# Chaitanya's Random Pages

## March 28, 2016

### Recent months of global warmth

Filed under: climate and weather — ckrao @ 5:02 am

According to both NASA’s Goddard Institute for Space Studies [1] and the NOAA National Centers for Environmental Information [2], February 2016 set another record of the highest deviation of global temperatures above the monthly mean. In fact NASA’s dataset has seen the past five months record the largest five monthly global warm anomalies [3]. Some plots of global temperatures from recent months can be seen at Makiko Sato’s page here. One case in point is Longyearbyen, Svalbard (78°N) whose temperatures have barely been below average for the past six months (data from [4-5]).

February set the record of greatest anomaly from mean monthly temperatures, beating the previous record (set only the previous month) by more than 0.2°C. The map here shows that the vast majority of the planet had above-average temperatures, with the greatest deviation in the arctic region. As an example, check out the temperatures of Salekhard, Russia on the arctic circle during this time (this is a place that registers temperatures below -40 during winters). Over the month its average was 12.5°C above the mean! Data is from [6].

[2] NOAA National Centers for Environmental Information, State of the Climate: Global Analysis for February 2016, published online March 2016, retrieved on March 27, 2016 from http://www.ncdc.noaa.gov/sotc/global/201602.

## June 30, 2015

### The Pakistan heat wave of 2015

Filed under: climate and weather — ckrao @ 11:39 am

This month a heatwave has killed over 1500 people in Pakistan, most of them in Karachi. Here are the temperatures recorded at Karachi airport at that time: note that the average for this time of year is 28-35°C with high humidity. Rarely does the temperature reach 39.5°C three days in a row but here it did so six days in a row plus there seemed to be no relief at night.

 Date 16-Jun 17-Jun 18-Jun 19-Jun 20-Jun 21-Jun 22-Jun 23-Jun 24-Jun Min (°C) 30 29.3 29.5 31 31.6 33 33 33 30.5 Max (°C) 36 38.5 39.5 40.5 44.8 42.5 42.5 41.2 37

Most of the dead were homeless and it was also during the time of Ramadan where fasting is observed during daylight hours. This and the recent heatwave in India are two of the three most fatal on the Indian subcontinent in recent times.

## June 29, 2014

### Melbourne’s late start to cooler temperatures in 2014

Filed under: climate and weather — ckrao @ 11:21 am

It occurred to me that Melbourne has had an unusual number of cooler days in 2014 up to the middle of June. After some checking here, I found that from January 1 to June 17 this year, the Melbourne Regional Office has only twice recorded days with a maximum temperature less than 15°C (May 2 [14.3°C] and May 4 [14.2°C]). This beats 2003 when the previous fewest number of 5 such instances took place prior to June 18. The graph and table below show that in the past this number has been as high as 40, but in recent years there is a clear downward trend.

 Melbourne Regional Office Average number of sub-15°C days before June 18 Average 1856-2013 21.6 Average 1971-2013 15.0 Average 2004-2013 11.7 2014 2

If we do the same calculation for a station further away from the city centre, say the international airport just over 20km away, there is not as much historical data and the effect is not as pronounced, but this year still equals the previous record of 2003 (11 times). In recent times the sub-15°C days prior to June 18 have been about twice as frequent here as the Regional Office.

 Melbourne Airport Average number of sub-15°C days before June 18 Average 1971-2013 24.7 Average 2004-2013 23.1 2014 11

The data is from Australia’s Bureau of Meteorology website.

## January 30, 2014

### The frequency of 40+ days in Melbourne

Filed under: climate and weather — ckrao @ 10:14 am

In a recent post I mentioned that Melbourne (the regional office weather station) has had 203 days of a maximum temperature of 40°C or more in the 159 years from 1855 to 2013. January 2014 alone has had 5 more such days, tying the record of instances in a month. There were two other times when Melbourne had 5 days reaching at least 40°C in a month: January 1905 and January 1908. The former of these had four of the hot days out of a string of five while the latter had all five in consecutive days. This year included a sequence of four consecutive instances above 41°C, the first time that has happened since records began.

The following plot, generated via the geom_smooth feature of ggplot2 in R, shows a dip in the frequency of these days in the mid 20th century, followed by an increasing frequency since 1980. (The year 2014, being incomplete to date, is not included.)

Interestingly the 10 years 1969-1978 only had 3 instances of 40+ degree days (including none during the four years 1969-1972). The table below shows the frequency per decade since records began, with the current period having the most. The most recent year Melbourne did not have a 40+ day was 2002.

