Based on atmospheric radiative transfer theory, the satellite-observed top-of-atmosphere (TOA) monochromatic radiance LTOA in the visible/near-infrared (VIS/NIR) and thermal infrared (TIR) channels can be expressed in the following simplified forms (Kotchenova et al., 2006): 1LVIS/NIRTOA=LscatT↑+(1-ϵ)πE0μ0T↓T↑2LTIRTOA=ϵB(Ts)T↑+∫0∞B(T(z))W(z)dz where Lscat denotes the combined contribution from both single and multiple scattering by particles (e.g., clouds and aerosols) as well as gas molecules. ϵ is the surface emissivity. E0 and μ0 represent the incoming solar irradiance and the cosine of the solar zenith angle, respectively. T with arrows indicates the atmospheric transmittance along the downward and upward paths. It is primarily controlled by the total extinction optical depth along the line of sight, which depends on gaseous absorption (e.g., H₂O, CO₂, O₃) and scattering by clouds and aerosols, as well as the atmospheric temperature–pressure structure and viewing geometry (path length/zenith angle). In Eq. (2), B is the Planck function, which is used to compute the emitted radiance associated with the surface temperature Ts. The integral term accounts for the radiance emitted from each atmospheric layer at altitude z, and W(z) is the corresponding weighting function. W(z) quantifies the relative contribution of emission from atmospheric layer (z) to the TOA radiance; it is essentially the product of the layer's absorptivity (or emissivity) and the transmittance from that layer to the sensor, thereby indicating the altitude range to which a given channel is most sensitive (Matricardi, 2010).

For the 3.75 µm channel, the daytime top-of-atmosphere radiance includes both thermal and solar contributions. The thermal part arises from atmospheric path emission and surface emission, whereas the solar part originates from atmospheric scattering and surface-reflected solar radiance. Consequently, neither Eq. (1) nor Eq. (2) alone can fully describe the daytime radiative behavior of this mixed channel. In the SFP framework, the radiative transfer for the 3.75 µm channel is therefore performed using the total band-integrated radiance, rather than a thermal-only component. At night, the solar contribution becomes negligible, and the channel behaves essentially as a purely thermal emissive band.

From the physical interpretation of the above two equations, the primary factors affecting satellite-observed radiance include the atmospheric thermodynamic structure (temperature and humidity profiles), satellite viewing geometry, surface reflective and emissive properties, and extinction by atmospheric gas composition, clouds, and aerosols. A key scientific challenge for the TL model is therefore to develop a generalizable framework that can accurately propagate these physical effects across satellites for spectrally similar channels. Because these channels are spectrally similar (e.g., the examples shown in Fig. 2), we aim to exploit their underlying physical relationships to enable robust transfer of spectral radiance features across satellite observations.

Building on the rationale outlined above, we develop a physics-constrained TL model using simulated, satellite-sensor-consistent high-resolution spectral radiances. Specifically, we employ the classical MODTRAN (Version 5.3.2) model (Berk et al., 2013) as the forward radiative transfer model (RTM) to generate TOA radiances (Unit = W (m² sr µm)⁻¹) over 0.40–13.5 µm at a spectral resolution of 1 cm⁻¹. For computational convenience, the simulations are conducted over two subranges: 0.3–2.4 µm (VIS and NIR) and 3.3–13.5 µm (TIR). To ensure diversity and global representativeness, we compile 83 representative atmospheric profiles from the European Centre for Medium-Range Weather Forecasts (ECMWF) archive spanning multiple climate regimes. In addition to the 83 independent atmospheric profiles, we further enhance the diversity of the simulations by specifying a comprehensive set of cloud, aerosol, surface, and viewing-geometry parameters, as summarized in Table 1. This shows that cloud optical depth at 550 nm ranges from 0 (clear sky) to 216 (cumulus), with other four different cloud types. Surface reflectivity (ρ) is prescribed by land-cover type, varying from 0.003–0.979 (snow) and 0.08–0.83 (forest) to 0.01–0.05 (ocean) and 0.019–0.137 (urban). The observation geometry is configured with a set of discrete angles, which together cover the major satellite observation modes. Overall, these configurations generated 55 600 VIS/NIR simulation cases and 18 000 IR simulation cases before validity screening. The resulting SFP dataset constitutes a large-scale database of simulated satellite hyperspectral radiances, primarily spanning two spectral ranges as noted above: 0.3–2.4 µm (VIS/NIR) and 3.3–13.5 µm (TIR).

