Layout 6 1 ANNALS OF GEOPHYSICS, 62, 2, VO219, 2019; doi: 10.4401/ag-7791 “ASSESSMENT OF THE DUAL-BAND METHOD BY AN INDOOR ANALOG EXPERIMENT„ Leonie Pick1,2, Valerio Lombardo3, Klemen Zakšek*,1,4 (1) University of Hamburg, Hamburg, Germany; (2) GFZ German Research Centre for Geosciences, Jacobs University, Bremen, Germany (3) Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy (4) University of Ljubljana, Ljubljana, Slovenia 1. INTRODUCTION The discipline of satellite thermal remote sensing provides physical insight into the processes governing volcanic activity and has become a valuable tool of vol− canology since the pioneering paper on the topic was published [Gawarecki et al., 1965]. The volcanological community is confronted with the problem, that none of the currently operational satellite sensors have been designed primarily for volcanological purposes. Conse− quently, the available data, mostly from meteorological satellites, is not ideal for volcano surveillance in two ba− sic regards. First, the characteristics of the spectrora− diometers themselves, essentially the three resolutions in the spatial, spectral, and radiometric domain, are not optimally balanced. Secondly, the satellite orbits are not well adapted, affecting the satellite volcano viewing ge− ometry and temporal resolution. Apart from these data limitations, there is the general difficulty that the radi− ance measured by the sensor differs from the radiance emitted by the ground heat source, mainly due to surface emissivity, atmospheric and geometric influences. To derive higher−level estimates of volcanic activity, such as lava discharge rate [Harris et al., 2005; Calvari Article history Receveid May 31, 2018; accepted November 17, 2018. Subject classification: Thermal anomaly; Lava flow; Remote sensing; Thermal cameras; Experiment. ABSTRACT The evaluation of infrared satellite images over active lava flows assists the identification of potentially threatened areas and thereby the overall lava inundation hazard assessment. The estimation of the lava flow’s size and temperature is not trivial as the lava occupies only a small fraction (< 1 %) of a typically resolved target pixel (e.g., from Landsat 7−ETM+; EOS−MODIS). Conventionally, this is solved by processing observations in at least two separate infrared spectral wavebands. We investigate the resolution limits of the Dual−Band (DB) method by means of a uniquely designed indoor analog experiment. A volcanic thermal anomaly is simulated by an electrical heating al− loy of 0.5 mm diameter installed on a plywood panel. Satellite observations are simulated by two thermographic cameras with wavebands comparable to those available from satellite data. These range from the short−wave infrared (SWIR) over the mid−wave infrared (MIR) to the thermal infrared (TIR). In the conducted experiment, the hotspot’s pixel fraction (p) was successively reduced by increasing the cam− era−to−target distance from 2 m (p = 41.7 %) to 38 m (p = 2.2 %). We carried out three experiments with different wire temperatures and compare different DB setups. In the case of the hottest wire (1019 K), the standard method gives relative deviations between the observed and theoretical hotspot area fractions below 16 % for about one third of the cases (i.e., distances). et al., 2010], the flow’s area and temperature have to be estimated first, usually using the so called Dual−Band (DB) method [Dozier, 1981]. This method allows thermal unmixing of a pixel composed of two temperature com− ponents [Crisp and Baloga, 1990; Dozier, 1981; Rothery et al., 1988]: 1) a hot component with temperature TH covering the pixel fraction p, and 2) a background component with temperature TB covering the pixel frac− tion 1–p. With sensors of coarse spatial resolution (e.g., Moderate Resolution Imaging Spectroradiometer – MODIS, Advanced Very High Resolution Radiometer – AVHRR) this is an unrealistic assumption, as each pixel might consist of several further components with dif− ferent thermal properties, which renders an error of more than 100 K in TH possible [Oppenheimer, 1993; Mouginis−Mark et al., 1994; Wright et al., 2000; Lom− bardo and Buongiorno, 2006; Vaughan et al., 2010, Za− kšek et al., 2013]. The influence of the interplay between all these components on the results of the DB method is still difficult to estimate. Here, we focus on the influence of the fractional area of an anomaly within a pixel (p). To systematically examine this effect, it needs to be iso− lated from the other influences. For this purpose, the satellites’ measurement situation is simulated in an ex− periment, using a steady heat source, which is observed by thermal cameras in spectra commonly found for satellite sensors. 