Spatial-Temporal Analysis of the Relationship Between Aerosol Optical Depth and Seasonal Land and Ocean Temperature Around Shanghai

. Few people use remote sensing data to simultaneously retrieve the seasonal changes in aerosol optical depth (AOD) on land and ocean, as well as its relationship with surface temperature. Aerosols, as one of the indicators of air pollution, directly or indirectly affect people's numerous activities. This article uses Terra satellite MODIS data as the data source and conducts AOD inversion work on the land and ocean areas around Shanghai, China based on IDL, 6S model, and dark pixel method. The results show that for land areas, the higher the surface temperature, the lower the AOD value, with summer being the most significant; On the ocean, the higher the ocean surface temperature, the greater the AOD value. This experiment provides a theoretical basis for the relationship between AOD and temperature, and confirms the possibility of retrieving ocean AOD from MODIS data.


Introduction
Remote sensing data is widely used in the inversion of ground objects and monitoring indicators due to its advantages such as large monitoring range, global coverage, instantaneous imaging, real-time transmission, fast processing, rapid acquisition of information and implementation of dynamic monitoring, and minimal impact from the ground. For example, research fields such as forest range monitoring, soil moisture inversion, and geological type classification have all formed relatively complete systems [1]. For this study, compared to traditional ground monitoring stations obtaining AOD data, the method of remote sensing data inversion is more time-saving and labor-saving.
Q. Guo, et al. successfully inverted land AOD using MODIS visible light bands, demonstrating the ability of MODIS data to invert AOD [2]. K.H. Lee, et al. proposed a novel land AOD inversion algorithm BAER based on MODIS data, which refined the results of land AOD inversion [3]. L. Mei, et al. improved previous algorithms based on OLCI data and developed a comprehensive new algorithm XBAER for land AOD inversion, expanding the range of remote sensing data for AOD inversion [4]. L. Mei, et al. conducted a good analysis of the spatiotemporal changes in global land AOD based on the dark pixel method, demonstrating the global monitoring capability of remote sensing data [5]. S.S. ROY, used ground observation data to statistically analyze the relationship between AOD changes over India and surface temperature, proving that there is indeed a connection between temperature and AOD [6].
According to previous research results, scholars lack research on AOD over the ocean, and there are few studies that link AOD with surface temperature. Due to the lack of fixed AOD measurement stations in the ocean, it is impossible to obtain real-time AOD data for specific areas. Therefore, it is necessary to use remote sensing data to invert AOD over the ocean and establish a relationship between it and surface temperature.
AOD is an important link in meteorological parameters, which is directly or indirectly related to many meteorological indicators. We processed MODIS images of land and ocean around Shanghai, used the dark pixel method and 6s model to simultaneously invert the AOD over land and ocean, and used remote sensing data to invert surface temperature, establishing a connection between the two. This study expands the application potential of MODIS data in retrieving AOD over the ocean, providing assistance and value for understanding AOD changes using temperature changes.

Site descriptions
The research area (27.846°N, 117.861°E -32.525°N, 124.695°E) is the surrounding land and marine area centered around Shanghai as shown in Figure 1. Shanghai is bordered by the river and the sea, and the coastal areas are mostly plains, which belong to the subtropical monsoon climate, showing the characteristics of monsoon and marine climate. Winter and summer alternate with cold and heat, with distinct four seasons. Spring and autumn are longer than winter and summer, with an average annual temperature of 15.8°C and moderate rainfall throughout the year. The surrounding land cities have a significant heat island effect, with a wide range of sources of AOD. The AOD over the surrounding oceans is greatly affected by coastal land.

