A Sensitivity Study of the 4.8 M Carbon Dioxide Absorption Band In

remote sensing

Letter A Sensitivity Study of the 4.8 µm Carbon Dioxide Absorption Band in the MWIR Spectral Range

Vito Romaniello *, Claudia Spinetti , Malvina Silvestri and Maria Fabrizia Buongiorno Istituto Nazionale di Geoﬁsica e Vulcanologia, Roma 00143, Italy; [email protected] (C.S.); [email protected] (M.S.); [email protected] (M.F.B.) * Correspondence: [email protected]

Received: 29 October 2019; Accepted: 27 December 2019; Published: 3 January 2020

Abstract: The measurements of gas concentrations in the atmosphere are recently developed thanks to the availability of gases absorbing spectral channels in space sensors and strictly depending on the instrument performances. In particular, measuring the sources of carbon dioxide is of high interest to know the distribution, both spatial and vertical, of this greenhouse gas and quantify the natural/anthropogenic sources. The present study aims to understand the sensitivity of the CO2 absorption band at 4.8 µm to possibly detect and measure the spatial distribution of emissions from point sources (i.e., degassing volcanic plumes, fires, and industrial emissions). With the aim to define the characteristics of future multispectral imaging space radiometers, the performance of the CO2 4.8 µm absorption band was investigated. Simulations of the “Top of Atmosphere” (TOA) radiance have been performed by using real input data to reproduce realistic scenarios on a volcanic high elevation point source (>2 km): actual atmospheric background of CO2 (~400 ppm) and vertical atmospheric profiles of pressure, temperature, and humidity obtained from probe balloons. The sensitivity of the channel to the CO2 concentration has been analyzed also varying surface temperatures as environmental conditions from standard to high temperature. Furthermore, response functions of operational imaging sensors in the middle wave infrared spectral region were used. The channel width values of 0.15 µm and 0.30 µm were tested in order to find changes in the gas concentration. Simulations provide results about the sensitivity necessary to appreciate carbon dioxide concentration changes considering a target variation of 10 ppm in gas column concentration. Moreover, the results show the strong dependence of at-sensor radiance on the surface temperature: radiances 2 1 1 2 1 1 sharply increase, from 1 Wm− sr− µm− (in the “standard condition”) to >1200 Wm− sr− µm− (in the warmest case) when temperatures increase from 300 to 1000 K. The highest sensitivity has been obtained considering the channel width equal to 0.15 µm with noise equivalent delta temperature (NEDT) values in the range from 0.045 to 0.56 K at surface temperatures ranging from 300 to 1000 K.

Keywords: carbon dioxide; multispectral sensor; earth observation; satellite; MWIR

1. Introduction The evidence of increasing Earth surface temperature in the last decades [1] is posing important questions about the causes and the influence of human activities on it. The greenhouse gases play a crucial role in the global warming trend [2] and their characterization is increasingly necessary. The individuation and quantification of gases point sources are pivotal to better understand the anthropogenic and natural origins. The measurements of gas concentrations taken remotely, with the identification of their spatial distribution, are developed thanks to the availability of the gases absorbing spectral channels in the sensors carried on satellite or airborne platforms. Atmospheric CO2 total columns can be measured by sensors acquiring spectra in the CO2 absorption bands at 1.6 µm and 2.0 µm in the short-wave infrared (SWIR) spectral region, at 4 µm in the midwave infrared (MWIR),

