Measurement of Downwelling Radiance Using a Low-Cost Compact Fourier-Transform Infrared System for Monitoring Atmospheric Conditions

: Temperature and water vapor play crucial roles in the Earth’s climate system, and it is important to understand and monitor the variation in the thermodynamic profile within the lower troposphere. Among various observation platforms for understanding the vertical structure of temperature and humidity, ground-based Fourier-transform infrared (FTIR) can provide detailed information about the lower troposphere by complementing the limitations of radiosonde or satellite methods. However, these ground-based systems have limitations in terms of cost, operation, and mobility. Herein, we introduce a cost-effective and easily deployable FTIR observation system designed to enhance monitoring capabilities for atmospheric conditions. The atmospheric downwelling radiance spectrum of sky is measured by applying a real-time radiative calibration using a blackbody. From the observed radiance spectrum, the thermodynamic profile (temperature and the water vapor mixing ratio) of the lower troposphere was retrieved using an algorithm based on the optimal estimation method (OEM). The retrieved vertical structure results in the lower troposphere were similar to the fifth-generation reanalysis database (ERA-5) of the European Center for Medium-range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction final analysis (NCEP FNL). This provides a potential possibility for monitoring atmospheric conditions by a compact FTIR system.


Introduction
Temperature and water vapor in the atmosphere play crucial roles in the Earth's climatic system.These are critical for the stable energy balance of the Earth, as the atmospheric temperature is a key parameter in the interplay of energy received from the sun and emitted back to space.This balance affects climate change and has direct influences on various meteorological phenomena, which means variations in temperature and water vapor drive the distinct formation of weather patterns and all atmospheric conditions including wind formation and distribution and the intensity of precipitation [1][2][3].
Particularly, examining the vertical profile of tropospheric temperature and water vapor within the planetary boundary layer (PBL) is crucial for various research applications.These include enhancing operational situational awareness during severe weather events [4], initializing numerical weather prediction (NWP) models [5], facilitating pollution dispersion modeling [6], and conducting research on heat and moisture exchange processes involving the Earth's surface with atmospheric layers [7].
Over the past 60 years, the World Meteorological Organization (WMO) has operated the Global Observing System (GOS), encompassing a comprehensive suite of observations, including surface measurements, aircraft data, ground-based and space-borne remote sensing, and weather radar observations [8].This extensive system has been focused on delivering reliable vertical profiles of temperature and water vapor information at a global scale.Furthermore, the Decadal Survey in 2017 highlighted the critical role of thermodynamic profiles within the PBL, emphasizing the need for focused observations as a key area for future investment [9].
Although radiosondes are highly applied as references for their precise and detailed vertical in situ measurements, the limitations in time and space coverage of the radiosonde network are not negligible, due to the costs and labor required for launching these systems.In response to these limitations, advancements in remote sensing technologies have emerged as valuable complements to in situ measurements, fulfilling gaps in the existing operational observing system.Satellite observations, such as those of the Infrared Atmospheric Sounding Interferometer (IASI) onboard the meteorological operational (MetOp) satellites operated by the European organization for the exploitation of meteorological satellite's (EUMETSAT) [10], and the Cross-Track Infrared Sounder (CrIS) onboard the Soumi-National Polar-orbiting Partnership (NPP) jointly operated by the National Oceanic and Atmospheric Administration (NOAA) and National Aeronautics and Space Administration (NASA) [11], offer global-scale coverage and have demonstrated improvements in forecast skills for global Numerical Weather Prediction (NWP) [12].Despite these advantages, challenges still exist due to the relatively poor horizontal resolution and difficulties in retrievals over iced surfaces, resulting in coarse vertical resolution and accuracy within the planetary layer (PBL) and vertical profiles under cloud cover [13].
Among the various remote sensing observation platforms, ground-based remote sensing instruments, such as the Microwave Radiometer (MWR) [14,15] ground-based Fourier-transform infrared (FTIR), and the Atmospheric Emitted Radiance Interferometer (AERI) [16], offer a highly complementary perspective to space-borne remote sensing.This synergy is derived from their exceptional sensitivity near the Earth's surface and their ability to provide higher vertical and temporal resolution compared to satellite-based remote sensing systems.With an acknowledgement of the importance of mesoscale monitoring and prediction, in 2009, the National Research Council (NRC) stressed the need to develop a global network of ground-based atmospheric profiling systems [17].In particular, thermodynamic profiles retrieved from the AERI have been used in diverse scientific studies, including those investigating cold fronts and drylines [18], identifying the change in various convective indices in tornadic and non-tornadic storms [4], examining the retrieval method for the cumulus entrainment rate [19], and retrieving aerosol information [20,21].However, these instruments not only require significant costs to purchase and operate, but also require placement in buildings, ships, or containers, limiting their mobility to specific observation locations.Therefore, an observation system that is more cost-effective and relatively convenient to move to various locations is required to monitor the thermodynamic profile of the lower troposphere.
In this study, we present a compact FTIR system, which offers significant mobility advantages due to its simple installation and stabilization, designed to measure the infrared spectral range for acquiring atmospheric information.Figure 1 shows the overall steps of the proposed observation platform from instrumental setting to the thermodynamic retrieval process, and that flowchart aligns with content flow in this research.In Sections 2 and 3, we introduce the detailed configuration of the instrument, the radiometric calibration method, and the determination of observation characteristics through the signal processing.The retrieval method for thermodynamic profiles from observed sky radiance data is described in Section 4, and Section 5 shows the evaluated results applied to actual observation data.

