**2. Emissivity Measurement Techniques**

Summarised in Table 1 are different field emissivity measurement techniques deployed in previous studies. The most utilised are variants of the emissivity box method, detailed in Rubio et al. [33,34], which provide broadband LWIR emissivity estimates, and approaches based on spectral radiance measurements made by field portable FTIR spectrometers, which provide spectrally resolved LWIR emissivity data [31]. As detailed by Rubio et al. [33,34], the two primary variants of the box method are the two-lid approach [35] and the one lid approach [36]. Both involve a bottomless box with highly reflective (for example polished aluminium) inner walls and a LWIR radiometer to make the broadband measurements. During each measurement, the box is covered by a lid with a small central hole through which the radiometric measurements are made, with the lid having either high reflectance (the "cold lid") or high emissivity (the "hot lid"). A sequence of four radiometer measurements with the box and lids in different configurations provide the data to estimate the broadband emissivity of the surface over which the box is placed [33,34].


**Table 1.** Overview of various different field emissivity measurement techniques, with variants of the first approaches considered in this study.

The field spectrometer approach to the emissivity measurement is detailed by Salvaggio and Miller [32], and involves the spectrometer measuring the emitted LWIR signal from the surface and using this, along with a measurement of the downwelling LWIR atmospheric radiation, to derive the surface's spectral emissivity. The downwelling component is most commonly assessed using a downward looking measurement of a gold Lambertian panel, which reflects almost all of the LWIR atmospheric radiation irradiating it.

In addition to field emissivity approaches, there exist a number of laboratory-based methods to assess surface emissivity, generally based on FTIR spectroscopic techniques, which provide surface spectral emissivity values. The spectrometers measure either LWIR sample emission or directional hemispherical reflectance (DHR) [10]. In the emission mode the emissivity estimate is derived through comparison of the spectral radiance emitted by the sample to that emitted by a blackbody at the same temperature (for example [19]). Being lab-based, this approach generally means the sample must be heated to temperatures significantly above the laboratory such that any low emissivity features in the resulting emissivity spectra are not simply "filled in" by reflected LWIR radiation coming from the surroundings at the same temperature as the sample. Consequently, the method is unsuited to samples such as vegetation [47]. To avoid this, FTIR spectrometers operating in the DHR mode are used, generally with a source of intense LWIR radiation that is used to illuminate the sample and assess its LWIR reflectance via consecutive measurements of the sample and a highly reflective reference standard such as Infragold [48]. Emissivity is then calculated from the LWIR reflectance spectra using Kirchhoff's law [49].

Many field emissivity and LST validation studies have used the box method since the equipment is relatively simple, inexpensive, easily portable, and with minimal power requirements (e.g., [11,14,50–54]). Multiple studies have assessed the quality of emissivities derived using the approach, typically by comparing them to full spectral emissivity data coming from laboratory measurements convolved to the waveband of the LWIR radiometer used in the box [15]. The conclusions of these studies generally indicate that the quality of the box-derived field emissivity data is highly dependent on the measurement conditions, particularly for the one-lid variant [11,15,33]. Under favourable measurement conditions, a strong degree of agreement is seen between the data derived by the box method and that of the various laboratory spectral measurement approaches applied. Mira et al. [15] and Nerry et al. [38] for example both observed that the two-lid box method produced broadband LWIR emissivity estimates with a mean error of ±0.5% under stable field conditions (low winds and constant cloud conditions that help keep the sample surface temperature consistent while the measurements are made). Göttsche and Hulley [11] reported less than 1% difference for sand samples in Gobabeb (Namibia) where clear, cold skies with low winds made measurement conditions optimum. However, under less suitable conditions (e.g., high winds and variable cloud cover), the sensitivity of the derived surface emissivity value to changes in the sample temperature during the measurement can result in large errors. A change of 3 K over the measurement period results in emissivity errors of up to 2% in the one-lid method for example [34]. While such percentage errors seem small, due to coupling of LST and emissivity, a 1% error in specified emissivity will generally result in about a 0.5 K error in the derived LST [9]. Hence the accuracy of surface emissivity data is key to accurate LST derivation.