 Decade # 40+ °C days 1855-1864 12 1865-1874 11 1875-1884 13 1885-1884 6 1895-1904 21 1905-1914 22 1915-1924 11 1925-1934 6 1935-1944 15 1945-1954 10 1955-1964 8 1965-1974 8 1975-1984 14 1985-1994 10 1995-2004 16 2005-2014 27+

Melbourne has so far never had 7 days of 40°C in a year (6 times was reached in 1898 and 1900), and 2014 has a chance of at least equalling that record (edit: 2014 has set a record with its 7th day of 40+°C temperatures, the mark reached on Jan 14-17, 28 and Feb 8-9).

## December 31, 2013

### Large day to day temperature increases for Melbourne

Filed under: climate and weather — ckrao @ 4:07 am

Recently Melbourne has had a few recent unusually large maximum temperature increases from one day to the next, and I wanted to see how often this occurs. For example this year the city weather station had maximums of 19.8°C and 31°C on Nov 30 and Dec 1, 26.9°C and 39.9°C on Dec 18-19, 22.4°C and 36.5°C (Dec 27-28), and 25.5°C and 40.8°C (Jan 16-17). Similarly large decreases in temperature are more frequent due to cold fronts sweeping south-eastern Australia.

The following analysis was carried out with data from Australia’s Bureau of Meteorology.

Firstly, the following boxplot illustrates the distribution of maximum temperature differences from one day to the next. In the summer months large increases occur more frequently than I had expected. (To interpret a box plot, the thick black line represents the median, the red boxes span the quartiles and the dashed lines extend 1.5 times the interquartile range in both directions. Outliers beyond this range are plotted separately.)

One data point that immediately stands out is at top left of the graph – it seems that in 1900 there was an increase from a maximum of 15.1°C to 40.3°C on 15-16 January 1900! This appears too large to be plausible.

As expected the temperature differences are negatively skewed in each month (lower tail fatter than the upper tail), with skewness values tabulated below.

 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC -0.37 -0.59 -0.46 -0.51 -0.37 -0.07 -0.09 -0.40 -0.52 -0.46 -0.43 -0.42

Zooming in on the warmer months December-March we have the following histograms showing the fatter lower tail. However the upper tail is larger than I had anticipated.

Here are answers to some questions I had posed regarding this data.

How often is the maximum temperature above 30°C after failing to reach 20°C the previous day?

This has happened on average 1.2 times per year in Melbourne with frequency-by-month shown below.

 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total 35 16 20 2 0 0 0 0 0 13 59 53 198

There have in fact been 13 occasions (6 in January, 4 in November) where the maximum was above 35°C after being less than 20°C the previous day. This happened most recently in 1983 (35.0°C on 25/1 after 19.4°C on 24/1).

How often is the maximum temperature above 40°C after failing to reach 25°C the previous day?

This has happened 25 times (14 in January) with 24.4°C and 44.7°C on 9-10 Jan 1939, and 24.1°C and 43.3°C (23-24 Dec 1868) being two of the bigger increases. Most recently we had maximums of 24.2°C and 40.8°C on 15-16 Jan 2007. Melbourne has experienced 203 40+ days in the 159 years of records.

How often is there a day-to-day increase of at least 15°C?

This has happened on average 0.8 times per year in Melbourne, about half the time in January as shown below.

 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total 62 19 5 0 0 0 0 0 0 0 13 31 130

Finally, listed below are some notable events.

• The days 8-13 January 1939 (the 13th was Black Friday) had maximum temperatures of 43.1, 24.4, 44.7, 33.5, 25.6 and 45.6°C respectively, hence containing two 20-degree increases! The only other 20-degree increase was the anomalous 15.1°C to 40.3°C jump from 15-16 January 1900 mentioned earlier.
• 9-10 Jan 1877: 19.7°C and 38.1°C
• 9-10 Jan 1882: 19.9°C and 37.1°C
• 26-28 Feb 1865 had maximum temperatures of 20.3, 39.7 then back to 19.9°C.
• 1-3 Mar 1893 had maximum temperatures of 23.0, 40.8 then back to 22.1°C.
• 4-5 Apr 1888: 17.9°C and 30.1°C, the biggest increase in April
• 29-30 Oct 1919: 20.1°C and 34.7°C, the biggest increase in October
• 13-14 Nov 1878: 22.3°C and 39.4°C, the biggest increase in November
• 23-24 Dec 1868: 24.1°C and 43.3°C (mentioned earlier)
• 15-16 Dec 1897 : 22.3°C and 41.7°C

## July 27, 2013

### Wide range in maximum temperatures within a month in Melbourne

Filed under: climate and weather,geography — ckrao @ 5:02 am

This month Melbourne recorded its highest July recorded maximum temperature of 23.3°C. Then just two days later the maximum was just 9.7°C. This temperature difference seemed highly unusual to me and indeed it was. The difference of 13.6°C is easily the highest recorded for the month of July in over 150 years of records (the previous record was 12° in 1975 when it was 11.1°C on the 3rd and 23.1°C on the 30th of the month). The graph below shows the distribution of the difference between highest maximum and lowest maximum temperatures for each month (data from the Australian Bureau of Meteorology website). In a box and whisker plot the thick horizontal lines represent the medians and the box boundaries are the 25th and 75th percentiles. Outliers are shown for data more than 1.5 times the inter-quartile range away from the 25th or 75th percentiles. We see that in Melbourne much larger maximum temperature fluctuations are expected in the warmer months. July has a median range of just 7.7°C between its highest and lowest maximum temperatures.

