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Revision of the Single-Channel Algorithm for Land Surface Temperature Retrieval

Revision of the Single-Channel Algorithm for Land Surface Temperature Retrieval From Landsat

Thermal-Infrared Data

Juan C.Jiménez-Mu?oz,Jordi Cristóbal,JoséA.Sobrino,Guillem Sòria,Miquel Ninyerola,and Xavier Pons

Abstract—This paper presents a revision,an update,and an extension of the generalized single-channel(SC)algorithm devel-oped by Jiménez-Mu?oz and Sobrino(2003),which was partic-ularized to the thermal-infrared(TIR)channel(band6)located in the Landsat-5Thematic Mapper(TM)sensor.The SC algo-rithm relies on the concept of atmospheric functions(AFs)which are dependent on atmospheric transmissivity and upwelling and downwelling atmospheric radiances.These AFs are?tted versus the atmospheric water vapor content for operational purposes.In this paper,we present updated?ts using MODTRAN4radiative transfer code,and we also extend the application of the SC algo-rithm to the TIR channel of the TM sensor onboard the Landsat-4 platform and the enhanced TM plus sensor onboard the Landsat-7 platform.Five different atmospheric sounding databases have been considered to create simulated data used for retrieving AFs and to test the algorithm.The test from independent simulated data provided root mean square error(rmse)values below1K in most cases when atmospheric water vapor content is lower than 2g·cm?2.For values higher than3g·cm?2,errors are not acceptable,as what occurs with other SC algorithms.Results were also tested using a land surface temperature map obtained from one Landsat-5image acquired over an agricultural area using inversion of the radiative transfer equation and the atmospheric pro?le measured in situ at the sensor overpass time.The compari-son with this“ground-truth”map provided an rmse of1.5K.

Index Terms—Landsat,land surface temperature(LST),single-channel(SC),thermal-infrared(TIR).

I.I NTRODUCTION

T HERMAL remote sensing is recognized to be a major source of quantitative and qualitative information on land

Manuscript received January28,2008;revised July21,2008and September3,2008.First published November25,2008;current version pub-lished December17,2008.This work was supported in part by the European Space Agency(SEN2FLEX,project RFQ3-11291/05/I-EC)and in part by Ministerio de Ciencia y Tecnología(TERMASAT,project ESP2005-07724-C05-04).

J.C.Jiménez-Mu?oz,J.A.Sobrino,and G.Sòria are with the Global Change Unit,Department of Earth Physics and Thermodynamics,University of Valencia,46100Valencia,Spain(e-mail:jcjm@uv.es;jose.a.sobrino@uv.es). J.Cristóbal is with the Department of Geography,Autonomous University of Barcelona,08193Cerdanyola del Vallès,Spain(e-mail:jordi.cristobal@ uab.es).

M.Ninyerola is with the Unit of Botany,Department of Animal Biology, Plant Biology and Ecology,Autonomous University of Barcelona,08193 Cerdanyola del Vallès,Spain(e-mail:miquel.ninyerola@uab.es).

X.Pons is with the Department of Geography,Autonomous University of Barcelona,08193Cerdanyola del Vallès,Spain,and also with the Centre for Ecological Research and Forestry Applications,08193Cerdanyola del Vallès, Spain(e-mail:xavier.pons@uab.es).

Color versions of one or more of the?gures in this paper are available online at https://www.wendangku.net/doc/6516575909.html,.

Digital Object Identi?er10.1109/TGRS.2008.2007125surface processes and for their characterization,analysis,and modeling[1],[2].The launch of the Landsat series has allowed the acquisition of a historical database(from1982to present) of thermal imagery at medium spatial resolution suitable for different environmental studies,for example,evapotranspira-tion and energy balance component estimations or water re-source studies.Thermal-infrared(TIR)data have been collected through band6(B6)of the Thematic Mapper(TM)instrument onboard Landsat-4(L4B6)and Landsat-5(L5B6)platforms and the enhanced TM plus instrument onboard the Landsat-7 (L7B6)platform.

Land surface temperature(LST)is the key variable to be retrieved from the TIR data.The interest on Landsat TIR data has increased in the last years,which has encouraged the emergence of different publications related to this issue. The most appropriate procedure to retrieve LST from a single-channel(SC)located in the TIR region,as is the case of Landsat series,is by inversion of the radiative transfer equation (RTE)according to the following expression applied to a certain sensor channel(or wavelength interval):

B(T s)=

L sen?L↑?τ(1?ε)L↓

τε

(1)

where

B Planck’s law,expressed as

Bλ(T)=

λ5exp

λT

?1(2) with c1and c2being the Planck’s radiation constants,

with values of1.19104·108W·μm4·m?2·sr?1

and14387.7μm·K,respectively;

λwavelength;

T s land surface temperature(LST);

L sen at-sensor registered radiance;

L↑upwelling atmospheric radiance(path radiance);

τatmospheric transmissivity;

εsurface emissivity;

L↓downwelling atmospheric radiance.

Radiances are in watts per square meter per steradian per micrometer,and wavelength is in micrometers.

