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Synergistic use of the two-temperatureand split-window methods for land-surface temperature retrievalL. F. Peres a b , C. C. Dacamara b , I. F. Trigo b c & S. C. Freitas ca Instituto Nacional de Pesquisas Espaciais – Centro de Previsãode Tempo e Estudos Climáticos – Rod. Pres Dutra , km 39, CEP12630-000, Cachoeira Paulista/SP, Brazilb Univesity of Lisbon , CGUL, IDL, Campo Grande, Ed C8, Piso 6,1749-016 , Lisbon , Portugalc Land SAF, Instituto de Meteorologia , 1749-077 , Lisbon ,PortugalPublished online: 13 Sep 2010.

To cite this article: L. F. Peres , C. C. Dacamara , I. F. Trigo & S. C. Freitas (2010) Synergisticuse of the two-temperature and split-window methods for land-surface temperature retrieval,International Journal of Remote Sensing, 31:16, 4387-4409, DOI: 10.1080/01431160903260973

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Synergistic use of the two-temperature and split-window methods forland-surface temperature retrieval

L. F. PERES*†‡, C. C. DACAMARA‡, I. F. TRIGO‡§ and S. C. FREITAS§

†Instituto Nacional de Pesquisas Espaciais – Centro de Previsao de Tempo e Estudos

Climaticos – Rod. Pres Dutra, km 39, CEP 12630-000, Cachoeira Paulista/SP, Brazil

‡Univesity of Lisbon, CGUL, IDL, Campo Grande, Ed C8,

Piso 6, 1749-016, Lisbon, Portugal

§Land SAF, Instituto de Meteorologia, 1749-077, Lisbon, Portugal

(Received 31 May 2007; in final form 2 November 2008)

A strategy is presented with the aim of achieving an operational accuracy of 2.0 K

in land-surface temperature (LST) from METEOSAT Second Generation (MSG)/

Spinning Enhanced Visible and Infrared Imager (SEVIRI) data. The proposed

method is based on a synergistic usage of the split-window (SW) and the two-

temperature method (TTM) and consists in combining the use of a priori land-

surface emissivity (LSE) estimates from emissivity maps with LST estimates

obtained from SW method with the endeavour of defining narrower and more

reliable ranges of admissible solutions before applying TTM. The method was

tested for different surface types, according to SEVIRI spatial resolution, and

atmospheric conditions occurring within the MSG disc. Performance of the

method was best in the case of relatively dry atmospheres (water-vapour content

less than 3 g cm-2), an important feature since in this case SW algorithms provide

the worst results because of their sensitivity to uncertainties in surface emissivity.

The hybrid method was also applied using real MSG/SEVIRI data and then

validated with the Moderate resolution Imaging Spectroradiometer (MODIS)/

Terra LST/LSE Monthly Global 0.05� geographic climate modeling grid (CMG)

product (MOD11C3) generated by the day/night algorithm. The LST and LSE

retrievals from the hybrid-method agree well (bias and root mean square error

(RMSE) of -0.2 K and 1.4 K for LST, and around 0.003–0.02 and 0.009–0.02 for

LSE) with the MOD11C3 product. These figures are also in conformity with the

MOD11C3 performance at a semi-desert where LST (LSE) values is 1–1.7 K (0.017)

higher (less) than the ground-based measurements.

1. Introduction

During the last two decades land-surface experiments (Beljaars and Bosveld 1997,

Chen et al. 1997, Chang et al. 1999, Jochum et al. 2000, Xia et al. 2002) have greatly

contributed to a better understanding of land-surface processes and their role in

weather and climate (Feddes et al. 1998). Systematic comparisons of land-surface

parameterization schemes (e.g. Henderson-Sellers et al. 1997) have in turn contrib-

uted to demonstrate the positive impact of a better characterization of land-surface

*Corresponding author. Email: [email protected]

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2010 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160903260973

International Journal of Remote Sensing

Vol. 31, No. 16, 20 August 2010, 4387–4409

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mailto:[email protected]

http://www.tandf.co.uk/journals

processes both in Numerical Weather Prediction (NWP) and Climate Modelling.

Therefore, most weather centres have already incorporated advanced surface para-

meterizations schemes (e.g. Viterbo and Beljaars 1995, Bazile and Giard 1996,

Bringfelt 1996, Zhang et al. 2001, Belair et al. 2003, Miao et al. 2007) in their

operational models. However, an accurate parameterization of the land-surfaceprocesses is still hampered by the complexity of the processes involved, as well as by

data availability of land-surface parameters. The most common approach is to

provide inputs based on point measurements and spatial interpolations, but this

procedure has proved to be time-consuming and, in many cases, impractical and

insufficient (Bach and Mauser 2003).

In such context, sufficiently accurate measurements of land-surface temperature

(LST) and an appropriate characterization of the diurnal cycle of LST (DCT) rise as

first priority due to their important role in the surface energy budget. Information onLST may be used to derive both sensible and latent heat fluxes, the former because of

its direct relationship with thermodynamic temperature and the latter, in an indirect

way, as a residual of the energy balance equation. Since LST varies spatially according

to soil type, land cover and land use, as well as temporally with the time of day,

weather conditions and season of the year, conventional ground observations of LST

are usually not representative for large areas. Instruments on-board Earth observa-

tion satellites working in the thermal infrared (TIR) spectrum may provide measure-

ments of LST on a global basis with uniformity (i.e. the same sensor being used atdifferent places) and continuity (i.e. a single sensor providing long time series of data)

at spatial and temporal resolutions that are suited for most modelling applications

(Bouyssel 2002, Viterbo 2002).

