Objective Comments and Analysis - All Science, No Politics
Primary Author Richard James
2010-2013 Author Rick Thoman
Monday, October 31, 2011
Coldest of the Season so Far
A cool airmass is in place over much of the Interior Alaska this Halloween morning. Over a small portion of the western Interior, skies cleared overnight, allowing temperatures to fall to the lowest levels of the early inter season. Here is the NOAA-19 Polar Orbiter infrared satellite photo from about 630am Monday. The clear skies in portions of the Middle Yukon, Koyukuk and Kobuk valleys stand out in this scale as the bright white colors and hints of the dendritic pattern that shows the cold air pooled in valley. Farther east, warmer (darker) and more uniform areas show a nearly continuous stratocumulus cloud cover. Though 10am, low temperatures include 18 below at Huslia, 17 below at the Selawik River RAWS (well upriver of the village of Selawik) and 11 below at Kaltag.
Fairbanks Finally Gets an Inch
Snowfall at the Fairbanks airport on Sunday was 1.0 inches. This is the first day with an inch or more of snow this season, and three weeks later than average. The snow was classic "arctic front" snow, produce by the lift associated with the eastward push of cold low level air. Here at Keystone Ridge I measured 2.1 inches, and out at Mile 42 Steese Highway, the coop observer reported 2.6 inches.
Saturday, October 29, 2011
First 40 below of the Winter--In Siberia
Oymyakon, one of the notorious cold spots in eastern Siberia, reported a low Sunday morning (Siberia time, OCT 30th UTC) of -42F. This is the first 40 below of the season at Oymyakon and as far I know in Siberia.
Sea Ice at Barrow
Meteorological Winter Begins
The power of the waning sunshine was in evident Friday in Fairbanks-land. With no winds and no more than some cirrus, the morning inversion could not quite break, resulting in high temperatures Friday afternoon slightly lower than in the hills (high of 25F at Keystone Ridge, 22F at the Airport, 21F at Goldstream Creek). I hereby declare meteorological winter underway. This is quite important: I have to know what tags to include on these posts :)
Friday, October 28, 2011
Strong Inversion
Mild air aloft, clear skies and a thin but continuous snow cover allowed for a strong inversion to develop overnight. Here is a plot of temperatures in the lowest 1200 meters from the upper air sounding launched at Fairbanks about 3am ADT Friday.
Low temperatures in Fairbanks-land through 10am reflect this:
Eielson AFB: -4F
Woodsmoke PWS: -2F
Goldstream Creek: -2F
Fairbanks Airport: +4F
Fort Wainwright: +5F
UAF West Ridge: +6F
Goldstream Hills CWOP: 19F (1100'MSL)
Ester Dome CWOP: 19F
Keystone Ridge: 18F
Cleary Summit: 18F
Parks Hwy RWIS near FNSB Boundary: 18F
Thursday, October 27, 2011
Heavy Snow
It looks like there was area between Healy and Nenana that received a decent snowfall Wednesday. The Clear Sky Lodge Coop site, near Mile 280 on the Parks Highway, reported 6.2 inches of snow, and the Kobe Hill Coop site, a bit west of the Nenana River bridge, reported 6.8 inches. The fairly wretched webcam imagery from the DOT at the bridge shows the road is not snow covered.
Snowfall in Fairbanks-land was light: no reports of more than two inches, with less than an inch in town.
Tuesday, October 25, 2011
Big Storm, Big Chinook
A vigorous storm plowed across the western Gulf of Alaska Monday night and early Tuesday. The 10AM ADT surface analysis from the Ocean Prediction Center:
Lots of warm air being pumped north, then chinooked off the Alaska Range and into the southern Interior. The surface inversion has broken almost everywhere in Fairbanks-land, with temperatures in the 40s.
Update: Through 4pm ADT Tuesday, some high temperatures include
Two Rivers PWS: 47F
Woodsmoke PWS: 46F (near North Pole)
Gilmore Creek Coop: 46F (near Fox)
Fairbanks Airport: 44F
Eielson AFB: 46F
Keystone Ridge: 42F
Nenana: 41F
Cleary Summit: 41F
Lots of warm air being pumped north, then chinooked off the Alaska Range and into the southern Interior. The surface inversion has broken almost everywhere in Fairbanks-land, with temperatures in the 40s.