Instrumentation Construction of Instrument Hardware
To measure the atmospheric emi ed radiance spectrum and derive atmospheric thermal dynamic profiles, we constructed a compact FTIR observing system using the M4400 spectrometer (Midac Corporation, Irvine, CA, USA).Previously, the MIDAC M4400 spectrometer was primarily used to measure the surface emissivity [22,23] or column gas composition in an open-path FTIR system [24].Unlike them, we build an additional front-end optical part to the FTIR instrument to acquire atmospheric infrared signals, as shown in Figure 2 (the compact FTIR environment is shown in Figure S1).The entire measurement platform consists of the FTIR instrument part and the front optics part, where the blackbody is located for radiometric calibration of the observation spectrum.

Instrumentation Construction of Instrument Hardware
To measure the atmospheric emitted radiance spectrum and derive atmospheric thermal dynamic profiles, we constructed a compact FTIR observing system using the M4400 spectrometer (Midac Corporation, Irvine, CA, USA).Previously, the MIDAC M4400 spectrometer was primarily used to measure the surface emissivity [22,23] or column gas composition in an open-path FTIR system [24].Unlike them, we build an additional frontend optical part to the FTIR instrument to acquire atmospheric infrared signals, as shown in Figure 2 (the compact FTIR environment is shown in Figure S1).The entire measurement platform consists of the FTIR instrument part and the front optics part, where the blackbody is located for radiometric calibration of the observation spectrum.
Detailed information on the FTIR and blackbody hardware is described in Table 1.The MIKRON M340 portable blackbody calibration sources (Mikron Instrument Company, Oakland, NJ, USA) for two temperatures (hot and ambient) are located on both sides.The blackbody emissivity is >0.98 within 8-15 µm, covering the atmospheric window.The hot blackbody temperature is fixed at 333 K, while the ambient blackbody temperature varies depending on the surrounding temperature at the time of observation.Blackbody temperatures are easily controlled within 0.1 • C by a self-tuning proportional integral differential (PID) controller from a digital temperature display.A single sky observation consists of a repeating sequence that measures the hot blackbody, sky-view, and ambient blackbody, at one-minute intervals.In the front optics, by adjusting the angle of the switching mirror located in the center of the structure, the incident atmospheric emitted radiative energy and each blackbody source are transmitted to the FTIR instrument in each sequence.Detailed information on the FTIR and blackbody hardware is described in Table 1.The MIKRON M340 portable blackbody calibration sources (Mikron Instrument Company, Oakland, NJ, USA) for two temperatures (hot and ambient) are located on both sides.The blackbody emissivity is >0.98 within 8-15 μm, covering the atmospheric window.The hot blackbody temperature is fixed at 333 K, while the ambient blackbody temperature varies depending on the surrounding temperature at the time of observation.Blackbody temperatures are easily controlled within 0.1 °C by a self-tuning proportional integral differential (PID) controller from a digital temperature display.A single sky observation consists of a repeating sequence that measures the hot blackbody, sky-view, and ambient blackbody, at one-minute intervals.In the front optics, by adjusting the angle of the switching mirror located in the center of the structure, the incident atmospheric emitted radiative energy and each blackbody source are transmi ed to the FTIR instrument in each sequence.
The MCT detector is a photon detector, and electrons are directly excited by the absorption radiation.In order to avoid thermal excitation, a cooling system is necessary.Since this FTIR is not equipped with an automated cooling system, liquid nitrogen (LN2) is used to achieve the temperature that acquires a high-sensitivity sensor.When the MCT detector is cooled sufficiently using LN2, which means that the interferogram is stable, the system is ready to observe.Moreover, a desiccant is placed inside, and nitrogen gas is purged due to the high sensitivity of moisture to the major components in the FTIR instrument.To improve the accuracy of the observation spectrum, 32 repeated scans are merged to generate a single spectrum.The observation system is primarily designed for  MIDAC M4400 FTIR is a Michelson interferometer consisting of a beam splitter, a fixed mirror, a moving mirror, a collimator, and a Mercury-Cadmium-Telluride (MCT) detector.It measures infrared radiance from 500 to 4000 cm −1 (2.5-20.0µm), with an unapodized spectral resolution of 1.0 cm −1 .This spectral range of the FTIR platform can cover the various absorption bands of gases in the atmosphere, such as ozone (O 3 ; 980-1080 cm −1 ), carbon dioxide (CO 2 ; 612-618, 624-660, 674-713, and 2223-2260 cm −1 ), methane (CH 4 ; 1150-1229 cm −1 ), and water vapor (H 2 O; 538-588, and 1250-1350 cm −1 ), as well as the atmospheric window (800-1250 cm −1 ).
The MCT detector is a photon detector, and electrons are directly excited by the absorption radiation.In order to avoid thermal excitation, a cooling system is necessary.Since this FTIR is not equipped with an automated cooling system, liquid nitrogen (LN2) is used to achieve the temperature that acquires a high-sensitivity sensor.When the MCT detector is cooled sufficiently using LN2, which means that the interferogram is stable, the system is ready to observe.Moreover, a desiccant is placed inside, and nitrogen gas is purged due to the high sensitivity of moisture to the major components in the FTIR instrument.To improve the accuracy of the observation spectrum, 32 repeated scans are merged to generate a single spectrum.The observation system is primarily designed for operation under clear sky to avoid interference from rain, and it requires manual operation by human sources, as it is not automated.

