Uncertainty Analysis of Remotely-Acquired Thermal Infrared Data to Extract the Thermal Properties of Active Lava Surfaces

: Using thermal infrared (TIR) data from multiple instruments and platforms for analysis of an entire active volcanic system is becoming more common with the increasing availability of new data. However, the accuracy and uncertainty associated with these combined datasets are poorly constrained over the full range of eruption temperatures and possible volcanic products. Here, four TIR datasets acquired over active lava surfaces are compared to quantify the uncertainty, accuracy, and variability in derived surface radiance, emissivity, and kinetic temperature. These data were acquired at K¯ılauea volcano in Hawai’i, USA, in January / February 2017 and 2018. The analysis reveals that spatial resolution strongly limits the accuracy of the derived surface thermal properties, resulting in values that are signiﬁcantly below the expected values for molten basaltic lava at its liquidus temperature. The surface radiance is ~2400% underestimated in the orbital data compared to only ~200% in ground-based data. As a result, the surface emissivity is overestimated and the kinetic temperature is underestimated by at least 30% and 200% in the airborne and orbital datasets, respectively. A thermal mixed pixel separation analysis is conducted to extract only the molten fraction within each pixel in an attempt to mitigate this complicating factor. This improved the orbital and airborne surface radiance values to within 15% of the expected values and the derived emissivity and kinetic temperature within 8% and 12%, respectively. It is, therefore, possible to use moderate spatial resolution TIR data to derive accurate and reliable emissivity and kinetic temperatures of a molten lava surface that are comparable to the higher resolution data from airborne and ground-based instruments. This approach, resulting in more accurate kinetic temperature and emissivity of the active surfaces, can improve estimates of ﬂow hazards by greatly improving lava ﬂow propagation models that rely on these data. lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Pu ʻ u ‘Ō’ō vent were active for ~30 years erupting in many locations numerous eruptive episodes, producing mostly pāhoehoe lava with occasional ‘a’ā lava flow This long eruption finally ended in 2018 cessation of lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017 – 2018 study were part of the 61g episode that erupted from the east flank of Pu ʻ u ‘Ō’ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes majority pāhoehoe, both sheet -like and ropey texture. Previous remote sensing studies of the Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. for the


Introduction
Using remote sensing data to monitor volcanic eruptions has improved our understanding of the precursory activity, eruptions dynamics, and eruptive products [1,2]. Thermal infrared (TIR) data between a spectral range of 8 to 12 µm have been utilized since the early 1960s, with major developments in orbital, airborne, and ground-based TIR technologies. These systems provide new data that are important for modeling volcanic activity over a variety of spatial, spectral, and temporal scales (e.g., [3]). For example, the data have improved the accuracy, reliability, and duration of precursory evaluations, constrained eruption dynamics, and improved both magma rheological and thermal models of all volcanic products [1,4,5].

Study Area
This study was conducted during two field campaigns at Kīlauea Volcan January/February 2017 and 2018, a period when both the summit lava lake and lava flows were active. It focused primarily on the lava lake in the Halem propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basalt has been erupting nearly continuously for the past 500 years [33]. The lava s during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was 2018 and varied in size with maximum dimensions of 160 meters wide and 22 1) [34]. During this period, there were fluctuations in lava lake activity with co and irregular small explosions, finally ending with the summit collapse in Ma time of the field campaigns, the lava lake level was relatively high b approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was con with fresh lava upwelling in the north that migrated to the south, cooled and fo solidified lava. The lava then sank in the south, distinguished by the occurrence and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 y locations over numerous eruptive episodes, producing mostly pāhoehoe occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 wit lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows 2017-2018 study were part of the 61g episode that erupted from the east flan flows propagated down the Pulama pali and entered the ocean at Kamokuna a surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows ob pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing stu Kīlauea eruption have investigated lava discharge rates [36], lava flow empla and lava pathway mechanisms [38]. The areas for this study were chosen for th observing molten lava surfaces combined with the availability of a variety o datasets.
u Crater and propagating lava flows from the Pu [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halema currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. uma currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 m wide and 225 m long ( Figure 1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 m below the Halema . 2019, 11, x REVISION 3 of 21 available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve um temperature or representative emissivity spectrum. There are relatively few studies (i.e., have investigated the influence of spatial and spectral resolution on these calculations over ures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten that has the maximum temperature within each pixel will improve the accuracy and ty of the emissivity, kinetic temperature, and radiant flux. suring accurate thermal properties of a molten lava surface is also critical to lava flow ion models [15,24]. With the increasing number of spectral bands in more recent TIR imagers ES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained can then be used with approaches such as linear spectral deconvolution modeling to ively determine possible spectral end-member that defines the mineralogical, textural, and ractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is to determine the runout distance and hazard potential using radiant heat flux in lava flow ion models [15,24]. However, the accuracy of these derived parameters over the cooling ure range of typical lavas is less well constrained at the various spatial resolutions of current ments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the y-determined molten fraction should then reduce the uncertainty in flow model analyses that ely on these thermal properties.
Area study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in ebruary 2017 and 2018, a period when both the summit lava lake and coastal plain surface s were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and ing lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced ng sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until varied in size with maximum dimensions of 160 meters wide and 225 meters long (Figure uring this period, there were fluctuations in lava lake activity with continuous gas plumes ular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the the field campaigns, the lava lake level was relatively high but not overflowing, ately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, lava. The lava then sank in the south, distinguished by the occurrence of strong splattering ssing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the l 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the st Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 8 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These pagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe va flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed , both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 ruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], pathway mechanisms [38]. The areas for this study were chosen for the high probability of molten lava surfaces combined with the availability of a variety of remote sensing TIR uma te Sens. 2019, 11, x REVISION 3 of 21 ently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., ) that have investigated the influence of spatial and spectral resolution on these calculations over peratures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten tion that has the maximum temperature within each pixel will improve the accuracy and ertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow agation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers ., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and ssivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained ssivity can then be used with approaches such as linear spectral deconvolution modeling to ntitatively determine possible spectral end-member that defines the mineralogical, textural, and mal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is ired to determine the runout distance and hazard potential using radiant heat flux in lava flow agation models [15,24]. However, the accuracy of these derived parameters over the cooling perature range of typical lavas is less well constrained at the various spatial resolutions of current instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the iously-determined molten fraction should then reduce the uncertainty in flow model analyses that ctly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in ary/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and pagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced ing long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced . The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  4]. During this period, there were fluctuations in lava lake activity with continuous gas plumes irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the of the field campaigns, the lava lake level was relatively high but not overflowing, roximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, dified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many tions over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the sional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the er East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our -2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These s propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe ace lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed oehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 uea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of erving molten lava surfaces combined with the availability of a variety of remote sensing TIR sets.
u Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Pu 1, x REVISION 3 of 21 le low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve mperature or representative emissivity spectrum. There are relatively few studies (i.e., nvestigated the influence of spatial and spectral resolution on these calculations over ere a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten s the maximum temperature within each pixel will improve the accuracy and e emissivity, kinetic temperature, and radiant flux. accurate thermal properties of a molten lava surface is also critical to lava flow dels [15,24]. With the increasing number of spectral bands in more recent TIR imagers ] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained then be used with approaches such as linear spectral deconvolution modeling to etermine possible spectral end-member that defines the mineralogical, textural, and s [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is rmine the runout distance and hazard potential using radiant heat flux in lava flow dels [15,24]. However, the accuracy of these derived parameters over the cooling ge of typical lavas is less well constrained at the various spatial resolutions of current . Therefore, improving the accuracy of the kinetic temperature and emissivity of the mined molten fraction should then reduce the uncertainty in flow model analyses that hese thermal properties.
was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in ry 2017 and 2018, a period when both the summit lava lake and coastal plain surface e active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and a flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that ng nearly continuously for the past 500 years [33]. The lava surfaces are produced tained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced ke in the Halemaʻumaʻu Crater observed during this study was active from 2008 until in size with maximum dimensions of 160 meters wide and 225 meters long (Figure his period, there were fluctuations in lava lake activity with continuous gas plumes all explosions, finally ending with the summit collapse in May 2018 [13,34]. At the ld campaigns, the lava lake level was relatively high but not overflowing, 00-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating pwelling in the north that migrated to the south, cooled and formed plates of cooler, he lava then sank in the south, distinguished by the occurrence of strong splattering 4]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many numerous eruptive episodes, producing mostly pāhoehoe lava flows with the ava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the one (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These d down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 n have investigated lava discharge rates [36], lava flow emplacement tracking [37], ay mechanisms [38]. The areas for this study were chosen for the high probability of n lava surfaces combined with the availability of a variety of remote sensing TIR u 'Ō'ō vent were active for~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Pu currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.

