a mono-window algorithm for retrieving land surface

int j remote sensing 2001 vol 22 no 18 3719ndash3746

A mono-window algorithm for retrieving land surface temperaturefrom Landsat TM data and its application to the Israel-Egypt borderregion

Z QIN A KARNIELIdagger

The Remote Sensing Laboratory Department of Environmental PhysicsJ Blaustein Institute for Desert Research Ben Gurion University of the NegevSede Boker Campus 84990 Israel

and P BERLINER

The Wyler Laboratory for Arid Land Conservation and DevelopmentDepartment of Dryland Agriculture J Blaustein Institute for Desert ResearchBen Gurion University of the Negev Sede Boker Campus 84990 Israel

(Received 28 September 1999 in nal form 9 June 2000)

Abstract Remote sensing of land surface temperature (LST) from the thermalband data of Landsat Thematic Mapper (TM) still remains unused in comparisonwith the extensive studies of its visible and near-infrared (NIR) bands for variousapplications The brightness temperature can be computed from the digitalnumber (DN) of TM6 data using the equation provided by the NationalAeronautics and Space Administration (NASA) However a proper algorithmfor retrieving LST from the only one thermal band of the sensor still remainsunavailable due to many diYculties in the atmospheric correction Based onthermal radiance transfer equation an attempt has been made in the paper todevelop a mono-window algorithm for retrieving LST from Landsat TM6 dataThree parameters are required for the algorithm emissivity transmittance andeVective mean atmospheric temperature Method about determination of atmo-spheric transmittance is given in the paper through the simulation of atmosphericconditions with LOWTRAN 7 program A practicable approach of estimatingeVective mean atmospheric temperature from local meteorological observation isalso proposed in the paper when the in situ atmospheric pro le data is unavailableat the satellite pass which is generally the case in the real world especially forthe images in the past Sensitivity analysis of the algorithm indicates that thepossible error of ground emissivity which is diYcult to estimate has relativelyinsigni cant impact on the probable LST estimation error dT which is sensibleto the possible error of transmittance dt6 and mean atmospheric temperaturedT

a Validation of the simulated data for various situations of seven typical

atmospheres indicates that the algorithm is able to provide an accurate LSTretrieval from TM6 data The LST diVerence between the retrieved and thesimulated ones is less than 04degC for most situations Application of the algorithmto the sand dunes across the IsraelndashEgypt border results in a reasonable LST

Current address of Z Qin is SMC the Spatial Modelling Center Box 839 S-981 28Kiruna Sweden e-mail qinzhihaosmckirunase

daggere-mail karnielibgumailbguacil

International Journal of Remote SensingISSN 0143-1161 printISSN 1366-5901 online copy 2001 Taylor amp Francis Ltd

httpwwwtandfcoukjournalsDOI 10108001431160010006971

Z Qin et al3720

estimation of the region Based on this LST estimation spatial variation ofthe interesting thermal phenomenon has been analysed for comparison of LSTdiVerence across the border The result shows that the Israeli side does havesigni cantly higher surface temperature in spite of its denser vegetation coverthan the Egyptian side where bare sand is prevalent

1 IntroductionThe Landsat Thematic Mapper (TM) images have been extensively studied for

various purposes (Kaneko and Hino 1996 Lo 1997 Caselles et al 1998) Searchingwith the keyword Landsat TM on the world-widely used CD-ROM scienti c abstractdatabase GEOBASE for the period 1980ndash1999 pops out 1043 papers written inEnglish Except the six bands in visible and near- infrared (NIR) wavelengths theremote sensor also has a thermal band (TM6) operating in the wavelength range of1045ndash1250mm with a nominal ground resolution of 120mtimes120 m This spatialresolution of Landsat TM6 is high enough for analysing the detailed spatial patternsof thermal variation on the Earthrsquos surface However when searching on theGEOBASE with the restricted keyword temperature only 73 papers were foundDetailed examination of these papers reveals that only 35 of them relating to thesurface temperature or thermal band data of Landsat TM This implies that thestudy of Landsat TM thermal band for surface temperature and its application stillremains as an ignored area This is especially true when referring to land surfacetemperature (LST) Due to its high spatial resolution Landsat TM6 has considerablepotential for many applications relating to LST Some studies relating to the thermalband of Landsat TM only use the brightness temperature at the satellite level(Mansor et al 1994 Saraf et al 1995 Zhang et al 1997) or just simply use thedigital number (DN) value for their applications (Ritchie et al 1990 Oppenheimer1997) The actual use of LST retrieved from Landsat TM6 is few (Hurtado et al1996 Sospedra et al 1998) In addition to its intrinsic weaknesses (no on-boardcalibration low repeat frequency and so on) the lack of a proper and easily-usedalgorithm for retrieval of LST from the only one thermal band of Landsat TM dataprobably is also the main reason leading to the few application

Up to present the studies of Landsat TM thermal data mainly concentrate onthe level of directly applying brightness temperature or DN value to the issues inthe real world and on the study of the sealake surface temperature corrected withatmospheric model using radiosonde data Zhang et al (1997) Saraf et al (1995)and Mansor et al (1994) demonstrated that the radiant temperature converting fromLandsat TM thermal data is capable of application for detection of subsurface coal res Sugita and Brutsaert (1993) compared the measured LST in the eld with thetemperature from satellite including Landsat TM The measured sea surface temper-ature is found to be about 78degC higher than the brightness temperature for LandsatTM6 around the outlet of a nuclear power plant (Liu and Kuo 1994) Haakstadet al (1994) demonstrated the importance of Landsat TM6 data in sea temperaturestudy for identifying the surface current patterns Relationship between water qualityindicators and Landsat TM digital data including TM6 DN value has been analysedin the study of Braga et al (1993) about water quality assessment at GuanabaraBay of Brazil Oppenheimer (1997) used the relationship between the measured lakesurface temperature and Landsat TM6 DN value to map the thermal variation ofvolcano lakes Correlation of lake suspended sediments with digital data of LandsatMSS and TM was analysed in Ritchie et al (1990) Based on the surface temperature

A mono-window algorithm for L andsat T M6 3721

derived from Landsat TM thermal data Moran et al (1989) estimated the latentheat and net radiant ux density and compared with the ground estimate based onBowen ratio measurement over mature elds of cotton wheat and alfalfa TheLandsat TM6 data has been used in several studies to investigate the thermalproperties of volcanoes (Reddy et al 1990 Andres and Rose 1995 Kaneko 1998)

Provided that ground emissivity is known (the determination of emissivity is verycomplicated and there is a great volume of literature on it) the retrieval of LSTfrom Landsat TM6 is mainly through the method of atmospheric correction Theprinciple of the correction is to subtract the upward atmospheric thermal radianceand the re ected atmospheric radiance from the observed radiance at satellite levelso that the brightness temperature at ground level can be directly computed Theatmospheric thermal radiance can be simulated using such atmospheric simulationprograms as LOWTRAN MODTRAN or 6S when in situ atmospheric pro le isavailable at the satellite pass Usually this is not the case for many applicationsThus an alternative is to use the available radiosonde data closed to the satellitepass or with similar atmospheric conditions for this atmospheric simulation (Hurtadoet al 1996) In many cases even the radiosonde data is also not available due todiYculties for the measuring This unavailability of in situ atmospheric pro le dataprevents the popular application of LST retrieval from Landsat TM6 for manystudies Alternately the standard atmospheric pro les provided in the atmosphericsimulation programs were used to simulate the atmospheric radiance for retrieval ofsurface temperature from the Landsat TM thermal data

An attempt was made by Hurtado et al (1996) to compare the two atmosphericcorrection methods for Landsat TM thermal band Using surface energy balanceequation and standard meteorological parameters they proposed a method of atmo-spheric correction for Landsat TM thermal data Alternately the required parametersfor atmospheric correction were calculated from a radiative transfer model using theatmospheric pro les obtained from local temporarily coincident radiosondes Thelatter atmospheric correction method has been on the right way of developing analgorithm for LST retrieval from Landsat TM6 data but it involves several para-meters that are not easy to estimate for most cases This is the only study publishedto attempt an algorithm development for LST retrieval from one thermal band data

Based on the thermal radiance transfer equation the current study attempts todevelop an algorithm for retrieving LST from Landsat TM6 data Because thisalgorithm is suitable for LST retrieval from only one thermal band data it has beentermed as the mono-window algorithm in order to distinguish from split windowalgorithm for two thermal channels Compared to the several atmospheric parametersrequired in the second correction method of Hurtado et al (1996) the mono-windowalgorithm only requires two atmospheric parameters (transmittance and mean atmo-spheric temperature) for LST retrieval Moreover the detailed estimation of thesetwo critical atmospheric parameters is also addressed for practical purpose of apply-ing the algorithm Then we perform the sensitivity analysis of the algorithm for thecritical parameters and validate it to the simulated data for various situations ofseven typical atmospheres Finally we try to present an example of its applicationto the sand dunes across the IsraelndashEgypt political border for examination of theLST diVerence on both sides of the border region

2 Computing brightness temperature of Landsat TM6 dataThe development of the mono-window algorithm for LST retrieval from the

thermal band data of Landsat TM is with premise that the brightness temperature

Z Qin et al3722

of the thermal band at the satellite level can be computed from the data Generallythe grey level of Landsat TM data is given as digital number (DN) ranging from 0to 255 Thus the computation of brightness temperature from TM6 data includesthe estimation of radiance from its DN value and the conversion of the radianceinto brightness temperature

The following equation developed by the National Aeronautics and SpaceAdministration (NASA) (Markham and Barker 1986) is generally used to computethe spectral radiance from DN value of TM data

L (l)=L min(l)+(L max(l) shy L min(l) )Qdn Qmax (1)

where L (l) is the spectral radiance received by the sensor (mW cm Otilde 2 sr Otilde 1 mm Otilde 1 )Q

maxis the maximum DN value with Q

max=255 and Q

dnis the grey level for the

analysed pixel of TM image Lmin(l)

and Lmax(l)

are the minimum and maximumdetected spectral radiance for Qdn=0 and Qdn=255 respectively For TM6 ofLandsat 5 with central wavelength of 11475mm it has been set that L min(l)=01238for Qdn=0 and L max(l)=156 mW cm Otilde 2 sr Otilde 1 mm Otilde 1 for Qdn=255 (Schneider andMauser 1996) Thus the above equation can be simpli ed into the following form

L (l)=01238+0005632156Qdn (2)

Once the spectral radiance L(l)

is computed the brightness temperature at thesatellite level can be directly calculated by either inverting Planckrsquos radiance functionfor temperature (Sospedra et al 1998) or using the following approximation formula(Schott and Volchok 1985 Wukelic et al 1989 Goetz et al 1995)

T 6=K2ln (1+K1L (l)) (3)

where T 6 is the eVective at-satellite brightness temperature of TM6 in K K1 and K2are pre-launch calibration constants For Landsat 5 which we will use in the studyK1=60776mW cm Otilde 2 sr Otilde 1 mm Otilde 1 and K2=126056 degK respectively (Schneiderand Mauser 1996) Though this is the most popular approach to compute brightnesstemperature from the observed thermal radiance other alternatives such as in Singh(1988) and Sospedra et al (1998) have also been proposed

