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A fundamental theorem for eco-environmental surface modelling and its applications

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Abstract

We propose a fundamental theorem for eco-environmental surface modelling (FTEEM) in order to apply it into the fields of ecology and environmental science more easily after the fundamental theorem for Earth’s surface system modeling (FTESM). The Beijing-Tianjin-Hebei (BTH) region is taken as a case area to conduct empirical studies of algorithms for spatial upscaling, spatial downscaling, spatial interpolation, data fusion and model-data assimilation, which are based on high accuracy surface modelling (HASM), corresponding with corollaries of FTEEM. The case studies demonstrate how eco-environmental surface modelling is substantially improved when both extrinsic and intrinsic information are used along with an appropriate method of HASM. Compared with classic algorithms, the HASM-based algorithm for spatial upscaling reduced the root-mean-square error of the BTH elevation surface by 9 m. The HASM-based algorithm for spatial downscaling reduced the relative error of future scenarios of annual mean temperature by 16%. The HASM-based algorithm for spatial interpolation reduced the relative error of change trend of annual mean precipitation by 0.2%. The HASM-based algorithm for data fusion reduced the relative error of change trend of annual mean temperature by 70%. The HASM-based algorithm for model-data assimilation reduced the relative error of carbon stocks by 40%. We propose five theoretical challenges and three application problems of HASM that need to be addressed to improve FTEEM.

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References

  • Akima H. 1978a. A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans Math Softw, 4: 148–159.

    Google Scholar 

  • Akima H. 1978b. Algorithm 526: Bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans Math Softw, 4: 160–164.

    Google Scholar 

  • Bagnara M, Silveyra Gonzalez R, Reifenberg S, Steinkamp J, Hickler T, Werner C, Dormann C F, Hartig F. 2019. An R package facilitating sensitivity analysis, calibration and forward simulations with the LPJ-GUESS dynamic vegetation model. Environ Model Softw, 111: 55–60.

    Google Scholar 

  • Bengtsson B E, Nordbeck S. 1964. Construction of isarithms and isarithmic maps by computers. BIT, 4: 87–105.

    Google Scholar 

  • Birkhoff G, Garabedian H L. 1960. Smooth surface interpolation. J Math Phys, 39: 258–268.

    Google Scholar 

  • Brill K F, Uccellini L W, Manobianco J, Kocin P J, Homan J H. 1991. The use of successive dynamic initialization by nudging to simulate cyclogenesis during GALE IOP 1. Meteorol Atmos Phys, 45: 15–40.

    Google Scholar 

  • Chen C F, Yue T X. 2010. A method of DEM construction and related error analysis. Comput Geosci, 36: 717–725.

    Google Scholar 

  • Chen C F, Yue T X, Dai H L, Tian M Y. 2013a. The smoothness of HASM. Int J Geogr Inf Sci, 27: 1651–1667.

    Google Scholar 

  • Chen C F, Li Y Y, Yue T X. 2013b. Surface modeling of DEMs based on a sequential adjustment method. Int J Geogr Inf Sci, 27: 1272–1291.

    Google Scholar 

  • Cheng W M, Zhou C H, Chai H X, Zhao S M, Liu H J, Zhou Z P. 2011. Research and compilation of the geomorphologic atlas of the People’s Republic of China (1:1000000). J Geogr Sci, 21: 89–100.

    Google Scholar 

  • Crow W T, Berg A A, Cosh M H, Loew A, Mohanty B P, Panciera R, de Rosnay P, Ryu D, Walker J P. 2012. Upscaling sparse ground-based soil moisture observations for the validation of coarse-resolution satellite soil moisture products. Rev Geophys, 50: RG2002

    Google Scholar 

  • De Boor C. 1962. Bicubic spline interpolation. J Math Phys, 41: 212–218.

    Google Scholar 

  • Djaferis T E, Schick I C. 2000. System theory: Modeling, analysis, and control. Boston: Kluwer

    Google Scholar 

  • Editorial Committee of Vegetation Map of China. 2007. Vegetation map of the People’s Republic of China. Beijing: Geological Publishing House

    Google Scholar 

  • Evans I S. 1980. An integrated system of terrain analysis and slope mapping. Z Geomorphol Suppl Bd, 36: 274–295.