Instruments
During the field campaigns, TIR data were acquired of the volcanic targets on 22 separate occasions. Of these, simultaneous data from all the sensors were acquired three times (Table 1). These included data from ground and airborne instruments made possible by two NASA-sponsored airborne campaigns to Hawaii in support of a proposed orbital mission data collection/analysis effort. The spaceborne data were acquired by the ASTER instrument, which has been in orbit aboard the Terra satellite since December 1999 [6]. Following the failure of the shortwave infrared (SWIR) system in 2008, ASTER is now a two-subsystem instrument with eight channels between 0.52 and 11.65 μm and a spatial resolution between 15 and 90 meters [6]. For this study, only the five TIR channels between 8.125 and 11.65 μm with a spatial resolution of 90 meters are used ( Table 2). The airborne MASTER and HyTES instruments were mounted on a NASA ER-2 aircraft that flew at an altitude of currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u Crater lava lake and Pu Remote Sens. 2019, 11, x REVISION 3 of 21 currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō lava flows at Kīlauea Volcano (white boxes). The ASTER data were acquired on March 7, 2017, at 10:06:02 HST. Insert shows the entire state of the Hawaiian island chain in the central Pacific Ocean, the red box indicating the area of the ASTER image shown.

Instruments
During the field campaigns, TIR data were acquired of the volcanic targets on 22 separate occasions. Of these, simultaneous data from all the sensors were acquired three times (Table 1). These included data from ground and airborne instruments made possible by two NASA-sponsored airborne campaigns to Hawaii in support of a proposed orbital mission data collection/analysis effort. The spaceborne data were acquired by the ASTER instrument, which has been in orbit aboard the Terra satellite since December 1999 [6]. Following the failure of the shortwave infrared (SWIR) system in 2008, ASTER is now a two-subsystem instrument with eight channels between 0.52 and 11.65 µm and a spatial resolution between 15 and 90 m [6]. For this study, only the five TIR channels between 8.125 and 11.65 µm with a spatial resolution of 90 m are used ( Table 2). The airborne MASTER and HyTES Remote Sens. 2020, 12, 193 5 of 21 instruments were mounted on a NASA ER-2 aircraft that flew at an altitude of~20 km. MASTER is a 50-channel instrument that detects radiance between 0.4 and 13.0 µm, with a FOV of 85.92 • resulting in a ground spatial resolution of~50 m from the flight altitude [21]. In this study, the seven TIR channels are used between 8.0 and 13 µm (Table 2). HyTES is a hyperspectral TIR instrument with 256 channels that detects radiance between 7.5 and 12 µm, with a FOV of 50 • resulting in a ground spatial resolution of~35 m at an altitude of~20 km [20]. In this study, 128 HyTES channels between 8.3 and 11.6 µm are used due to an instrument calibration resampling (Table 2). Finally, the MMT-Cam ground-based system acquired data in six spectral channels plus a broadband temperature channel between 8.0 and 11.5 µm, with a FOV of 45 • × 37 • (Table 2) [19].

Data Calibration
Before extracting the surface kinetic temperature and emissivity from the various datasets, the raw radiance data are calibrated and corrected for instrumentation and atmospheric effects ( Figure 2). The ASTER instrument data are radiometrically calibrated by viewing an internal constant temperature blackbody and cold space. Occasionally, the internal blackbody is heated and cooled to provide a multi-temperature radiometric calibration [6]. The MASTER and HyTES data are corrected for aircraft motion and orthorectified using digital terrain models [20,21]. The MASTER instrument is spectrally and radiometrically calibrated in the laboratory using two blackbodies pre-and post-campaign, with a cold blackbody used during the data acquisition [21]. In the laboratory, the HyTES instrument is spectrally calibrated using narrowband interference filters and radiometrically calibrated using a blackbody between 4 and 40 • C [20]. Finally, the MMT-Cam instrument is spectrally and radiometrically calibrated in the laboratory using a blackbody between 20 and 800 • C [19].
The ASTER, MASTER, HyTES, and MMT-Cam radiometrically calibrated at-sensor TIR radiance data are all atmospherically corrected to derive the at-surface radiance ( Figure 2). The MASTER and ASTER data are corrected using the MODTRAN radiative transfer model with the water vapor scaling method to optimize the atmospheric correction [39]. The HyTES data are corrected using the in-scene atmospheric correction method [40]. The MMT-Cam spectral channels are co-registered using a fast Fourier transform algorithm with centroid matching and then atmospherically corrected using the SpectralCalc simulator [19]. [28]. The algorithm first assumes a brightness temperature using a maximum scene emissivity and the spectral morphology of each pixel is derived. An emissivity calibration curve relating spectral contrast to the minimum emissivity is then used to constrain the true emissivity values from band ratios. The calibration curve is empirically determined for each instrument separately using data from a laboratory spectral library. Finally, the kinetic temperature is then calculated from the maximum derived emissivity using the inverse Planck function [28].

Thermally-Mixed Pixel (TMP) Separation Analysis
In most TIR remote sensing data of active volcanic thermal anomalies, a pixel contains multiple surface fractions (or end-members) that can include temperature, composition, and texture. The spectrum of a mixed pixel composed of two or more fractions represents the areal-weighted averages of those end-members rather than being dominated by any one [29]. This problem increases in complexity with lower spatial resolution data and the increased mixing of potentially more surface fractions [41]. However, the end-members within any given pixel can be deciphered with knowledge of radiance theory, a well-developed spectral deconvolution model, and an understanding of the spectral signatures of the end-members (e.g., an end-member spectral library).
A straightforward solution to the thermally-mixed pixel problem was originally developed by Dozier [42] using a dual-band approach to define the two thermal fractions within a pixel ( Figure 2). The method uses surface radiance values from two spectral channels to derive the unique combination of each fraction, both the value and proportion:

Kinetic Temperature and Emissivity
Kinetic temperature and emissivity are derived from the calibrated surface radiance data using the temperature emissivity separation (TES) algorithm ( Figure 2), first developed for ASTER data [28]. The algorithm first assumes a brightness temperature using a maximum scene emissivity and the spectral morphology of each pixel is derived. An emissivity calibration curve relating spectral contrast to the minimum emissivity is then used to constrain the true emissivity values from band ratios. The calibration curve is empirically determined for each instrument separately using data from a laboratory spectral library. Finally, the kinetic temperature is then calculated from the maximum derived emissivity using the inverse Planck function [28].

