Principle of Parsimony, Fake Science, and Scales

Dr. Tian-Chyi Jim Yeh, Professor, Department of Hydrology and Atmospheric Sciences, The University of Arizona, USA

Abstract for Weekly Colloquium on Thursday, September 14, 2017 at 4 pm in Harshbarger 206 ~ Refreshments at 3:45 pm

Environmental fluids migrate at velocities of many scales and are influenced by multi-scale factors. Considering difficulties in predicting exact motions of water molecules, and the scale of our interests (bulk behaviors of many molecules), Fick’s law (diffusion concept) has been created to predict solute diffusion process in space and time. G.I. Taylor (1921) demonstrated that random motion of the molecules reach the Fickian regime in less a second if our sampling scale is large enough to reach ergodic condition. Fick’s law is widely accepted for describing molecular diffusion as such.  This fits the definition of the parsimony principle at the scale of our concern. Similarly, advection-dispersion or convection-dispersion equation (ADE or CDE) has been found quite satisfactory for analysis of concentration breakthroughs of solute transport in uniformly packed soil columns. This is attributed to the solute is often released over the entire cross-section of the column, which has sampled many pore-scale heterogeneities and met the ergodicity assumption. Further, the uniformly packed column contains a large number of stationary pore-size heterogeneity. The solute thus can reach the Fickian regime after traveling a short distance along the column. Moreover, breakthrough curves are concentrations integrated over the column cross-section (the scale of our interest), and  they meet the ergodicity assumption embedded in the ADE and CDE.  To the contrary, scales of heterogeneity in most groundwater pollution problems evolve as contaminants travel. They are much larger than the scale of our observations and our interests. As a consequence, the ergodic and the Fickian conditions are difficult to satisfy. Upscaling and modifying Fick’s law for solution dispersion, and deriving universal scaling rules of the dispersion to the field- or basin-scale pollution migrations are merely misuse of the parsimony principle.  They create red herrings and fake sciences ( i.e., the development of theories for predicting processes that can not be observed.)  The appropriate principle of parsimony for these situations dictates mapping of large-scale heterogeneities as detailed as possible and adapting the Fick’s law for effects of small-scale heterogeneity resulting from our inability to characterize them at high resolutions.