An Operational Ground-Based Vicarious Radiometric Calibration Method for Thermal Infrared Sensors: A Case Study of GF-5A WTI

Highlights

What are the main findings?

• An operational, year-round automated ground-based vicarious calibration system for thermal infrared sensors was deployed at three Gobi pseudo-invariant sites, establishing a traceable surface–atmosphere–sensor radiometric chain.
• Applied to GF-5A WTI, the method yields band- and gain-specific linear calibration coefficients with stable radiometric response and brightness–temperature errors within mission requirements, as verified by independent on-orbit validation.

What are the implications of the main findings?

• The Gobi-based network demonstrates that autonomous ground stations can provide routine, low-manpower on-orbit radiometric calibration and long-term stability monitoring for high-resolution thermal infrared missions such as GF-5A WTI.
• The framework provides a scalable blueprint for arid-region calibration networks, enabling multi-gain consistency checks, robust vicarious calibration, and more reliable land-surface-temperature and related thermal infrared products.

Abstract

High-resolution TIR missions require sustained and well-characterized radiometric accuracy to support applications such as land surface temperature retrieval, drought monitoring, and surface energy budget analysis. To address this need, we develop an operational and automated ground-based vicarious radiometric calibration framework for TIR sensors and demonstrate its performance using the Wide-swath Thermal Infrared Imager (WTI) onboard Gaofen-5 01A (GF-5A). Three arid Gobi calibration sites were selected by integrating Moderate Resolution Imaging Spectroradiometer (MODIS) cloud products, Shuttle Radar Topography Mission (SRTM)-derived topography, and WTI-based radiometric uniformity metrics to ensure low cloud cover, flat terrain, and high spatial homogeneity. Automated ground stations deployed at Golmud, Dachaidan, and Dunhuang have continuously recorded 1 min contact surface temperature since October 2023. Field-measured emissivity spectra, Integrated Global Radiosonde Archive (IGRA) radiosonde profiles, and MODTRAN (MODerate resolution atmospheric TRANsmission) v5.2 simulations were combined to compute top-of-atmosphere (TOA) radiances, which were subsequently collocated with WTI imagery. After data screening and gain-stratified regression, linear calibration coefficients were derived for each TIR band. Based on 189 scenes from February–July 2024, all four bands exhibit strong linearity (R-squared greater than 0.979). Validation using 45 independent scenes yields a mean brightness–temperature root-mean-square error (RMSE) of 0.67 K. A full radiometric-chain uncertainty budget—including contact temperature, emissivity, atmospheric profiles, and radiative transfer modeling—results in a combined standard uncertainty of 1.41 K. The proposed framework provides a low-maintenance, traceable, and high-frequency solution for the long-term on-orbit radiometric calibration of GF-5A WTI and establishes a reproducible pathway for future TIR missions requiring sustained calibration stability.

1. Introduction

Gaofen-5 01A (GF-5A) is a key component of China’s civilian High-Resolution Earth Observation System, designed to support comprehensive environmental monitoring and resource assessment. Launched on 8 December 2022, the satellite carries three primary payloads: the Advanced Hyperspectral Imager (AHSI), the Environmental Trace Gas Monitoring Instrument (EMI), and the Wide-swath Thermal Infrared Imager (WTI) [1]. WTI employs a whiskbroom cross-track scanning configuration and provides an exceptionally wide swath of 1500 km with a ground sampling distance of 100 m across four longwave infrared bands. This combination of wide coverage and multiple thermal-window channels enables enhanced spatiotemporal observations for applications such as land surface temperature (LST), sea surface temperature (SST), drought monitoring, and urban thermal environment assessment [2]. Thermal infrared (TIR) remote sensing retrieves key parameters—such as land surface temperature, surface emissivity, and atmospheric characteristics—by measuring longwave radiance signals [3]. These products are widely used in climate diagnostics, surface energy budget analysis, disaster monitoring, and environmental assessment. Such applications require radiometric calibration that is accurate, temporally stable, and traceable across long-term satellite missions. Historical sensors such as Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), MODIS, and Landsat have demonstrated the importance of maintaining consistent and comparable TIR records [4,5,6,7].

TIR sensors are typically equipped with an onboard radiometric calibration subsystem. For GF-5A WTI, two temperature-controlled internal blackbodies are configured as the primary radiance reference sources. The high-temperature blackbody is maintained at an elevated operating temperature through dedicated heaters and thermal control components, whereas the low-temperature blackbody, in addition to the same types of components as the high-temperature blackbody, requires a heat dissipation surface and a heat pipe to regulate its temperature at a lower level. During routine operational imaging, the instrument periodically observes the onboard blackbodies for calibration, enabling on-orbit calibration coefficients to be updated and applied to the digital number (DN)-to-radiance conversion for product generation. Nevertheless, onboard calibration alone cannot fully eliminate long-term radiometric drift; residual systematic biases may still arise from stray-light contamination, orbit-driven thermal-environment perturbations, limitations in thermal control and thermometry stability, and instrument aging [8,9]. Therefore, vicarious calibration remains necessary to provide an independent, traceable external pathway for verifying and, when required, correcting the onboard-calibrated radiometric response [10,11,12].

Common approaches for TIR vicarious calibration include lake- or water-body–based methods using uniform temperature/radiance targets, as well as radiance-based methods employing ground-based or airborne radiometers. For example, the U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center has established a comprehensive on-orbit calibration and validation framework for the Landsat 8 Thermal Infrared Sensor (TIRS), which demonstrates sub-Kelvin radiometric stability under favorable observing conditions and thereby enhances the consistency of long-term thermal data records [13]. Additionally, studies over Qinghai Lake have conducted vicarious calibration and uncertainty evaluation for Fengyun-4A (FY-4A) Advanced Geostationary Radiation Imager (AGRI) TIR channels, quantifying the brightness temperature biases and stability characteristics of individual bands [14].

To enhance calibration frequency and repeatability without substantially increasing costs, the Radiometric Calibration Network (RadCalNet), established under the Committee on Earth Observation Satellites (CEOS) Working Group on Calibration and Validation (WGCV), has provided an operational service framework for radiometric calibration in the visible-to-shortwave infrared (VNIR–SWIR) spectral region. This framework integrates standardized automated sites with unified processing chains and enables cross-mission and cross-sensor radiometric-consistency assessments [15,16]. Meanwhile, methodologies based on automated stations and standardized processing pipelines have already been operationalized. For instance, the automated reflectance-based method designed for Landsat-8 Operational Land Imager (OLI) significantly reduces field deployment requirements while maintaining timely and robust calibration updates [17]; Similarly, a ground-based radiance-based method for Sentinel-2A MultiSpectral Instrument (MSI) has demonstrated a long-term radiometric-stability evaluation framework driven by automated observations [18]. Using the Baotou Desert automated calibration site, time-series vicarious calibration of Ziyuan-3 (ZY-3) multispectral camera (MUX) has also verified the effectiveness of the automated workflow and its capability to close the uncertainty budget [19].

However, automated vicarious calibration systems for the thermal infrared domain remain limited. Existing lake-based campaigns are typically short in duration, seasonally restricted, and difficult to maintain year-round. Furthermore, automated networks such as RadCalNet do not currently extend to the TIR spectral region, where radiance is more sensitive to atmospheric variability and surface emissivity. This gap highlights the need for a persistent, automated, traceable TIR calibration framework suitable for long-term operational missions.