METEOSAT Second Generation (MSG), i.e. the new generation of geostation-

ary meteorological satellites of the European Organisation for the Exploitation of

Meteorological Satellites (EUMETSAT), possesses temporal, spatial and spectral

characteristics that make it especially suitable for the retrieval of LST and

DCT. The Spinning Enhanced Visible and Infrared Imager (SEVIRI), MSG’smain payload, is a scanning radiometer that provides image data in 12 channels

covering a wide range of wavelengths from visible to TIR. The present study

utilizes the SEVIRI channels IR10.8 and IR12.0 that are located in the atmo-

spheric window where the atmospheric absorption is minimal, and accordingly

most of the emitted radiance by ground surface reaches the outer space. The

SEVIRI instrument is designed to produce the image of the Earth full disc from a

spinning geostationary satellite nominally centred over 0� longitude with a 3 km

sampling distance at the subsatellite point and with a nominal repeat cycle of15 min (Schmid 2000).

The splitting of the single broadband METEOSAT Visible and Infrared

Imager (MVIRI) TIR channel into two new channels (i.e. IR10.8 and IR12.0)

allows the new generation of METEOSAT satellites to correct for the atmo-

spheric effects on remotely sensed surface temperature through use of split-

window (SW) techniques. Such kind of method assumes an a priori knowledge

of land-surface emissivity (LSE) and this requirement is fulfilled for some sur-

face such as oceans and forests, where LSE remains essentially the same every-where. Taking advantage of the two adjacent IR10.8 and IR12.0 channels,

Madeira (2002) has developed and investigated a SW algorithm for LST retrie-

vals using MSG/SEVIRI data. Research was undertaken within the framework of

the Satellite Application Facility on Land Surface Analysis (LSA-SAF) that

4388 L. F. Peres et al.

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integrates the decentralized Ground Segment of EUMETSAT. The developed SW

algorithm is currently pre-operational (see the LSA-SAF web site at http://land-

saf.meteo.pt) and has proved to be computationally efficient, but its ability to meet

the pre-defined goal of 2.0 K in LST accuracy (LSA-SAF, 2003) crucially depends

on an adequate a priori knowledge of land-surface emissivity (LSE). Moreover,when used together with LSE maps that are currently being derived on a pre-

operational basis (Peres and DaCamara 2005), the developed SW algorithm does

not provide LST estimations within the prescribed accuracy over the desert and

semi-desert areas within the MSG disk. In fact, over these areas LSE is highly

variable and the above-mentioned studies have pointed out the inadequacy of the

SW algorithm and therefore the need of using methods that allow retrieving LST

without a direct knowledge of LSE. In this respect, Peres and DaCamara (2006)

have assessed the performance of the two-temperature method (TTM), which doesnot strictly assume an a priori knowledge of LSE and allows a separation of LST

and LSE from radiance measurements if surface is observed at two temperatures

and if LSE does not change between observations (Watson 1992, Faysash and

Smith 1999, 2000). Inversion methods, such as TTM, that allow recovering both

LST and LSE require independent atmospheric corrections, and therefore, both

land surface parameters will strongly depend on atmospheric profile uncertainties.

Accordingly, constrained optimization algorithms are usually needed in order to

obtain feasible estimations of LST and LSE. Results based on a least-squareoptimization algorithm suggest that TTM may be used as a complementary

method for LST retrievals in those areas where LSE is not well known a priori,

but there is the limitation due to the fact that the optimization approach imposes

substantial mathematical and numerical requirements (i.e. use of different initial

guess vectors), which may prevent the method of becoming operational given the

narrowness of the time window allowed by the MSG/SEVIRI system. In addition,

Peres and DaCamara (2006) have shown that the accuracy of the retrieved values

also depends upon the chosen constraints, as well as the initial guesses, and thereforean unreliable range of admissible solutions may deteriorate the TTM performance.

In order to circumvent these difficulties, we propose and investigate in this work a

new hybrid procedure that is based on a synergistic use of SW and TTM, and the goal

is to combine the most attractive features of both methods (table 1) while mitigating

some of the pitfalls.

Table 1. Comparison between advantages and disadvantages of TTMand SW. Advantages are in bold.

TTM SW

Not required ��!EmissivityRequired & sensible

(Poor LST accuracy)Required & sensible (poor

LST and LSE accuracy) ��!Atmospheric profile

Not required

Required (notcomputationally efficient)

��!Radiative transfer simulationsNot required

(computationallyefficient)

Synergistic use of two-temperature and split-window methods 4389

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http://land-saf.meteo.pt



2. Method and data

2.1 Hybrid method

The rationale of the hybrid procedure we are proposing consists of combining the use

of a priori LSE estimates from surface emissivity maps (Peres and DaCamara 2005)with LST estimates obtained from a SW algorithm (Madeira 2002) with the aim of

defining narrower and more reliable ranges of admissible solutions before applying

TTM. Accordingly, the LST (LSE) solution is constrained to lie between TSW� dTSW

(eM � deM), where TSW (eM) and dT SW (deM), respectively, denote the estimates and

the uncertainty in LST (LSE) provided by the SW algorithm (LSE maps). This

strategy is expected to increase the efficiency of TTM from a computational point

of view and especially to improve the quality of LST retrievals, namely by reaching the

required accuracy of 2.0 K over areas where LSE is not well known a priori.

