 However, both of these basic approaches to confirming models encounter serious difficulties when applied to nonlinear models, where the principle of linear superposition no longer holds. In the first approach, successive small refinements in the initial data used by nonlinear models is not guaranteed to lead to any convergence between model behavior and target system behavior. Any small refinements in initial data can lead to non-proportional changes in model behavior rendering this piecemeal convergence strategy ineffective as a means for confirming the model. A refinement of the quality of the data “in the right direction” is not guaranteed to lead to a nonlinear model monotonically improving in capturing the target system’s behavior. The small refinement in data quality may very well lead to the model behavior diverging away from the system’s  behavior.[6] 