ABSTRACT
This chapter contrasts non-deterministic and deterministic data that respectively cannot and can be forward modeled. Environmental parameters are related to non-deterministic data by numerical, statistical, and dimensional analyses, and to deterministic data by inversion. In electronic computer modeling, the dominant data format is the array or matrix that is manipulated by matrix addition, subtraction, and multiplication operations to assess the array's scalar determinant and symmetric, transpose, and inverse matrices. Dimensional analysis considers the data-attached measurement units of length, mass, time, temperature, and other dimensions that fundamentally constrain data modeling. Valid models are dimensionally homogenous where the measurement units are the same on both sides of the equality sign. Buckingham's π-theorem isolates the [n – m] dimensionless groupings of the n parameters in the m dimensions for insights on data modeling. Dimensional analysis also facilitates effective scale modeling studies of difficult-to-quantify environmental phenomena where the scale model and its environmental prototype must maintain similitude in their geometric, kinematic, and dynamic parameters.
