there is NO seasonal temperature lag!

[Irv Bromberg]

Dear Calendarists:

I found a web site that posts daily average temperatures for many locations around the world:

http://www.engr.udayton.edu/weather/

... and used their data to make a 2-year plot for Toronto, attached as a small PDF (20 KB).

(Watch out, when there is missing data, they have an entry of -99 as the temperature for the missing date.  Also, their data is degrees Fahrenheit, I converted to Celcius.)

The astronomical equinoxes and solstices (from SOLEX) are indicated as vertical lines, at the appropriate position in terms of standard time in Toronto.

To my surprise, and in direct contradiction to Mike's assertions otherwise, in terms of daily average temperature, the actual data shows that there is no seasonal lag -- the chart clearly shows that the maximum average is reached around the time of the north solstice (red), temperature falls off slightly by the time of the southward equinox (brown), the coldest average is reached around the time of the south solstice (blue), and temperature starts to rise by the time of the northward equinox.  I checked a lot more years than are shown here (1995-2009 as provided by U Dayton) but the chart is too cramped when it includes the full range.  I assure you that the pattern is consistent in any of those years.

(Don't judge the plot in your email client, if it can show PDF images, open it in a PDF viewer application to see the full quality.)

I'm open to suggestions for a limited set of other locales to generate such a plot for.  I am thinking about making an Excel macro that could open any of the downloaded files from U Dayton, extract the data from the format that they use (fixed spacing, oddly enough), clear the cells that contain -99, convert to Celcius, and automatically change the chart title to appropriately match the file name (U Dayton uses the file name format XXcity.txt where XX is a two-character country code and city is the name of the location).  It would suffice to show the equinox and solstice moments in terms of constant UT moments.  It could have scrolling arrows to allow the plotted date range to be scrolled by the user, plot would update in a moment or two.  Then anybody could plot whatever locale they want and see what interesting findings emerge.  I could be persuaded to make the choice of degrees Fahrenheit or Celcius a user-controlled option.  It would be neat to try fitting an appropriate curve, it looks quasi-sinusoidal, although that is not a built-in feature of Excel, my macro would have to carry out the fit.  At this point, even though the PDF is only 20 KB, the Excel spreadsheet is 2/3 MB, because it contains all the raw data (has both degrees F and C, doesn't need both).

The point is that the public perception of seasons lagging for some few weeks after the equinoxes and solstices is not based on average temperature but on other perceived factors such as vegetation, blooming, fruiting, harvesting, precipitation, social activities (school vacations), etc.  On the other hand, maybe the daily maximum and the minimum temperatures (as opposed to highest averages) aren't reached until the middle of summer and middle of winter, respectively.  The U Dayton site doesn't offer that data, as far as I could see.  There are different definitions of the "average" temperature.  Is it the daytime only?  Is it part of the daytime only?  Is it the average of hourly temperatures or the average of the minimum and maximum within each day?  Ideally (perhaps) it would be based on continuously measured temperature integration for as long as Sun is above the horizon.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[Irv Bromberg]

On 2009 Jun 25, at 18:52 , Irv Bromberg wrote:

It would be neat to try fitting an appropriate curve, it looks quasi-sinusoidal, although that is not a built-in feature of Excel, my macro would have to carry out the fit.

Irv adds:  A simple alternative would be to have the macro do a symmetrical moving average.  Excel's moving average trendlines are forward only, so they always lag behind the data.  A symmetrical moving average has the benefit of knowing the past and future, so can make each point the average of n points before and after itself, for lag-free smoothing.  Perhaps the value of n could be a user-specified setting.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[Irv Bromberg]

On 2009 Jun 25, at 18:52 , Irv Bromberg wrote:

To my surprise, and in direct contradiction to Mike's assertions otherwise, in terms of daily average temperature, the actual data shows that there is no seasonal lag -- the chart clearly shows that the maximum average is reached around the time of the north solstice (red), temperature falls off slightly by the time of the southward equinox (brown), the coldest average is reached around the time of the south solstice (blue), and temperature starts to rise by the time of the northward equinox.

(Irv sheepishly adds, very red-faced...)

OK, I went back and fit a sine wave to all of the Toronto average temperature data 1995 to date.

The Sine( ) expression is:  Temperature = HalfSpan x SinDegrees( SolarLongitude - Lag) + AnnualAverage

The temperature swings ±15°C (HalfSpan=15), with the annual average at +8°C, and to obtain the best alignment of the sine wave peaks relative to the temperature peaks, I needed to include a lag of about 35 days = 5 weeks.  (This is pretending that each degree of solar longitude is one calendar day, which is close enough.)

The daily solar longitude was calculated for noon in Toronto.

Therefore if a 5-week month starts at a solstice, then the next month will on average start at the seasonal extreme.

Well, I'm off to the couch to eat my hat...

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[MIKE OSSIPOFF]

 
Irv said:
 
 
> To my surprise, and in direct contradiction to Mike's assertions otherwise, in terms of daily average temperature, the actual data shows that there is no seasonal lag
 
I reply:
 
That isn't only in direct contradiction to what I said. It's also in direct contradiction to everything I've found written on the subject. The U.S. government publishes a book of climate information for the U.S. I don't remember the title. Its figures are consistent with my claim of .75 month to 1.75 month being the usual range of variation of the seasonal timelag in the north and south temperate zones. In other words, the govt publication agrees with the Timesbooks publication.
 
In the Timesbooks tables, I looked at daily maximum and daily minimum, averaged over each month. Their lags were consistent with the about .75 month to 1.75 month usual range of seasonal timelag that I've described here.
 
As every source seems to agree, the land and the ocean have heat capacity. It takes time to heat and cool them. As a result, when the sun's declination changes, temperatures tend to lag behind those changes.
 
