Thursday, January 30, 2014

Alaska Winter Advisory / Warning Critera

As a follow-up to yesterday's post, here are maps depicting the winter warning and advisory criteria for all the Alaska forecast zones. The red dashed lines represent the boundaries between the Fairbanks, Anchorage, and Juneau offices. The differences is advisory numbers as shown in yesterday's post is largely attributable to the different criteria.

Winter Weather Advisory:

This is the snowfall criteria map for a Winter Weather Advisory. 

In addition, all zones have a blowing snow criteria as follows:

When one of the following combinations are forecast to occur for at least 3 hours: 

1. Sustained wind or frequent gusts 25 mph or greater and visibility less than or equal 1/2 mile (but greater than 1/4 mile)
2. Visibility is 1/4 mile or less, and winds are at least 25 mph but less than 35 mph 

There is also a multiple event criteria for all zones as follows:

Mixed precipitation or multiple winter weather events even if only one precipitation type meets or exceeds advisory criteria, but remains below warning criteria (this may include wind and/or wind chill).

Winter Storm Warning:

Just like the Winter Weather Advisory, there is a rule that applies across all zones. Namely:

Mixed precipitation or multiple winter events, even if only one precipitation type meets or exceeds warning criteria (this may include wind and wind chill) .

Freezing Rain Advisory:

This one is self-explanatory. Any ice amount greater than the amount defined for the Freezing Rain Advisory qualifies as an Ice Storm Warning.

Wind Chill Advisory / Warning:

These should be pretty self-explanatory. Remember that it is not just the wind chill alone but there has to be a sustained wind as well.

Blizzard Warning:

There is no map for the Blizzard Warning. It is standardized across not just Alaska but the entire U.S. The criteria is as follows:

When forecast to occur for at least 3 hours: Blowing snow (with or without falling snow) reducing visibility to < 1/4 mile when accompanied by sustained wind or frequent gusts > 35 mph. 

The text of all the criteria can be found at the following site:

Wednesday, January 29, 2014

Alaska Winter Advisories 2009-2013

A few days ago Rick pointed me to the Iowa State site that contains NWS advisory archives. I have long been interested in the spatial distribution of weather phenomenon and this archive data set practically begs to be mapped. So, here is a map of total winter advisories for all of Alaska between January 1, 2009, and December 31, 2013 – a five year climatology. The types of advisories include: 1) Winter Storm Warnings, 2) Winter Weather Advisories, 3) Blizzard Warnings, 4) Freezing Rain Advisories, 5) Ice Storm Warnings, 6) Wind Chill Advisories, and 7) Wind Chill Warnings. Watches were not included. Any product with "WSW in the header and NEW, EXA, or EXB in the VTEC line was included.

Note: Many of the differences between adjacent zones are due to the specific criteria for those zones. For example, Cordova's zone does not have a Winter Weather Advisory criteria for snow but Yakutat's zone does. I will have a follow up post with maps of the advisory/warning criteria soon.

Total Number of Winter Advisories/Warnings:
Fig 1. Total number of Advisories and Warnings (all types) between 2009 and 2013.

There are a couple of important things to keep in mind. First, there are three NWS forecast offices in Alaska and they each have different advisory/warning thresholds for the zones in their area of responsibilities. Second, particularly with Winter Weather Advisories, sometimes they are the result of snowfall, sometimes they are the result of blowing snow, and sometimes they are a result of the combination of multiple factors. The same is true for Winter Storm Warnings to a lesser degree. In another post, I will display a series of maps showing the advisory criteria. In the meantime, you can find the Alaska Region text document here: .

Maps of Different Advisory/Warning Types:

Fig 2. Total number of Winter Storm Warnings between 2009 and 2013.

Fig 3. Total number of Winter Weather Advisories between 2009 and 2013.

Fig 4. Total number of Wind Chill Advisories/Warnings between 2009 and 2013.

Fig 5. Total number of Blizzard Warnings between 2009 and 2013.

Fig 6. Total number of Freezing Rain Advisories between 2009 and 2013.

