Many of the relationships used in coupled land-atmosphere models to describe interactions between the land surface and the atmosphere have been empirically parameterized and thus are inherently dependent on the observational scale for which they were derived and tested. However, they are often applied at scales quite different than the ones they were intended for due to practical necessity. In this paper, a study is presented on the scale-dependency of parameterization which are nonlinear functions of variables exhibiting considerable spatial variability across a wide range of scales. For illustration purposes, we focus on parameterizations which are explicit nonlinear functions of soil moisture. We use data from the 1997 Southern Great Plains Hydrology Experiment (SGP97) to quantify the spatial variability of soil moisture as a function of scale. By assuming that a parameterization keeps its general form the same over a range of scales, we quantify how the values of its parameters should change with scale in order to preserve the spatially averaged predicted fluxes at any scale of interest. The findings of this study illustrate that if modifications are not made to nonlinear parameterizations to account for the mismatch of scales between optimization and application, then significant systematic biases may result in model-predicted water and energy fluxes.
Bibliographical noteFunding Information:
This work has been supported by the joint NOAA/NASA GCIP program under a NASA grant NAG8-1519. The first author gratefully acknowledges the support of a USDA National Needs Fellowship in Water Science. Computer resources were kindly provided to us by the Minnesota Supercomputing Institute. The authors thank the SGP97 participants for collecting and processing the ESTAR derived soil moisture data and making it readily available to the research community.