Estimation of Land Surface Temperature from the Joint Polar-Orbiting Satellite System Missions: JPSS-1/NOAA-20 and JPSS-2/NOAA-21 †

: The accurate estimation of land surface temperature (LST) is a vital parameter in various fields, such as hydrology, meteorology, and surface energy balance analysis. This study focuses on the estimation of LST using data acquired from Joint Polar-Orbiting Satellite System (JPSS) satellites, specifically JPSS-1/NOAA-20 and JPSS-2/NOAA-21. The methodology for this research centers on the utilization of the split-window algorithm, a well-established and recognized technique renowned for its proficiency in extracting accurate land surface temperature (LST) values from remotely sensed data. This algorithm leverages the differential behavior of thermal infrared (TIR) radiance measured in two adjacent spectral channels to estimate LST, effectively mitigating the influence of atmospheric distortions on the acquired measurements. To establish the accuracy of the proposed approach, the coefficients of the split-window algorithm were determined using linear regression analysis, utilizing a dataset generated via extensive radiative transfer modeling. The calculated LST values were subsequently compared with LST products provided by the National Oceanic and Atmospheric Administration (NOAA). The evaluation process encompassed the computation of root mean square error (RMSE) values, offering insights into the performance of the algorithm for both JPSS-1/NOAA-20 and JPSS-2/NOAA-21 missions. LST retrieval validation with standard atmospheric simulation indicates that the JPSS-1/NOAA-20 and The JPSS-1/NOAA-21 algorithms have demonstrated an accuracy of 1.4 K in retrieval of LST with different errors. The obtained results demonstrate the potential of the split-window algorithm to effectively estimate LST from JPSS satellite data. The RMSE values, 2.05 and 1.71 for JPSS-1/NOAA-20 and JPSS-2/NOAA-21, respectively, highlight the algorithm’s capability to provide accurate LST estimates for different mission datasets. This research contributes to enhancing our understanding of land surface temperature dynamics using remote sensing technology and showcases the valuable insights that can be gained from JPSS missions in monitoring and studying Earth’s surface processes.

Surface emissivity corresponds to the radiative flux of thermal radiation emitted by a surface element.It is crucial for determining the thermal radiation from the Earth's surface and is a fundamental parameter that influences the accuracy and efficiency of LST retrieval.
Hence, fluctuations in atmospheric transmittance are closely linked to the dynamics of water vapor content within the atmospheric profile for thermal channels [28].In this paper, we compared operativity, performance, and effectivity of Joint Polar-Orbiting Satellites JPSS-1/NOAA-20 and JPSS-2/NOAA-21's algorithms for retrieving LST NOAA data [37].

The Radiative Transfer Equation Role in Land Surface Temperature Estimation
The radiative transfer equation represents a fundamental principle, used in various fields of science and engineering, including astrophysics, atmospheric science, remote sensing, and heat transfer.It describes the transport of radiant energy such as electromagnetic radiation through a medium.
The equation is particularly useful for understanding how energy is absorbed, scattered, and transmitted as it interacts with particles or substances within a medium.
In clear-sky conditions, the top-of-atmosphere radiance recorded with a space-borne sensor L sensor,λ comprises contributions from the surface emission.The atmospheric, upwelling and downwelling radiance L ↑ atm,λ and L ↓ atm,λ is reflected by the ground surface and attenuated by the atmosphere (Equation ( 1)).The retrieval algorithms depend on one or more top-of-atmosphere spectral measurements to account for atmospheric effects and estimate LST.
where B(Ts) refers to blackbody radiance as defined by Planck's law, Ts represents the land surface temperature, and ε λ stands for the land surface emissivity.The Visible Infrared Imaging Radiometer Suite (VIIRS) LST is established through comparisons with ground-based measurements and LST products from other instruments, particularly the NOAA series of LST products.

LST Inversion Techniques
Obtaining atmospheric parameters from in situ radiosoundings and using radiative transfer are common approaches in remote sensing and atmospheric science.These atmospheric parameters are essential for correcting remote sensing data, particularly for estimating land surface temperature accurately.
The atmospheric parameters are acquired through in situ radiosoundings and the utilization of radiative transfer codes, such as MODTRAN [38].Equation (1) has the potential to calculate Ts by inverting Planck's law.The inversion of Equation ( 1) can be achieved by correcting for atmospheric and emissivity effects.
The atmospheric parameters were derived from the Operational Vertical Sounder (TOVS) Thermodynamic Initial Guess Retrieval (TIGR3) database [39] and simulated using the MODTRAN model.