Several recent efforts have extended automated vicarious calibration to the TIR domain. Over radiometrically homogeneous lake surfaces, automated buoys, radiometers, and uncrewed surface vehicles (USV) have been used to reduce manual intervention and increase temporal sampling. For example, USV-based observations over Lake Qinghai have enabled multi-scene radiometric consistency assessments for the FY-4A/AGRI TIR channels [14]. Similarly, the Ziyuan-1 02E (ZY-1-02E) Infrared Spectrometer sensor (IRS) has been calibrated using coordinated ground measurements from a Fourier transform infrared (FTIR) spectrometer and an SI-111 infrared thermometer (Apogee Instruments, Inc., Logan, UT, USA), achieving an accuracy better than 0.6 K under diverse surface and atmospheric conditions [20]. In addition, Hu et al. established a lake-based ground-to-satellite synchronous calibration workflow for the Sustainable Development Goals Satellite-1 (SDGSAT-1) Thermal Infrared Spectrometer (TIS), utilizing high-resolution ground radiometer observations and atmospheric radiative transfer simulations to quantify systematic brightness temperature biases (approximately 0.3–1.1 K) across the three TIR bands, confirming the feasibility of routine on-orbit calibration and performance monitoring enabled by automated lake-based observation sites [21].

Despite these advances, lake-based calibration campaigns are limited in operational continuity. Their reliance on water bodies also restricts spatial scalability and limits radiometric coverage across gain states, because the limited dynamic range of water-surface temperature cannot adequately span the sensor’s full gain range. In contrast, the extensive Gobi regions of northwestern China offer naturally stable, spatially uniform, and low-humidity surfaces, making them ideal pseudo-invariant calibration sites (PICS) for thermal infrared sensors. However, no operational, year-round, multi-site automated calibration system has yet been established over these Gobi surfaces. Addressing this gap is essential for enabling persistent, traceable, and high-frequency vicarious calibration of modern TIR satellite missions.

To address this gap and to develop a long-term, low-maintenance, and traceable TIR calibration framework, we deployed automated ground-based observation systems at three Gobi sites in October 2023 and initiated a dedicated field experiment for GF-5A WTI. The framework integrates continuous contact surface-temperature measurements, field-measured emissivity spectra, radiosonde atmospheric profiles, and MODTRAN v5.2 radiative-transfer simulations to construct a complete surface–atmosphere–sensor radiometric chain. Using this chain, top-of-atmosphere radiances are computed, collocated with satellite observations, and used to derive on-orbit calibration coefficients. Although previous studies have investigated TIR vicarious calibration, no multi-site, year-round automated system has been established over Gobi pseudo-invariant calibration surfaces. The present work provides the first implementation of such a system and demonstrates its feasibility for routine TIR calibration.

This study proposes a long-term and traceable framework to support operational TIR vicarious calibration. We establish three year-round Gobi calibration sites selected under PICS-candidate criteria and deploy an automated ground-based observation system, whose accuracy is verified through metrological traceability and radiometric closure. By integrating ground observations with IGRA radiosonde profiles and MODTRAN v5.2 radiative-transfer simulations, we implement a traceable “surface–atmosphere–satellite” radiometric chain to derive on-orbit calibration coefficients for GF-5A/WTI in each band and gain mode. The resulting calibration is further validated by independent on-orbit samples and a comprehensive uncertainty budget.

The remainder of this paper is organized as follows: Section 2 provides detailed descriptions of the study area, data sources, measurement systems, and calibration methods. The calibration results are presented in Section 3. Section 4 discusses the findings, and Section 5 concludes the study.

2. Materials and Methods

2.1. Materials

2.1.1. GF-5A WTI

The Gaofen-5 01A (GF-5A) satellite is an important component of China’s “High-Resolution Earth Observation System.” It is also known as the Hyperspectral Comprehensive Observation Satellite and serves as the follow-up mission to the original Gaofen-5 satellite. Successfully launched into orbit in 2022, GF-5A continues to support environmental and resource monitoring tasks [1]. The mission enhances the integrated observation capability for atmospheric and surface parameters, enabling the retrieval of multidimensional remote sensing information covering atmospheric composition, ecosystem dynamics, and natural resource utilization [22,23].

GF-5A carries the Wide-swath Thermal Infrared Imager (WTI), developed by Beijing Institute of Space Mechanics and Electricity, Beijing, China.The instrument is characterized by medium-to-high spatial resolution and exceptionally large coverage, providing an observation swath of approximately 1500 km and a spatial resolution of about 100 m, and supporting both daytime and nighttime imaging. WTI is equipped with four longwave infrared bands, with the major spectral parameters summarized in

Table 1. Main characteristics of the GF-5A WTI thermal infrared bands.

GF-5A WTI	Description	Technical Parameter
Spectral Range	Band 1	8.01–8.39 μm
	Band 2	8.42–8.83 μm
	Band 3	10.3–11.3 μm
	Band 4	11.5–12.5 μm
Subsatellite Resolution	Band 1–4	≤100 m
Width	Band 1–4	≥1500 km

. These TIR bands offer abundant information for quantitative retrievals such as LST and SST [23]. Figure 1 presents the relative spectral response functions (RSRF) of the GF-5A WTI. Compared with the Landsat 8/9 Thermal Infrared Sensor (TIRS), which has a similar spatial resolution, WTI achieves an approximately sevenfold increase in swath width, substantially enhancing its potential for global-scale thermal environment monitoring [24].

2.1.2. Study Area

To ensure that the automated ground-based observation systems provide long-term, stable, and high-quality data for radiometric calibration, candidate sites should satisfy four criteria: (1) high spatial uniformity, (2) temporal stability, (3) flat terrain, and (4) persistently low cloud cover. Building upon the preliminary identification of more than thirty pseudo-invariant calibration sites (PICS) reported by Hu et al. (2020) [25], we performed a regional search and field reconnaissance across the arid and semi-arid regions of Northwest China. Considering long-term observational requirements and environmental constraints, the following three locations were selected for the deployment of automated surface temperature measurement stations.

Golmud, Qinghai

External field experiments and cross-validation studies conducted in the Golmud region have demonstrated its favorable spatial uniformity and practical suitability as a radiometric calibration and validation site [26]. The selected site is located west of Golmud City, on the northern flank of the Kunlun Mountains and southeast of Zhongzao volcano. The terrain slopes gently from south to north. The surface is primarily sandy desert, interspersed with areas of Gobi.

Dachaidan, Qinghai

This site is situated northwest of Xitieshan Town in Dachaidan and south of National Highway G315, within an uninhabited Gobi area. The surface is dominated by gravel-covered Gobi, exhibiting a north-to-south descending topographic trend. The region features large unobstructed areas, flat terrain, and spatially uniform, temporally stable surface properties, while remaining distant from roads and human disturbances. These characteristics make the site highly suitable for deploying automated ground-temperature measurement equipment for long-term vicarious calibration.

Dunhuang, Gansu

The Dunhuang site lies within a well-established radiometric calibration region characterized by a flat and homogeneous gravel Gobi surface with minimal interannual variability. Previous studies have demonstrated that this area exhibits excellent spatial uniformity and temporal stability, making it suitable for on-orbit calibration and cross-sensor consistency assessment [27,28]. The site is situated on the gravel-covered alluvial fan of the Danghe River, featuring a flat and vegetation-free Gobi surface. The region experiences an arid continental climate with dry conditions, low precipitation, clean atmosphere, minimal aerosol loading, and a high number of clear days per year. Its stable spectral properties and favorable natural environment make it an ideal location for radiometric calibration.

