# Fully Portraying Patch Area Scaling with Resolution: An Analytics and Descriptive Statistics-Combined Approach

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Formulating Patch Area Scaling

#### 2.2. Characterizing Patch Morphology

#### 2.3. Data and Their Processing

## 3. Results

#### 3.1. The Pair of Models Built

#### 3.2. Verifying the Models by Predicting Patch Area Scaling

#### 3.3. Applying the Patch Area Scaling Model to Predict Class Area Scaling

## 4. Discussions

#### 4.1. Selection of Metrics for Charactering Patches’ Morphology

#### 4.2. Inherent Uncertainty of Patch Area Scaling and That Resulting from Modeling Approximation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Turner, M.G.; O’Neill, R.V.; Milne, G.B.T. Effects of changing spatial scale on the analysis of landscape pattern. Landsc. Ecol.
**1989**, 3, 153–162. [Google Scholar] [CrossRef] - Openshaw, S. A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling. Trans. Inst. Br. Geogr.
**1977**, 2, 459–472. [Google Scholar] [CrossRef] - Lam, S.N.; Quattrochi, D.A. On the Issues of Scale, Resolution, and Fractal Analysis in the Mapping Sciences. Prof. Geogr.
**1992**, 44, 88–98. [Google Scholar] [CrossRef] - Chen, Y.; Zhou, Q. A scale-adaptive DEM for multi-scale terrain analysis. Int. J. Geogr. Inf. Sci.
**2013**, 27, 1329–1348. [Google Scholar] [CrossRef] - Sposito, G. Scale Dependence and Scale Invariance in Hydrology; Cambridge University Press: Cambridge, UK, 1998. [Google Scholar]
- Luan, H.J.; Tian, Q.J.; Yu, T.; Hu, X.L.; Huang, Y.; Du, L.T.; Zhao, L.M.; Wei, X.; Han, J.; Zhang, Z.W. Modeling Continuous Scaling of NDVI Based on Fractal Theory. Spectrosc. Spectr. Anal.
**2013**, 33, 1857–1862. [Google Scholar] - Dong, L.; Liu, H.; Riffat, S. Development of small-scale and micro-scale biomass-fuelled CHP systems—A literature review. Appl. Ther. Eng.
**2009**, 29, 2119–2126. [Google Scholar] [CrossRef] [Green Version] - Sandel, B. Towards a taxonomy of spatial scale-dependence. Ecography
**2015**, 38, 358–369. [Google Scholar] [CrossRef] - Goodchild, M.F. Scale in GIS: An overview. Geomorphology
**2011**, 130, 5–9. [Google Scholar] [CrossRef] - Li, X.; Wang, J.; Strahler, A.H. Scale effects and scaling-up by geometric-optical model. Sci. China Ser. E
**2000**, 43, 17–22. [Google Scholar] [CrossRef] - Moody, A.; Woodcock, C. Scale-Dependent Errors in the Estimation of Land-Cover Proportions: Implications for Global Land-Cover Datasets. Photogramm. Eng. Remote Sens.
**1994**, 60, 585–596. [Google Scholar] - Woodcock, C.E.; Strahler, A.H. The factor of scale in remote sensing. Remote Sens. Environ.
**1987**, 21, 311–332. [Google Scholar] [CrossRef] - Wu, J. Effects of changing scale on landscape pattern analysis: Scaling relations. Landsc. Ecol.