2.1.1 Two-temperature method (TTM). TTM allows retrieving LST and LSE from

radiance measurements if the surface is observed at two different temperatures. The

method assumes that LSE does not change between observations and that atmo-

spheric effects may be adequately estimated by means of a radiative transfer model

(RTM). Assuming the Earth’s surface as a Lambertian emitter-reflector and neglect-

ing atmospheric scattering, the radiance, recorded in a given channel c by a sensor

on-board a satellite observing the Earth’s surface under a zenith angle � may be

represented by the radiative transfer equation (RTE) and denoted by LRTEc:

LRTEcð�Þ ¼ ecBcðTSÞtcð�Þ þ L"cð�Þ þ L#cð1� ecÞtcð�Þ; (1)

where ec, Bc(TS), tc(�), L"cð�Þ and L#c respectively denote the LSE, the emitted radiancegiven by Planck’s function for the surface temperature TS, the atmospheric transmit-

tance and the atmospheric upward and downward radiances. Details may be found in

Peres and DaCamara (2006). The atmospheric parameters tc(�), L"cð�Þ and L#c in

equation (1) may be estimated based on information about the atmospheric state,

namely from humidity and temperature profiles, to be used as inputs to a

RTM. Taking into account TTM assumptions, we are led to a system of n � m

equations with n + m unknowns (i.e. LSE values at n channels plus LST values at m

observations), and such a system may be solved when n and m . 1. Assuming that apair of observations is available (performed at times t1 and t2 in the two SEVIRI

channels IR10.8 and IR12.0) then the four unknown surface parameters (i.e. e at

IR10.8 and IR12.0, and TS at t 1 and t 2) may be obtained by solving a system of four

equations, each one of the form given by equation (1). Previous studies (Faysash and

Smith 1999, 2000, Peres and DaCamara 2004, 2006) have shown that measurement

uncertainties induce large variations in LST and LSE solutions when the system of

equation (1) is solved algebraically and therefore an optimization approach that

allows constraining the solution has to be applied in order to stabilize the solution.Following the above-mentioned studies, a sequential quadratic programming (SQP)

method was used in the present work for solving the continuous constraint problem.

SQP methods represent the state of the art in nonlinear programming methods. It is

an iterative method starting from some initial point and converging to a constrained

local minimum. At each iteration, one solves a quadratic program (QP) that models

the original nonlinear constrained problem at the current point. The solution to the

QP is used as a search direction to find an improving point, which is used in the next


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iteration (Gill et al. 1981, Powell 1983, Fletcher 1987, Shang et al. 2001). The SQP solver

fmincon from the Matlab Optimization Toolbox is used in this study to find the

unknowns that minimize the objective function f(x) given by the root square differences

between radiances LtOBSc (observed radiances) and Lt

RTEc (computed radiances by

means of the RTE model as given by equation (1)) in channel c at time t:

f ðxÞ ¼X

c¼10:8; 12:0t¼t1; t2

LtOBScð�Þ � Lt

RTEcð�Þ� �2

264

375

1=2

(2)

subject to

CiðxÞ � 0: i ¼ 1; . . . ; k;

where x is the vector of the four land-surface parameters and the vector function Ci (x )returns a vector of length k containing the values of the inequality constraints evaluated

at x. It is worth mentioning that the Matlab fmincon solver accepts problems in the

constrained form and therefore, it is not necessary to convert a constraint problem into

an unconstrained penalty function problem (Nocedal and Wright 1999). Although

TTM allows a unique set of parameter values to be found, several combinations of

LST and LSE may lead to values of radiance that are quite alike to those associated with

the correct values of LST and LSE resulting in strings of local minima of f(x). As

discussed in Peres and DaCamara (2006), a one way of improving the solution is to runthe SQP solver several times starting from different initial solutions defined within a

region of physically admissible solutions and then, selecting the solution associated with

the minimum value of f(x); the better the starting point and the narrower the defined

region of admissible solutions the more efficient the search procedure will be.

2.1.2 Emissivity maps. The LSE maps relies on the vegetation cover method

(VCM) (Caselles and Sobrino 1989) that considers land-surface as an heterogeneous(both in LST and LSE) and rough system, that is made of a mixture of vegetation and

ground where the row crops form a cavity consisting of crop walls with ground in

between. Accordingly, the effective emissivity ec of such system in a given channel c is

given by (Caselles et al. 1997):

ec ¼ eDc þ eIc; (3)

where the first term on the right-hand side of equation (3) is related to the radiance

directly emitted by the system. Assuming that the vegetation top and side have thesame emissivity eVc, the term eDc becomes:

eDc ¼ eVc� þ eGcð1� �Þ; (4)

where eGc is the emissivity of the ground, and � denotes the fractional vegetation cover(FVC). The second term on the right-hand side of equation (3) is related to the

radiance indirectly emitted through internal reflections occurring between crop

walls and the ground, and is given by:

eIc ¼ ð1� eGcÞ eVc F ð1� �Þ þ ð1� eVcÞ eGc G þ ð1� eVcÞ eVc F 0½ � ps; (5)

where ps is the fractional amount of the vegetation side, and F, G and F 0 are

geometrical factors that determine the proportions of radiation respectively from


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vegetation side that reaches the ground, from the ground that reaches the vegetation

side, and from the vegetation side that reaches the adjacent vegetation side. These

geometrical factors are given by Valor and Caselles (1996) and may be determined if the

height H of the different boxes and the distance S between them are known. Since the

theoretical expression of eIc is quite complex, a quadratic form to simulate the factor eIc

was adopted following Valor and Caselles (1996). Accordingly, equation (5) becomes:

eIc ¼ 4heIci � ð1� �Þ; (6)

where heIci is defined in Peres and DaCamara (2005) by the mean of different values of

eIc that are computed for a reasonable range of H and S.The application of VCM consists of the following four steps. First, a database of

spectral reflectance measurements for different types of materials (e.g. Salisbury and

D’Aria 1992) is used to compute LSE values within SEVIRI channels. Then, a land-

cover map (e.g. Loveland et al. 2000, Friedl et al. 2002) is used in order to allow

distinguishing among the different types of land-surfaces occurring within the Earth

disk observed from MSG. The vegetation and ground proportions within a pixel are

then obtained by means of a vegetation index. Finally, the LSE values of vegetation

and ground samples (computed in the first step) are used to assign, respectively, thevalues of eVc and eGc for each land-cover class. The effective emissivity is readily

computed using equations (4) and (6).