 Fig 7. Total number of Ice Storm Warnings between 2009 and 2013.

Tuesday, January 28, 2014

January State Record Temperature in Port Alsworth

Rick noted today that the Alaska January temperature record of 62°F was tied yesterday (1/27) at the CRN station in Port Alsworth. This is quite a fortuitous observation. The CRN network was established to create a baseline of data for future climate change studies. The sites were selected to represent a  variety of ecological settings without the urbanization, land use, and equipment changes that may affect long term temperature measurements. Highly reliable equipment is used at CRN stations.

Port Alsworth is located on the southeast shore of Lake Clark approximately 170 miles southwest of Anchorage. Looking at recent VIIRS and Modis imagery, there appears to be no snow cover in the vicinity of the station (see second image below). Also, there is a state airport weather station in Port Alsworth (PALJ) and a RAWS station. The chart below shows the 15-minute observations from the CRN station plus the few airport and more numerous RAWS observations. Quite clearly, the airport and RAWS data support the CRN data. Finally, since the 62°F reading was one of the 15-minute observations, there is a chance that a higher reading occurred between the 15-minute readings.

Fig 1. Temperature plot of CRN, airport, and RAWS temperatures on 1.17/14.

Fig 2. Suomi NPP Landcover image from 1/28/14 showing the lack of snow cover in the region. Cyan is snow and brown indicats no snow. White indicates clouds (not snow). Port Alsworth is at the lower left end of the yellow line. Anchorage is at the upper right end of the yellow line. Click on image for a closer look.

Record Warmth Aloft in Barrow

You wouldn't know it from the surface conditions (4 °F and breezy), but this morning's balloon sounding from Barrow observed record warmth aloft for the time of year.  A temperature of +9.0 °C was measured at about 3500 feet above ground, which is more than 1 °C warmer than the previous highest temperature measured at any height above Barrow in January or February (data back to 1948).  The temperature of +7.0 °C at 850 mb broke the January-March record for that pressure level by a wide margin (previous record +4.2 °C).  Barrow has never measured an 850 mb temperature above 5 °C between December 2 and April 28 - until today.

The chart below shows this morning's temperature profile (blue line) along with the historical soundings that were previously the record-holders for temperature at any height (red line) and at 850 mb (green line).  The square markers indicate the 850 mb level in each sounding.

Monday, January 27, 2014

Record Winter Warmth in Nome

Nome airport is basking in warm midwinter sunshine this afternoon and reporting a temperature of 50 °F at 1 pm AKST, which is a new all-time high temperature record for January and for the period of December through March; historical temperature data in Nome go all the way back to 1907.  There appears to be little chance that today's measurement is erroneous, as nearby Golovin is also reporting 50 °F.

If the temperature rises any higher, the November-March record will also be broken (50 °F on November 1, 1928).  Nome has never before observed a temperature above 50 °F between October 17 and April 9.

[Update 4 pm AKST: The temperature has reached 51 °F, so it is unequivocally a new winter record.]

Sunday, January 26, 2014

Record Freezing Level at Fairbanks

The 12Z (3 a.m.) balloon sounding launched from the Fairbanks International Airport this morning set some quite impressive records.

1) The 850 mb temperature of 9.4°C is a January record and is also at or above any temperature measured in November, December, March or April; but not February.

2) The 700 mb temperature of 1.4°C is a record for any month between November and March.

3) The 1000-500 mb thickness of 5545 meters is also a  record for any month between November and March (from Rick).

4) The 850-500 mb thickness of 4202 m appears to be a record for November through April (from Richard).

5) The interpolated freezing level of 3,229 m is a January and seasonal record. The previous record was 3,217 m on Jan 18, 1963.

The chart below shows today's 12Z sounding and the 1/18/63 (12Z) sounding side by side. If you discount the very shallow surface inversion where temperatures were below freezing (~24m), you have to ascend another 10,000+ feet to drop back below freezing. For comparison, the 3,229 m freezing level was only slightly lower than the 3,395 m at Bermuda and the 3,329 m at Lake Charles, Louisiana.