Thermally-Mixed Pixel (TMP) Separation Analysis
In most TIR remote sensing data of active volcanic thermal anomalies, a pixel contains multiple surface fractions (or end-members) that can include temperature, composition, and texture. The spectrum of a mixed pixel composed of two or more fractions represents the areal-weighted averages of those end-members rather than being dominated by any one [29]. This problem increases in complexity with lower spatial resolution data and the increased mixing of potentially more surface fractions [41]. However, the end-members within any given pixel can be deciphered with knowledge of radiance theory, a well-developed spectral deconvolution model, and an understanding of the spectral signatures of the end-members (e.g., an end-member spectral library).
A straightforward solution to the thermally-mixed pixel problem was originally developed by Dozier [42] using a dual-band approach to define the two thermal fractions within a pixel ( Figure 2). The method uses surface radiance values from two spectral channels to derive the unique combination of each fraction, both the value and proportion: where, M (λ n ,T int ) is the mixed surface radiance in channel n for the mixed temperature (T int ). M (λ n ,T h ) and M (λ n ,T b ) are the surface radiances contributed by the hot temperature fraction and background temperature fraction, respectively; and p is the proportion of the hot fraction within the pixel area [42,43].
Equation (1) is solved with two simultaneous equations at two different wavelength channels, each containing two unknown variables. This approach provides a unique solution for the radiance of one fraction (either molten lava or the background) and its fractional proportion after assuming or knowing the value for the other radiance value.
In this study, the surface radiance values are unmixed within each pixel for each dataset using a channel at 8.5 µm and 11.0 µm. The background fraction applied to the analysis is the average value of the non-active regions for each scene and each channel in the dataset. After the thermal mixed pixel (TMP) separation analysis is applied, the molten fraction datasets are integrated into the TES algorithm in order to derive kinetic temperature and emissivity of the molten fractions only (Figure 2). These values for each pixel are then compared to the results from the same pixels prior to the unmixing analysis. Finally, the variability within each dataset is quantified to evaluate the effect of spatial and spectral resolution on the discrepancy and uniqueness.

Accuracy and Uncertainty Assessment
The accuracy and degree of variability of the measured surface radiance as well as the derived kinetic temperature and emissivity for each TIR dataset are quantified through comparative analysis ( Figure 2). The TMP separation analysis approach is held as constant as possible to evaluate only the influence of spatial resolution. After spatial resolution, the largest variability between the datasets is the spectral resolution, which has less of an effect because the channel locations are commonly within 0.5 µm of each other. The hyperspectral resolution of the HyTES data increases the level of complexity for the comparative analysis to the multispectral resolution datasets. All analyses on the HyTES data are computed at full resolution, however, these results are then spectrally degraded to perform the later comparison. The HyTES data also provide a spectral resolution comparison with the MASTER data acquired at the same time and at a similar spatial resolution, which allows the influence of spectral resolution to be quantified. Finally, the sensitivity of spatial resolution on the derived kinetic temperature and emissivity is determined to quantify constraints on the degree of uncertainty with spatial resolution change.

ASTER Data
Two regions of interest (ROI) of cooling lava surfaces (the lava lake at the Halema fraction that has the maximum temperature within each pixel will improv uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also propagation models [15,24]. With the increasing number of spectral bands in mor (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiat emissivity of an object's surface can be extracted with increasing accuracy [26-28 emissivity can then be used with approaches such as linear spectral deconv quantitatively determine possible spectral end-member that defines the minera thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser d required to determine the runout distance and hazard potential using radiant h propagation models [15,24]. However, the accuracy of these derived paramet temperature range of typical lavas is less well constrained at the various spatial r TIR instruments. Therefore, improving the accuracy of the kinetic temperature previously-determined molten fraction should then reduce the uncertainty in flow directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano January/February 2017 and 2018, a period when both the summit lava lake and lava flows were active. It focused primarily on the lava lake in the Halem propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basalti has been erupting nearly continuously for the past 500 years [33]. The lava su during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a' [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was a 2018 and varied in size with maximum dimensions of 160 meters wide and 225 1) [34]. During this period, there were fluctuations in lava lake activity with con and irregular small explosions, finally ending with the summit collapse in May time of the field campaigns, the lava lake level was relatively high bu approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was con with fresh lava upwelling in the north that migrated to the south, cooled and for solidified lava. The lava then sank in the south, distinguished by the occurrence and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 ye locations over numerous eruptive episodes, producing mostly pāhoehoe l occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows 2017-2018 study were part of the 61g episode that erupted from the east flank flows propagated down the Pulama pali and entered the ocean at Kamokuna as surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows obs pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing stu Kīlauea eruption have investigated lava discharge rates [36], lava flow emplac and lava pathway mechanisms [38]. The areas for this study were chosen for th observing molten lava surfaces combined with the availability of a variety of datasets.
uma fraction that has the maximum temperature within each pixel will im uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is propagation models [15,24]. With the increasing number of spectral bands i (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the r emissivity of an object's surface can be extracted with increasing accuracy [ emissivity can then be used with approaches such as linear spectral d quantitatively determine possible spectral end-member that defines the m thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a le required to determine the runout distance and hazard potential using rad propagation models [15,24]. However, the accuracy of these derived pa temperature range of typical lavas is less well constrained at the various sp TIR instruments. Therefore, improving the accuracy of the kinetic tempera previously-determined molten fraction should then reduce the uncertainty i directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Vo January/February 2017 and 2018, a period when both the summit lava lak lava flows were active. It focused primarily on the lava lake in the H propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a b has been erupting nearly continuously for the past 500 years [33]. The la during long sustained eruptions where pāhoehoe (tube-and surface-fed) a [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study 2018 and varied in size with maximum dimensions of 160 meters wide an 1) [34]. During this period, there were fluctuations in lava lake activity wi and irregular small explosions, finally ending with the summit collapse in time of the field campaigns, the lava lake level was relatively hig approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It wa with fresh lava upwelling in the north that migrated to the south, cooled an solidified lava. The lava then sank in the south, distinguished by the occur and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~ locations over numerous eruptive episodes, producing mostly pāhoe occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava f 2017-2018 study were part of the 61g episode that erupted from the east flows propagated down the Pulama pali and entered the ocean at Kamoku surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flow pāhoehoe, both sheet-like and ropey in texture. Previous remote sensin Kīlauea eruption have investigated lava discharge rates [36], lava flow em and lava pathway mechanisms [38]. The areas for this study were chosen observing molten lava surfaces combined with the availability of a varie datasets.
u Crater and the lava flows from Pu temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō on the coastal plain) are chosen to evaluate the retrieval of surface radiance, kinetic temperature, and emissivity from the ASTER data. Within these ROIs, mixtures of both the cool crust and molten lava surfaces are represented in most pixels (Figure 3).  The ASTER surface radiance of the active lava is lower than expected for molten basalt ( Figure  4) with an average of 19.74 W·m -2 ·sr -1 ·µ m -1 and a variability of 5.85 W·m -2 ·sr -1 ·µ m -1 . The emissivity spectra have an absorption feature at 8.63 µ m and higher spectral contrast in the lava lake data. The average pixel-integrated emissivity is 0.898 with a variability of 0.077 (Figure 4), whereas the average pixel-integrated kinetic temperature is 354.1 K with a variability of 23.8 K; both of which are significantly lower than expected for molten basaltic lavas [44,45]. temperatures where a molten lava surface cools (<1450 K). Therefore, simply d fraction that has the maximum temperature within each pixel will imp uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is al propagation models [15,24]. With the increasing number of spectral bands in m (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the rad emissivity of an object's surface can be extracted with increasing accuracy [26emissivity can then be used with approaches such as linear spectral deco quantitatively determine possible spectral end-member that defines the min thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesse required to determine the runout distance and hazard potential using radian propagation models [15,24]. However, the accuracy of these derived param temperature range of typical lavas is less well constrained at the various spati TIR instruments. Therefore, improving the accuracy of the kinetic temperatu previously-determined molten fraction should then reduce the uncertainty in f directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volca January/February 2017 and 2018, a period when both the summit lava lake a lava flows were active. It focused primarily on the lava lake in the Hale propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basa has been erupting nearly continuously for the past 500 years [33]. The lava during long sustained eruptions where pāhoehoe (tube-and surface-fed) and [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study wa 2018 and varied in size with maximum dimensions of 160 meters wide and 2 1) [34]. During this period, there were fluctuations in lava lake activity with and irregular small explosions, finally ending with the summit collapse in M time of the field campaigns, the lava lake level was relatively high approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was c with fresh lava upwelling in the north that migrated to the south, cooled and solidified lava. The lava then sank in the south, distinguished by the occurren and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 locations over numerous eruptive episodes, producing mostly pāhoeho occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 w lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flow 2017-2018 study were part of the 61g episode that erupted from the east fla flows propagated down the Pulama pali and entered the ocean at Kamokuna surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows o pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing Kīlauea eruption have investigated lava discharge rates [36], lava flow emp and lava pathway mechanisms [38]. The areas for this study were chosen for observing molten lava surfaces combined with the availability of a variety datasets. uma temperatures where a molten lava surface cools (<1450 K). Therefore, sim fraction that has the maximum temperature within each pixel will uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface propagation models [15,24]. With the increasing number of spectral band (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), th emissivity of an object's surface can be extracted with increasing accuracy emissivity can then be used with approaches such as linear spectral quantitatively determine possible spectral end-member that defines the thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a required to determine the runout distance and hazard potential using r propagation models [15,24]. However, the accuracy of these derived p temperature range of typical lavas is less well constrained at the various TIR instruments. Therefore, improving the accuracy of the kinetic temp previously-determined molten fraction should then reduce the uncertaint directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea January/February 2017 and 2018, a period when both the summit lava la lava flows were active. It focused primarily on the lava lake in the propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a has been erupting nearly continuously for the past 500 years [33]. The during long sustained eruptions where pāhoehoe (tubeand surface-fed) [33]. The lava lake in the Halemaʻumaʻu Crater observed during this stud 2018 and varied in size with maximum dimensions of 160 meters wide 1) [34]. During this period, there were fluctuations in lava lake activity and irregular small explosions, finally ending with the summit collapse time of the field campaigns, the lava lake level was relatively approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It w with fresh lava upwelling in the north that migrated to the south, cooled solidified lava. The lava then sank in the south, distinguished by the occ and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active fo locations over numerous eruptive episodes, producing mostly pāh occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 20 lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lav 2017-2018 study were part of the 61g episode that erupted from the ea flows propagated down the Pulama pali and entered the ocean at Kamo surface lava flow and lava tubes (Figure 1) [35]. The majority of the flo pāhoehoe, both sheet-like and ropey in texture. Previous remote sens Kīlauea eruption have investigated lava discharge rates [36], lava flow and lava pathway mechanisms [38]. The areas for this study were chose observing molten lava surfaces combined with the availability of a va datasets.
u Crater lava lake and Pu 3]) that have investigated the influence of spatial and spectral resolution on these calculations over mperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten action that has the maximum temperature within each pixel will improve the accuracy and ncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow ropagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers .g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and missivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained missivity can then be used with approaches such as linear spectral deconvolution modeling to uantitatively determine possible spectral end-member that defines the mineralogical, textural, and ermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is quired to determine the runout distance and hazard potential using radiant heat flux in lava flow ropagation models [15,24]. However, the accuracy of these derived parameters over the cooling mperature range of typical lavas is less well constrained at the various spatial resolutions of current IR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the reviously-determined molten fraction should then reduce the uncertainty in flow model analyses that irectly rely on these thermal properties.

