The dynamics of a surge tank, used to suppress damaging over-pressure in fluid lines, is described by a simple ordinary differential equation (ODE) the same as eqn. 1 in the recent paper by Spencer and Brasswell, “On the Misdiagnosis of Surface Temperature Feedbacks from Variations in Earth’s Radiant Energy Balance”, so very generally applicable to many systems.
1. The variability of the height of fluid in the tank (red) is suppressed and lagged, but there is no parameter in the model for lag. Lag is an emergent property of the system.
2. Increasing the periodicity of the flow into the tank increases the mean height of the water in the tank (try it). So the average of the water height is not directly related to the average inflow, but also depends on the period, another surprising emergent property.
This simple example shows how simple dynamics can lead to surprising behavior, and why misdiagnosis occurs by failing to account for dynamics when applying a simple linear regression, say. The first step in a correct analysis of a system is a valid physical model.
You can change the parameters and experiment with other aspects of the model.