2.1.3. Atmospheric Data Acquisition

In this study, atmospheric profiles were primarily obtained from the IGRA, which compiles radiosonde and pilot balloon observations from more than 2800 stations worldwide. IGRA provides continuous records dating back to 1905, with approximately 800 stations offering stable and routine observations in recent decades [29,30]. The dataset includes pressure, temperature, relative humidity, and wind variables reported on standard and significant levels, making it suitable for radiative-transfer modeling.

The IGRA stations used in this study are CHM00052418 (Dunhuang) and CHM00052818 (Golmud). Since the Dachaidan site is geographically closest to Dunhuang, the contemporaneous atmospheric profiles from station CHM00052418 were adopted for its calibration computations. Considering that operational radiosondes typically reach a maximum altitude of approximately 30 km, the region above the balloon’s burst height up to 120 km was supplemented using MODTRAN standard atmospheric profiles. These supplemental layers include altitude, pressure, temperature, and relative humidity, thereby providing a continuous and complete atmospheric profile for radiative-transfer modeling and calibration simulations.

Figure 2 illustrates the vertical profiles of pressure, temperature, and relative humidity measured on 3 April 2024, after merging the radiosonde observations with the upper-atmosphere standard profiles. These atmospheric parameters exhibit typical variations with altitude.

2.1.4. Ground-Based Synchronous Observations

Automated ground-based observation systems were deployed at the three calibration sites in October 2023 to obtain high-temporal-resolution surface parameters synchronized with satellite overpasses. Figure 3 illustrates the system configuration, which was jointly developed by our research group and UTAN Technology Co., Ltd. (Hangzhou, China). Each station is designed for long-term, unattended operation and is powered by a solar-panel and battery module. The instrument enclosure is weather-resistant and dust-proof, allowing stable operation under the large diurnal temperature variations and strong winds characteristic of Gobi environments. Data are sampled at preset intervals and transmitted via the BeiDou-3 communication system, with a reporting interval configured as one observation per minute.

Surface temperature was measured using semi-buried contact sensors installed according to standard meteorological protocols. The sensors have an accuracy of approximately 0.1 °C, providing continuous in-situ temperature time series for radiometric calibration and validation of GF-5A/WTI observations. This measurement chain ensures high temporal resolution, traceability, and long-term stability required for automated vicarious calibration.

2.2. Methods

2.2.1. Metrological and Radiometric-Closure Validation of Contact Temperature Sensors

To rigorously assess the accuracy and metrological reliability of the contact temperature sensors deployed at the field sites, two complementary and independent validation procedures were implemented. These procedures jointly quantify sensor performance under both controlled metrological conditions and physically realistic radiometric scenarios.

The first validation approach employed a metrological-chain comparison. A Jinming (JM) precision thermometer (Tianjin Jinming Instrument Co., Ltd., Tianjin, China), traceable to the National Institute of Metrology (NIM), China, was co-located with the contact sensor under controlled thermal-contact conditions to ensure identical thermal conditions. Two 90-minute experiments were conducted on 20 September 2024 (11:00 local time) and 27 September 2024 (22:00 local time), representing heating and cooling regimes, respectively. The instantaneous measurement bias was quantified from the time series of temperature differences:

$$T_{\mathrm{Bias}1}\left(t\right)=T_{\mathrm{contact}}\left(t\right)-T_{\mathrm{JM}}\left(t\right),$$

(1)

The second validation procedure consisted of a radiometric-closure experiment. Two experiments were conducted on 20 and 26 September 2024 over reference surfaces with comparable material composition and surface roughness, thereby minimizing emissivity-induced discrepancies. Under low-wind conditions, Turbo FT radiance spectra $L\left(\lambda \right)$ and simultaneous contact temperatures $T_{\mathrm{contact}}$ were acquired. Surface temperatures were then retrieved using the iterative spectrally smooth temperature and emissivity separation (ISSTES) algorithm [31], yielding $T_{\mathrm{ISSTES}}$. Radiometric consistency was subsequently evaluated through the deviation metric:

$$T_{\mathrm{Bias}2}\left(t\right)=T_{\mathrm{contact}}\left(t\right)-T_{\mathrm{ISSTES}}\left(t\right),$$

(2)

Together, the absolute metrological reference and the radiometric physical-constraint evaluations form a complementary validation framework that quantitatively characterizes the absolute accuracy of the deployed sensors.

2.2.2. Surface Emissivity Measurement

The surface emissivity spectra, denoted by ${\epsilon }_t\left(\lambda \right)$, were obtained in situ using an FTIR spectrometer (Turbo FT, Designs & Prototypes Instruments, Simsbury, CT, USA). The radiative transfer model can be written as

$$L_{\mathrm{at}\text{-}\mathrm{sensor}}\left(\lambda \right)=\tau \left(\lambda \right){\epsilon }_t\left(\lambda \right)B(\lambda ,T_t)+\tau \left(\lambda \right){\rho }_t\left(\lambda \right)L^{\downarrow }\left(\lambda \right)+L^{\uparrow }\left(\lambda \right).$$

(3)

where $L_{\mathrm{at}\text{-}\mathrm{sensor}}\left(\lambda \right)$ is the measured radiance, $\tau \left(\lambda \right)$ is the atmospheric transmittance, ${\epsilon }_t\left(\lambda \right)$ is the directional surface emissivity, $B(\lambda ,T_t)$ is the Planck radiance at the target surface temperature $T_t$, ${\rho }_t\left(\lambda \right)=1-{\epsilon }_t\left(\lambda \right)$ the surface reflectance according to Kirchhoff’s law, $L^{\downarrow }\left(\lambda \right)$ is the downwelling sky radiance incident on the surface, and $L^{\uparrow }\left(\lambda \right)$ is the atmospheric path radiance. $T_t$ denotes the physical target temperature, which is approximated by the contact-measured temperature $T_{\mathrm{contact}}$ under homogeneous and thermally stable surface conditions.

The downwelling radiance $L^{\downarrow }\left(\lambda \right)$ was estimated using observations of a calibrated infrared reference panel with known emissivity ${\epsilon }_g\left(\lambda \right)$ (specified by the manufacturer and periodically verified against a laboratory blackbody). $L_g\left(\lambda \right)$ is the measured spectral radiance from the reference panel at temperature $T_g$. $L^{\downarrow }\left(\lambda \right)$ is computed as

$$L^{\downarrow }\left(\lambda \right)={\displaystyle \frac{L_g\left(\lambda \right)-{\epsilon }_g\left(\lambda \right)B(\lambda ,T_g)}{1-{\epsilon }_g\left(\lambda \right)}}.$$

(4)

For the short sensor–target distance (≤1 m) used in the field FTIR measurements, MODTRAN v5.2-based short-path simulations indicate that atmospheric attenuation and path radiance are negligible over 8–14 μm ($\tau \left(\lambda \right)\approx 1$ and $L^{\uparrow }\left(\lambda \right)\approx 0$).