Saturday, January 25, 2014

Heat Burst in Yukon Territory

Yesterday afternoon brought a remarkable weather event to Burwash Landing, on the shores of Kluane Lake in the southwest Yukon Territory.  Kluane Lake and Burwash Landing lie just northeast of Kluane National Park and Reserve, which includes Mt Logan, the highest mountain in Canada; the St Elias mountain range forms a high barrier between the Pacific Ocean and the interior Yukon.  Yesterday a brief period of downsloping flow from the mountainous terrain brought dramatic warming to Burwash Landing and broke some longstanding temperature records.

Here are the hourly observations from Burwash airport yesterday from 9 am to 6 pm local time:

Hour (UTC)Temperature (°C)MSLP (mb)Wind Speed (knots)Wind Direction (°)

Here is the topographic map of the area, courtesy of Google; Burwash Landing is indicated with the purple marker.  Note the prominent valley running from southeast (Haines Junction area) to northwest; the Alaska Highway follows the valley for many miles.

In the morning, strong southeasterly winds were blowing along the valley, accompanied by extraordinarily warm air for the time of year (8 °C or 46 °F); wind gusts of 45 knots were measured at Burwash airport.  The pressure was rising steadily as low pressure over the Alaskan interior was weakening while the ridge over British Columbia was building northwest.  The chart below shows the surface analysis at 18 UTC and indicates a strong pressure gradient over the southwest Yukon, along with a front approaching from the west.

In the afternoon hours, the winds at Burwash airport veered to the south (2 pm), then southwest (3 pm) and eventually northwest (5 pm), and for two hours the reported temperature jumped up to 16 °C; the maximum temperature was reported as 16.5 °C (62 °F).  The surface analysis at 4 pm local time (below) shows a weak low pressure center very close to Burwash Landing.  By 4 pm the temperature was back down to 9 °C with rapidly rising pressure, indicating that the front/low had passed, and in the subsequent hours the temperature continued falling while the pressure kept rising.  It is also noteworthy that the visibility was reported as 30 miles throughout the day until 4 pm, when it dropped to 9 miles and remained there; the sudden change is also evidence of the arrival of a different air mass.

Is it plausible that the temperature could have exceeded 60 °F in the Yukon Territory in January?  I believe so: the chart below shows the 00 UTC sounding from Yakutat, the closest upper-air station, which is indicated with a green marker on the terrain map above.  Very warm air was observed aloft, with temperatures only slightly below freezing at 700 mb.  Note that the winds (indicated by the barbs on the right) were blowing from the southwest above about 800 mb, i.e. perpendicular to the coastal mountain range.  Therefore when the surface winds at Burwash Airport veered to the south and southwest in the early afternoon, the surface flow became aligned with the upper flow and the warm air aloft was able to descend the lee slope of the high terrain, undergoing strong warming during its descent.

A simple calculation reveals that the air would have had to descend from about 750 mb, or about 2400 m above sea level, to reach 16 °C at the altitude of Burwash airport.  Perhaps not coincidentally, this is just about the height of the terrain immediately to the southwest of Burwash Landing.  Physically, then, the observations at the airport seem to make sense.

Assuming that the temperature measurements were accurate, the high temperature yesterday was by far the highest ever recorded in January in Burwash Landing; historical data are mostly complete back to 1967.  The previous January record was 49 °F.  Yesterday's event is also the warmest ever observed in winter (November-March) there, the previous record being 57 °F.  It is possible that the event is a record for January in the Yukon Territory; I don't have complete historical data for all Yukon stations, but the highest January temperature at any of the 26 Yukon stations that have 1981-2010 normals is only 10.1 °C (50 °F).

Two questions spring to mind in regard to this event: first, if it's possible to bring warmth to the Yukon interior by this downsloping flow, why was yesterday's event so far beyond the previous January records?  I suggest that this event involved a very unusual set of circumstances that allowed the warm air aloft to reach the surface at Burwash Landing: the boundary layer was already thoroughly mixed and destabilized by extremely warm conditions and strong winds earlier in the day, so there was no surface-based inversion to scour out.  Also, the passage of a frontal disturbance very close to the area created additional vertical mixing that allowed warm air from aloft to descend.  I suspect that it is very rare to get deep vertical mixing all the way to the surface over the Yukon interior in winter, because snow cover, radiative imbalance, and pre-existing cold air in place so strongly favor low-level inversions.

