Landscape Invariants–Order Parmeters of a Dynamic System

The article considers theoretical and methodological substantiation of identifying invariants problem in nonlinear dynamic systems. Invariance in context of stable spatio-temporal structures in a landscape was proposed by V.B. Sochava in 1961. The accumulation of long-term series of landscape observations by means of multispectral imaging made it possible to identify invariants in practice. An analysis of Landsat multispectral measurements from 1987 to 2022 for the southern taiga landscape (Central Forest State Nature Biosphere Reserve) shows that invariants identified as order parameters primarily determine total aboveground vegetation biomass, the water content in vegetation and soils, and the intensity of photosynthesis, i.e. bioproduction process. The proposed scheme for analyzing time series of remote sensing data makes it possible to assess landscape cover at the time of survey with respect to invariants and to identify the main control parameters that determine changes in environmental conditions and self-development of geosystems. The assessment of vegetation and relief contribution to formation of invariants structure was made to reveal invariants physical meaning. The results showed that relief has little effect on order parameters, and vegetation cover make the greatest contribution to invariant structure formation. Since invariants make it possible to identify the most stationary states, they can be used to solve applied problems in agriculture and forestry, as well as in the assessment of various ecosystem services.

1. Allen T.F.H., Starr T.B. Hierarchy: perspectives for ecological complexity. Chicago: The University of Chicago Press, 1982. 310 p.

2. Bevz V.N. The invariant aspect of the spatio-temporal organization of slope landscapes, Vestn. Voronezh. Univ. Ser. Geogr. i Geoekol., 2002, no. 1, pp. 48–52. (In Russ.).

3. Bolshakov A.G. Osnovy teorii gradostroitel’stva i raionnoi planirovki [Fundamentals of the Theory of Urban Planning and District Planning]. Irkutsk: Irkutsk National Research Technical University, 2004. 216 p.

4. Borodin O.I., Bugai A.S., Gikhman I.I. Biograficheskii slovar’ deyatelei v oblasti matematiki [Biographical Dictionary of Actors in Mathematics]. Kyiv: Rad. Shkola, 1979. 607 p.

5. Campbell M.J., Congalton R.G. Landsat-based land cover change analysis in Northeastern Oregon’s timber resource dependent communities. American Society of Photogrammetry and Remote Sensing 2012 Annual Conference, 2012, pp. 19–23.

6. Cao W., Li B., Zhang Y. A remote sensing image fusion method based on PCA transform and wavelet packet transform. In International Conference on Neural Networks and Signal Processing, 2003, vol. 2, pp. 976–981.

7. Chang H., Yoon W.S. Improving the classification of Landsat data using standardized principal components analysis. KSCE J. Civ. Eng., 2003, vol. 7, no. 4, pp. 469–474.

8. Chernykh D.V. On the boundaries of the landscape: an unorthodox view of a physical geographer. Mezhdunar. Zh. Issled. Kultury, 2015, vol. 4, no. 21, pp. 63–72. (In Russ.).

9. Samonastraivayushchiesya sistemy: spravochnik [Self-adjusting Systems: A Reference Book]. Chinaev P.I., Ed. Kyiv: Naukova Dumka, 1969. 528 p.

10. Choi M. A new intensity-hue-saturation fusion approach to image fusion with a tradeoff parameter. IEEE Trans. Geosci. Remote Sens., 2006, no. 44, pp. 1672–1682.

11. Forman R.T. Land mosaics: the ecology of landscapes and regions. Cambridge Univ. Press, 1995. 217 p.

12. Forman R.T., Godron M. Landscape Ecology. New York: JohnWiley & Sons, Inc., 1986. 620 p.

13. Griffiths P., van der Linden S., Kuemmerle T., Hostert P. A pixel-based Landsat compositing algorithm for large area land cover mapping. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 2013, vol. 6, no. 5, pp. 2088–2101.

14. Gobattoni F., Lauro G., Monaco R., Pelorosso R. Mathematical models in landscape ecology: stability analysis and numerical tests. Acta Appl. Math., 2013, vol. 125, no. 1, pp. 173–192.

15. Haken G. Printsipy raboty golonogogo mozga: Sinergeticheskii podkhod k aktivnosti mozga, povedeniyu i kognitivnoi deyatel’nosti [Principles of the Bare-Legged Brain: A Synergistic Approach to Brain Activity, Behavior and Cognitive Activity]. Moscow: PER CE Publ., 2001. 351 p.

