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Exponential Gaussian approach for spectral modelling: The EGO algorithmII. Band asymmetry

Loredana Pompilio a,*, Giuseppe Pedrazzi b, Edward A. Cloutis c, Michael A. Craig d, Ted L. Roush e

a Strada Inzani, 29, Parma I-43125, Italyb Dipartimento di Sanità Pubblica, Sezione di Fisica, University of Parma, Via Volturno 39, Parma I-43100, Italyc Department of Geography, University of Winnipeg, 515 Portage Ave., Winnipeg, MB, Canada R3B 2E9d University of Western Ontario, 1151 Richmond St., London, ON, Canada N6A 5B7e NASA Ames Research Center, MS 245-3, Moffett Field, CA 94035-1000, USA

a r t i c l e i n f o

Article history:Received 16 September 2009Revised 9 February 2010Accepted 18 March 2010Available online 3 April 2010

Keywords:SpectroscopyThermal histories

a b s t r a c t

The present investigation is complementary to a previous paper which introduced the EGO approach tospectral modelling of reflectance measurements acquired in the visible and near-IR range (Pompilio, L.,Pedrazzi, G., Sgavetti, M., Cloutis, E.A., Craig, M.A., Roush, T.L. [2009]. Icarus, 201 (2), 781–794). Here,we show the performances of the EGO model in attempting to account for temperature-induced varia-tions in spectra, specifically band asymmetry.

Our main goals are: (1) to recognize and model thermal-induced band asymmetry in reflectancespectra; (2) to develop a basic approach for decomposition of remotely acquired spectra from plane-tary surfaces, where effects due to temperature variations are most prevalent; (3) to reduce theuncertainty related to quantitative estimation of band position and depth when band asymmetry isoccurring.

In order to accomplish these objectives, we tested the EGO algorithm on a number of measure-ments acquired on powdered pyroxenes at sample temperature ranging from 80 up to 400 K. Themain results arising from this study are: (1) EGO model is able to numerically account for the occur-rence of band asymmetry on reflectance spectra; (2) the returned set of EGO parameters can suggestthe influence of some additional effect other than the electronic transition responsible for the absorp-tion feature; (3) the returned set of EGO parameters can help in estimating the surface temperature ofa planetary body; (4) the occurrence of absorptions which are less affected by temperature variationscan be mapped for minerals and thus used for compositional estimates.

Further work is still required in order to analyze the behaviour of the EGO algorithm with respectto temperature-induced band asymmetry using powdered pyroxene spanning a range of compositionsand grain sizes and more complex band shapes.

� 2010 Elsevier Inc. All rights reserved.

1. Introduction

Curve fitting techniques applied to reflectance spectra offer aninvaluable resource to spectral modelling, both allowing the math-ematical description of the band shapes and the qualitative andquantitative estimation of the absorption components, at least insome cases. A widespread literature addresses this topic and a num-ber of references can be found in Pompilio et al. (2009), specificallyrelevant for the visible and near-IR reflectance measurements.

In addition to the centre and intensity of absorption bands inreflectance spectra, Pompilio et al. (2009) also modelled saturatedbands which no longer have Gaussian shapes. This effort has beenaccomplished by using the Exponential Gaussian Optimization

(EGO) algorithm. The authors showed that the t parameter of theEGO profile can be successfully used to account numerically forband saturation in visible and near-IR reflectance measurements.This paper is complimentary to Pompilio et al. (2009) and accountsfor a further aspect of the EGO model.

The spectra so far modelled using Gaussians or modified Gaussi-ans have been measurements of pure powdered minerals and mix-tures, rock chips or slices, all acquired at room temperature (RT).Although observed in a number of measurements (see Section 2),the effects due to sample temperature variations on spectra havenot been modelled yet.

This paper reports the results from the EGO modelling of spectro-scopic measurements acquired at different sample temperatures invacuum. These results are directly applicable to the interpretation ofhigh quality data acquired remotely from many solar system bodies,specifically Mars, Mercury, the Moon, asteroids and the Earth.

0019-1035/$ - see front matter � 2010 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2010.03.020

* Corresponding author.E-mail address: [email protected] (L. Pompilio).