Split-Window Algorithm for Land Surface Temperature Estimation
The SW algorithm is a widely used method for estimating land surface temperature (LST) based on remote sensing data in the thermal infrared region and depends on the differential absorption characteristics of two thermal infrared channels.
The SW algorithm applies quadratic combination of brightness temperatures to calculate LST [39].It estimates LST by exploiting the distinct atmospheric absorptions in two adjacent thermal infrared spectral regions, assuming known emissivity.SW algorithm coefficients are sensitive, affected by changing total column water vapor (WVC) and various viewing angles [19,34,36].
The SW algorithm has been widely used by researchers to retrieve both sea surface temperature (SST) and land surface temperature (LST) from remote sensing data.In this paper, the two-channel algorithm proposed by [36] has been used, which takes into account the emissivity and water vapor effects.
The formula of the SW algorithm is as follows: In this formula, Ts represents the surface temperature (in Kelvin), T i and T j are the brightness temperatures from different thermal channels (in Kelvin), ε is the mean effective emissivity, ∆ε is the emissivity difference, w is the total atmospheric water vapor (in grams per square centimeter), and c 0 to c 6 denote the SW coefficients.

MODTRAN for Simulating Atmospheric Parameters
The atmospheric parameters' determination is completed through simulations that account for local atmospheric conditions, particularly water vapor content.These simulations establish the relationship between atmospheric transmittance and water vapor content and are conducted using atmospheric modeling software like MODTRAN (MODerate spectral resolution atmospheric TRANsmission).MODTRAN is widely employed in the fields of remote sensing and atmospheric research to calculate anticipated brightness temperatures for specific thermal channels on JPSS-1/NOAA-20 and JPSS-2/NOAA-21 satellites.MODTRAN serves as a well-established tool for modeling the radiative transfer of electromagnetic radiation through Earth's atmosphere.
Temperature profiles were meticulously derived from radiosoundings, originating from the Television InfraRed Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) Thermodynamic Initial Guess Retrieval (TIGR3) database [39].These calculations spanned a wide spectrum of temperature gradients.
Furthermore, the calculations encompassed various viewing angles, a comprehensive range of atmospheric-water-vapor values, and 100 distinct emissivity values obtained from spectral responses of diverse surface types available in the Advanced Spaceborne Thermal Emission Reflection Radiometer (ASTER) spectral library [40].
The MODTRAN outputs provide essential atmospheric parameter values: atmospheric transmittances, atmospheric upwelling and downwelling radiances.These values are acquired through mathematical convolution employing two filter functions that correspond to the thermal infrared channels of the JPSS-1/NOAA-20 and JPSS-2/NOAA-21 satellites.

Numerical Coefficients and Sensitivity Analysis
The SW algorithm coefficients refer to the parameters used in the SW algorithm for estimating LST from TIR remote sensing satellite.These coefficients are crucial for the algorithm, as they are used in the mathematical equations to convert the observed radiance values into LST values.
The coefficients in Equation (1) were calculated through the minimization of simulations from a constructed database for the JPSS-1/NOAA-20 and JPSS-2/NOAA-21 satellites.
To assess the influence of individual error sources on the SW algorithm, a sensitivity analysis was conducted.This analysis aimed to evaluate the algorithm's performance across a range of meteorological conditions and land cover types: The total error in LST is calculated from elementary errors: the algorithm standard deviation, the impact of uncertainties in at-sensor temperatures, land surface emissivity, and atmospheric water vapor.

Analysis of Split-Window Algorithm Coefficients and Sensitivity Results
Sensitivity analysis, which includes factors such as land surface emissivity, channel noise, water vapor, is a crucial element in the assessment of the performance and precision of LST retrieval algorithms.
The SW coefficients present in Table 1 were obtained from regressions methods for the JPSS-1/NOAA-20 and JPSS-2/NOAA-21 satellites.Table 2 illustrates the impact of minimization errors for JPSS-1/NOAA-20 and JPSS-2/NOAA-21 in Kelvin (K).The respective values are 1.09K and 1.07 K, with corresponding correlation coefficients (R) of 0.91 and 0.93.Additionally, there are noise-induced errors of 0.23 K and 0.22 K, as well as errors attributed to atmospheric-water-vapor content uncertainty, which amount to 0.04 K and 0.02 K.When accounting for a 1% uncertainty in surface emissivity, the LST total error is 1.75 K and 1.67 K for JPSS-1/NOAA-20 and JPSS-2/NOAA-21, respectively.If the surface emissivity uncertainty is reduced to 0.05%, the total error becomes 1.30 K and 1.26 K for the two respective satellites.

