COS 264-3 - Modelling Energy Flow from Landscape Gradients to Mosaics with the Law of Energy Conservation

Abstract: Background/Question/Methods

Thermodynamics is believed as the essential cornerstone for governing and constraining landscape patterns, landscape process change, and propagation of pattern-process relationships. Using thermodynamics in ecological research at landscape scales requires the conceptualization of thermodynamic entropy that can help characterize landscape heterogeneity. Thus, computation methods of thermodynamic entropy of landscape models (i.e., landscape gradients and mosaics) have been proposed, providing researchers with powerful tools to investigate thermodynamic processes in ecological modelling. Unfortunately, we do not know how thermodynamics can be quantitatively linked to ecological studies with thermodynamic entropy, yet this knowledge is critical for providing a rigorous physic foundation for understanding the interaction of pattern-process relationships as well as the causes and consequences of ecological heterogeneity. Therefore, we aim to make a preliminary effort in investigating the energy flow from landscape gradients to mosaics with land cover classification. The first objective was to verify the feasibility of applying thermodynamic entropy to characterize the thermodynamic features of both landscape gradients and mosaics in a hierarchical way. Based on thermodynamic entropy, the second objective was to generalize the law of energy conservation to model the energy flow. To achieve those objectives, we first made an analogy between landscape models and thermodynamic ensembles where a 2×2 landscape patch is considered as the minimum unit. Thereafter, we employed a kinetic-theory-based approach to generate 100,000 simulated landscape patterns including gradients and mosaics patterns to examine the thermodynamic entropy in terms of its thermodynamic consistency. Finally, we proposed a generalized Jarzynski equation for the law of energy conservation to quantify the energy flow, containing parameters such as the number of land cover classes, thermodynamic entropy of landscape gradients and mosaics, and classification accuracy.

Results/Conclusions

Thermodynamic entropy is able to describe the thermodynamic features of landscape gradients and mosaics. A form of the law of energy conservation is discovered in the transformation of landscape gradients into mosaics, which takes a very strong linear relationship (R²=0.95) between the valid work and energy difference between landscape gradient and mosaics. In contrast, a nonlinear relationship is found between the energy of landscape gradients and that of landscape mosaics, particularly in extremely heterogeneous regions. This study provides a case for linking thermodynamic laws and concepts (i.e., work and energy flow) to the characterization and understanding of landscape heterogeneity.