Estimation of Top-of-Atmosphere Longwave Cloud Radiative Forcing Using FengYun-4A Geostationary Satellite Data

1. Introduction

Assuming that the climate system is in balance, the solar radiation will be exactly equal to the longwave radiation emitted into space [1]. Radiative forcing refers to any external factor that has the potential to disturb this balance and, consequently, alter Earth’s climate. Cloud radiative forcing (CRF) refers to the influence that clouds have on Earth’s atmospheric system; this is a key concept in climate science and is a valuable tool for quantifying and comparing the potential impacts of various human and natural factors on the climate [2]. Understanding the mechanisms behind CRF is crucial for improving the predictive ability of climate models—at present, there is still a significant amount of uncertainty regarding the nature of cloud feedback mechanisms in current models [3]. Consequently, in-depth research on the role of clouds in atmospheric longwave radiative forcing is crucial for accurately predicting future climate change as well as developing effective climate policies and adaptation measures [4,5].

To obtain CRF, significant amount of research on surface and top-of-atmosphere radiation has been conducted using satellite data and model simulations [6,7,8,9]. The accuracy of CRF primarily depends on the accuracy of radiation components since the CRF can be estimated by the difference in radiation between all-sky and clear-sky conditions [10]. Ever since Fritz et al. (1964) proposed the first radiation retrieval algorithm based on satellite remote sensing, there’s been a significant amount of research into the the measurement of radiation using remote sensing, including estimates of surface and atmospheric longwave radiation [11]. Traditional atmospheric radiation algorithms mostly rely on empirical formulas for calculation, and tend to have poor generalizability [12]. Consequently, the theoretical algorithms based on remote sensing-derived radiation measurements are constantly being improved. These algorithms can be divided into several categories, including radiative transfer models (RTM) [13], parameter algorithms [14], machine learning algorithms [15], and lookup table (LUT) algorithms [16,17].

Several methodologies have developed with the increasing availibility of broadband and multispectral satellite observations from polar orbit or geostationary satellites. Satellites equipped with broadband-based instruments, include the Clouds and the Earth’s Radiant Energy System (CERES) [18], the Scanner Radiometer for Radiation Budget (ScaRab) [7] and the Earth's Radiation Budget Experiment (ERBE) [19] . These instruments use shortwave and longwave (or full-wave) broadband channels for scanning observations. Since these instruments observe the earth at a specific viewing direction, angular distribution models (ADM) or RTMs utilize input from atmospheric and surface characteristics from other sources to calculate the reflected shortwave radiation (planetary albedo) or emitted longwave radiation [20]. However, the application of these retrieval algorithms, which are based on physical radiation transfer mechanisms, is challenging as they are based on strict physical mechanisms and require high-precision atmospheric parameters as inputs. This may result in errors as well as insufficient temporal and spatial resolutions. Indeed, the broadband sensors installed on polar-orbiting satellites only have a 12- or 24-hour revisit time, as well as a spatial resolution that is still insufficient for several applications [21].

With the development of more precise methods of obtaining cloud observations, as well as the measurement of surface and atmospheric features using satellites, radiation methods based on multispectral narrowband sensors have become increasingly attractive. These products are more diverse and provide higher spatial resolutions, such as the Advanced Very-High-Resolution Radiometer (AVHRR), the High Resolution Infrared Radiation Sounder (HIRS) [22], the Communication Oceanography Meteorological Satellite (COMS) [23], and the Rotating Enhanced Visible and Infrared Imager (SEVIRI) radiometer on the Meteosat second-generation (MSG) satellite [24]. Since the values recorded by these detection channels represent only a part of the radiation and include the main factors that influence reflected or emitted radiation, measurements of reflected and emitted terrestrial radiation can be achieved through specific retrieval models composed of spaceborne narrowband infrared radiometers as well as a combination of one or more radiation spectral regions. However, current LUT methods typically depend on a single band, which may be insufficient to accurately distinguish complex atmospheric conditions [15].