Examples of this procedure can be found in[3]and[4].The main problem when using(1)is that atmospheric parametersτ, L↑,and L↓must to be known.This implies the availability of at-mospheric soundings launched near the study area and near the acquisition time of the satellite image.Currently,this problem is

0196-2892/$25.00?2008IEEE

solved by using National Centers for Environmental Prediction (NCEP)modeled atmospheric pro?les,but these data are useful only on a global scale,and they need to be interpolated to a particular date,time,and location.A web-based tool for atmospheric correction of Landsat-5and Landsat-7TIR data from NCEP was proposed by Barsi et al.[5],[6].

In order to avoid the dependence on real or modeled at-mospheric pro?les and,therefore,to retrieve LST in a more operational way,different SC algorithms can be inferred from approximations of(1).Hence,an SC algorithm for L5B6data was developed by Qin et al.[7].This algorithm requires the knowledge of the atmospheric transmissivity(τ)and the at-mospheric mean temperature(T a),which is something similar to have atmospheric pro?les.For this reason,the authors used simulated data computed with LOWTRAN-7code[8]to?t τversus atmospheric water vapor content(w)and T a versus near-surface air temperature(T0)as input data.In this way,the algorithm uses w and T0as input data.However,relationships betweenτand w depend on not well-de?ned“high”and“low”air temperature values,whereas relationships between T a and T0are given for certain standard atmospheres.

To avoid the aforementioned problems,Jiménez-Mu?oz and Sobrino[9]developed a generalized SC algorithm a priori ap-plicable to any TIR channel with a bandwidth of around1μm. This algorithm was also adapted to L5B6data in the cited reference and compared with the algorithm of Qin et al.in[10]. The basis of this algorithm relies in the estimation of the so-called atmospheric functions(AFs),which were assumed to be dependent only on w.Therefore,in terms of its practical application to Landsat-5imagery,the main advantage is that only the knowledge of w is required.We will denote this algorithm as SC JM&S.

It should be noted that all SC algorithms based on(1)require the additional knowledge of the land surface emissivity(LSE). The purpose of this paper is to update the coef?cients involved in the relationship between AFs and w for L5B6 data and also to extend the calculations to AFs for L4B6and L7B6.In this way,an operative SC algorithm could be used to retrieve LST from the Landsat historical database and the new acquisitions in case of the program continuity.The problems of the LSE retrieval from Landsat data will not be addressed in this paper.The interested reader can consult,for example, [4],[10],and[11].Problems related to the calibration of the Landsat thermal data will not be addressed in this paper either. More information about this issue can be found,for example, in[12]and[13].

II.M ETHODOLOGY

In this section,we provide a summary of the SC JM&S al-gorithm[9]in order to clarify to the reader about the results presented in the next sections.We also include a brief analysis of the bandpass effect,which regards to the difference between brightness temperatures derived by inversion of the Planck’s law(monochromatic case)and brightness temperatures derived from band-averaged radiances.Moreover,we have included a description of the atmospheric radiosounding databases used in this paper.A.SC Algorithm

SC JM&S algorithm retrieves LST(T s)using the following general equation:

T s=γ

(ψ1L sen+ψ2)+ψ3

+δ(3)

whereεis the surface emissivity;γandδare two parameters dependent on the Planck’s function[see(4)and(5)];andψ1,ψ2,andψ3are referred to as AFs[see(6)].All the parameters involved in(3)are wavelength(or channel)dependent,but spectral notation will be omitted for simplicity.These parame-ters are given by

γ=

δ=?

(4)

α=B(T0)

λ4

B(T0)+

β=

c2B(T0)

T20

λ4B(T0)

(5)

ψ1=

ψ2=?L↓?

L↑

ψ3=L↓.(6)

In(5),λrefers to the effective wavelength of the channel considered and T0is an approximated value to the surface temperature(not to be confused with air temperature).We will deal with these aspects in Section II-B.The practical approach proposed in the SC JM&S algorithm consists on the approximation of the AFs de?ned in(6)versus the atmospheric water vapor content from a polynomial(second degree)?t.In matrix notation,this approximation can be expressed as

ψ1

ψ2

ψ3

c11c12c13

c21c22c23

c31c32c33

?(7)

where coef?cients c ij are obtained by simulation.The follow-ing matrix coef?cients were obtained for L5B6data in[9]:

0.14714?0.155831.1234

?1.1836?0.37607?0.52894

?0.045541.8719?0.39071

?.(8)

Simulation procedure was performed with a set of61at-mospheric soundings and MODTRAN3.5code to compute values ofτ,L↑,and L↓.These atmospheric soundings carry certain w values which were computed using the LOWTRAN-7 code.In Section III,we provide updated coef?cients using MODTRAN4computations forτ,L↑,and L↓and also for w. The study will also be extended to L4B6and L7B6data.

1)Approximations for Gamma and Delta Parameters:Pa-rametersγandδ,de?ned in(4)and(5)and involved in LST retrieval from(3),explicitly depend on T0and B(T0).As discussed in[9],T0can be chosen as the at-sensor brightness temperature T sen de?ned as L sen≡B(T sen).Therefore,T sen can be obtained from inversion of Planck’s law according to

T sen=

λln

λ5L sen

.(9)

JIMéNEZ-MU?OZ et al.:REVISION OF THE SC ALGORITHM FOR LST RETRIEV AL FROM LANDSAT TIR DATA

341

Fig.1.Spectral responses and effective wavelengths(λe?)for band6of Landsat-4(L4B6),Landsat-5(L5B6),and Landsat-7(L7B6)platforms.Vertical lines are the position on the x-axis ofλe?.