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(MWIR), and at 15 µm in the thermal infrared (TIR) spectral regions. Figure 1 shows absorption bands in the SWIR–MWIR spectral range. TIR has the advantage of providing day and night continuous measurements. The first retrieval of column averaged mixing ratio of CO2 in dry air (XCO2) has been from the infrared sounder TOVS (TIROS Operational Vertical Sounder) [3,4] demonstrating the limited capability to constrain CO2 sources and sinks [5]. The high-resolution infrared sounders, such as the AIRS (Atmospheric InfraRed Sounder) [6] and IASI (Infrared Atmospheric Sounding Interferometer) [7], were shown to attain a substantial gain of information mostly due to their broader spectral coverage and finer resolution. Therefore, the XCO2 retrieved from IASI measurements reached the precision of 2 ppm for a 5° × 5° spatial resolution on a monthly time scale [7–9]. CO2 absorption bands in the SWIR spectral range have the advantage of being sensitive down to the lowermost layers of the atmosphere, which contain information about surface fluxes useful for identification of CO2 sources and sinks. In this spectral region, XCO2 has been measured by SCIAMACHY (2002–2012) [10], TANSO-FTS (2009–present) [11], OCO-2 (2014–present) [12–14], TanSAT (2016 to present) [15], and the recent OCO-3 on board ISS [16]. The OCO-2 mission provides measurements up to now from space at higher spatial resolution of 1.30 km × 2.25 km reaching the 0.5 ppm precision for XCO2 necessary to identify CO2 gradients across large urban areas [17]. Instead, the CO2 absorption bands in the MWIR region lack studies in the literature, although this band is particularly suitable for remote sensing due to the position in an atmospheric window [18] on the MWIR spectral region. Indeed, this spectral region has several advantages: it is characterized by low values of Earth reflectance leading to low backscattering effects. Moreover, the radiance emitted by the Earth in this spectral range allows continuous acquisitions during day and night. Finally, we expect a measurable amount of energy at the sensor, independently from the pixel size, from high-temperature events due to the fact that Wien’s displacement law determines the temperature at which the maximum energy will radiate and the 3–5 µm range corresponds to the radiant energy peak for temperatures of 600 K and greater (see Figure 2), which are associated with fires, lava flows, and other hot features [19]. The scope of the present study is to understand the capability of the absorption band at 4.8 µm to detect and measure the spatial distribution of CO2 emissions from point sources as degassing volcanicRemote plumes Sens. 2020 [20],, 12, 172fires [21], and industrial emissions [22]. This study can be useful2 to of 12define the characteristics of multispectral imaging space radiometers to be employed in future space missions whose applicationsand at 15 µm in include the thermal greenhouse infrared (TIR) gas spectral observations. regions. Figure The1 showspossibility absorption of detecting bands in the CO2 point sourcesSWIR–MWIR is related to spectral both the range. sensitivity and the spatial resolution of the sensor itself.

Figure 1. Carbon dioxide absorption bands in the SWIR–MWIR spectral range. Figure 1. Carbon dioxide absorption bands in the SWIR–MWIR spectral range. TIR has the advantage of providing day and night continuous measurements. The first retrieval of column averaged mixing ratio of CO2 in dry air (XCO2) has been from the infrared sounder TOVS (TIROS Operational Vertical Sounder) [3,4] demonstrating the limited capability to constrain CO2 sources and sinks [5]. The high-resolution infrared sounders, such as the AIRS (Atmospheric InfraRed Sounder) [6] and IASI (Infrared Atmospheric Sounding Interferometer) [7], were shown to attain a substantial gain of information mostly due to their broader spectral coverage and finer resolution. Therefore, the XCO2 retrieved from IASI measurements reached the precision of 2 ppm for a 5 5 ◦ × ◦ spatial resolution on a monthly time scale [7–9]. CO2 absorption bands in the SWIR spectral range have the advantage of being sensitive down to the lowermost layers of the atmosphere, which contain information about surface fluxes useful for identification of CO2 sources and sinks. In this spectral region, XCO2 has been measured by SCIAMACHY (2002–2012) [10], TANSO-FTS (2009–present) [11], OCO-2 (2014–present) [12–14], TanSAT (2016 to present) [15], and the recent OCO-3 on board ISS [16]. The OCO-2 mission provides measurements up to now from space at higher spatial resolution of 1.30 km 2.25 km reaching the × 0.5 ppm precision for XCO2 necessary to identify CO2 gradients across large urban areas [17]. Instead, the CO2 absorption bands in the MWIR region lack studies in the literature, although this band is particularly suitable for remote sensing due to the position in an atmospheric window [18] on the MWIR spectral region. Indeed, this spectral region has several advantages: it is characterized by low values of Earth reflectance leading to low backscattering effects. Moreover, the radiance emitted by the Earth in this spectral range allows continuous acquisitions during day and night. Finally, we expect a measurable amount of energy at the sensor, independently from the pixel size, from high-temperature events due to the fact that Wien’s displacement law determines the temperature at which the maximum energy will radiate and the 3–5 µm range corresponds to the radiant energy peak for temperatures of 600 K and greater (see Figure2), which are associated with fires, lava flows, and other hot features [ 19]. Remote Sens. 2020, 12, x FOR PEER REVIEW 3 of 12

We expect several advantages in using the 4.8 µm absorption band. First of all, the band is located in an atmospheric window, just before the strong water absorption bands in the range 5–8 µm [18,23]. The 4.8 µm band has absorptivity comparable to the SWIR band at 2 µm, thus suggesting the amount of energy reaching a space sensor is sufficient to be a useful band for measuring the CO2 amount in the atmosphere, whereas the 4.2–4.4 µm absorption band has absorptivity close to one, so the energy reaching a space sensor is too low. The performance of the 4.8 µm absorption band in retrieving CO2 concentrations was analyzed by means of the MODerate resolution atmospheric TRANsmission (MODTRAN) radiative transfer model [24]. Specifically, the role of surface temperatures below gas emissions was investigated; the width of Remotethe channel Sens. 2020, 12was, 172 also considered in the analyses with the aim to understand its3 of 12influence on the sensitivity of multispectral space sensors.

