Monday, June 24, 2019

Utqiaġvik Temperature Records

Exceptional warmth occurred last week over much of northern Alaska, and a significant new record high temperature was set at Utqiaġvik (formerly Barrow), where the 73°F on Thursday was the highest on record for the month of June; the previous record was 72°F in 1996.  June therefore joins May, October, and January as having set or tied calendar-month high temperature records in the last few years.

There are some interesting aspects to the distribution of Utqiaġvik's calendar-month records over the decades, but first I'll state the obvious: average temperatures have increased very dramatically in the 100+ years of climate observations, and daily record high temperatures have been broken or tied with high frequency in recent years.  The second chart below shows a running 10-year total number of high temperature records, both for daily maximum temperature and for high daily minimum temperature.  Very nearly half of all of the calendar-day high temperature records have been set or tied since 1990.  Note that I'm only using the Weather Bureau/NWS era of 1930-present for the analysis of records.




The distribution of daily low temperature records is even more striking, because the frequency has dropped to just about zero in recent years.  In fact, the last time a calendar-day record was broken (not tied) for daily minimum temperature was in February 2009, and if we allow data from the 1920s, we have to go back to 2006 to find a new low temperature record.


In light of this, the much smaller sample of calendar-month records is interesting; see the chart below.  The red columns show the number of calendar-month high temperature records for non-overlapping decades since 1930; these are the monthly records (set or tied) for daily maximum temperature, of which four have been reached in the past few years.  The blue columns show the high records for daily minimum temperature, and a few of these have also been broken or tied in recent years (January, July, and November).


The obviously interesting aspect of this is how many of Utqiaġvik's calendar-month records were set in the 1930s and are still standing; in fact the largest number of warm records (daily max and daily min) from a single decade is from the 1930s.  This is really quite surprising, given the ramp-up in mean temperatures and daily warm records.  Of course the calendar-month records represent a very small and rather arbitrary sample of the most extreme events, and a more rigorous statistical analysis would be needed to make a definitive statement; but this does seem to suggest that the very extreme warm tails of the temperature distribution have not shifted as much as the less extreme parts of the distribution.  In other words, it appears that the modern warmer climate is not producing very-rare warm extremes of the same amplitude (relative to the mean) as the climate of the 1930s.  I've noted before on this blog that the 1930s was a time of wild extremes in Alaska climate, and this is another piece of evidence in that direction.

Here's the distribution of calendar-month cold records in Utqiaġvik.  The 1970s really stand out, and this is fairly consistent with the mean temperature and the daily records from that decade, although the monthly records suggest that extreme anomalies on the cold side were particularly concentrated in that decade, just as warm extremes were concentrated in the 1930s.



Saturday, June 15, 2019

Permafrost Update

Back in September I posted some brief analysis of soil temperature profiles at one of the Fairbanks monitoring sites run by UAF's Permafrost Laboratory.  Not surprisingly (in view of the remarkable warmth of recent years) the data showed a dramatic warming trend, and so it's of interest to do an update now that another year of data is available.

The charts below are the same as before, but with 2017's annual values appended with the dashed black lines.  2017's mean temperature was slightly lower than 2016 in most of the column, and the annual minimum was lower than for 2016 at each level between about 0.25m and 1.5m depth.  We know why this is: winter 2016-2017 was cooler than the other winters since 2013-14, and March 2017 in particular was unusually cold, so this provided a slight recovery in the condition of the permafrost.

Readers will note that the warming trend apparently continued unabated at the top layers just below the surface, but this appears to be at least partly related to some rather substantial ground subsidence relative to the temperature instrument in recent years.  From 2007 through 2016, the second level below ground was reported as 12cm, but in 2016-17 this changed to 8cm, and in the most recent year (2017-2018) it was reported as only 4cm.  The top-level sensor started at 2.5cm below ground but is apparently now 6cm above ground!  I haven't made the vertical adjustment on the chart, but obviously this could make a rather big difference at the top levels.




It's worth looking again at the temperature trace from the sensor at 0.525m (now 0.44m) - see below.  The effect of March 2017 is obvious, but I think what is more striking is the fact that this level almost failed to re-freeze in the subsequent winter (2017-2018); the temperature didn't drop below freezing until March 14, the minimum was -0.24°C on April 11, and it was back up to -0.09°C by the end of the data series on June 1.

Of course winter 2017-2018 was very warm in Fairbanks (13°F above normal in December), but the unusually deep snow cover probably also contributed to the lack of a subsurface cold wave in late winter; the ground was well insulated from the cold above, and there wasn't much cold to diffuse downward.