    Google Scholar 

  • Foley T A, Nielson G M. 1980. Multivariate interpolation to scattered data using delta iteration. In: Cheney E W, ed. Approximation Theory III. New York: Academic Press

    Google Scholar 

  • Franke R. 1982. Scattered data interpolation: Tests of some methods. Math Comput, 38: 181

    Google Scholar 

  • Fry J, Guber A K, Ladoni M, Munoz J D, Kravchenko A N. 2017. The effect of up-scaling soil properties and model parameters on predictive accuracy of DSSAT crop simulation model under variable weather conditions. Geoderma, 287: 105–115.

    Google Scholar 

  • Hamed K H. 2009. Exact distribution of the Mann-Kendall trend test statistic for persistent data. J Hydrol, 365: 86–94.

    Google Scholar 

  • Harder R L, Desmarais R N. 1972. Interpolation using surface Splines. J Aircraft, 9: 189–191.

    Google Scholar 

  • Hirsch A L, Pitman A J, Seneviratne S I, Evans J P, Haverd V. 2014. Summertime maximum and minimum temperature coupling asymmetry over Australia determined using WRF. Geophys Res Lett, 41: 1546–1552.

    Google Scholar 

  • Hull D J. 2003. Optimal Control Theory for Applications. New York: Springer

    Google Scholar 

  • IPBES (The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services). 2016. The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services. Secretariat of the Intergovernmental Science-Policy Platform on Biodiversity Ecosystem Services, Bonn, Germany

    Google Scholar 

  • IPBES (The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services). 2019. Global Assessment on Biodiversity and Ecosystem Services. Secretariat of the Intergovernmental Science-Policy Platform on Biodiversity Ecosystem Services, Bonn, Germany

    Google Scholar 

  • Isaaks E H, Srivastava R M. 1989. Applied Geostatistics. New York: Oxford University Press

    Google Scholar 

  • Kendall M G. 1948. Rank Correlation Methods. London: Griffin

    Google Scholar 

  • Kerimov I A. 2009. F-approximation of the Earth’s surface topography. Izv Phys Solid Earth, 45: 719–729.

    Google Scholar 

  • Krige D G. 1951. A statistical approach to some basic mine valuation problems on the Witwatersrand. J Chem Metall Min Soc South Africa, 52: 119–139.

    Google Scholar 

  • Laflamme E M, Linder E, Pan Y B. 2016. Statistical downscaling of regional climate model output to achieve projections of precipitation extremes. Weather Clim Extremes, 12: 15–23.

    Google Scholar 

  • Le Roux R, Katurji M, Zawar-Reza P, Quénol H, Sturman A. 2018. Comparison of statistical and dynamical downscaling results from the WRF model. Environ Model Softw, 100: 67–73.

    Google Scholar 

  • Li H K, Lei Y C. 2010. Evaluation of Forest Biomass and Carbon Storage in China (in Chinese). Beijing: China Forestry Publishing House

    Google Scholar 

  • Li J, Heap A D. 2014. Spatial interpolation methods applied in the environmental sciences: A review. Environ Model Softw, 53: 173–189.

    Google Scholar 

  • Li K, Jackson A, Livermore P W. 2014. Variational data assimilation for a forced, inertia-free magnetohydrodynamic dynamo model. Geophys J Int, 199: 1662–1676.

    Google Scholar 

  • Li Z L. 2007. Algorithmic Foundation of Multi-Scale Spatial Representation. London: CRC Press

    Google Scholar 

  • Magnussen S, Næsset E, Wulder M A. 2007. Efficient multiresolution spatial predictions for large data arrays. Remote Sens Environ, 109: 451–463.

    Google Scholar 

  • Mann H B. 1945. Nonparametric tests against trend. Econometrica, 13: 245–259.

    Google Scholar 

  • Maude A D. 1973. Interpolation—Mainly for graph plotters. Comput J, 16: 64–65.

    Google Scholar 

  • Misaghian N, Assareh M, Sadeghi M T. 2018. An upscaling approach using adaptive multi-resolution upgridding and automated relative permeability adjustment. Comput Geosci, 22: 261–282.

    Google Scholar 

  • Mitchell M N B. 2012. Data fusion: Concepts and Ideas. Berlin: Springer-Verlag

    Google Scholar 

  • National Bureau of Statistics of China. 2018. China Statistical Yearbook. Beijing: China Statistics Press

    Google Scholar 

  • Nichols N K. 2010. Mathematical concepts of data assimilation. In: Lahoz W, Khattatov B, Menard R, eds. Data Assimilation: Making Sense of Observations. Berlin: Springer. 13–39

    Google Scholar 

  • Peng C H, Guiot J, Wu H B, Jiang H, Luo Y Q. 2011. Integrating models with data in ecology and palaeoecology: Advances towards a model-data fusion approach. Ecol Lett, 14: 522–536.

