Chapter 2 Perspectives and Methods of Scaling

Transferring information between or across scales or organizational levels is inevitable in both basic research and its applications, a process generally known as "scaling" (Wu and Li, Chapter 1). Scaling is the essence of prediction and understanding both of which require cross-scale translation of information, and is at the core of ecological theory and application (Levin 1992, Levin and Pacala 1997, Wu 1999). While the importance of scaling in ecology has been acutely recognized in recent decades, how to conduct scaling across heterogeneous ecosystems remains a grand challenge (Turner et al. 1989, Wu and Hobbs 2002). A number of scaling approaches and methods have been developed and applied in different disciplines ranging from physics, engineering, biology, to social sciences. Two general scaling approaches can be distinguished: similarity-based scaling and dynamic model-based scaling methods (Bloschl and Sivapalan 1995). Similarity-based scaling methods are rooted in the concepts and principles of similarity and self-similarity and often characterized by relatively simple mathematical or statistical scaling functions, even though the underlying ecological processes of a phenomenon may be extremely complex. In contrast, dynamic modelbased scaling methods use deterministic or stochastic models to simulate the processes of interest, and to transfer information across scales by either modifling the parameters and input variables of the same model or developing multiple-scaled models. In this case, information transfer between different scales is accomplished through manipulating the inputs, outputs, and formulations of dynamic models. In both approaches, it is important to properly identify scaling thresholds at which scaling relations often change abruptly, reflecting hndamental shifts in underlying processes or controlling factors and defining the domains of applicability of specific scaling methods. While the previous chapter (Wu and Li, Chapter 1) discussed various concepts of scale and scaling, in this chapter we focus on the major characteristics of the two scaling approaches and several more specific upscaling and downscaling methods