Compared to the box method, fewer studies exist comparing field- and lab-derived emissivity data based on FTIR spectrometer measurements [31,32,47,55,56]. However, as with the box method, the studies that have been conducted found that the accuracy of the field-derived data is highly dependent on the environmental conditions that existed during the measurement. For example, Salvaggio and Miller [32] assessed the field spectral emissivity data coming from measurements made with the Designs and Prototypes (D&P) µFTIR system, specifically designed for field emissivity measurement. Under ideal measurement conditions (stable, low winds and clear skies), the mean absolute emissivity error was less than 1% for most surface samples, with the D&P spectral measurements processed to spectral emissivity using Horton et al.'s [57] spectral smoothness approach. However, more problems were observed with measurements made under conditions of high humidity

and air temperature, and/or more variable conditions [31,55]. Horton et al. [57] found that a 0.5 K change in sample temperature during the measurement procedure resulted in errors in the final calculated emissivity of 2.5%. As a result, samples with relatively low thermal inertia (such as dry soils) or samples that experience rapid evaporative cooling in the near-surface layer (such as water, damp soils, or dewy vegetation) can show higher errors under changing environmental conditions, such as high winds [17].

As well as these meteorological factors, observed differences between laboratory and field emissivity measurements (whether the latter be from the box- or FTIR-based approaches) are often attributed to physical changes in the sample, which may occur between the field and the laboratory, for example in terms of its structure and surface moisture [15]. Such possibilities for error further highlight the importance of field emissivity measurements. However, since the accuracy assessment of the field methodologies is often performed through comparison with laboratory-derived measurements, any differences between the laboratory and field sample conditions can affect the evaluation. Studies that intercompare the emissivities of the same samples derived by different field measurement approaches may help to redress this issue, but few such studies exist. Those that have been conducted considered are restricted to few sample types (e.g., soils or sands) or have been based on rather limited comparisons, for example due to differing instrument spectral responses [12]. A critical finding is that of Mira et al. [15], who observed emissivity differences between 2% and 7% in the 8–9 µm LWIR band between the values derived using the two-lid emissivity box and the TES-retrieved radiometer approach (see Table 1), corresponding to a 0.7–2.6 K error in derived LST.

#### **3. Methods**

Measurements were made of multiple manmade and natural samples with varying physical structures during two field campaigns in the UK and Italy using four methods: (i) a laboratory FTIR spectrometer setup at King's College London operating in DHR mode, (ii–iii) two portable field FTIR spectrometers with different processing approaches, and (iv) a two-lid emissivity box constructed at King's College London.

#### *3.1. Instrumentation, Measurements, and Post-Processing*

#### 3.1.1. Emissivity Determination Using the Laboratory FTIR Spectrometer

In the laboratory, high spectral resolution (4 cm−<sup>1</sup> ) surface emissivity spectra of the target samples were derived from directional hemispherical reflectance LWIR spectral measurements made by a Bruker Vertex 70 FTIR spectrometer with an external highly reflective gold integrating sphere and an external thermal infrared source, as shown in Figure 1. The full measurement setup is detailed in Langsdale et al. [30], and the measurements covered the spectral range 2.5–16 µm, extending beyond the normal LWIR atmospheric window (8–13 µm).

The data coming from the laboratory system shown in Figure 1 can be processed to surface spectral emissivity using either the substitution or comparative methods, which are detailed in Hecker at al. [58]. The authors of [30] found that surface spectral emissivities derived using the comparative method, which uses the internal wall of the diffusely coated gold integrating sphere as the reference target, on the same laboratory system were within 1.5% of the mean of those derived by a wide range of international laboratories' measurements (spectral range 8–14 µm). To measure emissivity using this comparative method, the target surface was placed directly underneath the sample port of the external integrating sphere and illuminated with the LWIR beam coming from the external source. The reflected spectral radiance (*V*s(λ)) was then measured and compared to a subsequent measurement of the reflected radiance from the internal wall of the integrating sphere (*V*r(λ)), enabling the calculation of sample reflectance (ρs(λ)):

$$\rho\_{\rm s}(\lambda) = \frac{V\_{\rm s}(\lambda) - V\_{\rm o}(\lambda)}{V\_{\rm r}(\lambda) - V\_{\rm o}(\lambda)} \rho\_{\rm r}(\lambda) \tag{1}$$