Figure 2.Figure Radiation 2. Radiation emitted emitted from from blackbodies blackbodies at Tat= T300, = 400,300 500,, 400, 600, 500, 700K 600, (Wien’s 700 displacement K (Wien’s law). displacement law). The scope of the present study is to understand the capability of the absorption band at 4.8 µm to detect and measure the spatial distribution of CO2 emissions from point sources as degassing 2. Simulationsvolcanic of plumes CO2 [Absorption20], fires [21], and Band industrial at 4.8 emissions µm [22]. This study can be useful to define the characteristics of multispectral imaging space radiometers to be employed in future space missions In orderwhose to applications simulate include the radiance greenhouse at gas the observations. satellite sensor, The possibility in the of MWIR detecting spectral CO2 point region, the MODTRANsources computer is related code to both [24], the sensitivity version and4, was the spatialused. resolutionThe MODTRAN of the sensor transfer itself. model is based on the µ radiative transferWe expect Equation several advantages(1). The at-sensor in using the 4.8measurm absorptioned radiance band. Firstin the of all,thermal the band spectral is located region is a in an atmospheric window, just before the strong water absorption bands in the range 5–8 µm [18,23]. combinationThe 4.8 ofµ mthree band primary has absorptivity terms: comparable the Earth-em to the SWIRitted band radiance, at 2 µm, thusreflected suggesting downwelling the amount radiance (thermal of+ solar energy components), reaching a space and sensor total is su atmospherifficient to be ac useful path bandradiance for measuring (thermal the + CO solar2 amount components): in the atmosphere, whereas the 4.2–4.4 µm absorption band has absorptivity close to one, so the energy ↓ ↓ ↑ ↑ reaching𝐿 a( space𝜆, 𝜃) sensor=𝜏( is𝜃) too𝜖 low.𝐵(𝜆, 𝑇 ) + 𝜌 𝐿(𝜆, 𝜃) +𝐿(𝜆, 𝜃) + 𝐿(𝜆, 𝜃) +𝐿(𝜆, 𝜃) (1) The performance of the 4.8 µm absorption band in retrieving CO2 concentrations was analyzed where 𝐿by( means𝜆, 𝜃) ofis thethe MODerate at-sensor resolution radiance, atmospheric 𝜆 is wavelength, TRANsmission 𝜃 (MODTRAN)is the satellite radiative viewing transfer angle, 𝜖 is model [24]. Specifically, the role of surface temperatures below gas emissions was investigated; the surface emissivity, 𝜌 is surface reflectance, 𝐵(𝜆, 𝑇 ) is the Planck function describing radiance emitted atthe surface width of temperature, the channel was also𝑇 , considered𝐿↓ is the intotal the analyses (diffuse with and the direct) aim to understand downwelling its influence solar radiance, on the sensitivity of multispectral space sensors. ↓ ↑ 𝐿 is the downwelling thermal irradiance, 𝜏(𝜃) is the atmospheric transmittance, 𝐿(𝜆, 𝜃) is the 2. Simulations of CO Absorption↑ Band at 4.8 µm upward path solar radiance,2 and 𝐿(𝜆, 𝜃) is the upward thermal path radiance reaching the sensor. In order to simulate the radiance at the satellite sensor, in the MWIR spectral region, the MODTRAN 2.1. MODTRANcomputer General code [24 ],Setup version and 4, wasPerformed used. The Runs MODTRAN transfer model is based on the radiative transfer Equation (1). The at-sensor measured radiance in the thermal spectral region is a combination In thisof three work, primary the terms:model the setup Earth-emitted considered radiance, was reflected the default downwelling [24], radiance assuming (thermal 37+ notsolar equispaced atmosphericcomponents), vertical and levels total atmosphericfrom 2 to path100 radiancekm as (thermalrepresentative+ solar components): of an elevated CO2 emitting point source in a volcanic or mountainh area with elevations >2 kmi (Figure 3d). The runs were operated Lobs(λ, θ) = τλ(θ) λB(λ, Ts) + ρλ Ls↓(λ, θ) + Lt↓(λ, θ) + Lt↑(λ, θ) + Ls↑(λ, θ) (1) using a real scenario with atmospheric profiles of pressure, temperature and water obtained from a