For the 3.75 µm channel, the retained infrared simulations were generated using MODTRAN's thermal-plus-solar radiance mode (IEMSCT = 2), with multiple scattering enabled (IMULT = 1). The TOTAL_RAD output in tape7 includes atmospheric and surface thermal emission, atmospheric solar scattering, and ground-reflected solar radiance. This total radiance was subsequently used for the spectral response function (SRF) convolution. Consequently, the transfer coefficients for FY-4A and FY-4B Channel 07 were fitted using their respective SRF-convolved total radiances, rather than thermal-only components. Surface reflection was represented by the Lambertian assumption as configured in the MODTRAN input settings.

This SFP model was originally developed for the cross-calibration of the reflective solar bands of FY-3D/MERSI-II. By employing TL, it enables the transfer of the radiometric reference from the MODIS sensor while preserving the inherent radiometric observation characteristics of MERSI-II (Yu et al., 2026). Application of this model to the FY-3D/MERSI-II solar reflective channels over a period of more than seven years resulted in a mean relative bias of approximately 1 %, with a 2 %–3 % improvement compared with the operational calibration coefficients. We emphasize that, unlike physics-informed neural network approaches that enforce physical consistency through an explicit penalty term in the loss function, physical consistency in this framework is embedded directly in the construction of the training data: the fitting pairs used in Sect. 2.2 are derived from these MODTRAN radiative transfer simulations convolved with the actual sensor SRFs, so the resulting transfer coefficients are, by construction, consistent with radiative transfer physics. This is also the mechanism by which the framework reduces SRF-driven bias between sensors, since the fitting pairs already encode the true SRF discrepancy rather than requiring it to be inferred from noisy real satellite matchups.

Radiance TL between the target and reference instruments (using FY-4A and FY-4B AGRI as an example) is achieved through an adaptive polynomial framework. In this approach, transfer coefficients are derived by fitting the simulated radiances of both the reference and target sensors, with the theoretical radiances generated from MODTRAN simulations mentioned in section 2.1. The underlying polynomial model is expressed as follows: 3y=∑i=0naixi where y (i.e., the radiance observed by the target sensor) denotes the fitted value of the dependent variable corresponding to the input variable x (i.e., the radiance observed by the reference sensor), n is the polynomial order, ai represents the polynomial coefficients to be estimated, and i is the index of the polynomial term.

The new physics-constrained TL framework uses a lowest-order-first adaptive polynomial fitting strategy. Fitting begins with a linear model (n=1), and the polynomial order is increased only when R2<0.95, up to a maximum of n=4. If the threshold is not reached at n=4, the model with the highest R2 is retained. Here, R2≥0.95 is used as an empirical goodness-of-fit criterion rather than as a test of statistical significance, while limiting the polynomial order to four constrains unnecessary model complexity and reduces the risk of overfitting. For the VIS/NIR channels, a common finite-value mask was applied across the six matched channel pairs. Of the initial 55 600 simulated pairs, 50 cases containing non-finite values in at least one matched channel were excluded, leaving the same 55 550 pairs for each VIS/NIR channel fit. Each IR channel fit used 18 000 valid simulated pairs from five atmospheric conditions. Before fitting, the MODTRAN-simulated hyperspectral TOA radiances are convolved with the SRFs of the target and reference sensors to obtain the corresponding broadband channel radiances. The channel-averaged radiance LAveragedTOA measured by a sensor channel is calculated by: 4LAveragedTOA=∫λ2λ1LTOAλ⋅SRF(λ)dλ∫λ2λ1SRF(λ)dλ where λ1 and λ2 denote the starting and ending wavelengths of the normalized spectral response function (SRF), respectively. Overall, Eqs. (3) and (4) are designed to provide physically consistently observed radiance for bridging the target and reference channels. Furthermore, for practical remote sensing applications, the observed radiances of the VIS/NIR channels and IR channels need to be converted into reflectance (ρ, Eq. 5) and brightness temperature (BT, Eq. 6), respectively, which are written as follows: 5ρ=πLAveragedTOAcosθ0F06BT=Planck(LAveragedTOA,λemw) where θ0 is the solar zenith angle, F0 represents the channel SRF-convolved solar exo-atmospheric irradiance. Additionally, Planck denotes the Planck function, and λemw corresponds to the effective middle wavelength weighted by the channel SRF. Note that, the IR channels require additional correction because they are not ideal narrowband filters. As a result, a slight difference exists between the nominal central wavelength and the effective central wavelength used in BT calculations based on the Planck function (Chen et al., 2012). The fitting coefficients and Planck-weighted correction coefficients (for IR channels only) for the FY-4A/B AGRI channels used in this study are provided in Tables S1 and S2 in the Supplement.