Icarus 208 (2010) 811–823

Contents lists available at ScienceDirect

Icarus

journal homepage: www.elsevier .com/locate / icarus


2. Background

A number of authors have performed laboratory experimentsand showed the effects of sample temperature variations on reflec-tance spectra in the visible and near-IR (Sung et al., 1977; Osborneet al., 1978; Parkin and Burns, 1980; Dyar and Burns, 1981; Roushand Singer, 1984a,b; Singer and Roush, 1985; Lucey et al., 1998;Schade and Wäsch, 1999; Moroz et al., 2000; Hinrichs and Lucey,2002 and references therein). The main temperature inducedeffects on absorption bands in the visible and near-IR range aresummarized below:

(1) The most prominent effect due to rising temperature is bandbroadening (e.g., Singer and Roush, 1985; Schade andWäsch, 1999). A band broadens as a consequence of theincreasing amplitude of thermally induced vibrations. Onthe other hand, band narrowing at low temperatures is alsocoupled with better resolution of the absorptions.

(2) Increasing temperature of the environment around materi-als also induces the shift of band centres, according to crystalfield considerations. The uniform expansion/contraction ofthe coordination site leads to a shifting of band centrestoward longer/shorter wavelengths; differential expansion/contraction induces less predictable behaviours (e.g., Sunget al., 1977; Burns, 1993).

(3) Intensities of absorption bands vary with temperature as aresult of vibronic coupling but the direction of this variationis not easily predictable (Parkin and Burns, 1980).

(4) Absorption bands become asymmetric toward longer wave-lengths (Roush and Singer, 1984a,b) for temperatures higherthan the room temperature. The physical law governing thisbehaviour has not been found yet, but the mechanism of vib-ronic coupling can be hypothesized to explain the develop-ment of band asymmetry at high temperatures.

3. Modelling strategy

Starting from the work of Hinrichs and Lucey (2002), we appliedthe EGO approach to model the spectral variations induced by vari-ations of the thermal environment around samples. The mainobjectives of our efforts are: (1) to test and validate the EGOapproach in recognizing and modelling band asymmetry due tosample temperature variations; (2) to calibrate the numericalparameters accounting for the shape variations of absorptionbands as a function of temperature; (3) to improve the spectralmodelling of measurements acquired from planetary surfaces,where the temperature ranges from around 60 up to 750 K (McKayand Davis, 2007; Taylor and McLennan, 2009).

Since pyroxenes are among the most widespread rock-formingminerals within the Solar System, and their spectroscopic behav-iour is well understood, we modelled pyroxene spectra affectedby temperature variations. Another reason to model pyroxeneabsorption bands relies on the nature of the crystal field (CF) fea-tures. Pyroxene and especially Mg-rich orthopyroxene, show twovery distinctive absorptions around 1 (band I) and 2 lm (band II)which are attributable to spin-allowed CF contributions of octahe-drally coordinated Fe2+ (Runciman et al., 1973; Burns, 1993 andreferences therein). The absence of separate contributions in thisspectral region due to CF transitions involving Fe2+ in slightly dif-ferent octahedral surroundings (as in clinopyroxene, olivine, Fe-rich orthopyroxene) allows us to both increase the accuracy ofthe mathematical model and calibrate band asymmetry as a func-tion of temperature.

In addition to bands I and II, the Mg-rich pyroxene we used forthis study shows two weak and narrow absorptions at 0.506 and

0.549 lm, which have been attributed to spin-forbidden CF transi-tions in Fe2+ located in M2 and M1 crystallographic sites, respec-tively (Cloutis, 2002; Klima et al., 2007 and references therein).In particular, the absorption band at 0.506 lm has been consideredby a number of authors for planetary investigations (e.g., Cochranand Vilas, 1997; Hiroi et al., 2001; Jarvis et al., 2001).

We first simulate temperature induced effects on absorptionbands using the EGO profile and following the indications derivedfrom the literature (Section 2). This simple exercise aims at visuallyevaluating the reliability of the EGO algorithm to model the bandasymmetry possibly induced by thermal effects. Then, we applythe EGO modelling to the spectral measurements of bronzite(En86) from Bamble, Norway, between 80 and 400 K, as kindly pro-vided by Dr. J.L. Hinrichs. These data are published in Hinrichs andLucey (2002) and pyroxene chemistry is reported in Singer (1981).This mathematical analysis aims at establishing tolerance limitsand variation trends for the EGO’s retrieved parameters. We alsoevaluate the errors in estimates of the target temperature relativeto the RT by using the results returned from the EGO modelling.

The EGO profile accounts for non-Gaussian behaviour of absorp-tion features that can arise from saturation and thermal effects.Therefore, it is able to model band flattening and asymmetry.When flattening and asymmetry are negligible, the single-processabsorption band is commonly fitted as a single Gaussian superim-posed on a proper background.