In this way,γandδcan be rewritten as presented in[10]

γ=

c2L sen

sen

λ4L sen

δ=?γL sen+T sen.(10) The parameterγcan also be expressed as

γ=

T2sen

aγL2sen+bγL sen

(11)

where

aγ≡c2λ4 c1

bγ≡c2

.(12)

It is easy to check that aγ bγand also aγL2sen bγL sen,so γandδcan?nally be easily obtained as

γ≈

T2sen bγL sen

δ≈T sen?T2sen

bγ

(13)

with bγequal to1290K,1256K,and1277K for L4B6,L5B6, and L7B6,respectively.

2)Effective Wavelength and Brightness Temperature Inver-sion:In previous expressions,the parameterλis the effective wavelength of the sensor,which is de?ned as

λe?ective=

λfλdλ

fλdλ

(14)

where fλis the?lter function or spectral response for a certain sensor channel.Fig.1shows the spectral responses and the effective wavelengths for L4B6,L5B6,and L7B6. Therefore,the computation of at-sensor brightness temper-atures from the at-sensor registered radiance using(9)should employ effective wavelengths.The use of a single wavelength value to retrieve temperature from radiance in the case of a sensor with a certain channel width(sometimes referred in the literature as bandpass effects)has been revised by different authors[14].A commonly used approximation of Planck’s function speci?c to Landsat is given by[15]

T sen=

L sen

(15)

where K1=671.62W·m?2·sr?1·μm?1and K2= 1284.30K for L4B6,K1=607.76W·m?2·sr?1·μm?1 and K2=1260.56K for L5B6,and K1=666.09W·m?2·sr?1·μm?1and K2=1282.71K for L7B6.These constants were estimated to solve,in part,the problem of the bandpass effect.Mean differences between(9)and(15)for a range of temperatures between270K and340K have been found to be of?0.6K for L4B6and L5B6and?0.3K for L7B6.For example,note that in case of an error on LST of1.5K,square root sum of errors leads to1.6K or1.5K(i.e.,[1.52+0.62]1/2 or[1.52+0.32]1/2),which is not a signi?cant contribution. Since the SC algorithm presented here was developed from Planck’s law and its derivatives,we will always employ the concept of effective wavelength.

B.Atmospheric Sounding Databases

In this section,we describe the?ve atmospheric sounding databases used to compute the AFs that will be presented later (see Section III-A).The atmospheric pro?les of the different databases include values of altitude,pressure,temperature,and relative humidity for each layer.The rest of the values for the atmospheric constituents were retrieved from default values included in the appropriate MODTRAN standard atmosphere. We have considered in this paper three thermodynamic initial guess retrieval(TIGR)databases described,for example,by Aires et al.[17]:1)TIGR1,composed by861atmospheres [18];2)TIGR2,which is a revision of TIGR1and is com-posed by1761atmospheres(assigned to the following model atmospheres:322tropical,388midlatitude summer,354mid-latitude winter,104subartic summer,and593subartic winter) [19],[20];and3)TIGR3,an extended version of TIGR2 and composed by2311atmospheres(same as TIGR2plus 550atmospheres assigned to the tropical model)[21].In fact, we have used TIGR2,TIGR3,and a selection of61atmospheres from TIGR1(28atmospheres assigned to the tropical model, 12to the midlatitude summer model,12to the subartic winter, and9to the U.S.Standard).This reduced TIGR1database was created by Sobrino et al.[22],and it has been used in numerous studies,including the development of the SC JM&S algorithm[9].For simplicity,these databases will be referred by the number of atmospheres,i.e.,TIGR61,TIGR1761,and TIGR2311.

In addition to the TIGR databases,we have also considered the SAFREE database presented in[23].This database includes 402cloud-free and latitude equally distributed pro?les repre-sentative of the world ocean.It has been made from four main radiosounding sources:TIGR2,TIGR3,and radiosoundings from Meteo France and the Norwegian Meteorological service. Despite the fact that SAFREE was originally developed for maritime conditions,we have used it also indistinctly over land.

342IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.47,NO.1,JANUARY

2009

Fig.2.Spatial distribution of the atmospheric pro?les included in the SAFREE and TIGR databases.TABLE I

A TMOSPHERIC S OUNDING D ATABASES C ONSIDERED IN THE S IMULATION

P ROCEDURE U SING MODTRAN R ADIATIVE T RANSFER C ODE .A BBREVIATIONS FOR M ODEL A TMOSPHERES :TRO =T ROPICAL ,MLS =M IDLATITUDE S UMMER ,MLW =M IDLATITUDE W INTER ,

SAS =S UBARTIC S UMMER ,SAW =S UBARTIC W INTER ,

AND USS =U.S.S

TANDARD

This database will be denoted as SAFREE402.Fig.2shows the spatial distribution of the atmospheric pro?les included in the TIGR and SAFREE databases.

