How can these climate changes be measured, and is there a mathematical mechanism that can be relied upon to prove that there is an actual change in climate elements?
Climatic factors include air and ocean temperature, air humidity, wind conditions, the presence and duration of seasons, etc. But the criterion for climate change is only temperature. Other parameters are derivatives of temperature.
It is believed that temperature depends on insolation and the "greenhouse effect", but temperature also depends on geothermal heat flows.
Thus, climate change has both external and internal causes.