Because the target is opaque in the thermal infrared, the constraint ${\rho }_t\left(\lambda \right)=1-{\epsilon }_t\left(\lambda \right)$ applies. Under these conditions, the surface emissivity ${\epsilon }_t\left(\lambda \right)$ can be retrieved as:

$${\epsilon }_t\left(\lambda \right)={\displaystyle \frac{L_{\mathrm{at}\text{-}\mathrm{sensor}}\left(\lambda \right)-L^{\downarrow }\left(\lambda \right)}{B(\lambda ,T_t)-L^{\downarrow }\left(\lambda \right)}}.$$

(5)

The retrieved emissivity spectra for the three calibration sites are shown in Figure 4.

2.2.3. Radiometric Calibration Method

The objective of this study is to construct a consistent “surface–atmosphere–satellite” radiometric chain for each calibration site at the time of satellite overpass. By computing the channel-equivalent at-sensor radiance and establishing a linear relationship between this radiance and the corresponding DN of the GF-5A WTI imagery, the on-orbit radiometric calibration coefficients are derived. The overall workflow is illustrated in Figure 5 and consists of five major components: automated ground measurements, atmospheric radiative transfer modeling, satellite–ground co-registration, sample selection, and derivation of calibration coefficients.

In this study, IGRA radiosonde atmospheric profiles and satellite overpass parameters are used as inputs to MODTRAN v5.2 to simulate the atmospheric transmittance $\tau \left(\lambda \right)$, path radiances $L_{\uparrow }\left(\lambda \right)$ and downwelling radiance $L_{\downarrow }\left(\lambda \right)$. Combined with the contact surface temperature $T_{\mathrm{contact}}\left(t\right)$ and the site emissivity spectrum ${\epsilon }_t\left(\lambda \right)$, these atmospheric terms enable the computation of the top-of-atmosphere (TOA) spectral radiance $L_{\mathrm{TOA}}\left(\lambda \right)$. The band-equivalent TOA radiance $L_{\mathrm{TOA},\mathrm{band}}$ is then obtained by convolving $L_{\mathrm{TOA}}\left(\lambda \right)$ with the spectral response function $R_{\mathrm{band}}\left(\lambda \right)$, and regressed against the collocated WTI digital numbers to derive on-orbit calibration coefficients for each band and gain mode.

At the three sites of Golmud, Dachaidan, and Dunhuang, the automated observation system continuously records contact surface temperature $T_{\mathrm{contact}}$, while ${\epsilon }_t\left(\lambda \right)$ for each site were measured in advance and used as inputs for the calibration workflow.

To ensure traceable atmospheric inputs, radiosonde profiles from the corresponding IGRA stations were used as the primary atmospheric state, and the layers above the balloon-burst altitude were extended with the MODTRAN standard atmosphere. For each overpass scenario, the IGRA-based profile together with the satellite viewing geometry was provided to MODTRAN v5.2 to compute the $\tau \left(\lambda \right)$, $L^{\uparrow }\left(\lambda \right)$, and  $L^{\downarrow }\left(\lambda \right)$.

Given the measured surface emissivity ${\epsilon }_t\left(\lambda \right)$ and the contact temperature $T_{\mathrm{contact}}$, the TOA spectral radiance follows directly from the general radiative-transfer expression in Equation (3) by substituting $L\left(\lambda \right)=L_{\mathrm{TOA}}\left(\lambda \right)$ and $T_t=T_{\mathrm{contact}}$, and using the opaque-surface constraint ${\rho }_t\left(\lambda \right)=1-{\epsilon }_t\left(\lambda \right)$.

The $L_{\mathrm{TOA},\mathrm{band}}\left(\lambda \right)$ can be converted into the WTI band-equivalent radiance by applying response-weighted integration using the corresponding relative spectral response function $R_{\mathrm{band}}\left(\lambda \right)$. The band-equivalent radiance is therefore computed as

$$L_{\mathrm{TOA},\mathrm{band}}={\displaystyle \frac{{\displaystyle {\int }_{{\lambda }_{min}}^{{\lambda }_{max}}{R}_{\mathrm{band}}\left(\lambda \right)L_{\mathrm{TOA}}\left(\lambda \right)d\lambda }}{{\displaystyle {\int }_{{\lambda }_{min}}^{{\lambda }_{max}}{R}_{\mathrm{band}}\left(\lambda \right)d\lambda }}}.$$

(6)

To guarantee the traceability and statistical reliability of satellite–ground matched samples, the same screening procedure was applied to both the calibration and validation datasets. First, a 200 × 200 pixel subimage centered on each ground measurement location was extracted and visually inspected to eliminate scenes affected by clouds or cloud shadows. Second, temperature stability within ±5 min of the satellite overpass time was examined to identify possible thin clouds or transient shading, and samples exhibiting abnormal fluctuations were removed.

If the sample passed these checks, a 5 × 5 pixel region centered on the ground point (approximately 500 m × 500 m) was extracted, and the mean DN value was taken as the matched radiometric observation. The DN standard deviation and sensor gain state were recorded for subsequent calibration.

Using all valid matched pairs, calibration coefficients for each band were derived using a least-squares linear regression. For sensors operating under multiple gain states (j), separate calibration coefficients were computed for each state. Outliers were identified using the residuals with respect to the fitted regression line: samples with an absolute residual exceeding twice the standard deviation of the residual distribution were removed, and the regression was then recomputed using the remaining samples. The calibration model is expressed as:

$$L_{\mathrm{TOA},i}={\mathrm{gain}}_{ij}D{N}_{ij}+{\mathrm{offset}}_{ij},$$

(7)

where $L_{\mathrm{TOA},i}$ is the band-i equivalent TOA radiance, and ${\mathrm{gain}}_{ij}$, $D{N}_{ij}$, and ${\mathrm{offset}}_{ij}$ denote the gain, digital number, and offset for band i under gain state j, respectively.

3. Results

3.1. Accuracy Verification of Ground-Based Temperature Measurements

To evaluate the performance of the ground-based contact temperature sensor across different thermal transition regimes, two field comparison experiments were conducted under warming (20 September 2024, 11:00–12:30 local time) and cooling (27 September 2024, 22:00–23:30 local time) conditions. In each experiment, the ground-based contact sensor was compared synchronously with a JM standard thermometer traceable to the National Institute of Metrology of China. The temperature difference time series $T_{\mathrm{Bias}1}\left(t\right)$, defined in Equation (1), was used to characterize the measurement bias between the two sensors.

Figure 6 presents the synchronous temperature measurements and the corresponding bias series. The two temperature profiles exhibit high temporal coherence, indicating consistent thermal response behavior between the contact sensor and the JM reference. During the warming experiment, surface temperature increased from approximately 28.6 °C to 36.6°C, with instantaneous deviations $T_{\mathrm{Bias}1}\left(t\right)$ generally confined within $\pm 0.4$°C. Statistically, the bias metrics are

$$T_{\mathrm{Bias}1,\mathrm{MEAN}}=0.078°\mathrm{C},T_{\mathrm{Bias}1,\mathrm{RMSE}}=0.173°\mathrm{C}.$$

During the cooling experiment, temperature decreased from 8.57°C to 5.77°C, with even bigger deviations:

$$T_{\mathrm{Bias}1,\mathrm{MEAN}}=0.175°\mathrm{C},T_{\mathrm{Bias}1,\mathrm{RMSE}}=0.177°\mathrm{C}.$$

Both experiments indicate that the bias remains small throughout the experiments. Such behavior suggests that the contact sensor and JM standard thermometer maintain robust agreement in both heating and cooling conditions. The slight positive bias may arise from the thermal interface between the probe and surface: higher contact pressure or marginally thicker thermal paste may cause the contact probe to sense heating slightly earlier than the standard thermometer.

