# An Overview of Infrared Remote Sensing of Volcanic Activity
## 5 Infrared Remote Sensing of Volcanoes: A History
One issue that had to be dealt with from the outset of the discipline was that volcanic surfaces may vary by several-hundred degrees over just a few centimetres [92], and given that 30 m (and often cruder) has been the highest spatial resolution of data available in the infrared, techniques were required to ensure that the data obtained were as accurate as possible. Take a 30-m ASTER or Landsat-8 SWIR pixel for example: the situation on the ground could feasibly match the simulated pixel area of Figure 7, consisting of two (or more) surfaces of different temperature (and consider the possibilities within the 1000 m \(\times\) 1000 m pixels of AVHRR or MODIS). As such, while radiance detected within one pixel might give an approximate indication of activity on the ground, such a pixel integrated value also hides much information. Given the varying sensitivity of different bands to surfaces of different temperature, any pixel integrated value detected will also be dependent on the band used to image it. For example, again taking the pixel modelled in Figure 7, if viewed in ASTER's SWIR Band 4, the radiance temperature detected would be 615 K, as compared with 505 K if imaged with ASTER's Band 9 (see Figure 8). This varying sensitivity is further demonstrated by the wider area of detection in Figure 9 where the Bands 4 and 9 signal detections are compared for the same volcanic surface. Figure 8: The pixel integrated temperature that would be detected by ASTER’s SWIR bands on viewing the modelled surface of Figure 7.  
Figure 7: A modelled 30-m (e.g., ASTER) pixel, with various hot components at 1200 K and a background surrounding temperature of 310 K. Given these characteristics, the pixel would have an integrated temperature of 615 K at 1.650 \(\upmu\)m (ASTER Band 4) and 505 K at 2.395 \(\upmu\)m (ASTER Band 9). The difference in band sensitivity can be harnessed for volcano monitoring, and this was first documented in [90], using a technique developed in ground breaking studies from 1981: [103; 104]. These studies had recognised the distinction between those scenarios in which a whole pixel's field of view was filled by a thermal anomaly and those in which only a portion of the field of view was thermally anomalous. In the former case, the pixel would measure the full radiance from the surface (e.g., a volcano), and the average temperature of the surface could be calculated; in the latter case, where the anomalous surface consisted of only a portion of the area, the radiance measured would be reduced by this portion, and this would be the case for all observing wavelengths. If the ratio of two pixel values was then taken, it would remain the same in both cases, effectively peak picking the radiance received by the pixel and allowing for an estimation of the sub-pixel two-component thermal structure. To characterise a pixel area into two components, non-linear, simultaneous equations, termed the 'dual-band' equations, can be used:  
\[R_{x}\ =\ P_{h}\ L_{x}(T_{h})\ +\ [(1-P_{h})\ L_{x}(T_{c})], \tag{3}\]  
and:  
\[R_{y}\ =\ P_{h}\ L_{y}(T_{h})\ +\ [(1-P_{h})\ L_{y}(T_{c})], \tag{4}\]  
where \(R_{x}\) and \(R_{y}\) = radiance detected in bands \(x\) and \(y\) (W m\({}^{-2}\) sr\({}^{-1}\) m\({}^{-1}\)), adjusted for atmospheric effects and surface emissivity; \(P_{h}\) = proportion of the pixel occupied by the hotspot; \(L_{x}(T_{h})\) and \(L_{y}(T_{c})\) = spectral radiance (\(L\), W m\({}^{-2}\) sr\({}^{-1}\) m\({}^{-1}\)) emitted in a particular band by a surface at temperature \(T_{h}\) (the hot component) or \(T_{c}\) (the cooling component), as determined by the Planck function (Equation (1)). As the 'dual-band' method relies on two equations and as there are three unknowns (\(T_{h}\), \(T_{c}\) and \(P_{h}\)), it requires the assumption of either \(T_{h}\), \(T_{c}\) or \(P_{h}\).