2.1.3 Split-window algorithm. SW algorithms correct for atmospheric effects based

on the differential absorption in adjacent TIR bands. As the SW technique has proved

to be very successful for the sea surface (McMillin 1971) and has the advantage of

simplicity, different extensions of the method for LST determination have been

proposed in recent years (Becker and Li 1990, Franca and Cracknell 1994, Wan andDozier 1996). The above-mentioned studies have shown that it is possible to extend

SW methods over land-surface provided that emissivity effects are accounted for. The

SW algorithm for LST retrievals with SEVIRI data follows the approach developed

by Becker and Li (1990) and Wan and Dozier (1996), i.e.

TS ¼ b0 þ b1 þ b2

1� eeþ b3

�ee2

� �TB10:8 þ TB12:0

2

þ b4 þ b5

1� eeþ b6

�ee2

� �TB10:8 � TB12:0

2;

(7)

where b0; . . . ; b6 are the so-called SW coefficients that were estimated by regression

analysis of simulation data, T B10.8 and T B12.0 are the brightness temperatures (BTs)

in channels IR10.8 and IR12.0, e ¼ e10:8 þ e12:0ð Þ=2 is the mean LSE in these channels,

and �e ¼ e10:8 � e12:0 is the respective LSE difference.

Following Wan and Dozier (1996), we have optimized the SW algorithm by comput-ing coefficients that vary with satellite zenith angle (SZA), atmospheric water vapour

and lower boundary air temperature TA (the air temperature at 2-metres). Accordingly,

the atmospheric temperature profiles were separated into two groups based on TA

values, namely cold (TA � 280.0 K) and warm (TA . 280.0 K) atmospheres. The water

vapour content w was split into intervals of 1.0 g cm-2 resulting in six different intervals

(table 2). Moreover, the coefficients were considered as SZA dependent in accordance

with eight selected angles.


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2.2 Simulated data

Simulations of top of atmosphere (TOA) radiances LOBS were made using MODTRAN4

(Berk et al. 2000) that allows prescribing the surface parameters LST and LSE, as well as

defining the geometrical path and the sensor characteristics. The atmospheric contribution

was computed using three geographical-seasonal standard atmospheres available inMODTRAN4, namely Mid-Latitude Summer (MLS), Mid-Latitude Winter (MLW)

and Tropical (TROP) atmospheres. During the radiative transfer simulations we have

prescribed three LST values in MODTRAN4 respectively given by (TA - 5.0 K), TA and

(T Aþ 5.0 K); LSE was in turn assumed to span from 0.90 to 0.98 in steps of 0.02. We have

also prescribed LST temperature differences �T of 2.0 K between each observation

(i.e. Tt2

S ¼ Tt1

S þ�T). We have also assumed differences in emissivity �e of - 0.01,

0.00 and þ 0.01 between channels IR10.8 and IR12.0 (i.e. e10:8 ¼ e12:0 þ�e). In

order to simulate a set of realistic cases, we have considered the following situa-tions: (1) LST is (a) overestimated (TSW ¼ LST þ dTSW), (b) correctly estimated

(TSW ¼ LST) and (c) underestimated (TSW ¼ LST - dTSW) by the SW algorithm;

(2) LSE is (a) overestimated (eM ¼ LSE þ deM), (b) correctly estimated (eM ¼ LSE)

and (c) underestimated (eM¼LSE - deM) from LSE maps. The above consideration

results in nine new simulations differing in the used initial vector and constraints.

The performance of the synergy between TTM and SW was assessed by perturbing

the simulated TOA radiances with the noise associated with the SEVIRI channels

(IR 10.8 and IR 12.0) and by introducing into the atmospheric profiles the inaccura-cies associated with the specified values of temperature and humidity. However, it is

worth emphasizing that the accuracy of the atmospheric correction was assumed to be

independent of the approximations used by the RTM.

Levels of noise introduced into the SEVIRI channels were based on the noise

equivalent temperature (NE�T ) at 300K of IR10.8 (0.11 K) and IR12.0 (0.15 K)

(Dammann and Mueller 2005) that were converted into noise equivalent radiances

(NE�L ), respectively 0.185 and 0.262 mW m-2 sr-1 (cm-1)-1 for channels IR10.8 and

IR12.0. A 100 randomly generated perturbations were then added to the simulatedTOA radiances, which were considered as normally distributed around the zero mean,

with standard deviations given by the NE�L of the SEVIRI channels. Because there

is no vertical sounding instrument on-board MSG, we have assumed that the required

information about the atmospheric state may be obtained from NWP forecasts.

Accordingly, the effect of the model errors in the temperature and humidity profiles

were simulated by perturbing the reference profiles MLS, MLW and TROP with

values based on the background error covariance matrix used in the assimilation

Table 2. Water vapour content intervals.

Atmospheres Water vapour intervalsWater vapour content

(g cm-2)

Warm w1 0 � w , 1w2 1 � w , 2w3 2 � w , 3w4 3 � w , 4w5 4 � w , 5w6 w � 5

Cold w1 0 � w , 1w2 1 � w , 2


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schemes of the Global Circulation Model operated at European Centre for Medium-

Range Weather Forecasts (ECMWF) (Fillion and Mahfouf 2000). The imposed

perturbations on the atmospheric profiles result into three sets of 100 perturbed

atmospheres based respectively on MLS, MLW and TROP and translate into uncer-

tainties on the atmospheric parameters in equation (1), namely, tc(�) (transmittance),L"cð�Þ (upward atmospheric radiance) and L#c (downward atmospheric radiance).