.1. Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in nuary/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface va flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and ropagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basaltic shield volcano that as been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced uring long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced 3]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  ) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes nd irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the me of the field campaigns, the lava lake level was relatively high but not overflowing, pproximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating ith fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, lidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering nd degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many cations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the ccasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the wer East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These ows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe rface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed āhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 īlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], nd lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of bserving molten lava surfaces combined with the availability of a variety of remote sensing TIR atasets. The ASTER surface radiance of the active lava is lower than expected for molten basalt (Figure 4) with an average of 19.74 W·m −2 ·sr −1 ·µm −1 and a variability of 5.85 W·m −2 ·sr −1 ·µm −1 . The emissivity spectra have an absorption feature at 8.63 µm and higher spectral contrast in the lava lake data. The average pixel-integrated emissivity is 0.898 with a variability of 0.077 (Figure 4), whereas the average pixel-integrated kinetic temperature is 354.1 K with a variability of 23.8 K; both of which are significantly lower than expected for molten basaltic lavas [44,45]. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.

MASTER and HyTES Data
The same two ROIs were selected in the MASTER and HyTES data; however, the number of pixels that constitute each of these are higher by a factor of approximately three compared to ASTER (Figure 3).
The MASTER surface radiance is also lower than expected for the temperatures of molten basalt (Figure 4)  The HyTES surface radiance data are lower than those extracted from MASTER over the lava flows but greater over the lava lake ( Figure 4). The average surface radiance is 34.83 W·m −2 ·sr −1 ·µm −1 with a variability of 13.81 W·m −2 ·sr −1 ·µm −1 . The emissivity spectra have an absorption feature at~9.48 µm (Figure 4). The average pixel-integrated emissivity is 0.805 with a variability of 0.114, and lower values are derived from the lava lake; whereas the average pixel-integrated kinetic temperature is 407.8 K with a variability of 32.5 K. These values are also lower than the MASTER-derived temperatures, but at a lower variability.

MMT-Cam Data
The MMT-Cam data presented here are extracted from ROIs covering similar activity to the airborne and orbital data ROIs, especially at the lava lake (Figure 3). The lava flow ROIs, however, are significantly smaller but more spatial detail is observed in these data due to the high spatial resolution (<0.1 m). The radiance and kinetic temperatures derived from the MMT-Cam data are higher than the other datasets analyzed in the study, as expected.
The radiance derived from the MMT-Cam ROIs is closer to the values for molten basalt at the wavelengths and bandwidths of the MMT-Cam instrument (Figure 4). The average is 162.91 W·m −2 ·sr −1 ·µm −1 with a variability of 76.31 W·m −2 ·sr −1 ·µm −1 . The emissivity spectra show a strong absorption between 8.55 and 9.55 µm, with both a single broad feature and two narrow features ( Figure 4). The average pixel-integrated emissivity is 0.739 with a variability of 0.087, and the average pixel-integrated kinetic temperature is 736.2 K with a variability of 163.0 K.

