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.

Breakup Dates

Yesterday evening the "official" breakup was recorded at 7:16pm (April 23rd) on the Yukon River at Dawson in the Yukon Territory.  Although the ice again had a very difficult time filling in the channel next to Dawson City this winter, in the end it held on just long enough to avoid setting a new record for early breakup; the record from 2016 stands at 11:15am on the same date.  (However, 2016 was a leap year, so arguably April 23rd was a day later that year.)

Here's a photo of the river this morning, taken from high above on the west side, courtesy of yukonriverbreakup.com.  (Click to enlarge.)

Most readers probably already know that breakup was easily the earliest of record on the Kuskokwim River at Bethel (April 12) and the Tanana River at Nenana (April 14).  The previous record was April 20 in both places.  In view of the extreme warmth that occurred in March, it's really no surprise that new records were set.

Readers may also recall that back in March I ventured to make some forward-looking statements about the likely early breakup at Nenana, so it's worth going back to see how that played out.  The figure below is an update of the one I showed earlier, and it depicts several different elements:

• Horizontal black line: the median value (141) of accumulated thaw degree days in Fairbanks as of the date of breakup at Nenana.  Historically speaking, breakup is equally likely to occur before or after this number of "heat units" has accumulated.
• Red and blue lines: 10th and 90th percentiles of thaw degree days (TDDs) at breakup; breakup is 80% likely to occur on a day when accumulated TDDs are in this range.
• Dashed black line: the median of the 15-day forecast for future TDDs, as of March 26 (the date of the blog post).
• Gray shading: the middle 80% range of the 15-day forecast distribution
• Green line: the observed accumulated TDDs this year

It turns out that the forecast from March 26 was considerably too warm, and thawing almost ceased for about 10 days after my post.  This possibility fell inside the range of uncertainty for the forecast, but it wasn't the most likely outcome, and so it pushed back the date of breakup compared to what I thought was most likely.

However, another aspect of the forecast worked out remarkably well: breakup eventually occurred on the day when Fairbanks TDDs reached 141, which coincidentally is exactly equal to the long-term median (i.e. the green line reached the black line on the very date of breakup).  This was lucky; we obviously don't expect to hit the median of a sampling distribution very often.  Nevertheless, it does provide some evidence that the general approach to predicting breakup is valid.

In the next post I'll describe some additional work I've done to extend the TDD/breakup modeling, leading to some interesting results about the sensitivity of breakup dates to long-term changes in average temperature (climate change).

Winter Lives

A couple of weeks ago I mentioned that the earliest recorded date for spring's permanent meltout of snow cover in Fairbanks was in 2016, when semi-continuous snow cover was seen for the last time on April 8th.  With this year's meltout on April 4th, the record was in jeopardy - but a slightly unusual early spring snowfall has changed the scene once again.

Of course there is usually still snow remaining on the ground at this date in Fairbanks, and last year the depth was measured at 17" on April 18th.  And it's not unusual to get a little bit of snow this late in the season; but the 2.2" that fell yesterday is somewhat unusual; this is only the 18th time with this much snow in Fairbanks after the middle of April (1930-present).  In 2002, 13" of snow fell in the second half of April, and 14" fell in 1992 between May 8 and May 17.

Here's the view from the UAF webcam yesterday morning at about 8:30am.

The balloon sounding from Fairbanks airport reported a temperature of -8.3°C at 850mb yesterday afternoon, and while this is not particularly unusual, it is striking to note that fully two-thirds of the winter (November-March) was warmer than this.  So in this respect we might say that the air mass bringing snow to Fairbanks this week is more wintry than most of the winter that just ended.  The November-March average 850mb temperature this winter was a mere -6.6°C, the warmest on record (2nd and 3rd place go to 2014-15 and 2015-16).

Here's what the 500mb analysis looked like yesterday afternoon, courtesy of Environment Canada; the healthy low pressure system over western Alaska is responsible for the chilly conditions.  (Click to enlarge.)

And here's a sequence of surface observation maps showing the cold air working its way down from the northwest between Monday afternoon and Wednesday afternoon.  The cold is really nothing to write home about at all, but it does feel refreshing to see something more like normal on the map.

Finally, as everyone knows, breakup has already occurred at Nenana and Bethel, and it was the earliest on record for both locations (more on that later).  This morning, however, the Kuskokwim at Bethel was glazed over again with a dusting of fresh snow; this seems like a pretty unusual event (freeze-over after spring breakup), but others might know if it's been seen before.

Snow Depth Conundrum

After last week's early meltout of snow in Fairbanks, I started thinking a bit more about the absence of a long-term trend in the meltout date.  It's a puzzle because late winter temperatures have increased over time; for example, March and April in Fairbanks have been about 3°F warmer since 1980 than they were before, and consequently the accumulated thawing degree days by April 23 (the long-term normal meltout date) have approximately doubled.  The trend towards earlier breakup at Nenana provides independent confirmation of the warming; see this post for the history at Nenana:

https://ak-wx.blogspot.com/2017/08/climate-normals-in-changing-environment.html

As mentioned before, a cursory analysis suggests that higher snow depth at the end of winter could explain the unexpected "resilience" of Fairbanks snow cover compared to earlier decades.  And so we might hypothesize that snowfall has increased over time, but this is not borne out by the data; the chart below shows the March 15 snow depth (purple markers) and the accumulated snowfall (green markers) between the date of establishment of the winter snowpack and March 15.  The long-term trend in snowfall is essentially zero, but there is a rising trend in snow depth (admittedly quite small - about 2.5" over the 90-year history).