Data and processing
NASA's MODIS is the main detection instrument for the EOS-AM1 series of satellites and the only Earth observation instrument directly broadcasted on the EOS platform, with 36 spectral channels and a spectral range of 0.4-14 μm [7]. The MODIS detector is mounted on two satellites, TERRA and AQUA, with a scanning width of 2330km and ground resolution of 250m, 500m, and 1000m, respectively. It can obtain global observation data once a day and has the characteristics of multispectral, wide coverage, and high resolution. The study used MYD021KM and MYD35_L2 data from TERRA satellites. Based on the 6s model and dark pixel method, the temperature and aerosol optical depth of the land and ocean around Shanghai were inverted, and the spatiotemporal distribution characteristics of AOD and temperature changes were analyzed.
The experimental process mainly includes geometric correction of angle data, geometric correction of reflectance, temperature inversion, establishment of LUT lookup table, cloud mask removal, and AOD inversion. The experimental process is completed based on IDL.

Principle of AOD inversion from satellite data
The inversion of AOD using satellite and ground-based remote sensing methods is mainly based on the process of solar radiation energy transmission to the surface, and its incident intensity and properties are changed by the scattering and absorption of atmospheric aerosol particles [8]. The optical characteristics of aerosol particles can be calculated by calculating the degree of change in solar incident radiation. If the apparent reflectance of the satellite remote sensing field of view angle received from the surface target is marked as ρ * , there is ρ * =πL/F 0 μ 0 , where L represents the radiation energy transmitted to the upper boundary of the atmosphere, F 0 represents the radiation energy transmitted to the outer section of the atmosphere in unit time, that is, the solar radiant flux outside the atmosphere, and μ 0 represents the cosine value of the angle between the solar incident light and the zenith direction, that is, the cosine value of the solar zenith angle, The correlation between the reflectance ρ * and the reflectance ρ of ground targets can be marked as: θv represents the angle between the zenith direction and the location and the satellite, which is the zenith angle of the observation field of the satellite remote sensing sensor. θs represents the angle between the solar incident light and the zenith direction, which is the zenith angle of the sun. φ represents the azimuth angle between the solar incident radiation and the scattered radiation in the observation field direction of the remote sensing sensor. ρ δ (θv,θs,φ) represents path radiation. F d (θs) represents assuming that the reflectivity of the ground target is zero, the sum of the solar radiation energy transmitted downward to the surface in unit time is the total normalized downward radiant flux. T(θ v ) represents the total transmittance when the radiation energy is transmitted upward into the observation field of the satellite sensor, and s represents the ratio of the backscattering section of the solar radiation transmission through the atmosphere to the incident light section, that is, the atmospheric backscattering ratio. In single scattering, aerosol optical depth ξ δ , aerosol scattering phase function ρ δ (θv,θs,φ), and single scattering albedo ω 0 determine path radiation, and their relationship is as follows: ρ δ (θv,θs,φ)= ρ m (θv,θs,φ)+ ω 0 ξ δ P δ (θv,θs,φ)/ (4μμ 0 ) (2) ρ m (θv,θs,φ) is the path radiation caused by molecular scattering, and μ 0 is the cosine value of the sensor zenith angle. As ω 0 、ξ δ 、P δ ultimately determines F d 、T、s, in order to reflect the aerosol optical depth ξ δ from the radiation values observed by the sensor, it is necessary to fully investigate the local climate and meteorological conditions to obtain an aerosol model with a more realistic ω 0 value and P δ value. By combining (1) with (2), we can obtain: From equation (3), when three geometric angles, ground reflectance, and aerosol modes are known, different ρ* can be calculated if different atmospheric AOD ξδ are given. If the apparent reflectance of the top layer of the atmosphere measured by the satellite sensor's observation field of view is consistent with the ρ* calculated by the formula, then the actual AOD is equal to the aerosol optical depth used to calculate ρ*.

