 0.786274521-6.1999998228.500.530.61808 0.817254878-6.0000000328.500.630.69608 0.639607867-4.5000000428.500.750.901508 0.93921568

12、6-4.5000000528.501.551.752008 0.128470589-1.0000000657.0010.4012.5021008 0.0668235330.00000000728.502.102.352508 0.044243138-0.3499999814.250.520.903808 0.786274521-6.1999998During 1G product rendering image pixels are converted to units ofabsolute radiance using 32 bit floating point calculations.

13、Pixel values are then scaled to byte values prior to media output. The followingequation is used to convert DNs in a 1G product back to radiance units:L = gain * QCAL + offsetwhich is also expressed as:L = (LMAX - LMIN ) /(QCALMAX-QCALMIN) * (QCAL-QCALMIN)+ LMINwhere:L? aperture in= Spectral Radianc

14、e at the sensorwatts/(meter squared * ster *m)gain= Rescaled gain (thedata productgaincontainedinthe Level 1 product header or ancillary data record)inwatts/(meter squared * ster *m)offset= Rescaled bias (the data product offset containedin the Level 1 product header or ancillary datarecord ) inwatt

15、s/(meter squared * ster *m)QCAL = the quantized calibrated pixel value in DNLMIN= the spectral radiance that is scaled to QCALMIN inwatts/(meter squared * ster *m)LMAX= the spectral radiance that is scaled to QCALMAX inwatts/(meter squared * ster *m)QCALMIN = the minimum quantized calibrated pixel v

16、alue(corresponding to LMIN) in DN1 (LPGS Products)0 (NLAPS Products)QCALMAX= the maximum quantized calibrated pixel value (corresponding to LMAX ) in DN= 255The LMINs and LMAXs are the spectral radiances for each band at digitalnumbers 0 or 1 and 255 (i.e QCALMIN, QCALMAX), respectively. LPGS used1

17、for QCALMIN while NLAPS used0 for QCALMIN for data products processedbefore April5, 2004. NLAPSfrom thatdate nowuses 1 for theQCALMINvalue.Other product differencesexist as well. One LMIN/LMAXsetexistsforeachgain state.These valueswill change slowly over timeas theETM+detectorsloseresponsivity.Table

18、11.2 liststwo sets ofLMINs and LMAXs.The firstsetshouldbe used for both LPGSand NLAPS1G products created beforeJuly1, 2000 and the second set for 1G products createdafterJuly 1, 2000.Please note the distinctionbetween acquisitionand processing dates.Useof the appropriate LMINs and LMAXs will ensure

19、accurate conversion toradiance units.Note for band 6:A bias was found in the pre-launchcalibrationby a team ofindependent investigatorspost launch.Thiswascorrected for in the LPGS processing system beginning Dec 20, 2000. Fordataprocessed before this, the image radiances given by the abovetransform

20、are 0.31 w/m2 ster um too high. See the official announcementfor more details.Table 11.2 ETM+ Spectral Radiance Rangewatts/(meter squared * ster *m)Before July 1, 2000After July 1, 2000BandLow GainHigh GainLow GainHigh GainNumberLMINLMAXLMINLMAXLMINLMAXLMINLMAX1-6.2297.5-6.2194.3-6.2293.7-6.2191.62-

21、6.0303.4-6.0202.4-6.4300.9-6.4196.53-4.5235.5-4.5158.6-5.0234.4-5.0152.94-4.5235.0-4.5157.5-5.1241.1-5.1157.45-1.047.70-1.031.76-1.047.57-1.031.0660.017.043.212.650.017.043.212.657-0.3516.60-0.3510.932-0.3516.54-0.3510.808-5.0244.00-5.0158.40-4.7243.1-4.7158.3For relatively clear Landsat scenes, a r

22、eduction in between-scenevariabilitycan be achieved through a normalizationforsolarirradianceby converting spectral radiance, as calculated above, to planetaryreflectanceor albedo.This combined surfaceand atmosphericreflectanceof the Earth is computed with the following formula:Where:Unitless planet

23、ary reflectanceSpectral radiance at the sensors apertureEarth-Sun distance in astronomical units from nautical handbook orinterpolated from values listed in Table11.4Mean solar exoatmospheric irradiances from Table 11.3Solar zenith angle in degreesTable 11.3ETM+ Solar Spectral IrradiancesBandwatts/(

24、meter squared *m)11969.00021840.00031551.00041044.0005225.700782.0781368.000Table 11.4 Earth-Sun Distance in Astronomical UnitsJulianDistanceJulianDistanceJulianDistanceJulianDistanceJulianDistanceDayDayDayDayDay1.983274.99451521.01402271.0128305.992515.983691.99931661.01582421.0092319.989232.98531061.0033182