Scale and the Nature of Spatial Variability: Field Examples Having Implications for Hydrologic Modeling

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Abstract
In this paper we examine how the nature of spatial variability affects hydrologic response over a range of scales using five field studies as examples. The nature of variability was characterized as either stochastic, when random, or deterministic, when due to known, nonrandom sources. We have emphasized how that characterization may change with the scale of hydrologic model. The five field examples, along with corresponding sources of variability, were (1) infiltration and surface runoff affected by shrub canopy, (2) groundwater recharge affected by soil depth, (3) groundwater recharge and streamflow affected by small‐scale topography, (4) frozen soil runoff affected by elevation, and (5) snowfall distribution affected by large‐scale topography. In each example there was a scale, the deterministic length scale, over which the hydrologic response was strongly dependent upon the specific, location‐dependent ecosystem properties. Smaller‐scale variability may be represented as either stochastic or homogeneous with nonspatial data. In addition, changes in scale or location sometimes resulted in the introduction of larger‐scale sources of variability that subsume smaller‐scale sources. Thus recognition of the nature and sources of variability can reduce data requirements by focusing on important sources of variability and using nonspatial data to characterize variability at scales smaller than the deterministic length scale. All the sources of variability described are present in the same watershed and affect hydrologic response simultaneously. Physically based models should therefore utilize both spatial and stochastic data where scale appropriate. Other implications for physically based modeling are that modeling algorithms should reflect larger‐scale variability which generally has greater impact and that model and measurement grids should be consistent with the nature of variability.