2. EXPERIMENTS 2.1 THE LAVA SIMULATOR The following list summarizes requirements for the simulated heat source: − Target should be a two component mixed pixel with a hot component of at least TH = 600 K compara− ble to crusted lava [Lombardo et al., 2012] and a background component of significantly lower tem− perature TB ≈ 330 K. − Target should be mobile to allow different camera− to−target distances and thereby different pixel sizes. − Hot component’s area percentage (p) should ulti− mately be comparable to those from satellite mea− surements, being ≈ 1 %. − Temperatures should be constant during the mea− surement campaign. − Influences of the target’s surroundings should be minimized. The “Lava Simulator’s” heat source is a single heating wire alloy (Figure 1). Electricity is converted into heat through Joule heating, with the heating power depend− ing on the electrical current and the resistivity. Consid− ering different materials, we decided to use an alloy with a 0.5 mm diameter made of Isachrom 60 (NiCr6015) be− cause of its high specific electrical resistivity and oxida− tion resistance. A laboratory power supply unit is used as a power source with a total maximal output of 400 W. 2.2 EXPERIMENTAL SETUP The pixel fraction p occupied by the hot wire decreases with increasing distance between the cameras and the Lava Simulator. The Simulator is seated on a trolley, that is pushed away from the cameras in a 40 m long hallway. The distance between the cameras and the Lava Simula− tor was increased by 2 m at each step, with the closest measurement at a distance of 2 m (p = 41.7 %) and the furthest at 38 m (p = 2.2 %). At each step, we recorded mean temperatures of 10 s lasting observations with two cameras, producing a SWIR, MIR and TIR image. The ex− periment was repeated three times, each time with a dif− ferent temperature of the alloy, i.e., amperage of the power supply. We call the runs LOW (small TH), MED (medium TH) and HOT (large TH). 2.3 CAMERAS We used two different cameras of the company In− fratec. VarioCam (VC) operates mainly in the thermal in− frared spectrum (TIR; centered at 10.3 μm). ImageIR 8300 (IR) is equipped with two filters covering the short−wave (SWIR; centered at 2.36 μm) and mid−wave infrared (MIR; centered at 3.90 μm) spectra. In both cameras, the detector elements are arranged in a Focal Plane Array, including 640×480 (VC) or 640×512 (IR) single detectors. VC has a lens with 30 mm focal length (angle resolution 0.8 mrad) and IR has a lens with 25 mm focal length (an− gle resolution 0.6 mrad). Both cameras provide observa− tions with 1 % accuracy. The cameras are fixed on a tri− pod by custom−made housing in order to keep the viewing directions parallel. 3. METHODS 3.1 SWIR EMISSIVITY ESTIMATION The temperature observations require an accurate de− termination of the emissivities of the emitting surfaces. Thus, in a darkroom environment, we collected spectra from the operating Lava Simulator using the field− PICK ET AL. 2 portable Spectroradiometer ASD FieldSpec Pro (FS). FS is composed of three spectrometers which measure the spectral radiation energy in different portions of the wavelength spectrum from 0.35 to 2.5 μm with a spec− tral resolution of 2–12 nm. The electromagnetic radiation emitted from the surface is collected by the instrument entry optics and projected into a holographic diffraction grating. FS is provided with a bare fiber optic and a conical field of view (FOV) of 35 . However, the bare fiber FOV has been further reduced us− ing alternative fore optic tubes of 1 and 3 . Given the temperature heterogeneities observed by the Lava Simulator, a new algorithm has been developed to take into account the radiance contributions from surfaces radiating at