Remote Sens. 2020, 12, x FOR PEER REVIEW 4 of 12 balloon sounding on Trapani (Sicily, Italy). These profiles (Figure 3a–c) were chosen following the criteriaRemote Sens. of the2020 representativeness, 12, 172 of the midlatitude autumn in a stable atmospheric day on Sicily4 of 12 island where Mount Etna volcano (3330 m a.s.l.) is located. Quiescent emissions from Mount Etna’s summit are a high natural point source of CO2 [25]. Table 1 reports the main parameters used as input where Lobs(λ, θ) is the at-sensor radiance, λ is wavelength, θ is the satellite viewing angle, λ is the for the MODTRAN simulations. The surface albedo has been set considering homogeneous lava surface emissivity, ρλ is surface reflectance, B(λ, Ts) is the Planck function describing radiance emitted surface [26]. at surface temperature, Ts, Ls↓ is the total (diffuse and direct) downwelling solar radiance, Lt↓ is the downwelling thermal irradiance, τ (θ) is the atmospheric transmittance, L↑(λ, θ) is the upward path Table 1. Input Parametersλ for MODTRAN Simulations in “Standards Conditions”. solar radiance, and Lt↑(λ, θ) is the upward thermal path radiance reaching the sensor. Input parameter Value 2.1. MODTRAN General SetupSpectral and Performed range Runs MWIR: 3–6 µm Balloon sounding on Trapani AtmosphericIn this work, profiles the model of temperature, setup considered pressure, was and the humidity default [24], assuming 37 not equispaced (October 1, 2018) atmospheric vertical levels from 2 to 100 km as representative of an elevated CO2 emitting point source in a volcanic or mountainSurface area temperature with elevations >2 km (Figure3d). The runs were 300 K operated using a real scenario with atmosphericCO2 concentration profiles of pressure, temperature and waterobtained 400 ppm from a balloon sounding on Trapani (Sicily, Italy).Albedo These profiles (Figure3a–c) were chosen following0.10 the criteria of the representativenessAltitude of the midlatitude of the first layer autumn in a stable atmospheric day 2 on km Sicily island where Mount Etna volcano (3330Altitude m a.s.l.)of the islast located. layer Quiescent emissions from Mount 600 km Etna’s summit are Number of vertical levels 37 a high natural point source of CO2 [25]. Table1 reports the main parameters used as input for the MODTRAN simulations. TheAerosol surface albedo has been set considering homogeneousNO lava surface [26].

FigureFigure 3. 3. AtmosphericAtmospheric profiles proﬁles of of pressure pressure (a (),a), temperature temperature (b (b),), and and humidity humidity (c ()c )obtained obtained from from a a balloonballoon sounding sounding on on Trapani Trapani (Sicily, (Sicily, Italy) Italy) and and simulated simulated vertical vertical levels levels ( (dd).).

In order to evaluate the sensitivity of the 4.8 μm channel to CO2 changes, several runs of the model were carried out considering incremental CO2 concentrations in atmosphere and temperatures at the ground. The CO2 concentrations were considered in the range 0–1000 ppm at intervals of 200

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Table 1. Input Parameters for MODTRAN Simulations in “Standard Conditions”.

Input Parameter Value Spectral range MWIR: 3–6 µm Atmospheric proﬁles of temperature, pressure, and humidity Balloon sounding on Trapani (1 October 2018) Surface temperature 300 K CO2 concentration 400 ppm Albedo 0.10 Altitude of the ﬁrst layer 2 km Altitude of the last layer 600 km Number of vertical levels 37 Aerosol NO

In order to evaluate the sensitivity of the 4.8 µm channel to CO changes, several runs of the model Remote Sens. 2020, 12, x FOR PEER REVIEW 2 5 of 12 were carried out considering incremental CO2 concentrations in atmosphere and temperatures at the ground.ppm, in a The first CO step2 concentrations fixing the surface were temperature considered at in 300 the K range (Figure 0–1000 4) and ppm in a at second intervals step of increasing 200 ppm, inthe a surface ﬁrst step temperatures ﬁxing the surface from temperature300 K to 1000 at K 300 at K in (Figuretervals4 of) and 100 in K. a So, second a total step of increasing 48 runs were the surfaceperformed temperatures to analyze from the sensitivity 300 K to 1000 as Ka function at intervals of ofCO 1002 concentration K. So, a total ofand 48 of runs ground were temperatures performed to analyzethat are thespread sensitivity in a wide as arange function in the of case CO2 ofconcentration a high-temperature and of ground event (HTE). temperatures that are spread in a wide range in the case of a high-temperature event (HTE).

Figure 4. MODTRAN CO2 vertical proﬁles. Figure 4. MODTRAN CO2 vertical profiles. 2.2. Response Functions and Convolution of Radiances 2.2. ResponseA main objectiveFunctions ofand the Convolution study is to of assess Radiances the usability of the channel for multispectral imaging spaceA radiometers. main objective So, withof the the study aim ofis evaluatingto assess the the usability response of of the satellite channel sensors for multispectral to incoming radiances, imaging itspace is necessary radiometers. to consider So, with the characteristicsthe aim of evaluating of the sensor the and response speciﬁcally of satellite the response sensors function to incoming for the 4.8radiances,µm absorption it is necessary band. Since to consider the current the characte multispectralristics imaging of the sensor space radiometersand specifically with the detectors response in thefunction MWIR for do the not 4.8 employ µm absorption this channel band. (e.g., Since MODIS the current and AVHRR), multispectral we considered imaging space typical radiometers response functionswith detectors of operational in the MWIR sensors do carried not employ on aircrafts; this channel in particular, (e.g., MODIS the response and AVHRR), functionof we the considered MASTER (Modistypical ASTER)response airborne functions simulator of operational [27,28] wassensors taken carried into account. on aircraft Then,s; in the particular, response functionthe response was adaptedfunction of for the our MASTER needs, maintaining(Modis ASTER) the airborne same shape simulator and changing [27,28] was the taken full into width account. half maximum Then, the response function was adapted for our needs, maintaining the same shape and changing the full width half maximum (FWHM) in order to test two different solutions: two response functions were considered with FWHM equal to 0.15 and 0.30 µm (see Figure 5).