Distributions of the perturbed atmospheric parameters and the respective means

and standard deviations (SD) are shown respectively in figures 1 and 2, and table 3.

Accordingly, the results for each sensitivity experiment (i.e. noise in the satellite

radiances and measurement errors in the atmospheric profiles) correspond to a set of

simulations based on five values of LSE � 3 values of LST � 100 perturbations � 9 a

priori estimates of the state (used to simulate a set of realistic cases) � 3 spectral LSE

Figure 1. Distributions of the perturbed atmospheric parameters, namely transmittance (a),atmospheric upward radiance (b) and atmospheric downward radiance (c), with regard tochannel IR10.8 for MLS (i), MLW (ii) and TROP (iii).


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differences ¼ 40 500 simulations for each reference atmospheric profile, i.e. MLS,

MLW and TROP standard atmospheres.Finally, it is worth noting that, in all cases, validation was performed based on

differences between the values of LST and LSE as retrieved with the hybrid

method and the corresponding values used in MODTRAN4 to simulate the

TOA radiances.

3. Results and analyses

3.1 Definition of reliable constrains

Since the used spectral libraries only provide reflectance measurements for individual

samples, TIR versions of bi-directional reflectance distribution function (BRDF)

Figure 2. Distributions of the perturbed atmospheric parameters, namely transmittance (a),atmospheric upward radiance (b) and atmospheric downward radiance (c), with regard tochannel IR12.0 for MLS (i), MLW (ii) and TROP (iii).


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models were first applied to relate these component reflectance measurements to those

of structured surfaces (Snyder and Wan 1998, Snyder et al. 1998). For instance, the

above-mentioned models were used to determine the BRDF and then hemisphericallyintegrate it in order to obtain the directional hemispherical reflectance (DHR) and

LSE of a given canopy from laboratory measurements taken on individual leaves.

Accordingly, the row crops LSE in VCM were computed from the BRDF volumetric

model (Roujean et al. 1992), whereas a rough-surface specular BRDF model (Snyder

and Wan 1998) was used in the case of water and ice. Assignment of LSE from direct

measurements (ground) and from the volumetric (vegetation) and specular (water and

ice) models to IGBP classes was performed using about 150 samples that were used

individually or combined in order to characterize the 17 IGBP land-cover classes:1 – Evergreen Needleleaf Forest; 2 – Evergreen Broadleaf Forest; 3 – Deciduous

Needleleaf Forest; 4 – Deciduous Broadleaf Forest; 5 – Mixed Forest; 6 – Closed

Shrublands; 7 – Open Shrublands; 8 – Woody Savannahs; 9 – Savannahs;

10 – Grasslands; 11 – Permanent Wetlands; 12 – Croplands; 13 – Urban and Built

Up; 14 – Cropland/Natural Vegetation; 15 – Snow and Ice; 16 – Barren or Sparsely

Vegetated; 17 – Water. Based on the combination of vegetation and ground samples

used to describe the IGBP classes, information on the maximum LSE error due to the

LSE variability in each class was obtained (see Peres and DaCamara (2005) fordetails). Using this information together with the uncertainty on heIci and with a

relative error on FVC of � 25%, which is an appropriate value for FVC estimates

based on vegetation indices (Caselles et al. 1997), a sensitivity analysis on VCM was

performed in order to assess the LSE error of each IGBP class for channels IR10.8 and

IR12.0 (figure 3). It is worth noting that solely classes 16 (Barren or Sparsely

Vegetated) and 15 (Snow and Ice) present relative errors greater than �1.5% for

channels IR10.8 and IR12.0. This is explained by the fact that class 16 is composed of

different materials and therefore it is the most difficult class to typify, thus presentinga larger LSE variation. On the other hand, the two components (snow and ice) of class

15 present different behaviour, the snow being Lambertian at all wavelengths and ice

being predominantly specular in TIR (Salisbury et al. 1994). It is worth noting that the

LSE error for each land-cover class must be taken into account together with the

respective proportion of the total land-surface area (Snyder et al. 1998). Accordingly,

Table 3. Means and standard deviations (SD) of the perturbed atmospheric parameters and thecorrect values of the atmospheric parameters relating to MLS, MLW and TROP for channels

IR10.8 and IR12.0. L"cð�Þ and L#c are given in mW m-2 sr-1 (cm-1)-1.

MLS MLW TROP

Parameter Correct Mean SD Correct Mean SD Correct Mean SD

Channel IR10.8tc(�) 0.61 0.60 0.08 0.90 0.90 0.02 0.44 0.44 0.08

L"cð�Þ 35.3 36.1 7.4 5.9 6.0 1.1 53.2 53.6 7.6

L#c 43.0 43.8 8.6 7.3 7.4 1.3 64.3 64.6 8.7

Channel IR12.0tc(�) 0.47 0.46 0.09 0.85 0.85 0.03 0.30 0.30 0.08

L"cð�Þ 54.9 55.6 9.6 11.1 11.2 2.0 76.5 76.5 8.3

L#c 66.4 67.0 10.8 13.87 14.0 2.4 91.9 91.8 9.4


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we have computed the percentage of pixels in the MSG disk that belong to each class

(table 2) for two land cover databases, namely IGBP-DIS land cover (Loveland et al.