**2004**, 19, 761–782. [Google Scholar] [CrossRef] - Jones, H.G.; Sirault, X.R.R. Scaling of Thermal Images at Different Spatial Resolution: The Mixed Pixel Problem. Agronomy
**2014**, 4, 380–396. [Google Scholar] [CrossRef] [Green Version] - Wu, J.; Jones, K.; Li, H.; Loucks, O. Scaling and Uncertainty Analysis in Ecology: Methods and Applications; Springer: New York, NY, USA, 2006; ISBN 1-4020-4662-6. [Google Scholar]
- Gallo, K.P.; Easterling, D.R.; Peterson, T.C. The influence of land use/land cover on climatological values of the diurnal temperature range. J. Clim.
**1996**, 9, 163–165. [Google Scholar] [CrossRef] [Green Version] - Kindu, M.; Schneider, T.; Döllerer, M.; Teketay, D.; Knoke, T. Scenario modelling of land use/land cover changes in Munessa-Shashemene landscape of the Ethiopian highlands. Sci. Total Environ.
**2018**, 622–623, 534–546. [Google Scholar] [CrossRef] - Mahmood, R.; Pielke, R.A., Sr.; Hubbard, K.G.; Yogi, D.N.; Syktus, J. Impacts of Land Use/Land Cover Change on Climate and Future Research Priorities. Bull. Am. Meteorol. Soc.
**2010**, 91, 37–46. [Google Scholar] [CrossRef] - Bhagawat, R.; Zhang, L.; Hamidreza, K.; Barry, H.; Sushila, R.; Zhang, P. Land Use/Land Cover Dynamics and Modeling of Urban Land Expansion by the Integration of Cellular Automata and Markov Chain. ISPRS Int. J. Geo Inf.
**2018**, 7, 154. [Google Scholar] - Baidya Roy, S.; Avissar, R. Impact of land use/land cover change on regional hydrometeorology in Amazonia. J. Geophys. Res. Atmos.
**2002**, 107, 8037. [Google Scholar] [CrossRef] [Green Version] - Pielke, R., Sr.; Pitman, A.; Niyogi, D.; Mahmood, R.; Mcalpine, C.; Hossain, F.; Klein Goldewijk, K.; Nair, U.; Betts, R.; Fall, S.; et al. Land use/land cover changes and climate: Modeling analysis and observational evidence. Wiley Interdiscip. Rev. Clim. Chang.
**2011**, 2, 828–850. [Google Scholar] [CrossRef] - Turner, B.L., II; Meyer, W.B.; Skole, D.L. Global land-use/land-cover change: Towards an integrated study. Integr. Earth Syst. Sci.
**1994**, 23, 91–95. [Google Scholar] [CrossRef] - Etienne, R.S. On optimal choices in increase of patch area and reduction of interpatch distance for metapopulation persistence. Ecol. Model.
**2015**, 179, 77–90. [Google Scholar] [CrossRef] - Ferraz, G.; Nichols, J.D.; Hines, J.E.; Stouffer, P.C.; Bierregaard, R.O.; Lovejoy, T.E. A Large-Scale Deforestation Experiment: Effects of Patch Area and Isolation on Amazon Birds. Science
**2007**, 315, 238–241. [Google Scholar] [CrossRef] [Green Version] - Hambäck, P.; Englund, G. Patch area, population density and the scaling of migration rates: The resource concentration hypothesis revisited. Ecol. Lett.
**2005**, 8, 1057–1065. [Google Scholar] [CrossRef] - Honnay, O.; Endels, P.; Vereecken, H.; Hermy, M. The role of patch area and habitat diversity in explaining native plant species richness in disturbed suburban forest patches in northern Belgium. Biodivers. Res.
