Scale and scaling in soils

- Comprehensive review of concepts and ideas on scale and scaling in soils
- Different types of scale definition discussed.
- General scaling methodology presented that is used in soil studies.
- Scaling methods that were developed in soil studies.
- Outlook and research directions are suggested.

Scale is recognized as a central concept in the description of the hierarchical organization of our world. Pressing environmental and societal problems require an understanding of how processes operate at different scales, and how they can be linked across scales. Soil science as many other disciplines obtain the bulk of their empirical information at fine scales, whereas results of environmental diagnostics, monitoring, and predictions are needed to make important policy decisions at much larger scales. It becomes imperative to relate the information that is available and produced at different scales. The objective of this work is to present an overview of concepts that are currently used to define and relate scales in soil studies. The paper is not intended to be a compendium, but rather should be viewed as material for discussion, reference, and critique. It discusses definitions and terminology, including general approaches of scale problems in environmental studies that are applicable to soils, including hierarchies, measurement metrics, similitude, non-geometric scale metrics, and notions of upscaling and downscaling. Concepts of general scaling methods and theories are dimensional analysis, power law scaling, space and time dependent scaling. A section on spatiotemporal patterns introduces scaling ideas that were used in soil studies such as empirical orthogonal functions, data assimilation, and cumulative distribution function matching. Reviewed scaling methods developed specifically to soil studies include geometric similitude of pore spaces, scaling with Richards equation, scale dependencies of water and solute flux model parameters, scaling based on temporal stability, overland flow and sediment transport as the scaling phenomenon, and the relevance of scaling to pedotransfer functions. An outlook for scaling research in soils is presented that shows the needs of additional research and the feasibility of using scaling to enrich and advance soil research to help face the grand challenges of modern times.