    Google Scholar 

  • Phillips J D. 2002. Global and local factors in earth surface systems. Ecol Model, 149: 257–272.

    Google Scholar 

  • Ponsar S, Luyten P, Dulière V. 2016. Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea. Ocean Dyn, 66: 955–971.

    Google Scholar 

  • Schneider B. 2001. Phenomenon-based specification of the digital representation of terrain surfaces. Trans GIS, 5: 39–52.

    Google Scholar 

  • Schoenberg I J. 1946. Contributions to the problem of approximation of equidistant data by analytic functions. Quar Appl Math, 4: 45–99., 112–141

    Google Scholar 

  • Seppelt R, Lautenbach S, Volk M. 2013. Identifying trade-offs between ecosystem services, land use, and biodiversity: A plea for combining scenario analysis and optimization on different spatial scales. Curr Opin Env Sust, 5: 458–463.

    Google Scholar 

  • Shepard D. 1968. A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 23rd ACM National Conference. New York: Association for Computing Machinery

    Google Scholar 

  • Shi W J, Yue T X, Fan Z M. 2011. An overview of high accuracy surface modeling of soil properties. Procedia Environ Sci, 13: 2304–2309.

    Google Scholar 

  • Shi W, Liu J, Du Z, Song Y, Chen C, Yue T. 2009. Surface modelling of soil pH. Geoderma, 150: 113–119.

    Google Scholar 

  • Smith B, Prentice I C, Sykes M T. 2001. Representation of vegetation dynamics in the modelling of terrestrial ecosystems: Comparing two contrasting approaches within European climate space. Glob Ecol Biogeogr, 10: 621–637.

    Google Scholar 

  • Smith B, Wårlind D, Arneth A, Hickler T, Leadley P, Siltberg J, Zaehle S. 2014. Implications of incorporating N cycling and N limitations on primary production in an individual-based dynamic vegetation model. Biogeosciences, 11: 2027–2054.

    Google Scholar 

  • Somasundaram D. 2005. Differential Geometry. Harrow: Alpha Science International

    Google Scholar 

  • Spivak M. 1979. A Comprehensive Introduction to Differential Geometry (Vol. 3). Boston: Publish or Peril

    Google Scholar 

  • Talmi A, Gilat G. 1977. Method for smooth approximation of data. J Comput Phys, 23: 93–123.

    Google Scholar 

  • Tse R O C, Gold C. 2004. TIN meets CAD—Extending the TIN concept in GIS. Future Generation Comput Syst, 20: 1171–1184.

    Google Scholar 

  • Usery E L, McMaster R B. 2005. Introduction to the UCGIS research agenda. In: Usery E L, McMaster R B, eds. A Research Agenda for Geographic Information Science. London: CRC Press. 1–16

    Google Scholar 

  • Wang H W, Wang Y H. 2012. Analysis of spatial interpolation methods. In: Qian Z H, Cao L, Su W L, Wang T K, Yang H M, eds. Recent Advances in Computer Science and Information Engineering (Lecture Notes in Electrical Engineering Vol. 129). Berlin: Springer. 507–512

    Google Scholar 

  • Yue T X, Ai N S. 1990. The mathematic model of cirque morphology. J Glaciol Geocryol, 12: 227–34.

    Google Scholar 

  • Yue T X, Chen S P, Xu B, Liu Q S, Li H G, Liu G H, Ye Q H. 2002. A curve-theorem based approach for change detection and its application to Yellow River Delta. Int J Remote Sens, 23: 2283–2292.

    Google Scholar 

  • Yue T X, Du Z P, Liu J Y. 2004. High accuracy surface modelling and its error analysis (in Chinese). Prog Nat Sci, 14: 300–306.

    Google Scholar 

  • Yue T X, Du Z P, Song D J, Gong Y. 2007. A new method of surface modeling and its application to DEM construction. Geomorphology, 91: 161–172.

    Google Scholar 

  • Yue T X, Song Y J. 2008. The YUE-HASM method. In: Li D, Ge Y, Foody G M, eds. Accuracy in Geomatics. Edgbaston: World Academic Union. 148–153

    Google Scholar 

  • Yue T X, Wang S H. 2010. Adjustment computation of HASM: A high-accuracy and high-speed method. Int J Geogr Inf Sci, 24: 1725–1743.

