Towns serve as the basic unit of implementation for comprehensive land consolidation and rehabilitation. The utilization of scaling law can provide a new perspective for construction land consolidation. From two perspectives of the town hierarchic system and the growth of a single town, this research applies the Rank-Size Rule and Allometric Scaling Law to analyze the scale structure, hierarchy and allometric scaling evolution relationship of population and construction land in the Loess Plateau at the town scale in 2000, 2010, and 2017. Furthermore, the consolidation potential of construction land is divided into five zones and puts forward recommendations for the comprehensive consolidation of the construction land. The results indicate: (1) The majority of towns have small or medium populations and 62% of the towns in the study show negative population growth. Geographically, the northern part has a smaller population size compared with the southern part. 96% of the towns show an increasing trend in the quantity of construction land, and the south and north parts of the study area have more construction land compared with the center part. The zone of the Valley Plain has the largest population size, and the zone of the Sandy and Desert Area has the largest quantity of construction land. (2) The rank-size distributions of both population and construction land comply with the power-law relation. The population hierarchy has changed from equilibrium to concentration, while the hierarchy of construction land shows an opposite pattern. So, the whole town hierarchic system of the Loess Plateau is gradually tending to the optimal distribution, which is the town hierarchic system gradually forming an ideal sequence structure. (3) The population-construction land relationship obeys the allometric scaling law, and the major allometric type is positive allometry. The human-land relationship tends to be coordinated, and the town system tends to be reasonable. The allometric scaling coefficient is not robust in different geographical areas, especially in Irrigated Agricultural Areas. Furthermore, 90% of the towns have weak coordination of human-land relationships, and 60% of the towns have a relatively faster growth rate of construction land than the relative growth (decline) rate of population. (4) The consolidation potential of construction land is divided into five types. High Consolidation Potential Area concentrates in the Eastern Loess Plateau, while Medium and Low Consolidation Potential Area concentrically distribute in the Western Loess Plateau. The Human-land Coordination Area has a small number and scattered spatial distribution. The land use of towns that are concentrated around prefecture-level cities or with unique resources is not intensive enough. The zoning of construction land consolidation potential based on the results of the allometric scale is in line with reality, and local governments should make use of the characteristics and trends of the town system to formulate planning schemes to promote the integrated development of urban and rural areas.
Keywords: allometric scaling; consolidation potential zone; rank-size; the Loess Plateau.