Update: Through 4pm ADT Tuesday, some high temperatures include
Two Rivers PWS: 47F
Woodsmoke PWS: 46F (near North Pole)
Gilmore Creek Coop: 46F (near Fox)
Fairbanks Airport: 44F
Eielson AFB: 46F
Keystone Ridge: 42F
Nenana: 41F
Cleary Summit: 41F
Sunday, October 23, 2011
Brooks Range Morning
Friday, October 21, 2011
Near Zero in the Lowlands
Now that there is a thin but continuous snowpack, the inversion growing season is well underway in Fairbanks-land. Clear skies overnight allowed temperatures to dip to right around zero in the colder low spots. Some minimum temperatures Friday morning included
Woodsmoke CWOP: 0F (near North Pole)
Goldstream Creek: +2F
Eielson AFB: +6F
Fairbaks Airport: +11F
In the eastern Interior there were a couple of subzero reports:
Circle Hot Springs: -2F
Chicken: -2F
With a fairly mild airmass in place, the hills were no where near as cold:
Keystone Ridge: 20F
Parks Highway RWIS: 21F (at FNSB boundary)
Cleary Summit: 23F
Woodsmoke CWOP: 0F (near North Pole)
Goldstream Creek: +2F
Eielson AFB: +6F
Fairbaks Airport: +11F
In the eastern Interior there were a couple of subzero reports:
Circle Hot Springs: -2F
Chicken: -2F
With a fairly mild airmass in place, the hills were no where near as cold:
Keystone Ridge: 20F
Parks Highway RWIS: 21F (at FNSB boundary)
Cleary Summit: 23F
Wednesday, October 19, 2011
1981-2010 Normals
Here's a couple of plots showing how the 1981-2010 normals that became effective August 1st have changed from the 1971-2000 normals at a number of first order stations around Alaska. Of particular note is that all the locations at least a little be wetter, and all locations are warmer. While the absolute temperature changes are largest in winter, the standardized change (the change divided by the standard deviation, not shown) is actually largest in June at nearly all the sites. This has important ramifications for both hydrology and fire weather. The big changes in precipitation at a few sites (but mostly Barrow) reflect a few really wet months in what are otherwise dry times of year, and highlight a problem with using the mean value of precipitation (and snowfall too) as "normal". In these cases the median is a much better statistic for expressing "normal".
Sunday, October 16, 2011
Fairbanks First Measurable Snow
I had not posted on this before due to conflicting data, but now this has been cleared up. The first measurable snow for Fairbanks was on Thursday, October 13th, with 0.1" of snow. This is two weeks later than the mean first measurable snow.
More "significant" snow, i.e. several tenths of an inch, fell early Sunday morning. Here is the 1030am ADT view from UAF West Ridge,from the Alaska Climate Research Center Webcam.
Saturday, October 15, 2011
2011 Temperatures
Here's a plot of temperatures thus far in 2011 at Fairbanks. I've plotted the mean daily temperature against the 1980-2010 normals and standard deviation. So, where the green line (2011 data) falls outside of the shaded area, this represents a statistically significant deviation from the expected. This way of looking at variations from normal is much more useful than the raw "departure from normal" in places with continental type climates, or high latitudes in general, where the potential variation in temperatures is much greater during the cold season than the warm season.
The very warm weather at the end of May is the most prominent feature, and to a lesser extent the cold weather in mid to late February. This autumn, the mild weather has been consistent, but not much outside of "expected" range.
Thursday, October 13, 2011
World gone White, or Not
Warm advection snow associated with the storm centered near the Bering Straits overspread central Interior Alaska Thursday morning. Here on Keystone Ridge, here's the view as of about 3pm ADT:
A little more than half an inch. Normally not much for mid October, but we'll take it.
Meanwhile, here's a view of UAF West Ridge just before 4pm ADT:
The most important reason for the difference is that there has been very little precipitation in town, with only a trace liquid at the Airport through 4pm ADT.
A little more than half an inch. Normally not much for mid October, but we'll take it.
Meanwhile, here's a view of UAF West Ridge just before 4pm ADT:
The most important reason for the difference is that there has been very little precipitation in town, with only a trace liquid at the Airport through 4pm ADT.