Mixed Pixel Derivation
All the TIR datasets were next subjected to a thermally-mixed pixel separation analysis to extract the values associated with the maximum thermal fraction within each pixel (i.e., molten lava). This step evaluates the ability to measure an accurate molten fraction (if one is present) regardless of spatial scale within a given pixel and the radiance values associated with it. The background radiance values applied to this analysis are calculated from the average values of pixels at the background temperature for each channel of each dataset and observation. The largest difference between the original data and the unmixed counterparts was observed in the ASTER data and the smallest was seen in the MMT-Cam data, as might be expected based on their pixel sizes.
Following the mixed pixel derivations using an average background radiance of 8.18 W·m −2 ·sr −1 ·µm −1 , the average ASTER surface radiance for the molten fraction increases to 493.22 W·m −2 ·sr −1 ·µm −1 as does the variability to 191.57 W·m −2 ·sr −1 ·µm −1 ( Figure 5). The emissivity spectra have an absorption feature at 8.63 µm (except in one lava flow dataset) with a strong decrease in emissivity at shorter wavelengths ( Figure 5). The absorption feature observed at 8.5-9.0 µm is associated with a molten Si-O absorption and is likely absent in the ASTER lava flow data due to the very low molten fractions (<0.05) observed with pixels at this target. The average molten fraction emissivity is 0.752 with a variability of 0.099; whereas the average molten fraction kinetic temperature is 1242.3 K with a variability of 337.0 K. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u Crater lava lake and (red) Pu Remote Sens. 2019, 11, x REVISION currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately re the maximum temperature or representative emissivity spectrum. There are relatively few studie [23]) that have investigated the influence of spatial and spectral resolution on these calculations temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the m fraction that has the maximum temperature within each pixel will improve the accuracy uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava propagation models [15,24]. With the increasing number of spectral bands in more recent TIR im (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperatur emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constr emissivity can then be used with approaches such as linear spectral deconvolution modeli quantitatively determine possible spectral end-member that defines the mineralogical, textura thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissiv required to determine the runout distance and hazard potential using radiant heat flux in lava propagation models [15,24]. However, the accuracy of these derived parameters over the co temperature range of typical lavas is less well constrained at the various spatial resolutions of cu TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity previously-determined molten fraction should then reduce the uncertainty in flow model analyse directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, US January/February 2017 and 2018, a period when both the summit lava lake and coastal plain su lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crate propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basaltic shield volcan has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are prod during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emp [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long (F 1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas pl and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. A time of the field campaigns, the lava lake level was relatively high but not overflo approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circu with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of c solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splat and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows wit occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed durin 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāho surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tub pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking and lava pathway mechanisms [38]. The areas for this study were chosen for the high probabi observing molten lava surfaces combined with the availability of a variety of remote sensin datasets.
u 'Ō'ō lava flows derived from the thermal mixed pixel molten fraction of the ASTER TIR, MASTER TIR, HyTES, and MMT-Cam data. The error bars represent the standard deviation variation in the ROI data. Note there are no HyTES data between 9.92 and 10.75 µm on 02/08/2018 so these data are not included in the lava lake plots.
For the unmixed MASTER data using an average background radiance of 8.38 W·m −2 ·sr −1 ·µm −1 , the average surface radiance derived for the maximum thermal fraction is 300.59 W·m −2 ·sr −1 ·µm −1 with a variability of 111.48 W·m −2 ·sr −1 ·µm −1 ( Figure 5). The emissivity spectra from the lava lake show an absorption feature at 8.63 µm and the lava flow ROIs show a broad absorption feature at 10.63 µm with a decrease at wavelengths shorter than 9.09 µm ( Figure 5). The average molten fraction emissivity is 0.584 with a variability of 0.141; whereas the average molten fraction kinetic temperature is 1128.2 K with a variability of 408.0 K.
Using an average calculated background radiance of 8.01 W·m −2 ·sr −1 ·µm −1 , the average HyTES surface radiance derived for the molten fraction is 402.64 W·m −2 ·sr −1 ·µm −1 with a variability of 146.68 W·m −2 ·sr −1 ·µm −1 . The emissivity spectra show an absorption feature at around 9.5 µm and a broader feature centered at 9.75 µm, with a decrease in overall emissivity at shorter wavelengths ( Figure 5). The average molten fraction emissivity and kinetic temperature are 0.604 and 1266.1 K with variabilities of 0.260 and 404.0 K, respectively.
Lastly, using an average background radiance of 15.26 W·m −2 ·sr −1 ·µm −1 , the average molten surface radiance derived from the MMT-Cam data is 454.27 W·m −2 ·sr −1 ·µm −1 with a variability of 158.12 W·m −2 ·sr −1 ·µm −1 . The derived lava lake emissivity spectra show a single absorption feature between 8.55 and 8.99 µm or a double feature at 8.55 and 9.55 µm ( Figure 5). The lava flow emissivity spectra decrease in emissivity below 10.05 µm and is centered at 8.55 µm ( Figure 5). The average molten fraction emissivity and kinetic temperature values are 0.711 and 1225.9 K with variabilities of 0.078 and 329.6 K, respectively.