The EGO profile is described as:

EGOðkÞ ¼ � s

1� e�12t

1� e

�12 te

�12

k�lrþkðk�lÞ

� �20@

1A

2666664

3777775

ð1Þ

where s is the band intensity, l the centre and r is the width of theEGO profile. The t and k parameters account for band flattening andasymmetry, respectively. Each EGO is intended to model a singleabsorption feature and the model algorithm is:

lnRðkÞ ¼ CðkÞ þX

EGOðkÞ ð2Þ

where (R) and (C) indicate the reflectance spectrum and the contin-uum as a function of the wavelength, respectively. Here, we used acontinuum linear in wavenumber for simplicity and consistency.Actual fitting was done to the data in log reflectance versus wave-number. The complete description of the fitting approach and opti-mization routine together with a number of references can be foundin Pompilio et al. (2009).

Fig. 1a and b shows the effect of varying only k in Eq. (1), start-ing from a pure Gaussian (where k is zero and t is negligible) withconstant parameters superimposed onto a horizontal continuum.We progressively increase the effect of band asymmetry towardlonger wavelengths by increasing positive k (Fig. 1a) and towardshorter wavelengths by increasing negative k (Fig. 1b). The result-ing EGOs retain the same centre, width and depth as the originalGaussian, while their shapes are changing, accordingly.

Fig. 1c shows the simulation of the behaviour of a hypotheticabsorption band as the temperature of the hypothetical targetmaterial increases, according to the observations already made byprevious authors and summarized in Section 2. Starting with a pureGaussian, we progressively shift the EGO’s centre toward longerwavelengths and increase width and asymmetry toward positivevalues, while intensity is decreasing. The initial values and incre-ments used for these simulations are arbitrary. The separateabsorptions in orthopyroxene spectra measured by Hinrichs andLucey (2002) at different sample temperatures are shown inFig. 2. The observed behaviour is consistent with the trends shownin Fig. 1 and allows us to be confident that the EGO algorithm is able

812 L. Pompilio et al. / Icarus 208 (2010) 811–823


to recognize and model band asymmetry due to sampletemperature variations. As the temperature increases, pyroxenebands broaden, shift toward longer wavelengths (band II shifts overa wider range of wavelengths than band I), become more asymmet-ric on the long wavelength wing and weaker, as shown in Fig. 1c. Inaddition, the measured bands show tilting continua that have notbeen simulated in Fig. 1c. The weak features beyond the 2 lm be-come resolvable at low temperatures (Fig. 2). The reflectance levelartefact near 0.98 lm that persists through the measurements(Fig. 2a) is due to different light detectors used for measurements.A photo-diode array spectrometer is used below 1 lm and two

scanning grating spectrometers with single-element InGaAs detec-tors each are used beyond 1 lm (Hinrichs and Lucey, 2002).

4. Spectral analyses

By using the EGO algorithm we modelled a set of 17 measure-ments acquired on powdered orthopyroxene (En86, 45–90 lmgrain size) at sample temperature varying from 80 up to 400 K withsteps of 20 K. The spectra over the entire wavelength range areshown in Fig. 3.

Fig. 1. Simulations of the EGO behaviour as k increases toward positive (a) and negative values (b), starting from a Gaussian with constant parameters superimposed onto ahorizontal continuum. The original Gaussian (black line) has the following parameters: s = 0.5; l = 0.950 lm; r = 0.070 lm. k varies as indicated in the legend. (c) Simulationof a band approximately located in the pyroxene band II region as the temperature increases, as follows from the literature. Starting from the black toward the light gray line,EGOs have the following parameters: s = 0.400, 0.395, 0.390, 0.385, 0.380, 0.375, 0.370; l = 1.800, 1.815, 1.840, 1.850, 1.865, 1.880, 1.890 lm; r = 0.070, 0.078, 0.086, 0.094,0.102, 0.110, 0.118 lm; t = 10�5. k varies as indicated in the legend. The parameters used for these simulations are set arbitrarily.

Fig. 2. Behaviour of pyroxene band I (a) and II (b) as the temperature increases. Temperature is displayed in the legend as K degrees. The bands here shown have been isolatedfrom the entire spectra which have been measured between 0.35 and 2.5 lm and published by Hinrichs and Lucey (2002).

L. Pompilio et al. / Icarus 208 (2010) 811–823 813


Absorption of energy in orthopyroxene is mainly due to Fe2+ lo-cated in the M2 crystallographic sites (Burns, 1993). Specimensincorporating large amount of Fe can show contributions fromFe2+ in the M1 site which causes absorption bands near 0.9 and1.15 lm. Klima et al. (2007) showed that the 1.2 lm band in lowFe pyroxenes is approximately 0.25 the strength of the 2 lm bandand this ratio increases for higher Fe2+ content. Additional absorp-tions due to Fe3+ can occur in the visible region with wings in thenear-IR.

