Scaling Issues

Scaling is an important issue for agricultural system models because results from fields or portions of a field often need to be extrapolated to another scale. A significant amount of new research in the refinement of agricultural system models is currently centered on determining scale-appropriate parameters for different model components. Generally, scaling-up involves both averaging spatial variability in parameters within a simulation unit, where the averaging process can be highly nonlinear, and incorporating process interactions beneath the simulation scale such that effects manifested at the scales of interest are captured by the upscaled parameters. For field and larger scales, uncertainty is most often due to unaccounted spatial variability of model parameters and processes within a simulation unit (typically assumed homogeneous) and errors in estimating so-called 'effective parameters'. For highly nonlinear soil-hydrologic processes, strictly speaking, there are no unique effective parameters; however, for practical purposes effective parameters may be calibrated to obtain a selected output variable.

For modeling and managing complex landscape and climate variability across multiple scales, ongoing research is helping to quantify the variability of soil parameters over space and time within a simulation unit using available spatial information about the causative factors, including physical soil properties and surrogate data such as terrain attributes. Management effects on soil hydraulic properties are being considered as well. For a given parent material, climate, biological factors, and time, topography is an important factor that has been shown to cause spatial variability of soil properties. Topographic data can now be rapidly and accurately measured at fine spatial intervals. An important question currently being researched is: can a set of topographic attributes in a given management system be related to spatial variability of soil properties, soil water content, and crop yield, and also used for upscaling?

New physically based methods of scaling up results from plots to field, farm, and watershed scales are also being developed. Historically, scaling of agricultural and landscape variables has been explored using a combination of empirical (data-based statistical) and theoretical (conceptual and numerical) methods. Both approaches have been used to explore scaling of soil properties and processes, field-scale relationships between grain yield, soil moisture, and topographic attributes, and theoretical scaling of infiltration using generated soils and rainfall patterns. Empirical methods provide evidence of real-world scaling behaviors that are useful for parameter estimation at different scales, while theoretical methods provide insights into process interactions in space and time that are currently infeasible to measure. Using measured spatial soil patterns in detailed spatial models allows one to simulate explicit interactions over space and time. Understanding and quantification of this information is being used to scale up responses over variable agricultural landscapes. In this way, the scale-dependence of agricultural management and conservation practices can be incorporated into larger scale (i.e., watershed and basin) models.

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