**1999**, 5, 129–141. [Google Scholar] [CrossRef] - Landeiro, V.L.; Hamada, N.; Godoy, B.S.; Melo, A.S. Effects of litter patch area on macroinvertebrate assemblage structure and leaf breakdown in Central Amazonian streams. Hydrobiologia
**2010**, 649, 355–363. [Google Scholar] [CrossRef] - Muad, A.; Foody, G. Impact of Land Cover Patch Size on the Accuracy of Patch Area Representation in HNN-Based Super Resolution Mapping. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2012**, 5, 1418–1427. [Google Scholar] [CrossRef] [Green Version] - Schtickzelle, N.; Baguette, M. Behavioural responses to habitat patch boundaries restrict dispersal and generate emigration–patch area relationships in fragmented landscapes. J. Anim. Ecol.
**2003**, 72, 533–545. [Google Scholar] [CrossRef] [PubMed] - Evans, P. Scaling and assessment of X-ray data quality. Acta Cryst. D. Biol. Cryst.
**2006**, 62, 72–82. [Google Scholar] [CrossRef] - Finke, P.A.; Bierkens, M.F.P.; Willigen, P. Choosing Appropriate Upscaling and Downscaling Methods for Environmental Research; IAHS: Wallingford, UK, 2002. [Google Scholar]
- Zhang, W.; Li, T.; Huang, Y.; Zhang, Q.; Bian, J.; Han, P. Estimation of uncertainties due to data scarcity in model upscaling: A case study of methane emissions from rice paddies in China. Geosci. Model Dev. Discuss.
**2014**, 7, 181–216. [Google Scholar] - Lechner, A.M.; Stein, A.; Jones, S.D.; Ferwerda, J.G. Remote sensing of small and linear features: Quantifying the effects of patch size and length, grid position and detectability on land cover mapping. Remote Sens. Environ.
**2009**, 113, 2194–2204. [Google Scholar] [CrossRef] - Tan, S.; Xu, Z.; Ti, P.; Li, Z. Morphology-based modeling of aggregation effect on the patch area size for GlobeLand30 data. Trans. GIS
**2018**, 22, 98–118. [Google Scholar] [CrossRef] - Mcgarigal, K.S.; Cushman, S.A.; Neel, M.C.; Ene, E. FRAGSTATS: Spatial Pattern Analysis Program for Categorical Maps; University of Massachusetts Amherst: Amherst, MA, USA, 2002. [Google Scholar]
- Chen, J.; Ban, Y.; Li, S. China: Open access to Earth land-cover map. Nature
**2014**, 514, 434. [Google Scholar] - Qi, Y.; Wu, J. Effects of changing spatial resolution on the results of landscape pattern analysis using spatial autocorrelation indices. Landsc. Ecol.
**1996**, 11, 39–49. [Google Scholar] [CrossRef] - Zhang, Q.; Tan, S.; Xu, Z.; Huang, Z. Applicability and simplification study of patch level landscape metrics based on GLC30. Remote Sens. L. Resour.
**2017**, 029, 98–105. [Google Scholar] [CrossRef] - Gustafson, E.J. Quantifying landscape spatial pattern: What is the state of the art? Ecosystems
**1998**, 1, 143–156. [Google Scholar] [CrossRef] - Lausch, A.; Salbach, C.; Schmidt, A.; Doktor, D.; Pause, M. Deriving phenology of barley with imaging hyperspectral remote sensing. Ecol. Model.
**2015**, 295. [Google Scholar] [CrossRef]