Given the intrinsic single-point measurement uncertainty of the contact sensor (approximately ± 0.1$°\mathrm{C}$), and considering the experiment-derived statistics ($T_{\mathrm{Bias}1,\mathrm{MEAN}}<0.18$$°\mathrm{C}$; $T_{\mathrm{Bias}1,\mathrm{RMSE}}<0.18$$°\mathrm{C}$), the observed deviation is far smaller than typical uncertainties in thermal infrared inversion or on-orbit radiometric calibration (often $<1$ K). Thus, the accuracy is sufficient for validating TIR products and evaluating retrieval algorithms.

To independently assess the suitability of contact temperature measurements for serving as reference inputs in radiative-transfer calculations, a radiometric-closure experiment was performed. This experiment evaluates whether temperatures derived from FTIR-based radiometric inversion are consistent with direct contact measurements under controlled surface and atmospheric conditions. Turbo FT radiance spectra $L\left(\lambda \right)$ and contact temperatures $T_{\mathrm{contact}}$ were collected simultaneously, and the ISSTES algorithm was applied to retrieve temperature $T_{\mathrm{ISSTES}}$ [31]. The radiometric consistency metric $T_{\mathrm{Bias}2}\left(t\right)$, as defined in Equation (2), was then used to quantify the difference between the contact measurements and the ISSTES-derived temperatures.

The experiments covered a high-temperature case (approximately 40$°\mathrm{C}$, 20 September 2024) and a low-temperature case (approximately 7$°\mathrm{C}$, 26 September 2024). As shown in Figure 7, the deviations $T_{\mathrm{Bias}2}\left(t\right)$ are generally confined within $\pm 0.25$$°\mathrm{C}$. The overall statistics are

$$T_{\mathrm{Bias}2,\mathrm{MEAN}}=-0.019°\mathrm{C},T_{\mathrm{Bias}2,\mathrm{RMSE}}=0.128°\mathrm{C},$$

indicating that the contact temperatures are consistent with the ISSTES-retrieved radiometric temperatures at a level well within the accuracy requirements for thermal infrared calibration in this study.

Across both dynamic thermal transitions and radiometrically retrieved temperature ranges, the contact sensors demonstrate high consistency ($T_{\mathrm{Bias},\mathrm{MEAN}}\approx 0.1$–$0.18$$°\mathrm{C}$; $T_{\mathrm{Bias},\mathrm{RMSE}}\approx 0.13$–$0.18$$°\mathrm{C}$). This accuracy level is fully sufficient for thermal infrared calibration requirements and supports both on-orbit and field-based radiometric calibration as well as emissivity algorithm validation. Based on these results, the contact temperature measurements are adopted as the reference temperature input for subsequent surface temperature retrieval and calibration procedures.

3.2. Analysis of Surface Temperature Variations

In October 2023, the automated ground measurement systems were successfully deployed at the three calibration sites of Dunhuang, Dachaidan, and Golmud, and stable data acquisition has since been achieved. Analysis of the 2024 contact temperature time series enables an assessment of the long-term suitability of the three Gobi sites for persistent vicarious calibration. The annual thermal dynamics provide insight into the stability, representativeness, and radiometric diversity required for calibrating thermal infrared sensors across their full dynamic range.

As shown in Figure 8, all three sites exhibit a typical seasonal cycle characterized by low temperatures in winter and high temperatures in summer. A sustained high-temperature plateau lasting approximately two months is observed in summer, while maximum winter temperatures do not exceed 20$°\mathrm{C}$. The annual warmest period occurs in late July, and the coldest temperatures appear in January (Dachaidan) and December (Dunhuang and Golmud), consistent with regional radiative climate characteristics. These seasonal behaviors enable seasonal calibration strategies, with high-temperature calibration in summer and low-temperature calibration in winter.

Due to planned maintenance and system switching, data gaps occur between 1 November and 15 November 2024; however, the overall coverage and continuity remain sufficient for statistical analysis and do not affect the interpretation of seasonal patterns or thermal extremes. The annual temperature dynamic range is large across all sites, with Dunhuang spanning 87.3$°\mathrm{C}$, Dachaidan 95.3$°\mathrm{C}$, and Golmud 89.2$°\mathrm{C}$. This broad thermal range ensures that the three sites collectively cover the full spectrum of surface temperatures from cold to hot throughout the year. Consequently, ample calibration samples can be obtained to support dynamic-range extension and long-term drift monitoring of thermal infrared sensors, providing continuous and traceable ground-based reference measurements for radiometric calibration.

3.3. Radiometric Calibration Results

GF-5A WTI imagery acquired from 1 February 2024 to 31 July 2024 was selected for calibration analysis (182 days in total). During this period, approximately six WTI scenes per day were available over the calibration sites, yielding 1092 candidate scenes. Following the satellite–ground matchup and the quality-control procedure described in Section 2.2.3, 903 unsuitable scenes were excluded, and a total of 189 valid overpass samples remained across the three calibration sites.

This dataset provides both a sufficiently wide radiometric dynamic range and a representative distribution of multiple gain states, meeting the requirements of linear regression–based calibration. Notably, GF-5A/WTI employs multiple gain modes within a given band, and gain switching introduces gain-dependent offsets and response variations. Consequently, the DN–radiance relationship is not globally continuous across gain modes, and pooling samples from different gains in a single regression will bias the fitted coefficients. Therefore, we perform gain-stratified regression and derive the calibration coefficients for each gain mode using the linear model in Equation (7).

Figure 9 presents the on-orbit calibration results for WTI channels B1–B4 under different gain modes (Z2, Z3, Z4). For each band–gain combination, linear regression was performed using all valid matched samples, and the regression equation and corresponding coefficient of determination ($R^2$) were obtained. A larger $R^2$ indicates a stronger linear correspondence between DN and radiance $L_{\mathrm{TOA}}$. Overall, all channel–gain combinations exhibit clear and statistically significant linear responses, with coefficients of determination ranging from $R^2=0.979$ to $0.993$ and RMSE ranging from 0.12 to 0.24. These results demonstrate that the on-orbit response of GF-5A WTI is well described by a first-order linear model across its operational dynamic range, with no evidence of nonlinear distortion.

From a channel-by-channel perspective, distinct patterns emerge in sample size n and residual characteristics (RMSE) across gain states. Band 1 under gain mode Z2 exhibits the best overall performance ($R^2=0.993$, RMSE = 0.18, $n=189$), indicating a favorable signal-to-noise ratio and sufficient radiance coverage, making it the most stable channel in the current calibration framework. Band 2 demonstrates excellent cross-gain consistency between Z2 and Z3, with identical coefficients of determination ($R^2=0.989$) and RMSE values of 0.12 and 0.24 ($n=149/40$). This suggests that transitioning between gain states does not introduce systematic response deviations and that the linear relationship remains portable and internally consistent.