Landsat TM observed the thermal radiance emitted by the ground at an altitudeof about 705km When the radiance travels through the atmosphere it will beattenuated by the absorption of the atmosphere in the wavelength Moreover theatmosphere also has ability of emitting thermal radiance The upwelling atmosphericemittance will combine with the ground thermal radiance to reach the sensor inspace Besides the ground surface also has ability to re ect the downward atmo-spheric emittance These atmospheric impacts in the observed thermal radiancehave to be considered when applying Landsat TM6 data for surface temperatureestimation and its consequent applications

3 Correction of brightness temperature for LST retrievalIt has been well known that the impacts of the atmosphere and the emitted

ground are unavoidably involved in the sensor-observed radiance Thus correctionis necessary for retrieving true LST from Landsat TM6 data (Hurtado et al 1996)The correction is based on the radiance transfer equation which states that thesensor-observed radiance is impacted by the atmosphere and the emitted ground Inaccordance with blackbody theory the thermal emittance from an object can be


expressed as Planckrsquos radiance function

Bl(T )=

C1l5 (eC2lT shy 1)

(4)

where Bl(T ) is the spectral radiance of the blackbody generally measured in W m Otilde 2

sr Otilde 1 mm Otilde 1 l is wavelength in metre (1 m=106 mm) C1

and C2

are the spectralconstants with C

1=119104356times10Otilde 16 W m2 and C

2=14387685times104mm degK T

is temperature in degK The change of Planckrsquos radiance with temperature is shownin gure 1 for TM6

Blackbody is only a theoretical concept Most natural surfaces are in fact notblackbodies Thus emissivity has to be considered for constructing the radiancetransfer equation Moreover while transferring from the emitted ground to theremote sensor the ground emittance is attenuated by the atmospheric absorptionOn the other hand the atmosphere also contributes the emittance that reaches thesensor either directly or indirectly (re ected by the surface) Considering all thesecomponents and eVects the sensor-observed radiance for Landsat TM6 can beexpressed as

B6(T

6)=t

6[e

6B

6(T

s)+ (1 shy e

6)I3

6]+I(

6(5)

where Ts

is land surface temperature and T 6 is brightness temperature of TM6 t6is atmospheric transmittance and e6 is ground emissivity B6 (T 6 ) is radiance receivedby the sensor B6 (T

s) is ground radiance I36 and I(6 are the down welling and

upwelling atmospheric radiances respectivelyThe upwelling atmospheric radiance I(

6is usually computed (Franca and

Cracknell 1994 Cracknell 1997) as

I(6=P Z

0B6 (T

z)ccedil t6 (z Z )

ccedil zdz (6)

where Tz

is atmospheric temperature at altitude z Z is altitude of the sensor t6 (z Z )represents the upwelling atmospheric transmittance from altitude z to the sensorheight Z Following McMillin (1975) Prata (1993) and Coll et al (1994) we employ

Temperature (iexclC)

Figure 1 Change of Planckrsquos radiance B6 (T ) (a) and the parameter L 6 (b) with temperaturefor Landsat TM6

Z Qin et al3724

the mean value theorem to express the upwelling atmospheric radiance as

B6 (Ta)=

1

1 shy t6 PZ

0B6 (T

z)ccedil t

6(z Z )

ccedil zdz (7)

where Ta

is the eVective mean atmospheric temperature and B6 (Ta) represents the

eVective mean atmospheric radiance with Ta

for TM6 Thus we get

I(6=(1 shy t

6)B

6(T

a) (8)

The down-welling atmospheric radiance is generally viewed as from a hemi-spherical direction hence can be computed (Franca and Cracknell 1994) as

I36=2 P p2

0P 0

2

B6(T

z)ccedil t frac34

6 (h ecirc z 0)

ccedil zcosh ecirc sinh ecirc dz dhecirc (9)

where h ecirc is the down-welling direction of atmospheric radiance and t frac346(h ecirc z 0) repres-

ents the down-welling atmospheric transmittance from altitude z to the groundsurface According to Franca and Cracknell (1994) it is rational to assume thatdtfrac34

6(h ecirc z 0)=dt6 (z Z ) for the thin layers of the whole atmosphere when the sky isclear Based on this assumption application of mean value theorem to equation (9)gives

I36=2 P p2

0(1 shy t6 )B6 (T 3

a) cosh ecirc sinh ecirc dhecirc (10)

where T 3a

is the downward eVective mean atmospheric temperature The integrationterm of this equation can be solved as

2 P p2

0cosh ecirc sinh ecirc dhecirc =(sinh ecirc )2 |p20 =1 (11)

Thus the downward atmospheric radiance cab be estimated as

I36=(1 shy t

6) B

6(T 3

a) (12)

Substitution into equation (5 ) gives

B6(T

6)=e

6t6B

6(T

s)+t

6(1 shy e

6) (1 shy t

6)B

6(T 3

a)+(1 shy t

6) B

6(T

a) (13)

In order to solve this equation for LST we need to analyse the eVect of B6 (T 3a)

on the observed LST by TM6 Due to the vertical diVerence of atmosphere theupward atmospheric radiance is generally greater than the downward oneConsequently B

6(T

a) is greater than B

6(T 3

a) or T

agtT 3

a Under the clear sky the

diVerence between Ta

and T 3a

is usually within 5degC ie |Tashy T 3

a|lt5degC

For convenience of analysis we denote D ecirc =t6 (1 shy e6 ) (1 shy t6 ) Since the emissivitye6 is generally 096ndash098 for most natural surfaces the value of D ecirc is very smallmainly depended on t6 Provided t6=07 and e6=096 we get D ecirc =00084 The verysmall value of D ecirc makes the approximate of B6 (T 3

a) with B6(T

a) possible and feasible

for the derivation of an algorithm from the above equationBefore we go on our derivation we need to simulate the eVect of approximating

B6 (T 3a) with B6 (T

a) on the change of T

sin equation (13) Since B6 (T

a)gtB6(T 3

a) the

approximation of B6(T 3a) with B6 (T

a) would lead to the underestimate of both B6 (T

s)

and B6(Ta) in equation (13) for the xed B6 (T 6 ) Consequently it will lead to the

underestimate of Ts The magnitude of the underestimate of B

6(T

s) and B

6(T

a) in


equation (13) depends on their coeYcients in the equation ie e6 t6 for B6(Ts) and

(1 shy t6 )[1+t6 (1 shy e6 )] for B6 (Ta) We consider three cases of |T

ashy T 3

a| and two cases

of e6 and t6 for the simulation which gives the results shown in table 1 Theunderestimates of T

sfor all cases are quite small For |T

ashy T 3

a|=5degC and t

6=08

the approximation of B6 (T 3a) with B6(T

a) can only lead to the underestimate of T

s00255degC at T

s=20degC and 00205degC at T

s=50degC The underestimates of T

sare even

smaller for t6=07 (table 1) Therefore we can conclude that the approximation ofB6 (T 3

a) with B6 (T

a) will have an insigni cant eVect on the estimate of T

sfrom the

above equation With this approximation the observed radiance of Landsat TM6can be expressed as

B6(T

6)=e

6t6B

6(T

s)+(1 shy t

6)[1+t

6(1 shy e

6)]B

6(T

a) (14)

which enables us to solve Ts

for LST retrievalIn order to solve T

sfrom equation (14) we need to linearize Planckrsquos radiance

function Because the change of Planckrsquos radiance with temperature is very close tolinearity in a narrow temperature range (say lt15degC) for a speci c wavelength( gure 1) the linearization of Planckrsquos function can be done by Taylorrsquos expansionkeeping the rst two terms

B6(T

j)=B

6(T )+(T

jshy T )ccedil B

6(T ) ccedil T =(L

6+T

jshy T )ccedil B

6(T ) ccedil T (15)

where Tj

refers to the brightness temperatures ( j=6) land surface temperature( j=s) and mean atmospheric temperature ( j=a) The parameter L

6is de ned as

L6=B

6(T )[ ccedil B

6(T ) ccedil T ] (16)

in which L6

has the dimension of temperature in degK The physical meaning ofTaylorrsquos expansion in this case is to expresses the radiance of B6 (T

j) in terms of the

radiance B6 (T ) with a xed temperature T Considering the possible TsgtT 6gtT

afor most cases we de ned T in Taylorrsquos expansion as T

6 Thus to express the

Planckrsquos radiance of Ts

and Ta

for T 6 we have

B6 (Ts)=(L 6+T

sshy T 6 )ccedil B6 (T 6 ) ccedil T (17a)

B6 (Ta)=(L 6+T

ashy T 6 )ccedil B6 (T 6 ) ccedil T (17b)

B6(T

6)=(L

6+T

6shy T

6)ccedil B

6(T

6) ccedil T )=L

6ccedil B

6(T

6) ccedil T (17c)

Substituting into equation (15) and eliminating the term ccedil B6(T 6 ) ccedil T we obtain

L 6=e6t6 (L 6+Tsshy T 6 )+(1 shy t6 )[1+(1 shy e6 )t6](L 6+T

ashy T 6 ) (18)

For simpli cation we de ne

C6=e6 t6 (19)

D6=(1 shy t

6)[1+(1 shy e

6) t

6] (20)

Thus we have

L 6=C6 (L 6+Tsshy T 6 )+D6 (L 6+T

ashy T 6 ) (21)

For Landsat TM6 we nd that L 6 has a relation with temperature close to linearity( gure 1) Thus this property enables us to use the following equation to approximateit for the derivation

L 6=a6+b6T 6 (22)

where a6

and b6

are the coeYcients For the possible temperature range 0ndash70degC

Z Qin et al3726

(273ndash343 degK) in most cases the coeYcients of equation (22) are approximated asa6=shy 67355351 and b6=0458606 with relative estimate error REE=032 cor-relation R2=09994 T-test T test=1625 and F-test Ftest=1083286 Both T-test andF-test are statistically signi cant at a=0001 indicating that the approximation isvery successful For the smaller temperature ranges the relative estimate error (REE)can be even reduced to below 013 (table 2) All the equations in table 2 arestatistically signi cant at a=0001 Therefore with this relation we have

a6+b6T 6=C6(a6+b6T 6+Tsshy T 6 )+D6 (a6+b6T 6+T

ashy T 6 ) (23)

Solving for Ts we obtain the algorithm for LST retrieval from Landsat TM6

data as follows

Ts=[a6 (1 shy C6 shy D6 )+(b6 (1 shy C6 shy D6 )+C6+D6 )T 6 shy D6T a

]C6 (24)

Provided that ground emissivity is known the computation of LST from TM6data is depended on the determination of atmospheric transmittance t

6and eVective

mean atmospheric temperature Ta Because this algorithm only requires one thermal

band for LST estimation we term it as a mono-window algorithm in order todistinguish from the split window algorithm used for two thermal channels