These results are all taken from just one location; what about others?  I did similar analysis with data from two sensors at the Bonanza Creek ecological research site, which is about half way between Fairbanks and Nenana.  At the first sensor, the trends since 2010 are similar to those at Smith Lake, but 2017 produced very similar temperatures to 2016 instead of seeing a small recovery towards colder conditions.  (Note that the sensor depths have trended in the opposite direction at this location, with the top sensor dropping from 7cm in 2010 to 11cm in 2017-18.)





The temperature time series at 52cm depth is quite remarkable when we look at the late winter minima; there has been a stair-step pattern of 2°C increases at two-year intervals (2014, 2016, 2018).  And just like at Smith Lake, the last winter in the series shows no hard freeze at this level about 20 inches below the surface; the winter's minimum was only -0.1°C.


The same thing is evident closer to the surface; even at the shallow level of 22cm (now 26cm), the 2017-2018 winter minimum was only -0.7°C.


And for comparison, here's a quick look at the same levels from the second permafrost site at Bonanza Creek.  It's essentially the same story, although winter 2015-2016 also saw very minimal re-freeze at the half-meter depth.




In conclusion, it's striking to see the rapid pace of change at these permafrost sites in interior Alaska.  Not only has warming occurred throughout, and the active layer deepened (i.e. seasonal thaw extends deeper), but we're seeing layers that were formally permafrost now almost fail to refreeze in winter (e.g. 0.5m level at Smith Lake).

In last September's post I said that "Smith Lake #1 may soon see seasonal ice atop permanent thaw", but I wasn't imagining that something like this would appear in the very next year of data.  What will the next annual update reveal?

Saturday, June 8, 2019

Peak Rainfall Rates

Intrigued by the extreme rainfall rate that was reported last Sunday at Fairbanks airport, I procured the history of 1-minute precipitation observations from the Fairbanks ASOS; this data goes back to 2000 and now provides a nearly two-decade history of high-resolution rainfall data in the warm season.  I had to pick out about 40 obviously erroneous data points, and it's likely I didn't find all the problems, but I checked the most extreme events of each year in the remaining data and they all look fine.

There is a lot of interesting analysis that could be done on the data, but the charts below provide the perspective for last week's rain.  The greatest 5-minute rainfall amount was 0.36" on July 4, 2005, and the top 10-minute and 15-minute totals occurred on July 21, 2010.  Both of these events saw peak 1-minute rates of 0.09", or 5.4"/hour, and that's also the highest observed for a 1-minute total.

The 1-minute data is only updated once a month, so we won't know for a few more weeks whether the recent event broke these records, but the realtime data from the ASOS does suggest so: 0.55" in 8 minutes is greater than the 10-minute record of 0.53".

What's perhaps even more striking is that the 10-minute record for June is only 0.22"; it's much more common (relatively) for extremely heavy rain to fall in July.  There have been only 6 events in total with at least 0.25" in 10 minutes, and of these 5 were in July and 1 was in August (August 17, 2008).

It's also curious to note something of a discrepancy with the NOAA precipitation atlas: the NOAA frequency estimates indicate a recurrence interval of about 20 years for 0.25" in 5 minutes, but it appears Fairbanks has now seen this happen 4 times in 20 years.




Tuesday, June 4, 2019

Early Morning Storms Up North

I saw this posted today by the NWS in Fairbanks and thought it was neat:



5am AKDT is of course 4am standard time, but Allakaket is more than an hour west of the true time zone center, so the picture was taken before 3am local solar time.  Tomorrow is the last day with a sunset in Allakaket until July 7th.

Monday, June 3, 2019

Intense Thunderstorm in Fairbanks

Yesterday evening the Fairbanks area experienced a very strong thunderstorm system that prompted a rare severe thunderstorm warning from the National Weather Service.  Here's the NWS public information statement from shortly after the event:

"Public Information Statement National Weather Service Fairbanks AK 802 PM AKDT Sun Jun 2 2019 ...Strong Thunderstorm Hits Fairbanks... Fairbanks had a thunderstorm move west across the city between 6pm and 7pm this evening. An NWS Weather Spotter in Hamilton Acres reported half inch size hail, and radar indicated hail of up to one inch diameter. There were numerous reports of pea size hail and frequent lightning in the Fairbanks area. The Fairbanks International Airport had 65 hundredths (0.65) of an inch of rain in a period of 21 minutes, which is one of the highest rainfall rates in recent memory in Fairbanks. There have been about 200 lightning strikes in the Fairbanks North Star Borough since the thunderstorms began around 3pm. As of 745 pm this evening, thunderstorms had moved south and west of Fairbanks and North Pole."