Wednesday, October 12, 2011
Freezing at last
With a low of 19F this morning, Fairbanks will have the first day this autumn with a mean temperature below freezing today, October 12th. This is right at the 90 percentile of the distribution. That is, only 10 percent of years 1930-2011 have the first day with a mean temperature below freezing on October 12 or later. At this point it looks like except for a brief chinook Friday/Saturday, the freezing season is upon us. No if we could just get some snow…
Monday, October 10, 2011
Brooks Range Snow Drought
It isn't just Fairbanks-land that's suffering from a dearth of snow. Here's a lovely morning photo (courtesy of the FAA) from Arctic Village in the eastern Brooks Range. Frosty, but snowfree, at valley elevation (about 2000' MSL). There are no long term stats for this part of the world, but my sense is that it very unusual to go into mid-October without a snow cover at Arctic Village.
Saturday, October 8, 2011
Active Sky at Northway
Still No Snow for Fairbanks
Snow is getting closer to Fairbanks. There was a report of eight inches of snow at Summit Lake (on the Richardson Highway), elevation 3200' MSL, Friday night and early Saturday, and some places above 2000' MSL around Fairbanks had a skiff of snow in a brief shower Friday evening. Still, the greater Fairbanks metro area has yet to have measurable snow. We are now past the 75th percentile of dates with measurable snow, i.e. more three-quarters of the time Fairbanks has received measurable snow by this point in the calendar. Here is a histogram showing how the dates are distributed:
The lack of snow is not (just) because it's been too warm. There has been hardly any precipitation recently. Since September 17th the Airport has received just 0.04 inches of precipitation, and none measurable in the past two weeks.
The current forecast is for very little chance of any snow (or rain) in Fairbanks at least through Tuesday and probably beyond that.
The lack of snow is not (just) because it's been too warm. There has been hardly any precipitation recently. Since September 17th the Airport has received just 0.04 inches of precipitation, and none measurable in the past two weeks.
The current forecast is for very little chance of any snow (or rain) in Fairbanks at least through Tuesday and probably beyond that.
Wednesday, October 5, 2011
Winter Encroaches
Coldest of the Season so Far
Clear skies overnight allowed valley temperatures to fall to the lowest levels of the autumn thus far. Lows included:
Goldstream Creek: 15F
Woodsmoke PWS: 16F (near North Pole)
Eileson AFB: 18F
Gilmore Creek: 20F near Fox
Fairbanks Airport: 23F
UAF West Ridge: 23F
In the hills this was not the coolest night so far: lows were at or just slightly below freezing. Here on Keystone Ridge, the low was 30F but the heavy frost sure was pretty.
Goldstream Creek: 15F
Woodsmoke PWS: 16F (near North Pole)
Eileson AFB: 18F
Gilmore Creek: 20F near Fox
Fairbanks Airport: 23F
UAF West Ridge: 23F
In the hills this was not the coolest night so far: lows were at or just slightly below freezing. Here on Keystone Ridge, the low was 30F but the heavy frost sure was pretty.
Tuesday, October 4, 2011
More on First Freezing Day
I'm a big believer in the maxim "statistics don't lie, only people do". Okay, I've never actually heard anyone but me say that, but still…
So, here are the statistics on when in the autumn Fairbanks has its first day with the daily mean temperature below freezing. It turns out that the average date in the WB/NWS era (1930-2010) is October 3rd. The time series shows a weak but statistically insignificant trend toward later dates:
When we put the dates into a histogram, we see that presently (Oct 04) we're right in the peak of the distribution:
If Fairbanks were to go through the weekend without a day with a mean temperature below freezing, that would be beyond the 75th percentile and into the realm of "unusually late".
So, here are the statistics on when in the autumn Fairbanks has its first day with the daily mean temperature below freezing. It turns out that the average date in the WB/NWS era (1930-2010) is October 3rd. The time series shows a weak but statistically insignificant trend toward later dates:
When we put the dates into a histogram, we see that presently (Oct 04) we're right in the peak of the distribution:
If Fairbanks were to go through the weekend without a day with a mean temperature below freezing, that would be beyond the 75th percentile and into the realm of "unusually late".
New Barrow Webcam
The long awaited FAA webcam at Barrow is now online. This does not have a coastline view like the UAF Sea Ice program does, but should be more reliable. Here's the view looking east across the runway noon Tuesday.