4 Determination of eVective mean atmospheric temperatureThough it is diYcult to directly measure the in situ eVective mean atmospheric

temperature at the satellite pass there are several ways to have its estimation forthe LST retrieval Here we intend to follow the method of Sobrino et al (1991) forthe estimation which relates the determination of T

awith water vapour distribution

in the atmospheric pro le According to Sobrino et al (1991) the eVective meanatmospheric temperature T

acan be approximated as

Ta=

1

w P w

0T

zdw(z Z ) (25)

Table 1 Underestimate of Ts

by approximating B6 (T 3a) with B6(T

a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205

Table 2 CoeYcients of parameter L 6 for diVerent temperature ranges

Range degC a6 b6 REE R2 T test Ftest

0ndash30 shy 603263 043436 00833 09998 1867 150 147810ndash40 shy 631885 044411 00973 09997 1516 100 984820ndash50 shy 679542 045987 01225 09995 1175 60 141830ndash60 shy 719992 047271 00621 09999 2239 218 8198


where w is total water vapour content in the atmosphere from ground to the sensoraltitude Z T

zis atmospheric temperature at altitude z w(z Z ) represents water

vapour content between z and ZThus the determination of T

arequires the in situ distribution of atmospheric

temperature and water vapour content at each layer of the pro le This is generallyunavailable for many studies such as our case Atmospheric simulation modelLOWTRAN 7 provides several standard atmospheres containing the standard distri-butions of many atmospheric quantities (temperature pressure H2O CO2 CO etc) which was computed from a number of real atmospheric pro le data Therefore thestandard atmospheres represent the general case of atmospheric conditions (clearsky and without great turbulence) in the corresponding regions (Kneizys et al 1988)These standard atmospheric distributions have been extensively used for atmosphericsimulation to estimate the required atmospheric parameters in remote sensing whenin situ atmospheric pro le data is not available (Sobrino et al 1991) Here weattempt to demonstrate that these standard pro les can also be used to combinewith local meteorological data for T

aestimation

In order to determine the eVective mean atmospheric Ta we examine the distribu-

tions of water vapour content and atmospheric temperature in the standard atmo-spheres provided by LOWTRAN 7 model Figure 2 shows the distribution of watervapour content and its ratio to the total against the altitude Four standard atmo-spheres are considered USA 1976 tropical mid-latitude summer and mid-latitude

Water vapor (g cm

shy2)

(a)

(b)

Figure 2 Distribution of water vapour content (a) and its ratio to the total (b) against thealtitude of the pro le

Z Qin et al3728

winter It is the fact that most atmospheric water vapour is concentrated in the loweratmosphere (Sobrino et al 1991) especially in the rst 3 km of the pro le ( gure 2(a))Though total water vapour content is diVerent (144gcm Otilde 2 for USA 1976 433g cm Otilde 2for tropical ) the distributions of the ratio of water vapour content to the total inthe atmospheric pro les are very similar ( gure 2(b)) The rst layer (0ndash1 km) containsabout 40206 of the total water vapour content in USA 1976 about 4335 inmid-latitude summer pro le Details of the distributions are given in table 3 for thepro les Therefore using the standard distributions of the atmospheres or just theiraverage for simpli cation we can develop a simple method to generate the requireddistribution of the water vapour content at each layer of the atmosphere from themeasurement of total water vapour content in the atmosphere as follows

w(z)=wRw(z) (26)

where w(z) is water vapour content at altitude z Rw(z) is the ratio of water vapour

content to the total in the standard atmospheric pro les given in table 3 As indicatedby gure 2(b) and table 3 the water vapour ratio at the upper layers (gt10 km)is negligibly small due to negligibly small water vapour content at the layers( gure 2(a)) Thus at the sensor altitude we can rationally assume w(Z )=0

The nite term of equation (25) at altitude z can be approximated as watervapour content of the layer ie dw(z Z )=w(z) With this approximation equation(25) can be transformed as

Ta=

1

waeligm

z= 0

Tzw(z) (27)

where m is number of the atmospheric layers under consideration Because w(z)in the upper atmospheric layers is very small the eVective mean atmospherictemperature is mainly determined by T

zin the lower atmospheric layers

It is well known that atmospheric temperature decreases with altitude in the

Table 3 Ratio of water vapour content to the total in diVerent atmospheric pro les

Altitude USA Mid-latitude Mid-latitude Average(km) 1976 Tropical summer winter R

w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004


lower atmosphere ie troposphere Figure 3 perfectly depicts the change of atmo-

spheric temperature and its decrease with altitude for the four atmospheres Even

though the atmospheric temperature of the four pro les diVers greatly at the ground

surface it seems that it is very close to each other at about 13 km height ( gure 3(a))

Atmospheric temperature at this altitude varies from 2167 degK in USA 1976

through 217 degK in tropical to 2182 degK in mid-latitude winter pro le with an

average of 217 degK With this property we can compute the decrease rate of

atmospheric temperature for the four pro les

Rt(z)=(T

0shy T

z)(T

0shy 217) (28)

where Rt(z) is decrease rate of atmospheric temperature at altitude z and T 0 is

atmospheric temperature at the ground Figure 3(b) plots the decrease rate for the

four standard atmospheric pro les Again gure 3(b) indicates that the distributions

of the decrease rate are similar with each other This small variation of the decrease

rate in the four diVerent pro les provides the possibility of developing a simple

method to generate the distribution of atmospheric temperature Tz

for each layer of

the atmosphere Using the distributions of the decrease rate in the standard atmo-

spheres or just their average for simpli cation we propose the following formula to

(a)

(b)

Figure 3 Distribution of atmospheric temperature (a) and its attenuation rate (b) againstthe altitude of the pro le

Z Qin et al3730

calculate the distribution of atmospheric temperature from near-surface air tem-perature for each layer of the atmosphere under consideration in correspondentclimate zones

Tz=T

0shy R

t(z) (T

0shy 217) (29)

where T 0 is air temperature of the ground (at about 2 m height) Rt(z) is the standard

atmospheric temperature decrease rate at z given in table 4 for correspondentatmospheres

Therefore when T0

is given the atmospheric temperature distribution at eachlayer can be directly computed from equation (29) Generally speaking T

0is available

in local meteorological observation data Therefore when the local in situ atmo-spheric pro les of water vapour and atmospheric temperature are not available atthe satellite pass the following procedure can be used to determine T

afor LST

retrieval from Landsat TM6 data

(1) Use available atmospheric pro les of the study region to compute Rw(z) and

Rt(z) for water vapour content and atmospheric temperature at each layer and use

the average of the ratio and the rates to represent the general atmospheric distributionof the region If the pro les are also unavailable (such as our case) select one of thestandard atmospheric distributions in tables 3 and 4 as the distribution accordingto the latitude and climate type of the region

(2) Use equation (26) and the total atmospheric water vapour content to t intothe distribution of water vapour ratio for computation of water vapour content ateach layer of the pro le If total atmospheric water vapour content is not availableit can be approximately estimated as w=w(0)R

w(0) in which w(0) is water vapour

content near the surface (at about 2 m height) Usually we can obtain w(0) fromlocal meteorological data

(3) Use equation (29) and the known local air temperature near the surface asT 0 to t into the distribution for computation of atmospheric temperature at eachlayer

Table 4 Decrease rate of atmospheric temperature in diVerent pro les


t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630


(4) Use equation (28) to compute the eVective mean atmospheric temperatureT

athrough summation of atmospheric temperature multiplied with water vapour

content at each layer for the whole pro le

When using the standard atmospheric distribution of water vapour content andtemperature given in tables 3 and 4 one should remember that it involves the basicassumption that the sky is clear and there is not great vertical turbulence in theatmosphere (Kneizys et al 1988) This assumption is very important because turbu-lence in the atmosphere may produce a great change in the distribution of watervapour content and atmospheric temperature at each layer which consequentlymakes the estimation of T

aobviously biased

Actually with the above standard distributions of water vapour content andatmospheric temperature we can further derive a simpler formula for approximationof T

a From equation (27) we obtain

Ta=ST

zw(z)w=ST

zR

w(z) (30)

This formula implies that Ta

is dependent on the distributions of both water vapourrate and air temperature in the atmosphere Replacing T

zwith formula (29) we

obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)

With the standard distributions given in tables 3 and 4 we derive the simplelinear relations for approximation of T

afrom T 0 for the four standard atmospheres

as follows

For USA 1976 Ta=259396+088045T 0 (32a)

For tropical Ta=179769+091715T 0 (32b)

For mid-latitude summer Ta=160110+092621T 0 (32c)

For mid-latitude winter Ta=192704+091118T

0(32d)

where both Ta

and T0

are with dimension in K These formulae imply that underthe standard atmospheric distributions (clear sky and without great turbulence) theeVective mean atmospheric temperature T

ais a linear function of near-surface air

temperature T 0 This is because the impacts of water vapour distribution andatmospheric temperature distribution on T

aare assumed to be constant for the

standard distributionsOnce T

ahas been calculated the LST can be retrieved using the mono-window

algorithm described in equation (24) when the atmospheric transmittance is given

5 Determination of atmospheric transmittanceProvided e

6available and T

adetermined atmospheric transmittance now

becomes the only parameter unknown for the algorithm Generally speaking thedetermination of atmospheric transmittance for Landsat TM6 is undertaken throughthe simulation of atmospheric conditions using such atmospheric simulationprograms as LOWTRAN MODTRAN or 6S Due to its extreme importance inin uencing the variation of atmospheric transmittance water vapour content has

Z Qin et al3732

been extensively used as the determinant in estimation of atmospheric transmittance(Sobrino et al 1991 Coll et al 1994 Cracknell 1997)

In the study LOWTRAN 7 program is used to simulate the relation of watervapour content to atmospheric transmittance The general water vapour range of04ndash40 g cm Otilde 2 is considered for the simulation under two pro les low and hightemperature pro les The atmospheric temperature near the surface for the hightemperature pro le is de ned as 35degC and for the low one 18degC The swath ofLandsat TM is about 185km which results in a viewing zenith angle of about 6degfor its edge pixels Thus we consider an average zenith angle of 3deg for the simulationof atmospheric impact on transmittance Simulation results are shown in gure 4from which we can see that TM6 transmittance decreases steadily with water vapourcontent increase Atmospheric transmittance of TM6 is high up to above 09 forwater vapour content less than 08gcm Otilde 2 The transmittance decreases to about 08at 20g cm Otilde 2 and 07 at 25 g cm Otilde 2 It may be lower than 05 for water vapour contentgreater than 40gcm Otilde 2 Another feature shown in gure 4 is the transmittancediVerence between the two pro les The diVerence is very small when water vapourcontent is low However it increases rapidly with the water vapour content Hightemperature pro le has higher transmittance than low temperature pro le for thesame water vapour content The transmittance diVerence between high and lowtemperature pro les is about 0007 at water vapour content 1 g cm Otilde 2 The diVerenceincreases to 0031 at 2 g cm Otilde 2 00558 at 3 g cm Otilde 2 and 00799 at 4 g cm Otilde 2 The changeof transmittance with water vapour is not linear for the whole range 04ndash4 g cm Otilde 2but for a small segment the relationship is close to linearity This characteristicprovides the possibility of establishing some simple linear equations to estimatetransmittance from water content for Landsat TM6 operating in 105ndash125mm AneVort of establishing the estimation equations is given in table 4 for the range04ndash3 g cm Otilde 2 which is the general case