μ

where *V*o(λ) is an open port measurement as detailed in Hecker et al. [58] and ρr(λ) is the absolute reflectance of the internal gold wall of the integrating sphere (ρr(λ) ≈ 0.97 across 2.5–14 µm) used as the reference target. An internal rotating mirror was used to move the infrared beam illumination between the sample and the reference position. Sample spectral emissivity (εs(λ)) was then calculated from reflectance using Kirchhoff's law [59]: −

$$
\varepsilon\_{\rm s}(\lambda) = 1 - \rho\_{\rm s}(\lambda) \tag{2}
$$

μ

**Figure 1.** (**a**) Laboratory setup for surface spectral emissivity determination based on measurements made by a Bruker Vertex 70 FTIR spectrometer installed at King's College London along with an external water-cooled longwave infrared (LWIR) radiation source and a gold-coated integrating sphere. (**b**) Details of the inside of the integrating sphere, showing the gold coating used as the reference target in the comparative method and rotating mirror to direct the measurement beam from entrance port to sample port/internal wall.

For each sample, a minimum of the three emissivity measurements was collected to enable consideration of measurement variability. More measurements were made for low reflectance samples (card, grass and water) and for inhomogeneous samples (gravel and grass). Each individual spectral measurement consisted of either 500 or 1000 coadded scans, with the higher number of scans used for samples with low LWIR reflectances.

#### 3.1.2. Emissivity Determination Using the Field Portable FTIR Spectrometers

Two portable FTIR spectrometers were deployed in this study (Table 2). The first was the aforementioned D&P µFTIR spectrometer [31,32,40], specifically designed for surface emissivity measurement in the field (Figure 2). The instrument operates in passive emission mode to measure emitted LWIR radiation, and uses the two-temperature blackbody approach for its calibration. It has a 45◦ mirror (rotating to allow angled measurements) within an enclosed tube. The main improvement on the µFTIR design described originally in Korb et al. [31] and Hook and Kahle [40] is the inclusion of a Stirling cycle cooling for the detector in place of liquid nitrogen. The second FTIR deployed was a Bruker EM27, also with a Stirling cycle cooled detector and an internal blackbody target that can be rapidly heated and cooled to provide the necessary two point calibration [30]. Though this system is designed primarily for atmospheric remote sensing, it is easily adapted to assess surface emitted LWIR radiation via attachment of a 45◦ flat high IR reflectance gold mirror as shown in Figure 2. This mirror can then be used to reflect the surface target emitted and gold-panel reflected LWIR radiation into the spectrometer. The system, its 12 V battery/inverter and a controlling laptop were mounted on a rugged trolley for relatively easy transport around a field site. Spectral resolutions used were the maximum

for the two systems, namely 0.5 cm−<sup>1</sup> for the EM27 and 4 cm−<sup>1</sup> for the D&P µFTIR, with spectral sampling intervals in practice of 0.25 cm−<sup>1</sup> and 3 cm−<sup>1</sup> . The D&P was available for the measurements in Italy only.

**Table 2.** Instrument specifications for the portable FTIR spectrometers deployed herein, namely a Bruker EM27 FTIR spectrometer and the Designs and Prototypes µFTIR [31,40,60].


μ **Figure 2.** (**a**) Field-deployed Designs and Prototypes µFTIR spectrometer and (**b**) field-deployed Bruker EM27 FTIR spectrometer with a 45◦ mirror attachment fitted to view upwelling radiation from the surface, here shown assessing downwelling LWIR atmospheric radiation via observations of an Infragold panel.

ܮ ܮ୮ୟ୬ୣ୪ To retrieve surface spectral emissivities from the passive LWIR spectra collected by either of the FTIR instruments, the calibration blackbody temperatures were first set to appropriately bracket the sample temperature [17]. As recommended by Salvaggio and Miller [41], the hot and cold blackbody temperatures used for the calibrations were set to approximately 10 K above and below the estimated sample temperature to reduce extrapolation error, although very high ambient air temperatures encountered at the Italian field site required the cool blackbody to be elevated above this limit. Sample temperature was itself estimated using a FLIR i7 handheld LWIR thermal imaging camera. Consecutive spectral measurements were then made of the sample (*L*) and of a 13 cm × 13 cm Labsphere Infragold panel (*L*panel), with the panel measurement used as a proxy for the downwelling

μ

μ <sup>−</sup> μ − − − −

**μ**

LWIR atmospheric signal. The panel has a known and spectrally flat emissivity (εpanel*)*, provided by the manufacturer as 0.03 ± 0.01 across 2.5–14 µm range. The panel was placed in the same configuration as the sample, positioned just above the sample location.