Therefore, the integrated retrieval of radiation measurements based on multiple channels is widely expected to become a mainstream in the remote sensing industry [20]. In addition, there are still potential means of improving the spatiotemporal resolution and accuracy of CRF measurements. Machine learning methods represent the latest frontier in remote sensing retrieval, and are greatly suited to the handling of complex linear and nonlinear relationships. They can extract continuous and accurate spatiotemporal radiation measurements and have been increasingly adopted in radiation estimation in recent years [25]. In particular, the new generation of geostationary satellites, including FY-4, Himawari-8, GOES-R, and Meteosat-8, can capture long-term, wide-range, and continuous data about the state of the atmosphere [14]. These datasets are extremely useful for monitoring weather phenomena and recording extreme events for scientific analysis and simulation and will help to improve research on large-scale weather phenomena and disastrous weather conditions.

The objective of this study is to build a model capable of generating to estimate the top-of-atmosphere outgoing longwave radiation products under clear-sky conditions (OLR_clear) aimed at constructing LCRF_TOA dataset based on sensitivity analysis of the influence of atmospheric parameters on OLR_clear using the Santa Barbara DISORT Atmospheric Radiation Transfer (SBDART) RTM. Here, a highly efficient machine learning method is applied to estimate OLR_clear to further improve the spatiotemporal resolution of LCRF_TOA using FY-4A satellite. The final dataset can be used for energy budget studies as well as an analysis of the spatiotemporal changes of LCRF_TOA. The paper is organized as follows: Section 2 presents the RTM and satellite data used in this study, as well as the method used to estimate OLR_clear and, subsequently, LCRF_TOA. Section 3 introduces the sensitivity analysis based on the SBDART results and the verification of radiation measurements before the study is concluded in Section 4.

2. Data and Methods

2.1. Data

2.1.1. The SBDART Model

The atmospheric RTM used in this study is the SBDART model, an advanced numerical atmospheric RTM used to calculate the planar parallel radiation transfer in the Earth's atmosphere and at the surface under both clear-sky and cloud conditions [26]. The model accounts for important processes associated with the ultraviolet, visible, and infrared portions of the electromagnetic spectrum. It can be used for case studies and sensitivity analysis and is highly suitable for atmospheric radiation energy balance and remote sensing studies. This RTM model is based on the DISORT (Discrete Sequence Radiation Transfer) algorithm and can accurately simulate the scattering, absorption, and emission of solar radiation as well as longwave radiation.

SBDART accounts for various atmospheric components, including gases, aerosols, and clouds, while also considering the impact of characteristics that influence surface reflection. It is widely used in climate research, the interpretation of remote sensing data, atmospheric composition monitoring, and environmental assessment. It has been extremely important in understanding the radiation balance of the atmosphere, climate change, and atmospheric chemical processes. The SBDART model has been highly praised for its flexibility and accuracy in scientific research, and it is an important tool in atmospheric and earth science research.

The SBDART model has flexible calculation schemes, a high calculation accuracy, considers multiple influential factors, and provides rich output results. When calculating longwave radiation, it is necessary to consider the interaction between the optical properties of various components in the atmosphere and radiation, including gases, clouds and aerosol. These components have different optical properties at different wavelengths; consequently, their presence can affect radiation transfer. To obtain accurate simulations, RTMs require parameter input from meteorological and atmospheric composition observations, such as the vertical structure of the atmosphere, temperature, humidity, and cloud cover. These data are usually obtained from meteorological observations or the outputs of meteorological models. By simulating the process of radiative transfer, researchers can understand and measure the distribution of radiation within the atmosphere, the solar radiation received at the surface, and the outward release of terrestrial radiation. These measurements are an important foundation for the interpretation of remote sensing data and climate change research [27].