    Google Scholar 

  • Yue T X, Chen C F, Li B L. 2010a. An adaptive method of high accuracy surface modeling and its application to simulating elevation surfaces. Trans GIS, 14: 615–630.

    Google Scholar 

  • Yue T X, Song D J, Du Z P, Wang W. 2010b. High-accuracy surface modelling and its application to DEM generation. Int J Remote Sens, 31: 2205–2226.

    Google Scholar 

  • Yue T X. 2011. Surface Modelling: High Accuracy and High Speed Methods. Boca Raton: CRC Press

    Google Scholar 

  • Yue T X, Chen C F, Li B L. 2012. A high-accuracy method for filling voids and its verification. Int J Remote Sens, 33: 2815–2830.

    Google Scholar 

  • Yue T X, Zhao N, Yang H, Song Y J, Du Z P, Fan Z M, Song D J. 2013a. A multi-grid method of high accuracy surface modeling and its validation. Trans GIS, 17: 943–952.

    Google Scholar 

  • Yue T X, Zhao N, Ramsey R D, Wang C L, Fan Z M, Chen C F, Lu Y M, Li B L. 2013b. Climate change trend in China, with improved accuracy. Clim Change, 120: 137–151.

    Google Scholar 

  • Yue T X, Zhang L L, Zhao N, Zhao M W, Chen C F, Du Z P, Song D J, Fan Z M, Shi W J, Wang S H, Yan C Q, Li Q Q, Sun X F, Yang H, Wilson J, Xu B. 2015a. A review of recent developments in HASM. Environ Earth Sci, 74: 6541–6549.

    Google Scholar 

  • Yue T X, Zhao M W, Zhang X Y. 2015b. A high-accuracy method for filling voids on remotely sensed XCO2 surfaces and its verification. J Cleaner Product, 103: 819–827.

    Google Scholar 

  • Yue T X, Du Z P, Lu M, Fan Z M, Wang C L, Tian Y Z, Xu B. 2015c. Surface modeling of ecosystem responses to climatic change in Poyang Lake Basin of China. Ecol Model, 306: 16–23.

    Google Scholar 

  • Yue T X, Liu Y, Zhao M W, Du Z P, Zhao N. 2016a. A fundamental theorem of Earth’s surface modelling. Environ Earth Sci, 75: 751

    Google Scholar 

  • Yue T X, Zhao N, Fan Z M, Li J, Chen C F, Lu Y M, Wang C L, Xu B, Wilson J. 2016b. CMIP5 Downscaling and its uncertainty in China. Glob Planet Change, 146: 30–37.

    Google Scholar 

  • Yue T X, Wang Y F, Du Z P, Zhao M W, Li Zhang L, Zhao N, Lu M, Larocque G R, Wilson J P. 2016c. Analysing the uncertainty of estimating forest carbon stocks in China. Biogeosciences, 13: 3991–4004.

    Google Scholar 

  • Zhang L L, Yue T X, Wilson J P, Zhao N, Zhao Y P, Du Z P, Liu Y. 2017a. A comparison of satellite observations with the XCO2 surface obtained by fusing TCCON measurements and GEOS-Chem model outputs. Sci Total Env, 601–602: 1575–1590

    Google Scholar 

  • Zhao C Y, Nan Z G, Cheng G D. 2005. Methods for modelling of temporal and spatial distribution of air temperature at landscape scale in the southern Qilian mountains, China. Ecol Model, 189: 209–220.

    Google Scholar 

  • Zhao M W, Zhang X Y, Yue T X, Wang C, Jiang L, Sun J L. 2017. A high-accuracy method for simulating the XCO2 global distribution using GOSAT retrieval data. Sci China Earth Sci, 60: 143–155.

    Google Scholar 

  • Zhao N, Yue T. 2014a. A modification of HASM for interpolating precipitation in China. Theor Appl Climatol, 116: 273–285.

    Google Scholar 

  • Zhao N, Yue T X. 2014b. Sensitivity studies of a high accuracy surface modelling method. Sci China Earth Sci, 57: 1–11.

    Google Scholar 

  • Zhao N, Yue T, Chen C, Zhao M, Du Z. 2018. An improved HASM method for dealing with large spatial data sets. Sci China Earth Sci, 61: 1078–1087.