2000) and MODIS MOD12Q1 land cover product (Friedl et al. 2002). Results shown

in figure 3 and in table 4 indicate that about 73% of the land-surfaces within the MSGdisk present relative errors less than �1.5% for channels IR10.8 and IR12.0 and

almost all (i.e. 26%) of the remaining areas, corresponding to class 16 (Barren or

Sparsely Vegetated), have relative errors of�2.0%. These results will be used to assess

the sensitivity of the developed SW algorithm to the uncertainties in the LSE maps.

In the case of SW the accuracy of LST essentially depends on the following three

main sources of error; (1) the error from the atmospheric correction, which was

quantified by the error of the regression model, (2) the error due to the uncertainty

in the LSE values, which was assumed to be known a priori and was directly used inthe input to the SW algorithm and (3) the error due to the instrument performance

Figure 3. LSE relative errors for channels IR10.8 (a) and IR12.0 (b) with respect to an error of�25% in FVC.

Table 4. Percentage of each land cover class.

Percentage (%)

IGBP class MOD12Q1 IGBP-DIS

1 ¼ Evergreen needleleaf forest 1.9 0.82 ¼ Evergreen broadleaf forest 2.8 14.53 ¼ Deciduous needleleaf forest 0.0 0.04 ¼ Deciduous broadleaf forest 0.5 0.85 ¼Mixed forest 1.1 1.16 ¼ Closed shrublands 0.7 2.07 ¼ Open shrublands 15.8 8.28 ¼Woody savannas 10.7 10.69 ¼ Savannas 18.0 11.2

10 ¼ Grasslands 0.0 5.611 ¼ Permanent wetlands 0.1 0.212 ¼ Croplands 7.0 9.513 ¼ Urban and built up 0.1 0.114 ¼ Cropland/natural vegetation 4.2 9.115 ¼ Snow and Ice 0.9 0.616 ¼ Barren or sparsely vegetated 26.2 25.7Total 100.0 100.0


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that was quantified by the NE�T at 300 K of channels IR 10.8 (0.11 K) and IR 12.0

(0.15 K). It may be noted that the total LST error dT SW was computed under the

assumption that the three sources of errors are independent:

dTSW ¼ ðdTATMÞ2 þ ðdTeÞ2 þ ðdTNÞ2h i1=2

; (5)

where dTATM, dT e and dT N are the errors due to the atmospheric correction, the LSE

uncertainty and the radiometric noise, respectively. The SZA dependence of the total

LST error for uncertainties of 0.010, 0.015 and 0.020 in LSE are shown in figures 4–6,respectively. It is worth mentioning that the values of 0.010, 0.015 and 0.020 are based

on the range of errors in the LSE maps.

Results shown in figures 3–6, as well as in table 4, indicate that using a SW algorithm

together with emissivity maps allows to retrieve LST within the established goal of 2.0 K

in accuracy for virtually all atmospheric conditions over areas where errors on LSE

maps are of the order of 0.015. Such areas cover 73% of the land-surfaces within

the MSG disk and for almost all of the remaining areas (i.e. 26%), where the

LSE maps have an inaccuracy deM of the order of 0.020, the error dTSW in LST isabout �3.0 K. Based on the uncertainties of LSE maps as well as on the sensitivity of

SW to LSE errors, we have constrained the LST and the LSE solutions to lie respec-

tively between TSW � 3.0 K and eM � 0.02.

3.2 Results for the hybrid-method

In order to assess the improvements on LST and LSE estimations allowed by the

proposed hybrid method, we have considered the following three cases: (1) TTM isused alone, (2) SW is used alone and (3) the new hybrid method is applied. Results of

the TTM alone and the SW method alone were obtained for the same simulated cases

that were used to assess the sensitivity of the hybrid method. Accordingly we have

followed Peres and DaCamara (2006) and constrained LSE and LST to lie respec-

tively between 0.90 and 0.99, and between BT and BTþ 10.0 K. The set of initial guess

vectors was then defined within the space of admissible solutions in steps of 0.01 for

LSE and 1.0 K for LST resulting in a set of 110 initial guess vectors. It may be noted

that the number of initial guesses for the hybrid method is reduced to 35, a figure thatis one-third of the original set of 110 considered when using TTM alone. It is also

worth noting that results for SW refer to an uncertainty of 0.020 in LSE, a figure that

reflects the largest error in the LSE maps.

Values of bias and root mean square error (RMSE) for LST and LSE are shown in

table 5 for the three considered atmospheres (MLS, MLW and TROP). Histograms of

errors in LST and LSE for MLS, MLW and TROP are also shown in figure 7 for the

proposed hybrid method.

The synergy between TTM and SW methods has provided LST values with bias(RMSE) of 0.2 (1.3), 0.0 (1.0) and 0.4 K (2.0 K) for MLS, MLW and TROP,

respectively, whereas for LSE retrievals the corresponding obtained values were

0.000 (0.018), 0.000 (0.018) and 0.006 (0.020). These figures demonstrate the better

performance of the hybrid method and are worth being compared with those obtained

when using TTM alone, namely the bias (RMSE) of LST and LSE that ranged

respectively from 0.1 to 0.4 K (from 2.1 to 2.8 K) and from 0.005 to 0.010 (from

0.040 to 0.055). Results in table 5 also show that the hybrid method is capable of

providing better estimates of LST than SW technique in the case of MLS and MLW


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Figure 4. Comparison between the total LST error for the six w intervals in warm (a) and cold(b) conditions. Numbers 1 to 6 refer to w1, w2, w3, w4, w5 and w6, respectively. Results refer to anuncertainty of 0.010 in LSE. Different scales are used for warm and cold conditions in order toallow a better display of the total LST error.




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atmospheric profiles. However, this is not true for TROP, i.e. in the case of very wet

atmospheres, a feature that is discussed below.