No, not always. At the equator, probably due to cloudiness, I didn't notice a consistent relation. In the tropics away from the equator, in the high-declination season for a particular tropical place, the .75 to 1.75 relation likewise wasn't evident to me. I noticed that, in many places in temperate South America there does seem to be little or no seasonal timelag. Of course that's possible--the timing of cloudiness could do that.
 
But, in general, in the temperate zones, all the record books that I've looked at show a lag that nearly always varies between about .75 months and 1.75 months.
 
Mike Ossipoff
 
 
 
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[Irv Bromberg]

On 2009 Jun 29, at 11:49 , MIKE OSSIPOFF wrote:

But, in general, in the temperate zones, all the record books that I've looked at show a lag that nearly always varies between about .75 months and 1.75 months.

Irv replies:  Mike responded to an earlier message that I subsequently corrected (where the subject heading ends with "Oh YES there is").

Since posting that correction, I have repeated the analysis using solar declination instead of solar longitude.

For Toronto, a 35-day lag yielded a good sine-wave fit to the average daily temperature.

For the purposes of such a chart, the difference between solar longitude and solar declination with respect to the timing of the equinoxes and solstices is negligible.

It was easier to do the sine-wave fit to the solar longitude because it so happens that the solar longitude increases by almost one degree per day.

Yesterday I spoke to an experienced meteorologist from Montreal, who happens to have done his PhD on this subject.  His thesis included expressions for variation of the seasonal average temperature with latitude and longitude and elevation.  He says that in Montreal the typical lag was 30 days -- that city is further north than Toronto, closer to the Atlantic, and adjacent to the semi-salty St. Lawrence Seaway (Toronto is on the north shore of Lake Ontario, but that is fresh water).  He also pointed out that the seasonal "blips" where warm weather happens just before the coldest days, and where cool weather happens just before the hottest days, are calendrically amazingly reproducible.

I could look at some other cities in my plot and sine-wave fit, but so far nobody has suggested a city to try -- Mike, how about your city, where do you live?

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[MIKE OSSIPOFF]

 
Irv--
 
You wrote:
 
> I could look at some other cities in my plot and sine-wave fit, but so far nobody has suggested a city to try -- Mike, how about your city, where do you live?
 
Do Santa Cruz, California.
 
I've lived most of my life in Santa Cruz, California. That's where I used daily records to measure a 38-day lag of midwinter behind the winter solstice, when I defined midwinter as a winter day that has equal summed temperatures for the 2 months before and after it.
 
Mike Ossipoff

 
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[Irv Bromberg]

On 2009 Jun 29, at 12:58 , MIKE OSSIPOFF wrote:

Irv wrote:  I could look at some other cities in my plot and sine-wave fit, but so far nobody has suggested a city to try -- Mike, how about your city, where do you live?

Do Santa Cruz, California.

I've lived most of my life in Santa Cruz, California. That's where I used daily records to measure a 38-day lag of midwinter behind the winter solstice, when I defined midwinter as a winter day that has equal summed temperatures for the 2 months before and after it.

Irv replies:  Well, Santa Cruz is not in the U Dayton list, although nearby San Francisco is, so I'll run that city, hope that's OK.  The U Dayton list of US cities is at:

http://www.engr.udayton.edu/weather/citylistUS.htm

Hmm, it's a west coast locale with prevailing westerlies, some variations with ocean current directions, approximately 37+3/4 degrees north...

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[Brillig]

Weatherunderground usually has graphs available for US cities. Here is
the graph for Santa Cruz.

http://www.wunderground.com/NORMS/DisplayNORMS.asp?AirportCode=KWVI&SafeCityName=Santa_Cruz&StateCode=CA&Units=none&IATA=SJC

and here's the one for San Francisco.

http://www.wunderground.com/NORMS/DisplayNORMS.asp?AirportCode=KSFO&SafeCityName=San_Francisco&StateCode=CA&Units=none&IATA=SFO

The SF one is smoother, so I assume it averages more years. I do note
that the high for the year is in September for San Francisco.

No doubt the Pacific ocean and wind currents play a major role in SF
weather patterns.

Victor

On Mon, Jun 29, 2009 at 5:20 PM, Irv Bromberg<irv.bromberg@...> wrote:

> On 2009 Jun 29, at 12:58 , MIKE OSSIPOFF wrote:
>
> Irv wrote:  I could look at some other cities in my plot and sine-wave fit,
> but so far nobody has suggested a city to try -- Mike, how about your city,
> where do you live?
>
> Do Santa Cruz, California.
>
> I've lived most of my life in Santa Cruz, California. That's where I used
> daily records to measure a 38-day lag of midwinter behind the winter
> solstice, when I defined midwinter as a winter day that has equal summed
> temperatures for the 2 months before and after it.
>
> Irv replies:  Well, Santa Cruz is not in the U Dayton list, although nearby
> San Francisco is, so I'll run that city, hope that's OK.  The U Dayton list
> of US cities is at:
> http://www.engr.udayton.edu/weather/citylistUS.htm
> Hmm, it's a west coast locale with prevailing westerlies, some variations
> with ocean current directions, approximately 37+3/4 degrees north...
>
> -- Irv Bromberg, Toronto, Canada
> <http://www.sym454.org/>
>

[MIKE OSSIPOFF]

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Victor wrote:
 
> No doubt the Pacific ocean and wind currents play a major role in SF
> weather patterns.

San Francisco has heavy summer fog and stratus, with its direct unsheltered exposure to the prevailing wind off the ocean, and with the Sacramento Valley convection "fog machine", which probably cools what would otherwise be the warmest part of the year.
 
Mark Twain said that the coldest winter he ever spent was a summer in San Francisco.
 
Mike Ossipoff
 
 

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