表观反射率反射率反照率的计算Word格式文档下载.docx
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300.9
196.5
3
-4.5
235.5
158.6
-5.0
234.4
152.9
4
157.5
-5.1
241.1
157.4
5
-1.0
47.7
31.76
47.57
31.06
7
-0.35
16.6
10.932
16.54
10.8
表2Landsat-5TM各反射波段的Lmax和Lmin值
Table2ThevaluesofLmaxandLminforreflectingbandsofLandsat-5TM(W˙m-2-sr-1˙μm-1)
1984/03/01至2003/05/04
2003/05/04之后
-1.52
152.10
193.0
-2.84
296.81
365.0
-1.17
204.30
264.0
-1.51
206.20
221.0
-0.37
27.19
30.2
-0.15
14.38
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)时也用高增益参数,反之则用低增益参数。
详见文献(NASALandsatProjectScienceOffice,1998b)。
第二步、计算各波段反射率(反照率、反射率)ρ:
式中,p为人气层顶(TOA)表观反射率(无量纲),π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-1˙μm-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-1˙μm-1),θ为太阳的天顶角(θ=90˚-β,β为太阳高度角,Cos(θ)也可以这样计算:
Cos(θ)=Sinφ*Sinδ+Cosφ*Cosδ*Cosh,式中φ甲为地理纬度,φ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,θs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(λ)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θ人射到该面,该表面的辐照度为E=ESUN*Cos(θ)/D2(吕斯哗,1981)。
该表面的辐射出射度M=πL(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
表3随时间变化的日地距离(天文单位)
Table3Earth-Sundistanceatdifferenttime(Astonomicalunits)
日数
day
距离
0.9832
74
0.9945
152
1.0140
227
1.0128
305
0.9925
15
0.9836
91
0.9993
166
1.0158
242
1.0092
319
0.9892
32
0.9853
106
1.0033
182
1.0167
258
1.0057
335
0.9860
46
0.9878
121
1.0076
196
1.0165
274
1.0011
349
0.9843
60
0.9909
135
1.0109
213
1.0149
288
0.9972
365
0.9830
表4Landsat-7和Landsat-5的大气层顶平均太阳光谱辐照度ESUN(W˙m-2-sr-1˙μm-1)
TahlP4MeansolarspectraliwadianceattheatmosphemictopforLandsat-7andLandsat-5
波段Band
Landsat-7ESUN
1969
1840
1551
1044
225.7
82.07
Landsat-5ESUN
1957
1826
1554
1036
215
80.67
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:
TM1~TM4波段所对应的宽波段反照率可表示为
Table1.CharacteristicsoftheEnhancedThematicMapperPlus(ETM+)bands.
Spatialresolution(m)
Lowerlimit(µ
m)
Upperlimit(µ
Bandwidth(nm)
Bitsperpixel
Gain
Offset
28.50
0.45
0.52
70
8
0.786274521
-6.1999998
0.53
0.61
80
0.817254878
-6.0000000
0.63
0.69
0.639607867
-4.5000000
0.75
0.90
150
0.939215686
1.55
1.75
200
0.128470589
-1.0000000
6
57.00
10.40
12.50
2100
0.066823533
0.00000000
2.10
2.35
250
0.044243138
-0.3499999
14.25
380
11.3.1ConversiontoRadiance
During1Gproductrenderingimagepixelsareconvertedtounitsofabsoluteradianceusing32bitfloatingpointcalculations.Pixelvaluesarethenscaledtobytevaluespriortomediaoutput.ThefollowingequationisusedtoconvertDN'
sina1Gproductbacktoradianceunits:
Lλ="
gain"
*QCAL+"
offset"
whichisalsoexpressedas:
Lλ=((LMAXλ-LMINλ)/(QCALMAX-QCALMIN))*(QCAL-QCALMIN)+LMINλ
where:
Lλ
=SpectralRadianceatthesensorճapertureinwatts/(metersquared*ster*μm)
"
=Rescaledgain(thedataproduct"
containedintheLevel1productheaderorancillarydatarecord)inwatts/(metersquared*ster*μm)
=Rescaledbias(thedataproduct"
containedintheLevel1productheaderorancillarydatarecord)inwatts/(metersquared*ster*μm)
QCAL
=thequantizedcalibratedpixelvalueinDN
LMINλ