The proposed new hybrid method seems therefore to provide better results than those

from the single usage of either TTM or SW and this is especially true in the case of

atmospheric profiles characterized by a lower water vapour content w, namely MLW

(w ¼ 0.85 g cm-2) and MLS (w ¼ 2.92 g cm-2). This is an important feature since SW

algorithms are more sensitive to LSE uncertainties in the case of dry atmospheric condi-tions. Besides, results shown in table 5 indicate that it is not necessary to know LSE with

high accuracy for wet atmospheres since the sensitivity of SW to LSE decreases as the

atmospheric water vapour content increases. This is due to the fact that the emissivity

effect on the emitted surface radiance is largely compensated by the downward atmo-

spheric TIR radiance that is reflected by the surface (Sobrino et al. 1991, Wan and

Dozier 1996). In fact, in the case of wet atmospheres (i.e. w . 3.0 g cm-2), the SW

algorithm may retrieve LST values within the desired accuracy of 2.0 K even when errors

in LSE are as large as 0.020. Conversely, for dry conditions, the LST error due touncertainties in LSE may be quite significant. For instance, in the case of relatively dry

atmospheres (i.e. w , 3.0 g cm-2), errors less than 2.0 K are only achievable when LSE is

known with an accuracy not exceeding 0.015. Since the hybrid method is able to provide

LST retrievals with accuracy better than 1.3 K for atmospheres with w , 3.0 g cm-2 it

proves to be especially useful for those surface and atmospheric conditions where SW is

not accurate enough.

3.3 Validation using satellite data

The aim of the present section is to perform a quality assessment of the proposed

hybrid method using real satellite data. In order to compare the results, LST values

are also retrieved using the SW method alone. In such context, the MOD11C3

Table 5. LST and LSE bias and RMSE for the simulated cases. For each atmosphere the bestresults obtained for LST are shown in bold.

Atmospheres MLS MLW TROPWater vapour content (g cm-2) 2.92 0.85 4.11

TTMLST (K)

RMSEBias

2.1 2.8 2.50.4 0.1 0.2

LSERMSEBias

0.040 0.055 0.0450.005 0.005 0.010

SWLST (K)

RMSEBias

2.4 3.2 1.60.1 0.0 0.2

Hybrid methodLST (K)

RMSEBias

1.3 1.0 2.00.2 0.0 0.4

LSERMSEBias

0.018 0.018 0.0200.000 0.000 0.006


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monthly climate modelling grid (CMG) LST/LSE product was used as the reference

data to quantify the performance of both hybrid method and SW algorithm. The

MOD11C3 product, based on the day/night method (Wan and Li 1997), providescomposites of monthly averaged LST and LSE values for MODIS bands 20, 22, 23, 29

and 31–33 at 0.05� latitude/longitude grids and has been validated over a widely

distributed set of locations and time periods via several ground data. Results from

the validation activities show that MOD11C3 is accurate over semi-arid and arid

regions (Wan et al. 2002, 2004, Wang et al. 2007). Figure 8 displays the MOD11C3

LST and LSE product used in this study respecting to bands 31 and 32 over a region

from 80� S to 80� N and 80� W to 80� E for September 2005.

Figure 7. Histogram of errors (retrieved minus prescribed values) in LST (i) and LSE (ii) withregard to the hybrid method retrieval for MLS (a), MLW (b) and TROP (c) as a result of thecombined effects of uncertainties due to noise in the satellite radiances and errors in theatmospheric profile. Bin sizes are 1.0 K and 0.02 for LST and LSE respectively.


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In order to allow a proper comparison between the previously validated product

from in orbit MODIS instrument and the retrievals from the hybrid method and SW

technique using MSG/SEVIRI data, MOD11C3 product was re-projected to the

SEVIRI instrument resolution and to the normalized geostationary projection by

averaging all pixels within each grid box. Results from the re-projection processes

respecting to LST and LSE in MODIS bands 31 and 32 are shown in figure 9 for

North Africa window where the hybrid method and the SW algorithm are applied andvalidated (grid box in figure 9). Accordingly, we have focused on the Sahara Desert,

which is an area in the MSG disk that presents relatively high LSE variability and

where the highest errors are located in the LSE maps that are used as first guess to the

hybrid method and as input to the SW algorithm. The independent atmospheric

correction required by the hybrid method, i.e. estimation of tc(�), L"cð�Þ and L#c in

equation (1), was performed using the RTM MODTRAN4 and the ECMWF tem-

perature and humidity profiles. The ECMWF forecasts with steps not longer than 18

Figure 8. MOD11C3 LST (a) and LSE product relating to MODIS bands 31 (b) and 32 (c) forSeptember 2005.

Figure 9. MOD11C3 LST (a) and LSE products (b, c) re-projected to the SEVIRI instrumentresolution and to the normalized geostationary projection for North Africa window. The gridbox shows the area where the hybrid method and the SW algorithm are applied and validated.See figures 10–13.


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h and with a maximum spatial resolution of about 50 km are bilinearly interpolated to

the SEVIRI full resolution (3 km at nadir).

Monthly averaged LST values from the SW algorithm, hybrid method and

MOD11C3 product are shown in figure 10 where it is possible to observe a reason-

able agreement and identify common features, indicating consistency among theLST fields in terms of spatial variability. Figure 11 displays the LST error, based on

the comparison with the MODIS product, for both SW algorithm and hybrid

method. The hybrid method has provided LST values with bias (RMSE) of -0.2 K

(1.4 K) for all pixels within the study area and these results demonstrate that the

hybrid method is capable of providing better estimates than those obtained when

using the SW technique, namely bias (RMSE) of -1.7 K (2.3 K). On the other hand,

the LSE fields and the LSE difference displayed respectively in figures 12 and 13

reveal some inconsistencies and in general the LSE values from the hybrid methodare higher than those from MOD11C3. In the case of LSE, the hybrid method has

estimated values with bias (RMSE) of 0.003 (0.009) and 0.02 (0.02) for channel

IR10.8 and IR12.0, respectively.