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(FWHM)Remote Sens. in order 2020, 12 to, x test FOR two PEER di REVIEWﬀerent solutions: two response functions were considered with FWHM6 of 12 equal to 0.15 and 0.30 µm (see Figure5).

Figure 5. Simulated TOA radiances for several CO2 concentrations in the MWIR spectral range; theFigure considered 5. Simulated response TOA functions radiances are depictedfor several (dotted CO2 concentrations green line: FWHM in the =MWIR0.30 µ spectralm; dotted range; blue the line: FWHMconsidered= 0.15 responseµm). A zoom functions on the are absorption depicted (do bandtted is green also reportedline: FWHM in the = 0.30 bottom. µm; dotted blue line: FWHM = 0.15 µm). A zoom on the absorption band is also reported in the bottom.

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3. Simulation Results As described in Section 2.1, a total number of 48 runs was performed; for each considered surface temperature, the dependence of the radiance on the CO2 concentration was analyzed. Figure5 shows the simulated radiances at the top of atmosphere (TOA), with a ﬁxed surface temperature of 300 K (standard condition), for CO2 concentrations ranging from 0 to 1000 ppm in the lower troposphere. The response functions derived from the MASTER instrument and used in the present work are also reported in Figure5 (green and blue dotted lines). The maximum CO 2 concentrations of 1000 ppm 2 1 1 generated a decrease of about 1 Wm− sr− µm− in the radiance simulations (Figure5 zoom). TheRemote strong Sens. 2020 water, 12, x FOR absorption PEER REVIEW started from about 5 µm and could have partially aﬀ7ected of 12 the CO2 band; so, a large response function could have included the contribution of the water in the atmosphere.The The strong sensitivity water absorption of the absorption started from band about to increasing 5 µm and concentrationscould have partially of carbon affected dioxide the CO is2 also band; so, a large response function could have included the contribution of the water in the highlighted in Figure5: the radiance at the sensor decreased, in the range 4.7–4.9 µm, with increasing atmosphere. The sensitivity of the absorption band to increasing concentrations of carbon dioxide is gas concentration. Moreover, the very strong CO band in the spectral range 4.2–4.4 µm [29] was also highlighted in Figure 5: the radiance at the 2sensor decreased, in the range 4.7–4.9 µm, with unusable due to the strong absorption of the remote signal at atmospheric background conditions increasing gas concentration. Moreover, the very strong CO2 band in the spectral range 4.2–4.4 µm (~400[29] ppm). was unusable due to the strong absorption of the remote signal at atmospheric background conditions (~400 ppm). 3.1. Radiance as Function of CO2 and T

3.1. Radiance as Function of CO2 and T In order to analyze the behavior of the channel at 4.8 µm as a function of CO2 concentrations and surfaceIn temperatures,order to analyze TOA the behavior simulated of the radiances channel at were 4.8 µm convolved as a function on response of CO2 concentrations functions described and above.surface In the temperatures, following analyses, TOA simulated a function radiances with were FWHM convolved= 0.15 µonm response was firstly functions considered, described since a narrowerabove. response In the following function analyses, is less a ffaected function by with the presence FWHM = of0.15 water µm was in the firstly atmosphere; considered, furthermore, since a narrower response function is less affected by the presence of water in the atmosphere; furthermore, this is the typical width employed in operational sensors carried on aircrafts such as the MASTER this is the typical width employed in operational sensors carried on aircrafts such as the MASTER airborne simulator. Once the surface temperature was fixed, the TOA radiance was convolved for airborne simulator. Once the surface temperature was fixed, the TOA radiance was convolved for several CO concentrations ranging from 0 to 1000 ppm; the dependence of radiance on the gas several2 CO2 concentrations ranging from 0 to 1000 ppm; the dependence of radiance on the gas concentrationconcentration could could be thus be thus obtained. obtained. Moreover, Moreover, thisthis function was was derived derived for for different different temperatures temperatures at ground,at ground, ranging ranging from from 300 300 to 1000to 1000 K, K, and and results results areare reported in in Figure Figure 6;6 for; for a better a better representation, representation, the logarithmicthe logarithmic scale scale is usedis used for for radiance radiance values. values. As As we weexpected, expected, the radiance the radiance sharply sharplyincreased increased with −2 −21 1−1 1 with increasingincreasing temperatures, reaching reaching values values more more than than 1200 1200 Wm Wmsr− srµm− µ min −thein warmest the warmest case. case. Considering that typical values of radiance are 1–2 Wm−2sr2−1µm1−1 in the1 “standard condition”, the Considering that typical values of radiance are 1–2 Wm− sr− µm− in the “standard condition”, the surfacesurface temperature temperature plays a a crucial crucial role role in indete determiningrmining the total the total energy energy retrieved retrieved by sensors. by sensors.