As luck would have it, a very intense part of the storm complex occurred over the international airport, and the ASOS instruments reported extremely heavy rain as well as hail of 3/8" diameter.  I have only been able to find a few instances of hail being reported from the Fairbanks ASOS (May 15, 2012, August 9, 2002, and June 9, 1997), and only the 2002 report included a hailstone size observation (1/4").

The ASOS precipitation data also show that 0.65" of rain fell in 21 minutes, and of that 0.55" fell in 8 minutes, which equates to a rate of 4.1" per hour.  This is a truly remarkable rainfall rate for such a high latitude, and I suspect it may contend for an all-time record for Fairbanks; more investigation would be justified.

According to the NOAA precipitation atlas, the estimated recurrence interval for a 0.55" rain amount is near 200 years for a 10-minute interval and over 500 years for a 5-minute interval, so this event lay somewhere in between.  In the graphics below, the black lines represent the recurrence interval estimates, and the green and red lines show the limits of the 90% confidence interval.




Here's a sequence of radar images showing the evolution of the storm system; its development was really explosive.  It's remarkable to see radar reflectivities of well over 60 dBZ, which is strongly indicative of hail.  This would be more typical of, say, the western Plains in Kansas or Nebraska at this time of year.









Looking at the balloon sounding from Fairbanks just a couple of hours earlier, the standard metrics don't show a particularly notable amount of instability (see below).   However, the northerly winds aloft produced a modest amount of wind shear (favorable for organized thunderstorms), and it was a moist environment.  Moreover, yesterday afternoon the NWS forecasters noted an upper-level wave that was expected to kick off some storm activity:

"Central and Eastern Interior: A shortwave moving to the south over the area will bring some scattered showers this afternoon and evening. The shortwave will be moving over an area with decent instability thanks to relatively moist antecedent conditions. The current GFS is showing surface based CAPE values of 300-500 J/kg across much of the Interior south of Livengood with weakly negative LI values. This swill be sufficient for some isolated thunderstorms across the area. Some thunderstorms may produce small hail or gusty winds."




Finally, here's a simple animation of the radar imagery.  An impressive event, indeed!


Friday, May 24, 2019

Seasonal Outlook

Veteran Alaska climate expert Rick Thoman delivered the latest in his longstanding series of monthly climate outlook seminars today at UAF, providing all the ins and outs of the seasonal forecast for the next few months in Alaska.  Here's a link to the presentation slides; it contains a wealth of information and is well worth a look.

https://accap.uaf.edu/sites/default/files/2019_May_Alaska_Region_Climate_Outlook_0.pdf

The bottom line from the seasonal outlook is that the probabilities favor a warmer than normal summer across the entire state, and there's a tilt towards above-normal rainfall in all but Southeast Alaska and the Alaska Peninsula and Aleutians.  In this context, "normal" is defined by the 1981-2010 period, so the ongoing exceptional warmth in the oceans surrounding Alaska is a major impetus for the warm forecast.





After enjoying Rick's presentation, I was reminded of a curiosity that I noticed a few weeks ago involving an apparent connection between late summer rainfall in northwestern Alaska and the phase of the QBO.  The QBO (Quasi-Biennial Oscillation) is a slowly-evolving, semi-periodic fluctuation in winds up in the stratosphere above the equator.  These winds shift from westerly to easterly and back again on a timescale of a couple of years.

Now you might well ask what stratospheric winds above the equator could possibly have to do with Alaska weather, and if you did, I wouldn't be able to give a good explanation.  According to my very limited understanding, the QBO phase is thought to affect the way in which large-scale waves propagate around the globe at higher latitudes and in the troposphere; the details have to do with atmospheric wave physics, but I believe there's still considerable debate about the detailed mechanisms.

Fortunately we don't need to understand the QBO to know that it exists and is predictable, and to see the historical relationship with weather at ground level.  For example, here's a map showing the July-August precipitation pattern for years with a strongly positive QBO:



And here's the analysis for the negative phase:


The QBO is currently strongly positive and is likely to remain so for a few more months, so this obviously favors a drier July-August period in northwestern Alaska.