The D&P µFTIR spectrometer comes with its own software to estimate sample emissivity across 7.5–12.0 µm from these measurements. Sample temperatures are estimated using the "Maximum Spectral Temperature" method detailed in Salvaggio and Miller [32] and developed by Korb et al. [31] and Hook and Kahle [40]. Emissivity uncertainties were taken as the standard deviation of multiple measurements. The measurement procedure takes around 25 min for a complete set of measurements. For the EM27 we developed our own emissivity measurement approach and software, with the full measurement sequence (three consecutive and repeated measurements of the sample and Infragold panel along with spectral calibration) typically taking around 20 min. From the measurements of the gold panel, downwelling radiance (*L* ↓ ) spectra were first estimated as:

$$L^{\downarrow}(\lambda) = \frac{L\_{\text{panel}}(\lambda) - \varepsilon\_{\text{panel}}(\lambda)L\_{\text{BB}}\{T\_{\text{panel}}, \lambda\}}{1 - \varepsilon\_{\text{panel}}(\lambda)}\tag{3}$$

where *T*panel is the kinetic temperature of the Infragold panel (K), measured with a contact k-type thermocouple (manufacturer-stated accuracy <sup>±</sup>0.1 K) and *<sup>L</sup>*BB *T*panel, λ is the blackbody spectral radiance at temperature *T*panel calculated using the Planck function such that:

$$L\_{\rm BB} \left( T\_{\rm panel}, \,\,\lambda \right) = \frac{2hc^2}{\lambda^5 \left( e^{\frac{hc}{\lambda kT\_{\rm panel}}} - 1 \right)} \tag{4}$$

where *h* is the Planck constant (6.62606957 × 10−<sup>34</sup> Js), *c* is the speed of light (299, 792, 458 ms−<sup>1</sup> ), and k is the Boltzmann constant (1.3806488 × 10−<sup>23</sup> *JK*−<sup>1</sup> ).

If the sample temperature (*T*s) is accurately known, the surface spectral emissivity (ε(λ)) of the sample can be retrieved through use of a rearranged radiative transfer equation appropriate to a surface-viewing sensor positioned close to the target [32]:

$$\varepsilon(\lambda) = \frac{L(\lambda) - L^{\downarrow}(\lambda)}{L\_{\text{BB}}(T\_{\text{s}\prime}\,\lambda) - L^{\downarrow}(\lambda)}\tag{5}$$

where *L*BB(*T*s) is the blackbody spectral radiance at temperature (*T*s). However, sample temperature can vary even over short timescales (e.g., due to wind), and can be hard to assess accurately in the field for certain targets (e.g., vegetation) even under good measurement conditions. We therefore avoided having to specify *T*<sup>s</sup> by using the "spectral smoothness" approach [57], an approach determined as optimal for emissivity derivation based on field-portable FTIR measurements by Salvaggio and Miller [32]. We implemented this by identifying a realistic sample temperature range as in Salvaggio and Miller [32] and calculating emissivity using Equation (5) for all temperatures within this range (in increments of 0.01 K). The sample temperature was taken to be the temperature, which minimised residuals in the resulting emissivity spectra that were clearly associated with atmospheric absorption and emission features in the 8.12–8.60 µm range of the short wavelength lobe of the silicate doublet. Emissivity uncertainties for the EM27 were calculated through propagation of the uncertainties in the input parameters. Uncertainties in the gold panel temperature and emissivity were taken as the manufacturer-stated accuracy (0.01 K and 0.01 respectively), which in the sample temperature as the 0.01 K precision, and that in the sample and gold panel spectra as the standard deviation of the measurement coadds (minimum 12 per spectra). Due to its extremely low emissivity, no adjustment was made for self-emission of the 45◦ mirror used to direct LWIR radiation from the sample to the spectrometer, nor for errors related to the fact that the cold sky temperatures are far lower than the minimum temperature of the two-point blackbody calibration. The typically low values of the

downwelling radiation from the cold (clear) sky compared to the LWIR emission from the samples, along with the high emissivities (and thus low reflectances) of the samples, mean that uncertainties in the assessment of the downwelling sky radiation do not have much impact on the final emissivity uncertainty [31].