The other question is, has a similar temperature ever been observed before in winter in the Yukon Territory?  If so, we might have more confidence that yesterday's temperature report was not erroneous.  The answer is yes: the all-time winter (Nov-Mar) record high temperature for the 26 Yukon stations mentioned above is 18.9 °C (66 °F) on February 4, 1941, at Carcross (indicated with a red marker on the terrain map above).  On the same day, Mayo, in the central Yukon, recorded 51 °F, a near-record for February.  The map below shows the estimated sea-level pressure and 700 mb height on that day in 1941; while not identical to yesterday's pattern, it was fairly similar with deep flow from the south crossing the coastal range and bringing strong chinook warming to the interior northwest.  To put the event in context, Anchorage recorded 45 °F on February 3, 1941, and Fairbanks reported 42 °F on the 4th.

Friday, January 24, 2014

What Might February Look Like

Several people have asked me if the rest of the winter will be as warm as the last several weeks have been. While there is no way to tell for sure, it is helpful to look back at February's that follow exceptionally warm January's. To do this, I looked at all of the GHCN data from NWS and COOP stations (no RAWS) and organized them by climate division according to Bieniek et al (citation at the end of the post). Then, each climate division was weighted according to the proportion of the state that the division encompasses. Between 1940 and 2013, here are the ten warmest and coldest January's.

What I wanted to know was not only how those ten January's looked (first map below) but more importantly, how the February's afterward looked. To my surprise, the February's were essentially normal. In one sense, the temperatures always tend to drift toward normality; however, I expected the forcings that caused the warm January's to have a residual effect in February too. The ESRL database that I used to generate the maps has data beginning in 1948 so any years from the top 10 list that fell between 1940 and 1948 was substituted with the next year down on the list. Unfortunately the ESRL database that goes back to the beginning of he 20th century is temporarily out of order.

Bieniek, Peter A., and Coauthors, 2012: Climate Divisions for Alaska Based on Objective Methods. J. Appl. Meteor. Climatol.51, 1276–1289.

Thursday, January 23, 2014

Eagle Record Warmth

Update January 24: the airport temperature data from Eagle yesterday was incorrect, as the ASOS aspirator has failed (information courtesy of Rick).  The high temperature at the COOP station was "only" 42 °F - still a record for the date, but not for the month.  However, with warmth aloft intensifying over the next few days, many more temperature records will undoubtedly fall.

Original post:
This post will need updating when the final data is in, but the current [noon AKST] temperature of 54 °F at Eagle airport appears to be the highest January temperature on record for any observing station in Eagle, the previous January record being 50 °F in 1981.

Today's temperature is also higher than any temperature recorded in November, December, or March in Eagle; the only higher temperature in the winter season was 57 °F on February 10, 2006.

Wednesday, January 22, 2014

Sunrise in Barrow

The sun rose in Barrow today for the first time since November 19th last year (64 days). It was up from 1:29 p.m. to 1:51 p.m. Below is the FAA webcam picture looking south at 1:31 p.m. – 2 minutes after sunrise. Here is the only METAR from when the sun was up: 

Site M/A Day Time Sky Conditions           VIS Weather Temp DP Wind(kt)  Alt  RH  Chill Peak
PABR  MP 22 1349  OVC055                     3 BS-       0  -8 06018     997  68% -22    

(PABR 222249Z 06018KT 3SM BLSN OVC055 M18/M22 A2997=)

Rain in Nome

Unseasonably warm air over western Alaska brought rain to Nome yesterday - both the freezing kind and just plain rain.  The temperature reached 36 °F at the surface - not quite a record for the date - and 37 °F was measured a few hundred feet above the surface in the afternoon.