Below are scatter plots of the full joint distribution of QBO and July-August precipitation at Kotzebue and Bettles since 1979.  I won't claim the relationship is "strong", but it is statistically significant.  Note that the two wettest July-August periods on record in Kotzebue (2012 and 1994) also had the most negative July-August QBO on record (the two points are almost on top of each other on the chart).

So it will be interesting to see if the QBO influence shows up later this summer in the northwest; or will CPC's expectation for wetter conditions prove more reliable?



Thursday, May 16, 2019

ERA5 Data for Alaska - Including Download Link

Back in November I took an initial look at the new ERA5 reanalysis data set from the world-leading ECMWF weather modeling and forecasting center in Europe.  At the time, the ERA5 data was only available for 2000-2017, but the reanalysis now extends back to 1979, and a further extension to 1950 will soon come online.  The high quality of the data assimilation and modeling framework that's used to produce the reanalysis makes this a real treasure trove of historical climate data.

It's an interesting exercise to compare the ERA5 data for Alaska to NOAA's climate division data, produced by NCEI.  For many years the climate division data was only available for the lower 48, but in 2015 the data set was expanded to include 13 climate zones in Alaska; here's a map.

To facilitate a direct comparison, I calculated area-averages for several ERA5 variables within each of Alaska's climate divisions.  For example, there are 605 ERA5 grid cells that at least partially intersect the Southeast Interior division; so I calculated the area of the intersection for each grid cell and added up the fractional contributions to the total area of the Southeast Interior zone.

Here's a chart showing the mean temperatures for January and for July in the Southeast Interior (which includes Fairbanks).  Aside from a modest cold bias in the ERA5 values in January, the performance is outstanding.


The situation is not quite as good in the North Slope division, which is not surprising as the observing network is more sparse, and moreover weather analysis and forecasting models (like the ECMWF model that underpins ERA5) often have a more difficult time with atmospheric physics in the Arctic.


Interestingly the 1979-2018 linear temperature trends are similar for January, but the ERA5 trend is much smaller than NCEI's trend for July in the North Slope division.

Looking at precipitation, ERA5 does fairly well for the Southeast Interior in both January and July, but again the agreement is not as good for the North Slope.  Precipitation is always a major challenge for reanalysis, and so these results are pretty good.



Finally, I did a quick comparison of ERA5 solar radiation to the CERES gridded data for the Southeast Interior, and again I used an area average for both data sets.  The results show a very close correspondence for the month of March, but there is only modest agreement in July.


We could of course keep going with all sorts of comparisons between ERA5 and other data sets, and between ERA5 and historical climate observations around the state, but there's no doubt that ERA5 is a very high quality reanalysis.  Beyond the pure fidelity of the data, however, the real value of the reanalysis is that it's spatially and temporally complete; and ERA5 even includes uncertainty estimates, although I haven't looked at that aspect yet.

For readers who might like to take a look at the Alaska data themselves, the following link provides the area-averaged data for the 13 climate divisions, including mean temperature, precipitation, solar radiation, and 10m wind speed.


Thursday, May 9, 2019

Follow-Up on Break-Up

As a quick follow-up on the topic of predicting breakup dates, I looked at whether breakup is more closely related to hourly temperatures above freezing rather than daily mean temperatures above freezing.  This is something that reader Eric suggested a while back, and reader BJ re-emphasized that daily average temperatures could be misleading.

I pulled out hourly temperature data from 1998-2018 in Fairbanks and calculated the accumulation of thaw degree hours up until the date of breakup in Nenana, i.e. the sum of the hourly temperature excess (if any) above 32°F.  Historical hourly data from Nenana is not quite complete enough for this task, so data from Fairbanks will have to do.

Here's a scatter plot of thaw degree hours (TDHs) versus thaw degree days (TDDs) accumulated through breakup; click to enlarge.


Not surprisingly, it's a very good relationship, but the best-fit line is flatter than would be expected for a one-to-one relationship.  Superficially, this suggests that hourly data is indeed a better predictor of breakup date than daily data, because there is less variance in TDHs at breakup than in TDDs at breakup.  (Imagine if TDHs were a perfect predictor: the best-fit line would be horizontal.)  The standard deviations of the two variables demonstrate the difference: the standard deviation of TDHs at breakup is 25% of their mean value, whereas TDDs have a standard deviation of 31% of the mean value.