16. Haken G. Sinergetika [Synergetics]. Moscow: PER CE Publ., 1980. 405 p.

17. Holben B.N. Characteristics of maximum-value composite images from temporal AVHRR data. Int. J. Remote Sens., 1986, vol. 7, no. 11, pp. 1417–1434.

18. Ingebritsen S. E., Lyon R. J.P. Principal components analysis of multitemporal image pairs. Int. J. Remote Sens., 1985, vol. 6, no. 5, pp. 687–696.

19. Kobernichenko V.G., Trenikhin V.A. Methods for the synthesis of images based on remote sensing data of the Earth of various resolutions. Usp. Sovrem. Radioelektroniki, 2007, no. 4, pp. 22–31. (In Russ.).

20. Krauklis A.A. Problemy eksperimental’nogo landshaftovedeniya [Problems of Experimental Landscape Science]. Novosibirsk: Nauka Publ., 1979. 282 p.

21. Krenke A.N., Puzachenko Yu.G., Puzachenko M.Yu. Spatial Organization of Regional Mesoclimate. Izv. Ross. Akad. Nauk. Ser. Geogr., 2019, no. 3, pp. 116–130. (In Russ.). https://doi.org/10.31857/S2587-556620193116-130

22. Kwarteng P., Chavez A. Extracting spectral contrast in Landsat Thematic Mapper image data using selective principal component analysis. Photogramm. Eng. Remote Sens., 1989, vol. 55, no. 1, pp. 339–348.

23. Luo Y., Trishchenko A.P., Khlopenkov K.V. Developing clear-sky, cloud and cloud shadow mask for producing clear-sky composites at 250-meter spatial resolution for the seven MODIS land bands over Canada and North America. Remote Sens. Environ., 2008, vol. 112 (12), pp. 4167–4185.

24. Makunina G.S. Geophysical systems of landscapes. Geogr. Nat. Resour., 2011, no. 32, pp. 301–307.

25. Metwalli M.R., Nasr A.H., Allah O.S.F., El-Rabaie S., Abd El-Samie F.E. Satellite image fusion based on principal component analysis and high-pass filtering. J. Opt. Soc. Am., 2010, no. 27, pp. 1385–1394.

26. Milkov F.N. Fizicheskaya geografiya: uchenie o landshafte i geograficheskaya zonal’nost’ [Physical Geography: Landscape Studies and Geographic Zoning]. Voronezh: Voronezh. Univ. Publ., 1986. 326 p.

27. Naidu V.P.S., Raol J.R. Pixel-level image fusion using wavelets and principal component analysis. Def. Sci. J., 2008, no. 58, pp. 338–352.

28. Nunez J., Otazu X., Fors O., Prades A., Pala V., Arbiol R. Multiresolution-based image fusion with additive wavelet decomposition. IEEE Trans. Geosci. Remote Sens., 1999, no. 37, pp. 1204–1211.

29. O’Neill R.V., Deangelis D.L., Waide J.B., Allen T.F., Allen G.E. A hierarchical concept of ecosystems. Princeton University Press, 1986, no. 23. 254 p.

30. O’Neill R.V., Milne B.T., Turner M.G., Gardner R.H. Resource utilization scales and landscape pattern. Landscape Ecol., 1988, vol. 2, no. 1, pp. 63–69.

31. Petrishchev V.P. et al. The formation features of landscapes in the Inderskii salt-dome area (Precaspian Hollow). Geogr. Nat. Resour., 2011, no. 32, pp. 146–151.

32. Potapov P., Turubanova S., Hansen M.C. Regional-scale boreal forest cover and change mapping using Landsat data composites for European Russia. Remote Sens. Environ., 2011, vol. 115, no. 2, pp. 548–561.

33. Preobrazhensky V.S., Aleksandrova T.D. Primary analysis of the terms of landscape dynamics. Izv. VGO, 1975, vol. 107, no. 5, pp. 397–404. (In Russ.).

34. Puzachenko Yu.G. Invariance of geosystems and their components. In Ustoichivost’ geosistem [Stability of Geosystems]. Moscow: Nauka Publ., 1983, pp. 32–41. (In Russ.).

35. Puzachenko Yu.G. Invariants of the dynamic geosystems. Izv. Akad. Nauk, Ser. Geogr., 2010, no. 5, pp. 6–16. (In Russ.).

36. Puzachenko Yu.G., Baibar A.S., Varlagin A.V., Krenke A.N., Sandlersky R.B. Thermal field of the southern taiga landscape of the Russian Hidden. Izv. Akad. Nauk. Geogr. Ser., 2019, no. 2, pp. 51–68. (In Russ.).