Channel 07 is processed through the thermal-channel branch, as the operational FY-4A and FY-4B products provide it in brightness-temperature form. During daytime, this brightness temperature should be regarded as an effective brightness temperature corresponding to the total measured band radiance. In practice, the observed brightness temperature is first converted to radiance; the inter-sensor transfer is then performed in radiance space, and the transferred radiance is subsequently converted to the target-sensor brightness temperature. This procedure retains the mixed daytime signal but does not explicitly isolate or remove the solar-reflected component. Consequently, the brightness-temperature-based formulation represents the transfer of the total channel signal, rather than a purely thermal treatment of the 3.75 µm channel.

Figure 3 illustrates the TL models used to convert four representative FY-4B/AGRI channels (Channels 1 (0.47 µm), 5 (1.61 µm), 13 (10.80 µm), and 15 (13.30 µm)) to their corresponding FY-4A/AGRI channels within the new physics-constrained framework. This conversion spans VIS, NIR, and TIR spectral bands, and includes a case employing higher-order polynomial fitting. As shown in this figure, the fitting performance is excellent in the solar reflective bands, such as Channels 1 and 5, with only very small fitting residuals. In contrast, the longer-wavelength Channel 15 exhibits not only larger residuals but also a need for a quadratic term in the fitting. Besides the slight differences in the central wavelengths of this channel (see the bottom panel in Fig. 2), the larger errors in the TIR bands are primarily caused by the more complex gaseous absorption characteristics at these wavelengths, especially carbon dioxide (CO₂) absorption (Teixeira et al., 2024).

Differences in central wavelengths or SRFs, combined with strong path absorption and emission, introduce substantial nonlinearities into the radiative transfer process. As a result, lower-order linear fitting becomes insufficient, and higher-order terms must be incorporated. Therefore, the next Sect. 3 investigates the sensitivity of the physics-constrained TL model to those discrepancies in the SRFs of satellite sensors and their radiometric calibration uncertainties, using the AGRIs aboard the FY-4A and FY-4B satellites as examples.

We simulate discrepancies in the SRFs of spaceborne imager by scaling the spectral width and shifting the central wavelength. The spectral width scaling factor ranges from 0.1 to 2.0 in increments of 0.1. The central wavelength is shifted from -100 cm⁻¹ (“-” means a leftward shift) to +100 cm⁻¹ (“+” means a rightward shift) in increments of 10 cm⁻¹ for IR channels. For VIS/NIR channels, due to the relatively large wavenumber, the central wavenumber is shifted from -1000 to +1000 cm⁻¹ in increments of 100 cm⁻¹. Figure 4 shows examples of these simulated (or adjusted) SRFs for FY-4B/AGRI Channel 2 (0.66 µm) and Channel 13 (10.80 µm), including cases with narrower and wider spectral widths as well as shifts in central wavelength. As shown in Fig. 4, the discrepancies between the adjusted SRFs and the original SRFs are still substantial. Whether excessively large SRF differences between the target and reference sensors may affect the performance of this new TL approach is a question that warrants careful evaluation and consideration.

In this investigation, we employ three classical metrics, namely Jensen–Shannon divergence (JSD), Wasserstein distance, and Kolmogorov–Smirnov distance (KS), to evaluate the similarity between the adjusted SRFs and the original SRFs. For the calculation of the Jensen–Shannon divergence (Endres and Schindelin, 2006), the two curves (or SRFs) are first discretized into histograms or grids and represented as probability distributions, which is defined as: 7P=p1,p2,…,pn,Q=q1,q2,…,qn where ∑pi=∑qi=1 and M=12P+Q. JSD is a symmetric and smoothed variant of the Kullback–Leibler divergence (KL), which is defined as follows: 8JSDP||Q=12KLP||M+12KLQ||M9KLP||M=∑ipilog(pimi)

The JSD is dimensionless and ranges from 0 to 1, with smaller values indicating greater similarity between the two curves.