To evaluate the effect that the increasing temperature has onabsorption bands in reflectance spectra, we properly used theset of measurements shown in Fig. 3 because of the strong dom-inance of the main CF features diagnostic of Fe2+/M2 sites and theabsence of contributions due to Fe2+/M1 sites and to Fe3+. Twonarrow and weak absorptions near 1.4 and 2.3 lm have beeninterpreted as vibrational bands due to the incompletely removedhydroxylated contaminant suspected to be tremolite (Singer,1981). However, those weak bands do not affect the fitting resultssignificantly; even at cryogenic temperature, where they becomebetter resolved (Fig. 2).

By looking at the spectra shown in Fig. 3, we also observe thatthe pyroxene diagnostic bands show a differential shift towardlonger wavelengths as the temperature increases. Specifically,band II shift is larger than band I shift. Both absorptions becomemore asymmetric toward the long wavelength side and reducetheir intensity, especially band II. Increasing temperature also re-duces the reflectance of maxima between absorptions, thus affect-ing the continuum shape, more strongly at the longer wavelengths.

By zooming in the visible region (inset in Fig. 3) we notice thatthe spin-forbidden absorptions show only minor changes in theirshapes as the temperature increases. In addition, those variationsare not linear with the temperature.

Spectra were modelled using a single EGO per band superim-posed onto a continuum linear in wavenumber. We used bothspin-allowed and spin-forbidden pyroxene bands for testing the

EGO fitting technique. In order to better characterize the spectro-scopic processes causing the absorption of visible and near-IR light,we fit each absorption band individually using a single EGO withall the parameters free to change. All the absorptions were isolatedby using a straight line continuum tangent to the local reflectancemaxima located on either side of the feature (Clark and Roush,1984). Once localized, the continuum remained constant for allthe trials aimed at assessing the best fit result. Spin-forbiddenbands have been modelled by both assuming that saturation willnot occur (t � 0) and with all the other EGO parameters free tochange during optimization.

No further trials (e.g., using two or more EGOs; allowing thecontinua to change slope and intercept during the optimizationroutine) are considered here, because the single EGO and a straightand constant continuum were always able to fit the feature ofinterest, thus allowing the best fit results. In addition, fitting eachof the bands considered here using more than a single EGO wouldimply the occurrence of several transitions which is in contrastwith the crystal field considerations we made before. The MGManalysis was not adopted because modified Gaussians are stillsymmetric curves (Sunshine et al., 1990) and our objective herewas to account numerically for the temperature-induced asymme-try of absorption features.

4.1. Spin-allowed CF bands

Fig. 4 shows some fitting results for pyroxene band II modelling.Fitting results for band I modelling are not shown. The parametersretrieved using the EGO model are listed in Tables 1 and 2. Basedon the assumptions for residuals behind classical regression analy-sis, one expects them to be roughly normal and approximatelyindependently distributed with a mean of 0 and some constantvariance. We observe departures from this behaviour around0.98, 1.10, 1.40 and beyond 2.20 lm, thus showing that the resid-uals contain structure that is not accounted for in the model. Those

Fig. 3. Dataset used in this study. The measurements have been acquired on powdered bronzite (En86) from Bamble, Norway, wet sieved to 45–90 lm grain size, at sampletemperature varying from 80 up to 400 K with steps of 20 K. Spectra were kindly provided by Dr. J.L. Hinrichs and are published in Hinrichs and Lucey (2002); pyroxenechemistry is reported in Singer (1981). Data beyond 2.3 lm have not shown because they display a high amount of noise. The inset shows a zooming of the spin-forbidden CFbands centred in the visible region.



structures are the additional weak bands that have been describedabove and a discontinuity within the measurements due to chang-ing detectors (0.98 lm). The broad discrepancy in the residual dis-tribution around 1.10 lm is probably diagnostic of the occurrenceof an additional structure (probably Fe2+/M1 site) which becomesdetectable at temperatures below the room temperature (Fig. 3).We have intentionally avoided fitting those weak bands becauseof their very small intensity compared to the most prominentbands in the spectra. Otherwise, we would retrieve a larger num-ber of parameters in the fitting results and different models forthe different spectra, which would be no longer comparable.

Fig. 5 shows the main results of fitting pyroxene bands I and II.The EGO parameters as a function of T show some variation trend.According to the observations made by previous authors, band cen-tres shift toward longer wavelengths (Fig. 5d) as the T increases.Nevertheless, there is a differential shift of band centres for pyrox-ene bands I and II. The total amount of shift for band I is about4 nm (from 0.909 to 0.913 lm), while band II moves within a rangeof 70 nm (from 1.801 to 1.871 lm) as temperature changes. Schadeand Wäsch (1999) also found a different amount of shift of ortho-pyroxene bands I and II as a function of temperature. Within the80–473 K temperature range, they measured about 20 (between0.935 and 0.955 lm) and 90 nm (between 1.900 and 1.990 lm)shift of bands I and II positions, respectively. They used a hyper-sthene with a higher content of total Fe than the enstatite used

here. The higher concentration of Fe is possibly responsible forthe higher sensitivity of band position to temperature variations.