A bit more work confirms that the typical range of thaw degree hours at breakup is associated with a slightly smaller date window than for thaw degree days.  See the chart below, which attempts to illustrate this.  If we're using daily data, we find that a typical (80%) range of TDDs at breakup corresponds to a 7-day climatological window, but if we use hourly data the window is narrowed to about 6 days.  It's obviously a small difference - hourly data is no holy grail for breakup prediction - but it seems that readers were correct to suggest that we can do better than daily average temperatures.  A more thorough investigation would require a more careful modeling effort with daily data... perhaps I'll return to that next spring.


Friday, May 3, 2019

Snow After Green-Up

According to the National Weather Service office in Fairbanks, green-up occurred on West Chena Ridge on Wednesday evening after the temperature reached a summer-like 70°F earlier in the day.  This means that the hillside turned distinctly green for the first time as birch and aspen leaves emerged en masse.

SPECIAL WEATHER STATEMENT
NATIONAL WEATHER SERVICE FAIRBANKS AK
1101 PM AKDT WED MAY 1 2019

AKZ222-021400-
MIDDLE TANANA VALLEY-
INCLUDING FAIRBANKS, FORT WAINWRIGHT, EIELSON AFB, ESTER, 
NORTH POLE, MOOSE CREEK, TWO RIVERS, FOX, CHATANIKA, 
CHENA HOT SPRINGS, AND SOURDOUGH CAMP
1101 PM AKDT WED MAY 1 2019

...GREEN UP OCCURRED IN FAIRBANKS THIS EVENING...

GREEN UP OCCURRED IN FAIRBANKS THIS EVENING, MAY 1, 2019. CHENA 
RIDGE WAS BEGINNING TO SHOW A FAINT SHADE OF GREEN THIS 
AFTERNOON, BUT THE RIDGE TURNED MORE DISTINCTLY GREEN BY THIS 
EVENING. 

THE MEAN DATE OF GREEN UP IN FAIRBANKS IS MAY 9. THE EARLIEST 
GREEN UP DATE RECORDED IN FAIRBANKS WAS APRIL 26, 2016.
 

The 70°F on May 1st was one of the earliest occurrences on record for such warmth, but a wild swing back to colder weather has occurred in the short time since.  This morning rain turned to mixed rain and snow at valley level, and then finally to plain snow before tapering off.  Some accumulations were observed in the hills, but apparently not in Fairbanks itself.

Looking back at the history of Fairbanks hourly weather data since 1950, I can't find any other instance of plain snow in the hourly observations after the date of the first 70°F.  There have been a number of instances of light mixed rain and snow, but most were very light with visibility of 10 miles or more, and plain snow (as occurred for a couple of hours this morning) appears to be unprecedented after the first 70°F day.  However, it should be noted that May 27, 1978 brought enough wet rain/snow to accumulate 0.1" , and that was 2 weeks after the first 70°F of the year.

More substantial snow occurred today at locations farther up the Tanana River valley, such as Tok and Northway.  And the history shows this isn't unprecedented; in mid-May 1995, 5 inches of snow fell in Northway less than a week after the temperature reached a remarkable 82°F.  The temperature only reached that level on 3 more days that year in Northway (elevation 1715').


Saturday, April 27, 2019

Breakup Modeling

Following on from the last post, I'd like to discuss briefly some results that came out of an attempt to simulate the distribution of breakup dates for the Tanana River at Nenana.  The annual Nenana guessing game is of course a venerable Alaskan tradition, and the resulting historical record of breakup is an invaluable piece of climate data extending back to a time when modern weather measurements were sparse and sometimes rudimentary.  Here's a chart of the long-term Nenana history, courtesy of Rick Thoman; click to enlarge.


It goes without saying that the trend towards earlier breakup dates is consistent with the long-term warming trend, but it's interesting to consider whether we can say anything about how consistent the breakup trend is with the measured temperature trend.  Has breakup advanced more or less than we would expect based on observed temperatures?

In previous posts I've expressed the view that breakup dates can be modeled quite well using the accumulation of thaw degree days (TDDs), i.e. the excess of daily mean temperatures above 32°F; the ice typically goes out within a fairly well-defined range of  TDD values.  Of course there are other factors at play, including ice thickness, the amount of sunshine, and occasionally heavy precipitation that brings forward the breakup date, but there's no doubt that air temperature is the key variable that drives breakup timing in most years.

Assuming then that we need to model breakup in terms of TDDs, we have to deal with the complication that TDDs are not linearly related to mean temperature (unless the daily mean temperature always stays on one side of freezing).  As a consequence, there's no simple way to translate a long-term temperature change of X°F into Y TDDs and thereby derive the change in breakup date using the observed TDD-breakup relationship.  Finding the change in TDDs requires a more careful approach that deals adequately with the temperature-TDD relationship.