2.1.2. ERA5 Reanalysis Data

The ERA5 dataset is a global climate and weather reanalysis dataset provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). It provides data on atmospheric, land surface, and oceanic variables at an hourly temporal resolution and a spatial resolution of approximately 25 kilometers, with data available from as early as 1979 [28]. The ERA5 dataset utilizes observations from hundreds of satellite and ground observation datasets, generated through advanced numerical weather forecasting models and data assimilation systems, and aims to provide high-quality, assimilated, and consistent global data for climate research, weather forecasting, and environmental monitoring. Users can access the Climate Data Store and obtain ERA5 data through their official website (https://cds.climate.copernicus.eu/). The ERA5 skin temperature and water vapor product used in this study is provided by the ECMWF as part of its fifth generation global climate reanalysis project, which provides hourly data at a global scale. These data reflect real-time temperature and water vapor conditions on the Earth's surface and can be applied to studies involving energy balance, climate change, weather patterns, environmental monitoring, and agriculture.

2.1.3. Satellite Data

(1)

FY-4A

FY-4A satellite is an advanced geostationary satellite operated by the National Meteorological Satellite Center of China (NSMC). It is the fourth-generation meteorological satellite from the FengYun satellite series and was successfully launched on December 11, 2016 [29]. The Advanced Geosynchronous Radiation Imager (AGRI), one of the main payloads on the satellite, has multispectral imaging capabilities at a high temporal and spatial resolution. AGRI is capable of global imaging every 15 minutes and regional imaging every 5 minutes at a spatial resolution ranging from 0.5 kilometers (in the visible spectrum) to 4 kilometers (in the infrared channels). The varying spatial resolutions at different wavelenghs are an attempt to balance the need for spatial coverage and highly detailed maps, allowing AGRI to continuously monitor the Earth on a global scale while still capturing subtle changes in key areas. This mission has been instrumental in improving the quality of meteorological services and supporting scientific research. In general, the deployment of the FY-4A/AGRI marks an important step in Chinese geostationary meteorological observation technology, and provides strong technical support for global meteorological services, as well as disaster prevention and environmental monitoring initiatives.

The paper used the infrared channels (6.25–13.5 µm) obtained from AGRI to estimate OLR_clear. These data have undergone basic processing such as signal correction and data formatting. The outgoing longwave radiation and cloud top height products from FY-4A were downloaded from the NSMC website (http://www.nsmc.org.cn/).

(2)

CERES

The CERES sensor is a satellite instrument developed as part of NASA’s Earth Observing System (EOS) program. CERES has three main data products: Single Scanner Footprint (SSF), Synaptic TOA and surface fluxes and clouds (SYN), and Energy Balanced and Filled (EBAF). These data help scientists understand the Earth's energy balance and how clouds, aerosols, and greenhouse gases can affect this balance [30]. These data are available from the official CERES website (https://ceres.larc.nasa.gov/data/).

This paper uses the SYN global radiation product with a temporal resolution of 1 hour and a spatial resolution of 100 km. Its radiation products are mainly based on cloud, aerosol, and atmospheric gas data that is processed using an improved Fu Liu RTM [18]. At present, the accuracy of CERES-SYN's radiation products has been fully validated by surface measurement data and has been widely used for comparison against other radiation products [16,17]. The CERES Level III SYN radiation product (version 4.1) was used to comprehensively validate the final LCRF_TOA results.

2.2. Research Methods

2.2.1. ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ Algorithm

The ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ quantifies the changes in net longwave energy at the top of the atmosphere due to the presence of clouds, specifically, these changed are dependment on the macro- and micro-physical properties of clouds [20]. Positive radiative forcing often warms the Earth's surface by capturing more heat, while negative radiative forcing results in global cooling by allowing more energy to escape into space. The universal formula used to calculate radiative forcing is as follows [31]:

$$\mathrm{C}\mathrm{R}\mathrm{F}={\mathrm{F}}^{\downarrow }\left(\mathrm{a}\mathrm{l}\mathrm{l}\right)-{\mathrm{F}}^{\uparrow }\left(\mathrm{a}\mathrm{l}\mathrm{l}\right){-\mathrm{F}}^{\downarrow }\left(\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}\right)+{\mathrm{F}}^{\uparrow }\left(\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}\right)$$

(1)