Rain with above-freezing temperatures is obviously unusual at this time of year in Nome, but it has happened many times before in the climate record.  The first chart below shows the number of January days with plain rain reported in the hourly observations since 1936 (red columns); note that there is a big gap in the data from 1947 to 1972.  Also, a number of years have incomplete or missing data in the early years (marked with asterisks).  The blue columns show the frequency of above-freezing temperatures (with or without rain) in the hourly data.  The second chart shows the same information for the December-February period each year.

The climate shift in 1976 with the change to a positive Pacific Decadal Oscillation stands out very clearly, as the frequency of warm and warm-rainy days appears to have increased dramatically.  For the winter as a whole, above-freezing and plain rain events have been less common in the past decade than in the first decade of the positive PDO regime; this reflects the shift back towards the negative PDO phase (see the PDO time series chart below; image credit:  However, in January plain rain has now occurred in 9 of the past 13 years, which is a higher annual rate of recurrence than earlier in the climate record.

Saturday, January 18, 2014

Fairbanks Warming Event

Fairbanks briefly experienced above-freezing temperatures at the airport on Friday afternoon for the first time since November 14, and even warmer conditions were observed in favored locations in the southern interior of Alaska.  An interesting aspect of the event in Fairbanks is that the valley-level wind was out of the north or northeast throughout the warming.  Of course, the warm air mass was coming from the south, as winds were out of the south less than 1500 m above ground, but the wind aloft was not particularly strong and did not mix down to the surface.  In this sense, I'm not sure whether it's right to call this a "chinook" event in Fairbanks.

The chart below shows the hourly observations of temperature and wind speed and direction at the airport, along with the twice-daily measurements of temperature at 850 mb.  Temperatures rose in tandem with the low-level northerly wind speed, but as soon as the wind died away, the temperature dropped back to its former level.

Surface observations from across Alaska at the peak of the warmth in Fairbanks show an impressive temperature gradient both across the entire state and in the central interior, as temperatures remained much cooler to the north and west of Fairbanks.

Thursday, January 16, 2014

Jan. 16, 2009, Revisited

Today is the 5-year anniversary of perhaps the warmest day ever recorded in Alaska during the month of January. On January 16, 2009, the high temperature in Fairbanks was 52°F – a daily and monthly record. In Anchorage, the high temperature of 50°F was the second highest on record for January and the low of 37°F and the daily average temperature of 44°F were the warmest on record for any day in the month of January. Many other stations recorded daily and monthly records. It was the third day in a multi-day Chinook event.

Here are three maps that show how remarkable it was. The maps show, 1) the actual high temperature on January 16, 2009, 2) the normal high temperature on January 16, 2009, and 3) the departure from normal of the high temperature on January 16, 2009. As you can see, there were pockets of areas a full 50°F above normal and at least half of the state was more than 35°F above normal.

Here in Anchorage the snow depth dropped from 17" down to 5". All of the snow disappeared from the roofs in town and many shingles were blown off. I spent several hours replacing missing shingles in the middle of January!

Weak Inversion

The brief cold spells in interior Alaska over Christmas and earlier this week brought strong low-level temperature inversions to the Fairbanks area, as is typical for the time of year; but since the beginning of the climatological inversion season (October 19), far more days have had weak or non-existent inversions than strong inversions.  The chart below shows the daily inversion strength based on the daily mean temperatures at Keystone Ridge and Fairbanks International Airport.  (Note the missing data from Keystone Ridge in early December.)  Remarkably, there were seven consecutive days in December with a positive mean temperature lapse rate (no inversion); the average number of such days in December is only two.

Looking at the mean inversion strength from October 19 through January 13, this winter so far has the weakest mean inversion since records began on Keystone Ridge in 1996 (see chart below).  Over the same dates, airport temperatures have averaged 4.7 °F above normal while Keystone Ridge has been 1.8 °F above normal; and so the inversion has been 2.9 °F weaker than normal.