The estimation equations listed in table 5 have high squared correlation and lowstandard error which means that the estimation of transmittance with water vapourcontent by these equations will have a high accuracy For a possible measurement

error of 02 g cm Otilde 2 (this is the general accuracy of water vapour content estimation

Water vapor (g cmshy 2)

Figure 4 Change of atmospheric transmittancewith water vapour content for Landsat TM6


Table 5 Estimation of atmospheric transmittance for Landsat TM channel 6

Water vapour Transmittance Squared StandardPro les (w) (g cmOtilde 2 ) estimation equation correlation R2 error

High air 04ndash16 t6=0974290shy 008007w 099611 0002368

temperature16ndash30 t6

=1031412shy 011536w 099827 0002539Low airtemperature 04ndash16 t6

=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375

from sunphotometer measurements) the possible maximal estimation error of atmo-spheric transmittance for Landsat TM6 is lt0029 An accurate estimation of trans-mittance as indicated in following section is very important in retrieval of LSTfrom Landsat TM6 data

6 Sensitivity analysis of the mono-window algorithmThe mono-window algorithm for Landsat TM requires three critical parameters

to estimate LST ground emissivity atmospheric transmittance and eVective meanatmospheric temperature Due to many diYculties such as unavailability of precisepro le data about the atmosphere and the complexity of the emitted ground surfacein terms of material composition the determination of these parameters will unavoid-ably involve some errors In order to analyse the impact of the possible estimationerror of these critical parameters on the possible LST estimation error sensitivityanalysis is necessary For convenience the following formula is used to express thepossible LST estimation error

dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs

is LST estimation error x is the variable to which the sensitivity analysisorients (e6 t6 and T

a) dx is possible error of the variable x T

s(x+dx) and T

s(x)

are the LST simulated by our algorithm in equation (24) for x+dx and x respectivelySensitivity analysis is performed under several conditions First of all natural

surfaces generally have an emissivity of about 095ndash098 in the thermal wavelength10ndash13 mm (Price 1984 Sutherland 1986 Takashima and Masuda 1987) We assumean emissivity of 097 for the sensitivity analysis Secondly a clear sky is very importantand we assumed a transmittance of 080 for the analysis The overpass of Landsat 5in many regions was at about 930ndash1000 am local time when the atmospherictemperature is generally not very high Thus the eVective mean temperature isarbitrarily given as 15degC The air temperature near the surface corresponding to thismean temperature is about 25degC for water vapour content of about 2 g cm Otilde 2 Underthese conditions we perform the sensitivity analysis of the mono-window algor-ithm for estimation errors of ground emissivity transmittance and eVective meanatmospheric temperature

Figure 5 illustrates the probable LST estimation error due to the possible groundemissivity error Several important features can be seen in gure 5(a) which plotsthe LST estimation error against brightness temperature of TM6 for the four possibleemissivity errors LST estimation error dT decreases with brightness temperatureincrease when it is below 13degC which is a transition point From this point dTincreases rapidly with temperature in all cases Linear correlation between LST error

Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)

Figure 5 Probable LST estimation error due to the possible emissivity error (a) LST erroragainst brightness temperature and (b) average LST error against emissivity error

and temperature is also very clear in all the cases According to these relationshipswe can expect that dT is less than 02degC for de6=001 and 04degC for de6=002 intemperature range 0ndash55degC ( gure 5(a)) This LST estimation error corresponding toemissivity error is relatively small Generally the estimation of ground emissivity inthe range of 10ndash13 mm can reach an accuracy of less than 002 Provided thisassumption the mono-window algorithm is able to produce a quite accurate LSTestimation from Landsat TM6 data in spite of some possible emissivity errors

Considered the most possible temperature in many regions an average dT intemperature range of 10ndash55degC has been plotted against the possible de6 ( gure 5(b))Four ground emissivity cases are plotted in gure 5(b) which indicates that the LSTerror has very small change with the ground emissivity This means that dT is onlysensible to emissivity error but not to the level of ground emissivity itself For de6=002 dT is 024degC at e6=092 and 022degC at e6=098 with a negligible diVerence ofabout 002degC ( gure 5(b)) This little change of dT with e6 supports our aboveconclusion about the applicability of the algorithm in many cases

In contrast with the insensible response to emissivity error the algorithm is quitesensible with transmittance error Figure 6 shows the probable LST estimation errordT due to possible transmittance error dt6 Again dT is 0 at brightness temperaturelevel of about 13degC for all cases of transmittance error ( gure 6(a)) When brightnesstemperature is below this level dT is less than 025degC for dt6 002 However dTincreases rapidly with temperature and transmittance For dt

6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)

Figure 6 Probable LST estimation due to the possible atmospheric transmittance error(a) LST error against brightness temperature and (b) average LST error againsttransmittance error

0577degC at temperature T =30degC and it increases to abut 1058degC at T =45degC and1378degC at T =55degC ( gure 6(a)) For dt6=0025 dT may reach above 3degC atTgt45degC Therefore an accurate estimation of atmospheric transmittance is muchmore important in using the algorithm for LST retrieval than the emissivityestimation

Moreover dT is also very sensible to the change of atmospheric transmittance( gure 6(b)) Average LST error in the temperature range of 10ndash55degC is plottedagainst transmittance error for several transmittance levels When transmittance ishigh the increase of average dT against dt

6is much slower Speci cally average dT

is about 074ndash096degC for dt6=002 when t

6is within 07ndash08 For the same dt

6 the

average dT increases to 129ndash184degC when t6 decreases to 05ndash06 Generally speakingthe accuracy of atmospheric water vapour measurement is about 02 g cm Otilde 2 Consequently it produces an error of 0016ndash028 in t6 estimation (table 4) Thereforewe can expect that the algorithm is able to provide a LST estimation with anerrorlt1degC for t

6gt07 This accuracy is generally acceptable for most study purposes

using Landsat TM6 data (Kerr et al 1992)Sensitivity analysis of the algorithm to eVective mean atmospheric temperature

Ta

indicates that dT does not change with brightness temperature and the meanatmospheric temperature itself but does change linearly with the possible error ofthe mean temperature This can be understood through the derivation of the LST

Z Qin et al3736

estimation error dT according to equation (33) For a small error of Ta we can

derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |

=|[a6 (1 shy C6shy D6 )+(b6 (1 shy C6 shy D6 )+C6+D6 )T 6 shy D6 (Ta+dT

a)]C6

shy [a6 (1 shy C6shy D6 )+(b6 (1 shy C6 shy D6 )+C6+D6 )T 6shy D6T a]C6 |

=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)

For a given emissivity and transmittance parameters C6 and D6 are xed accord-ing to equations (19) and (20) Therefore dT only varies with dT

abut not T 6 or T

aitself In order to analyse the change of dT with dT

a we compute the ratio of D6 to

C6 for several combinations The results are given in table 6 which indicates thatthe ratio D

6C

6is mainly dependent on transmittance though emissivity has slightly

eVect on it The ratio changes from 0259 for e6=098 to 0279 for e

6=094 with an

average of 0269 when the transmittance is 08 It changes in the range of 0443ndash0475for the emissivity range 094ndash098 when t6=07 Based on the average ratio of thecombinations for diVerent transmittances we plot the change of dT against dT

ain gure 7

Figure 7 indicates that LST estimation error increases rapidly with the possiblemean atmospheric temperature error and the average ratio D

6C

6 which is mainly

dependent on transmittance (table 5) When mean atmospheric estimation error isabout 1degC the probable LST estimation error is about 027degC for the average ratioD6C6=027 which corresponds to t6=08 However the dT may reach up to 071degCfor the same dT

abut the ratio D6C6=071 or t6=06 If dT

ais greater than 2degC

Table 6 Comparison of the ratio D6C6 for diVerent combinations

Parameter Parameter Ratio AverageEmissivity Transmittance C

6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)

Figure 7 Probable LST estimation error due to the possible mean atmospheric temperatureerror

the dT is about 054degC for t6=08 and about 091degC for t6=07 Therefore theaccurate estimation of mean atmospheric temperature is very important for anaccurate LST retrieval from the only one thermal band of Landsat TM data Whent6lt065 and dT

agt2degC an obvious LST estimation error (gt1degC) is generally

unavoidable However if the sky is very clear so that t6gt08 the possible dT willbe less than 1degC for dT

aof high up to 4degC And such a big dT

ararely happens in

the real world Therefore a clear sky with lower water vapour content is an idealatmospheric condition for remote sensing of LST with Landsat TM6 data

7 Validation of the algorithmThe sensitivity analysis is to provide an assessment of the relative accuracy of

the algorithm ie the eVect of possible error in parameter estimation on the LSTretrieval Validation of the algorithm is also necessary in order to understand howwell the retrieved LST with the algorithm matches to the actual one in the real world

The best way to validate the algorithm is to compare the in situ ground truthmeasurements of LST with the retrieved ones with the algorithm from the LandsatTM6 data of a speci c region However this is not feasible because it is extremelydiYcult to obtain the in situ ground truth measurements comparable to the pixelsize of Landsat TM6 data at the satellite pass An alternative or the practical wayis to use the simulated data generated by atmospheric simulation programs such asLOWTRAN MODTRAN or 6S These programs can simulate the thermal radiancereaching the remote sensor at the satellite level for the input pro le data with theknown ground thermal properties (LST and emissivity) The required atmosphericquantities such as transmittance for remote sensing of LST is also able to computefrom the output of the simulation with the programs The simulated total radiancecan be used to convert into the brightness temperature for TM6 Then the LST canbe estimated with our mono-window algorithm Comparison of the assumed LSTused for the simulation with the retrieved one from the simulated total radianceenables us to examine the accuracy of the algorithm for the true TM6 data

The validation of our algorithm was done through simulation with LOWTRAN70 (Kneizys et al 1988) A number of situations were designed for the validation

Z Qin et al3738

Four land surface temperatures (20degC 30degC 40degC and 50degC) with four correspondentsurface air temperatures (18degC 23degC 30degC and 38degC) were arbitrarily assumed forthe simulation Seven atmospheric pro les were used USA1976 from LOWTRAN70 as well as the tropical 15deg N the subtropical 30deg N July and January and themid-latitude 45deg N July and January given in Cole et al (1965) For any combinationof these temperatures and pro les ve cases of total water vapour content (1 g cm Otilde 2 2 g cm2 25 g cm Otilde 2 3 g cm Otilde 2 and 35 g cm Otilde 2 ) were considered Since most naturalsurfaces of the Earth have emissivity of 095ndash098 we used e6=0965 for thesimulation

In actual operation the atmospheric temperature and water vapour pro le datawere rst estimated for each situation according to the distributions of these atmo-spheric pro les Second the LOWTRAN 70 program was run for radiance andtransmittance The outputs were then used to compute the total thermal radianceand atmospheric transmittance for TM6 Brightness temperature was converted fromthe total thermal radiance using Planckrsquos function for each situation This brightnesstemperature was nally used to put into our mono-window algorithm for LSTretrieval The diVerence between the assumed LST for the simulation and the retrievedone represents how good the algorithm works in LST retrieval from TM6 data