different temperatures. We assume a two thermal components model for the Lava Simula− tor. The radiance R detected by FS at wavelength λ is the average of the radiances emitted by the hot (at TH) and cold (at TB) surfaces, weighted by their corresponding pixel fractions: R(Ti, λ) = ε(λ) [p⋅R(TH, λ) + (1 – p)⋅R(TB, λ)] ( 1 ) R is the radiance of a blackbody at temperature T and wavelength λ according to Planck’s Law, Ti is the inte− grated temperature and ε(λ) is the spectral emissivity. The Draping algorithm allows the simultaneous estimation of TH, TB, p, and ε(λ) through the following steps: − Identification of the maximum measured radiance Rmax = max[R(λ)] across all wavelengths. − Creation of a lookup table of spectra derived from Equation 1. Only spectra respecting the condition R(Ti, λ) ≥ Rmax are considered. This guarantees that ε(λ) ≤ 1. 3 EXPERIMENTAL ASSESSMENT OF DUAL-BAND METHOD FIGURE 1. Lava Simulator setup. a: Front view. 1) 50 cm × 50 cm plywood panel, 2) high emissivity (0.95) area colored with Senotherm spray, 3) Isachrom 60 alloy, 4) tensioning mechanism, 5) weights to support alloy tensioning, 6) revolvable and tiltable base, 7) electrical supply unit, 8) trolley. b: Side view. c: Close−up of heated alloy. PICK ET AL. 4 − Calculation of the Spearman rank correlation coef− ficient (ρ) between the measured radiances and each spectrum of the lookup table. − Maximum ρ identifies the spectrum R(Ti, λ) derived from Equation 1 that best matches the measured ra− diances R(λ) and therefore fixes the parameter triplet TH, TB, p of the underlying two thermal components model. − Spectral emissivity: ε(λ) = R(λ) / R(Ti, λ) (2) Figure 2 shows the emissivity spectrum derived from the radiance measurements. The emissivity is seen to be 0.93 at the central wavelength of IR’s SWIR filter (dashed lines). The iterative method (section 3.2) gives a very sim− ilar value of 0.95. We keep the latter value to account for the fact that the Draping algorithm determines a lower bound of the SWIR emissivity as well as ensuring con− sistency with the emissivity calculations in MIR and TIR. 3.2 MIR AND TIR EMISSIVITY CALCULATIONS As we had emissivity observations available only for the SWIR spectrum, we had to determine the emissivity of the metal alloy in the MIR and TIR differently. We car− ried out an iterative procedure based on the camera ob− servations from all distances. First, we estimated the theoretical anomalous pixel fraction ptheo as a function of the distance between the Lava Simulator and the cameras, see Figure 3a. Then, we performed various runs of the DB method using our SWIR and MIR camera observations to calculate p (and TH, see section 4.1). For these runs, we set the SWIR emissivity to be constant (0.95, see section 3.1) and var− ied the MIR emissivity between zero and one in steps of 0.05. A MIR emissivity of 0.85 gave the p−solution with the smallest cumulative deviation from ptheo across all distances and was finally chosen. We per− formed the same procedure for SWIR and TIR camera observations, which resulted in an emissivity of 0.25 for the alloy in the TIR. The emissivity of the sprayed background (black, see Figure 1) was set to 0.95 for all wavelengths, following the Senotherm spray spec− ifications. 4. RESULTS 4.1 DB METHOD: TB IS KNOWN DB needs two observations and one assumption to solve a system with three variables. Typically, one as− sumes a background temperature TB and solves for the temperature of the anomaly TH and its fraction p (“standard method”). With three independent obser− vations (section 2.2), we can produce different solu− tions, shown in Figure 3 for the HOT setup. Overall, the solutions involving SWIR observations are most accurate with regard to the Root Mean Squared Error (RMSE, panel a). The smallest relative FIGURE 2. Spectral emissivity of the hot wire derived with the Draping algorithm. Gray area: SWIR filter of IR cam− era. Dashed lines: Emissivity (0.93) at filter’s central wavelength (2.36 μm). FIGURE 3. Solution of the DB method (a: pixel fraction p, b: TH) for the HOT setup and three band combinations with assumed TB = 370 K. Dashed lines indicate the expected values for p (known) and TH (mean of solutions over distances, values annotated). 