Tuesday, January 14, 2014

Cold Snow

It's never too cold to snow. However, sometimes the fact that it snows with extreme cold temperatures is a little surprising. Here is a list of the coldest daily average temperature for several snow thresholds. The amount of the threshold is in the far lefthand column. If there are two entries for that threshold, it means the first entry represents a questionable value. If the station name is hyperlinked, that means the scanned cooperative form will display when clicked. I QC'd all the forms and added some notes in the far right column. For example, the coldest daily temperature when over 3"+ of snow fell was in Nabesna on 1/28/1989. The daily average temperature was -42.0°F. I need to do some more research on the Trims Camp station. It is on the Richardson Highway near the Pipeline. Their season average for snow was 270".

Threshold Station Date Max Min Ave Precip Snow Notes
>=1.0" ALLAKAKET 12/22/1911 -53 -59 -56.0 0.14 1.5 Rampart has a low of -48 that day.
>=2.0" RAMPART 1/14/1906 -29 -58 -43.5 0.23 2.5 Univ. Exp. St. had low of -57 with 0.10 precip.
>=3.0" NABESNA 1/28/1989 -36 -48 -42.0 0.3 3.5 Brutal cold snap.
>=4.0" UNIVERSITY EXP STN 12/30/1974 -30 -51 -40.5 0.35 4.0 Fairbanks only recorded 0.1" but 4.0" on 12/31/74.
>=4.0" CIRCLE CITY 1/29/1984 -34 -45 -39.5 0.32 4.0 Seems Reasonable
>=6.0" STRELNA 1/24/1924 -22 -47 -34.5 M 6.0 No form available. Near Chitina. Most of Southeast received heavy snow. Questionable.
>=6.0" DOT LAKE 12/25/1965 -28 -40 -34.0 0.5 6.0 Seems like a good observation. Very wet day in much of AK.
>=9.0" TANANA CALHOUN MEM AP 1/9/1932 -21 -38 -29.5 0.36 10.0 Questionable. Holy Cross only other city over 2".
>=9.0" TRIMS CAMP 3/3/1971 -20 -31 -25.5 1.47 19.5 Very cold and snowy period. High winds. Drifting? Station averages 270" per year.

Monday, January 13, 2014

Cold and Visibility Trends

In a continued quest to fully understand the long-term decline in extremely cold days in Fairbanks (see previous posts here and here), I decided to look at historical visibility observations to see whether any notable changes have taken place in tandem with the warming that has been observed.  Part of the motivation here is that I have long entertained a hypothesis that increased human emissions of water vapor on extremely cold days might be allowing ice fog to form more frequently and at higher temperatures than in earlier years, and that this could slow or prevent the drop of temperatures to extremely low levels (from latent heat release or changes to the radiation balance).  I came across this idea in a blog post by Haines, AK resident Jim Green a couple of years ago:

An initial examination of the data fails to support the hypothesis, because it appears that low visibility conditions have actually become less common in Fairbanks over the years.  The chart below shows the annual (seasonal) fraction of hourly observations in December through February for which the visibility was 1/4 mile or less (red columns), 1/2 mile or less (blue columns), and 1 mile or less (green columns); the purple line is the 15-year trailing average of the 1/2 mile or less frequency.  There was a rather pronounced increase in low visibility conditions from the late 1960s to the mid 1980s, but in recent decades there has been an overall slow decline in the frequency of fog conditions.

Since I looked at McGrath in the previous post, and Jim Green's article made a point of comparing between McGrath and Fairbanks, below is the corresponding chart for McGrath (no hourly observations prior to 1948). Note that the vertical scale is much different from the Fairbanks chart, because low visibility is much less common in McGrath in winter.  McGrath also shows a decline in frequency of 1/2 mile or less visibility in recent years, with the 15-year average of 1/2 mile frequency reaching its lowest level in the past few years.

The following histograms illustrate the multi-decadal changes in the winter frequency distribution for visibility at both locations.  In Fairbanks, the frequency of sub-1 mile visibility dropped from 9.3% to 5.8% between 1951-1980 and 1981-2010, while in McGrath the rare cases of less than 1/2 mile visibility became even less common.