Table 7 lists the detailed results of the validation for USA1976 atmosphere withthe total water vapour 25 g cm Otilde 2 Table 8 gives the main results for all situationsused in the simulation The results shown in both tables 7 and 8 indicate thealgorithm is able to provide a quite accurate estimate of LST in most cases TheLST diVerence between the assumed and the retrieved ones are less than 04degC inmost cases In many regions the satellite overpass was at 900ndash1000 am when theground surface is not very hot Usually the LST at this time is less than 40degC inmany cases Provided this condition the LST diVerence is even smaller For instancethe LST diVerence is only about 023degC for mid-latitude summer atmosphere withtotal water vapour content up to 25 g cm Otilde 2 and a LST up to 40degC This goodmatching of the retrieved LST to the actual one con rms the applicability of themono-window algorithm

8 Spatial variation of LST in the Israel-Egypt border regionIn order to provide an example of the algorithmrsquos application we used it to

retrieve LST from Landsat TM6 data of the IsraelndashEgypt border region where aninteresting thermal phenomenon was found across the border The geomorphologicalstructure is the same on both sides of the border that is the linear sand dunesstretching from south to north Fine sand with a diameter of about 005ndash05 mm isthe principal material of soil constituents in the region though silt and clay also

Table 7 Validation of the algorithm for the USA 1976 atmosphere

SimulatedLST B6(T

6) Retrieved DiVerence

Ts

Estimated (W m Otilde 2 srOtilde 1 Simulated Transmittance LST Tsecirc T

secirc shy T

s(degC) T

a(degC) mm Otilde 1 ) T 6 (degC) t6 (degC) (degC)

20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421


Table 8 Main results of validating the algorithm for various situations

LST diVerence Tsecirc shy T

s(degC)

Water vapour LST Sub- Sub- Mid- Mid-content T

sUSA tropical tropical latitude latitude

(g cmOtilde 2 ) (degC) 1976 Tropical July January July January

20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313

accounts some percentages of the surface layer especially on the Israeli side where athin biogenic crust (1ndash5 mm) covers most of its surfaces Average annual rainfall ofthe region is 95 mm (Kidron and Yair 1997)

On the Egyptian side (Sinai) the region is under intensive use by Bedouinnomads who use the sand surface for grazing goats camels and other cattle as wellas some activities of cropping High plants (shrubs) have been subjected to severegathering for rewood (Tsoar and Moslashller 1986) In contrast to the free-use in theEgyptian side the Israeli side (Negev) has been managed under strict conservationpolicies The limited anthropogenic activities on the Israel side have led to theestablishment of vegetation (shrubs and annuals) and biogenic crust (composed oflichen fungi and other microphytes especially chlorophyll-containing cyanobacteria)on the surface of the sand dune region (Karnieli 1997)

The diVerence in land use between Israel and Egypt has a pronounced eVect onremote sensing imagery On the image of visible bands a sharp spectral contrastcan be seen between the Egyptian Sinai and the Israeli Negev (Karnieli and Tsoar1995 Tsoar and Karnieli 1996 Karnieli 1997) The relatively higher re ectance valueof the remote sensing image on the Egyptian side was believed to be directly resultedfrom severe anthropogenic impact of the Sinai Bedouin including overgrazing and rewood gathering (Tsoar and Moslashller 1986)

The contrast between the two sides of Israel-Egypt border is also observed inthe thermal channel of remote sensing data such as NOAA-AVHRR and LandsatTM The Israeli side has obviously higher brightness temperature on both AVHRRand TM images Because bare sand usually has lower ground emissivity than biogeniccrust we still do not know if the Israeli side really has higher LST than the Egyptian

Z Qin et al3740

side In order to answer this question and analyse the spatial patterns of the thermalvariation in the border region we apply the above mono-window algorithm to theavailable Landsat-5 TM images

Figure 8 represents one result of the eVorts which shows the spatial variation ofLST distribution in the region This image was taken on 29 March 1995 which isin the blooming season The satellite Landsat-5 passed the area at about 930 amAccording to the measurement of CIMEL sunphotometer on the roof of our laborat-ory at Sede Boker about 30 km from the region the water vapour content in theatmospheric pro le was 1185g cm Otilde 2 at the pass By this water vapour content weestimate the atmospheric transmittance was about 08681 at the time when the imagewas acquired Data from Meteorological Observation Station at Sede Boker indicatesthat air temperature near the surface at about 930 am of the date was 145degC Thusthe eVective mean atmospheric temperature was estimated to be 717degC at the satellitepass According to our experiments with samples taken from the eld the biogeniccrust has an average emissivity of about 097 and the bare sand 095 Using thesharp contrast on both sides in the visible channels we assign the emissivity diVerenceto the pixels according to its DN value

The LST images produced from the retrieval eVorts demonstrate that a sharpdiVerence of LST does exist across the border ( gure 8) Generally speaking theIsraeli side has an obvious higher LST than the Egyptian side On average LST is3433degC on the Israeli side and 3095degC on the Egyptian side Thus the diVerence isabout 338degC This LST diVerence can also be clearly seen on the image ( gure 8)The highest LST mainly distributes on the Israeli side in the right upper corner ofthe image The LST in this area is high up to 35ndash37degC Low LST mainly concentrates

Figure 8 Land surface temperature variation in the sand dunes across the IsraelndashEgyptborder retrieved from Landsat TM6 data of 29 March 1995


in the middle part of the Egyptian side The LST in this part is only about 28ndash29degCLST in the area close to the border is about 31ndash33degC on Israeli side and 29ndash30degCon Egyptian side Sharp contrast of LST can still be distinguished in this area nextto the border on both sides even though the diVerence is lower than the averageone This contrast of LST distribution on both sides makes the border very clearlyseen in the sand dune region

Considered more vegetation cover on the Israeli side and the blooming seasonthe higher LST on the Israeli side is really interesting The main reason is that theIsraeli side has much higher biogenic crust cover while the Egyptian side is dominantwith much more bare sand Biogenic crust cover on the Israeli side is estimated toreach above 72 and bare sand on the Egyptian side is above 80 Due to lowalbedo the biogenic crust usually has much higher surface temperature than thebare sand Our ground truth measurements indicate that surface temperature onbiogenic crust is about 2ndash3degC higher than that on bare sand ( gure 9) The measure-ments were carried out in the Nizzana research site close to the border on the Israeliside The time required for the measurements was controlled within an hour so thatthe eVect of measurement time is minimized Figure 9 indicates that the average LSTdiVerence between biogenic crust and bare sand was 223degC on 19 March ( gure 9(a))and 285degC on 26 March1997 ( gure 9(b)) Therefore the higher LST on the Israeli

(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)

Figure 9 Comparison of land surface temperature on biogenic crust and bare sand in thesand dunes across the IsraelndashEgypt border These ground truth measurements weretaken on the Israeli side with a hand-hold radiant thermometer (a) at 1116ndash1204 on19 March 1997 (b) and at 1120ndash1200 on 26 March 1997

Z Qin et al3742

side is due to the contribution of biogenic crust overcoming the cooling process ofits higher vegetation cover Detailed examination of this mechanism is given inanother paper

Due to the probable errors in estimating the key parameters for the LST retrievalsome possible errors may unavoidably involve in this image We need to evaluatethe accuracy of LST estimation in the image according to the possible error in theparameter estimation As mentioned in above sensitivity analysis ground emissivityerror has slight eVect on LST error Considered a possible error of 001 in emissivityestimation ie the emissivity for bare sand in the range of 094ndash096 and for biogeniccrust 096ndash098 the possible LST estimation error is about 012degC in the image( gure 5(b)) According to Price (1984) Takashima and Masuda (1987) and Humeset al (1993) this estimation of emissivity in the range is reasonable Therefore wecan conclude that the possible LST error contributed by possible emissivity error isvery small

For the LST error contributed from transmittance error we consider a moderateerror of water vapour measurement in 01 g m Otilde 2 At this measurement error weexpect a transmittance error of less than 0015 according to the equation given intable 4 for the water vapour range 04ndash16 g cm Otilde 2 The average LST error due tothis transmittance error is less than 05degC for transmittance of 085 ( gure 6(b))Because the eVective mean atmospheric temperature is diYcult to have an accurateestimation we consider an error of up to 25degC at our T

adetermination With this

Ta

error the LST estimation error is about 048degC for transmittance of 085 Asimple summation of these error components gives the probable error of our LSTretrieval less than 11degC in the image ( gure 8) This error is within the generallyaccepted level 15degC (Kerr et al 1992 Li and Becker 1993) If the possible mutualcompensation of these error components is considered the LST distribution shownin this image is even closer to the actual one

9 ConclusionLandsat TM images have been extensively applied for various studies of the

Earthrsquos resources due to its high spatial resolution However the thermal band dataof the remote sensor still remains an ignored area in comparison with the extensiveapplications of its other bands in visible and NIR ranges One of the main reasonsprobably is the diYculties of atmospheric correction for LST retrieval from the singlethermal band data The spatial resolution of the Landsat TM thermal band is about120mtimes120 m Even though this spatial resolution is much lower than its visible andNIR channels it is quite large for analysing the spatial patterns of thermal phenom-enon in a macro-scale region

A mono-window algorithm has been developed in the study for the retrieval ofLST from Landsat TM6 data which is assumed to be reliable though radiometriccalibration is necessary for many applications The derivation of the algorithm isbased on the thermal radiance transfer equation and the linearization of Planckrsquosradiance function Totally there are three critical parameters in the algorithm emissiv-ity transmittance and mean atmospheric temperature If these three parameters aregiven it is very easy to use this algorithm for LST estimation from Landsat TM6data The principle of algorithm can be also extended to other sources of one-thermal-channel data for LST retrieval

The determination of ground emissivity is a complicated issue and there is agreat volume of literature addressing it Generally the change of atmospheric


transmittance is mainly depended on the variation of water vapour content in thepro le This characteristic has been widely used to determine the atmospheric trans-mittance through the simulation with such programs as LOWTRAN or MODTRANBased on the simulation results with LOWTRAN 7 program equations have beenestablished for estimation of atmospheric transmittance from water vapour contentin the general range 04ndash30 g cm Otilde 2 for Landsat TM6 data These equations canprovide quite accurate estimation of transmittance if the measurement of watervapour content is accurate

A practicable and simple method has been proposed for estimation of the requiredeVective mean atmospheric temperature for LST retrieval using the mono-windowalgorithm When the in situ pro le at satellite pass is available the computation ofthe mean atmospheric temperature can be easily done with the equation (22) pro-posed by Sobrino et al(1991) However this is not the general case Study of diVerentstandard pro les indicates that the distributions of water vapour and temperaturein the atmospheres are quite similar when the sky is very clear and there is no greatturbulence With this similarity a method is proposed for the calculation of themean atmospheric temperature from local meteorological observation data whichis usually accessible Therefore when the pro le is not available water vapourcontent and atmospheric temperature at each layer can be approximated using thelocal meteorological observation data to t into the standard distributions of theclimate zone