A related challenge is that the variance of temperature is an essential component of the TDD accumulation, and so temperature variance and even skewness must be accounted for in the model.  If the daily mean temperature just followed the long-term normal each day, with no other variance, then TDDs would accumulate much more slowly than they actually do, because it's the above-normal days that provide most of the TDDs in the early and middle part of the meltout process each year.  Only later in the thaw can merely normal temperatures do any real damage to the ice.

In light of these considerations, I set up a simulation of daily mean temperatures in Nenana using an ARIMA model based on the statistical characteristics of observed April temperatures from 1999 to 2018.  I decided to use Nenana data rather than Fairbanks because the 1999-2018 relationship between TDDs and breakup is better for Nenana than for Fairbanks (not really a surprise!).  In creating the synthetic temperature data, I accounted for both the changing variance of temperatures through the melt season (i.e. decreasing variance as spring advances) and also the fairly substantial skewness of the temperature distribution (i.e. a heavier tail on the cold side of normal).

Here are some examples of synthetic temperatures for the first half of the year, with the black line being the 1981-2010 normal.  There is a slight tendency towards above-normal temperatures, because that is what has been observed in April (and most other months) in the last 20 years.  I won't claim that the synthetic series are perfectly realistic, but the final results suggest they are adequate for the purpose of the breakup model.





For each simulation it is straightforward to add up the TDDs and estimate the probability of breakup on each date by referring to the observed joint distribution of TDDs and breakup dates.  For example, the median (1999-2018) TDD value in Nenana on breakup day is 116, so for each simulation we can say that the cumulative probability of breakup reaches 50% when TDDs reach 116.  If we do this not just for the median but for each empirical quantile, then we obtain a cumulative distribution for each simulation; and if we repeat the process many times, we get a smooth result - see below.


The empirical cumulative probability curve is shown with the blue markers; note that several of the breakup dates have occurred more than once, with 1 May occurring 4 times since 1999.

The agreement between the observed and simulated curves is quite good; for example, the median of the simulated curve falls between April 30 and May 1, which is spot on according to the 1999-2018 history.  It's important to note that this good agreement is not guaranteed to occur, because the simulated temperatures may or may not produce realistic rates and timing of TDD accumulations.  To cite an extreme example of a poor simulation, if we assume perfectly normal temperatures every day, the cumulative probability of breakup is much too late and also too narrow - see below.  As I noted above, purely normal temperatures would produce far too few TDDs in the typical date window for breakup.


As an aside, it's interesting to observe how extreme the 2013 outlier was.  According to the simulated distribution - based on the 1999-2018 temperature distribution - there is less than a 0.01% chance of breakup being as late as May 20; this implies it was a one in ten-thousand year event for the modern climate, although I'd be very skeptical of my model's ability to estimate probabilities this far out in the tail.

The final step (for now) in the investigation is to shift the mean temperature up or down to examine how the breakup distribution changes.  Using 5000 simulations at each 1°F increment from 10°F of cooling to 10°F of warming, we arrive at the following result.


It's interesting to see that the sensitivity of breakup date is slightly greater for temperatures below the recent climate, and slightly less for higher temperatures.  This is a consequence of the changing variance through the season, and the fact that I've assumed no change in variance relative to the recent climate.  Under this (probably false) assumption, as the climate warms and breakup moves into a higher-variance portion of the year, it takes more warming to produce the same increase in TDDs (because of the increasing variance).  Alternatively, in a colder climate, with breakup in a lower variance part of the spring, there is a larger response of TDDs to mean temperatures, and breakup dates respond a bit more quickly.

Finally, to address the question I posed at the beginning - what about the observed change in breakup dates?  Well, the helpful trend lines on Rick's chart show that breakup has advanced about 6-7 days since before 1970, and based on the cool side of the chart above, this would correspond to about 3-3.5°F of temperature change.  And this is about right; the mean temperature change in Fairbanks between 1930-1970 and 1999-2018 was +3.2°F in April.  Using this approach, we can say that the long-term breakup history at Nenana strongly supports the long-term historical temperature data from the area, and I find this very encouraging from a climate science perspective.

If we assume then that the modeling results are reliable, how much warming would be needed before an April 14 breakup (as this year) would be typical?  April 14 falls right at the upper edge of my results; about 10°F of climate warming would be required.  Of course, this ignores the many other factors that could influence breakup with such a dramatic degree of climate change, such as the response of ice thickness to massive winter warming.