The second metric is the Wasserstein distance (Mémoli, 2011), also referred to as the Earth Mover's Distance, which measures the minimum transportation cost required to transform one probability distribution into another. For one-dimensional distributions, the first-order Wasserstein distance can be expressed as: 10WP,Q=∫-∞+∞|FPx-FQ(x)|dx where FP(x) and FQ(x) are the cumulative distribution functions (CDFs) of P and Q curves, respectively. This metric reflects not only distributional overlap but also the geometric displacement between them.

The third metric is the Kolmogorov–Smirnov distance (Massey, 1951), which is defined as the maximum absolute difference between the two CDFs and can be written as: 11DKS=supx|FPx-FQ(x)|.

It characterizes the largest pointwise discrepancy between two curve distributions. Together, these three metrics provide complementary perspectives on distributional differences: JSD emphasizes probabilistic similarity, Wasserstein distance captures transportation-based discrepancy, and KS measures the maximum deviation between cumulative distributions.

Figures 5 and 6 show the distributions of Jensen–Shannon divergence, Wasserstein distance, and Kolmogorov–Smirnov distance as functions of the scaling factor (from 0.1 to 2.0) for FY-4B/AGRI Channel 2 (0.66 µm, with shifted wavenumber from -1000 to +1000 cm⁻¹) and Channel 13 (10.80 µm, with shifted wavenumber from -100 to +100 cm⁻¹), respectively. From these two figures, the shortwave band, Channel 2 (0.66 µm), exhibits relatively low sensitivity to wavenumber shifts within ±1000 cm⁻¹ because of its comparatively broad spectral width (about 3000 cm⁻¹), whereas the narrower longwave band, Channel 13 (10.80 µm), is considerably more sensitive. However, when the wavenumber shift reaches more than 1000 cm⁻¹, even the shortwave band is likely to be affected significantly. Considering the limitation of the manuscript length and the similar distribution characteristics, the results of other FY-4B/AGRI channels are presented in Figs. S1 to S13.

Moreover, both the VIS and IR channels of FY-4B/AGRI exhibit much greater sensitivity to variations in SRF width than to shifts in central wavenumber. When the SRF becomes narrower, all three similarity metrics mentioned above increase markedly (smaller values indicate greater similarity); for example, the JSD approaches 1.0. These results indirectly indicate that excessively large discrepancies in central wavelength and SRF width between the target and reference channels could seriously impair the effectiveness of the proposed transfer learning method.

To more quantitatively evaluate the impact of SRF discrepancies, fitting experiments are conducted using both simulated SRFs and the original SRFs of FY-4B/AGRI mentioned before. The fitting errors in physics-constrained TL between reference and target channel radiance observations are calculated using simulated FY-4B/AGRI SRFs, with the following configurations: spectral width scaling factor from 0.1 to 2.0 (step 0.1); central wavelength shift from -100 to +100 cm⁻¹ (step 10 cm⁻¹) for IR channels, and from -1000 to +1000 cm⁻¹ (step 100 cm⁻¹) for VIS/NIR channels.

During the fitting process, the coefficient of determination (R2) is further used to determine whether a first-order linear fit or a second-order polynomial fit is more appropriate, and it is given by: 12R2=1-∑i=1nyi-y^i2∑i=1nyi-y‾2 where y, y^, and y‾ denote the observed value, the fitted value, and the mean of the observed values, respectively. R2 is commonly used to measure the extent to which the fitted model explains the variability in the observed data, with values closer to 1.0 indicating better agreement between fitted and observed values and stronger explanatory power of the model. In this study, a second-order polynomial fit is adopted when the R2 value of the initial linear fit is below 0.95.

In addition, three metrics are used for assessing the fitting performance of the TL model, including the RMSE (root-mean-square-error), the correlation coefficient (R), and the number of outliers (Noutlier). They can be written as follows: 13RMSE=1n∑i=1nyi-y^i214R=∑i=1nyi-y‾(y^i-y^‾)∑i=1nyi-y‾2∑i=1n(y^i-y^‾)2 where y^‾ denotes the mean of the fitted values. For the final metric, Noutlier, outliers are identified using the upper and lower fences. Any value lying beyond these two fences is regarded as an abnormal value, defined as: 15Noutlier=NoutlierUpperFence=Q75+1.5×IQRNoutlierLowerFence=Q25-1.5×IQR16IQR=Q75-Q25 where Q25 and Q75 represent the 25th and 75th percentiles of the residuals, respectively. A higher outlier count (Noutlier) corresponds to an increased presence of extreme errors (or abnormal value).