Usually it is very diYcult to reach an accurate estimation of ground emissivityin spite of several methods have been proposed (Li and Becker 1993 Humes et al1994) Fortunately results from sensitivity analysis of the algorithm indicates thatthe probable LST estimation error dT due to ground emissivity error de6 is muchlower than the LST error due to transmittance error dt6 and mean atmospherictemperature error dT

a On average probable dT is less than 012degC for de

6lt001

and 024degC for de6lt002 Moreover LST error slightly changes with emissivity forthe same de6 On the other hand LST error is sensible to the transmittance errorand mean atmospheric temperature error The relation between dT and dt6 is linearfor speci c temperature and transmittance On average the LST error increases withtransmittance error at the rate of 037degC for t

6=08 and 048degC for t

6=07 For

mean atmospheric temperature dT only depends on dTa

but does not change withT

a The increase rate of dT with dT

ais determined by the ratio of parameter D6 to

C6 ( gure 7) Because the ratio is strongly aVected by transmittance the dT due todT

ais also strongly related to transmittance The higher the transmittance the less

the dT due to dTa For the ratio D6C6=027 which corresponds to t6=08 the

probable dT is about 1degC for dTa=35degC Therefore high transmittance due to low

water vapour in the atmospheric pro le is the best condition for an accurate LSTretrieval from Landsat TM6 data When transmittance is above 08 the comprehens-ive LST error due to a moderate error in emissivity transmittance and meanatmospheric temperature estimation is about 10ndash15degC

The validation of the algorithm has been done to the various simulated situationsfor seven typical atmospheres Using the atmospheric simulation programLOWTRAN 70 we simulate the thermal radiance at the satellite level and then usethe radiance to convert into brightness temperature of TM6 for LST retrievalValidation results indicate that the algorithm is able to provide a quite accurate LSTestimate from TM6 data The LST diVerence between the assumed and the retrievedones is less than 04degC for most situations

Z Qin et al3744

The algorithm has been applied to the IsraelndashEgypt border region as an examplefor analysing the spatial distribution of LST diVerence on both sides from theLandsat TM image taken on 29 March 1995 Based on the available measurementof water vapour content and air temperature we estimate the transmittance andmean atmospheric temperature for the retrieval The result shown in gure 8 supportsthe observed surface temperature diVerence across the border in remote sensingimagery The Israeli side does have obviously higher LST than the Egyptian sideThis is because the biogenic crust that covers most of the ground surface on theIsraeli side has much higher surface temperature than the bare sand prevailing onthe Egyptian side ( gure 9) Furthermore the contribution of higher LST frombiogenic crust covering up to two-thirds of ground surface on the Israeli sideoverwhelms the weak cooling process from more desert vegetation coverComprehensive assessment indicates that the probable LST estimation error due tothe possible error in estimating the critical parameters of the algorithm is less than11degC in the image This error is lower than the generally accepted level 15degC Thusit can be concluded that the estimated LST distribution in the image is very closeto the true one

AcknowledgmentsThe authors would like to express the thanks to the Jacob Blaustein International

Center for Desert Research for providing the fellowship to Zhihao Qin to conducthis study at the Laboratory We also would like to thank Simon M Berkowicsadministrator of The Arid Ecosystem Research Center (AERC) Hebrew Universityof Jerusalem for his allowance to perform the ground truth measurement of thisstudy in the Nizzana research site of AERC on the Israeli side of the border region

References

Andres R J and Rose W I 1995 Description of thermal anomalies on two activeGuatemalan volcanoes using Landsat Thematic Mapper imagery PhotogrammetricEngineering and Remote Sensing 61 775ndash782

Braga C Z F Setzer A W and De Lacerda L D 1993 Water quality assessmentwith simultaneous Landsat 5 TM data at Guanabara Bay Rio de Janeiro BrazilRemote Sensing of Environment 45 95ndash106

Caselles V Artigao M M Hurtado E Coll C and Brasa A 1998 Mapping actualevapotranspiration by combining Landsat TM and NOAA AVHRR imagesApplication to the barrax area Albacete Spain Remote Sensing of Environment63 1ndash10

Cole A E Court A and Kantor A J 1965 Model atmospheres In Handbook ofGeophysics and Space Enviornments edited by S L Valley Air Force(CambridgeCambridge Research Laboratories OYce of Aerospace Research UnitedStates Air Force)

Coll C Caselles V Sobrino A and Valor E 1994 On the atmospheric dependenceof the split-window equation for land surface temperature International Journal ofRemote Sensing 15 105ndash122

Cracknell A P 1997 T he Advanced Very high Resolution Radiometer (AVHRR) (LondonTaylor amp Francis)

Franca G B and Cracknell A P 1994 Retrieval of land and sea surface temperatureusing NOAA-11 AVHRR data in north-eastern Brazil International Journal of RemoteSensing 15 1695ndash1712

Goetz S J Halthore R N Hall F G and Markham B L 1995 Surface temperatureretrieval in a temperate grassland with multiresolution sensors Journal of GeophysicalResearch 100 25397ndash25410


Haakstaad M Kogeler J W and Dahle S 1994 Studies of sea surface temperatures inselected northern Norwegian fjords using Landsat TM data Polar Research 1395ndash104

Humes K S Kustas W P Moran M S Nichols W D and Weltz M A 1994Variability of emissivity and surface temperature over a sparsely vegetated surfaceWater Resources Research 30 1299ndash1310

Hurtado E Vidal A and Caselles V 1996 Comparison of two atmospheric correctionmethods for Landsat TM thermal band International Journal of Remote Sensing17 237ndash247

Kaneko T 1998 Thermal observation of the 1986 eruption of Izu Oshima Volcano (Japan)using Landsat TM data Advances in Space Research 21 517ndash520

Kaneko D and Hino M 1996 Proposal and investigation of a method for estimatingsurface energy balance in regional forests using TM derived vegetation index andobservatory routine data International Journal of Remote Sensing 17 1129ndash1148

Karnieli A 1997 Development and implementation of spectral crust index over dune sandsInternational Journal of Remote Sensing 18 1207ndash1220

Karnieli A and Tsoar H 1995 Spectral re ectance of biogenic crust developed on desertdune sand along the IsraelndashEgypt border International Journal of Remote Sensing16 369ndash374

Kerr Y H Lagouarde J P and Imbernon J 1992 Accurate land surface temperatureretrieval from AVHRR data with use of an improved split window algorithm RemoteSensing of Environment 41 197ndash209

Kidron G J and Yair A 1997 Rainfall-runoV relationship over encrusted dune surfacesNizzana Western Negev Israel Earth Surface Processes and L andforms 22 1169ndash1184

Kneizys F X Shettle E P Abreu L W Anderson G P Chetwynd J H GalleryW O Selby J E A and Clough S A 1988 Users guide to LOWTRAN-7Technical Report AFGL-TR-88-0177 OpticalInfrared Technology Division US AirForce Geophysics Laboratory Hascom Air Forace Base Massachusetts

Liu G R and Kuo T H 1994 Improved atmospheric correction process in monitoringSST around the outfall of a nuclear power plant International Journal of RemoteSensing 15 2627ndash2636

Li Z L and Becker F 1993 Feasibility of land surface temperature and emissivity deter-mination from AVHRR data Remote Sensing of Environment 43 67ndash85

Lo C P 1997 Application of Landsat TM data for quality of life assessment in an urbanenvironment Computers Environment and Urban Systems 21 259ndash276

Mansor S B Cracknell A P Shilin B V and Gornyi V I 1994 Monitoring ofunderground coal res using thermal infrared data International Journal of RemoteSensing 15 1675ndash1685

Markham B L and Barker J L 1986 Landsat-MSS and TM post calibration dynamicranges atmospheric re ectance and at-satellite temperature EOSAT L andsat T echnicalNotes 1 (Lanham Maryland Earth Observation Satellite Company) pp 3ndash8

McMillin L M 1975 Estimation of sea surface temperatures from two infrared windowmeasurements with diVerent absorption Journal of Geophysical Research 365113ndash5117

Moran M S Jackson R D Raymond L H Gay L W and Slater P N 1989Mapping surface energy balance componentsby combining Landsat Thematic Mapperand ground based meteorological data Remote Sensing of Environment 30 77ndash87

Oppenheimer C 1997 Remote sensing of the color and temperature of volcanic lakesInternational Journal of Remote Sensing 18 5ndash37

Prata A J 1993 Land surface temperature from the advanced very high resolution radio-meter and the along-track scanning radiometer 1 Theory Journal of GeographicalResearch 98 16689ndash16 702

Price J C 1984 Land surface temperature measurements from the split window channelsof the NOAA 7 Advanced Very High Resolution Radiometer Journal of GeophysicalResearch 89 7231ndash7237

Reddy C S S Bhattacharya A and Srivastav S K 1993 Night time TM shortwavelength infrared data analysis of Barren Island volcano South Andaman IndiaInternational Journal of Remote Sensing 14 783ndash787

A mono-window algorithm for L andsat T M63746

Ritchie J C Cooper C M and Schiebe F R 1990 The relationship of MSS and TMdigital data with suspended sediments chlorophyll and temperature in Moon LakeMississippi Remote Sensing of Environment 33 137ndash148

Saraf A K Prakash A Sengupta S and Gupta R P 1995 Landsat TM data forestimating ground temperature and depth of subsurface coal re in the Jharia coal eldIndia International Journal of Remote Sensing 16 2111ndash2124

Schneider K and Mauser W 1996 Processing and accuracy of Landsat Thematic Mapperdata for lake surface temperature measurement International Journal of RemoteSensing 17 2027ndash2041

Schott J R and Volchok W J 1985 Thematic Mapper thermal infrared calibrationPhotogrammetric Engineering and Remote Sensing 51 1351ndash1357

Singh S M 1988 Brightness temperature algorithms for Landsat Thematic Mapper DataRemote Sensing of Environment 24 509ndash512

Sobrino J A Coll C and Caselles V 1991 Atmospheric correction for land surfacetemperature using NOAA-11 AVHRR channels 4 and 5 Remote Sensing ofEnvironment 38 19ndash34

Sospedra F Caselles V and Valor E 1998 EVective wavenumber for thermal infraredbands application to Landsat TM International Journal of Remote Sensing 192105ndash2117

Sugita M and Brutsaert W 1993 Comparison of land surface temperatures derived fromsatellite observations with ground truth during FIFE International Journal of RemoteSensing 14 1659ndash1676

Sutherland R A 1986 Broadband and spectral (2ndash18 mm) emissivity of some natural soilsand vegetation Journal of Atmospheric and Oceanic T echnology 3 199ndash202

Takashima T and Masuda K 1987 Emissivities of quartz and Sahara dust powers in theinfrared region (1ndash17mm) Remote Sensing of Environment 23 51ndash63

Tsoar H and Karnieli A 1996 What determines the spectral re ectance of the Negev-Sinai sand dunes International Journal of Remote Sensing 17 3513ndash3525