Bands 3 and 4 also maintain strong linearity under Z3/Z4 modes (Band 3: $R^2=0.981/$$0.989$, RMSE = 0.16/0.23; Band 4: $R^2=0.979/0.981$, RMSE = 0.14/0.23). The slightly higher residuals observed in the high-gain modes are primarily attributable to the limited number of samples ($n=40$) and the broader distribution of operating radiance levels, reflecting the influence of sample size and radiance coverage on regression stability rather than any intrinsic nonlinearity of the sensor.

In summary, all WTI channels exhibit highly consistent linear behavior across gain states, with strong model fits and well-controlled residuals, meeting the requirements of on-orbit radiometric calibration. To further evaluate cross-gain coherence and the applicability of the derived calibration coefficients, the next section analyzes error characteristics in overlapping gain regions and validation results from independent imagery.

4. Discussion

4.1. Selection of Calibration Sites

To ensure that automated ground-based observation systems provide long-term, high-quality data for satellite radiometric calibration and validation, calibration sites must satisfy several core criteria, including spatial homogeneity, temporal stability, flat terrain, and low cloud cover. The overarching principle is to prioritize surface types with highly stable radiometric properties and minimal anthropogenic disturbance—such as desert and gravel–gobi surfaces—and to include regions that span different thermal regimes so that sensor performance can be evaluated under diverse surface temperature conditions. Spatially uniform regions with minimal topographic variation and weak spatial gradients in reflectance/emissivity help improve the geometric consistency between satellite and ground observations, whereas persistent low cloudiness and low aerosol loading ensure high ratios of valid overpasses and robust temporal continuity.

For candidate site selection, this study builds upon the preliminary site inventory of Hu et al. (2020), which identified 32 Pseudo-Invariant Calibration Sites (PICS) [25]. A regional search and field surveys were conducted across the arid to semi-arid regions of northwestern China. To further refine site suitability, we used the MODIS MOD09GA cloud-mask product from 2001–2020 to derive 20-year clear-sky statistics for all PICS candidates, using the annual mean clear-sky fraction averaged over the 20-year period. MOD09GA provides two sets of cloud-related flags (cloud state and internal cloud algorithm flag). Based on these, two clear-sky indicators were defined:

• Clear-Sky Probability 1: fraction of pixels within the 10 km × 10 km window that satisfy cloud state = 0 or internal cloud algorithm flag = 0;
• Clear-Sky Probability 2: fraction of pixels within the 10 km × 10 km window that satisfy cloud state = 0 and internal cloud algorithm flag = 0.

These metrics jointly characterize the long-term clear-sky availability under “cloud-free/low-cloud” (Clear-Sky Probability 1) and “strictly cloud-free” (Clear-Sky Probability 2) conditions.

To meet the spatial homogeneity requirements, we further calculated the mean slope and slope standard deviation within a 10 km × 10 km window around each candidate site using SRTM digital elevation model (DEM) data, providing quantitative constraints on terrain flatness and spatial uniformity.

As shown in

Table 2. Basic characteristics of the selected calibration sites, including terrain slope statistics and long-term clear-sky probabilities.

Site	Mean Slope (°)	Slope Std. Dev. (°)	Clear-Sky Prob. 1	Clear-Sky Prob. 2
Golmud	1.780	0.859	0.69	0.53
Dunhuang	1.542	0.793	0.54	0.34
Dachaidan	2.048	0.951	0.70	0.55
Overall mean of candidate sites (N = 32)	4.759	2.420	0.63	0.46

, the three selected sites—Golmud, Dachaidan, and Dunhuang—perform well in terms of spatial homogeneity and clear-sky frequency. Although Dunhuang exhibits slightly higher cloudiness, its low slope and high spatial uniformity make it an excellent candidate. Golmud and Dachaidan, both located within typical gravel–gobi regions, show consistently high clear-sky probabilities and therefore provide highly favorable conditions for long-term, stable ground-based calibration observations.

4.2. Spatial Uniformity of Surface Thermal Infrared Emission

To evaluate the spatial uniformity of surface thermal infrared emission over the candidate calibration regions, thermal infrared band images from the GF-5A WTI instrument were analyzed within a 2 km × 2 km area centered on each candidate site. Spatial radiometric uniformity was quantified using the coefficient of variation (CV), a dimensionless statistic widely used in calibration-site characterization studies [25], defined as:

$$\mathrm{CV}={\displaystyle \frac{D{N}_{\mathrm{std}}}{D{N}_{\mathrm{mean}}}}\times 100\%,$$

(8)

where $D{N}_{\mathrm{std}}$ represents the standard deviation of digital numbers (DN) within the region of interest, and $D{N}_{\mathrm{mean}}$ denotes the corresponding mean DN value. A smaller CV indicates a more spatially homogeneous thermal radiance field.

As summarized in

Table 3. Statistics of surface thermal infrared uniformity around the calibration sites, expressed as coefficient of variation (CV, %) within a 2 km × 2 km area centered at each site for GF-5A WTI thermal infrared bands.

Band	Dachaidan CV (%)		Dunhuang CV (%)		Golmud CV (%)
	Daytime	Nighttime	Daytime	Nighttime	Daytime	Nighttime
Band 1	1.7	1.1	0.8	0.63	1.6	0.81
Band 2	1.8	1.1	0.9	0.45	1.6	0.98
Band 3	1.0	0.5	0.5	0.26	0.85	0.75
Band 4	0.6	0.3	0.3	0.18	0.59	0.42

, all three candidate calibration sites exhibit excellent spatial radiometric uniformity, with CV values consistently below 2% across all thermal infrared bands. The Dunhuang site shows the lowest CV values among the three regions for both daytime (0.3%–0.9%) and nighttime (0.18%–0.63%) scenes, indicating superior radiance homogeneity. The Golmud site ranks second (daytime 0.6%–1.6%, nighttime 0.42%–0.98%), while the Dachaidan site displays slightly higher CV values but remains well within acceptable uniformity thresholds (daytime 0.6%–1.8%, nighttime 0.3%–1.1%).

Across all sites, nighttime CV values are systematically lower than their daytime counterparts, suggesting that surface thermal emission fields are more stable under weak or absent solar heating. Taken together, the three regions exhibit favorable characteristics—uniform surface composition, minimal temporal variability, flat terrain, and a high frequency of clear-sky conditions—supporting their suitability for establishing persistent vicarious calibration fields and meeting the radiometric accuracy requirements of high-resolution thermal infrared sensors.

4.3. Analysis of Calibration Coefficients

To accommodate calibration requirements across different gain modes within the same spectral band, calibration coefficients were derived independently for each mode. During the calibration process, it was observed that DN values differ across gain states even when corresponding to the same physical radiance $L_{\mathrm{TOA}}$.

To compare calibration consistency across gain settings under equivalent radiance levels, this study defines the overlap region as the radiance interval between the minimum $L_{\mathrm{TOA}}$ observed in a lower-gain mode and the maximum $L_{\mathrm{TOA}}$ observed in the adjacent higher-gain mode. Within this interval, radiance residuals were computed using the calibration coefficients listed in

Table 4. Field-derived calibration coefficients for the GF-5A WTI instrument.