No Freezing Degree Days
Here on Keystone, through Monday, October 3rd, there has been no freezing degree days (FDD) yet, which makes this the latest in the autumn we've gone with zero FDD. What is a freezing degree day? It's the sum of 32F minus the daily mean temperature. Like most degree day statistics, there are no negative values: if the mean temperature is above freezing, the FDD is zero.
However, there are only 16 years of obs here on the hill, and two years, 2001 and 2006, had only 1 FDD through Oct 3rd.
If we look at the Fairbanks data for FDD, it turns out that it is by no means unusual to go this late in the autumn without any FDD yet. In 2009, 1979 and 1943, there were no FDD until October 18th, and the record warm October 1938 had no FDD until the 27th.
This is not quite an apples to apples comparison; I'd expect Keystone Ridge to have earlier occurrence of FDD, but it's probably safe to say that the lack of freeze not yet terribly unusual. The current numerical guidance suggests though that it will be at least the weekend and probably longer, so the lack of freeze may become extreme.
However, there are only 16 years of obs here on the hill, and two years, 2001 and 2006, had only 1 FDD through Oct 3rd.
If we look at the Fairbanks data for FDD, it turns out that it is by no means unusual to go this late in the autumn without any FDD yet. In 2009, 1979 and 1943, there were no FDD until October 18th, and the record warm October 1938 had no FDD until the 27th.
This is not quite an apples to apples comparison; I'd expect Keystone Ridge to have earlier occurrence of FDD, but it's probably safe to say that the lack of freeze not yet terribly unusual. The current numerical guidance suggests though that it will be at least the weekend and probably longer, so the lack of freeze may become extreme.
Sunday, October 2, 2011
5th Warmest September of record at Barrow
Last month was the 5th warmest September of record at Barrow. Here are the rankings, temperatures in degrees F.
1. 37.7 (1998)
2. 37.6 (2007)
3. 37.4 (2010)
4. 36.8 (1986)
5. 36.7 (2011)
Weather observations start in Oct 1921 in Barrow, so this is based on 90 years of data.
1. 37.7 (1998)
2. 37.6 (2007)
3. 37.4 (2010)
4. 36.8 (1986)
5. 36.7 (2011)
Weather observations start in Oct 1921 in Barrow, so this is based on 90 years of data.
Saturday, October 1, 2011
September Summary
The Fairbanks-land weather summary for September…
PUBLIC INFORMATION STATEMENT
NATIONAL WEATHER SERVICE FAIRBANKS AK
1142 AM AKDT SAT OCT 1 2011
...SEPTEMBER 2011 IN FAIRBANKS...
...DRY AND MILD...
SEPTEMBER WAS A PLEASANT AUTUMN MONTH WITH PERSISTENTLY ABOVE
NORMAL TEMPERATURES AND MOSTLY DRY DAYS.
ONLY THREE DAYS DURING THE MONTH HAD AN AVERAGE DAILY TEMPERATURE
EVEN SLIGHTLY BELOW NORMAL...WHILE AN EQUAL NUMBER OF DAYS HAD AN
AVERAGE DAILY TEMPERATURE MORE THAN 10 DEGREES ABOVE NORMAL.
OVERALL...THE AVERAGE HIGH IN SEPTEMBER AT THE FAIRBANKS
INTERNATIONAL AIRPORT WAS 59 DEGREES AND THE AVERAGE LOW WAS
39 DEGREES. THE AVERAGE TEMPERATURE FOR THE MONTH OF 49.0 DEGREES
MADE THIS THE 10TH WARMEST SEPTEMBER IN MORE THAN A CENTURY OF
WEATHER OBSERVATIONS IN FAIRBANKS. THIS IS THE 7TH CONSECUTIVE
SEPTEMBER TO BE SIGNIFICANTLY WARMER THAN NORMAL...AND FOUR OF THE
TEN WARMEST SEPTEMBERS OF RECORD HAVE OCCURRED IN THE PAST 20
YEARS.
THE HIGH TEMPERATURE AT THE AIRPORT FOR SEPTEMBER WAS 72 DEGREES ON
THE 5TH AND 13TH...WHILE THE LOW OF 28 DEGREES OCCURRED LATE IN
THE EVENING ON THE 30TH. THE FIRST FREEZE OF THE AUTUMN AT THE
AIRPORT OCCURRED ON THE 25TH...WHICH TIED WITH 2006 FOR THE SECOND
LATEST FIRST FREEZE OF RECORD. AMAZINGLY...ALTHOUGH THE LONG-TERM
AVERAGE DATE FOR THE FIRST FREEZE AT THE AIRPORT IS SEPTEMBER
7TH...THIS IS THE SIXTH CONSECUTIVE YEAR IT HAS BEEN AFTER
SEPTEMBER 20TH.
