# An Overview of Infrared Remote Sensing of Volcanic Activity
## 2 Infrared Remote Sensing: Theory  
All objects above 0 K (absolute zero) emit electromagnetic radiation, but the radiant flux density (i.e., rate of energy flow per unit area) and spectral composition of these emissions depend on the temperature of the emitting object. According to the [PERSON] law [2; 3], the radiant flux density emitted by an object is directly proportional to the fourth power of the object's surface temperature, meaning that the hotter an object, the greater the total energy it will radiate, and this applies to all wavelengths of emission (see Figure 1). According to Wien's displacement law [4], the peak wavelength of spectral radiant emissions also becomes shorter with increasing temperature, (also see Figure 1). The energy radiated from an object, otherwise termed radiant flux, is quantified in terms of radiance per unit of wavelength and is referred to as spectral radiance. The spectral radiance, \(L_{\lambda}(T)\), (in units of W m\({}^{2}\) sr\({}^{-1}\) um\({}^{-1}\)), emitted by a blackbody at temperature (\(T\)) and wavelength (\(\lambda\)), can be calculated using the Planck function [5] below and as represented in Figure 1:  
\[L_{\lambda}(T)=\frac{C_{1}}{\lambda^{5}\left(\exp\left(\frac{C_{2}}{\lambda T }\right)-1\right)} \tag{1}\]  
where \(C_{1}\) and \(C_{2}\) = constants of \(1.19\times 10^{-16}\) and \(1.44\times 10^{-2}\) m K, respectively [6]. The temperature of volcanic features varies widely. Fresh lava may be between 1073 and 1273 K, although the temperature of lava lakes has been measured at up to 1473 K, while cooler active surfaces may reach 673 K [7; 8]. At these temperatures, the chief radiant emissions are in the thermal infrared (TIR), middle infrared (MIR) and shortwave infrared (SWIR) portions of the spectrum (see Figure 1). Various Earth-observing satellites have sensors capable of observing these infrared emissions and as such are routinely used for volcanic observations (Table 1), despite their original purposes often being far removed from such geological applications. One complication, however, is that all components of the Earth's surface, by virtue of their temperature, also produce detectable radiant emissions in the MIR and TIR portions of the spectrum, and these signals must be removed if those attributable to active volcanism are to be accurately quantified. In contrast, SWIR radiation is only emitted in detectable quantities from very hot surfaces (e.g., fires and incandescent lava), and as such, in nighttime imagery,  
Figure 1: Relationship between the spectral radiant emissions (in terms of quantity and wavelength) and temperature of the emitting surface, thus representing the Planck function and both the Stefan–Boltzmann and Wien displacement laws. Different portions of the infrared spectrum are also depicted (VNIR: visual and near infrared; SWIR: short-wave infrared; MIR: mid-infrared; TIR: thermal infrared). such removal steps are not required, although in daytime imagery, reflected solar radiation must be removed from any SWIR signals. Early satellites such as the National Aeronautics and Space Administration's (NASA's) Television Infrared Observation Satellite (TIROS) series, launched throughout the 1960s, possessed TIR Earth-observation capabilities for meteorological observations. Since this period, infrared observations have remained crucial for meteorological purposes while also providing an excellent means of observing terrestrial 'hot phenomena', ranging from wildfires to active volcanoes. Some examples of using orbiting infrared sensors for this purpose include [9], in which it was shown that subtle precursory TIR signals could be detected prior to a 2006 eruption of Bezymianny Volcano in Russia and [10], which similarly showed how TIR observations of Bezymianny could be used to monitor the volcano's changing state during a later eruption.