Figure 7 shows the distributions of RMSE, R, and Noutlier as functions of scaling factor (0.1–2.0) and shifted wavenumber (-1000 to +1000 cm⁻¹) for FY-4B/AGRI Channel 2 (0.66 µm) and Channel 5 (1.61 µm). The results in the left panel for Channel 2 are generally consistent with those in Fig. 5: as the scaling factor increases, the discrepancy between the target and reference SRFs becomes larger, resulting in higher RMSE and Noutlier and a lower R. When the scaling factor exceeds 1.8, most cases require second-order polynomial fitting, suggesting that the relationship no longer follows a simple linear conversion. Notably, although scaling factors of about 0.1–0.2 correspond to large similarity differences in Fig. 5, they do not substantially degrade the TL performance, and the fitting remains predominantly linear. This may be because the narrower target channel still preserves particle scattering characteristics similar to those of the reference channel. By contrast, due to relatively low wavenumber, Channel 5 (1.61 µm) is much more sensitive to wavenumber shifts. Once the shift exceeds about 300 cm⁻¹, the RMSE increases significantly, the correlation coefficient decreases markedly, and both the fitting type and Noutlier exhibit abrupt changes.

Figure 8 presents the results for FY-4B/AGRI Channel 9 (6.25 µm) and Channel 13 (10.80 µm). Channel 9 is a typical upper-tropospheric water vapor absorption channel, with its weighting function peaking around 300–400 hPa, corresponding to an altitude of approximately 8–9 km (Li et al., 2022). In terms of the correlation coefficient R, Channel 9 appears to be more sensitive to consistency in SRF shape. However, the RMSE results shown in the upper panels indicate that Channel 9 yields smaller fitting errors, suggesting that it is more suitable for observation radiance transfer by using the physics-constrained TL model. It is also noteworthy that, compared with the VIS/NIR channels discussed above (see Fig. 7), the IR channels produce Noutlier values about one order of magnitude smaller, indicating that particle scattering in the VIS/NIR bands introduces larger deviations into the TL performance.

The results of Figs. 7 and 8 indicate that the performance of the physics-constrained TL model is strongly affected by SRF discrepancies. Larger differences in scaling factor or shifted wavenumber generally lead to higher fitting errors, more outliers, and lower correlation, while IR channels show better transfer performance than VIS/NIR channels, likely because particle scattering introduces larger deviations in the latter. As a conservative guideline, for VIS/NIR channels, the difference in central wavenumber should be kept below 200 cm⁻¹, while the scaling factor should be constrained to the range of 0.5–1.5. In comparison, IR channels, particularly the water-vapor bands, appear to be somewhat more tolerant. However, for atmospheric window channels around 11 µm, the shifted wavenumber should ideally remain below 20 cm⁻¹, with the scaling factor likewise limited to 0.5–1.5. If the similarity between the target and reference channels is too low, reliable conversion becomes infeasible; the resulting conversion errors will then propagate into the retrieval model and further degrade retrieval performance. To facilitate practical application of the proposed framework, the empirical SRF-similarity guidelines derived from Figs. 7 and 8 are summarized by channel type in Table 2. These values should be interpreted as conservative screening criteria for the simulated SRF perturbations examined in this study, rather than as universal limits applicable to all satellite sensors.

Using the existing simulated convolution dataset, we evaluated the transfer performance of the 3.75 µm channel at the available discrete solar zenith angles. The analysis comprised 18 000 matched FY-4A and FY-4B Channel 07 samples drawn from five infrared atmospheric conditions. The relative RMSEs at solar zenith angles of 0, 30, and 60° were 2.020 %, 2.004 %, and 2.012 %, respectively, showing no monotonic degradation with increasing solar zenith angle within the simulation range. The relative RMSE varied modestly, ranging from approximately 1.82 % to 2.19 % across different viewing azimuth configurations. These results suggest that the total-radiance transfer relationship remains broadly stable over the daytime geometries examined. Nevertheless, this assessment should be viewed as an internal consistency analysis of the simulated transfer relationship, rather than an independent validation of solar-reflection correction or downstream retrieval accuracy.

