## Data  
### HIRS OLR Data  
The HIRS sensor is an atmospheric sounding instrument that has been in operation on the NOAA series of satellites since 1978, with three types of HIRS instruments in use since 1982, namely HIRS/2 for NOAA 1-14, HIRS/3 for NOAA 15-17, and HIRS/4 for NOAA-18 and Metop-B [21]. The High-Resolution Infrared Radiation Sounder/4 (HIRS/4) comprises 19 infrared channels. A total of 12 thermal infrared channels (6.7-15 \(\upmu\)m) were defined as the longwave band, 7 near-infrared channels (3.7-4.6 \(\upmu\)m) were defined as the short-wave band, and 1 channel (0.69 \(\upmu\)m) was identified as visible [22]. Compared to HIRS/3, the latest HIRS/4 has a 10 km instantaneous field of view (IFOV) and a 20 km ground sample distance (GSD), facilitating increased instrument observations in cloud-free conditions. The HIRS instrument has a rich set of objects and is capable of acquiring data on ocean surface temperature, total atmospheric ozone, cloud top height, and coverage, water vapor distribution, and surface radiance [23].  
The HIRS OLR product was developed in the 1980s by [PERSON] et al. The unit of OLR values is W/m\({}^{2}\). If radiance data were available from several spectral intervals encompassing the entire spectrum at a given viewing angle, a first-order estimate of the OLR could be obtained by summing the radiance for each spectral interval. The estimation equation for the flux (OLR) was, therefore, chosen as a weighted sum of the HIRS radiance observations, given as:  
\[OLR=a_{0}+\sum_{k}a_{k}(\theta)N_{k}(\theta) \tag{1}\]  
where the _a_'s are regression coefficients, \(\theta\) is the satellite zenith angle, and \(N\) is the observed radiance which is related to the specific intensity \(I\) at wavenumber \(v\) and the instrument responsivity \(\phi\). \(N_{k}(\theta)\) is defined as:  
\[N_{k}(\theta)=\int_{\Delta v}I(v,\theta)\phi_{k}dv \tag{2}\]  
The outgoing flux for an axisymmetric atmosphere is related to the specific intensity as:  
\[OLR=2\pi\int_{0}^{\infty}dv\int_{0}^{\pi/2}I(v,\theta)\cos\theta\sin\theta d\theta \tag{3}\]  
The spectral intervals and the regression coefficients for (1) were determined with a stepwise regression analysis of calculations from a theoretical radiation model using 1600 soundings as input data. [PERSON] et al. [24] used multispectral regression technology to evaluate OLR values from four HIRS channels (channels: 3, 7, 10, and 12). The outgoing flux error of this method was about 4 times smaller than the error of NOAA using AVHRR to estimate flux. Because the spectral response function for channel 10 has changed in the HIRS instruments developed after HIRS/2, the algorithm used channels 3, 10, 11, and 12 [25].  
The \(1^{\circ}\times 1^{\circ}\) OLR data from the NOAA-18 satellite used can be downloaded from the National Centers for Environmental Prediction (NCEP) FTP server. The downloaded data were in a binary ASCII format with \"1\" for daytime data and \"2\" for nighttime data, and the daytime and nighttime data were in a 180 \(\times\) 360 array. We chose nighttime data for the study to minimize interference from solar radiation and human activity [23]. NOAA-18 satellite 1\({}^{\circ}\)\(\times\) 1\({}^{\circ}\) OLR data can be downloaded via NCEP's FTP server (ftp: //ftp.cpc.ncep.noaa.gov/precip/noaa18_1x1/) (accessed on 20 December 2022).