Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides

The asymptotic behavior of a linear compartment model for the environmental movement of radionuclides is investigated. Here, the expression asymptotic behavior is used to designate the behavior of q(t) as t → ∞, where q is the solution of a vector differential equation of the form dq/dt = h + Kq. The asymptotic behavior of such equations is described. For the model and conditions under consideration, each element of q converges monotonically to a steady-state value. A hydrologic system is defined and used to illustrate this behavior. An approach to sensitivity analysis employing Latin hypercube sampling, rank transformations and stepwise regression is presented and then applied to this system. A total of 20 independent variables is introduced and the following dependent variables are investigated for the various components of the system: amount of radionuclide present at steady state. concentration of radionuclide at steady state, and time required to reach 90% of steady state. Finally, an application of asymptotic behavior in the analysis of a hypothetical site for the geologic isolation of high-level radioactive waste is described and a brief discussion of differential sensitivity analysis is given.