5 EXPERIMENTAL ASSESSMENT OF DUAL-BAND METHOD error in p of ~1 % is reached by the MIR−SWIR com− bination at a distance of 16 m (p = 5.2 %). At the max. distance of 38 m (p = 2.2 %), the MIR−SWIR solution gives a relative error of 28.7 %. Calculated TH values vary notably around their means (panel b) with a min− imum RMSE of 96.1 K for the MIR−SWIR combina− tion. They seem to converge only at distances 26 m (p = 3.2 %). 4.2 DB METHOD: P IS KNOWN Our experimental setup allows to evaluate a less com− mon variation of the DB method (“assumed p method”). We provide the theoretical hot pixel fraction p (Figure 3a, black) and estimate TH and TB. Figure 4 shows the solutions for the experimental se− tups HOT, MED & LOW using the TIR−MIR band combi− nation, most sensitive to low temperatures (i.e., TB). The background temperature is most robustly determined for the HOT setup (TB = 372 K, RMSE = 9.7 K, panel a). Vari− ations originate primarily from close distances 6 m (p = 13.9 %), beyond which the results converge towards the mean (dashed). The variability in TH is remarkably re− duced compared to the results of the standard method. HOT gives TH = 1054 K and the lowest RMSE = 39.2 K, while the runs with lower wire temperatures give RMSEs more than twice as large due to one outlier in MED and two in LOW (noisiest, panel b). 4.3 TRI-BAND METHOD: NO ASSUMPTIONS According to Figure 4a, the assumption of a con− stant background temperature may result in significant errors. A better solution for the two thermal compo− nents case can be achieved by using the observations of all three wavebands [Flynn et al., 1994]. Then, no assumption is needed and p, TH and TB are simultane− ously estimated (Figure 5). The RMSEs for p (panel a) and TH (97.4 K) are neg− ligibly larger than those of the SWIR solutions using the standard method (Figure 3, orange & red). How− ever, improvements compared to the standard method are registered: First, the smallest relative error in p has reduced to 0.6 % at 16 m. Secondly, the relative errors at 38 m, the case most relevant for satellite thermal re− mote sensing, have decreased to 24.9 % for p and 3.6 % for TH. The mean of TB (372 K) is in excellent agree− ment with that calculated by the best assumed p method (see Figure 4a, yellow). Likewise, the mean of TH (1019 K) agrees well with that given by the best standard method (see Figure 3b, red). 5. DISCUSSION Overall, the presented solutions obtained by the dif− ferent methods are coherent, lending support to the ser− FIGURE 4. Solution of the DB method (a: TB and b: TH) for the TIR−MIR band combination and three runs of the ex− periment with given pixel fraction p. Dashed lines in− dicate the mean values for TB and TH (annotated). FIGURE 5. Solution of the DB method for the HOT setup (a: p, b: TH, and c: TB). Dashed lines indicate the expected values for p (known), TH and TB (mean of solutions over distances, values annotated). viceability of the experimental setup and the relevance of the results. Subpixel characterization techniques are piv− otal in remote sensing of active lava flows. Although the reliability of the DB method has frequently been chal− lenged in this context [e.g., Wright et al., 2003; Harris, 2013], it is still widely used until today [e.g., Aufaristama et al., 2018] due to the lack of satellite sensors with mul− tiple infrared channels across the spectrum. To our knowledge this study is the first that system− atically evaluates the dependence of the DB method on the hot pixel fraction p under “controlled” measurement conditions. It complements studies that test the DB method using synthetic data, as in Murphy et al. [2014]. The authors calculate synthetic radiance spectra in the SWIR from two thermal components pixel and conclude that DB is statistically incapable of reliably, i.e., with 95 % confidence, constraining p, TH or TB (deviations ≥ 11 %). In our experiment, we use different infrared wavelength bands and succeed in estimating p with de− viations down to ~ 1% (MIR−SWIR, Figure 3a). However, the standard DB method (assumed TB) will likely result in large p deviations (≥ 29 %) for small pixel fractions (≤ 2.2 %). Best results are obtained by using SWIR ob− servations, for which we determined