In equation (1), “F(all)” and “F(clear)” refer to the radiative flux under all-sky and clear-sky conditions, respectively. Since the downward longwave radiation at the top of the atmosphere is negligible, the formula for calculating the CLRF_TOA can be simplified as follows:

$$\begin{gathered} {\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}={\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}^{\uparrow }\left({\mathrm{L}\mathrm{W}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}\right)-{\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}^{\uparrow }\left({\mathrm{L}\mathrm{W}}_{\mathrm{a}\mathrm{l}\mathrm{l}}\right) \\ {\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}={\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}-{\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{a}\mathrm{l}\mathrm{l}} \end{gathered}$$

(2)

In equation (2): ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{a}\mathrm{l}\mathrm{l}}$ refers to outgoing longwave radiation under all-sky conditions, which can obtained from publicly available FY-4A satellite products. This section describes the algorithm used to generate ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ values.

${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ refers to radiation exchange under clear-sky conditions (i.e., without cloud obstruction) such that the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ of clear-sky pixels is 0. Radiation under clear-sky conditions in pixels with clouds must be calculated as if the clouds in that pixel did not exist, i.e., ignoring the influence of cloud parameters. Consequently, this requires simulating the physical processes of radiation transfer in the atmosphere. To accomplish this, the parameter settings for clouds are first turned off in the RTM such that only non-relevant cloud parameters, such as surface temperature, surface albedo, water vapor, and ozone content, are considered. Based on the sensitivity analysis conducted using SBDART, the input parameters in the algorithm include water vapor column, surface temperature, and all infrared channels from AGRI; ERA5 ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ data was selected as the benchmark for this algorithm. In this study, Extreme Random Trees (ERT) were selected as the machine learning method of choice for improved computational efficiency. ERT is an ensemble classification method that introduces more randomness to the Random Forest methods, which increases the diversity of the model. The goal of ERT is to improve the overall generalizability of the model by increasing its diversity and reducing its variance. This approach is particularly effective in dealing with high-dimensional data and complex feature interactions [32]. A training dataset comprising 3 million observations from the 5th and 15th of every month in 2019 from ERA5 ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ was selected (there were no abnormalities in the quality of the data in the product). We preprocessed the matched data, which included scaling the data and partitioning the dataset into the training, validation, and testing sets. 10% of the data was used as an independent validation set and was not used to train the machine learning model. This ensured the independence of the validation data and the reliability of any validation tests carried out on the model. Finally, a non-linear regression relationship between input parameters and predicted values (${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ ) was constructed to calculate the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ .

2.2.2. Evaluation Metrics

The following metrics were used to assess the performance of the model developed in this study: Correlation coefficient (R), evaluation bias (MBE), and root mean squared error (RMSE).

(1)

The correlation coefficient is used to represent the linear correlation between the predicted values and the actual data and is calculated as follows:

$$\mathrm{R}=\frac{\sum _{i=1}^n\left(x_{\dot{i}}-\overline{x}\right)\left(y_i-\overline{y}\right)}{\sqrt{\sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2\sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(3)

(2)

The RMSE represents the error between the retrieved parameter values and the actual data: the smaller the RMSE, the smaller the error between the two values. The RMSE is calculated as follows

$$RMSE=\sqrt{\frac{\sum _{i=1}^n{\left(x_i-y_i\right)}^2}{n}}$$

(4)

(3)

The MBE represents the degree to which the parameter values approximate the real data as well as the direction of the deviation between predicted and true values. The MBE is calculated as follows

$$MBE=\frac{1}{\mathrm{n}}\sum _{i=1}^n{(x}_i-y_i)$$

(5)

In the formula obve, n is the number of samples; x_i represents the reference value (i.e., the true value of the parameter retrieved result); and y_i represents the predicted result.

While RMSE reflects the overall error between predicted and true values, MBE reflects the direction in which the predicted values differ from the true values: When MBE is positive, the predicted values overestimate the target variable, and when MBE is negative, the predicted values underestimate the retrieved result. The value of R ranges between 0 and 1, where higher values indicate a strong correlation between the predicted and true values. Figure 1 illustrates the process of model construction.