Comparisons and Trends
Qualitatively, significant variations are observed between the four datasets as a consequence of differences in spatial resolutions (Figure 3). The low spatial resolution ASTER data provide the least lava surface detail, whereas the high-resolution MMT-Cam data provide the greatest details. For example, crustal plates and molten spreading margins at the lava lake are observed in the MMT-Cam data but not in the ASTER data ( Figure 3). However, the entire lava flow field is underrepresented in the MMT-Cam data due to the proximity of the instrument to the target. Additionally, greater spatial details of lava surface features are discerned in the HyTES data compared to the MASTER data, likely the result of a higher number of spectral channels (Figure 3). In general, the spatial resolution of the instrument strongly correlates to the scale of spatial detail qualitatively observed of the lava surfaces.
In all datasets, the surface radiance increases after the TMP separation analysis as would be expected. The ASTER surface radiance increases the most in the lava lake (2100%) and lava flow (2700%) data, compared to only a 70% and 330% increase in the MMT-Cam data, respectively ( Figure 6 and Table 3). The MASTER and HyTES surface radiances increase by 500% and 200% in the lava lake data and 2800% and 3200% in the lava flow data, respectively. The highest increases are observed at shorter wavelengths (Figure 6), which is consistent with Wein's Law where the peak radiance shifts to shorter wavelengths with increasing temperature [41]. The TMP separation analysis appears to provide a consistent and reasonable method for extracting the higher temperature fractions and allows more accurate values of surface radiance, kinetic temperature, and emissivity to be extracted from the lower spatial resolution datasets. Table 3. The combined spatial and spectral average emissivity and kinetic temperature values preand post-thermal mixed pixel (TMP) separation analysis for each dataset, including the percentage improvement. The values in parenthesizes represent the standard deviation variation in the data.  currently available low spatial resolution (>500 m) TIR datasets that are not ab the maximum temperature or representative emissivity spectrum. There are re [23]) that have investigated the influence of spatial and spectral resolution on temperatures where a molten lava surface cools (<1450 K). Therefore, simply d fraction that has the maximum temperature within each pixel will impr uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is al propagation models [15,24]. With the increasing number of spectral bands in m (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the rad emissivity of an object's surface can be extracted with increasing accuracy [26emissivity can then be used with approaches such as linear spectral deco quantitatively determine possible spectral end-member that defines the min thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesse required to determine the runout distance and hazard potential using radian propagation models [15,24]. However, the accuracy of these derived param temperature range of typical lavas is less well constrained at the various spati TIR instruments. Therefore, improving the accuracy of the kinetic temperatu previously-determined molten fraction should then reduce the uncertainty in f directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volca January/February 2017 and 2018, a period when both the summit lava lake a lava flows were active. It focused primarily on the lava lake in the Hale propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basa has been erupting nearly continuously for the past 500 years [33]. The lava during long sustained eruptions where pāhoehoe (tube-and surface-fed) and [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study wa 2018 and varied in size with maximum dimensions of 160 meters wide and 2 1) [34]. During this period, there were fluctuations in lava lake activity with and irregular small explosions, finally ending with the summit collapse in M time of the field campaigns, the lava lake level was relatively high approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was c with fresh lava upwelling in the north that migrated to the south, cooled and solidified lava. The lava then sank in the south, distinguished by the occurren and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 locations over numerous eruptive episodes, producing mostly pāhoehoe occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 w lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flow 2017-2018 study were part of the 61g episode that erupted from the east fla flows propagated down the Pulama pali and entered the ocean at Kamokuna surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows o pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing s Kīlauea eruption have investigated lava discharge rates [36], lava flow emp and lava pathway mechanisms [38]. The areas for this study were chosen for observing molten lava surfaces combined with the availability of a variety datasets.
uma Remote Sens. 2019, 11, x REVISION currently available low spatial resolution (>500 m) TIR datasets that are n the maximum temperature or representative emissivity spectrum. There a [23]) that have investigated the influence of spatial and spectral resolutio temperatures where a molten lava surface cools (<1450 K). Therefore, sim fraction that has the maximum temperature within each pixel will uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface propagation models [15,24]. With the increasing number of spectral band (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), th emissivity of an object's surface can be extracted with increasing accuracy emissivity can then be used with approaches such as linear spectral quantitatively determine possible spectral end-member that defines the thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a required to determine the runout distance and hazard potential using r propagation models [15,24]. However, the accuracy of these derived p temperature range of typical lavas is less well constrained at the various TIR instruments. Therefore, improving the accuracy of the kinetic tempe previously-determined molten fraction should then reduce the uncertaint directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea January/February 2017 and 2018, a period when both the summit lava la lava flows were active. It focused primarily on the lava lake in the propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a has been erupting nearly continuously for the past 500 years [33]. The during long sustained eruptions where pāhoehoe (tubeand surface-fed) [33]. The lava lake in the Halemaʻumaʻu Crater observed during this stud 2018 and varied in size with maximum dimensions of 160 meters wide 1) [34]. During this period, there were fluctuations in lava lake activity and irregular small explosions, finally ending with the summit collapse time of the field campaigns, the lava lake level was relatively approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It w with fresh lava upwelling in the north that migrated to the south, cooled solidified lava. The lava then sank in the south, distinguished by the occ and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active fo locations over numerous eruptive episodes, producing mostly pāh occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 20 lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lav 2017-2018 study were part of the 61g episode that erupted from the ea flows propagated down the Pulama pali and entered the ocean at Kamo surface lava flow and lava tubes (Figure 1) [35]. The majority of the flo pāhoehoe, both sheet-like and ropey in texture. Previous remote sens Kīlauea eruption have investigated lava discharge rates [36], lava flow and lava pathway mechanisms [38]. The areas for this study were chose observing molten lava surfaces combined with the availability of a va datasets. currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux. Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent (Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tubeand surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō lava flows on January 30, 2019. The error bars represent the standard deviation variation in the ROI data. Note there are no HyTES data between 9.92 and 10.75 µm on 02/08/2018 so these data are not included in the lava lake plots.
In general, the pixel-integrated temperatures derived from data prior to the TMP separation analysis show an inverse relationship with spatial resolution, with the larger pixels potentially containing the smallest fraction of molten lava. The ASTER data have the lowest kinetic temperatures and the MMT-Cam have the highest. Compared with the 35-m spatial resolution HyTES data, however, the 50-m spatial resolution MASTER data do have a higher derived pixel integrated temperature but at a higher variability. All the kinetic temperatures derived from the mixed-pixel data are significantly below that expected for a molten basaltic lava surface (~1450 K). In contrast, the average derived molten fraction temperature in every dataset is above 1100 K, significantly closer to what is expected for molten basaltic lava. Unmixing the HyTES data produced the highest average molten fraction temperature (1266.1 K) but with a high variability (404 K), implying there is still significant uncertainty at 35-m resolution. The MMT-Cam derived molten fraction temperatures span the liquidus temperatures of basaltic lava at the lowest variability, which provides the highest constraint on the derived data.
The integration of the TMP calculation into the derivation of temperature improves the accuracy of the measured kinetic temperature associated with the molten lava fraction in all the datasets.
Emissivity spectra derived from these data before the TMP separation analysis have similar spectral morphologies to laboratory-derived results of molten basalts [44][45][46]. However, the spectral contrast is less than expected from laboratory results by up to 40% for ASTER ( Figure 6). The MMT-Cam emissivity values are less than 15% shallower than laboratory data, with the MASTER and HyTES emissivity values being within 20%-30% ( Figure 6). Following the TMP separation analysis, the spectral depths and contrasts increased to values consistent with those derived from laboratory experiments ( Figure 6) [44][45][46]. The spectral morphology remained similar with a decrease in emissivity at shorter wavelengths and an increase at longer wavelengths. These results are also more exaggerated in the lava flow data (Figure 6), implying that there is high thermal mixing within a pixel representing the lava flow than the lava lake. For example, the improvement in the ASTER data highlights an absorption feature centered at~8.5 µm with an increase in emissivity at longer wavelengths compared to absorption features centered at~8.0 µm and~10.5 µm in the improved MMT-Cam data. The improvements are attributed to variations in spatial and spectral resolution between the two instruments, as well as the difference in channel locations that resolve slightly different Si-O bonding. Similar trends are also detected in the HyTES and MMT-Cam data.

Discussion
The ability to remotely measure accurate surface radiance, kinetic temperature, and emissivity of a molten lava surface within a thermally-mixed pixel is important. Developing a methodology to extract only the molten fraction within every pixel of these datasets and constrain the uncertainty improves the subsequently-derived thermal data required for monitoring, scientific analysis, and later modeling studies. The results from the TMP separation analysis show that greatly improved radiance, kinetic temperature, and emissivity values can be extracted at different spatial and spectral scales. This methodology can be implemented with a variety of data quickly and uncertainties quantified. The TMP separation analysis is not new but has had limited application in volcanic hazard prediction models and assessments. Prior studies have shown that a typical lava surface has multiple thermal fractions (up to 8) at high spatial scales [7,23,47]. However, the processing required to analyze these fractions can be daunting at the scale of an entire flow field or slow in the case of an ongoing eruption. Furthermore, there is a somewhat limited applicability for this level of multiple fraction analysis in current lava flow propagation models where only the maximum molten fraction has the greatest influence on model results [15,24]. Therefore, improving the analysis of remote sensing data to provide rapid kinetic temperature and emissivity values of the highest temperature fractions within TIR image pixels will greatly improve and further constrain lava flow propagation models.

Emissivity
The spatial resolution of the TIR dataset has only a limited effect on the morphology of the emissivity spectra but does strongly influence the spectral depth. This result shows that the efficiency of radiative heat loss from a molten surface is overestimated more in TIR data with lower spatial resolutions. The emissivity spectra of the molten fraction show improved accuracy in the spectral contrast to those values expected for molten basaltic lava surfaces within the uncertainty calculated ( Figure 6). The average minimum emissivity decreases by 20%, with the largest decrease observed in the HyTES data (33%) and the smallest decrease observed in the MMT-Cam data (4%). Additionally, larger decreases in emissivity are observed at the shorter wavelengths in all the datasets (Figure 6), which highlights the non-uniform influence of kinetic temperature on emissivity and the non-uniform mixing of thermal anomalies. Our results show that for future thermal studies of molten basaltic surface, a more appropriate value for the minimum emissivity would be 0.66 rather than the common values of 0.95 to 1.0 used in prior studies (i.e., [18,44,[48][49][50]) and thermorheological models of lava flow propagation (i.e., [15,24]). This minimum emissivity value is consistent with a previous study of 0.55 for a cooling basaltic lava from Pu 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes (Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō at 1323 K [44] and a laboratory study of melts (albeit silicic ones) that measured emissivity of 0.68 at 1573 K [46]. However, the use of these higher maximum emissivity values used in these past studies of cooled basaltic lava surfaces is appropriate given the results calculated in this study. The TMP separation analysis identifying the molten fraction provides a useful approach for deriving and evaluating the actual emissivity of molten material seen in a variety of TIR instruments independent of spatial and spectral resolution.

