Wavelength influence in sub-pixel temperature retrieval using the dual-band technique

The thermal model proposed by Crisp and Baloga (1990) for active lava flows considers thermal flux as a function of the fractional area of two thermally distinct radiant surfaces. In this model, the larger surface area corresponds to the cooler crust of the flow and the other, much smaller to fractures in the crust. These cracks temperature is much higher than the crust one and approaches the temperature of the molten or plastic interior flow. The dual-band method needs two distinct SWIR (short wave infrared) bands to formulate a two equations system from the simultaneous solution of the Planck equation in each band. The system solutions consist in the crust temperature and the fractional area of the hot component. The dual band technique originally builds on data acquired by sensors (such as Landsat TM) with two SWIR bands only. The use of hyperspectral imaging spectrometers allows us to test the dual-band technique using different wavelengths in the SWIR range of the spectrum. DAIS 7915 is equipped with 40 bands into the range 1.54-2.49 nm which represent potential input in dual band calculation. This study aims to compare results derived by inserting assorted couples of wavelengths into the equation system. The analysis of these data provides useful information on dual-band technique accuracy. Mailing address: Dr. Valerio Lombardo, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143, Roma, Italy; e-mail: lombardo@ingv.it


Introduction
«Dual-band» is a remote-sensing technique used to determine the thermal structure of active lava flows.Following Crisp and Baloga (1990), we consider a two thermal components model: the first component is the cooler crust of the flow and the second one is the smaller surface corresponding to hot cracks.We suppose the cracks temperature Th to be related to the molten core of the flow (Oppenheimer, 1993b).
The dual band technique allows us to estimate the crust temperature Tc and the fractional area of hot cracks fh, once we have set Th as boundary condition.A value of 1080°C is suitable for Etnean lavas according to in situ measurements (Gauthier, 1973;Archambault and Tanguy, 1976;GVN, 1993GVN, , 1996;;Calvari et al., 1994).This method requires a spectrometer equipped with two distinct SWIR bands (b 1, b2) to formulate a system of two equations (1.1) where Rad1 and Rad2 are respectively the total radiance detected by the sensor in band b1 and b2, Rhx is the radiance of the hot crack component in band x (x=b1 or b2 in our case), Rcx is the radiance of the cooler crust component in band x and fh is the fractional area of the pixel with the hottest temperature Th.Originally pro- posed by Dozier (1981), this technique has been successfully applied by several authors (Pieri et al., 1990;Oppenheimer, 1991;Oppenheimer et al., 1993a-c;Harris et al., 1999;Flynn et al., 2001;Wright et al., 2001) to estimate the surface thermal structure of aa and pahoehoe lava-flows, as well as lava domes and lakes (Oppenheimer, 1993a;Wooster et al., 2000).The dual-band technique was at first applied to data collected by multi-spectral sensors such as Landsat TM and AVHRR.These sensors include a small number of bands in the SWIR region of the spectrum useful in dual-band calculation (in some cases just two bands).Therefore, we cannot validate the accuracy of our solutions considering the effect of the wavelength choice.Hyperspectral sensors have many more bands available in the SWIR region.The DAIS instrument consists of four spectrometers named VIS-NIR, SWIR-1, SWIR-2 and Thermal, covering a spectral range of 0.4 nm-12.6 nm with a total of 79 bands (see table I for more details).The constraints of lava temperature are well represented by II SWIR-1 and III SWIR-2 spectrometers.These sensors are equipped with 37 bands in the range 1.54 nm-2.49nm that can be input into the dual band system calculations.A further remarkable question originates from the hyperspectral technology: how does the band wavelength choice affects the dual-band solutions?

Data reduction
Hyperspectral airborne images of June 1996 volcanic eruption of Mt.Etna (Eastern Sicily, Italy) were collected using the DAIS 7915 spectrometer during the multi-sensor campaign of Italian volcanic systems (Horne et al., 1997).The 1996 Mt.Etna eruptive activity was imaged on, July 16th and 18th.In this study, we use the July 16th dataset to test dual-band technique as function of the wavelength.Figure 1 shows the DAIS flight line and the zoom of the Etnean craters area.On July 16th three craters were ac-
Main geometric parameters IFoV: 3.3 mrad (2.5 or 5.0 mrad optical).Swath angle max ±39°(depending on aircraft).Pixels per line: 512.tive: the Northern-East, Bocca Nuova and Voragine (GVN, 1996).We applied the dual-band calculation to the pixels of the lava pond located within the Northern-East crater selecting the described area on the image by means of a suitable mask.Initially we used DAIS band 36 and 57 corresponding to a center-band of 1.637 and 2.215 nm respectively.We needed a pair of bands to refer to in our comparison and we chose those wavelengths because they are closer to the 2 corresponding Landsat TM SWIR bands (band 5 and 7 corresponding to a centerband of 1.65 and 2.22 nm respectively).Obviously the chosen wavelengths fall within the two main atmospheric windows making the correction of data for the atmospheric contribution much easier.