3. Results

3.1. Sensitivity Analysis Using SBDART

3.1.1. Total Water Vapor Column

Atmospheric parameters are essential physical quantities that characterize atmospheric conditions. They play a pivotal role in understanding meteorological and climatic phenomena, making weather predictions, and advancing atmospheric science research. The most important atmospheric parameter in the context of longwave radiation is the total water vapor column (TWVC), which refers to the total amount of water vapor in the atmosphere, usually expressed in specific regions or vertical columns. This parameter includes the entire height and all types of water vapor in the atmosphere, including water vapor, liquid water droplets, and ice crystals. The sensitivity of longwave radiation to changes in water vapor levels is crucial for understanding how changes in atmospheric water vapor affect climate change and its feedback mechanisms.

An increase in TWVC enhances the absorption of longwave radiation. Water vapor molecules are particularly effective in absorbing infrared radiation, especially at wavelengths associated with thermal radiation. Figure 2 shows the changes in longwave radiation irradiance (W/m²/μm) corresponding to different TWVC between 0–100 g/cm² at wavelengths between 3–30 μm, and the values in parentheses in the legend represent the integrated radiation flux values for all bands (equal to ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ ). It can be seen that lower TWVC result in higher values of ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ . The difference in the maximum and minimum radiation values is 82 W/m² (from a minimum of 160 W/m² to a maximum of 242 W/m²). The impact of TWVC on ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ is significant and must be included in the input parameters of the ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ algorithm. Higher levels of TWVC also increase the strength of greenhouse effects by capturing more heat in the atmosphere. In contrast, lower water vapor concentrations can lead to the reduced absorption of longwave radiation, allowing more infrared radiation to escape into space, and resulting in enhanced atmospheric radiative cooling. Thus, the impact of water vapor on longwave radiation is a key factor in climate modeling.

3.1.2. Atmospheric Profiles

In the context of RTMs, the atmospheric profile refers to the variation of several physical atmospheric characteristics with altitude, including temperature, humidity, and pressure. Because these physical atmospheric parameters directly affect the absorption, emission, and scattering of radiation, measuring and analyzing atmospheric profiles can help researchers understand the vertical structure of the atmosphere and reveal differences in meteorological and climatic processes at different altitudes. This information is crucial for simulating and understanding the mechanisms behind radiation transfer processes. Generally, RTMs use built-in atmospheric profile data. Figure 3 presents the impact of different atmospheric profile models on longwave radiation irradiance (W/m²/μm) at wavelengths between 3–30 μm, with each color representing one of six SBDART atmospheric profile models. The figure shows that the tropical model has the highest ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ , followed by the mid-latitude summer, mid-latitude winter, high-latitude summer, high-latitude winter, and the US standard models in descending order. Tropical regions usually have a high incidence of solar radiation, resulting in relatively high surface temperatures; consequently, more longwave radiation is emitted from the surface. In addition, the atmosphere above tropical regions is usually characterized by high water vapor contents and high cloud coverage, which are factors that have a significant impact on ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ .

3.1.3. Surface Temperature

Another influential parameter on ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ is surface temperature. Surface temperature has a strong influence on the radiation balance of the Earth system. Increases in surface temperature lead to increases in the intensity of surface radiation and, consequently, stronger ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ . Figure 4 presents the variation in longwave radiation irradiance (W/m²/μm) with surface temperature (K) at wavelengths between 3–30 μm. Surface temperatures between 210–330 K were used for this assessment, as this represents the general range of surface temperatures that would be expected on Earth. The figure shows that higher surface temperatures result in greater ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ . The impact of surface temperature on atmospheric longwave radiation is evident and must be included in the input parameters. The changes in surface temperature can also alter the intensity and wavelength of transmitted radiation, which affects the distribution and characteristics of atmospheric longwave radiation.