Kinetic Temperature
The maximum temperatures derived from all the datasets following the TMP separation are closer to the liquidus temperatures of Hawaiian basalt [51], within the variability of the data ( Table 3). The analysis improves the derived kinetic temperatures by up to 250% (ASTER TIR) and 70% in the MMT-Cam data. Although the eruption temperature of Hawaiian basalt is well-known from past direct measurements and petrologic analysis, the variability in the temperatures from this approach is critical for evaluating the uncertainty in subsequent studies that rely upon these measurements. The quantification of the temperature uncertainty improves the confidence and understanding of those model predictions, allowing more informed conclusions to be drawn from their forecasting estimates, for example.

Accuracy Assessment
The ability to measure accurate thermal properties of a surface from calibrated TIR data is influenced by numerous instrument factors including the spatial, spectral, and temporal resolution of those data as well as external factors such as the spatiotemporal variability of the surface itself. Molten lava surfaces vary, over seconds to minutes and centimeters to meters, either by lava flow propagation (breakouts) or lava lake overturning. To analyze the influence of the spatial and temporal scales, a variety of TIR datasets with different resolutions were needed. Most importantly, the new MMT-Cam data are used to validate the lower resolution datasets and determine whether both the anomalies and processes (e.g., lava lake overturning and flow crustal formation/morphology) are captured [12]. Typically, lower spatial resolution increases aggregation that leads to an increase in variability and a decrease in the ability to quantify the small-scale details.
Our analysis shows that the airborne and orbital data provide reliable and accurate results for the larger-scale anomalies and processes. Typically, anomalies 1.5 to 2 times the size of the spatial resolution of the dataset are required for more accurate estimates of kinetic temperature and emissivity, whereas even larger volcanic processes are required to be discerned individually. For example, the~200 m diameter lava lake and >100 m long lava flows provide good targets for anomaly detection; however, the overturning and crustal formation observed within these anomalies are not identified in ASTER data and rarely in the airborne TIR data.
The temporal resolution also significantly influences the reliability of the TIR data, especially if the repeat time is greater than hours (which is the case for the ASTER and airborne instruments). As a result, these data underestimate the percentage of molten lava on the surface and its accurate radiance, kinetic temperature, and emissivity. Compared to the MMT-Cam TMP separation analysis, the same analysis of the airborne and orbital data underestimates the surface radiance by as much as 430% and 800%, respectively (Figures 4, 7 and 8). This translates to a lava emissivity error of 5% and 20% with a corresponding kinetic temperature error of 80% and 120%, respectively (Figures 4, 7 and 8). Separately evaluating the lava lake and lava flow data reveals the airborne and orbital data of the lava lake are 30% better compared to the lava flow data due mainly to the larger spatial scale and more uniform surface state of the lake (Figures 4, 7 and 8).
the same analysis of the airborne and orbital data underestimates the surface radiance by as much as 430% and 800%, respectively (Figures 4, 7, and 8). This translates to a lava emissivity error of 5% and 20% with a corresponding kinetic temperature error of 80% and 120%, respectively (Figures 4, 7, and  8). Separately evaluating the lava lake and lava flow data reveals the airborne and orbital data of the lava lake are 30% better compared to the lava flow data due mainly to the larger spatial scale and more uniform surface state of the lake (Figures 4, 7, and 8). Values closer to 1.0 require less TMP separation processing. The error bars represent the standard deviation variation in the ROI data. Note there are no HyTES data between 9.92 and 10.75 µ m on 02/08/2018 so these data are not included in the lava lake plots.
Larger pixel sizes also have a higher probability of integrating more than one surface thermal property, which leads to errors in the data analysis and ultimately subsequent results that are inaccurate. The dual-band mixed pixel approach is one possible solution and results show that it does improve the deviation of thermal properties of molten lava surfaces (Figures 7 and 8). The molten Figure 7. The ratio between the pre-and post-TMP separation of the molten fraction for the (A) surface radiance and (B) emissivity for the Halema currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets. uma currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u Crater lava lake acquired on February 6, 2018. Values closer to 1.0 require less TMP separation processing. The error bars represent the standard deviation variation in the ROI data. Note there are no HyTES data between 9.92 and 10.75 µm on 02/08/2018 so these data are not included in the lava lake plots.
Larger pixel sizes also have a higher probability of integrating more than one surface thermal property, which leads to errors in the data analysis and ultimately subsequent results that are inaccurate. The dual-band mixed pixel approach is one possible solution and results show that it does improve the deviation of thermal properties of molten lava surfaces (Figures 7 and 8). The molten surface radiance values are all within 25% of the MMT-Cam values, an improvement of up to 300% (Figures 7 and 8). The molten emissivity and kinetic temperature values derived from the airborne and orbital data are all within 25% and 10% of the MMT-Cam values (Figures 7 and 8), respectively, and more consistent with laboratory and field measurements [44][45][46]51]. surface radiance values are all within 25% of the MMT-Cam values, an improvement of up to 300% (Figures 7 and 8). The molten emissivity and kinetic temperature values derived from the airborne and orbital data are all within 25% and 10% of the MMT-Cam values (Figures 7 and 8), respectively, and more consistent with laboratory and field measurements [44][45][46]51].

Implications and Reasons for Uncertainty
The results extracted from the lava flow data before and after the TMP separation analysis are less uniform across all wavelengths where compared to the lava lake data (Figures 7 and 8). The ratio of pre-versus post-TMP analysis is higher at shorter wavelengths in the surface radiance data and lower at shorter wavelengths in the emissivity data as expected from the relationship modeled in the Planck equation. This ratio is closer to one at longer wavelengths for all the thermal properties, implying the thermal mixing is less of a factor at these wavelengths, again, as one might predict based on the mixing of multi-temperature emissions. The non-uniform ratio in the lava flow data (most notable at larger pixel sizes) implies a more complex mixing and distribution of thermal fractions and a greater uncertainty in these properties at shorter wavelengths. Hence, the greatest errors are observed at shorter wavelengths in the mixed pixels and are more extreme in lower spatial resolution datasets (Figures 7 and 8).
Although the greatest uncertainty and errors are observed in the mixed pixels acquired at lower spatial resolutions; these uncertainties fall within the expected values following the TMP separation for all the datasets. The variability within each dataset is used to quantify the uncertainty of the currently available low spatial resolution (>500 m) TIR datasets that are not able to accurately resolve the maximum temperature or representative emissivity spectrum. There are relatively few studies (i.e., [23]) that have investigated the influence of spatial and spectral resolution on these calculations over temperatures where a molten lava surface cools (<1450 K). Therefore, simply deconvolving the molten fraction that has the maximum temperature within each pixel will improve the accuracy and uncertainty of the emissivity, kinetic temperature, and radiant flux.
Measuring accurate thermal properties of a molten lava surface is also critical to lava flow propagation models [15,24]. With the increasing number of spectral bands in more recent TIR imagers (e.g., HyTES [20] and the Mineral and Gas Identifier (MAGI) [25]), the radiative temperature and emissivity of an object's surface can be extracted with increasing accuracy [26][27][28]. A well-constrained emissivity can then be used with approaches such as linear spectral deconvolution modeling to quantitatively determine possible spectral end-member that defines the mineralogical, textural, and thermal fractions [29][30][31][32]. Additionally, kinetic temperature (and to a lesser degree, emissivity) is required to determine the runout distance and hazard potential using radiant heat flux in lava flow propagation models [15,24]. However, the accuracy of these derived parameters over the cooling temperature range of typical lavas is less well constrained at the various spatial resolutions of current TIR instruments. Therefore, improving the accuracy of the kinetic temperature and emissivity of the previously-determined molten fraction should then reduce the uncertainty in flow model analyses that directly rely on these thermal properties.