This behaviour has some implications for planetary remotesensing, because if correctly calibrated, the differential shift ofthe two features diagnostic of pyroxene could in principle helpus in estimating the surface temperature of the planetary body(Roush and Singer, 1987; Lucey et al., 1998; Hinrichs et al.,1999). Fig. 6 shows how this goal could be achieved. The differen-tial shift between bands I and II (measured as wavenumbers) hasbeen plotted against temperature. As the temperature increases,the distance between pyroxene bands I and II progressively in-creases in a strongly linear fashion. The linear model here has beencalculated excluding the first value (measurement at 80 K) whichlikely appears as an outlier. It is likely that the reflectance mea-surement at 80 K was affected by the light source radiative heating,as hypothesized by Hinrichs and Lucey (2002), thus reducing theaccuracy of the temperature measurement. The maximum residualis around 8 cm�1, well below the resolution of remote measure-ments. Therefore, the maximum error we have when retrievingtemperature is around 10 K, in the temperature range between100 and 400 K. As a consequence, after a proper calibration ofthe relationship between T and differential shift of band centresusing pyroxenes spanning a range of compositions, we could esti-mate the material’s temperature within a few degrees of uncer-tainty. Analogously, we apply this concept to band II centres. In

Fig. 4. Fit results of pyroxene band II modelling. Each plot shows the best fit results including the residual distribution (top curve in each plot), continuum tangent to theabsorption to model (dotted line), the data (light gray dots) and the fitting curve (black line). Only a subset of the whole dataset is shown, for clarity. Temperature ofacquisition is reported at the bottom of each plot.



the linear model of band II centres versus temperature, the statis-tics account for a good correlation, as in the previous model (Fig. 6),thus allowing us to use only one of the possible parameters derivedfrom a pyroxene spectrum, if we assume that only a single pyrox-ene is present. In Fig. 5d we plot band centres as wavelength versustemperature, for consistency with the units commonly displayed inreflectance measurements. However, whether we use wavelengthor wavenumber as band centres unit, the statistics retrieved forlinear regression of centres with temperature are comparable.Band I shift is too small to allow realistic estimates of temperatureif used alone. As a consequence, in attempting to retrieve temper-

ature of planetary bodies, band centres have to be considered care-fully and correctly calibrated with T.

Band positions retrieved with the EGO models fall within theorthopyroxene compositional cluster, based on the work of Cloutisand Gaffey (1991) and thus independently from the temperature ofacquisition (Fig. 7a). However, errors in the estimates of the Mg/Fecontent of pyroxene are within 30% mol of ferrosilite, depending onthe T of acquisition (Fig. 7b and c). In particular, there is up to ±15%shift compared to the composition estimated using RT measure-ments. Therefore, in the absence of accurate calibrations, the com-positional determinations can undergo a 15% error in terms of

Table 1EGO fitting results for pyroxene band I shown in Fig. 2a as a function of the temperature (T).a

T (K) s Uncert. l (lm) Uncert. r (lm) Uncert. t Uncert. k Uncert.

Bronzite band I – EGO model – Continuum fixed80 1.592 3.80E�03 0.909 3.00E�04 0.052 2.60E�04 4.789 1.14E�01 �0.077 1.65E�03

Low High Low High Low High Low High Low High1.585 1.600 0.908 0.909 0.051 0.052 4.564 5.014 �0.080 �0.074

100 1.595 4.11E�03 0.910 3.29E�04 0.052 2.78E�04 5.014 1.26E�01 �0.080 1.78E�03Low High Low High Low High Low High Low High1.587 1.603 0.910 0.911 0.051 0.052 4.767 5.262 �0.084 �0.077










300 1.577 2.81E�03 0.910 2.44E�04 0.072 3.04E�04 2.296 7.48E�02 0.006 1.29E�03Low High Low High Low High Low High Low High1.571 1.582 0.910 0.911 0.071 0.073 2.149 2.443 0.003 0.008






a See Eq. (1) for definition of symbols. ‘‘Uncert.” means uncertainty on the parameter. ‘‘Low” and ‘‘high” indicates the lower and upper limits of the 95% confidence interval.



ferrosilite content for measurements acquired at temperatures dif-ferent from the RT (Fig. 7b and c).