Split-Window Algorithm Validation
Validation methods are essential for assessing whether land surface temperature (LST) data conform to the specified standards or accuracy requirements.Ground-based validation is a common approach that involves comparing remote sensing-derived LST values with measurements collected on the ground.This method has been widely employed to validate LST products.
Sensitivity analysis serves to evaluate the impact of potential errors in the SW algorithm retrieval.Additionally, validation is imperative to discover the algorithm's alignment with real-world LST values.In this study, two distinct validation methods were employed: standard atmospheric simulations and ground truth datasets supplied by [41].
Two homogeneous surface sites located in Australia were used for LST validation; their geolocation and surface type are presented in Table 3.The mean emissivity was given by Prata in [41] of 0.98 for both sites.The AD592 solid-state temperature transducers were employed to perform in situ temperature measurements at both sites.Detailed information about the functioning of these devices is provided by [42].
Table 4 presents the validation for NOAA algorithm series in comparison to the ground truth dataset.The last column of the table provides the RMSE values for the algorithms when applied to the total data acquired at the sites, Hay and Walpeup.The results demonstrate the successful derivation of an LST NOAA series using these algorithms, characterized by mean difference values of 1.10 K for JPSS-1/NOAA-20 and 0.97 K for JPSS-2/NOAA-21, respectively.Additionally, these algorithms yield LST data with a standard deviation of approximately 2.05 K for JPSS-1/NOAA-20 and less than 1.71 K for JPSS-2/NOAA-21 at both the Hay and Walpeup sites.
The analysis results demonstrate the SW capability to generate LST RMSE values ranging between 1.61 K and 1.96 K for the Hay and Walpeup locations (NOAA11 dataset) and between 1.71 K and 2.05 K for the Hay and Walpeup locations (NOAA12 dataset).Furthermore, Figure 1 shows good matching between the NOAA-20 and NOAA-21 retrieved LSTs and the measured ones, with a correlation coefficient of 0.98.The satisfactory performance of the JPSS algorithms during the validation process, utilizing datasets, underscores the algorithm's capability to deliver precise land surface temperature (LST) estimations under well-defined atmospheric transmittances, ground emissivity, and atmospheric-water-vapor conditions.The accuracy of algorithms, establishes this as a favorable choice for applications involving the retrieval of LST from VIIRS satellites data.The satisfactory performance of the JPSS algorithms during the validation process, utilizing datasets, underscores the algorithm's capability to deliver precise land surface temperature (LST) estimations under well-defined atmospheric transmittances, ground emissivity, and atmospheric-water-vapor conditions.The accuracy of algorithms, establishes this as a favorable choice for applications involving the retrieval of LST from VIIRS satellites data.

Conclusions
The JPSS-1/NOAA-20 and The JPSS-1/NOAA-21 algorithms are used to retrieve LST in this study.The algorithms' coefficients were obtained from the atmospheric profiles' dataset simulation.The ground data was used to evaluate the algorithms.
The validation and comparison using the ground truth datasets from two Australian sites, confirm JPSS algorithm performances.Basing the RMSE of the retrieved LSTs on the measured data, the algorithm is very powerful in its LST calculation.The accuracy of LST retrieval is compared to that of NOAA-11 and 12.The algorithms have a higher accuracy with the ground truth dataset for NOAA-11 and 12 with precise in situ atmosphericwater-vapor contents.The sensitivity analysis validation, shows accuracy of 1.4 K in LST retrieval for the JPSS-1/NOAA-20 and JPSS-1/NOAA-21 algorithms.The accuracy of these algorithms is about 1.71 K and 2.05 for the ground truth dataset.

Table 3 .
Geolocation and surface type of the two sites.

Table 4 .
SW algorithms' validation using ground truth datasets.