3.2. Validation

3.2.1. Quantitative Verification of ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$

This study used monthly data from 2018 to quantitatively evaluate the ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ obtained from the AGRI instrument. Figure 5 compares the ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ values obtained from our algorithm with the ERA5 data recorded in April, August, and December 2018. The results showed that the correlation coefficients of the relationship between the ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ and ERA5 values were 0.92, 0.94, and 0.93 for April, August, and December 2018, respectively. The corresponding MBE and RMSE for each month were 1.87 W/m² and 5.64 W/m² in April, 1.43 W/m2 and 4.66 W/m2 in August, 1.46 W/m2 and 4.84 W/m² in December, respectively. These results suggest that the ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ values obtained from the AGRI instrument were very close to the values recorded by international mainstream products, and can thus be effectively applied to AGRI data from other international and domestic satellites. In addition, FY-4A has a better spatiotemporal resolution compared to ERA5, allowing for improved capturing of subtle changes. The ERT-based ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ product developed in this study has thus been shown to have high accuracy and has been validated against ERA5 observations, which indirectly validates the accuracy of any calculated ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values.

3.2.2. The Spatial Distribution of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ Results

To validate the detailed spatial distribution of${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ estimates made by the algorithm, the predicted values were compared with different products in smaller localized areas. Figure 6 compares the ERA5, CERES, and the estimated values of${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ in two selected subregions. The fact that the low value of OLR in these areas is due to the absorption of longwave radiation from the surface by clouds and the lower temperatures at the cloud top, resulting in lower OLR. Figure 6 shows that the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ in all three products has relatively similar spatial distributions. It should be noted that the spatial resolution of CERES products is 100 km, making it difficult to distinguish the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ in these local areas. While the spatial resolution of the ERA5 reanalysis data is better than the CERES products (25-km resolution), its resolution is still relatively coarse. The inversion results obtained by the algorithm developed in this study not only match well with the spatial distribution of the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ results obtained from CERES but also have a spatial resolution of 4 km, which is significantly better than the ERA5 products. The results of our quantitative evaluation also confirm that the inversion results obtained by our model are closer to the CERES data compared to the ERA5 products and that the accuracy of the product is relatively high. Figure 6 also shows that the resolution of the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ product obtained by the algorithm is significantly higher than the other two products, just to detect changes in ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ in greater spatial detail. In general, the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ products from the algorithm developed in this study have a wide coverage, a high spatial resolution, and a 24-hour revisit time, providing insights into the study of top-of-atmosphere radiation energy balance.

Long-term trends in radiation levels can be identified by analyzing daily and monthly averages, which can provide researchers with a deeper understanding of the Earth's energy balance, help monitor climate change processes, and validate meteorological and weather models. Three months’ worth of OLR under all-sky and clear-sky conditions were obtained from the ERA5 and CERES websites and used to calculate the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values for these months. Figure 7 shows the spatial distribution of the daily mean ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values on 1^st April, 1^st August, and 1^st December 2018 as calculated by our algorithm, as well as the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values calculated from ERA5 and CERES data during the same period. Once again, the spatial distribution of the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values calculated by our algorithm has strong similarities with the results generated by the ERA5 and CERES products. Figure 8 shows the spatial distribution of the monthly average ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values in April, August, and December 2018 as calculated by our algorithm, ERA5, and CERES data. This figure highlights the stable and reliable results obtained by our model, with ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values ranging between 0–100 W/m² over monthly timescales. Figure 8 also shows that clouds have a positive feedback effect on warming, with ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values ranging from 0–100 W/m². For example, Australia is located in the southern hemisphere and belongs to a semi-arid and arid climate. Here, the air is relatively dry, and the relatively low water vapor content leads to less cloud formation. Consequently, the Australian region experiences low ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values across all seasons.