Band width increases regularly with temperature, as illustratedin Fig. 5b. The total increment of band width as the temperature in-creases is�30 nm (from 0.050 to 0.080 lm) and 60 nm (from 0.140up to 0.200 lm) for pyroxene for bands I and II, respectively. Dueto the great linearity of band width variation, especially band I,the temperature could in principle be calibrated using band width.However, due to the slope of the correlation line, errors in the esti-mates of temperature using band width can be on the order of

100 K for variations of only few nanometres in width. Since severalabsorptions are allowed to occur at 1 and 2 lm wavelength regions(e.g., clinopyroxene, olivine), band width cannot be considered agood indicator of temperature. In addition, band width is stronglyinfluenced by zoning, compositional variability, and grain size,thus reducing the effectiveness of any calibration attempts.

Band I shows quite constant depth within the range of temper-atures (Fig. 5f). Band II depths as a function of T decrease quitelinearly. Therefore, band I depth cannot be considered as diagnos-tic of temperature variations. Band II depth does, although it is

Table 2EGO fitting results for pyroxene band II shown in Fig. 2b, as a function of the temperature (T).a

T (K) s Uncert. l (lm) Uncert. r (lm) Uncert. t Uncert. k Uncert.

Bronzite band II – EGO model – Continuum fixed80 1.224 2.91E�03 1.801 6.72E�04 0.145 8.32E�04 2.454 1.00E�01 �0.072 1.68E�03

Low High Low High Low High Low High Low High1.218 1.229 1.800 1.803 0.143 0.147 2.257 2.651 �0.075 �0.069







220 1.131 1.55E�03 1.820 4.53E�04 0.187 6.74E�04 1.493 5.81E�02 0.001 1.02E�03Low High Low High Low High Low High Low High1.128 1.134 1.819 1.821 0.186 0.189 1.379 1.607 �0.001 0.003


260 1.093 1.08E�03 1.827 3.79E�04 0.198 – 1.405 1.56E�02 0.013 8.21E�04Low High Low High Low High Low High Low High1.091 1.095 1.827 1.828 – – 1.375 1.436 0.011 0.014








a See Eq. (1) for definition of symbols. ‘‘Uncert.” means uncertainty on the parameter. ‘‘Low” and ‘‘high” indicate the lower and upper limits of the 95% confidence interval.



straightforward that using band intensity for estimating tempera-ture is always challenging, due to the compositional variable andgrain size also affecting band depths.

The t parameter which Pompilio et al. (2009) have described asdiagnostic of saturation, assumes a very different behaviour in thetwo cases. The whole set of measurements show that pyroxeneband I is saturated (all the values above 1.5) and saturation de-creases with T (Fig. 5c). Band II is saturated at all temperatures ex-cept within 200–260 K. t values higher than 1.5 thresholds occur attemperatures outside of this range. This means that the t parame-ter is not a good indicator of temperature at wavelengths as long as2 lm. At 1 lm, band saturation is shown to be inversely dependenton temperature. In order to establish how saturation of CF transi-tion is related to temperature of materials, we need further inves-tigations using pyroxene spanning a range of both Mg/Fe contentand grain sizes. Nevertheless, this issue is beyond the scope ofthe present investigation. Here, we can certainly understand thatthe behaviour shown in Fig. 5c is possibly due to compensation be-tween t and r, occurring as interfering effects of band broadening,which is a remarkable effect of T variations, and flattening. There-fore, we reject t as a possible temperature indicator.

The increasing temperature has a remarkable effect on bandasymmetry. As shown in Fig. 5a, pyroxene bands I and II are alwaysasymmetric except within 280–320 K (band I) and 200–240 K(band II). At colder temperatures than these two different intervals,bands I and II show asymmetry toward shorter wavelengths. Thisbehaviour reverts at higher temperatures (Fig. 5a). k variations inband I are strongly linear with T and therefore can be used for cal-ibrating T all over the range examined here. In addition, the k

Fig. 5. Plots of the EGO parameters as a function of temperature (a, b, c, d, f) from modelling pyroxene band I (black circles) and II (gray circles) shown in Fig. 2. (e) The kparameter has been plotted against band width in order to show the different behaviour of the two pyroxene bands. Correlation lines have been shown when the statisticswere very good (R2

adj > 0:9). See the text for discussion.