Figure 6. Simulated TOA radiances (in logarithmic scale), after the convolution considering Figure 6. Simulated TOA radiances (in logarithmic scale), after the convolution considering FWHM = FWHM = 0.15 µm, as function of CO2 concentrations for several surface temperatures. 0.15 µm, as function of CO2 concentrations for several surface temperatures.

A nearest-neighbor interpolation technique was applied to the simulated radiances with the aim to obtain a continuous function of the two parameters, CO2 concentration and temperature. The result is a three-dimensional function, describing the behavior of the 4.8 μm absorption band (Figure 7).

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A nearest-neighbor interpolation technique was applied to the simulated radiances with the aim Remote Sens. 2020, 12, x FOR PEER REVIEW 8 of 12 to obtain a continuous function of the two parameters, CO2 concentration and temperature. The result is a three-dimensional function, describing the behavior of the 4.8 µm absorption band (Figure7).

Figure 7. Simulated at-sensor radiances (interpolated), after the convolution considering

FWHM = 0.15 µm, as function of CO2 concentration and surface temperature. Figure 7. Simulated at-sensor radiances (interpolated), after the convolution considering FWHM = 3.2.0.15 Sensitivity µm, as function Analyses: of NoiseCO2 concentration Equivalent Delta and surface Temperature temperature. and Signal-to-Noise Ratio

3.2. SensitivityThe analysis Analyses: of at-sensor Noise Equivalent radiance Delta as afunction Temperature of CO and2 concentrationSignal-to-Noise andRatio surface temperature is propaedeutic for calculating and defining characteristics for future space sensors employing the consideredThe analysis spectral of at-sensor channel. radiance In particular, as a function the required of CO accuracy2 concentration of MWIR and sensors surface is temperature a fundamental is propaedeuticparameter which for allowscalculating detecting and anddefining distinguishing characteristics gas emission for future phenomena. space sensors So, sensitivity employing analyses the consideredare useful tospectral answer channel. the question: In particular, what is the the instrumental required accuracy accuracy of necessaryMWIR sensors to observe is a fundamental a variation of parameter which allows detecting and distinguishing gas emission phenomena. So, sensitivity CO2 concentration in the atmosphere by using the channel at 4.8 µm? Considering the signal-to-noise analysesratio definition are useful (Equation to answer (2)), the minimum question: conditions what is the to instrumental observe gas variationsaccuracy necessary can be defined. to observe a variation of CO2 concentration in the atmosphere by using the channel at 4.8 µm? Considering the signal-to-noise ratio definition (Equation (2)), minimumRλ conditionsRλ to observe gas variations can be SNRλ = m (2) defined. NedR ≥ ∆Rλ

𝑅 𝑅 where SNRλ = signal-to-noise ratio, Rλ = radiance at the sensor, NedR = noise equivalent delta 𝑆𝑁𝑅 = ≥ (2) m 𝑁𝑒𝑑𝑅 𝛥𝑅 radiance, ∆Rλ = delta radiance value (signature to measure). whereThen, SNR in = order signal-to-noise to detect the ratio, radiance R changes= radiance due toat gasthe concentration sensor, NedR changes, = noise the equivalent noise equivalent delta radiance,delta radiance ΔR =of delta the sensor radiance must value be less(signature than the to delta measure). radiance value (Equation (3)). Then, in order to detect the radiance changes due to gas concentration changes, the noise NedR ∆Rm (3) equivalent delta radiance of the sensor must be less≤ thanλ the delta radiance value (Equation (3)). Now, we can calculate the decreasing rate𝑁𝑒𝑑𝑅 of at-sensor ≤𝛥𝑅 radiance for increasing CO2 concentrations(3) (see Figure6) and derive the angular coe ﬃcient under the ﬁrst approximation of linear behavior. In Now, we can calculate the decreasing rate of at-sensor radiance for increasing CO2 concentrationsthe following, (see we consider,Figure 6) asand signature derive the to angula measure,r coefficient the delta under radiance the value first approximation due to a CO2 increasing of linear behavior.of 10 ppm In inthe the following, entire atmospheric we consider, column. as signature This to allows measure, calculating the delta sensitivity radiance value parameters due to fora each temperature considered in the MODTRAN simulations (Table2). The noise equivalent delta CO2 increasing of 10 ppm in the entire atmospheric column. This allows calculating sensitivity parameterstemperature for (NEDT) each temperature parameter was considered derived from in the NedRMODTRAN by means simulations of the Planck (Table law; 2). the The considered noise equivalenttemperatures delta for temperature black body (NEDT) emissions parameter are reported was inderived Table2 from. the NedR by means of the Planck law; the considered temperatures for black body emissions are reported in Table 2.

