PRINCIPLE OF PARSIMONY, FAKE SCIENCE, AND SCALES (Invited Presentation)

Environmental fluids migrate at velocities of many scales, influenced by many factors at a multiplicity of scales. Due to difficulties in predicting exact motions of water molecules, and consideration of the scale of our interests (bulk behaviors of many molecules), Fick’s law (diffusion concept) has been developed for predicting solute diffusion process in space and time. Further, Taylor (1921) demonstrated that random motion of the molecules reach the Fickian regime in less a second and will reach the ergodic condition if our sampling scale is large enough. 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 or convection-dispersion equation (ADE or CDE) generally has been found suitable for predicting solute concentration breakthroughs in uniformly packed soil columns. This is due to the fact that the solute is released over the entire cross-section of the column, and it thus has encountered 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. Besides, observed breakthrough curves are the concentrations integrated over the column cross-section (the scale of our interest), and they meet the ergodicity assumption embedded in 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 interests. The ergodic and the Fickian conditions are thus difficult to be met. Upscaling and modifying Fick’s law for solute dispersion, and deriving universal scaling rules of the dispersion for the field- or basin-scale pollutant migrations are merely misuse of the parsimony principle. They create red herrings and fake sciences. The appropriate principle of parsimony for these situations is to map large-scale heterogeneities as detailed as possible (or to the scale of our observations and interests) and to adapt Fick’s law for effects of small-scale heterogeneity resulting from our inability to characterize them at high resolutions.