What about liquid equivalent precipitation?  If snow density has increased, then precipitation and snowpack water content may have increased despite no change in accumulated snowfall.  Surprisingly, liquid equivalent precipitation also fails to show an increase over time, and in fact there is a slight decreasing trend, although that's mostly because of the incredibly wet winter of 1936-37.

So if precipitation and snowfall haven't increased, then is the snow depth trend just an artifact of changing measurement practices and/or location?  Perhaps, but I'm inclined to believe that snow depth (and presumably snowpack water content) really have increased, because it helps explain the meltout dates.

If we take the ratio of the snow depth to total precipitation, we find a result that suggests there really has been a change in the characteristics of Fairbanks winter precipitation over time; recent decades have produced a notably higher end-of-winter snow depth per inch of precipitation in the previous winter.

Assuming that measurement practices are not to blame, there are only a couple of explanations I can think of here.  One is that cloudiness may have increased, perhaps along with humidity, so that snow evaporation has declined and there is more snow left at the end of winter.  There would be little actual melting of snow prior to March 15, but snowpack can be affected by sunshine, humidity, and wind.  I wouldn't be surprised if cloudiness has increased, but rising temperatures typically dictate rising evaporation rates even if relative humidity increases a bit, so I am not sure how plausible this explanation is.

Another possibility is that Fairbanks used to see more of its winter precipitation as rain, not snow.  Admittedly this seems like an absurd proposition, because freezing (or plain) rain has been a notable winter problem in recent years and seems unlikely to have occurred more often in the colder winters of the past.  However, we do know that a few winters of long ago (e.g. 1936-37) produced some extreme rainfall events, so perhaps we shouldn't dismiss the idea out of hand.  It may be conceivable that the recent climate has produced more of the winter's precipitation as snow, thereby contributing more to the snow pack - but more dense snow, so as not to increase the total snowfall (or else snow depth measuring practices have changed over time).

Can anyone suggest other aspects of the problem that I may have overlooked?  It would be nice to be able to nail down a good explanation for why meltout dates have defied the long-term warming trend.

Meltout in Fairbanks

Snow depth dropped to only a trace in Fairbanks on Thursday, according to the daily NWS climate report, meaning that April 4th marked this year's meltout of the seasonal snowpack.  Somewhat surprisingly this is not the earliest on record; that distinction belongs to 1970, which saw meltout one day earlier, although snow returned that very same day in 1970 and then remained for another 10 days.  The earliest for a permanent meltout (no subsequent observations of an inch or more of snow depth) was just 3 years ago: April 9, 2016.

Here's a chart of Fairbanks meltout date since 1930.  As noted on previous occasions, there is no long-term trend, and it's possible that this has to do with greater late winter snow depths in recent decades - see here for my comments from 2016.

Temperature Persistence by Season

In light of the extraordinary recent persistence of (far) above-normal temperatures in Alaska, it's interesting to look at historical data to see how "persistence" typically varies in space and time in Alaska's climate.  For example, we tend to think of highly maritime climates as having more persistent temperature regimes, because the state of the ocean surface exerts a strong influence in these locations; so if a warm ocean anomaly becomes established, then air temperatures in the vicinity tend to remain elevated for some time afterwards.  Similarly, if sea ice abundance differs substantially from normal, then air temperatures nearby tend to follow.

A few years ago I looked at a customized index to measure persistence on one side or the other of normal (see here), but here I'm simply using the lagged correlation (autocorrelation) coefficient to describe the degree of persistence in daily temperature departures from normal.  I performed the calculation for a 7-day lag using 1981-2018 daily temperature anomalies relative to the 1981-2010 daily normals, and I used 31-day calculation windows centered on each day of the year in order to capture the seasonal variation.  Smoothing over the course of the year was done with two harmonics.

The seasonal variation in this measure of persistence is quite similar for large parts of the state extending from Anchorage to the interior, west, and north of Alaska, with a peak in early spring and a second, higher, peak in autumn, while persistence is relatively weak in high summer and mid-winter.  Click to enlarge the charts below.

It seems likely that the peaks in spring and autumn are related to year-to-year variations or long-term trends in snow and ice cover, which can have a positive feedback effect on temperatures in the transition seasons.  For example, if spring meltout occurs early (like this year), then subsequent temperatures will be higher than they would be otherwise.  This is certainly what is going on in Utqiaġvik (Barrow), where the presence or absence of sea ice in autumn creates persistent temperature anomalies of one sign or another, and in this case the results may be as much a symptom of the long-term decline in sea ice than of year-to-year variability.

Temperature persistence behaves quite differently in sites that are dominated by the Bering Sea or the Gulf of Alaska - see below.  St Paul Island has a prominent peak in temperature autocorrelation in summer, which I think reflects the canonical maritime influence, but Kodiak and Juneau have surprisingly low autocorrelation for much of the year, and I'm not sure how to explain that.

Finally, temperature persistence in the southeastern interior (Northway and Gulkana) shows a double peak, similar to locations farther west and north, but here the autumn peak is much less prominent; the behavior looks something like a blend of the Gulf of Alaska climate with the northern climate.

Beyond the intriguing regional variations, I think it's interesting to note that the only time of year with at least modest autocorrelation at all of the sites is right around now: late March or early April.  It seems clear that early spring is a climatologically favored time for unusual temperature regimes to become persistent in Alaska, and recent weeks have provided a remarkably amplified instance of this.