37. Puzachenko Yu.G., Onufrenya I.A., Aleshchenko G.M. Spectral analysis of the hierarchical organization of the relief. Izv. Akad. Nauk, Ser. Geogr., 2002, no. 4, pp. 29–38. (In Russ.).

38. Puzachenko Yu. G., Skulkin V.P. Independence within the whole and in the biotic part of the geosystem. System approach in geography. Tezisy Dokl., M., 1972, pp. 22–23. (In Russ.).

39. Riasati V.R., Zhou H. Reduced data projection slice image fusion using principal component analysis. Proc. SPIE, 2005, no. 5813, pp. 1–15.

40. Roy D.P., Ju J., Kline K., Scaramuzza P.L., Kovalskyy V., Hansen M., Loveland T.R., Vermote E., Zhang C. Web-enabled Landsat Data (WELD): Landsat ETM+ composited mosaics of the conterminous United States. Remote Sens. Environ., 2010, vol. 114, no. 1, pp. 35–49.

41. Sandlersky R.B. Revealing the invariant of the energy field of the landscape based on remote spectrozonal information. Available at: http://www.landscape.edu.ru/ files/sand_lomonos_2007.pdf (accessed 03.25.2019)

42. Sandlersky R., Krenke A. Solar energy transformation strategies by ecosystems of the boreal zone (thermodynamic analysis based on remote sensing data). Entropy, 2020, vol. 22, no. 10, pp. 1132–1140.

43. Sandlersky R.B., Puzachenko Yu.G. Energy characteristics of the geosystems of the Central Forest Reserve according to remote sensing data. Proceedings of the Central Forest State Natural Biosphere Reserve, 2007, no. 5, pp. 429–440. (In Russ.).

44. Shahdoosti H.R., Ghassemian H. Spatial PCA as a new method for image fusion. In The 16th CSI International Symposium on Artificial Intelligence and Signal Processing (AISP 2012), 2012, pp. 90–94.

45. Skulkin V.S. Empirical small-scale model of vegetation of the USSR. Extended Abstract of Cand. Sci. (Geography) Dissertation. Inst. Geogr. Akad. Nauk SSSR, 1979. 24 p.

46. Sochava V.B. Questions of classification of vegetation, typology of physical-geographical facies and biogeocenoses. In Voprosy klassifikatsii rastitel’nosti [Issues of Vegetation Classification]. Sverdlovsk: Ural Branch of the Academy of Sciences of the USSR, 1961, pp. 5–22. (In Russ.).

47. Sochava V.B. Vvedenie v uchenie o geosistemakh [Introduction to the Theory of Geosystems]. Novosibirsk: Nauka Publ., 1978. 319 p.

48. Tu T.-M., Su S.-C., Shyu H.-C., Huang P.S. A new look at IHS-like image fusion methods. Information Fusion, 2001a, vol. 2, no. 3, pp. 177–186.

49. Tu T.-M., Su S.-C., Shyu H.-C., Huang P.S. Efficient intensity-hue-saturation-based image fusion with saturation compensation. Opt. Eng., 2001b, no. 40, pp. 720– 728.

50. Turner M.G. Landscape ecology: the effect of pattern on process. Annu. Rev. Ecol. Syst., 1989, vol. 20(1), pp. 171–197.

51. Turner M.G. Landscape ecology: what is the state of the science? Annu. Rev. Ecol. Evol. Syst., 2005, vol. 36, pp. 319–344.

52. Turner M.G., Gardner R.H., O’Neill R.V. Landscape ecology in theory and practice. New York: Springer, 2001, vol. 401. 499 p.

53. Vasiliev I.S. et al. Stability of cryogenic landscapes on the northern section of the Yakutia railway line. Prir. Resur. Arktiki i Subarktiki, 2009, no. 2, pp. 4–8. (In Russ.).

54. White J.C., Wulder M.A. The Landsat observation record of Canada: 1972–2012. Canadian J. Remote Sens., 2014, vol. 39, no. 6, pp. 455–467.

55. Wu J.G. Scale and scaling: a cross-disciplinary perspective. In Key topics in landscape ecology. Wu J.G., Hobbs R., Eds. Cambridge University Press, Cambridge, 2006, pp. 115–142.

56. Wu J. Effects of changing scale on landscape pattern analysis: scaling relations. Landsc. Ecol., 2004, vol. 19, no. 2, pp. 125–138.

57. Zhu Z., Woodcock C.E., Holden C., Yang Z. Generating synthetic Landsat images based on all available Landsat data: Predicting Landsat surface reflectance at any given time. Remote Sens. Environ., 2015, no. 162, pp. 67–83.