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Table 2. Sensitivity Parameters for Several Surface Temperatures Considering a Variation of 10 ppm Table 2. Sensitivity Parameters for Several Surface Temperatures Considering a Variation of 10 ppm with a FHWM = 0.15 μm. with a FHWM = 0.15 µm. Parameters\Temp. 300 K 400 K 500 K 600 K 700 K 800 K 900 K 1000 K Parameters Temp. 300 K 400 K 500 K 600 K 700 K 800 K 900 K 1000 K Angular coefficient\ –0.0033 –0.046 –0.21 –0.56 –1.15 –1.98 –3.03 –4.29 Angular−2 −1 coe−1ﬃcient−1 (Wm sr µm ppm ) –0.0033 –0.046 –0.21 –0.56 –1.15 –1.98 –3.03 –4.29 (Wm 2sr 1µm 1ppm 1) − NedR− − − NedR <3.3 <46 <210 <560 <1150 <1980 <3030 <4290 (mWm−22sr−1µm1 −1)1 <3.3 <46 <210 <560 <1150 <1980 <3030 <4290 (mWm− sr− µm− ) NEDTNEDT (K) (K) <0.045<0.045 < <0.0950.095 < <0.150.15 < <00.21.21 <<0.280.28 <<0.360.36 <<0.450.45 <0.56<0.56 SNRSNR >405.5>405.5 > >306.0306.0 >>297.0297.0 >>303.1303.1 >>303.1303.1 >>303.6303.6 >>304.6304.6 >>304.6304.6

AsAs wewe expected,expected, thethe NEDTNEDT increasedincreased withwith increasingincreasing temperaturestemperatures atat thethe groundground becausebecause ofof greatergreater energyenergy receivedreceived byby thethe instrument.instrument. A higherhigher sensitivitysensitivity of thethe sensorsensor isis requiredrequired forfor lowerlower temperaturestemperatures to to detect detect changes changes in in gas gas concentration. concentration. A A lower lower sensitivity sensitivity is insteadis instead necessary necessary in casein case of HTEs;of HTEs; considering, considering, for for example, example, a surfacea surface temperature temperature of of 600 600 K K in in the the radiative radiative transfer transfer model, model, thethe NEDT must be less than 0.21 K in order to detect a variation of 10 ppm in the CO2 concentration. NEDT must be less than 0.21 K in order to detect a variation of 10 ppm in the CO2 concentration. TheThe FWHMFWHM parameter parameter of of the the sensor sensor response response function function is alsois also crucial crucial for retrievingfor retrieving changes changes in gas in concentration.gas concentration. All calculationsAll calculations above above were were performed performed considering considering a FWHM a FWHM= 0.15 = 0.15µm; µm; it is it useful is useful to evaluateto evaluate the impactthe impact of a widerof a /narrowerwider/narrower response resp function.onse function. Following Following the characteristics the characteristics of operative of multispectraloperative multispectral space sensors, space a FWHM sensors,= a0.30 FWHMµm was = 0. considered;30 µm was theconsidered; NEDT values the NEDT were recalculatedvalues were andrecalculated are reported and in are Figure reported8. The in NEDT Figure was 8. The greater, NEDT for was all ground greater, temperatures, for all ground in temperatures, the case of 0.15 inµ them: thecase results of 0.15 indicate µm: the the results best performancesindicate the best by perf usingormances the narrower by using response the narrower function. response This is probablyfunction. This is probably due also to the closest N2 absorption band that can influence the larger channel. due also to the closest N2 absorption band that can inﬂuence the larger channel.

