ACCURACY AND NUMERICAL LIMITATIONS

When using SWIFT the question of accuracy arises. This is the particular concern for modeling waste concentrations which typically vary over many orders of magnitude. To address this issue an interpretation scale is defined. The brine and nuclide equations are formally defined in terms of mass fraction, that is, mass of constituent per mass of water. A consistent scale can be defined using the largest value of concentration and normalizing all other values. Readers should use the interpretation as guidance in model application. Inherent to developing the scale is the computer precision. Double precision variables are used consistently in SWIFT. This provides at least 15 significant figures for all real numbers.

In the table below, several limitations of model application are shown. At the lower end, the computer capable of only 15 significant figures, thus "normalized" concentrations less than 10^-15 are meaningless. In the next range, 10^-14 to 10^-12 we encountered numerical error. In this range results are accurate only to an order of magnitude. In using a numerical model, the code imposes further restrictions on the results. The numerical model solves a set of partial differential equations by matrix inversion. This process of repetitive additions, subtractions and multiplications requires at least six significant figures.

At the next higher level, 10^-8, the conceptual model limitation is defined. Based on modeling experience, the assumption inherent in the development of a conceptual model limit the range of defensible analysis.

In the defensible analysis, model results are highly reliable and accurate. The range is from 1 to approximately 10^-7. This range typically exceeds the observed in natural systems. For example a hazardous waste source may be 100,000 ug/L or ppb and the detection limit from laboratory analysis is only 1 ug/L (ppb). This range is only 10⁵.

Log of Concentration	Normalized Concentration
-1	Range of Defensible Analysis
-2
-3
-4
-5
-6
-7
-8	Conceptual Model Limitations
-9	Computer Code Accuracy Limitations
-10
-11
-12	Numerical Error
-13
-14
-15	Computer Precision Limits (i.e., double precision with 15 significant digits)

Interpretation Scale.