Radiometric Calibration
The atmospheric emitted measured signals by the instrument need to be converted into the known radiometric calibrated radiance unit (i.e., mWm −2 sr −1 cm).As mentioned in Section 2, we performed a two-point radiometric calibration using two well-defined black-bodies (hot and ambient) radiation sources.The single sky-view observation is pairing with measurements of both the hot blackbody and the ambient blackbody at one minute before and after observing sky.Then, the radiometric calibration is performed according to the function described by [25] as follows: where N v is the calibrated radiance at the wavenumber of v. C v and Bv are the observed spectrum and Plank function radiance at the blackbody temperature (T), respectively.h, c, and k are the Plank constant, the speed of light, and the Boltzmann constant, respectively.The upper labels of A, H, and S denote 'ambient', 'hot', and 'sky', respectively.To obtain the real quantity of the measured spectral data, all values used for radiometric calibration use the real part of the complex [26-28].

Noise-Equivalent Spectral Radiance
The instrumental responsivity, which represents the conversion factor, can be determined as the inverse of the slope of the radiometric calibration from Equation (1) [28,29].
Because all components of an FTIR spectrometer do not respond perfectly at all wavelengths, the instrument's interferometric response (R v ) varies with changes in wavelength.
The noise-equivalent spectral radiance (NESR), which represents the precision of each measurement, can be determined as the ratio between the standard deviation of the spectrum of repeated measurements and the interferometric responsivity as follows: where C RBB v represents each individual measured spectrum of all measured spectra as functions of wavenumber at a reference temperature of a blackbody (RBB).N refers to the number of repeated measurements.Figure 3 shows the NESR, calculated from 30 repeated measurements of a blackbody at 300 K, which is the typical atmospheric temperature near the surface (or room condition).The NESR shows a sharp increase in noise driven by influences of CO 2 absorption (around667 cm −1 ) and water vapor (1400-1700 cm −1 and 3000-3500 cm −1 ) that exist in the interferometric path and the front optics.
The instrumental responsivity, which represents the conversion factor, can be determined as the inverse of the slope of the radiometric calibration from Equation (1) [28,29].
Because all components of an FTIR spectrometer do not respond perfectly at all wavelengths, the instrument's interferometric response ( ) varies with changes in wavelength.
The noise-equivalent spectral radiance (NESR), which represents the precision of each measurement, can be determined as the ratio between the standard deviation of the spectrum of repeated measurements and the interferometric responsivity as follows: where  represents each individual measured spectrum of all measured spectra as functions of wavenumber at a reference temperature of a blackbody (RBB).N refers to the number of repeated measurements.Figure 3 shows the NESR, calculated from 30 repeated measurements of a blackbody at 300 K, which is the typical atmospheric temperature near the surface (or room condition).The NESR shows a sharp increase in noise driven by influences of CO2 absorption (around667 cm −1 ) and water vapor (1400-1700 cm −1 and 3000-3500 cm −1 ) that exist in the interferometric path and the front optics.

The Thermodynamic Profile Retrieval Algorithm 4.1. The Line-by-Line Radiative Transfer Model
The monochromatic downwelling radiance, measured at the bottom of the atmosphere (BOA) in the thermal infrared region, is calculated based on contributions from atmospheric layers extending from the ground to the top of the atmosphere.Each atmosphere layer, divided into several sections, is assumed to be a plane-parallel atmosphere with uniform characteristics, such as temperature, pressure, water vapor, and the mixing ratios of various absorbing gases.
where µ is the cosine of the solar zenith angle.γ v is monochromatic transmittance.For a specific wavenumber, the optical depth of each layer of the atmosphere can be calculated using the Line-By-Line method by adding the contributions from neighboring absorption lines.The optical depth (τ v ) at a given wavenumber for an atmospheric vertical optical path (∆z) is where S ij denotes the intensity of the line (jth) of the species (ith).The f v − v 0 ji term refers to the spectral line-broadening effect centered at v 0 ji .n i is the number density of the species (ith).σ cont v n cont refers to the contribution of the continuum spectrum.To simulate the atmospheric transfer process, we adopted the Radiative Transfer Model, LBLDIS, which integrated the Line-By-Line Radiative Transfer Model (LBLRTM) [30,31] to calculate the gas spectral optical depth and Discrete Ordinates Radiative Transfer (DIS-ORT) [32,33] to consider the aerosol effect.In the progress of radiative transfer, the HIghresolution Transmission molecular absorption database (HITRAN) 2012 [34], and Mlaw-erTobinCloughKneizysDavies (MT_CKD) [35] are adopted for optical properties of trace gases and water vapor continuum, respectively.The Voight profile was applied to consider for spectral absorption line broadening [36].