Assuming that the historical data are reliable, then, it seems clear that low visibility conditions have become less common in Fairbanks in winter.  This rules out the basic initial hypothesis, but still leaves the question of whether fog frequency has become more or less common at comparable (low) temperatures.  In other words, we know that ice fog is a common occurrence when temperatures dip to very low levels, and we know that long-term warming has occurred; so do we still see as much fog at the same temperatures (e.g. -40°), or is fog less common even at the same temperatures?  To answer this we need to look at the joint distribution of temperature and visibility.

The next two histograms show the visibility distribution for only temperatures between -50 °F and -40 °F inclusive.  We see that there has been a modest increase in the lowest visibility (less than 1/4 mile) category for Fairbanks at these cold temperatures, and a slight decrease in the 2-5 mile category, but overall the distribution has not changed a great deal.  The changes are actually more dramatic at McGrath, where visibility less than 1/2 mile has all but disappeared in recent decades under these cold conditions.

The next chart shows how the mean visibility varied with temperature for the two locations and in the two 30-year periods (red and blue for Fairbanks, purple and green for McGrath).  [Update: note that an earlier version of this chart failed to account for the change to automated visibility measurements, which do not report values greater than 10 miles; so I have updated the chart to show mean visibility after truncating all values to 10 miles.]  Again we see that the Fairbanks visibility distribution is not greatly different between the two periods; there is a modest decrease at the lowest temperatures but an increase between -40°F and -25 °F.

Given that visibility and temperature are still related in much the same way at Fairbanks, it seems we can conclude that the decline in low visibility conditions is largely attributable to the declining frequency of very cold conditions; ice fog is not as common as it used to be, because it's not as cold as it used to be.  However, in McGrath there has been an interesting decrease in the frequency of ice fog that can't be explained by the warming trend.

In relation to the initial hypothesis for Fairbanks warming, there seems to be no evidence that changes in fog frequency have contributed to the pronounced lack of extremely cold temperatures in recent decades.

Finally, for those who find this as interesting as I do, I'll include a couple more charts I made during the investigation; these show the temperature at which 1/2 mile or less visibility was observed, for both sites and both periods.  Fog in winter in Fairbanks is observed mostly but not exclusively at very low temperatures, but in McGrath it occurs mostly at relatively high temperatures associated with frontal zones and mixing of contrasting air masses.  Both locations have seen a sharp drop in the proportion of low visibility events at very low temperatures: fog is now more often associated with warm conditions than it used to be.

Saturday, January 11, 2014

Was 2013 Fairbanks' Most Extreme Year Ever?

Last Fall I drafted a post that displayed a measure of temperature extremeness that I developed using the Chi-Square Goodness-of-Fit test statistic. The test compares an actual distribution with an expected distribution. This is a lengthy follow up to that post. I have submitted a journal article describing the methodology that is still in the peer-review process.

If we consider the distribution of temperatures to be normally distributed, we can compare the standardized temperature anomalies with readily published z-score tables. For example, 68% of observations will be within 1 standard deviation of the mean if the data are normally distributed. The first chart below shows the distribution of daily temperatures in Fairbanks by standard deviation categories since 1930 (note: all standard deviation values are based on an adjustment to the published NCDC values that Richard developed last year). The year 1930 was chosen due to the oftentimes poor data quality prior to that year. The categories in the first chart below are 1/2 standard deviation wide and take into account the sign of the anomaly. The categories on the ends (over/under 1.5 standard deviations are grouped together so that those categories are not too small. Notice the bias toward temperature being above normal versus below normal. This is most likely a reflection of the upward trend in low temperatures over the years. The second chart groups the data together in whole standard deviation increments and without regard to sign. On both charts, the blue line is the expected value based on the normal distribution.


So how did the distribution of temperatures in 2013 look? Using the same groupings as the two charts above, what clearly stands out is the large number of values over +/- 1.5 standard deviations from the mean in the first chart below and over +/- 2.0 standard deviations from the mean in the second chart below.

