Are Models Too Simple? Arguments for Increased Parameterization

The idea that models should be as simple as possible is often accepted without question. However, too much simplification and parsimony may degrade a model's utility. Models are often constructed to make predictions; yet, they are commonly parameterized with a focus on calibration, regardless of whether (1) the calibration data can constrain simulated predictions or (2) the number and type of calibration parameters are commensurate with the hydraulic property details on which key predictions may depend. Parameterization estimated through the calibration process is commonly limited by the necessity that the number of calibration parameters be smaller than the number of observations. This limitation largely stems from historical restrictions in calibration and computing capability; we argue here that better methods and computing capabilities are now available and should become more widely used. To make this case, two approaches to model calibration are contrasted: (1) a traditional approach based on a small number of homogeneous parameter zones defined by the modeler a priori and (2) regularized inversion, which includes many more parameters than the traditional approach. We discuss some advantages of regularized inversion, focusing on the increased insight that can be gained from calibration data. We present these issues using reasoning that we believe has a common sense appeal to modelers; knowledge of mathematics is not required to follow our arguments. We present equations in an Appendix, however, to illustrate the fundamental differences between traditional model calibration and a regularized inversion approach.     

Stable isotope and trace element status of subsistence-hunted bowhead and beluga whales in Alaska and gray whales in Chukotka

Tissues of bowhead, beluga, and gray whales were analyzed for Ag, Cd, Cu, Se, Zn, THg and MeHg (belugas only). Delta15N and delta13C in muscle were used to estimate trophic position and feeding habitat, respectively. Trace element concentrations in tissues were significantly different among whale species. Hepatic Ag was higher in belugas than bowheads and gray whales. Gray whales had lower Cd concentrations in liver and kidney than bowhead and belugas and a sigmoid correlation of Cd with length was noted for all whales. Renal and hepatic Se and THg were higher in belugas than in baleen whales. The hepatic molar ratio of Se:THg exceeded 1:1 in all species and was negatively correlated to body length. Hepatic and renal Zn in subsistence-harvested gray whales was lower than concentrations for stranded whales. Se:THg molar ratios and tissue concentrations of Zn may show promise as potential indicators of immune status and animal health.