Data analysis
In order to assess the influence of the bands' wavelength on the dual band system solutions, we performed the calculation using every band of the spectrometer II combined with each band of the III.Table II lists the band number and the corresponding center band wavelength of the second and third DAIS spectrometers (SWIR-1 and SWIR-2).
For any couple of bands of the two SWIR spectrometers the convergent solutions of the algorithm give an estimation of Tc and fh.The following results apply to the whole set of DAIS band pairs chosen from SWIR-1 and SWIR-2 spectrometers.For a clearer graphic visualization we have represented the results obtained by varying the SWIR-2 band versus the same SWIR-1 band, namely band 36 that for reference corresponds to the band 5 of Landsat TM.
The estimated values of fh range between 0.000 and 0.013% while values of Tc range between 100 and 500°C for non-saturated pixels that in this case represent the 96% of the whole image.Figure 2 shows the fh solutions calculated for each pixel and plotted together as a function of the DAIS band. Figure 4 offers a similar representation for the Tc solutions where a decreasing Tc trend appears for increasing wavelength.
We obtain a clearer view of the ensemble of f h solutions if we subtract for each pixel the mean <f h> to the fh values calculated on each SWIR-2 band. Figure 3 shows this deviation from the mean <fh> as function of the DAIS band number.This calculation yields more stable results with a maximum deviation of 0.002 % for 26 of the 32 channels of the third spectrometer.The dual band algorithm applied to the lava pool area selected by masking the DAIS image can or cannot converge to a solution.The histogram in fig.6 shows the pixel number of the   image where no solution was found for the system.When the system converges to a possible solution (considering the whole set of results) it is possible to accept or reject the estimated temperature and the fractional area values.
The (Tc, fh) estimated solutions statistics has been calculated for every pixel.
For a specified band of the SWIR-2 spectrometer, a pixel can be either rejected or accepted, this choice depends on the existence or not existence of anomalous (T c, fh) values when Chauvenet criteria are applied.
Figures 7 and 8 show the histograms of the rejected and accepted pixels as functions of the  DAIS bands corresponding to the SWIR-2 sensor.Once again these figures point out that the (Tc, fh) estimations of the first six channels of the SWIR-2 sensor are not reliable.This occurs because these channels are highly affected by water vapor absorption: as shown in fig. 9 the center band wavelengths reported in table II for the first six SWIR-2 channels fall at the edge of the water vapor window around 1.9 and 2.0 nm.AVHRR.The analysis presented here is referred to the image collected by the DAIS air borne spectrometer on July 16 1996 on Mt.Etna (Sicily).A good stability was found in the estimation of the crustal temperature and fractional area provided by the dual band algorithm for all the band pairs possible selections from the second and third spectrometers of the DAIS sensor.An exception to this result was pointed out for the first six bands of the third DAIS spectrometer due to the water vapor absorption in that wavelength range.The 60th band that is also in the third spectrometer gave unreliable estimations due to an exceedingly noisy signal.The increasing f h and the corresponding decreasing Tc trends when represented against the DAIS band number, that is the wavelength, needs to be better understood.Possible influences of the emissivity in the SWIR range, contribution of the reflectance and atmospheric correction will be the matter of further investigations.
Moreover the deviation from <fh> rises to 0.005 % for the first six SWIR-2 bands and band 60 shows an anomalous deviation.With regard to the crustal temperature Tc−<Tc>, fig.5displays a maximum deviation of about ±50°C, except for the first six bands and for band 60 where the maximum deviation approximately increases twofold.

Fig. 2 .
Fig. 2. fh solutions calculated for each pixel as a function of the DAIS band number.

Fig. 3 .
Fig. 3. Tc solutions calculated for each pixel as a function of the DAIS band number.

Fig. 7 .
Fig. 7. Histogram of the number of pixels where the DB algorithm does give solutions, but pixels are rejected by the chosen selection criteria.The rejected pixels are concentrated in the first channels of the third spectrometer.

Fig 6 .
Fig 6.Histogram of the number of pixels in the case of no solutions from DB algorithm.

Fig. 8 .
Fig. 8. Histogram of the number of pixels where the DB algorithm does give solutions and pixels are accepted by the chosen selection criteria.

Table I .
Main features of the DAIS sensor.