**Figure 1.**The area scaling behaviors of a pair of similar patches of different area. (

**a**) The area scaling of the smaller patch; (

**b**) The area scaling of the bigger patch. The initial patch at 30 m resolution (

**a**) was extracted from the year-2010 Globeland30 data, and the initial patch in (

**b**) was generated by magnifying that of (

**a**) four times. For other resolutions, the patches were obtained by aggregating the initial patches.

**Figure 2.**The area scaling behaviors of a pair of dissimilar patches of the same area. (

**a**) The area scaling of an elongated patch; (

**b**) The area scaling of a compact patch. The initial patches at 30 m resolution in (

**a**,

**b**) were extracted from the year-2010 Globeland30 data. For other resolutions, the patches were obtained by aggregating the initial patches.

**Figure 3.**The flow chart of building the patch area scaling model and its uncertainty model. Globeland30 is the 30-m resolution global land cover data product developed by NGCC and could be downloaded from http://www.globallandcover.com (accessed on 2 December 2020).

**Figure 5.**The patch area scaling model in 2- and 3-dimentional views. (

**a**) A two-dimensional view of the patch area scaling model; (

**b**) A three-dimensional view of the patch area scaling model.

**Figure 6.**The uncertainty model of patch area scaling in 2- and 3- dimensional views. (

**a**) A two-dimensional view of the uncertainty model; (

**b**) A three-dimensional view of the uncertainty model.

**Figure 8.**The predicted and real area scaling behaviors of the test patches (RAR stands for real area ratio. PAR stands for predicted area ratio. σ stands for the standard deviation of PAR given by the uncertainty model.). (

**a**) P1; (

**b**) P2;(

**c**) P3; (

**d**) P4; (

**e**) P5; (

**f**) P6; (

**g**) P7; (

**h**) P8; (

**i**) P9; (

**j**) P10; (

**k**) P11; (

**l**) P12; (

**m**) P13; (

**n**) P14.

**Figure 9.**Eight single-class landscapes for test. (

**a**) C1; (

**b**) C2; (

**c**) C3; (

**d**) C4; (

**e**) C5; (

**f**) C6; (

**g**) C7; (

**h**) C8.

**Figure 10.**The predicted and real area scaling behaviors of the eight single-class landscapes for test (RCAR stands for real class area ratio, and PCAR stands for predicted class area ratio). (

**a**) C1; (

**b**) C2; (

**c**) C3; (

**d**) C4; (

**e**) C5; (

**f**) C6; (

**g**) C7; (

**h**) C8.

**Figure 11.**The uncertainty resulting from random rasterization and modeling approximation. (

**a**) The uncertainty resulting from random rasterization (the a_sd_ar part); (

**b**) The uncertainty resulting from modeling approximation (the sd_a_ar part).

Name | Area (m^{2}) | Filling | SRS (m) | Name | Area (m^{2}) | Filling | SRS (m) |
---|---|---|---|---|---|---|---|

P1 | 6,930,000 | 0.01 | 307.39 | P8 | 5,108,400 | 0.35 | 1330.31 |

P2 | 1,449,900 | 0.05 | 356.68 | P9 | 2,479,500 | 0.40 | 1224.44 |

P3 | 3,710,700 | 0.10 | 612.33 | P10 | 1,053,000 | 0.45 | 650.00 |

P4 | 8,761,500 | 0.15 | 975.13 | P11 | 617,400 | 0.50 | 663.87 |

P5 | 8,414,100 | 0.20 | 1048.49 | P12 | 198,900 | 0.55 | 401.82 |

P6 | 15,228,900 | 0.25 | 1377.56 | P13 | 252,000 | 0.60 | 494.12 |

P7 | 14,400,900 | 0.30 | 2222.36 | P14 | 152,100 | 0.64 | 390.00 |

Name | Land Cover Class | Number of Patches | Average Area (×10,000 m^{2}) | Average Filling |
---|---|---|---|---|

C1 | Waterbody | 208 | 6.11 | 0.41 |

C2 | Grassland | 1597 | 9.72 | 0.386 |

C3 | Wetland | 292 | 33.22 | 0.30 |

C4 | Grassland | 1645 | 9.022 | 0.40 |

C5 | Forest | 1332 | 18.73 | 0.39 |

C6 | Wetland | 172 | 103.27 | 0.291 |

C7 | Artificial surface | 523 | 77.02 | 0.337 |

C8 | Cultivated land | 599 | 195.61 | 0.35 |

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**MDPI and ACS Style**

Zhang, Q.; Xu, Z.
Fully Portraying Patch Area Scaling with Resolution: An Analytics and Descriptive Statistics-Combined Approach. *Land* **2021**, *10*, 262.
https://doi.org/10.3390/land10030262

**AMA Style**

Zhang Q, Xu Z.
Fully Portraying Patch Area Scaling with Resolution: An Analytics and Descriptive Statistics-Combined Approach. *Land*. 2021; 10(3):262.
https://doi.org/10.3390/land10030262

**Chicago/Turabian Style**

Zhang, Qianning, and Zhu Xu.
2021. "Fully Portraying Patch Area Scaling with Resolution: An Analytics and Descriptive Statistics-Combined Approach" *Land* 10, no. 3: 262.
https://doi.org/10.3390/land10030262