Optimal Estimation Retreival
To retrieve the thermodynamic profile, we apply the physical retrieval algorithm based on the optical estimation method (OEM) [37], which was developed by [21] and has origins in the tropospheric optimal estimation retrieval (TROPoe) algorithm [38] (for the detailed algorithm and performance, refer to [21,38]).
The OEM relies on the Levenberg-Marquardt approach, which provides efficient retrieval of thermodynamic profiles.This optimized method, which uses gradient descent along with the Gauss-Newton methods, iteratively determines the best solution for the nonlinear problem.The thermodynamic profiles (iteratively state vector, X n+1 ) are determined as follows: Here, the a priori of state vector (X a ) and the covariance matrix (S a ) are adopted from the atmospheric composition data of the whole atmosphere community climate model (WACCM) [39].F(X) represents the radiance spectrum simulated by LBLDIS.K n is the Jacobian matrix.The standard deviation of the calibrated radiance spectrum is used to calculate the observation error covariance (S ϵ ).The optimized solution minimizes the discrepancy function, named the cost function (c) given by: The Levenberg Parameter (LP), denoted as γ, acts as a damping factor, Imposing variable weights between the observation and the solution from the preceding iteration step.For high LP values, prior information is given greater weight than observations, while for low LP values, observations are emphasized.The value of LP is determined in each iteration based on the ratio of each step of the cost functions (R), which is calculated as follows: R = ( The calculation of c n+1,FC is based on the assumption of F(X n+1 ) = F(X n ) + K n dX n+1 .The iteration is deemed converged when R falls below 0.25, at which point LP is halved to give more weight to the observations.If R lies between 0.25 and 0.75, LP remains unchanged.However, if R exceeds 0.75, LP is increased tenfold.Convergence at each iteration is determined by: N and S are the dimensions of the state vector and the posterior error covariance matrix, respectively.S is determined as: Convergence is declared based on the difference in state vectors between the current and previous iteration steps.This algorithm is applied to discrete continuous spectral bands, as presented in Table 2.
Table 2. Spectral bands utilized for temperature and the water vapor mixing ratio in the retrieval algorithm.