Finally,we have constructed an additional database by con-sidering the six standard (std)atmospheric pro?les (tropical,midlatitude summer,midlatitude winter,subartic summer,sub-artic winter,and U.S.Standard)included in the

MODTRAN

Fig. 3.Atmospheric water vapor content histogram for the differ-ent atmospheric sounding databases employed:(a)STD66,(b)TIGR61,(c)TIGR1761,(d)TIGR2311,and (e)SAFREE402.

code and a scaling water vapor factor from 0.5to 1.5in steps of 0.1.This leads to a total amount of 66atmospheres,so we denote this database as STD66.The atmospheric database characteristics are summarized in Table I.

Fig.3shows the histogram in terms of the atmospheric water vapor content distribution for each database.Hence,TIGR1761and TIGR2311are centered at low w values,around 1g/cm 2.The rest of databases are not clearly centered at any particular

JIMéNEZ-MU?OZ et al.:REVISION OF THE SC ALGORITHM FOR LST RETRIEV AL FROM LANDSAT TIR DATA 343

Fig.4.Output atmospheric water vapor content from LOWTRAN and MOD-TRAN for each atmospheric pro?le included in the TIGR61database.Model atmosphere in which each atmospheric sounding is assigned is also shown.

w value.TIGR61seems to be the better distributed database in terms of water vapor.

As commented in Section II-A,the ?rst version of the AFs involved in the SC JM&S algorithm was retrieved from LOWTRAN calculations for the total atmospheric water vapor content but from MODTRAN calculations for atmospheric transmissivity and atmospheric radiances.This was done be-cause in older versions of MODTRAN,w values were provided in units of g ·cm ?2only when it was executed in LOWTRAN mode.Newer versions of MODTRAN,such as version 4,pro-vide w values in units of atm ·cm and g ·cm ?2,so in this paper,AFs have been computed only using MODTRAN calculations.Signi?cant differences between LOWTRAN and MODTRAN estimations of w values have been found,and they are reported in Fig.4.A root mean square error (rmse)value of 0.7g ·cm ?2(taking w obtained by MODTRAN as the reference)has been obtained in the case of TIGR61.These differences can be higher than 1g ·cm ?2for high w values.In the next section,we present the revised coef?cients obtained from TIGR61using only MODTRAN calculations.

III.R ESULTS

In this section,we provide recalculated coef?cients for the AFs of L5B6and also the ?rst calculations for L4B6and L7B6.These calculations have been performed using simulated data extracted from different atmospheric sounding databases (see Section II-B)and MODTRAN-4code [16].Final results on LST have been tested using independent simulated data.An ef-fort has been made to also include a test from Landsat imagery and ground data.However,the authors do not have a complete database of imagery and measurements to ensure a complete validation.A “ground-truth”LST map over an agricultural area obtained from inversion of RTE and an atmospheric sounding launched in situ has been used instead,as will be explained in Section III-C.It is worth to remark that the SC JM&S algorithm was previously validated with ground-based measurements in [9]and tested using simulated and Landsat-5TM data in [10].A.AFs

Atmospheric pro?les included in the different databases have been introduced in the MODTRAN-4code to produce spectral

TABLE II

C OEFFICIENTS FOR THE AF S F OLLOWING M ATRIX N OTATION E XPRESSE

D IN (7).V ALUES H AV

E B EEN O BTAINED U SING D IFFERENT A TMOSPHERIC

S OUNDING D ATABASES FOR B AND 6OF L ANDSAT -4,

L ANDSAT -5,AND L ANDSAT -7P LATFORMS

values of τ,L ↑,and L ↓.Band-averaged (effective)values were retrieved using spectral responses (see Fig.1)and (14),in which λmust be replaced by the parameter considered (τ,L ↑,or L ↓).Then,AFs were calculated from (6)and ?tted against w .The coef?cients obtained for each AF,database,and sensor are given in Table II,in which matrix notation has been considered as presented in Section II-A.

Coef?cients of determination (r 2)and standard error of estimations (σ)obtained in the statistical ?ts of AFs were also calculated,but they are not shown in Table II.Values of r 2were typically >0.96,which indicated a good correlation between AFs and w .Values of σfor the AFs do not provide useful information per se .For this reason,LST has been retrieved from

344IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.47,NO.1,JANUARY2009

Fig.5.Test of the SC algorithm using the same simulated data than used for retrieving the AFs.Plots show the difference between the LST retrieved with the SC algorithm(T algorithm)and the one included in the simulated database(T simulated)(left column)for the whole range of water vapor values and(right column) only for the range between0.5and2g·cm?2.Values of bias,standard deviation,and rmse are also given.Surface emissivity has been assumed to be1.0.From top to bottom,plots correspond to STD66,TIGR61,TIGR1761,TIGR2311,and SAFREE402databases.