In fact, there were a remarkable 54 days where the daily average temperature was < -2 standard deviations or > +2 standard deviations from the daily mean. The year with the second greatest count of such days is 1992 with a total of 40. Using the normal distribution, the expected number of days in any give year to reach that threshold is 16.6. (Note: the y-axis in the charts above use 'Percent of Days' and the table below uses a raw count.)

Chi-Square Goodness of Fit:

There are many goodness-of-fit tests used in statistics. The benefit of using chi-square is that use can use ratio, interval, or ordinal data, and the significance threshold is a function of the number of categories more so than the size of the sample. For each category, the value is calculated by the formula (O-E)^2 / E. Where O = the observed category frequency and E is the expected category frequency. You then add up the value of that calculation for each category. Ideally, a category will not have an expected frequency of less than 5%. That is why I did some groupings at the tails of the distribution. When the frequency within a category is relatively close to the expected value, the chi-square value for that category is low. The table below shows a sample for the calculation in 2013 using 3 categories. 

In this case, Everything over 2 standard deviations was grouped together to ensure that the expected frequencies were at least 5%. As it turns out, the value of 27.0 is not only the largest on record, but it is by far the largest on record. The next highest annual chi-square value is 10.0 in 1992. Using this number of categories (3), any value greater than 5.99 is considered to be not normally distributed. The next chart shows the value of the chi-square test statistic (orange line) along with the frequency distribution for the standard deviation categories between 1930 and 2013.

Different Grouping Strategy:

The chart above uses groups that are a whole standard deviation in size and ignores their signs. However, sign matters. Remember that 68% of observations are expected to fall within 1 standard deviation from the mean. If a year observed exactly 68% of days within 1 standard deviation but 50% were between -1 and 0 standard deviations and 18% were between 0 and +1 standard deviations, we would start to think that the temperature distribution wasn't quite normally distributed after all.

If we look at the frequency distributions using 0.5 standard deviation categories, the numbers look somewhat different. In fact, the three years with the largest chi-square values are different when the grouping strategy is different. The first chart below shows the standard deviation categories for six years using whole standard deviation units without regard to sign. The rightmost columns show the chi-square values for those years. The three largest chi-square years were among the six years shown.

The next chart shows the distribution of standard deviation categories using 1/2-standard deviation units with signs taken into account. To preserve the 5% rule described earlier, categories were grouped together at the tails. The same six years that are shown in the table above are also shown in the table below. In this case, the top three years are different. Note that the significance threshold for the chi-square statistic is larger when there are 8 categories (14.07 vs. 5.99).

As mentioned earlier, taking signs into account can reveal more to the story. Let's take 1987 as an example. Using the 3-category method, it had the 20th (out of 87) most extreme temperature distribution. However, using the 8-category method, it had the 1st most extreme temperature distribution. Why is that? As an example, if you don't look at signs, you would expect for 13.3% of days to be more than 1.5 standard deviations from the mean (+/-). In 1987, it was 10.1% of days. Certainly below normal not not especially noteworthy. If that were a grouped (unsigned) category, it would have a chi-square value of 0.77. If we take signs into account, we see that 1.6% of days were at least 1.5 standard deviations below the mean and 8.5% were at least 1.5 standard deviations above the mean. This gives a chi-square value of 4.4 just for those two categories (out of 8). 1987 was a full 4.5°F above normal so every category was strongly skewed toward the warm-sign category. However, when you add up companion warm/cold categories, the skew was masked.

A scatterplot shows that this type of occurrence is not unexpected. That is, years that are strongly above or below normal (the chart uses absolute value of annual temperature value) often have large chi-square values. 2013 is quite unique in having a large chi-square value along with a low annual temperature variation.

Where does 2013 rank?

So is 2013 the most extreme temperature year on record (since 1930) or is it the 6th most extreme year on record. The answer is, both. Like many endeavors in statistics, the parameters that you choose make a huge difference.

****** Chart for response to comment No. 1 ****

This chart simulates the temperature frequency distribution in a warming climate. I generated 1000 daily temperatures with a constant mean and standard deviation. I then added an incremental background warming to the data and charted the standard deviations from the mean. Notice how the chart is similar to the first one in this post.