=thespectralradiancethatisscaledtoQCALMINinwatts/(metersquared*ster*μm)
LMAXλ
=thespectralradiancethatisscaledtoQCALMAXinwatts/(metersquared*ster*μm)
QCALMIN
=theminimumquantizedcalibratedpixelvalue(correspondingtoLMINλ)inDN
=1(LPGSProducts)
=0(NLAPSProducts)
QCALMAX
=themaximumquantizedcalibratedpixelvalue(correspondingtoLMAXλ)inDN
=255
TheLMINsandLMAXsarethespectralradiancesforeachbandatdigitalnumbers0or1and255(i.eQCALMIN,QCALMAX),respectively.LPGSused1forQCALMINwhileNLAPSused0forQCALMINfordataproductsprocessedbeforeApril5,2004.NLAPSfromthatdatenowuses1fortheQCALMINvalue.Otherproductdifferencesexistaswell.OneLMIN/LMAXsetexistsforeachgainstate.ThesevalueswillchangeslowlyovertimeastheETM+detectorsloseresponsivity.Table11.2liststwosetsofLMINsandLMAXs.ThefirstsetshouldbeusedforbothLPGSandNLAPS1GproductscreatedbeforeJuly1,2000andthesecondsetfor1GproductscreatedafterJuly1,2000.Pleasenotethedistinctionbetweenacquisitionandprocessingdates.UseoftheappropriateLMINsandLMAXswillensureaccurateconversiontoradianceunits.Noteforband6:
Abiaswasfoundinthepre-launchcalibrationbyateamofindependentinvestigatorspostlaunch.ThiswascorrectedforintheLPGSprocessingsystembeginningDec20,2000.Fordataprocessedbeforethis,theimageradiancesgivenbytheabovetransformare0.31w/m2sterumtoohigh.Seetheofficialannouncementformoredetails.
Table11.2ETM+SpectralRadianceRange
watts/(metersquared*ster*μm)
BandNumber
BeforeJuly1,2000
AfterJuly1,2000
LowGain
HighGain
LMIN
LMAX
235.0
47.70
0.0
17.04
3.2
12.65
16.60
10.80
244.00
158.40
-4.7
243.1
158.3
11.3.2RadiancetoReflectance
ForrelativelyclearLandsatscenes,areductioninbetween-scenevariabilitycanbeachievedthroughanormalizationforsolarirradiancebyconvertingspectralradiance,ascalculatedabove,toplanetaryreflectanceoralbedo.ThiscombinedsurfaceandatmosphericreflectanceoftheEarthiscomputedwiththefollowingformula:
Where:
=
Unitlessplanetaryreflectance
Spectralradianceatthesensor'
saperture
Earth-Sundistanceinastronomicalunitsfromnauticalhandbookor
interpolatedfromvalueslistedinTable11.4
MeansolarexoatmosphericirradiancesfromTable11.3
Solarzenithangleindegrees
Table11.3
ETM+SolarSpectralIrradiances
watts/(metersquared*μm)
1969.000
1840.000
1551.000
1044.000
225.700
82.07
1368.000
Table11.4Earth-SunDistanceinAstronomicalUnits
JulianDay
Distance
.9832
.9945
.9925
.9836
.9993
.9892
.9853
.9860
.9878
.9843
.9909
.9972
.9833
11.3.3Band6ConversiontoTemperature
ETM+Band6imagerycanalsobeconvertedfromspectralradiance(asdescribedabove)toamorephysicallyusefulvariable.Thisistheeffectiveat-satellitetemperaturesoftheviewedEarth-atmospheresystemunderanassumptionofunityemmissivityandusingpre-launchcalibrationconstantslistedinTable11.5.Theconversionformulais:
T
Effectiveat-satellitetemperatureinKelvin
K2
Calibrationconstant2fromTable11.5
K1
Calibrationconstant1fromTable11.5
L
Spectralradianceinwatts/(metersquared*ster*?
Table11.5
ETM+andTMThermalBandCalibrationConstants
Constant1-K1
Constant2-K2
Kelvin
Landsat7
666.09
1282.71
Landsat5
607.76
1260.56