Beyond SRF differences, radiometric calibration uncertainty in each target channel can also influence the stability and reliability of the physics-constrained TL model. We clarify the scope of the error-propagation derivation presented below. The propagation in Eqs. (17)–(21) and (A20)–(A21) takes the radiometric calibration uncertainty of the target channel (2 %–5 % in reflectance for VIS/NIR channels, Xiong et al., 2019; 0.1–1.0 K in brightness temperature for IR channels, He et al., 2021) as an externally imposed input and propagates it through the already-fitted TL model. Uncertainty associated with the fitted coefficients themselves, the SRF characterization, and the underlying RTM simulations is not included in this derivation and is assumed to be small relative to the imposed target-channel uncertainty. For consistency, throughout this section “error” and “uncertainty” are used interchangeably to denote the propagated standard deviation (σ), while “bias” refers specifically to the assumed radiometric calibration offset of the target channel that is propagated. According to Eq. (3) and Fig. 3, when the TL model is linear, i.e., y=ax+b, where a and b are fitted coefficients, and x and y denote the radiances in the target (FY-4B/AGRI) and reference (FY-4A/AGRI) channels, respectively, the associated error (σ, or uncertainty) propagation is obtained by differentiating the linear relationship, as follows: 17σy=|a|×σx.

However, as shown in Fig. 3d (FY-4B/AGRI Channel 15 centered at 13.30 µm), when the TL model is nonlinear and represented by a quadratic function, i.e., y=ax2+bx+c, the corresponding error propagation can be expressed as follows (first-order approximation): 18σy=|2ax+b|×σx.

This equation suggests that the error in the reference-channel radiance (y) is strongly dependent on the magnitude of the radiance observed in the target channel (x).

According to Eq. (5), the propagation of uncertainties or errors in the reflectance observed by the VIS/NIR channels, which are typically on the order of 2 %–5 % (Xiong et al., 2019), can be readily expressed as follows: 19σx=|F0,tπ|×σρ,t.

By combining Eqs. (5), (17), (18), and (19), the reflectance errors (σρ,r) in the reference channel with different fitting formula (Eqs. 17 and 18) can be expressed as follows: 20σρ,r=|a|×|F0,tF0,r|×σρ,t21σρ,r=|2aF0,tπρt+b|×|F0,tF0,r|×σρ,t where the footnotes of ρ, t, and r respectively signify the reflectance, target, and reference. It should be noted that the formulation of ρt does not explicitly include the term of cos(θ0). According to Eq. (20), the propagation of reflectance error in ρt is controlled solely by the slope of the TL model and the solar irradiance terms of the two different channels. By comparison, the nonlinear form in Eq. (21) additionally depends on the reflectance observed by the target channel.

Compared with the VIS/NIR channels, the propagation of uncertainties (0.1 ∼ 1.0 K) (He et al., 2021) in the BTs measured in the target IR channels is nonlinear and more complex, owing to the additional Planck-function conversion and Planck-weighted correction calculation (Chen et al., 2012). In this study, the final equations for uncertainty propagation in the IR channels are given as Eqs. (A20) and (A21), with the full derivation provided in the Appendix A.

To address the inherent calibration-drift errors among different spectral channels, chain-rule-based error-propagation sensitivity experiments were conducted according to Eqs. (20), (21), (A20), and (A21). Figure 9 presents the heatmaps derived from the corresponding error-sensitivity analysis for the FY-4/AGRI sensors based on the physics-constrained TL models. Note that the A → B case in Fig. 9 follows the same target/reference assignment as Fig. 3 (FY-4A as the target, FY-4B as the reference), while the B → A case represents the reverse assignment, enabling a symmetric assessment of transfer errors in both directions. For the solar reflective channels, propagated errors are generally attenuated because the error-transfer relationship is predominantly linear, with absolute slopes smaller than unity. However, Channel 4 at 1.38 µm exhibits notably unstable behavior and pronounced error amplification. This channel is primarily sensitive to upper-level ice crystals and is widely used for cirrus cloud detection (Gao et al., 1993). In addition, as shown in Fig. 2, the SRF of FY-4B/AGRI Channel 4 (1.38 µm) covers a substantially narrower range than that of FY-4A/AGRI, which may directly result in a relatively large slope in the fitted TL model and, consequently, a larger difference between the two F0 terms in Eq. (20). Regardless of the specific mechanism, Fig. 9 further indicates that when the radiometric calibration bias becomes large (e.g., reaching 6 %), the resulting transfer error also increases approximately linearly. In other words, channels subject to substantial radiometric calibration bias are not well suited for transfer-learning-based retrieval applications.