JIMéNEZ-MU?OZ et al.:REVISION OF THE SC ALGORITHM FOR LST RETRIEV AL FROM LANDSAT TIR DATA345

(3)using AFs computed with the same simulated data,and then compared to LST extracted from the atmospheric soundings (temperature at?rst level).Since emissivity is assumed to be known,a value of1.0has been considered(same results are also obtained for emissivity values different to the unity).This procedure provides an idea of theσvalue in terms of tempera-ture and not in terms of AFs.Fig.5shows the results obtained for L5B6.Plots included in Fig.5represent the difference between LST retrieved with the SC JM&S algorithm and LST simulated versus the atmospheric water vapor content.These plots clearly show that poor results are obtained for very low w values(w<0.5g·cm?2),and overall for high w values, w>3g·cm?2.There is also a“transition zone”between2 and3g·cm?2,in which the algorithm can provide acceptable results in some cases.For this reason,we have also plotted in Fig.5the results obtained only for w values between0.5 and2g·cm?2,which can be considered the range of good performance for the algorithm.When results are focused in this range of w values,rmse<0.7K are obtained for all the databases,except for the SAFREE one,with rmse<1K.Note that when the full range of w values is considered,STD66, TIGR1761,and SAFREE402still provide acceptable results, with rmse<2K,whereas TIGR61and TIGR2311provide rmse～3K.

B.Algorithm Testing Using Independent Simulated Data

In the previous section,we provided a test for the SC algo-rithm using the same simulated data than used to retrieve the coef?cients for the AFs,which indicates expected errors only due to the statistical?t between AFs and w,i.e.,something similar to a standard error of estimation.In this section,we show results obtained when the SC JM&S algorithm is applied to an independent simulated database.For this purpose,we will use AFs calculated from one atmospheric database,and we will apply the algorithm to the rest of the atmospheric databases.In this case,surface emissivities involved in(3)have been obtained from the ASTER spectral library(108samples used in[24]).The results obtained in this test for L4B6,L5B6, and L7B6are presented in Table III.Note that TIGR1761, TIGR2311,and SAFREE402have not been intercompared because they share some atmospheric pro?les,which could lead to an underestimation of the rmse.

According to the results presented in Table III,similar con-clusions than in the previous section can be extracted,i.e., SC JM&S algorithm shows a good performance for w values between0.5and2g·cm?2,with rmse values below1K, except for the SAFREE database,with rmse values between 1.3K and1.6K.This is probably due to the fact that the SAFREE database was designed only for maritime conditions. Acceptable results are obtained in some cases for the full range of w values.For example,when AFs are retrieved with the three TIGR databases and the SC JM&S is compared to the STD66database,rmse values are below2K.AFs retrieved from TIGR2311and SC JM&S compared to TIGR1761also provide satisfactory results for the full range of w values,with an rmse of1.5K.

TABLE III

T EST OF THE SC A LGORITHM U SING I NDEPENDENT S IMULATED D ATA.

AF S A RE R ETRIEVED F ROM O NE D ATABASE,AND SC A LGORITHM I S T ESTED W ITH THE R EST OF THE D ATABASES C ONSIDERED IN T HIS P APER.RMSE I S THE R OOT M EAN S QUARE E RROR

C.Algorithm Testing Using Satellite Data

As has been commented before,the authors do not have a complete Landsat imagery database in coincidence with ground-based LSTs to provide a complete validation.Instead, we provide in this section a brief analysis using one Landsat-5image acquired on July13,2005over the agricultural area of Barrax(Albacete,Spain,39.05?N,2.1?W,700m)in the framework of the SEN2FLEX?eld campaign[25].Landsat image was resized to393×391pixels(～138km2),which includes the study area under clear-sky conditions.Ground-based measurements were collected to validate high-resolution airborne data,with pixel size<5m,so these plots are not valid at Landsat-5scale(pixel size of120m).For this reason, we have obtained an LST image by inversion of the RTE(1), where atmospheric parametersτ,L↑,and L↓were obtained from MODTRAN,and the atmospheric sounding launched

346IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.47,NO.1,JANUARY2009 in situ at10:48GMT,close to the Landsat overpass time

(10:31GMT).LSE was obtained using the simpli?ed normal-

ized difference vegetation index(SNDVI)method[11]

ε=εs(1?FVC)+εv FVC(16)

whereεs andεv refer to soil and vegetation emissivities,

assumed to be of0.97and0.99,respectively,for the Barrax

area.Fractional vegetation cover(FVC)can be retrieved from

NDVI according to Carlson and Ripley[26]

FVC=

NDVI?NDVI s

v?NDVI s

(17)

where NDVI s and NDVI v refer to soil and vegetation NDVI, with respective values extracted from the NDVI histogram of0.18and0.85.NDVI was computed using re?ectances at Landsat bands3and4,atmospherically corrected using the algorithm developed by Guanter et al.[27],and adapted to Landsat characteristics.For those pixels where NDVI< NDVI s,FVC is set to zero,whereas for pixels with NDVI> NDVI v,FVC is set to one.

The LST image retrieved using the aforementioned proce-dure has been considered as a“ground-truth”map(denoted as RTE_truth),and LST retrievals considering different cases have been compared to it.The different ways cases considered in the LST retrieval are as follows.

1)Use the RTE,in which atmospheric parameters(τ,L↑,

and L↓)are retrieved using the atmospheric correction parameter calculator(ACPC)developed in[5]and[6] (denoted as RTE_ACPC).

2)Use the SC JM&S algorithm,in which AFs are calculated

directly from(6)and using values for the atmospheric parameters(τ,L↑,and L↓)obtained from the atmospheric sounding and MODTRAN(denoted as SC_theory).