It is worth noting that virtually all results from the hybrid method (except

LSE in channel IR12.0) are in agreement with the MOD11C3 performance at a

semi-desert where LST (LSE) values is 1–1.7 K (0.017) higher (less) than the

ground-based measurements. The numbers from the alternative validation

scheme presented in this section demonstrate that the hybrid method is capableof providing accurately LST and LSE values and corroborate the results based

on simulated data.

4. Discussion and conclusions

We have developed a new hybrid method based on a synergistic usage of SW and

TTM, which combines the attractive features of both methods while mitigating someof their drawbacks. Inversion methods, such as the proposed hybrid method, that

allow recovering both LST and LSE require independent atmospheric corrections,

and therefore, the accuracy will strongly depend on atmospheric profile uncertainties.

In addition, there is a technical problem related to the registration of multiple images

from different times since the hybrid method is a multitemporal approach (based on

the hypothesis that LSE does not change between observations). Because LST and

LSE errors due to misregistration depend on the difference between the surface

Figure 10. Monthly averaged LST values from the SW algorithm (a), hybrid method (b) andMOD11C3 product (c).


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characteristics of the physical regions mistakenly matched, the error is expected to be

small for homogeneous areas. Conversely, for heterogeneous areas, the error could be

large depending on the variation of vegetation and soil proportions (i.e. mixed pixels)

due to misregistration effects (Wan 1999). On the one hand, real terrestrial surfaces

are not commonly homogeneous and isothermal at the spatial scale of MSG/SEVIRI

measurement and are far from a smooth surface with two dimensions. Most usuallyscene elements are composed of many terrestrial surfaces having different emissivity

and temperature with various geometries. On the other hand, problems related to

registration are avoided when using geostationary satellites like MSG/SEVIRI

because the satellite-viewing angle does not change for each pixel. In the case of

polar orbiters, changes in the satellite-viewing angle may originate differences in

magnitude of LSE.

The hybrid method was tested for those surface types and atmospheric conditions

where the LST goal accuracy of 2.0 K is neither achieved by SW nor by TTM. Weshow that the hybrid method is able to provide better estimates of LST and this is

especially true for atmospheric profiles with lower water vapour content, an impor-

tant feature since SW algorithms are more sensitive to uncertainties on LSE precisely

in the case of dry atmospheric conditions. For those areas where LSE is highly

variable and relatively dry atmospheres are observed the hybrid method provides

LST with an accuracy better than 1.3 K, i.e. less than one-half of the accuracy of 3.0 K

provided by the SW algorithm.

The hybrid method was also applied using real MSG/SEVIRI data on the SaharaDesert, which is an area that presents relatively high LSE variability, and then

validated with the MOD11C3 monthly GMC LST/LSE product. The bias (RMSE)

associated with LST was -0.2 K (1.4 K) for the hybrid method and -1.7 K (2.3 K) for

the SW algorithm, whereas it was 0.003 (0.009) and 0.02 (0.02) for LSE in channel

IR10.8 and IR12.0, respectively. Accordingly, the alternative validation scheme

reveals that the hybrid method is capable of providing better estimates than those

obtained when using the SW technique. It is worth noting that almost all results

obtained with the hybrid method (except LSE in channel IR12.0) are in agreementwith the MOD11C3 performance supporting the sensitivity analysis based on simu-

lated data.

Figure 11. LST error for the SW (a) technique and the hybrid method (b).


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It is worth emphasizing that there are different emissivity-temperature separation

algorithms to obtain LST/LSE from MSG/SEVERI and other sensors, which some

may achieve higher accuracies. For instance, sensitive analysis based on Advanced

Spaceborne Thermal Emission and Reflection Radiometer (ASTER) numerically

simulated data (Gillespie et al. 1999), has shown that temperature/emissivity separa-

tion (TES) might recover LST to within about �1.5 K and LSE to within about

�0.015. However, as the alpha derived emissivity (Kealy and Gabell 1990, Kealy and

Hook 1993) and the greybody emissivity (Barducci and Pippi 1996) algorithms, theTES method is essentially multispectral and not really applicable to the SEVIRI

sensor. Temperature independent spectral index (TISI) method is also a multitem-

poral approach and like the proposed hybrid method requires only two TIR bands to

determine LST and LSE. Dash et al. (2002) have reported LSE retrievals with RMSE

of 0.031 for MSG/SEVIRI channel IR3.9, 0.016 for channel IR10.8, and 0.009 for

channel IR12.0, but it is worth mentioning that errors due to the MSG/SEVIRI

channel noise and the atmospheric correction were not taken into account.

In short, the hybrid method has shown to be adequate to retrieve LST for areaswhere LSE is highly variable and relatively dry atmospheres are observed.

Figure 12. Monthly averaged LSE values from the hybrid (a), (b) method and the MOD11C3product (c), (d).


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Acknowledgements

We would like to thank the Institute for Applied Science and Technology of theFaculty of Sciences of the University of Lisbon (ICAT-FCUL) for providing the

computing resources. The Portuguese Foundation of Science and Technology (FCT)

has supported the research performed by the first author (Grant No. PRAXIS XXI/

BD/21566/99). The research was performed within the framework of the Project LSA-

SAF, an R&D Project sponsored by EUMETSAT. The ASTER spectral library was

available courtesy of the Jet Propulsion Laboratory, California Institute of

Technology, Pasadena, CA.

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