Tsoar H and Moslashller J T 1986 The role of vegetation in the formation of linear sanddunes In Aeolian Geomorphology edited by W G Nickling (Boston Allen and Unwin)pp75ndash95

Wukelic G E Gibbons D E Martucci L M and Foote H P 1989 Radiometriccalibration of Landsat Thermatic Mapper Thermal Band Remote Sensing ofEnvironment 28 339ndash347

Zhang X Van Genderen J L and Kroonenberg S B 1997 A method to evaluate thecapability of Landsat 5 TM band 6 data for sub pixel coal re detection InternationalJournal of Remote Sensing 18 3279ndash3288

Z Qin et al3720

estimation of the region Based on this LST estimation spatial variation ofthe interesting thermal phenomenon has been analysed for comparison of LSTdiVerence across the border The result shows that the Israeli side does havesigni cantly higher surface temperature in spite of its denser vegetation coverthan the Egyptian side where bare sand is prevalent

1 IntroductionThe Landsat Thematic Mapper (TM) images have been extensively studied for

various purposes (Kaneko and Hino 1996 Lo 1997 Caselles et al 1998) Searchingwith the keyword Landsat TM on the world-widely used CD-ROM scienti c abstractdatabase GEOBASE for the period 1980ndash1999 pops out 1043 papers written inEnglish Except the six bands in visible and near- infrared (NIR) wavelengths theremote sensor also has a thermal band (TM6) operating in the wavelength range of1045ndash1250mm with a nominal ground resolution of 120mtimes120 m This spatialresolution of Landsat TM6 is high enough for analysing the detailed spatial patternsof thermal variation on the Earthrsquos surface However when searching on theGEOBASE with the restricted keyword temperature only 73 papers were foundDetailed examination of these papers reveals that only 35 of them relating to thesurface temperature or thermal band data of Landsat TM This implies that thestudy of Landsat TM thermal band for surface temperature and its application stillremains as an ignored area This is especially true when referring to land surfacetemperature (LST) Due to its high spatial resolution Landsat TM6 has considerablepotential for many applications relating to LST Some studies relating to the thermalband of Landsat TM only use the brightness temperature at the satellite level(Mansor et al 1994 Saraf et al 1995 Zhang et al 1997) or just simply use thedigital number (DN) value for their applications (Ritchie et al 1990 Oppenheimer1997) The actual use of LST retrieved from Landsat TM6 is few (Hurtado et al1996 Sospedra et al 1998) In addition to its intrinsic weaknesses (no on-boardcalibration low repeat frequency and so on) the lack of a proper and easily-usedalgorithm for retrieval of LST from the only one thermal band of Landsat TM dataprobably is also the main reason leading to the few application

Up to present the studies of Landsat TM thermal data mainly concentrate onthe level of directly applying brightness temperature or DN value to the issues inthe real world and on the study of the sealake surface temperature corrected withatmospheric model using radiosonde data Zhang et al (1997) Saraf et al (1995)and Mansor et al (1994) demonstrated that the radiant temperature converting fromLandsat TM thermal data is capable of application for detection of subsurface coal res Sugita and Brutsaert (1993) compared the measured LST in the eld with thetemperature from satellite including Landsat TM The measured sea surface temper-ature is found to be about 78degC higher than the brightness temperature for LandsatTM6 around the outlet of a nuclear power plant (Liu and Kuo 1994) Haakstadet al (1994) demonstrated the importance of Landsat TM6 data in sea temperaturestudy for identifying the surface current patterns Relationship between water qualityindicators and Landsat TM digital data including TM6 DN value has been analysedin the study of Braga et al (1993) about water quality assessment at GuanabaraBay of Brazil Oppenheimer (1997) used the relationship between the measured lakesurface temperature and Landsat TM6 DN value to map the thermal variation ofvolcano lakes Correlation of lake suspended sediments with digital data of LandsatMSS and TM was analysed in Ritchie et al (1990) Based on the surface temperature








Z Qin et al3722






max=255 and Q



and Lmax(l)


L (l)=01238+0005632156Qdn (2)



T 6=K2ln (1+K1L (l)) (3)







Bl(T )=

C1l5 (eC2lT shy 1)

(4)



and C2






B6(T

6)=t

6[e

6B

6(T

s)+ (1 shy e

6)I3

6]+I(

6(5)

where Ts






I(6=P Z

0B6 (T

z)ccedil t6 (z Z )

ccedil zdz (6)

where Tz




Z Qin et al3724


B6 (Ta)=

1

1 shy t6 PZ

0B6 (T

z)ccedil t

6(z Z )

ccedil zdz (7)

where Ta



for TM6 Thus we get

I(6=(1 shy t

6)B

6(T

a) (8)


I36=2 P p2

0P 0

2

B6(T

z)ccedil t frac34

6 (h ecirc z 0)





I36=2 P p2

0(1 shy t6 )B6 (T 3


where T 3a


2 P p2



I36=(1 shy t

6) B

6(T 3

a) (12)


B6(T

6)=e

6t6B

6(T

s)+t

6(1 shy e

6) (1 shy t

6)B

6(T 3

a)+(1 shy t

6) B

6(T

a) (13)



6(T


6(T 3

a) or T

agtT 3



and T 3a


a|lt5degC


a) with B6(T






a)gtB6(T 3

a) the



s)



6(T

s) and B

6(T

a) in




ashy T 3

a| and two cases



ashy T 3

a|=5degC and t

6=08



s00255degC at T



sare even


a) with B6 (T


sfrom the


B6(T

6)=e

6t6B

6(T

s)+(1 shy t

6)[1+t

6(1 shy e

6)]B

6(T

a) (14)





B6(T

j)=B

6(T )+(T

jshy T )ccedil B

6(T ) ccedil T =(L

6+T

jshy T )ccedil B

6(T ) ccedil T (15)

where Tj


6is de ned as

L6=B

6(T )[ ccedil B

6(T ) ccedil T ] (16)

in which L6


j) in terms of the





and Ta

for T 6 we have

B6 (Ts)=(L 6+T


B6 (Ta)=(L 6+T


B6(T

6)=(L

6+T

6shy T

6)ccedil B

6(T

6) ccedil T )=L

6ccedil B

6(T

6) ccedil T (17c)



ashy T 6 ) (18)


C6=e6 t6 (19)

D6=(1 shy t

6)[1+(1 shy e

6) t

6] (20)

Thus we have

L 6=C6 (L 6+Tsshy T 6 )+D6 (L 6+T

ashy T 6 ) (21)


L 6=a6+b6T 6 (22)

where a6

and b6


Z Qin et al3726



ashy T 6 ) (23)


data as follows


]C6 (24)


6and eVective








Ta=

1

w P w

0T

zdw(z Z ) (25)



a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205










aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References





















































Z Qin et al3722






max=255 and Q



and Lmax(l)


L (l)=01238+0005632156Qdn (2)



T 6=K2ln (1+K1L (l)) (3)







Bl(T )=

C1l5 (eC2lT shy 1)

(4)



and C2






B6(T

6)=t

6[e

6B

6(T

s)+ (1 shy e

6)I3

6]+I(

6(5)

where Ts






I(6=P Z

0B6 (T

z)ccedil t6 (z Z )

ccedil zdz (6)

where Tz




Z Qin et al3724


B6 (Ta)=

1

1 shy t6 PZ

0B6 (T

z)ccedil t

6(z Z )

ccedil zdz (7)

where Ta



for TM6 Thus we get

I(6=(1 shy t

6)B

6(T

a) (8)


I36=2 P p2

0P 0

2

B6(T

z)ccedil t frac34

6 (h ecirc z 0)





I36=2 P p2

0(1 shy t6 )B6 (T 3


where T 3a


2 P p2



I36=(1 shy t

6) B

6(T 3

a) (12)


B6(T

6)=e

6t6B

6(T

s)+t

6(1 shy e

6) (1 shy t

6)B

6(T 3

a)+(1 shy t

6) B

6(T

a) (13)



6(T


6(T 3

a) or T

agtT 3



and T 3a


a|lt5degC


a) with B6(T






a)gtB6(T 3

a) the



s)



6(T

s) and B

6(T

a) in




ashy T 3

a| and two cases



ashy T 3

a|=5degC and t

6=08



s00255degC at T



sare even


a) with B6 (T


sfrom the


B6(T

6)=e

6t6B

6(T

s)+(1 shy t

6)[1+t

6(1 shy e

6)]B

6(T

a) (14)





B6(T

j)=B

6(T )+(T

jshy T )ccedil B

6(T ) ccedil T =(L

6+T

jshy T )ccedil B

6(T ) ccedil T (15)

where Tj


6is de ned as

L6=B

6(T )[ ccedil B

6(T ) ccedil T ] (16)

in which L6


j) in terms of the





and Ta

for T 6 we have

B6 (Ts)=(L 6+T


B6 (Ta)=(L 6+T


B6(T

6)=(L

6+T

6shy T

6)ccedil B

6(T

6) ccedil T )=L

6ccedil B

6(T

6) ccedil T (17c)



ashy T 6 ) (18)


C6=e6 t6 (19)

D6=(1 shy t

6)[1+(1 shy e

6) t

6] (20)

Thus we have

L 6=C6 (L 6+Tsshy T 6 )+D6 (L 6+T

ashy T 6 ) (21)


L 6=a6+b6T 6 (22)

where a6

and b6


Z Qin et al3726



ashy T 6 ) (23)


data as follows


]C6 (24)


6and eVective








Ta=

1

w P w

0T

zdw(z Z ) (25)



a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205










aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References
















































Bl(T )=

C1l5 (eC2lT shy 1)

(4)



and C2






B6(T

6)=t

6[e

6B

6(T

s)+ (1 shy e

6)I3

6]+I(

6(5)

where Ts






I(6=P Z

0B6 (T

z)ccedil t6 (z Z )

ccedil zdz (6)

where Tz




Z Qin et al3724


B6 (Ta)=

1

1 shy t6 PZ

0B6 (T

z)ccedil t

6(z Z )

ccedil zdz (7)

where Ta



for TM6 Thus we get

I(6=(1 shy t

6)B

6(T

a) (8)


I36=2 P p2

0P 0

2

B6(T

z)ccedil t frac34

6 (h ecirc z 0)





I36=2 P p2

0(1 shy t6 )B6 (T 3


where T 3a


2 P p2



I36=(1 shy t

6) B

6(T 3

a) (12)


B6(T

6)=e

6t6B

6(T

s)+t

6(1 shy e

6) (1 shy t

6)B

6(T 3

a)+(1 shy t

6) B

6(T

a) (13)



6(T


6(T 3

a) or T

agtT 3



and T 3a


a|lt5degC


a) with B6(T






a)gtB6(T 3

a) the



s)



6(T

s) and B

6(T

a) in




ashy T 3

a| and two cases



ashy T 3

a|=5degC and t

6=08



s00255degC at T



sare even


a) with B6 (T


sfrom the


B6(T

6)=e

6t6B

6(T

s)+(1 shy t

6)[1+t

6(1 shy e

6)]B

6(T

a) (14)