EVEN IN TYPICALLY COLDER LOW LYING AREAS...TEMPERATURES IN
SEPTEMBER FAILED TO DROP BELOW THE 20S...WITH MONTHLY LOWS OF
20 DEGREES AT GOLDSTREAM VALLEY BOTTOM AND 23 DEGREES AT WOODSMOKE
NEAR NORTH POLE.
PRECIPITATION WAS SIGNIFICANTLY BELOW NORMAL. THE TOTAL FOR THE
MONTH OF 0.65 INCHES AT THE AIRPORT IS ABOUT 60 PERCENT OF NORMAL.
MEASURABLE RAIN FELL ON JUST NINE DAYS...AND ABOUT TWO- THIRD OF
THE MONTHLY TOTAL FELL ON THE 9TH AND 10TH. THE FIRST SNOW
FLURRIES OF THE SEASON FELL ON THE LAST DAY OF THE MONTH OVER MUCH
OF THE AREA. AT THE AIRPORT THIS IS ABOUT A WEEK LATER THAN NORMAL
FOR THE FIRST SNOW.
AUTUMN COLORS SEEMED UNUSUALLY LONG LIVED IN SEPTEMBER...AND ONLY
AFTER THE EQUINOX WERE TREES LARGELY BARE. THE MONTH ALSO FEATURED
SEVERAL NIGHTS WITH ACTIVE NORTHERN LIGHTS.
LOOKING AHEAD TO OCTOBER...THE WINTER SNOW PACK IS NEARLY ALWAYS
ESTABLISHED SOMETIME DURING THE MONTH...AND THIS HELPS
TEMPERATURES TO FALL DRAMATICALLY. THE AVERAGE HIGH TEMPERATURE
DROPS FROM 45 ON THE 1ST TO 19 ON HALLOWEEN...WHILE THE AVERAGE LOW
TEMPERATURE FALLS FROM 28 DEGREES ON THE FIRST TO 4 ABOVE ON THE
31ST. TOTAL PRECIPITATION AVERAGES 0.83 INCHES AND AVERAGE
SNOWFALL 10.8 INCHES. SIGNIFICANT AMOUNTS OF RAIN ARE UNCOMMON IN
FAIRBANKS AFTER THE FIRST WEEK OF THE MONTH. THE PERMANENT
WINTER SNOW COVER IS ESTABLISHED...ON AVERAGE...ON OCTOBER 18TH.
POSSIBLE SUNSHINE DECREASES FROM OVER 11 HOURS DURING THE FIRST
THREE DAYS OF THE MONTH TO LESS THAN EIGHT HOURS ON THE 31ST. THE
FORECAST FOR THIS OCTOBER FROM NOAA'S CLIMATE PREDICTION CENTER
CALLS FOR SLIGHTLY INCREASED CHANCES OF SIGNIFICANTLY BELOW NORMAL
TEMPERATURES.
$$
RT OCT 2011
PUBLIC INFORMATION STATEMENT
NATIONAL WEATHER SERVICE FAIRBANKS AK
1142 AM AKDT SAT OCT 1 2011
...SEPTEMBER 2011 IN FAIRBANKS...
...DRY AND MILD...
SEPTEMBER WAS A PLEASANT AUTUMN MONTH WITH PERSISTENTLY ABOVE
NORMAL TEMPERATURES AND MOSTLY DRY DAYS.
ONLY THREE DAYS DURING THE MONTH HAD AN AVERAGE DAILY TEMPERATURE
EVEN SLIGHTLY BELOW NORMAL...WHILE AN EQUAL NUMBER OF DAYS HAD AN
AVERAGE DAILY TEMPERATURE MORE THAN 10 DEGREES ABOVE NORMAL.