Fig. 6. The differential wavelength shift between bands I and II has been plottedagainst temperature. A linear (solid line) fitting have been applied to the data. Thegoodness of fit has been estimated using adjusted R2. See the text for discussion.



parameter here shows a remarkable characteristic. Band I is sym-metric at RT. At colder T, the band asymmetry is toward shorterwavelengths; at higher T, band I asymmetry reverts. Band II asym-metry increases quite linearly with T and reaches a plateau at themaximum positive value of 0.02 and temperatures higher than280 K. Therefore, values useful for calibration lie below the RT lim-it. At temperatures higher than 280 K, when the pyroxene band II

becomes as large as 0.200–0.210 lm, its asymmetry remainsapproximately constant around 0.02 (Fig. 5e) while the band be-comes flatter at the bottom as t increases (Fig. 5c).

In summary, the variation of temperature dramatically affectspyroxene bands I and II. EGO profile is able to account for banddeformation with T. Some of the EGO parameters if correctly cali-brated using a larger number of measurements, can be used forretrieving the T of the target material at time of acquisition. Thispoint has significant implications in planetary investigation.

4.2. Spin-forbidden CF bands

Spin-forbidden CF bands in the visible region were fit using upto two EGOs superimposed onto a linear background in wavenum-ber. As a result, the feature at 0.506 lm is well fitted using a singleEGO, while the statistics show little improvement when fitting thefeature at 0.549 lm using two EGOs. Nevertheless, this improve-ment is only minor compared to the uncertainty following theintroduction of an additional band at approximately 0.560 lmwhich has not been described by previous authors (Cloutis, 2002;Klima et al., 2007). In addition, in order to achieve our goal, weelect to retain the results of fitting both bands using single EGOcomponents. We also avoided including saturation when model-ling spin-forbidden bands, because saturated spin-forbidden bandshave not been documented in the literature (Clark, 1999 and refer-ences therein). Moreover, the band shapes bind the t value to bearound 0 with a very high uncertainty. Statistically, when theuncertainty on a value is some orders of magnitude higher thanthe value itself, the parameter is not meaningful. Therefore, themodels of spin-forbidden bands are asymmetric EGOs with t � 0,as listed in Tables 3 and 4.

Fig. 8 shows the main fitting results of the two spin-forbiddenbands. Apparently the main effect induced by increasing tempera-ture is to slightly reduce band depth. The band at 0.506 lm alsoshows a slight broadening with increasing T. The other parametersare roughly constant within the temperature range, except for somesmall variation trend of band centres (1–2 nm) which is very diffi-cult to detect spectroscopically. The EGO parameters retrieved afterfitting the band at 0.549 lm show at least two outliers at 220 and240 K. The main reason for this behaviour is in the spectra. By look-ing at the inset in Fig. 3 we observe that two spectra have differentoverall shapes due to the position of the shoulders between the fea-tures at 0.506 and 0.549 lm. These spectra correspond to the mea-surements at 220 and 240 K. It is straightforward that the differentshapes affect all the band parameters, thus causing deviations fromthe preferential trends shown in Fig. 8.

Band asymmetry for the spin-forbidden bands is not diagnosticof temperature and therefore it has not been plotted. We observecontrasting behaviour for the two bands. The band at 0.506 lm isasymmetric toward shorter wavelengths (negative k), while theband at 0.549 lm is asymmetric toward longer wavelengths (posi-tive k). However, asymmetry is independent of temperature.

Therefore, we cannot use spin-forbidden bands occurring in thevisible region to estimate the temperature of the surface materialfrom remote observations. Nevertheless, we can still use thesebands for compositional considerations (Klima et al., 2007) sincethey are not affected by temperature changes over the range oftemperatures measured.

5. Conclusions

The present investigation follows Pompilio et al. (2009) wherethe EGO algorithm was introduced and tested for modelling satu-rated absorption bands in near-IR spectra of pyroxene. In the pre-vious work, the bands were treated and modelled as symmetric

Fig. 7. (a) Variation trend of band I versus band II minima (modified after Cloutisand Gaffey (1991)). The data points corresponding to the measurements used in thepresent investigation (black circles) plot within the orthopyroxene cluster, thusindependently from the temperature. The arrow indicates the RT measurement. (b)Wavelength positions of band I as a function of the amount of ferrosilite (modifiedafter Cloutis and Gaffey (1991)). (c) Wavelength positions of band II as a function ofthe amount of ferrosilite (modified after Cloutis and Gaffey (1991)). The light grayboxes in figures b and c are error boxes in estimating pyroxene composition. Theblack circle is the point corresponding to the RT measurement.



EGOs. As shown in Eq. (1) in the present work, the EGO profile in-cludes a further parameter accounting for asymmetry of bands (k).Here we present the results achieved from modelling pyroxene vis-ible and near-IR spectra acquired at temperatures ranging from 80up to 400 K.