Figure 8. NEDT as function of surface temperature considering a response function with Figure 8. NEDT as function of surface temperature considering a response function with FWHM = FWHM = 0.15 µm (red line) and FWHM = 0.30 µm (black line). 0.15 µm (red line) and FWHM = 0.30 µm (black line). 4. Discussion 4. Discussion The model simulation results highlighted the radiance diﬀerence to be appreciated from a multispectralThe model space simulation imaging sensorresults with highlighted the absorption the ra banddiance at 4.8differenceµm for COto 2beconcentration appreciated startingfrom a frommultispectral atmospheric space background imaging sensor (400 with ppm) the to absorption 1000 ppm. band This at di 4.8ﬀerence µm for has CO been2 concentration transformed starting in a from atmospheric background (400 ppm) to 1000 ppm. This difference has been transformed in a NEDT (Table 2). The values of NEDT strongly depend on the ground temperature and the FWHM of

Remote Sens. 2020, 12, 172 10 of 12

NEDT (Table2). The values of NEDT strongly depend on the ground temperature and the FWHM of the response function. Higher temperatures under emitting point sources induce NEDT higher values, allowing the possibility to retrieve CO2 changes. Considering the current space instruments, the MWIR bands (4.4 µm and 4.5 µm) of the MODIS instrument on board Terra satellite have a NEDT of 0.25 K as the predicted was 0.15 K at 300 K [30]. Instead, the more recent MWIR channel 3.74 µm of AVHRR-3 on board the METOP satellites is 0.12 K at 300 K [31]. Taking into account also the TIR operational sensor ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) [32], the NEDT is 0.2 K at 300 K for the five thermal bands (8–11 µm). Moreover, considering the SNR of ≤ the actual SWIR bands of TANSO-FTS on board GOSAT-2 and the OCO-2 instrument of SNR > 300, the difference in sensitivity with our results (Table2) is for a target surface at temperature values >400 K. This means that the sensitivity of 4.8 µm channel is satisfied for high-temperature events (>400K) by using the actual technologies. From our results, in order to appreciate a CO2 variation of 10 ppm and considering a surface at 300 K, the necessary NEDT is 0.045 K for a FWHM of 0.15 µm and 0.03 K for a FWHM of 0.30 µm. So, the required characteristics of a new space sensor employing the 4.8 µm channel, with a NEDT of about 0.045 K, are not so far from actual available technologies (e.g., AVHRR-3). Moreover, tests on the width of sensor response function give best results for the narrower one (0.15 µm). This NEDT is calculated for a ‘cold’ surface at standard condition (300 K). Instead, for a ‘hot’ surface >600 K, the NEDT result <0.21 K is completely compliant with the actual technologies for both FWHM. Future space instruments should consider this wide range of values to retrieve CO2 concentrations on point sources and also to avoid saturation problems that actually characterized the acquisition of high-temperature events. Instrument sensitivity as well as repeat cycles are expected to increase significantly in the near future with new technological solutions [25]. The possibility of detecting CO2 point sources is related to both the sensitivity and the spatial resolution of the sensor itself.

5. Conclusions

In this work, MODTRAN simulations were focused on the CO2 absorption band at 4.8 µm, in the MWIR spectral region. Model runs were performed for a set of surface temperatures, in the range 300–1000 K, with the aim to characterize the channel performance in the case of HTEs with emission of carbon dioxide. The at-sensor radiance sharply increases with increasing temperatures, ranging 2 1 1 2 1 1 from 1 Wm− sr− µm− (in the standard condition) to more than 1200 Wm− sr− µm− (in the warmest case). Furthermore, the FWHM parameter is very important to detect changes in the gas concentration: two values (0.15 and 0.30 µm) are considered in the present paper. The narrower function leads to best challenges in order to detect gas emissions due to the highest values of NEDT calculated for this case. So, simulation results provide indications on the sensitivity necessary to appreciate carbon dioxide variations and then retrieve their concentrations from a space sensor. In this study, a variation of 10 ppm in gas concentration was considered as target; this value is equivalent to about 2 kg/m2 more in the columnar abundance XCO2. The values of NEDT closest to the actual technologies are obtained considering the FWHM equal to 0.15 µm in the range from 0.045 to 0.56 K depending on the ground temperature. The current operative spaceborne multispectral imaging space radiometers do not include the channel at 4.8 µm; however, sensors with MWIR channels as MODIS and AVHRR have a NEDT in the range 0.1–0.2 K. Considering our results, we can say that current space technology could be able to detect changes of tens ppm in CO2 concentration for standard condition (at 300 K), and very little changes on HTEs emitting greenhouse gases. In the framework of the studies addressed to the next generation of multispectral space sensors, this work represents a ﬁrst step to understand the behavior of the considered CO2 absorption band, less studied in the literature, and the possibility to include the 4.8 µm band in a new instrument dedicated to the Earth’s observation. Remote Sens. 2020, 12, 172 11 of 12

Author Contributions: Methodology, V.R.; Writing-Review & Editing, C.S.; M.S.; M.F.B.; Supervision, V.R.; Project Administration, V.R.; Funding Acquisition, V.R. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Agenzia Spaziale Italiana (ASI) through the contract n. 2018-17-HH.0 between ASI and the Istituto Nazionale di Geofisica e Vulcanologia (INGV). Acknowledgments: This work was supported by the Agenzia Spaziale Italiana (ASI) in the framework of a joint study between ASI and NASA/JPL. Conflicts of Interest: The author declares no conflict of interest.

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