| In the mid-to-late 20 th century,cities in developed countries in Europe and the United States experienced widespread shrinkage due to global industrial restructuring,suburbanization,childlessness and aging.This phenomenon is mainly manifested in largescale urban population decline,economic downturn,vacant infrastructure.Currently,1/4 of the world’s cities are considered shrinking cities.In recent years,urban shrinkage has become increasingly evident in China,which accounts for 13.6% of the world’s shrinking cities in an empirical study of global urban shrinkage from 2000-2019.A number of studies have empirically analyzed urban shrinkage in China and typical domestic regions,and these studies have greatly deepened the understanding of urban shrinkage in China,yet there are still aspects that need improvement.First,most of the existing studies on urban shrinkage are based on the Western context,lacking the consideration of the context of urban shrinkage in China and the condensed summary of the characteristics of urban shrinkage in China;second,most of the existing studies on urban shrinkage are based on the administrative perspective of cities,which is contrary to the Western definition of the concept of "city";third,most of the existing studies are based on the prefecture-level scale,while the shrinkage of county-level cities,as a basic component of China’s urban system,needs more attention.In 2019,the ecological protection and high-quality development of the Yellow River Basin has been promoted as a national strategy,and the urban growth and shrinkage of the Yellow River Basin has received more attention from scholars,and revelant studies also indicate that the phenomenon of urban shrinkage in the Yellow River Basin has existed for a long time.In this paper,we focus on 735 county-level cities(built-up areas of 735 countylevel administrative units)in the Yellow River Basin as the study area,and identify shrinking cities in the Yellow River Basin between 2000-2010 and 2010-2020 through a shrinkage degree model using Worldpop population raster data for 2000,2010 and 2020.Then,we analyze the spatial and temporal distribution patterns of shrinking cities in the Yellow River Basin and explore the clustering characteristics of shrinking cities in the Yellow River Basin with the help of spatial autocorrelation.In addition,the shrinking cities at county level in the Yellow River basin are classified from two perspectives: city scale and regional spatial structure,and the common characteristics of shrinking cities at county level in the basin are summarized and condensed under the scale structure and regional structure.Thereafter,the least squares linear regression method and the geographically weighted regression method are applied to explore the factors influencing the shrinkage of county-level cities in the Yellow River basin and the spatial heterogeneity of the effects of each factor.Finally,the results of measuring the influencing factors of urban shrinkage in the Yellow River basin are synthesized to propose coping strategies for the shrinkage of county-level cities in the Yellow River basin.The following conclusions are drawn from this study:(1)The number of shrinking cities in the Yellow River Basin has increased significantly from 53 in 2000-2010 to 301 in 2010-2020;in terms of the degree of shrinkage,the number of shrinking cities in both study periods shows the characteristics of "light shrinking cities >moderate shrinking cities > heavy shrinking cities";from the perspective of urban shrinkage trajectory,the number of shrinking cities shows the characteristics of "recently shrinking cities > intensifying shrinking cities > stage shrinking cities > slow shrinking cities".The shrinking county-level cities are concentrated in the middle and upper reaches of the Yellow River Basin,with the spatial characteristics of large cities and core cities in a block-like and ring-like layout,forming a typical "core-edge" structure.The shrinking county-level cities in the Yellow River Basin show significant spatial clustering characteristics,mainly presenting a low-low clustering pattern in space.(2)Based on the scale structure perspective,the number of shrinking cities in the Yellow River Basin show the characteristics of "county-level cities with population size less than or equal to 200,000 > county-level cities with population size between 200,000 and 500,000 >county-level cities with population size greater than 500,000" in both study periods,showing that the smaller the size of county-level cities,the more likely the cities will shrink;based on the regional structure perspective,the number of shrinking cities in the Yellow River Basin shows the characteristics of "absolute shrinkage > potential shrinkage > suburbanization shrinkage" in both study periods.(3)The factors affecting the shrinkage of county-level cities in the Yellow River Basin include the strength of urban economic development,the degree of population aging,industrial transformation and upgrading,population concentration scale,financial investment,scientific and technological innovation,and elevation conditions,etc.,and the degree of influence of each factor on urban shrinkage has significant spatial heterogeneity;in order to cope with the shrinkage phenomenon,we should focus on establish correct strategies for urban shrinkage,pay attention to regional coordinated development,promote the transformation and upgrade of urban industrial structure,promote the rationalization of population structure,strengthen urban facility construction,and encourag public participation in construction in the future. |