    Google Scholar 

  • Zhu A X. 2005. Research issues on uncertainty in geographic data and GIS-based analysis. In: Usery E L, McMaster R B, eds. A Research Agenda for Geographic Information Science. London: CRC Press. 197–223

    Google Scholar 

  • Zienkiewlcz O C. 1967. The Finite Element Method in Structural and Continuum Mechanics. London: McGraw Hill

    Google Scholar 

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Acknowledgements

All data, corresponding to Figures 3–17, can be found from appended datasets at https://link.springer.com/journal/11430. This work was supported by the National Natural Science Foundation of China (Grant Nos. 41930647, 41590844, 41421001 & 41971358), the Strategic Priority Research Program (A) of the Chinese Academy of Sciences (Grant No. XDA20030203), the Innovation Project of LREIS (Grant No. O88RA600YA) and the Biodiversity Investigation, Observation and Assessment Program (2019–2023) of the Ministry of Ecology and Environment of China.

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Authors and Affiliations

  1. State Key Laboratory of Resources and Environment Information System, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China

    Tianxiang Yue, Na Zhao, Zhengping Du, Zemeng Fan, Wenjiao Shi, Shihai Wang, Yinjun Song, Chenliang Wang, Wei Zhou, Yi Liu, Xiaozhe Yin, Zong Wang, Zhengyi Bao, Miaomiao Zhao, Yapeng Zhao, Yimeng Jiao, Ufra Naseer, Bin Fan, Saibo Li, Yang Yang & John P. Wilson

  2. College of Resources and Environment, University of Chinese Academy of Sciences, Beijing, 100049, China

    Tianxiang Yue, Na Zhao, Zemeng Fan, Wenjiao Shi, Yi Liu, Zong Wang, Zhengyi Bao, Miaomiao Zhao, Yapeng Zhao, Yimeng Jiao, Ufra Naseer, Bin Fan, Saibo Li, Yang Yang & John P. Wilson

  3. College of Land Resources and Environment, Jiangxi Agricultural University, Nanchang, 330045, China

    Tianxiang Yue & Hongsheng Huang

  4. College of Geomatics, Shandong University of Science and Technology, Qingdao, 266590, China

    Yu Liu & Chuanfa Chen

  5. College of Forestry, Beijing Forestry University, Beijing, 100083, China

    Yifu Wang

  6. School of Land and Resources, China West Normal University, Nanchong, 637002, China

    Bin Zhang

  7. College of Geographical Information and Tourism, Chuzhou University, Chuzhou, 239000, China

    Mingwei Zhao

  8. Institutes of Science and Development, Chinese Academy of Sciences, Beijing, 100190, China

    Dunjiang Song

  9. Department of Information Engineering, Shandong University of Science and Technology, Tai’an, 271019, China

    Changqing Yan

  10. College of Resources, Sichuan Agricultural University, Chengdu, 611130, China

    Qiquan Li

  11. College of Geography and Tourism, Qufu Normal University, Rizhao, 276828, China

    Xiaofang Sun

  12. Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, 100101, China

    Lili Zhang

  13. School of Geographical Science, Southwest University, Chongqing, 400715, China

    Yongzhong Tian & Wei Zhou

  14. National Disaster Reduction Center of China, Ministry of Emergency Management, Beijing, 100721, China

    Wei Wang

  15. Department for Population Data, China Population and Development Research Center, Beijing, 100081, China

    Ying’an Wang

  16. Department for Industrial Standard, China Standardization Administration, Beijing, 100088, China

    Shengnan Ma

  17. The Academy of Digital China, Fuzhou University, Fuzhou, 350002, China

    Yimin Lu

  18. National Institute of Environmental Health, Chinese Center for Disease Control and Prevention, Beijing, 100021, China

    Qing Wang

  19. School of Information Engineering, China University of Geoscience, Beijing, 100083, China

    Yuzhu Wang

  20. Qian Xuesen Laboratory of Space Technology, Beijing, 100094, China

    Ming Lu

  21. College of Architecture and Urban Planning, Chongqing Jiaotong University, Chongqing, 400074, China

    Wei Zhou

  22. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210023, China

    Tianxiang Yue, Na Zhao & Zemeng Fan

  23. Spatial Sciences Institute, University of Southern California, Los Angeles, CA, 90089-0374, USA

    John P. Wilson

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  1. Tianxiang Yue
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  37. Bin Fan
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  38. Saibo Li
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Correspondence to Tianxiang Yue or Zemeng Fan.

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Yue, T., Zhao, N., Liu, Y. et al. A fundamental theorem for eco-environmental surface modelling and its applications. Sci. China Earth Sci. 63, 1092–1112 (2020). https://doi.org/10.1007/s11430-019-9594-3

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