Remarkably, the 12-month running total precipitation hasn't dipped below about 12" since the record wet summer of 2014, and such a lengthy wet spell is clearly unprecedented in the roughly 100-year period of record. When we consider that the long-term median annual precipitation is less than 11", it's quite extraordinary to see six straight years well above that level.
If we assume that each year is statistically independent of the last - which is not true but may not be too far off the mark (at least prior to 2014) - then we can do a crude estimate of the probability that 6 straight years will have such high precipitation by random chance. The driest of the last 6 years was 2018, with 13.75", and this level was only exceeded 14 times from 1930-2013, i.e. 14 of 84 years, or an annual probability of 16.7%. The chance that this happens 6 times in a row is then only 0.002%, and (naïvely) the recurrence interval is about 50,000 years. It seems overwhelmingly likely, therefore, that the climate has changed; the rainfall statistics are not stationary over time.
An interesting question to consider in connection with this change is the seasonal distribution of the increase in precipitation. June of this year was very wet; did June contribute significantly to the overall increase in 2014-2019? The answer is yes, but larger increases have occurred in July through September, and in percentage terms the change in September is most striking (see below). September 2015 and 2014 were the wettest and 3rd wettest on record, respectively, and September 2016 and 2018 were also very wet.
It's inevitable that the largest changes in total precipitation have occurred in the warm season, because that's when most of Fairbanks' liquid-equivalent precipitation falls; and if we imagine a percentage increase in water vapor content (related to, say, warming oceans), the impact in absolute terms would be most noticeable in summer.
The increase in September is interesting, and it's tempting to suggest it has to do with reduced Arctic sea ice; we would expect a large increase in lower atmospheric warmth and moisture at high latitudes as the Arctic Ocean opens up in autumn. However, I suspect the Arctic warming only provides a background influence on September precipitation, and that other, more immediate causes (such as recent storm tracks and circulation anomalies) can be identified to explain the dramatic difference in the past few years.
Finally, it's fascinating to look at how the distribution of daily precipitation amounts has changed during June through September, the months that contribute most of the total precipitation increase. The chart below shows that the frequency has increased in all daily precipitation categories above 0.1", and the percentage change in frequency has been very substantial for the wettest days, i.e. those with more than 0.5".
Of course a change in the frequency of the wettest days makes a relatively outsized contribution to the total precipitation increase, and this is illustrated below. The lion's share of the total increase has arisen from a jump in daily precipitation totals above 0.5". In 2014-2019, there were 32 of these events in June through September, amounting to an average of 4.62" per year; but from 1930 to 2013, these events occurred at less than half the frequency, and amounted to only 1.83" per year on average. This difference accounts for about two-thirds of the overall increase in total annual precipitation.
If we consider the rate of observing events of 0.5" or more, we can do another crude estimate of the probability that the past six years could have occurred by random chance. Using a Poisson distribution with an occurrence rate (1930-2013) of 2.35 events/year, the probability of seeing 32 or more events in 6 years is 0.003%, which is surprisingly close to the 0.002% estimated above from the annual totals. Either way, the level of statistical significance is very high, and so I think we can say with very high confidence that the past six years represent a different climate regime from earlier decades. As noted in this 2018 post by Rick on a similar topic, this has important implications for city management and planning.