Band	Gain Mode	Gain	Offset
B1	Z2	$3.734\times {10}^{-3}$	$9.271\times {10}^{-1}$
B2	Z2	$3.263\times {10}^{-3}$	$1.205$
	Z3	$3.944\times {10}^{-3}$	$1.906$
B3	Z3	$5.214\times {10}^{-3}$	$-1.073$
	Z4	$6.014\times {10}^{-3}$	$-6.354\times {10}^{-1}$
B4	Z3	$6.309\times {10}^{-3}$	$-4.019$
	Z4	$7.008\times {10}^{-3}$	$-3.641$

, following:

$$L_{\mathrm{TOA}\_\mathrm{BIAS}}=L_{\mathrm{TOA}}-\left({\mathrm{gain}}_{ij}·D{N}_{ij}+{\mathrm{offset}}_{ij}\right),$$

(9)

where ${\mathrm{gain}}_{ij}$ and ${\mathrm{offset}}_{ij}$ indicate the calibration slope and intercept of the i spectral band under the j gain mode. For each overlap interval, three statistical metrics—systematic bias (Bias), standard deviation (Std), and root-mean-square error (RMSE)—were used to characterize the error distribution and evaluate whether different gain settings maintain consistent radiometric responses under identical radiance conditions.

Figure 10 illustrates the radiometric consistency across gain modes for each spectral band within their respective $L_{\mathrm{TOA}}$ overlap intervals. These results provide a systematic basis for evaluating whether different gain configurations maintain comparable statistical behavior and response stability under identical radiance conditions, thereby testing the robustness of the calibration model across the instrument’s operational dynamic range. A few extreme samples are present in the overlap region, which are retained because they reflect gain-state behavior near the overlap boundary.

Across-band comparisons reveal distinct cross-mode behaviors. For Band 2, gain mode Z2 shows a clear statistical advantage in the overlap region: its $RMSE$, $\left|\mathrm{Mean}\mathrm{Bias}\right|$ and $Std$ are 0.1695, 0.0182 and 0.1685, respectively, all lower than the corresponding values for Z3 (0.2145, 0.0595 and 0.2060). Under the current calibration model and sample distribution, this indicates that the calibration samples for Band 2 provide denser coverage on the low-radiance side (e.g., nighttime or low-temperature conditions), so that the linear fit and noise characteristics in this radiance interval are better constrained. Since Z2 is typically used for lower-radiance observations, the present dataset suggests that low-brightness samples exert a stronger constraint on the Z2 calibration parameters, leading to smaller apparent errors and higher stability for this gain mode under the current calibration setup.

For Band 3, the overlap-region statistics show a different pattern: Z4 outperforms Z3 across all three metrics, with $RMSE$ decreasing from 0.2788 to 0.1971, $\left|\mathrm{Mean}\mathrm{Bias}\right|$ from 0.1232 to 0.0436, and $Std$ from 0.2501 to 0.1923. Under the current calibration model and dataset, this indicates that the available calibration samples in the overlap region are more concentrated in the higher-radiance range (e.g., daytime or stronger surface emission), so that the high-radiance responses of Z4 are more fully constrained by the data. This feature suggests that, for Band 3 under the present calibration model and sample conditions, the high-radiance samples provide a more pronounced constraint on the Z4 fit, with system noise and potential nonlinearity being more effectively suppressed for this gain mode in the overlap interval.

Band 4 exhibits a similar behavior to Band 3 within the overlap region. With only a small difference in dispersion ($Std$ differing by about 0.006), Z4 achieves smaller errors than Z3 (for Z3: $RMSE=0.1943$, $\left|\mathrm{Mean}\mathrm{Bias}\right|=0.1100$; for Z4: $RMSE=0.1699$, $\left|\mathrm{Mean}\mathrm{Bias}\right|=0.0350$). Under the present sample size and calibration procedure, this indicates that Z4 yields smaller fitting errors for the higher-radiance samples in the Band 4 overlap region.

Overall, the overlap-region statistics for the three bands jointly reflect the behavior of the current calibration parameters across different radiance levels. For Band 2, the better error statistics of Z2 indicate that, within the present dataset, nighttime or low-radiance samples provide more effective constraints for this gain mode. For Bands 3 and 4, the smaller errors of Z4 suggest that, under the current calibration model and sample distribution, high-radiance samples in the overlap regions exert stronger constraints on the corresponding fits. Taken together, these results indicate that, for GF-5A WTI under the present calibration framework and sample conditions, consistent responses and good error convergence are achieved across different radiance regimes.

4.4. Validation of Calibration Coefficients

To assess the applicability and radiometric accuracy of the derived calibration coefficients under real observational conditions, thermal infrared imagery acquired by the GF-5A WTI instrument from 1 August to 10 September 2024 was used for validation. For each scene, the WTI spectral response functions, MODTRAN-derived atmospheric radiative transfer components (including upward transmittance and path radiance), together with in situ surface temperature and emissivity measurements, were combined to compute the band-equivalent at-sensor radiance. The radiance was subsequently converted to the simulated brightness temperature $T_{\mathrm{sim}}$ using the Planck function. In parallel, the satellite-side brightness temperature $T_{\mathrm{sat}}$ was retrieved using the calibration coefficients derived in Section 3.3 of this study by applying them to the corresponding WTI observations to obtain the at-sensor radiance, followed by inversion of the Planck function. Comparison with the satellite-derived brightness temperature $T_{\mathrm{sat}}$ yields the brightness–temperature deviation:

$$\Delta T_B=T_{\mathrm{sat}}-T_{\mathrm{sim}}.$$

(10)

After removing samples affected by cloud contamination or unstable surface temperature conditions, 201 out of 246 candidate samples were excluded, and the remaining 45 valid cases were retained for quantitatively assessing the stability and accuracy of the calibration coefficients under on-orbit conditions.

As shown in Figure 11, the brightness temperature deviations for the four thermal infrared bands exhibit strong consistency across the 45 valid samples. The deviation range is within $\pm 1.6\mathrm{K}$ for all bands, and the maximum RMSE does not exceed 0.76 K, indicating that the calibration results achieved in this study are both accurate and reliable. The error distributions for each channel are relatively compact, further demonstrating that the calibration model remains stable and that the retrieval uncertainties are well controlled.

From a per-band perspective, although slight differences exist in deviation magnitude and distribution shape, the overall behavior is coherent across bands. Band 1 shows a nearly symmetric deviation distribution with $\mathrm{Mean}\mathrm{Bias}=+0.091\mathrm{K}$ and $\mathrm{RMSE}=0.758\mathrm{K}$, indicating stable radiometric response without obvious systematic shifts. Band 2 exhibits a small negative bias ($\mathrm{Mean}\mathrm{Bias}=-0.166\mathrm{K}$) and achieves the smallest RMSE among all bands ($\mathrm{RMSE}=0.619\mathrm{K}$), suggesting that this channel currently attains the highest calibration accuracy. Band 3 presents a small positive bias ($\mathrm{Mean}\mathrm{Bias}=+0.169\mathrm{K}$, $\mathrm{RMSE}=0.642\mathrm{K}$) with tightly clustered residuals and limited random dispersion. Band 4 behaves similarly to Band 3, showing $\mathrm{Mean}\mathrm{Bias}=+0.153\mathrm{K}$ and $\mathrm{RMSE}=0.648\mathrm{K}$, consistent with stable linear response and controlled random errors.

Overall, the mean absolute deviation across all four channels is approximately $0.145\mathrm{K}$, with an average RMSE of $0.667\mathrm{K}$. These results demonstrate that the calibration coefficients derived in this study are highly reliable and applicable under on-orbit observation conditions. Furthermore, after applying the calibration coefficients, the GF-5A WTI instrument maintains strong radiometric consistency and effective noise control across all channels.

