Spatial scaling of multiple landscape features in the conterminous United States

  • Chunxue Xu
  • Shuqing ZhaoEmail author
  • Shuguang Liu
Research Article



Spatial heterogeneity is scale-dependent. Understanding the scaling rules of spatial features across wide ranges of scale is a major challenge in landscape ecology. The lack of scientific justification in choosing proper scale may lead to unexpected outcomes in landscape pattern analysis and result in biases in subsequent process analysis.


The goal is to provide an extensive analysis on scaling relationships for a variety of landscape metrics as functions of grain size and extent. Specific research objectives are to: (1) identify scaling relationships of landscape metrics as functions of grain size, (2) define scale domains of these scaling relationships, and (3) explore how scaling relations of landscape metrics with respect to grain size would change with spatial extent.


Expanding the approach of Wu and Hobbs (Landsc Ecol 17:355–365, 2002) and Wu (Landsc Ecol 19:125–138, 2004) using a much bigger dataset and covering a wider range of scales, we examined the patterns of scalograms of 38 landscape metrics within 96 sampled landscapes ranging from 25 to 221 km2 in the conterminous United States. Scaling models were derived from the scalograms as a function of grain size, and the scale domains of these models were identified as the critical scales along the dimensions of grain size and spatial extent where the performance of the models fell below a given error limit.


The responses of landscape metrics with respect to changing resolutions fall into three categories: predictable across the whole spectrum of grain size investigated (Type I), predictable in a limited range of grain size (Type II), and unpredictable (Type III). For Type II metrics, the critical aggregation resolutions were identified based on the predefined error limit, and scale-invariant power-law scaling relationships were found between critical resolutions and spatial extents. All the scaling exponents are positive, suggesting that critical aggregation resolutions can be relaxed as the spatial extent expands. Furthermore, the coefficients of scaling relations for Type I and II metrics vary with spatial extents, and robust scaling functions between the coefficients and the extent can be observed for some metrics.


This study addresses a fundamental scale issue in landscape ecology: how a particular spatial pattern would change with scale and how information could be adequately transferred from one scale to another. A variety of scaling relationships exist on the spatial patterns of landscape metrics, and they could provide guidance to researchers on how to select an appropriate scale for a study of interest. In addition, the findings support the empirical perception that coarser grain size might be used for a larger spatial extent.


Spatial heterogeneity Landscape metrics Scale effect Scale domain Spatial resolution Geospatial extent 



This study was supported by the National Natural Science Foundation of China (#41771093 and 41571079 and #31621091).


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Urban and Environmental Sciences, and Key Laboratory for Earth Surface Processes of the Ministry of EducationPeking UniversityBeijingChina
  2. 2.National Engineering Laboratory for Applied Technology of Forestry & Ecology in South China, and College of Biological Science and TechnologyCentral South University of Forestry and TechnologyChangshaChina

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