Here are a few other outliers indicated on the graph when there were large extremes in maximum temperatures during the month.

• Dec 1867: 10.4°C (12th – coldest Dec maximum on record), 40.3°C (19th)
• May 1905: 28.7°C (9th – warmest May day on record), 11.4°C (11th)
• Nov 1911: 12.2°C (1st), 40.7°C (30th)
• Oct 1922: 35.8°C (22nd), 9.0°C (29th – coldest Oct maximum on record)
• Dec 1924: 40.1°C (12th), 11.5°C (26th)

It’s interesting that it has been so long since we have had such an anomaly in maximum temperatures within a month!

## January 16, 2013

### Australia’s recent heat wave

Filed under: climate and weather — ckrao @ 11:09 am

Australia has started 2013 with something like 10 of its first 11 days among the hottest 20 previously determined over some 100 years of records! The previous record area-averaged maximum of 40.17°C (set in December 1972) was broken on January 7 with 40.33°C. The two striking features of this heat wave have been its duration and wide-reaching nature. It included Hobart’s highest recorded maximum of 41.8°C and Australia’s hottest day for 15 years (49.6°C at Moomba, SA). Other very high temperatures included 49.0 at both Leonora (WA) and Birdsville (QLD).

The following graph based on data in [1] shows the maximum temperatures over the states and territories over this period. Note that the southern states of VIC and TAS are the smallest and have the least impact on the average temperature for Australia. For information on how area averages are calculated based on the weather station locations, refer to [2].

Birdsville probably was probably the hottest town in Australia over this period with the following maximum temperatures recorded (an average maximum of 45.6°C over the 13 days!). (Data from here).

 Date (Jan 2013) Maximum Temp (°C) 1 43.9 2 45.2 3 45.5 4 47.3 5 46.7 6 46.3 7 45.1 8 44.6 9 44.2 10 40.8 11 46.2 12 48.6 13 49.0

#### References

[1] Extreme January heat: Special Climate Statement Issued 7th of January 2013, updated 25th January 2013, Bureau of Meterology, Australia.

[2] D. Jones, W. Wang and R. Fawcett, High-quality spatial climate data-sets for Australia, Australian Meteorological and Oceanographic Journal 58 (2009) 233-248.

## October 28, 2012

### The declining arctic sea ice

Filed under: climate and weather — ckrao @ 10:30 am

The following graphs are cause for concern. They show that

(1) the area of arctic ice at its minimum yearly extent (usually in September) was this year only a half of the average value of the 1980s.

(2) the volume of arctic ice at its minimum yearly extent  is on the decline with this year’s level just a fifth of that in 1979!

(3) Since the volume is decreasing at a faster rate than the area, this indicates that the mean ice thickness is also decreasing.

(Data from here and here.)

More on this at the following links.

Poles apart: A record-breaking summer and winter – Arctic Sea Ice News & Analysis, NSIDC

Ice records fall at both poles – New Scientist

Arctic sea ice graphs (Nevin Acropolis)

PIOMAS September 2012 (minimum) – Arctic Sea Ice in Arctic Sea Ice Blog (Nevin Acropolis)

## June 23, 2012

### The shortest day of the year

Filed under: climate and weather,mathematics — ckrao @ 1:14 pm

June 21 was the shortest day of this year here in Melbourne, Australia and I saw on timeanddate.com that the length of the day was 9h 32m 31s. I was curious to see how close this was to the rough estimate that one can derive for the length of day on the winter solstice based on the calculation I give below. We make the following simplifying assumptions.

• The earth is spherical
• On the winter solstice for the southern hemisphere the sun is directly over the tropic of cancer (i.e. directly overhead there at some time during the day)

We use the figure below to visualise the situation at this time. Assume the sun is a long way to the right of screen. It shows the sun directly overhead at the tropic of cancer (C) and Melbourne at solar noon. The left half of the image experiences night. Imagine the earth rotating about the axis joining the north and south poles (NS). Melbourne will then rotate around this axis and in this image it will always be somewhere on the line passing through D and M. When it is at the point D it corresponds to dawn or dusk. Hence the length of its daylight will the time in which it is in the red region.

Note that the angle $\theta$ is equal to the earth’s angle of tilt, which is known to be approximately 23.5 degrees.

Below is another look at the red region from a different angle of perspective. In this figure below the line $DQD'$ corresponds to the single point $D$ in the figure above. Let $\alpha = \angle MPD$. Then the fraction of the day in daylight will be $\alpha/\pi$ where $\alpha$ is measured in radians.