In contrast, for most IR channels, small perturbations tend to be amplified, whereas larger perturbations remain close to the magnitude of the original input. A notable exception is FY-4A/AGRI Channel 14 (13.30 µm), which is modeled using a polynomial relationship (see Fig. 3d). The propagated errors for this channel are substantially amplified, owing to pronounced SRF discrepancies and its high sensitivity to atmospheric variability. In addition, the 7.10 and 10.80 µm channels exhibit relatively larger transfer errors because these bands underwent notable upgrades from FY-4A to FY-4B, whereas the remaining channels are generally more stable. Overall, although the IR channels involve a more complicated Planck-function-based conversion (see Eqs. A20 and A21), they are comparatively more stable and thus more suitable for TL applications. This is largely because onboard blackbody calibration constrains the radiometric biases of most IR channels to within about 0.5 K (Min et al., 2022; He et al., 2021), leading to perturbations of a similar magnitude. Relative to typical observed BTs of around 270 K, this corresponds to a relative error of only about 0.2 %, which is much smaller than that in the solar reflective channels (about 2 %–5 %).

Lin et al. (2025) developed CLANN (Cloud Amount Neural Network), a ML framework designed to retrieve three-dimensional (3D) cloud amount profiles from observations acquired by the FY-4A geostationary meteorological satellite passive imager, with important applications in cloud climatology and weather analysis (Lin et al., 2025). The model integrates multi-channel observations from FY-4A/AGRI, including VIS/NIR (0.47, 0.66, and 0.86, 1.38, 1.61, and 2.25 µm), and IR channels (3.75, 6.25, 7.10, 8.60, 10.80, 12.00 µm), together with reanalysis-based environmental predictors. CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations)/CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) cloud products from 1 March 2018 to 31 December 2020 were used as the reference for model training and independent evaluation. In essence, CLANN learns the vertical distribution of cloud amount from collocated passive-sensor radiances and environmental fields, thereby extending 3D cloud information beyond the narrow swath of active sensors. Validation results showed a correlation coefficient of 0.73 for cloud amount profile retrieval. In addition, the cloud-amount-weighted height derived from CLANN agreed well with CALIOP, with an RMSE of approximately 1.88 km and a correlation coefficient of 0.92. Feature-importance analysis further indicated that AGRI water-vapor-band observation BTs and upper-tropospheric temperature are among the most influential predictors for improving CLANN retrieval skill (Lin et al., 2025).

FY-4B did not enter operational service until December 2022 (Xia et al., 2025). By the time reliable FY-4B/AGRI observations became routinely available, CALIPSO observations had largely ceased in the second half of 2023, leaving only a limited period of effective overlap between FY-4B/AGRI and CALIPSO (approximately June 2022 to March 2023). Consequently, previous work did not attempt to develop an FY-4B/AGRI-based CLANN retrieval model. Nevertheless, this limited overlap provides an opportunity for a targeted evaluation of the physics-constrained TL model using the available collocated FY-4B/AGRI and CALIPSO observations. In the first control experiment, FY-4B/AGRI observations from channels corresponding to those used in CLANN training were directly ingested into the FY-4A/AGRI-based CLANN model mentioned above (Lin et al., 2025) to retrieve cloud amount profiles. In the second sensitivity experiment, the newly developed TL models (Fig. 3 and Table S1) were applied to convert each FY-4B/AGRI channel observation, in either reflectance (VIS/NIR) or BT (IR) form (reference), into its FY-4A/AGRI-equivalent value (target), which was then used as input to the CLANN model for estimating cloud amount profile. Finally, independent CALIPSO observations from 1 June 2022 to 31 March 2023, were used to comprehensively and accurately evaluate the effectiveness of the TL model.