Results
The experiments were carried out at the Kyungpook National University (Daegu, Republic of Korea; 35.9 • N, 128.6 • E), using a FTIR observation system for atmospheric observation.Before starting the observation, we sufficiently lowered the temperature of the MCT detector by cooling with LN2.After that, we were able to secure stabilized measurement signals by checking the alignment in real time.
The downwelling atmospheric radiance and the blackbody emitted source (measured by FTIR) are expressed as interference spectra for all wavelengths.Figure 4 shows an example of a short double-sided interferogram measured for an ambient blackbody at 304 K, which shows the commonly named zero path difference (ZPD), i.e., where maximum interference occurs due to the moving mirror in the instrument.The interferogram produced at the ZPD point serves as a reference point for phase correction, since the entire spectral range of the light source produces an ideal interference pattern at this location [40].The interferometric spectrum can be expressed as a function of wavelength in terms of signal intensity using the fast-Fourier transform (FFT).Figure 5 shows the FFT converted measured intensity of the sky view, the hot black body, and the ambient black body from 500 to 4000 cm −1 at 0300 UTC on 18 July 2018 (Local Time = UTC + 9 h).The observations have clearly revealed significant features, including the difference in intensity magnitude due to temperature variations between 'hot' and 'ambient' blackbody conditions.Additionally, the atmospheric spectrum fluctuates highly across different wavelengths.Unlike the purged interior of the instrument, the irregular non-smooth spectral shapes at wavelengths of around 667 cm −1 , 1400-1700 cm −1 , and 3000-3500 cm −1 are due to the presence of CO2 and H2O in the optical path at the front optics.
However, the instrument intensity spectrum, expressed in terms of machine unit intensity, does not allow precise delineation of the atmospheric radiation signal targeted for analysis.Therefore, an atmospheric downwelling radiance spectrum could be obtained by conducting a radiometric calibration using Equation 1, as shown in Figure 6.The clear sky condition is insured by the communication, oceanography, and meteorology satellite The interferometric spectrum can be expressed as a function of wavelength in terms of signal intensity using the fast-Fourier transform (FFT).Figure 5 shows the FFT converted measured intensity of the sky view, the hot black body, and the ambient black body from 500 to 4000 cm −1 at 0300 UTC on 18 July 2018 (Local Time = UTC + 9 h).The observations have clearly revealed significant features, including the difference in intensity magnitude due to temperature variations between 'hot' and 'ambient' blackbody conditions.Additionally, the atmospheric spectrum fluctuates highly across different wavelengths.Unlike the purged interior of the instrument, the irregular non-smooth spectral shapes at wavelengths of around 667 cm −1 , 1400-1700 cm −1 , and 3000-3500 cm −1 are due to the presence of CO 2 and H 2 O in the optical path at the front optics.However, the instrument intensity spectrum, expressed in terms of machine unit intensity, does not allow precise delineation of the atmospheric radiation signal targeted for analysis.Therefore, an atmospheric downwelling radiance spectrum could be obtained by conducting a radiometric calibration using Equation 1, as shown in Figure 6.The clear sky condition is insured by the communication, oceanography, and meteorology satellite (COMS) meteorological imager (MI) infrared 1 channel (IR1; 10.8 µm) observations (Figure 7).This 10.8 µm channel measures infrared radiation emitted from the top of cloud and the Earth's surface.Consequently, clouds exhibit a cooler brightness temperature, whereas clear skies display a warmer temperature.The edge curvature of the radiometric calibrated spectrum follows the Planck function of the ambient blackbody temperature between 500 and 4000 cm −1 .The observed radiances above 1600 cm −1 are very small in magnitude and are not utilized in this study.Generally, the spectrum of atmospheric downwelling radiance in the infrared region is greatly influenced by atmospheric conditions [16,18,20,21].The spike feature that increases steeply between 650 and 700 cm −1 was caused by the emission of CO 2 present in the optical path at the higher temperature, especially due to the CO 2 Q-branch effect.In this way, if the measurement system is not completely purged, the influence of trace gases present inside may be included in the interferogram and radiance spectrum.However, this inevitable influence of CO 2 has little effect because it is not included in the thermodynamic profile retrieval band (Table 2).We performed a thermodynamic profile retrieval algorithm using the radiance spectrum generated for clear sky conditions at 0300 UTC on 18 July 2018.Figure 8 shows the changes in the fitting residuals which represent the difference between observations and simulation results for temperature and the water vapor mixing ratio band during the iterative execution of the retrieval algorithm.As spectral fitting was repeated to find an optimal solution, the difference between observed radiance and calculated radiance from the Radiative Transfer Model is decreased, and the Root Mean Square Error (RMSE) of radiance within the fitting spectral region decreases from 3.781 to 0.604 mWm −2 sr −1 cm.
To investigate the impact of trace gases on the performance of radiance and thermodynamic profile retrieval performance, we generated synthetic radiance using the RTM by adopting thermodynamic profiles from in situ radiosonde data.We performed sensitivity tests for the concentrations of three representative trace gases, CO 2 , N 2 O and CH 4 , for which strong absorption lines exist in the infrared regions.The prior gas concentrations are 410 ppm, 330 ppb, and 1860 ppb, respectively, which are the global average mixing ratios.
Figure 9 shows the change in the radiance spectrum as the concentration of each gas is varied by −1%, +1%, 5%, and 10%.The differences in radiance at ±1% tests are considered negligible.The maximum difference radiance at +10% test is approximately 0.5 radiance unit (RU) for CO 2 .This difference is small (within 1 RU) compared to the actual radiance, which ranges from 160 to 165 RU.The range of differences for N 2 O and CH 4 is similar to the results of the CO 2 sensitivity test.However, the radiances between 1250 and 1350 cm −1 are low at 40-60 RU, so the relative difference is larger than that between 600 and 720 cm −1 .We performed a thermodynamic profile retrieval algorithm using the radiance spectrum generated for clear sky conditions at 0300 UTC on 18 July 2018.Figure 8 shows the changes in the fi ing residuals which represent the difference between observations and simulation results for temperature and the water vapor mixing ratio band during the iterative execution of the retrieval algorithm.As spectral fi ing was repeated to find an optimal solution, the difference between observed radiance and calculated radiance from the Radiative Transfer Model is decreased, and the Root Mean Square Error (RMSE) of radiance within the fi ing spectral region decreases from 3.781 to 0.604 mWm −2 sr −1 cm. Figure 10 shows the impact of varying the concentration of each trace gas from −1% to +10% thermodynamic profile retrieval.The differences in temperature and water vapor derived from ±1% errors are very small.The maximum difference from 10% concentration uncertainty in temperature is approximately 0.25 K and the water vapor mixing ratio is approximately 0.5 g/kg, respectively.In case of N 2 O and CH 4 , the differences in temperature, which is approximately 0.9 K, are larger than results from CO 2 .However, the maximum differences in water vapor are similar with CO 2 even though the shapes are all distinct between different trace gases.These results indicate that the impact of the concentration of each trace gas on the retrieval of thermodynamic structures is minor.In particular, the effect on temperature below the atmospheric boundary layer (below 1 km) is very small.In actual atmospheric conditions, these trace gases do not vary dramatically, so that the impact from uncertainty of trace gas concentrations can be considered small when prior values are used appropriately.