B6(T

j)=B

6(T )+(T

jshy T )ccedil B

6(T ) ccedil T =(L

6+T

jshy T )ccedil B

6(T ) ccedil T (15)

where Tj


6is de ned as

L6=B

6(T )[ ccedil B

6(T ) ccedil T ] (16)

in which L6


j) in terms of the





and Ta

for T 6 we have

B6 (Ts)=(L 6+T


B6 (Ta)=(L 6+T


B6(T

6)=(L

6+T

6shy T

6)ccedil B

6(T

6) ccedil T )=L

6ccedil B

6(T

6) ccedil T (17c)



ashy T 6 ) (18)


C6=e6 t6 (19)

D6=(1 shy t

6)[1+(1 shy e

6) t

6] (20)

Thus we have

L 6=C6 (L 6+Tsshy T 6 )+D6 (L 6+T

ashy T 6 ) (21)


L 6=a6+b6T 6 (22)

where a6

and b6


Z Qin et al3726



ashy T 6 ) (23)


data as follows


]C6 (24)


6and eVective








Ta=

1

w P w

0T

zdw(z Z ) (25)



a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205










aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3724


B6 (Ta)=

1

1 shy t6 PZ

0B6 (T

z)ccedil t

6(z Z )

ccedil zdz (7)

where Ta



for TM6 Thus we get

I(6=(1 shy t

6)B

6(T

a) (8)


I36=2 P p2

0P 0

2

B6(T

z)ccedil t frac34

6 (h ecirc z 0)





I36=2 P p2

0(1 shy t6 )B6 (T 3


where T 3a


2 P p2



I36=(1 shy t

6) B

6(T 3

a) (12)


B6(T

6)=e

6t6B

6(T

s)+t

6(1 shy e

6) (1 shy t

6)B

6(T 3

a)+(1 shy t

6) B

6(T

a) (13)



6(T


6(T 3

a) or T

agtT 3



and T 3a


a|lt5degC


a) with B6(T






a)gtB6(T 3

a) the



s)



6(T

s) and B

6(T

a) in




ashy T 3

a| and two cases



ashy T 3

a|=5degC and t

6=08



s00255degC at T



sare even


a) with B6 (T


sfrom the


B6(T

6)=e

6t6B

6(T

s)+(1 shy t

6)[1+t

6(1 shy e

6)]B

6(T

a) (14)





B6(T

j)=B

6(T )+(T

jshy T )ccedil B

6(T ) ccedil T =(L

6+T

jshy T )ccedil B

6(T ) ccedil T (15)

where Tj


6is de ned as

L6=B

6(T )[ ccedil B

6(T ) ccedil T ] (16)

in which L6


j) in terms of the





and Ta

for T 6 we have

B6 (Ts)=(L 6+T


B6 (Ta)=(L 6+T


B6(T

6)=(L

6+T

6shy T

6)ccedil B

6(T

6) ccedil T )=L

6ccedil B

6(T

6) ccedil T (17c)



ashy T 6 ) (18)


C6=e6 t6 (19)

D6=(1 shy t

6)[1+(1 shy e

6) t

6] (20)

Thus we have

L 6=C6 (L 6+Tsshy T 6 )+D6 (L 6+T

ashy T 6 ) (21)


L 6=a6+b6T 6 (22)

where a6

and b6


Z Qin et al3726



ashy T 6 ) (23)


data as follows


]C6 (24)


6and eVective








Ta=

1

w P w

0T

zdw(z Z ) (25)



a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205










aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References

















































ashy T 3

a| and two cases



ashy T 3

a|=5degC and t

6=08



s00255degC at T



sare even


a) with B6 (T


sfrom the


B6(T

6)=e

6t6B

6(T

s)+(1 shy t

6)[1+t

6(1 shy e

6)]B

6(T

a) (14)





B6(T

j)=B

6(T )+(T

jshy T )ccedil B

6(T ) ccedil T =(L

6+T

jshy T )ccedil B

6(T ) ccedil T (15)

where Tj


6is de ned as

L6=B

6(T )[ ccedil B

6(T ) ccedil T ] (16)

in which L6


j) in terms of the





and Ta

for T 6 we have

B6 (Ts)=(L 6+T


B6 (Ta)=(L 6+T


B6(T

6)=(L

6+T

6shy T

6)ccedil B

6(T

6) ccedil T )=L

6ccedil B

6(T

6) ccedil T (17c)



ashy T 6 ) (18)


C6=e6 t6 (19)

D6=(1 shy t

6)[1+(1 shy e

6) t

6] (20)

Thus we have

L 6=C6 (L 6+Tsshy T 6 )+D6 (L 6+T

ashy T 6 ) (21)


L 6=a6+b6T 6 (22)

where a6

and b6


Z Qin et al3726



ashy T 6 ) (23)


data as follows


]C6 (24)


6and eVective








Ta=

1

w P w

0T

zdw(z Z ) (25)



a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205










aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3726



ashy T 6 ) (23)


data as follows


]C6 (24)


6and eVective








Ta=

1

w P w

0T

zdw(z Z ) (25)



a)

Underestimate of Ts

in degC

For t6=07 and e6

=096 For t6=08 and e6

=096

T 3ashy T

ain degC At T

s=20 At T

s=35 At T

s=50 At T

s=20 At T

s=35 At T

s=50

2 00087 00077 00070 00100 00089 000813 00130 00116 00105 00150 00134 001215 00220 00196 00177 00255 00227 00205










aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References




















































aestimation



Water vapor (g cm

shy2)

(a)

(b)


Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3728


w(z)=wRw(z) (26)




Ta=

1

waeligm

z= 0

Tzw(z) (27)






w(z)

0 0402058 0425043 0438446 0400124 04164181 0256234 0261032 0262100 0254210 02583942 0158323 0168400 0148943 0161873 01593853 0087495 0075999 0074471 0095528 00833734 0047497 0031878 0038364 0046510 00410625 0024512 0019381 0017925 0023711 00213826 0012846 0009771 0009736 0011514 00109677 0006250 0004782 0005223 0004092 00050878 0003132 0002257 0002611 0001471 00023689 0001049 0000954 0001315 0000587 0000976

10 0000358 0000349 0000616 0000238 000039011 0000142 0000104 0000185 0000060 000012312 0000055 0000032 0000044 0000026 000003913 0000023 0000008 0000009 0000016 000001414 0000009 0000004 0000004 0000011 000000715 0000006 0000002 0000002 0000008 0000004










Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References























































Rt(z)=(T

0shy T

z)(T

0shy 217) (28)







for each layer of



(a)

(b)


Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3730


Tz=T

0shy R

t(z) (T

0shy 217) (29)



Therefore when T0


0is available


afor LST











t(z)

0 0 0 0 0 01 00912921 00725514 00582902 00634058 007138492 01825843 01451028 01165803 01268116 014276973 02738764 01934704 01943005 01902174 021296624 03651685 02744861 02720207 02989130 030264715 04564607 03555018 03497409 04076087 039232806 05477528 04365175 04274611 05163043 048200907 06390449 05163241 05116580 06250000 057300688 07303371 05973398 05958549 07336957 066430699 08216292 06783555 06800518 08423913 07556070

10 09115169 07581620 07629534 09510870 0845929811 10028090 08415961 08471503 09601449 0912925112 10042135 09201935 09313472 09692029 0956239313 10042135 1 10155440 09782609 0999504614 10042135 10810157 10168394 09873188 1022346915 10042135 11608222 10168394 09963768 10445630






aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References



















































aobviously biased



Ta=ST

zw(z)w=ST

zR

w(z) (30)




obtain

Ta=S(T 0 shy R

t(z) (T 0 shy 217))R

w(z)

=ST0R

w(z) shy ST

0R

t(z)R

w(z)+S217R

t(z)R

w(z)

=T 0 (SRw(z) shy SR

t(z)R

w(z))+217SR

t(z)R

w(z) (31)



as follows

For USA 1976 Ta=259396+088045T 0 (32a)




0(32d)

where both Ta

and T0









6available and T



Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3732













=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References




















































=0982007shy 009611w 099463 000334016ndash30 t6

=1053710shy 014142w 099899 0002375




dTs=|T

s(x+dx) shy T

s(x) | (33)

where dTs



s(x+dx) and T

s(x)




Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3734

(a)

(b)


LST error (iexclC)

LST error (iexclC)





6=002 dT is about


(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References















































(a)

(b)


LST error (iexclC)

LST error (iexclC)







6 the




Ta


Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3736


derive that

dT =|Ts(T

a+dT )shy T

s(T

a) |


a)]C6


=|[D6T ashy D6 (T

a+dT

a)]C6 |

=|(D6C

6)dT

a| (34)


abut not T 6 or T




6C



6=094 with an


ain gure 7


6C

6 which is mainly






6D

6D

6C

6ratio

094 06 0564 04144 0734752095 06 0570 04120 0722807096 06 0576 04096 0711111 0711352097 06 0582 04072 0699656098 06 0588 04048 0688435094 07 0658 03126 0475076095 07 0665 03105 0466917096 07 0672 03084 0458929 0459093097 07 0679 03063 0451105098 07 0686 03042 0443440094 08 0752 02096 0278723095 08 0760 02080 0273684096 08 0768 02064 0268750 0268852097 08 0776 02048 0263918098 08 0784 02032 0259184094 09 0846 01054 0124586095 09 0855 01045 0122222096 09 0864 01036 0119907 0119955097 09 0873 01027 011764098 09 0882 01018 011542


LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References















































LST error (iexclC)

Ta error (iexclC)






ararely happens in






Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3738







SimulatedLST B6(T


Ts


secirc shy T

s(degC) T


20 9132 78865 15568 0701747 20128 012830 13534 89523 24126 0721060 30283 028340 19697 101903 33392 0744298 40371 037150 26741 115488 42890 0761250 50421 0421




s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References

















































s(degC)




20 0049 0024 0028 0018 0019 00271 30 0114 0075 0082 0066 0067 0081

40 0151 0105 0114 0094 0095 011250 0173 0121 0131 0109 0110 012920 0098 0046 0055 0035 0035 0053

2 30 0213 0137 0151 0120 0121 014940 0285 0196 0212 0175 0176 020950 0333 0232 0251 0209 0210 024820 0128 0060 0072 0045 0046 007

25 30 0283 0181 0200 0158 0160 019740 0371 0254 0276 0227 0229 027250 0421 0293 0316 0263 0265 031320 0161 0075 0090 0057 0058 0088

3 30 0353 0226 0249 0197 0199 024540 0462 0315 0342 0282 0284 033850 0502 0349 0377 0314 0316 037320 0181 0084 0101 0064 0065 0099

35 30 0388 0248 0274 0216 0218 026940 0516 0352 0382 0314 0316 037750 0421 0293 0316 0263 0265 0313





Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3740








(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References

















































(a)

(b)

Tem

perature (iexclC)

Tem

perature (iexclC)


Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3742





Ta











6lt001



6=07 For











Z Qin et al3744




References



















































6lt001



6=07 For











Z Qin et al3744




References














































Z Qin et al3744




References














































a mono-window algorithm for retrieving land surface

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