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Bias and variance in model results associated with spatial scaling of measurements for parameterization in regional assessments


Stephen M. Ogle, fax +1970 491 1965, e-mail:


Models are central to global change analyses, but they are often parameterized using data that represent only a portion of heterogeneity in a region. This creates uncertainty in the results and constrains the reliability of model inferences. Our objective was to evaluate the uncertainty associated with differential scaling of parameterization data to model soil organic carbon stock changes as a function of US agricultural land use and management. Specifically, we compared analyses in which model parameters were derived from field experimental data that were scaled to the entire US vs. the same data scaled to climate regions within the country. We evaluated the effect of differential scaling on both bias and variance in model results.

Model results had less variance by scaling data to the entire country because of a larger sample size for deriving individual parameter values, although there was a relatively large bias associated with this parameterization, estimated at 2.7 Tg C yr−1. Even with the large bias, resulting confidence intervals from the two parameterizations had considerable overlap for the estimated national rate of SOC change (i.e. 77% overlap in those intervals). Consequently, the results were relatively similar when focusing on the uncertainty rather than solely on the mean estimate. In contrast, large biases created less overlap in confidence intervals for the change rates within individual climate regions, compared with the national estimates. For example, the overlap in resulting intervals from the two parameterizations was only 32% for the warm temperate moist region, with a corresponding bias of 3.1 Tg C yr−1.

These findings demonstrate that there is a greater risk of making erroneous inferences because of large biases if models are parameterized with broader scale information, such as an entire country, and then used to address impacts at a finer spatial scale, such as sub-regions within a country. In addition, the study demonstrates a trade-off between variance and bias in model results that depends on the scaling of data for model parameterization.