Figure 11 shows the retrieved thermodynamic profile (temperature and the water vapor mixing ratio) in the lower troposphere below 5 km.To evaluate the thermodynamic profiles obtained from our compact FTIR observations, the retrieved results were compared with those of the fifth-generation reanalysis database (ERA-5) of European Centre for Medium-range Weather Forecasts (ECMWF) [41] and the National Centers for Environmental Prediction Final analysis (NCEP FNL) data [42].Since both reanalysis meteorological fields are provided at 6 h intervals each day (00, 06, 12, and 18 UTC), the retrieved results were compared accordingly.The ERA-5 data were compared with the 00 UTC analysis, which is 3 h before the actual ground observation time.Meanwhile, the NCEP FNL data were compared with the 03 UTC meteorological field, which is 3 h forecasted from 00 UTC.The derived temperature and water vapor mixing ratio profiles show strong similarities to those from ERA-5 and NCEP FNL, show small differences above 2 km.Notably, the derived surface temperature (33.4 • C) is higher than that of ERA-5 three hours earlier (31.To investigate the impact of trace gases on the performance of radiance and thermodynamic profile retrieval performance, we generated synthetic radiance using the RTM by adopting thermodynamic profiles from in situ radiosonde data.We performed sensitivity tests for the concentrations of three representative trace gases, CO2, N2O and CH4, for which strong absorption lines exist in the infrared regions.The prior gas concentrations are 410 ppm, 330 ppb, and 1860 ppb, respectively, which are the global average mixing ratios. Figure 9 shows the change in the radiance spectrum as the concentration of each gas is varied by −1%, +1%, 5%, and 10%.The differences in radiance at ±1% tests are considered negligible.The maximum difference radiance at +10% test is approximately 0.5 radiance unit (RU) for CO2.This difference is small (within 1 RU) compared to the actual radiance, which ranges from 160 to 165 RU.The range of differences for N2O and CH4 is similar to the results of the CO2 sensitivity test.However, the radiances between 1250 and 1350 cm −1 are low at 40-60 RU, so the relative difference is larger than that between 600 and 720 cm −1 .Figure 10 shows the impact of varying the concentration of each trace gas from −1% to +10% thermodynamic profile retrieval.The differences in temperature and water vapor derived from ±1% errors are very small.The maximum difference from 10% concentration uncertainty in temperature is approximately 0.25 K and the water vapor mixing ratio is approximately 0.5 g/kg, respectively.In case of N2O and CH4, the differences in temperature, which is approximately 0.9 K, are larger than results from CO2.However, the maximum differences in water vapor are similar with CO2 even though the shapes are all dis-   (d,e) are for N2O, and (c,f) are for CH4, respectively.Each color represents different concentrations (red: −1%, green: +1%, blue: +5%, and magenta red: −1%, green: +1%, blue: +5%, and magenta: +10%).
Figure 11 shows the retrieved thermodynamic profile (temperature and the water vapor mixing ratio) in the lower troposphere below 5 km.To evaluate the thermodynamic profiles obtained from our compact FTIR observations, the retrieved results were compared with those of the fifth-generation reanalysis database (ERA-5) of European Centre for Medium-range Weather Forecasts (ECMWF) [41] and the National Centers for Environmental Prediction Final analysis (NCEP FNL) data [42].Since both reanalysis meteorological fields are provided at 6 h intervals each day (00, 06, 12, and 18 UTC), the retrieved results were compared accordingly.The ERA-5 data were compared with the 00 UTC analysis, which is 3 h before the actual ground observation time.Meanwhile, the NCEP FNL data were compared with the 03 UTC meteorological field, which is 3 h forecasted from 00 UTC.The derived temperature and water vapor mixing ratio profiles show strong similarities to those from ERA-5 and NCEP FNL, show small differences above 2 km.Notably, the derived surface temperature (33.4 °C) is higher than that of ERA-5 three hours earlier (31.3 °C), and closer to the NCEP FNL (34.3 °C) and the surface temperature from This suggests a capture of atmospheric changes due to heating by solar radiation.Particularly, the difference below 2 km with ERA-5 indicates that the downwelling emitted radiance spectrum observed by ground-based FTIR effectively reflects changes in the vertical temperature structure of the lower troposphere.The water vapor mixing ratio profile also shows a very similar feature in vertical distribution and magnitude across the overall altitude.In the lower troposphere, the differences between the three datasets are less than 2 g/kg.These results prove the positive potential for retrieving thermodynamic profiles through a compact ground-based FTIR measurement system and demonstrate the effective performance of the retrieval algorithm.
profile also shows a very similar feature in vertical distribution and magnitude across the overall altitude.In the lower troposphere, the differences between the three datasets are less than 2 g/kg.These results prove the positive potential for retrieving thermodynamic profiles through a compact ground-based FTIR measurement system and demonstrate the effective performance of the retrieval algorithm.Since our semi-portable compact FTIR measurement system does not have a rain detection sensor and is manually observed by human labor, the algorithm is designed to operate only under clear sky conditions.Nevertheless, we investigated whether radiance spectrum observations were possible on cloudy days.Figure 12 show the measured radiometric calibrated radiance spectrum for cloudy sky.The observed spectrum shows a significant difference in radiative intensity compared to the simulated spectrum, which assumed clear sky conditions without aerosols and clouds, using NCEP FNL thermodynamic profiles.This difference was predominantly revealed in the spectral range from 700 to 1300 cm −1 .This discrepancy is a ributed to the influence of clouds.As the clouds become thicker and closer to the surface, the observed radiance spectrum increasingly resembles that of a blackbody.At this time, ASOS recorded a total cloud cover of 30% and the cloud type was Altocumulus (Ac).Additionally, the presence of clouds over the observation site was confirmed in the COMS/MI satellite image.The successful observation of the downward emission radiance spectrum of a cloudy sky suggests that continuous observations, including the effects of clouds, might be feasible in the future.Since our semi-portable compact FTIR measurement system does not have a rain detection sensor and is manually observed by human labor, the algorithm is designed to operate only under clear sky conditions.Nevertheless, we investigated whether radiance spectrum observations were possible on cloudy days.Figure 12 show the measured radiometric calibrated radiance spectrum for cloudy sky.The observed spectrum shows a significant difference in radiative intensity compared to the simulated spectrum, which assumed clear sky conditions without aerosols and clouds, using NCEP FNL thermodynamic profiles.This difference was predominantly revealed in the spectral range from 700 to 1300 cm −1 .This discrepancy is attributed to the influence of clouds.As the clouds become thicker and closer to the surface, the observed radiance spectrum increasingly resembles that of a blackbody.At this time, ASOS recorded a total cloud cover of 30% and the cloud type was Altocumulus (Ac).Additionally, the presence of clouds over the observation site was confirmed in the COMS/MI satellite image.The successful observation of the downward emission radiance spectrum of a cloudy sky suggests that continuous observations, including the effects of clouds, might be feasible in the future.