3)Use the SC JM&S algorithm,in which AFs are calculated

using the coef?cients obtained with the TIGR61database and the water vapor value extracted from the atmospheric sounding(denoted as SC_w).

Values of the atmospheric parameters extracted from the at-mospheric sounding and from the ACPC are given in Table IV. RTE_truth has been subtracted to LST images obtained in the three different cases.The results are included in Table V,which shows that RTE_ACPC and SC_w are clearly biased in1.5K, with maximum differences up to2K.SC_theory provided almost the same results than RTE_truth,with a bias below 0.2K.This low bias suggests that the“theoretical”approxima-tions involved in the SC JM&S algorithm are satisfactory,and as it is expected,accuracy is lost due to the strong approximation of the AFs versus only a single atmospheric parameter as the water vapor content.The signi?cant bias obtained with the RTE_ACPC suggests that atmospheric corrections based on NCEP models can be very useful at global scales,but its accuracy at regional scales and for a particular case is uncertain. We have also checked if surface emissivity estimation from FVC values according to(16)and(17)is sensitive to the atmospheric correction for Landsat bands3and4.For this purpose,we have estimated FVC from NDVI computed using

TABLE IV

V ALUES OF A TMOSPHERIC P ARAMETERS O BTAINED F ROM THE

A TMOSPHERIC S OUNDING L AUNCHED ON J ULY13,2005AT10:48GMT O VER THE

B ARRAX A REA AND THE O NES E XTRACTED F ROM THE

ACPC

TABLE V

V ALUES OF THE D IFFERENCE B ETWEEN T HREE D IFFERENT R ETRIEVED LST I MAGES AND THE“G ROUND-T RUTH”LST I MAGE O BTAINED F ROM

I NVERSION OF THE RTE U SING AN A TMOSPHERIC S OUNDING AND MODTRAN C ODE.LST I MAGES H AVE B EEN R ETRIEVED U SING RTE AND A TMOSPHERIC P ARAMETERS F ROM THE ACPC(RTE_ACPC),U SING THE SC A LGORITHM W ITH AF S D IRECTLY C ALCULATED F ROM A TMOSPHERIC P ARAMETERS E XTRACTED F ROM THE A TMOSPHERIC S OUNDING (SC_T HEORY),AND U SING THE SC A LGORITHM W ITH THE E MPIRICAL AF S O BTAINED F ROM THE TIGR61D ATABASE

(SC_W)

digital counts(DCs).In this case,values of NDVI s=0.02and NDVI v=0.61were found.FVC values obtained from NDVI computed in DCs were used to obtain surface emissivity,which was used to retrieve LST from inversion of https://www.wendangku.net/doc/6516575909.html,parison against RTE_truth provided a mean difference(bias)of?0.1K and standard deviation of0.3K.A difference of?0.005K was found for60.5%of the pixels.This result suggests that in this particular case,it is not totally necessary to perform radiometric and atmospheric correction to retrieve FVC from a scaled NDVI as proposed in(17),at least in terms of LST retrieval using surface emissivities estimated from(16).

D.Implementation of the SC Algorithm

Once the SC JM&S algorithm has been revised and updated, we provided in this section a guide to implement the algorithm. Hence,to apply the SC algorithm to Landsat imagery,one can use the following procedures.

1)Convert DCs in band6into at-sensor thermal radiances

(L sen)using the linear relationship L sen=gain×DC+ offset.

2)Convert to brightness temperatures using(9)and effective

wavelengths presented in Fig.1.

3)Calculateγandδparameters using the simpli?ed expres-

sion given in(13).Original expression given in(10)can also be used.

4)Select appropriate coef?cients for the AFs,ψ1,ψ2,and

ψ3,according to Table II.One can select,for example, coef?cients obtained from TIGR61database,composed by a reduced set of atmospheric pro?les representative at

JIMéNEZ-MU?OZ et al.:REVISION OF THE SC ALGORITHM FOR LST RETRIEV AL FROM LANDSAT TIR DATA

347

Fig.6.Example of LST map obtained from Landsat-5data using the SC al-gorithm revised in this paper.Index map constructed from an RGB composition (bands3,2,and1),NDVI,and LSE maps are also https://www.wendangku.net/doc/6516575909.html,ndsat image was acquired on July13,2005over the agricultural area of Barrax(Albacete,Spain).

world-wide scale.However,if the study area is located in high latitudes usually with a low w content,TIGR1761 should be selected,since it is more suitable for lower w.

For open water or coastal areas,SAFREE402database could be used instead.

5)Once the coef?cients(c ij)for the AFs have been selected,

select an atmospheric water vapor content value(w) and calculate them from(7).Water vapor values can be obtained,for example,from ground-based measurements, atmospheric soundings,or MODIS products(MOD05).

6)Estimate LSE(ε).Selection of the appropriate method

forεretrieval relies on the user criteria.In Section III-D, we used a simple approximation betweenεand FVC, referred to as SNDVI method in[11].

7)At this stage,once L sen,γ,δ,ψ1,ψ2,ψ3,andεhave been

calculated,LST is?nally retrieved using(3).