Using the notation below, the daylight time will be $\alpha/\pi \times 24$ hours.

We use trigonometry to find $\alpha$. Firstly in triangle $OPM$,

$\displaystyle r = R \cos \phi \quad \quad (1),$

where $\phi$ represents the latitude of Melbourne (38 degrees).

Secondly $OP = R \sin \phi$. Hence

$\displaystyle PQ = OP \tan \theta = R \sin \phi \tan \theta. \quad \quad (2)$

Finally, in triangle $PDQ$, $\cos \alpha = PQ/r$ so combining this with (1) and (2) gives

$\displaystyle \cos \alpha = \frac{R \sin \phi \tan \theta}{ R \cos \phi} = \frac{\sin \phi \tan \theta}{\cos \phi}.$

Hence $\alpha = \arccos\left(\tan \phi \tan \theta\right)$ and for Melbourne the predicted length of daylight is

$\displaystyle \alpha/\pi \times 24 = \frac{24 \arccos\left(\tan 37.783^{\circ} \tan 23.438^{\circ}\right)}{\pi} \approx$ 9h 22m 54s.

This is about 10 minutes (1.8%) shorter than the actual time, the difference being due to effects such as the sun not being a point object, diffraction of light through the atmosphere and the approximations listed above. However the above calculation is a handy guide. A more precise calculation is shown here.

Incidentally, the shortest day here this year was curious temperature-wise as the graph below shows (data from the Australian Bureau of Meteorology).

The temperature hovered between 9.5°C and 9.9°C (at the half-hour sampling instances) between 6:30am and 7:30pm, with higher temperatures on either side! The maximum (after 9am) of 10.5°C was only reached at around 10pm.

## June 11, 2012

### Curious high or low temperature spots

Filed under: climate and weather,geography — ckrao @ 12:17 am

Here I provide a list of some places that go against our intuition about being surprisingly hot or cold at a certain time of the year given their latitude. Most of the places chosen are close enough to sea level so that elevation is not the cause (more likely ocean or continental influence).

1. The east coast of Australia up to Sydney and Newcastle has a mid summer average maximum temperature of only 25.5°C – highly unusual for the east coast of a continent. At a corresponding latitude (33° from equator) the mid summer maximum at the east coast of Asia (Shanghai at 31°N) is 31.8°C, of South America (Buenos Aires at 34.6°S) is 30.4°C and in North America (Charleston, NC, USA) is 32.8°C.
2. Walvis Bay, Namibia is in the tropics (23°S) yet has a mid summer average maximum temperature of only 22°C! Western South America is similarly cool with a mid summer average maximum of 25°C (Antofagasta, Chile). The corresponding west coast place in Australia has an average maximum of 32.4°C (Carnarvon at 25°S), in Africa 27°C (Dakhla, Western Sahara at 23.7°N), and in North America 32.4°C (Mazatlán, Mexico).
3. Eureka, CA (USA) at 40.8°N has an average maximum of only 17.7°C in its warmest month. Contrast this with Fairbanks, Alaska at 65°N which still reaches an average 23°C in its warmest month with an all-time high of 37°C!
4. Kyzyl, the capital of the Tuva republic in Russia, has an average maximum of 27°C in July and average minimum of -35°C in January! London is at the same latitude.
5. Iceland and Ireland have very low variation between summer and winter temperatures due to ocean currents of the East Atlantic. Reykjavik, Iceland averages 2°C maximum in its coldest month up to 13°C in its warmest.
6. The Turpan depression in northwest China surely has the hottest summer temperatures for a place so far from the equator. For example Turpan at 43°N has an average maximum of 40°C in July! A similar hot spot is Ashgabat, Turkmenistan (38°N) with an average maximum of 38°C in July. It has the same distance from the equator as Melbourne, Australia which only has an average maximum of 26°C in mid summer.
7. Tromsø, Norway is at 69.7°N (hence beyond the arctic circle) yet in its coldest month its average temperature range is -6.5 to -2.2°C.
8. Some parts of southern China are surprisingly cool for their latitude in winter. For example Guilin in Guangxi province is at 25°N and only 150m in elevation, yet has a range of 5.4 to 11.5°C in January (cooler than Tromsø’s warmest month!)
9. Lima, Peru is coastal, only 12° south of the equator, yet has a maximum temperature range from 18.4° to 26.5°C from coolest to warmest months. Contrast this with Chennai, India which is also coastal and whose corresponding range is 29° to 38°C.
10. The Southern Ocean shows very little variation between summer and winter temperatures. For example Bird Island in South Georgia at 54°S ranges from an average minimum of -5.4°C in its coldest month to an average maximum of 5.6°C in its warmest month.

Below is a map of showing all the places mentioned in this post.

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