4.5. Uncertainty Analysis

The uncertainty of brightness temperature estimation in this study primarily originates from four contributing factors: (1) contact temperature measurement, (2) surface emissivity measurement, (3) atmospheric profile acquisition, and (4) radiative transfer modeling using MODTRAN v5.2. These components collectively determine the overall accuracy of the surrogate radiometric calibration.

(1)

Uncertainty of Contact Temperature Measurement

To quantify the measurement uncertainty of the contact temperature sensor, synchronous heating–cooling comparison experiments were conducted using a JM standard thermometer traceable to national metrology institutes. The results show that the RMSE between the contact thermometer and the standard reference thermometer lies within 0.173–0.177$°\mathrm{C}$. This RMSE already includes practical factors such as thermal coupling between the probe and target surface and differences in response time. Therefore, the RMSE is treated as the standard uncertainty of the contact temperature sensor under the conditions of this study:

$${\sigma }_{\mathrm{contact}}=0.18\mathrm{K}.$$

(11)

(2)

Uncertainty of Surface Emissivity Measurement

Surface emissivity was measured in the field using a portable Fourier-transform infrared spectrometer. As defined by Equation (5), emissivity uncertainty arises primarily from radiance measurement errors and temperature measurement errors propagated through the emissivity formulation. In addition, it also includes the algorithmic uncertainty in the emissivity measurement. When these effects are further propagated through the surface–atmosphere–sensor radiative transfer chain, the resulting brightness temperature uncertainty is less than 0.5 K. Therefore, the emissivity-related uncertainty is taken as:

$${\sigma }_{\mathrm{emis}}=0.5\mathrm{K}.$$

(12)

(3)

Uncertainty of Atmospheric Profile Data

Atmospheric correction in this study relies on radiosonde profiles from the Integrated Global Radiosonde Archive (IGRA). These profiles undergo operational quality control and exhibit good temporal and spatial consistency [29,30]. Under cold and dry conditions, radiosonde relative humidity biases are typically within 5–10%. Previous studies show that a 10% relative increase in precipitable water vapor (PWV) leads to a brightness temperature deviation of approximately 0.13 K [32]. As the study area is located in an arid to semi-arid Gobi region with generally low and slowly varying PWV, the atmospheric-profile uncertainty is taken as:

$${\sigma }_{\mathrm{atm}}=0.13\mathrm{K}.$$

(13)

(4)

Uncertainty of the Radiative Transfer Model (MODTRAN)

The uncertainty of the radiative transfer model mainly arises from band-model approximations, absorption-line parameter uncertainties, and numerical integration discretization. Within the 8–14 μm atmospheric window, the inherent MODTRAN v5.2 model error is generally below 2%. Therefore, we apply a $\pm 2\%$ relative perturbation to the MODTRAN-simulated band-equivalent TOA radiance for each channel and retrieve the corresponding brightness temperature using the inverse Planck relation. We then summarize the differences before and after perturbation in the brightness–temperature domain, and take the mean of all differences to quantify this uncertainty term.

Based on our dataset, the mean brightness–temperature uncertainties induced by MODTRAN v5.2 are 0.9 K (Band 1), 0.9 K (Band 2), 1.2 K (Band 3), and 1.3 K (Band 4). Accordingly, the MODTRAN v5.2-related brightness-temperature uncertainty is taken as:

$${\sigma }_{\mathrm{mod}}=1.30\mathrm{K}.$$

(14)

(5)

Total Uncertainty

The combined standard uncertainty of the at-sensor brightness temperature derived via the radiative transfer chain is computed using the root-sum-of-squares (RSS):

$${\sigma }_{T,\mathrm{total}}=\sqrt{{\sigma }_{\mathrm{contact}}^2+{\sigma }_{\mathrm{emis}}^2+{\sigma }_{\mathrm{atm}}^2+{\sigma }_{\mathrm{mod}}^2}.$$

(15)

Substituting the adopted values ${\sigma }_{\mathrm{contact}}=0.18\mathrm{K}$, ${\sigma }_{\mathrm{emis}}=0.50\mathrm{K}$, ${\sigma }_{\mathrm{atm}}=0.13\mathrm{K}$, ${\sigma }_{\mathrm{mod}}=1.30\mathrm{K}$, yields:

$${\sigma }_{T,\mathrm{total}}\approx 1.41\mathrm{K}.$$

(16)

Overall, brightness temperature retrievals based on the radiative transfer model exhibit a conservative combined standard uncertainty of approximately 1.41 K under the conditions of this study. Among the individual contributors, the MODTRAN-related uncertainty dominates the total error budget, followed by surface emissivity uncertainty, while uncertainties from contact temperature measurements and atmospheric profiles are comparatively minor. This indicates that even in dry, low-water-vapor environments, radiative transfer modeling uncertainty can be a primary contributor to the absolute brightness–temperature uncertainty when propagated in the brightness–temperature domain.

5. Conclusions

In response to the need for long-term stability and high-frequency calibration of TIR satellite sensors, this study developed a continuous, automated ground-based observation system centered on Gobi pseudo-invariant calibration sites and dedicated in situ observations. The framework has been validated using the GF-5A WTI instrument through comprehensive analyses of calibration-coefficient stability, inter-gain consistency, and on-orbit brightness–temperature comparisons.

Three calibration sites located in arid to semi-arid Gobi regions were selected through comprehensive screening based on terrain flatness, cloud-occurrence probability, and TIR spatial uniformity. Using metrology-traceable reference thermometers together with dual validation from Turbo FT emissivity measurements and ISSTES-based temperature–emissivity separation, the deployed automated ground system was demonstrated to provide a reliable, traceable surface-temperature reference suitable for long-term TIR radiometric calibration.

By integrating high-accuracy emissivity measurements, IGRA atmospheric-sounding profiles, and MODTRAN v5.2-based radiative-transfer modeling, an end-to-end “surface–atmosphere–sensor” calibration chain was established, enabling routine updates of on-orbit gain and offset parameters at a cadence compatible with operational practice and supporting a physically consistent, traceable radiometric link between ground measurements and satellite observations.

Results derived from GF-5A WTI indicate that the linear calibration coefficients exhibit highly stable responses across all bands and gain states, with coefficients of determination consistently exceeding $R^2>0.98$. Overlap-region analyses further show that inter-gain brightness–temperature differences (bias and RMSE) are generally constrained within about $0.3\mathrm{K}$. Band-dependent behaviors are also observed: Band 2 calibration benefits from low-radiance samples (nighttime or low-temperature conditions), whereas Bands 3 and 4 achieve improved model fitting under high-radiance conditions (daytime or warm-surface cases). Independent on-orbit image validation confirms that the RMSE for all bands remains below $0.76\mathrm{K}$, which is smaller than the conservative estimated total uncertainty of approximately $1.41\mathrm{K}$ derived from the full radiative chain.

Overall, the proposed continuous ground-based surrogate calibration approach provides GF-5A WTI with a low-maintenance, traceable, and operationally practical on-orbit calibration solution. The methodology offers a reproducible technical pathway for quality assurance, long-term stability assessment, and cross-sensor or multi-mission consistency analysis for future high-resolution thermal infrared satellite missions.