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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L = L* fin* (QCAL QCAL min ) + L mn QCAL max -QCAL min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 Ar
2、chive Production System )，贝U 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):L 一 LL =上* (DN 一1) Lmin254对于Landsat-5来说，可以改写为(QCALmin=0):L = Lmax fn * dn +Lmin255mm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+(W m-2-s
3、r-1 ' m-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 GainLminLmaxLminLmaxLminLmaxLminLmax1-6.2297.5-6.2194.3-6.2293.7-6.2191.62-6.0303.4-6.0202.4-6.4300.9-6.4196.53-4.5235.5-4.5158.6-5.0234.4-5.0152.94-4.5235.5-4.5157.5-5.1241.1-5.1157.45-1.047.7-1.031.76-1.047.57-1.031.067-0.3516.6-0.3510.
4、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 (W m-2-sr-1 ' m-1)波段1984/03/01 至 2003/05/042003/05/04 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.
5、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 ScienceOffic
6、e , 1998b ）。第二步、计算各波段反射率（反照率、反射率）_ 2（i为第i波段）一 L D（刁? i ESUN .Cos（无量纲），兀为常量（球面度str）, L为大气层顶进 m-1）, D为日地之间距离（天文单位）,ESUN为大 m-1）, 0为太阳的大顶角（0 =90? 3 , 3为太阳高式中，p为人气层顶（TOA）表观反射率 人卫星传感器的光谱辐射亮度（W m-2-sr-1气层顶的平均太阳光谱辐照度（W m-2-sr-1度角， Cos（ 0 ）也可以这样计算：Cos（ 0 ）=Sin力*Sin a +Cos 4 *Cos a *Cosh,式中力甲为地理纬度，4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：?T-土。）其中，。s为太阳大顶角，D为儒略历（Julian） 日期，这两个参数可由数据头文件读 出。L （入）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0人射到该面，该表面的辐照度为E = ESUN*Cos（ 0 ）/D2（吕斯哗，1981）。该表面的辐射出射度M=兀L（吕斯骤，1981）。根据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2E = M =" ,L ,D（i 为第 i 波段）E ESUN .C
8、os 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day10.9832740.99451521.01402271.01283050.9925150.9836910.99931661.01582421.00923190.9892320.98531061.00331821.01672581.00573350.9860460.98781211.00761961.01652741.00113
9、490.9843600.99091351.01092131.01492880.99723650.9830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-1 - m-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 ESUN195718261554103621580.67两步合为一步计算如下:2
10、 : , D|L ma x - L min:'i =ESUN Cos (刁 |QCAL max -QCAL，(QCAL -QCAL min ) +Lmnmin（i为第i波段）对于Landsat-7上试简化为:"i =ESUNL max - L min“QCAL -1) - Lmin Cos(<i)|L 254对于Landsat-5上试简化为:QCAL L min D| L max - L min255ESUN .Cos 其中，QCAL为图像灰度值 DN。反照率的计算：TM卜TM破段所对应的宽波段反照率可表示为4;-i1（Pi为TM第i个波段的反射率）Table 1. C
11、haracteristics of the Enhanced Thematic Mapper Plus (ETM+) bands.SpatialLowerUpperBandwidth (nm)BitsBandresolutionlimitlimitperGainOffset(m)(i m)(i 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 0.9392
12、15686 -4.5000000528.501.551.752008 0.128470589 -1.0000000657.0010.4012.5021008 0.066823533 0.00000000728.502.102.352508 0.044243138 -0.3499999814.250.520.903808 0.786274521 -6.199999811.3.1 Conversion to RadianceDuring 1G product rendering image pixels are converted to units of absolute radiance usi
13、ng 32 bit floating point calculations. Pixel values are then scaled to byte values prior to media output. The following equation is used to convert DN's in a 1G product back to radiance units:L 入="gain" * QCAL + "offset"which is also expressed as:where:L入=(LMAX ,-LMIN 入)/(QCA
14、LMAX-QCALMIN) * (QCAL-QCALMIN+ LMIN=Spectral Radiance at the sensor ? aperture inwatts/(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 * ster *m)offset" = Rescaled bia
15、s (the data product "offset" containedin the Level 1 product header or ancillary datarecord ) in watts/(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 radia
16、nce that is scaled to QCALMAX inwatts/(meter squared * ster *m)QCALMIN = the minimum quantized calibrated pixel value (corresponding to LMIN入)in DN=1 (LPGS Products) =0 (NLAPS Products)QCALMAX= the maximum quantized calibrated pixel value (corresponding to LMAX 入)in DN=255The LMINs and LMAXs are the
17、 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 used0 for QCALMIN for data products processed before April 5, 2004. NLAPSfrom that date nowuses 1 for the QCALMINalue. Other product differences exist as well
18、. OneLMIN/LMAXset exists for each gain state. These values will change slowly over time as the ETMTetectors lose responsivity. Table 11.2 lists two sets of LMINsand LMAXs.The first set should be used for both LPGSand NLAPSG products created before July 1,2000 and the second set for 1G products creat
19、edafter 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 by a team of independent investigators post launch. This
20、 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 ETM+ Spectral Radiance Rangewatts/(meter squared * ster
21、*m)Band NumberBefore July 1,2000After July 1,2000Low GainHigh GainLow GainHigh GainLMINLMAXLMINLMAXLMINLMAXLMINLMAX1-6.2297.5-6.2194.3-6.2293.7-6.2191.62-6.0303.4-6.0202.4-6.4300.9-6.4196.53-4.5235.5-4.5158.6-5.0234.4-5.0152.94-4.5235.0-4.5157.5-5.1241.1-5.1157.45-1.047.70-1.031.76-1.047.57-1.031.06
22、60.017.043.212.650.017.043.212.657-0.3516.60-0.3510.932-0.3516.54-0.3510.808-5.0244.00-5.0158.40-4.7243.1-4.7158.311.3.2 Radiance to ReflectanceFor relatively clear Landsat scenes, a reduction in between-scene variability can be achieved through a normalization for solar irradiance by converting spe
23、ctral radiance, as calculated above, to planetaryreflectance or albedo. This combined surface and atmospheric reflectance of the Earth is computed with the following formula:- Jt Lx* d2Pp =ESUN cos的Where:Op= Unitless planetary reflectanceL= Spectral radiance at the sensor's aperture= Earth-Sun d
24、istance in astronomical units froml nautical handbook orinterpolated from values listed in Table 11.4N = Mean solar exoatmospheric irradiances from Table, 11.3= Solar zenith angle in degreesTable 11.3 ETM+ Solar Spectral IrradiancesBandwatts/(meter squared *p m)11969.00021840.00031551.00041044.00052
25、25.700782.0781368.000Table 11.4 Earth-Sun Distance in Astronomical UnitsJulianDayDistanceJulianDayDistanceJulianDayDistanceJulianDayDistanceJulianDayDistance1.983274.99451521.01402271.0128305.992515.983691.99931661.01582421.0092319.989232.98531061.00331821.01672581.0057335.986046.98781211.00761961.0
26、1652741.0011349.984360.99091351.01092131.0149288.9972365.983311.3.3 Band 6 Conversion to TemperatureETM+ Band 6 imagery can also 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-atmosphe
27、re system under an assumption of unity emmissivity and using pre-launch calibration constants listed in Table 11.5. The conversion formula is:K2Where:= 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- K1Constant 2 - K2watts/(meter squared * ster *p m)KelvinLandsat 7666.091282.71Landsat 5607.761260.56