3.3. Analysis of ${LCRF}_{TOA}$ Changes

3.3.1. Analysis of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ Changes due to Varying Clouds Heights

Clouds at different heights can affect the absorption, reflection, and emission of longwave radiation, and their ability to regulate atmospheric radiation varies greatly; consequently, clouds at different heights have a strong impact on ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values. A deeper understanding of the changes in ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ caused by different cloud heights will help researchers achieve a greater understanding of the dynamic processes of the climate system, supporting research in meteorology and climate modeling, and helping to address climate change. Figure 9 presents the diurnal variation and frequency distribution of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ during periods of high-, medium-, and low-height clouds in different months in 2019. High-height clouds are mainly composed of ice crystals with high albedo, while low-height clouds are usually composed of water droplets with relatively low albedo. Therefore, the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values are highest during periods of high-cloud conditions, followed by medium- and low-height clouds (Figure 9). This suggests that high-height clouds have the greatest impact on positive radiative forcing. Figure 9 also shows that the range of radiation forcing for clouds of each height is relatively small even over monthly timescales. The (b) column of Figure 9 shows the frequency distribution of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values under different cloud conditions, with the peak density distribution of high-height clouds found at the higher range of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values. In contrast, the density distribution curve of the middle-height clouds has a broader peak that falls between the middle range of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values, while low clouds have a sharper peak at the lower range of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values. These results suggest that high-height clouds exert a greater degree of radiative forcing more frequently, while low-height clouds are more frequently found in the lower forcing range.

3.3.2. Extreme Event Analysis

The high spatiotemporal resolution radiation of the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ products presents significant advantages for extreme event analysis. These advantages help researchers better understand, monitor, and respond to extreme weather and climate events, which include typhoons, rainstorms, high temperatures, droughts, and floods. These events can significantly change the dynamics and thermodynamic processes of the atmospheric system and have direct and indirect effects on the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ . For example, rainstorms may lead to a sharp increase in water vapor content in the atmosphere, while also resulting in a wider range of cloud cover. Extreme high-temperature events and extreme low-temperature events can both affect the temperature distribution of the atmosphere, which could potentially lead to increases in surface temperature, changes in the vertical distribution of atmospheric temperature, or the formation of an inversion layer. Due to the close relationship between radiation and temperature, these temperature changes have a direct impact on ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ .

Typhoons are an example of how high spatial resolution radiation data can be helpful for extreme event analysis. Typhoon systems are often accompanied by large-scale cloud clusters and precipitation, which have a strong impact on ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ . In the path of a typhoon, increases in cloud cover lead to a decrease in top-of-atmosphere longwave radiation. Figure 10 shows the distribution of ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values at different spatial resolutions in typhoon areas at 00:00, 04:00, 08:00, 12:00, 16:00, and 20:00 UTC on October 1, 2018. The figure clearly shows that the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ changes several times throughout the day due to changes in cloud cover and other atmospheric conditions. The comparison of two sets of images shows that the distribution of the typhoon eyes can be clearly distinguished in the high-resolution images generated by the proposed algorithm, while the same cannot be said of the low-resolution images from the CERES product.

4. Discussion and Conclusions

This paper uses the SBDART model to simulate the entire process of how radiation passes through the atmosphere based on the principle of atmospheric radiation transfer. Sensitivity analyses were conducted on important factors such as surface temperature and total water vapor column, and the quantitative effects of these factors on ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ were calculated. Based on the results of the sensitivity analyses, a highly efficient machine learning method was used to estimate ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ using infrared channels from the AGRI instrument onboard the FY-4A geostationary satellite and was validated against the ERA5 reanalysis data. The FY-4A-based ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ product was intended to provide highly accurate ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ data at higher spatiotemporal resolutions. The correlation coefficient between the instantaneous ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ values obtained by the proposed algorithm and the corresponding ERA5 product was 0.93 with an RMSE of 5.04 W/m² and MBE of 1.58 W/m². In addition, the calculated ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ results were compared to the instantaneous, daily average, and monthly average ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ values obtained from ERA5 and CERES observations. The results show that the ${\mathrm{L}\mathrm{C}\mathrm{R}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ product generated from the proposed ${\mathrm{O}\mathrm{L}\mathrm{R}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{r}}$ algorithm had similar spatial distributions to the mainstream products, and had a reasonable degree of agreement with the internationally recognized high-precision CERES radiation results. These results highlight the effectiveness and generalizability of the algorithm to both international and domestic satellites.