OVERALL...THE AVERAGE HIGH IN SEPTEMBER AT THE FAIRBANKS
INTERNATIONAL AIRPORT WAS 59 DEGREES AND THE AVERAGE LOW WAS
39 DEGREES. THE AVERAGE TEMPERATURE FOR THE MONTH OF 49.0 DEGREES
MADE THIS THE 10TH WARMEST SEPTEMBER IN MORE THAN A CENTURY OF
WEATHER OBSERVATIONS IN FAIRBANKS. THIS IS THE 7TH CONSECUTIVE
SEPTEMBER TO BE SIGNIFICANTLY WARMER THAN NORMAL...AND FOUR OF THE
TEN WARMEST SEPTEMBERS OF RECORD HAVE OCCURRED IN THE PAST 20
YEARS.
THE HIGH TEMPERATURE AT THE AIRPORT FOR SEPTEMBER WAS 72 DEGREES ON
THE 5TH AND 13TH...WHILE THE LOW OF 28 DEGREES OCCURRED LATE IN
THE EVENING ON THE 30TH. THE FIRST FREEZE OF THE AUTUMN AT THE
AIRPORT OCCURRED ON THE 25TH...WHICH TIED WITH 2006 FOR THE SECOND
LATEST FIRST FREEZE OF RECORD. AMAZINGLY...ALTHOUGH THE LONG-TERM
AVERAGE DATE FOR THE FIRST FREEZE AT THE AIRPORT IS SEPTEMBER
7TH...THIS IS THE SIXTH CONSECUTIVE YEAR IT HAS BEEN AFTER
SEPTEMBER 20TH.
EVEN IN TYPICALLY COLDER LOW LYING AREAS...TEMPERATURES IN
SEPTEMBER FAILED TO DROP BELOW THE 20S...WITH MONTHLY LOWS OF
20 DEGREES AT GOLDSTREAM VALLEY BOTTOM AND 23 DEGREES AT WOODSMOKE
NEAR NORTH POLE.
PRECIPITATION WAS SIGNIFICANTLY BELOW NORMAL. THE TOTAL FOR THE
MONTH OF 0.65 INCHES AT THE AIRPORT IS ABOUT 60 PERCENT OF NORMAL.
MEASURABLE RAIN FELL ON JUST NINE DAYS...AND ABOUT TWO- THIRD OF
THE MONTHLY TOTAL FELL ON THE 9TH AND 10TH. THE FIRST SNOW
FLURRIES OF THE SEASON FELL ON THE LAST DAY OF THE MONTH OVER MUCH
OF THE AREA. AT THE AIRPORT THIS IS ABOUT A WEEK LATER THAN NORMAL
FOR THE FIRST SNOW.
AUTUMN COLORS SEEMED UNUSUALLY LONG LIVED IN SEPTEMBER...AND ONLY
AFTER THE EQUINOX WERE TREES LARGELY BARE. THE MONTH ALSO FEATURED
SEVERAL NIGHTS WITH ACTIVE NORTHERN LIGHTS.
LOOKING AHEAD TO OCTOBER...THE WINTER SNOW PACK IS NEARLY ALWAYS
ESTABLISHED SOMETIME DURING THE MONTH...AND THIS HELPS
TEMPERATURES TO FALL DRAMATICALLY. THE AVERAGE HIGH TEMPERATURE
DROPS FROM 45 ON THE 1ST TO 19 ON HALLOWEEN...WHILE THE AVERAGE LOW
TEMPERATURE FALLS FROM 28 DEGREES ON THE FIRST TO 4 ABOVE ON THE
31ST. TOTAL PRECIPITATION AVERAGES 0.83 INCHES AND AVERAGE
SNOWFALL 10.8 INCHES. SIGNIFICANT AMOUNTS OF RAIN ARE UNCOMMON IN
FAIRBANKS AFTER THE FIRST WEEK OF THE MONTH. THE PERMANENT
WINTER SNOW COVER IS ESTABLISHED...ON AVERAGE...ON OCTOBER 18TH.
POSSIBLE SUNSHINE DECREASES FROM OVER 11 HOURS DURING THE FIRST
THREE DAYS OF THE MONTH TO LESS THAN EIGHT HOURS ON THE 31ST. THE
FORECAST FOR THIS OCTOBER FROM NOAA'S CLIMATE PREDICTION CENTER
CALLS FOR SLIGHTLY INCREASED CHANCES OF SIGNIFICANTLY BELOW NORMAL
TEMPERATURES.
$$
RT OCT 2011