  Using observational data and an elementary rigorous statistical fact it is
easily shown that the distribution of Earth's climate is non-stationary.
Examination of records of hundreds of local Industrial Era temperature
histories in the Northern Hemisphere were used to show this fact.
Statistically, the mean of the ensemble has been rising during the Industrial
Era. All of this confirms what climate scientists already know. The issue of
predictions under uncertainties was tackled as well: a simple balance model was
tuned to track an ensemble of climate records. Stochastic parametrizations were
created to capture natural and anthropogenic CO2 forcings. The resulting
stochastic model was then tested against historical data and then used to make
future predictions. This exercise confirmed as well climate science attribution
to significant global warming during the Industrial Era to anthropogenic
activities. The variability of the model due to uncertainties is simply not
large enough to obfuscate a clear rise in the mean temperature in the
Industrial Era. Further, even if the variance of the natural CO2 contribution
is greatly increased artificially (in the model), the fluctuations cannot
account for the current change in the historical mean.
  These outcomes weaken the factual validity of the US administration,
2016-2020, claims that there are too many uncertainties in climate and climate
science to make climate predictions, and further that contemporary reports of
floods, extreme weather, even a rising global mean temperature are simply
manifestations of a climate that always fluctuates within a nature-derived
statistical distribution.