Figure 10 presents the cloud-amount-weighted mean height comparisons between CLANN (trained using FY-4A data) and CALIPSO based on FY-4B/AGRI observations, with and without the physics-constrained transfer learning model. As shown in Fig. 10b and c, the incorporation of the TL model produces a modest numerical reduction in RMSE of 0.08 km and increases the correlation coefficient from 0.841 to 0.851. Because the two correlations were calculated from the same 517 958 collocated CALIPSO–AGRI profile pairs and shared CALIPSO as the common reference variable, they were compared as dependent and overlapping correlations. The correlation between the retrievals obtained with and without TL was 0.927. At the individual-profile level, Zou's 99 % confidence interval for the increase in the correlation coefficient (ΔR= 0.010) was 0.0093–0.0107, excluding zero. Thus, the increase in R is statistically detectable at the profile level under the sampling assumptions of the test. However, neighboring profiles along the same CALIPSO track may exhibit spatial dependence, which was not explicitly accounted for in this analysis. The confidence interval should therefore not be interpreted as a fully dependence-adjusted assessment of statistical significance, and the reduction in RMSE is reported as a descriptive numerical change rather than a statistically significant difference. Although the R value remains lower than that achieved using FY-4A/AGRI data (R=0.92) (Lin et al., 2025), the results suggest a modest improvement within the available FY-4B validation period. In addition, cross-sectional cloud amount profiles for two representative cases (05:35 UTC on 8 June 2022, and 07:15 UTC on 21 June 2022) are presented in the middle and bottom panels, respectively. These cases qualitatively illustrate that the physics-constrained TL model can improve the representation of the vertical cloud amount distribution, but they are not regarded as independent evidence of statistical significance. The approximately 10-month validation period and the potential along-track dependence of neighboring profiles should be considered when interpreting the generalizability of these results.

We also evaluate the impact of the physics-constrained TL model on quantitative precipitation estimation (QPE) using a Multi-Task UNet model (Ronneberger et al., 2015) trained on four FY-4A/AGRI IR channels (C09, C10, C12, and C13 at 6.25, 7.10, 10.80, 12.00 µm), with GPM (Global Precipitation Measurement) IMERG (Integrated Multi-satellitE Retrievals for GPM) products as the reference (Skofronick-Jackson et al., 2017). The FY-4A-based model was trained and validated using observations from 2019, with data from May to August used as the primary training period and randomly selected days from each of the remaining months included to ensure seasonal representativeness across both the validation and inference stages. The study domain covered 90–130° E and 0–40° N. To assess cross-satellite generalizability, three independent FY-4B/AGRI observation cases were selected from the extrapolation period spanning June 2023 to August 2024, which was entirely outside the FY-4A training window. These cases include Case 1 on 11 July 2024 at 09:15 UTC, Case 2 on 10 August 2024 at 00:00 UTC, and Case 3 on 12 July 2024.

Figure 11a–c and d–f show the spatial distributions of QPE results for Cases 1 and 2 mentioned above, respectively, including GPM IMERG rain rates, the raw FY-4B model output, and the TL corrected FY-4B output. Without TL correction, the raw FY-4B model systematically underestimates precipitation in both cases, producing substantially lower rain rates than GPM IMERG. The corresponding CSI (Critical Success Index) values are 0.392 and 0.412 for Cases 1 and 2, respectively. After applying the physics-constrained TL, the predicted precipitation fields become much more consistent with GPM IMERG, with the CSI increasing to 0.498 in both cases. This improvement indicates a robust and reproducible enhancement in precipitation detection skill.

Figure 11g–i further evaluate model performance using the FY-4A in-domain latitudinal rain-rate profile and scatter-density comparisons between the FY-4B model estimates and GPM IMERG. The FY-4A in-domain baseline (Fig. 11g; 15 May 2019), selected from the primary training period, achieves a CSI of 0.537, confirming the expected performance of the retrieval model under the original FY-4A observation domain. For the raw FY-4B configuration (Fig. 11h), the model yields R (correlation coefficient) = 0.462, MAE (Mean Absolute Error) = 1.678 mm h⁻¹, and bias = -0.959 mm h⁻¹, indicating a systematic underestimation when the FY-4A-trained model is directly applied to FY-4B observations without correction. The underestimation of precipitation, especially for extreme rainfall intensities, is a common issue in AI-based QPE models (Kühnlein et al., 2014a). After TL correction (Fig. 11i), R increases to 0.475, MAE decreases to 1.564 mm h⁻¹, and bias improves to -0.450 mm h⁻¹, demonstrating a reduction in systematic error.

The latitudinal rain-rate profiles in Fig. 11j–l further confirm the improvement across all three cases. The raw FY-4B model consistently underestimates the precipitation structure represented by GPM IMERG, whereas the transfer-learning-corrected FY-4B output better captures the overall latitudinal variability. The consistent improvement across Cases 1–3, which were selected from the FY-4B extrapolation period and span different months and meteorological conditions, demonstrates that the physics-constrained TL model can effectively recover the retrieval capability of the FY-4A-trained model when applied to FY-4B observations.