One of the best examples of transient modelling is transient climate simulation.

The transient climate simulation introduced realistic oceans.

Coupled ocean-atmosphere GCMs use transient climate simulations to project/predict future temperature changes under various scenarios.

A transient climate simulation is a mode of running a global climate model (GCM) in which a period of time (typically 1850-2100) is simulated with continuously-varying concentrations of greenhouse gases so that the climate of the model represents a realistic mode of possible change in the real world.