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 miniminaxi )(*LQCAQCAL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 )
2、，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) ：minminax)1(*254LDNL对于 Landsat-5 来说，可以改写为(QCALmin=0)： minminax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)2000 年 7 月 1 日之前 2000 年 7 月 1 日之后低 Ga
3、in 高 Gain 低 Gain 高 Gain波段BandLmin Lmax Lmin Lmax Lmin Lmax Lmin Lmax1 -6.2 297.5 -6.2 194.3 -6.2 293.7 -6.2 191.62 -6.0 303.4 -6.0 202.4 -6.4 300.9 -6.4 196.53 -4.5 235.5 -4.5 158.6 -5.0 234.4 -5.0 152.94 -4.5 235.5 -4.5 157.5 -5.1 241.1 -5.1 157.45 -1.0 47.7 -1.0 31.76 -1.0 47.57 -1.0 31.067 -0.35
4、16.6 -0.35 10.932 -0.35 16.54 -0.35 10.8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-sr-1m-1)1984/03/01 至 2003/05/04 2003/05/04 之后波段Band Lmin Lmax Lmin Lmax1 -1.52 152.10 -1.52 193.02 -2.84 296.81 -2.84 365.03 -1.17 204.30 -1.17
5、264.04 -1.51 206.20 -1.51 221.05 -0.37 27.19 -0.37 30.27 -0.15 14.38 -0.15 16.5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
6、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）： 波 段 ）为 第 iCosESUNDLi ()(2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-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
7、,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： 2)365.9(2sin017.(cos)( DELsunT 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 Lanbertian 反射率定义，大气层
8、顶的表观反射率 P等于 M 和 E 的比值，即 波 段 ）为 第 iCosSUNDLi ()(2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day1 0.9832 74 0.9945 152 1.0140 227 1.0128 305 0.992515 0.9836 91 0.9993 166 1.0158 242 1.0092 319 0.989232 0.9853 106 1
9、.0033 182 1.0167 258 1.0057 335 0.986046 0.9878 121 1.0076 196 1.0165 274 1.0011 349 0.984360 0.9909 135 1.0109 213 1.0149 288 0.9972 365 0.9830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 Band 1
10、 2 3 4 5 7Landsat-7 ESUN 1969 1840 1551 1044 225.7 82.07Landsat-5 ESUN 1957 1826 1554 1036 215 80.67两步合为一步计算如下： 波 段 ）为 第 iLQCALQCALCosESUNDxmai ()()( miniini2 对于 Landsat-7 上试简化为： minminax2 )1(54)(osSi 对于 Landsat-5 上试简化为： minminax2)(LQCALCsEUNDi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 个 波 段 的
11、反 射 率 ）第为 iTMii (41Table 1. Characteristics of the Enhanced Thematic Mapper Plus (ETM+) bands.BandSpatial resolution (m)Lower limit (m)Upper limit (m)Bandwidth (nm)Bits per pixelGain Offset1 28.50 0.45 0.52 70 80.786274521 -6.19999982 28.50 0.53 0.61 80 80.817254878 -6.00000003 28.50 0.63 0.69 60 80
12、.639607867 -4.50000004 28.50 0.75 0.90 150 80.939215686 -4.50000005 28.50 1.55 1.75 200 80.128470589 -1.00000006 57.00 10.40 12.50 2100 80.066823533 0.000000007 28.50 2.10 2.35 250 80.044243138 -0.34999998 14.25 0.52 0.90 380 80.786274521 -6.199999811.3.1 Conversion to RadianceDuring 1G product rend
13、ering 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 units: L = “gain“ * QCAL + “offset“ which is also
14、 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 data record) in watts/(meter squared
15、* 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 watts/(meter squared * ster
16、* 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 (corresponding to LMAX ) i
17、n DN = 255The LMINs and LMAXs are the spectral radiances for each band at digital numbers 0 or 1 and 255 (i.e QCALMIN, QCALMAX), respectively. LPGS used 1 for QCALMIN while NLAPS used 0 for QCALMIN for data products processed before April 5, 2004. NLAPS from that date now uses 1 for the QCALMIN valu
