Research on the effect of urban territorial expansion on thermal environment using the inverse S-function curve- Taking Beijing-Tianjin-Hebei China Capital Economic Circle as an Example
Authors: Zhang Xu , Roca Cladera Josep , Arellano Ramos Blanca 
Published: February 2023

The inverse S function can not only fit the spatial attenuation of construction land density, but also fit the spatial attenuation characteristics of various urban characteristics. Therefore, we assume that the inverse S-function curve is also applicable to the spatial variation law of urban LST. We hope to conduct an inverse S function model fitting analysis of the surface temperature of the three major cities in Beijing, Tianjin, Hebei, China's capital economic circle in 2001 and 2020 in winter, summer, day and night in eight periods&#160;to verify that they all conform to the characteristics of the function curve, and use the fitting parameters to analyze the urban development process and its impact on the thermal environment.First, we draw concentric circles at intervals of 1KM from the center points of the three cities, and then extract the land surface temperature (LST) of each circle and process it dimensionlessly. Finally, the inverse S function model is fitted to all LST data, and the expression of the inverse S function is as follows. And combined with the characteristics of LST, the fitting parameters in the function are given corresponding meanings.Analyzing the results of fitting parameters, LST conforms to the law of the reverse S-curve model in most cases.Since the LST in the most periods can be simulated by the inverse S model, it is proved that their change law is that they first decrease slowly with the increase of the radius of the concentric circle, then decrease rapidly, and finally decelerate to zero.The fit parameter "a" controls the slope of the curve. The larger "a" is, the faster the curve decays, indicating that the urban thermal environment is more compact.The "a" of each city of winter is greater than that of summer.Except for the smallest "a" in winter night in Beijing in 2020, the "a" in summer in 2001 was the smallest in other cities. The distribution of urban thermal environment in this period is the most scattered.The "a" results for Beijing and Tianjin are similar every time, but Beijing has a wider range of values. Tianjin's is generally larger than them.The fitting parameter "c" is the mean value of surface temperature at the city fringes.The&#160;most cities are distributed between 0 and 0.2.Only Tianjin Xiaye in 2020 reached 0.53. It shows that the temperature around Tianjin is on the high side during this period.The fitting parameter "D" reflects the radius of the urban thermal environment.The "D" of each city sample has increased to varying degrees, indicating that the urban high-temperature thermal environment has also expanded.The thermal environment radii of Beijing and Shijiazhuang are the smallest at night in winter, while Tianjin is the smallest at night in summer.The fastest growth rate was during summer nights, with each city adding more than 10 kilometers.The slowest growth in Beijing is during the daytime in summer, while that in Tianjin and Shijiazhuang is during the night in winter.