Discussion
The hyperspectral downwelling emi ed radiance is measured using a compact FTIR system configured to real-time radiometric calibration.In this study, the compact FTIR system shows well characterize the downwelling emi ed radiance spectrum under both clear and cloudy sky conditions.
However, there are several points that need to be considered when the observation system starts to operate.If the temperature of the MCT detector is not cooled sufficiently or the alignment is not stabilized, the observed interferogram and the radiance spectrum will provide incorrect information.The use of equipment equipped with cryocooling components can minimize the hassle associated with the use of LN2.Additionally, it is necessary to replace periodically the laser source due to aging and desiccants to remove

Discussion
The hyperspectral downwelling emitted radiance is measured using a compact FTIR system configured to real-time radiometric calibration.In this study, the compact FTIR system shows well characterize the downwelling emitted radiance spectrum under both clear and cloudy sky conditions.
However, there are several points that need to be considered when the observation system starts to operate.If the temperature of the MCT detector is not cooled sufficiently or the alignment is not stabilized, the observed interferogram and the radiance spectrum will provide incorrect information.The use of equipment equipped with cryocooling components can minimize the hassle associated with the use of LN2.Additionally, it is necessary to replace periodically the laser source due to aging and desiccants to remove moisture from inside the equipment.After opening the outer casing of the equipment, it should be completely purged using nitrogen gas to minimize the residual effects of CO 2 and H 2 O.
The thermodynamic vertical structure of the atmosphere is then estimated using an OEM-based algorithm that uses observed radiance and simulated radiance using the RTM.Consequently, the performance of the retrieval algorithm is sensitive to the intensity of the radiance spectrum as a function of wavenumber, which is simulated by the RTM and takes into account various atmospheric conditions (such as thermodynamic and trace gas profiles) as well as the instrument measurement performance.Because uncertainties from CO 2 line mixing and water vapor continuum absorption used in the RTM are still existing, the accuracy can be improved through continuous efforts about better understanding in radiative transfer equation and optical properties of atmospheric compositions including absorption lines of O 3 , as well as the greenhouse gases CO 2 and CH 4 .As shown in the O 3 channel spectrum shown in Figure S3, it will be possible to improve the algorithm in the future to simultaneously consider and derive information from these trace gases.
As noted above, the presence of clouds in the atmosphere alters the feature of the radiance spectrum.Unlike the thick clouds shown in Figure 12, which exhibit a significant increase in overall radiance intensity (approaching the blackbody spectrum) compared to clear sky conditions, fractional clouds or cirrus clouds are semi-transparent.This semitransparency can lead to misidentification, confusing these clouds with conditions of low aerosol optical depth or attributing their effects to atmospheric vertical structures due to water vapor, especially under clear sky conditions.This confusion arises because these clouds have thin optical thickness and emit less energy.Therefore, additional filters or observations are required to distinguish the influence of clouds within the continuous observations.It can be possible to identify and separate signals that are affected by the presence of thin, high altitude cirrus or fractional clouds using cloud information (cloud cover or cloud type) from high-resolution satellites or a ground-based Total Sky Imager (TSI) system.

Summary and Conclusions
In this study, we built a compact FTIR system in which the MCT detector is cooled using LN2 and real-time radiometric calibration can be applied using two blackbodies, and the downwelling atmospheric radiance was successfully measured for both clear and cloudy skies.The observed spectrum of the sky reflected the characteristics of the atmosphere and was similar to the spectrum simulated by the RTM, demonstrating the reliable performance of the observation.In addition, the lower troposphere thermodynamic profile obtained using the OEM-based algorithm agreed well with ERA-5 and NCEP FNL data as well as the ASOS surface.Therefore, these results demonstrate the potential of monitoring the thermodynamic profile of the lower troposphere using the compact observation system that we have built.In conclusion, our proposed compact, low-cost FTIR system offers significant cost benefits compared to traditional high-cost instruments.Despite some limitations, such as the need for manual operation and lower accuracy, its portability and real-time observation performance make it a valuable tool for specific applications and field campaigns.This system represents a promising approach for atmospheric observations, especially in scenarios where cost and mobility are critical considerations.
In this study, we used a limited sample of observations to configure an instrument for atmospheric observations and evaluate the applicability of the thermodynamic profile retrieval algorithm in the infrared region.Future work will therefore involve conducting continuous observations and analyzing the variation of the vertical structure of the atmosphere.Through long-term observation, we will be able to check whether systematic drift occurs in the equipment and perform statistical analysis on the accuracy and error characteristics of the results to improve the retrieval algorithm based on this.Identification of the continuous thermal vertical structure of the lower troposphere using compact FTIR can contribute to very short-term forecasting through data assimilation into NWP models in the future.

Figure 1 .
Figure 1.The flowchart from observation to the thermodynamic profile retrieval process.

Figure 1 .
Figure 1.The flowchart from observation to the thermodynamic profile retrieval process.