Inversion of temperature
Although MODIS has 8 thermal infrared bands, the 31 and 32 bands are the most suitable for surface temperature inversion [9]. Based on in-depth research on the split window algorithm and the characteristics of MODIS data, M.F. Gao, et al. proposed a land surface temperature remote sensing inversion algorithm suitable for MODIS data, and its calculation formula is as follows: In the formula: T S is the surface temperature (K), T 31 and T 32 are the brightness temperature of the 31st and 32nd bands of MODIS respectively. Calculate based on the image DN values of these two bands; A 0 , A 1 and A 2 are parameters of the split window algorithm. Due to the relatively mature algorithm, the parameters of the split window algorithm reference come from M.F. Gao, et al.
Based on the data obtained at the corresponding time in Table 1, the surface temperature was inverted using the split window algorithm to obtain Figure 3.  Figure  2 for the specific inversion process. The AOD inversion results using MODIS data from the surrounding mainland and ocean of Shanghai on March 24, July 10, October 1, and December 21, 2022 are shown in Figure 4.

Data validation
The measured data of the ground station comes from the AOD data of the AERONET station. AERONET is a ground-based aerosol monitoring network established by NASA that covers the world [10]. The observation equipment of the station mainly adopts the polarization Solar luminosity CE318-II and the standard Solar luminosity CE318-I of the French CI-MEL company. There are eight observation bands: 0.340µm, 0.380µm, 0.440µm, 0.500µm, 0.675µm, 0.870µm, 0.936µm, 1.020µm. AERONET aerosol optical depth data is divided into three levels: Level 1 data does not undergo cloud removal; Level 1.5 data only underwent cloud removal; Level 2 data is both cloud removed and manually checked. This article uses Level 2 AOD data published on its official website (http://aeronet. gsfc. nasa. gov) to verify the aerosol optical depth retrieved by the satellite. The accuracy of AERONET level 2 AOD data is ± 0.02, so it can be considered as the true value of AOD. The AERONET station does not have AOD observations at a wavelength of 0.55µm, and this article uses the Angstrom formula to fit them.
In the formula: β is the atmospheric turbidity index, α is the Angstrom index, λ is the wavelength, and τ λ is the corresponding aerosol optical depth. Two AERONET stations, Shanghai Station (located in the land area) and Okinawa-Hedo Station (located in the ocean area), were used to verify the inversion results.

Result and discussion
Firstly, for the inversion results, the black area in the figure is the result of cloud masking and cloud removal, representing no data. The data from other regions is the correct inversion result without cloud coverage. The temperature inversion results in Figure 3 show that the land temperature is the highest in summer and the lowest in winter. The land temperature in summer is higher than the ocean temperature, and the ocean temperature in winter is higher than the land temperature. The surface temperature in spring and autumn is mostly between 293K and 313K. The AOD inversion results in Figure 4 indicate that both land and ocean have the highest AOD in spring, followed by winter, and the lowest in summer. The ocean AOD in the same season is significantly higher than that on land. The AOD value will not exceed 5, and most of the time the AOD value is less than 1. Low AOD may mean a hotter future [11]. According to the verification of actual data from AERONET site in Table 2, the inversion accuracy exceeds 95% and the inversion results are good. Combining various results, it can be seen that there is an inevitable connection between temperature and AOD.
Comparative analysis shows that, firstly, for land, the higher the temperature, the lower the AOD, and summer is the most significant. Then for the ocean, the higher the temperature, the higher the AOD. The lower the temperature, the lower the AOD.

Conclusions
This article uses Terra satellite MODIS data as the data source, and uses IDL, 6S model, and dark pixel method to perform cloud removed AOD inversion on the land and marine areas around Shanghai, China. The results show that: (1) For land areas, the higher the surface temperature, the lower the AOD value, with summer being the most significant.
(2) On the ocean, the higher the ocean surface temperature, the greater the AOD value.
(3) Based on MODIS data, the error of AOD inversion results using IDL, 6S models, and dark pixel method is between 1% and 6%, with good accuracy and feasibility of the method.
This experiment provides a theoretical basis for the relationship between AOD and temperature, filling the gap in research on the relationship between the two. It also confirms the possibility of retrieving ocean AOD from MODIS data.