The spectra distinctly show the development of a clear asym-metry toward the longer wavelength in both of the Fe2+ spin-al-lowed absorptions of pyroxene. Along with the asymmetry, bandshapes change as does the position of the minimum, width anddepth. We tested the ability of the EGO profile to model these datain order to develop a method for tracking the changing band shape

as a function of the temperature. This also has significant implica-tions in the remote sensing of planetary surfaces. In addition, weapplied the same analysis to the very weak and narrow spin-for-bidden bands occurring in the spectra.

Our study has yielded the following results:

– The EGO profile is suitable to model the asymmetry inabsorption bands which develops with rising temperature.The k parameter of Eq. (1) allows for the occurrence of asym-metry in spectra to be recognized and accounted fornumerically.

Table 3EGO fitting results for pyroxene band at 0.506 lm shown in Fig. 3, as a function of the temperature (T).a

T (K) s Uncert. l (lm) Uncert. r (lm) Uncert. k Uncert.

Bronzite Band at 0.506 lm – EGO model with t � 0 – Continuum fixed80 0.061 1.75E�03 0.506 1.19E�04 0.002 7.69E�05 �0.049 2.66E�02

Low High Low High Low High Low High0.058 0.065 0.505 0.506 0.002 0.002 �0.104 0.006

100 0.057 1.80E�03 0.506 1.27E�04 0.002 9.43E�05 �0.143 2.65E�02Low High Low High Low High Low High0.053 0.061 0.506 0.506 0.002 0.003 �0.198 �0.088








260 0.053 1.90E�03 0.506 1.87E�04 0.003 1.21E�04 �0.052 3.36E�02Low High Low High Low High Low High0.049 0.057 0.506 0.507 0.003 0.003 �0.121 0.018




340 0.048 1.68E�03 0.506 1.93E�04 0.003 1.26E�04 �0.053 3.24E�02Low High Low High Low High Low High0.045 0.052 0.506 0.507 0.003 0.003 �0.120 0.014




a See Eq. (1) for definition of symbols. ‘‘Uncert.” means uncertainty on the parameter. ‘‘Low” and ‘‘high” indicates the lower and upper limits of the 95% confidence interval.



– The relationship between k and the temperature is linear withinthe whole range of T examined here for pyroxene band I. Band IIasymmetry can be calibrated with temperature up to roomtemperature.

– Band I k is very sensitive to the temperature changes.– Additional parameters allowing for calibration of the tempera-

ture are band width and the differential band shift towardlonger wavelength with increasing T. However, errors in theestimates of temperature are in the order of 100 and 10 K, usingband width and differential band shift, respectively.

– The proper calibration of band centres and asymmetry using alarger number of measurements, can allow for the retrieval ofT of the target material within a few tens of degrees error. Thispoint has remarkable implications in planetary investigation.

– Spin-forbidden bands occurring in the visible region do notallow estimating the temperature of the surface material fromremote observations. Nevertheless, they can still be used forcompositional considerations, within the all range of tempera-ture here examined, since they are subtly affected by tempera-ture changes.

Table 4EGO fitting results for pyroxene band at 0.549 lm shown in Fig. 3, as a function of the temperature (T).a

T (K) s Uncert. l (lm) Uncert. r (lm) Uncert. k Uncert.

Bronzite Band at 0.549 lm – EGO model with t � 0 – Continuum fixed80 0.035 7.80E�04 0.549 3.05E�04 0.008 2.23E�04 0.130 1.91E�02

Low High Low High Low High Low High0.033 0.036 0.548 0.550 0.007 0.008 0.092 0.168

100 0.034 8.92E�04 0.549 3.78E�04 0.008 2.96E�04 0.171 2.10E�02Low High Low High Low High Low High0.032 0.036 0.548 0.550 0.008 0.009 0.129 0.213
















a See Eq. (1) for definition of symbols. ‘‘Uncert.” means uncertainty on the parameter. ‘‘Low” and ‘‘high” indicate the lower and upper limits of the 95% confidence interval.



Further work is still required in order to analyze the behaviourof the EGO fitting technique using powdered pyroxene spanning arange of compositions and grain sizes and more complex bandshapes. In order to have a better understanding of planetary sur-face composition we have to deal with the temperature effect onspectra and thus we need a proper tool for investigating them.The EGO model could be a powerful tool for the analysis of thenon-Gaussian shape of absorption bands due to a number ofphenomena.

Acknowledgments

We thank Dr. J.L. Hinrichs and P.G. Lucey who kindly providedus with the data for this study, and an anonymous reviewer whoseuseful comments allowed us with improving our manuscript. Lore-dana Pompilio also gratefully recognizes financial support from theSPINNER Consortium, which allowed this work to be carried out.E.A. Cloutis thanks the CSA and NSERC for their support.

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