22 Figure 2 .
Figure 2. The schematic diagram of the FTIR instrument system.The solid and dashed lines within the instrument represent the path of incoming light before and after being reflected by the mirror.

Figure 2 .
Figure 2. The schematic diagram of the FTIR instrument system.The solid and dashed lines within the instrument represent the path of incoming light before and after being reflected by the mirror.

Figure 4 .
Figure 4.The short, double-sided asymmetric interferogram measure for an ambient blackbody at a temperature of 304 K.The entire interferogram is expressed as a single-sided asymmetric interferogram, as shown in Figure S2.

Figure 4 .
Figure 4.The short, double-sided asymmetric interferogram measure for an ambient blackbody at a temperature of 304 K.The entire interferogram is expressed as a single-sided asymmetric interferogram, as shown in Figure S2.

22 Figure 5 .
Figure 5.The fast-Fourier transformed observed intensity for sky-view (black) and hot (red) and ambient (blue) blackbody temperatures.

Figure 5 .
Figure 5.The fast-Fourier transformed observed intensity for sky-view (black) and hot (red) and ambient (blue) blackbody temperatures.

Figure 6 .
Figure 6.The radiometric calibrated sky downwelling radiance spectrum (black) and Plank function at hot (red) and ambient (blue) blackbody temperatures.

Figure 6 .
Figure 6.The radiometric calibrated sky downwelling radiance spectrum (black) and Plank function at hot (red) and ambient (blue) blackbody temperatures.
Figure10shows the impact of varying the concentration of each trace gas from −1% to +10% thermodynamic profile retrieval.The differences in temperature and water vapor derived from ±1% errors are very small.The maximum difference from 10% concentration uncertainty in temperature is approximately 0.25 K and the water vapor mixing ratio is approximately 0.5 g/kg, respectively.In case of N 2 O and CH 4 , the differences in temperature, which is approximately 0.9 K, are larger than results from CO 2 .However, the maximum differences in water vapor are similar with CO 2 even though the shapes are all distinct between different trace gases.These results indicate that the impact of the concentration of each trace gas on the retrieval of thermodynamic structures is minor.In particular, the effect on temperature below the atmospheric boundary layer (below 1 km) is very small.In actual atmospheric conditions, these trace gases do not vary dramatically, so that the impact from uncertainty of trace gas concentrations can be considered small when prior values are used appropriately.Figure11shows the retrieved thermodynamic profile (temperature and the water vapor mixing ratio) in the lower troposphere below 5 km.To evaluate the thermodynamic profiles obtained from our compact FTIR observations, the retrieved results were compared with those of the fifth-generation reanalysis database (ERA-5) of European Centre for Medium-range Weather Forecasts (ECMWF)[41] and the National Centers for Environmental Prediction Final analysis (NCEP FNL) data[42].Since both reanalysis meteorological fields are provided at 6 h intervals each day (00, 06, 12, and 18 UTC), the retrieved results were compared accordingly.The ERA-5 data were compared with the 00 UTC analysis, which is 3 h before the actual ground observation time.Meanwhile, the NCEP FNL data were compared with the 03 UTC meteorological field, which is 3 h forecasted from 00 UTC.The derived temperature and water vapor mixing ratio profiles show strong similarities to those from ERA-5 and NCEP FNL, show small differences above 2 km.Notably, the derived surface temperature (33.4 • C) is higher than that of ERA-5 three hours earlier (31.3 • C), and closer to the NCEP FNL (34.3 • C) and the surface temperature from the automated synoptic observing system (ASOS) site of Korea meteorological administration (KMA) (34.1 • C), approximately 4.5 km away from the observation site.

Figure 8 .
Figure 8.The change in the radiance spectrum residual (observation-simulation) during the iterative retrieval process for temperature and the water vapor mixing ratio.Each color represents each step of iteration.

Figure 8 . 22 Figure 9 .
Figure 8.The change in the radiance spectrum residual (observation-simulation) during the iterative retrieval process for temperature and the water vapor mixing ratio.Each color represents each step of iteration.Remote Sens. 2024, 16, x FOR PEER REVIEW 14 of 22

Figure 11 .
Figure 11.Comparison between the retrieved temperature (left) and the water vapor mixing ratio (right) with NCEP NFL and ECMWF ERA-5 at 0300 UTC on 18 July 2018.

Figure 11 .
Figure 11.Comparison between the retrieved temperature (left) and the water vapor mixing ratio (right) with NCEP NFL and ECMWF ERA-5 at 0300 UTC on 18 July 2018.

Figure 12 .
Figure 12.(a) The observed radiance spectrum of a cloudy sky at 0300 UTC on 29 November 2018 (black) compared to the radiance spectrum simulated by the RTM, which assumes clear sky conditions (orange).(b) The brightness temperature of COMS/MI IR 1 channel at the same time.It can be noticed that clouds exist over the observation site.

Figure 12 .
Figure 12.(a) The observed radiance spectrum of a cloudy sky at 0300 UTC on 29 November 2018 (black) compared to the radiance spectrum simulated by the RTM, which assumes clear sky conditions (orange).(b) The brightness temperature of COMS/MI IR 1 channel at the same time.It can be noticed that clouds exist over the observation site.

Table 1 .
Specification of Instrument and blackbody.