a reliable wire emis− sivity of 0.95. The iteratively estimated emissivities in TIR (0.25) and MIR (0.85) are smaller and relatively uncertain, as they were not validated independently based on spec− trometer measurements (section 3.1). The TIR−MIR com− bination thus gives the least accurate p results. They can not be transferred to an active lava flow, for which one would expect a far greater emissivity above 0.9 across the infrared spectrum. A higher accuracy of the p estimate can be achieved if observations in TIR, MIR and SWIR wavebands are available (Figure 5a), as for instance at the Visible Infrared Imaging Radiometer Suite (VIIRS). How− ever, the spatial resolution of VIIRS may be considered as too coarse. A preferable option is HyspIRI mission sched− uled for launch in 2022. Meanwhile, the fusion of high resolution optical data with that from thermal sensors can boost the accuracy of the fractional area estimate. Subpixel temperatures TH and TB can be calculated most robustly (RMSEs 10 K, 40 K) if p is known (Figure 4). Such a measurement setup is provided today by nu− merous high resolution satellite data (e.g., Sentinel 1 and 2, GeoEye, WorldView, Planet). Their integration in a standard workflow based on, e.g., MODIS data can sig− nificantly increase the quality of the results. The DB method operates best in the case of hot anomalies (Figure 4). A sensor similar to the Advanced Spaceborne Thermal Emission and Reflection Radiome− ter – ASTER (with an additional MIR band) or FireBIRD [Zakšek et al., 2015; with an additional SWIR band] is therefore desirable in terms of DB method accuracy. 6. CONCLUSIONS We implemented a simulation environment for the quantitative estimation of subpixel sizes and tempera− tures. It is important to understand quantitative relation− ships between instrumental spectral and radiometric characteristics and data exploitable for lava flow subpixel features. Our analyses show that the standard DB method leads to a large percent deviation of ~29 % for small p (2.2 %). This can be mitigated by − using MIR, SWIR and TIR wavebands simultane− ously. This confirms simulations by Lombardo et al. [2012], stating that observations in three appropri− ate, independent spectral bands are necessary to obtain reliable solutions. − a more accurate determination of surface emissiv− ities, possibly using a spectral library approach [Murphy et al., 2014]. − the fusion of thermal data with high−resolution optical / radar data. − additional SWIR and MIR sensors. The above points suggest improvements in future payload development regarding the dynamic range and band wavelengths. This research has been supported by a grant from the German Science Foundation (DFG), number ZA659/1-1. We would like to thank Joachim Bülow and Thomas Schön for supporting the construction of the Lava Simulator as well as Matthias Hort for his valuable comments regarding the design of the whole experiment. REFERENCES Aufaristama, M., A. Hoskuldsson, I. Jonsdottir, M.O. Ulfarsson and T. Thordarson (2018). New Insights for Detecting and Deriving Thermal Properties of Lava Flow Using Infrared Satellite during 2014– 2015 Effusive Eruption at Holuhraun, Iceland. Remote Sens. 10(1), 151. doi: https://doi.org/ 10.3390/rs10010151. PICK ET AL. 6 Calvari, S., L. Lodato, A. Steffke, A. Cristaldi, A.J.L Har− ris, L. Spampinato and E. Boschi 2010. The 2007 Stromboli eruption: Event chronology and effu− sion rates using thermal infrared data. J. Geophys. Res. Solid Earth 115, B04201. Crisp, J., S. Baloga (1990). A method for estimating eruption rates of planetary lava flows. Icarus 85, 512–515. Dozier, J. (1981). 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Publ. 380, 137–160. doi: https://doi.org/10.1144/SP380.5. Zakšek, K., M. Hort, and L. Eckehard (2015). Satellite and Ground Based Thermal Observation of the 2014 Effusive Eruption at Stromboli Volcano. Re− mote Sens. 7(12), 17190–17211. doi: https://doi.org/10.3390/rs71215876. *CORRESPONDING AUTHOR: Klemen ZAKŠEK, University of Hamburg, Hamburg (GER); now at University of Ljubljana, Ljubljana, Slovenia email: klemen.zaksek.geo@gmail.com © 2019 the Istituto Nazionale di Geofisica e Vulcanologia. 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