Study Area
This study was conducted during two field campaigns at Kīlauea Volcano in Hawai'i, USA, in January/February 2017 and 2018, a period when both the summit lava lake and coastal plain surface lava flows were active. It focused primarily on the lava lake in the Halemaʻumaʻu Crater and propagating lava flows from the Puʻu 'Ō'ō vent ( Figure 1). Kīlauea is a basaltic shield volcano that has been erupting nearly continuously for the past 500 years [33]. The lava surfaces are produced during long sustained eruptions where pāhoehoe (tube-and surface-fed) and 'a'ā flows are emplaced [33]. The lava lake in the Halemaʻumaʻu Crater observed during this study was active from 2008 until 2018 and varied in size with maximum dimensions of 160 meters wide and 225 meters long ( Figure  1) [34]. During this period, there were fluctuations in lava lake activity with continuous gas plumes and irregular small explosions, finally ending with the summit collapse in May 2018 [13,34]. At the time of the field campaigns, the lava lake level was relatively high but not overflowing, approximately 100-130 meters below the Halemaʻumaʻu Crater rim. It was continuously circulating with fresh lava upwelling in the north that migrated to the south, cooled and formed plates of cooler, solidified lava. The lava then sank in the south, distinguished by the occurrence of strong splattering and degassing [34]. The lava flows from the Puʻu 'Ō'ō vent were active for ~30 years erupting in many locations over numerous eruptive episodes, producing mostly pāhoehoe lava flows with the occasional 'a'ā lava flow [33,35]. This long eruption finally ended in 2018 with the cessation of the lower East Rift Zone (LERZ) eruption in the Leilani Estates [14]. The lava flows observed during our 2017-2018 study were part of the 61g episode that erupted from the east flank of Puʻu 'Ō'ō. These flows propagated down the Pulama pali and entered the ocean at Kamokuna as a series of pāhoehoe surface lava flow and lava tubes ( Figure 1) [35]. The majority of the flows observed were tube-fed pāhoehoe, both sheet-like and ropey in texture. Previous remote sensing studies of the pre-2018 Kīlauea eruption have investigated lava discharge rates [36], lava flow emplacement tracking [37], and lava pathway mechanisms [38]. The areas for this study were chosen for the high probability of observing molten lava surfaces combined with the availability of a variety of remote sensing TIR datasets.
u 'Ō'ō lava flows acquired on January 30, 2018. Values closer to 1.0 require less TMP separation processing. The error bars represent the standard deviation variation in the ROI data.

Implications and Reasons for Uncertainty
The results extracted from the lava flow data before and after the TMP separation analysis are less uniform across all wavelengths where compared to the lava lake data (Figures 7 and 8). The ratio of pre-versus post-TMP analysis is higher at shorter wavelengths in the surface radiance data and lower at shorter wavelengths in the emissivity data as expected from the relationship modeled in the Planck equation. This ratio is closer to one at longer wavelengths for all the thermal properties, implying the thermal mixing is less of a factor at these wavelengths, again, as one might predict based on the mixing of multi-temperature emissions. The non-uniform ratio in the lava flow data (most notable at larger pixel sizes) implies a more complex mixing and distribution of thermal fractions and a greater uncertainty in these properties at shorter wavelengths. Hence, the greatest errors are observed at shorter wavelengths in the mixed pixels and are more extreme in lower spatial resolution datasets (Figures 7 and 8).
Although the greatest uncertainty and errors are observed in the mixed pixels acquired at lower spatial resolutions; these uncertainties fall within the expected values following the TMP separation for all the datasets. The variability within each dataset is used to quantify the uncertainty of the derived thermal properties of molten basaltic lava surfaces. Although the dual-band mixed pixel separation approach does provide data more similar to laboratory results, it ultimately increases the variability in the derived properties that results in a decrease in precision and therefore, an increase in uncertainty. This uncertainty is related to the spatial resolution of the dataset with lower resolution data having higher uncertainty. This is a function of smaller proportions of the molten lava fraction being present within a given larger pixel, which can be less than 5% in an ASTER pixel. Figures 7 and 8 show the ratio in radiance and emissivity between pre-and post-TMP separation analysis, with values close to one requiring the least separation processing. In the majority of instances, the MMT-Cam data requires the least processing and the ASTER data requires the most. However, the HyTES lava lake surface radiance data requires the least separation processing, a function of the hyperspectral resolution, which offsets the lower spatial resolution (Figure 7a). The HyTES variability in the unmixed surface radiance data is significantly lower than that from MASTER at a very similar spatial resolution. Therefore, where spatial resolution is similar, data uncertainty drops by using higher spectral resolution data (decrease variability by~40%), which is highly relevant for future orbital instrument design.

Conclusions
The accuracy and uncertainty in the thermal properties derived from remotely acquired TIR data of active lava surfaces were investigated using a variety of instruments acquiring data of two active basaltic lava surfaces (lava lake and lava flow). The effect of spatial and spectral resolution on the measured surface radiance and derived emissivity and kinetic temperature were quantified by comparing them to values expected for basaltic lava at liquidus temperatures based on prior laboratory and field results. Because a majority of currently available TIR instruments do not have the radiometric range or spatial resolution to derive the thermal properties of a molten lava surface accurately, the application of a dual-band mixed pixel separation analysis approach is one solution to improve results. This thermal unmixing can deconvolve the signature of the molten fraction within a pixel. By determining the accuracy and uncertainty in these thermal properties across four different TIR datasets acquired at the same time and with different spatial and spectral resolutions, the temperature, emissivity, and radiance results are compared and constrained. For example, prior to extracting the molten fraction within each pixel, it was impossible to compare thermal properties ( Figure 4) as they are strongly dependent on the instrument position with respect to the surface and their individual specifications (Table 2). However, post-unmixing, the molten fraction ( Figure 5) is more directly comparable between these datasets (Table 3).
Mixed pixel surface radiance values derived from the ASTER data are~2400% underestimated, with the MASTER and HyTES data underestimated by~1000%. Similar underestimates are seen in the extracted emissivity and kinetic temperature by approximately 20% and 250% in the ASTER data, and 25% and~200% in the MASTER and HyTES data, respectively. However, this impact of spatial resolution is mitigated to a degree by improved spectral resolution. Following the TMP separation analysis, all surface radiance values are within 15% of the expected values, whereas the emissivity and kinetic temperature are within 8% and 12% of the expected values, respectively [44][45][46]. These results quantify the inherent TIR data uncertainty in the measured and derived thermal properties, demonstrate a significant improvement on previous estimates, and further constrains the errors associated with these values. The more accurate constraint of lava temperature, emissivity, and the emitted radiance from active surfaces derived from TIR measurements will ultimately improve the accuracy and reduce the unknown uncertainty in future flow models that rely upon these properties (e.g., [11]). Furthermore, these datasets can be directly compared with other measurements (i.e., terrain elevation, in situ thermocouple temperatures, and deformation change) to improve analysis of the synoptic eruption process and quantify the uncertainty in the results and conclusions.