18、e. Other product differences exist as well. One LMIN/LMAX set exists for each gain state. These values will change slowly over time as the ETM+ detectors lose responsivity. Table 11.2 lists two sets of LMINs and LMAXs. The first set should be used for both LPGS and NLAPS 1G products created before J
19、uly 1, 2000 and the second set for 1G products created after July 1, 2000. Please note the distinction between acquisition and processing dates. Use of the appropriate LMINs and LMAXs will ensure accurate conversion to radiance units. Note for band 6: A bias was found in the pre-launch calibration b
20、y a team of independent investigators post launch. This was corrected for in the LPGS processing system beginning Dec 20, 2000. For data processed before this, the image radiances given by the above transform are 0.31 w/m2 ster um too high. See the official announcement for more details. Table 11.2
21、ETM+ Spectral Radiance Rangewatts/(meter squared * ster * m)Before July 1, 2000 After July 1, 2000Low Gain High Gain Low Gain High GainBand Number LMIN LMAX LMIN LMAX LMIN LMAX LMIN LMAX1 -6.2 297.5 -6.2 194.3 -6.2 293.7 -6.2 191.62 -6.0 303.4 -6.0 202.4 -6.4 300.9 -6.4 196.53 -4.5 235.5 -4.5 158.6
22、-5.0 234.4 -5.0 152.94 -4.5 235.0 -4.5 157.5 -5.1 241.1 -5.1 157.45 -1.0 47.70 -1.0 31.76 -1.0 47.57 -1.0 31.066 0.0 17.04 3.2 12.65 0.0 17.04 3.2 12.657 -0.35 16.60 -0.35 10.932 -0.35 16.54 -0.35 10.808 -5.0 244.00 -5.0 158.40 -4.7 243.1 -4.7 158.311.3.2 Radiance to ReflectanceFor relatively clear
23、Landsat scenes, a reduction in between-scene variability can be achieved through a normalization for solar irradiance by converting spectral radiance, as calculated above, to planetary reflectance or albedo. This combined surface and atmospheric reflectance of the Earth is computed with the followin
24、g formula: Where:= Unitless planetary reflectance= Spectral radiance at the sensors aperture= Earth-Sun distance in astronomical units from nautical handbook or interpolated from values listed in Table 11.4 = Mean solar exoatmospheric irradiances from Table 11.3= Solar zenith angle in degreesTable 1
25、1.3 ETM+ Solar Spectral IrradiancesBand watts/(meter squared * m)1 1969.000 2 1840.000 3 1551.000 4 1044.000 5 225.7007 82.07 8 1368.000 Table 11.4 Earth-Sun Distance in Astronomical UnitsJulian Day DistanceJulian Day DistanceJulian Day DistanceJulian Day DistanceJulian Day Distance1 .9832 74 .9945
26、152 1.0140 227 1.0128 305 .992515 .9836 91 .9993 166 1.0158 242 1.0092 319 .989232 .9853 106 1.0033 182 1.0167 258 1.0057 335 .986046 .9878 121 1.0076 196 1.0165 274 1.0011 349 .984360 .9909 135 1.0109 213 1.0149 288 .9972 365 .983311.3.3 Band 6 Conversion to TemperatureETM+ Band 6 imagery can also
27、be converted from spectral radiance (as described above) to a more physically useful variable. This is the effective at-satellite temperatures of the viewed Earth-atmosphere system under an assumption of unity emmissivity and using pre-launch calibration constants listed in Table 11.5. The conversio
28、n formula is: Where:T = Effective at-satellite temperature in KelvinK2 = Calibration constant 2 from Table 11.5K1 = Calibration constant 1 from Table 11.5L = Spectral radiance in watts/(meter squared * ster * ?m)Table 11.5 ETM+ and TM Thermal Band Calibration ConstantsConstant 1- K1watts/(meter squared * ster * m)Constant 2 - K2 KelvinLandsat 7 666.09 1282.71Landsat 5 607.76 1260.56