Fig.6shows an example of the LST map obtained using the SC JM&S algorithm from the Landsat-5data discussed in Section III-D.

E.Feasibility of Using an LUT

We would like to emphasize that the SC JM&S algorithm does not pretend to be more accurate than other SC algorithms but to be an operational algorithm with minimum input data require-ments(onlyεand w).As was discussed in Section II-B,coef-?cients for AFs depend on the atmospheric sounding database used or,in other words,depend on the mean atmospheric water vapor content of these databases.Therefore,LST retrievals will depend also on the atmospheric sounding databases used to retrieve the AFs.In addition,SC algorithms provide poor results for high w values(typically w>3g·cm?2),which indicates that relationships between atmospheric parameters(τ, L↑,L↓)and water vapor are not satisfactory for a full range of w values.This fact suggests that coef?cients could be calculated

TABLE VI

S AME AS T ABLE V,BUT U SING LST I MAGES R ETRIEVED F ROM

I NVERSION OF THE RTE AND AN LUT OF A TMOSPHERIC

P ARAMETERS(RTE_LUT)AND U SING THE SC

A LGORITHM AND AN LUT OF AF S

(SC_LUT)

for different ranges of w values.For example,two different ranges were considered by Qin et al.[7],such as0.4–1.6 and1.6–3g·cm?2.Narrower ranges could also be considered to improve the estimation of atmospheric parameters from w values.Another possibility is to build a lookup table(LUT)and then interpolate according to the w value.This option has also been explored for the SC JM&S algorithm.For this purpose,the STD66database has been used,since it is composed by differ-ent standard atmospheres but scaled for a full range of w values. LUT has been constructed for the AFs.Then,according to the most appropriate standard atmosphere for the acquired Landsat image and the w value,AFs are interpolated.To compare results,an LUT in terms ofτ,L↑,and L↓instead of AFs has also been constructed.The results obtained in the comparison against the“ground-truth”map discussed in Section III-D are presented in Table VI.Note that by using an LUT,the SC JM&S algorithm decreases the error from1.5(see Table V)to0.9K. This error is similar to the one obtained when using the RTE and the LUT(0.7K).Note also that these errors are also lower than the one obtained with the RTE and the ACPC.We would like to emphasize that,as it is expected,the use of an LUT provides more accurate results than using statistical?ts for the AFs versus w,but at the same time,the use of an LUT prevents the user to apply an operational algorithm easily implemented following the guidelines presented in Section III-E.

IV.S UMMARY AND C ONCLUSION

SC algorithms are the unique algorithms for LST retrieval that can be applied to sensors with only one thermal chan-nel,which is the case of the sensors onboard the Landsat platforms.Inversion of the RTE is a priori the best option for LST retrieval from one thermal band,since it does not involve additional approximations.However,this technique requires an accurate knowledge of atmospheric parameters such as transmissivity and atmospheric upwelling and downwelling radiances,which is not always possible.In order to solve this problem,these atmospheric parameters are?tted versus more accessible parameters such as atmospheric water vapor content, air temperature,etc.However,these relationships involve a strong approximation,which implies that they are not valid for a full range of w values but only for low/moderate w values (w<3g·cm?2).Inaccuracies can also be found for very low w values(w<0.5g·cm?2),which indicates that the error introduced in the atmospheric correction procedure is higher than if no atmospheric correction is performed,due to the almost negligible atmospheric effect at this low w values.In these cases,only an emissivity correction as proposed by Artis and Carnahan[28]could be considered.In this paper,we have

348IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.47,NO.1,JANUARY2009

revised and updated in the case of Landsat-5and extended to Landsat-4and Landsat-7platforms the SC algorithm developed by Jimenez-Mu?oz and Sobrino[9],denoted throughout the paper as SC JM&S.In this way,LST could be retrieved from historical Landsat imagery databases.The algorithm relies in the concept of AFs,which are empirically expressed in terms only of water vapor content to minimize input data require-ments.It is dif?cult to establish?xed criteria in order to select the atmospheric database(STD,TIGR,SAFREE,or others) needed to compute the AFs,but the knowledge of w ranges in the test area can help in selecting the appropriate database.For instance,in the case of TIGR61database,its w range is well balanced,and it could be used as a global database.However, if the study area is located at high latitudes usually with a low w content,TIGR1761database should be more suitable.When in situ measurements of surface temperatures are available for a set of images,one can apply the SC algorithm using all the atmospheric databases and then select for the complete imagery data set that atmospheric database for which the best results in the validation were obtained.

SC JM&S is totally operational,and it can be adapted to any thermal band.Expected errors are between1and2K for w values between0.5and2g·cm?2.In one particular case,with w=1.58g·cm?2,the algorithm provided the same accuracy than inversion of RTE using atmospheric data extracted from NCEP models.Note that accurate LSTs for a wider range of w values can be obtained using an LUT,but this option prevents the reader to apply the algorithm by himself to its particular Landsat imagery.

The authors are working on the application of the SC al-gorithm to a long series of Landsat imagery over Catalonia (north–east of the Iberian Peninsula),which will illustrate better the performance of the algorithm.

