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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 product generation 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 Production System )，则QCALmin=0 (Ldsat-5的TM数据属于此类型)。 根据以
2、上情况，对于Landsat-7来说，可以改写为(QCALmin=1)： 对于Landsat-5来说，可以改写为(QCALmin=0)：表1 Iandsa-7 ETM+各个反射波段的Lmax和Lmin值Table1The values of Lmmax and Lmin for reflecting bands of Landsat-7 ETM+(Wm-2-sr-1m-1)波段Band2000年7月1日之前2000年7月1日之后低Gain高Gain低Gain高GainLminLmaxLminLmaxLminLmaxLminLmax1-6.2297.5-6.2194.3-6.2293.7-6.21
3、91.62-6.0303.4-6.0202.4-6.4300.9-6.4196.53-4.5235.5-4.5158.6-5.0234.4-5.0152.94-4.5235.5-4.5157.5-5.1241.1-5.1157.45-1.047.7-1.031.76-1.047.57-1.031.067-0.3516.6-0.3510.932-0.3516.54-0.3510.8表2 Landsat-5 TM各反射波段的Lmax和Lmin值Table 2 The values of Lmax and Lmin for reflecting bands of Landsat-5 TM (Wm-2
4、-sr-1m-1)波段Band1984/03/01至2003/05/042003/05/04之后LminLmaxLminLmax1-1.52152.10-1.52193.02-2.84296.81-2.84365.03-1.17204.30-1.17264.04-1.51206.20-1.51221.05-0.3727.19-0.3730.27-0.1514.38-0.1516.5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、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 ScienceOffice , 1998b )。第二步、计算各波段反射率（反照率、反射率）：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(Wm-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(Wm-2-sr-1m
6、-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：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()/D2(吕斯哗，1981)。该表面的辐射出射度M=L(吕斯骤，1981)。根据
7、Lanbertian反射率定义，大气层顶的表观反射率P等于M和E的比值，即表 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day距离day日数day日数day日数day日数day日数day日数day日数day日数day10.9832740.99451521.01402271.01283050.9925150.9836910.99931661.01582421.00923190.9892320.98531061.00331821.01672581.00573350.9860
8、460.98781211.00761961.01652741.00113490.9843600.99091351.01092131.01492880.99723650.9830表 4 Landsat-7 和Landsat-5的大气层顶平均太阳光谱辐照度ESUN(Wm-2-sr-1m-1)TahlP 4 Mean solar spectral iwadiance at the atmosphemic top for Landsat-7 and Landsat-5波段Band123457Landsat-7 ESUN1969184015511044225.782.07Landsat-5 ESUN19
9、5718261554103621580.67两步合为一步计算如下：对于Landsat-7上试简化为：对于Landsat-5上试简化为： 其中，QCAL为图像灰度值DN。反照率的计算：TM1TM4波段所对应的宽波段反照率可表示为Table 1. Characteristics of the Enhanced Thematic Mapper Plus (ETM+) bands.BandSpatial resolution (m)Lower limit (m)Upper limit (m)Bandwidth (nm)Bits per pixelGainOffset128.500.450.527080
10、.786274521-6.1999998228.500.530.618080.817254878-6.0000000328.500.630.696080.639607867-4.5000000428.500.750.9015080.939215686-4.5000000528.501.551.7520080.128470589-1.0000000657.0010.4012.50210080.0668235330.00000000728.502.102.3525080.044243138-0.3499999814.250.520.9038080.786274521-6.199999811.3.1
11、 Conversion to RadianceDuring 1G product rendering image pixels are converted to units of absolute radiance using 32 bit floating point calculations. Pixel values are then scaled to byte values prior to media output. The following equation is used to convert DNs in a 1G product back to radiance unit
12、s: L = gain * QCAL + offset which is also expressed as: L = (LMAX - LMIN)/(QCALMAX-QCALMIN) * (QCAL-QCALMIN) + LMINwhere: L= Spectral Radiance at the sensor aperture in watts/(meter squared * ster * m)gain= Rescaled gain (the data product gain contained in the Level 1 product header or ancillary dat
13、a record) in watts/(meter squared * ster * m)offset= Rescaled bias (the data product offset contained in the Level 1 product header or ancillary data record ) in watts/(meter squared * ster * m)QCAL= the quantized calibrated pixel value in DNLMIN= the spectral radiance that is scaled to QCALMIN in w
14、atts/(meter squared * ster * m)LMAX= the spectral radiance that is scaled to QCALMAX in watts/(meter squared * ster * m)QCALMIN= the minimum quantized calibrated pixel value (corresponding to LMIN) in DN = 1 (LPGS Products)= 0 (NLAPS Products)QCALMAX= the maximum quantized calibrated pixel value (correspo