A CKNOWLEDGMENT

The authors would like to thank C.Fran?ois and P.Leborgne(Météo-France)for providing the SAFREE database,and B.Sebag and C.Crevoisier from the Laboratoire de Météorologie Dynamique/Groupe Analyse du Rayonnement Atmosphérique of the Ecole Polytechnique(Paris,France)for providing the TIGR-3database and for the help in the database conversion to MODTRAN format.The authors would also like to thank L.Guanter(GeoForschungsZentrum Potsdam, Germany)who processed the atmospheric correction of the Landsat image.

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1982.

Juan C.Jiménez-Mu?oz received the Ph.D.degree in physics from the University of Valencia,Valencia, Spain,in2005.

He is currently a Research Scientist with the Global Change Unit,Department of Earth Physics and Thermodynamics,University of Valencia.His main research interests include thermal remote sens-ing and temperature/emissivity

retrieval.

Jordi Cristóbal received the B.S.degree in biology,

the M.S.degree in botany,and the M.S.degree in

environmental sciences from the Autonomous Uni-

versity of Barcelona,Cerdanyola del Vallès,Spain,in

1996,1998,and in2003,respectively,and the M.S.

degree in remote sensing and GIS from the Institute

for Space Studies of Catalonia,Barcelona,Spain,

in1999.He is currently working toward the Ph.D.

degree at the Autonomous University of Barcelona,

focusing on forest evapotranspiration retrieval by

means of medium and coarse spatial resolution re-

mote sensing data and GIS modeling.

He is also currently an Associate Professor with the Department of Geog-

raphy,Autonomous University of Barcelona.His main work has been done

in climate modeling using remote sensing and geographical data,in thermal

atmospheric corrections of satellite imagery,and in energy?ux modeling.He

has recently worked in water usage and snow coverage from long series of

satellite images and in landscape modeling.

Prof.Cristóbal is a member of the GRUMETS(Research Group of Methods

in Remote Sensing and

GIS).

JoséA.Sobrino received the Ph.D.degree in physics

from the University Of Valencia,Valencia,Spain

in1989.

He is currently a Professor of physics and remote

sensing and the Head of the Global Change Unit

(http://www.uv.es/ucg),Department of Earth Physics

and Thermodynamics,University of Valencia,

Valencia,Spain.He is the author of more than

100papers and a Coordinator of the European

projects WATERMED and EAGLE.His research

interest include atmospheric correction in visible and

infrared domains,the retrieval of emissivity and surface temperature from

satellite images,and the development of remote sensing methods for land cover

dynamic monitoring.

Prof.Sobrino has been a member of the Earth Science Advisory Committee

of the European Space Agency since November2003.He is the Chairperson

of First and Second International Symposium RAQRS(Recent Advances in

Quantitative Remote Sensing)

http://www.uv.es/raqrs.

Guillem Sòria received the Ph.D.degree in physics

from the University of Valencia,Valencia,Spain,

in2006.

He is currently a Research Scientist with the

Global Change Unit,Department of Earth Physics

and Thermodynamics,University of Valencia.His

present investigation includes the retrieval of sur-

face temperature,including land,ice,and sea

through multichannel and multiangle algorithms

from thermal-infrared remotely sensed data sup-

plied by ATSR-1,ATSR-2,and ENVISAT-AATSR

sensors.

Miquel Ninyerola received the B.S.degree in biol-

ogy and the Ph.D.degree in GIS modeling from the

Autonomous University of Barcelona,Cerdanyola

del Vallès,Spain,in1994and2001,respectively.

First,his research focused on climatological map-

ping by combining spatial interpolation,multivariate

statistics,and GIS.In addition,he developed DEM-

based solar radiation maps and climatic-envelope-

based vegetation suitability maps.He has recently

worked on re?ning(mainly by introducing remote

sensing information)and applying these climatic and

suitability models in?elds such as landscape ecology,natural hazards,or plant

ecophysiology.He is currently a Full Professor with the Department of Animal

Biology,Plant Biology and Ecology,Autonomous University of Barcelona.

His current research deals with statistical downscaling techniques to develop

future climatic scenarios where to project the present-day vegetation suitability

models.

Prof.Ninyerola is a member of the GRUMETS(Research Group of Methods

in Remote Sensing and

GIS).

Xavier Pons received the B.S.degree in biology,

the M.S.degree in botany,and the Ph.D.degree in

remote sensing and GIS from the Autonomous Uni-

versity of Barcelona,Cerdanyola del Vallès,Spain,

in1988,1990,and,1992,respectively.

His main work has been done in radiometric and

geometric corrections of satellite imagery,in cartog-

raphy of ecological and forest parameters from air-

borne sensors,in studies of the spectral response of

Mediterranean vegetation,and in GIS development,

both in terms of data structure and organization and

in terms of software writing(MiraMon).He has recently worked in descriptive

climatology models,in modeling forest?re hazards,and in analysis of land-

scape changes,water usage,and snow coverage from long series of satellite

images.He is currently working in the implications of image compression

on remote sensing.He is currently a Full Professor with the Department of

Geography,Autonomous University of Barcelona,and coordinates research

activities in GIS and remote sensing with the Centre for Ecological Research

and Forestry Applications,Cerdanyola del Vallès.

Prof.Pons is a member of the GRUMETS(Research Group of Methods in

Remote Sensing and GIS).