Wherein a method is described for extracting some interesting data from your local daily sun appearance - or disappearance.

Background

Having moved in 1997 to a place where I could enjoy the sunrise with my coffee, I began to note the time and place the sun rose.  At our previous home we could see the sun setting.  The south most spot (winter solstice) was the southern support of the Golden Gate Bridge, and the northern most was to the north of Mt. Tamalpais, in Marin County.  I was not always in place to catch the sunset, but waking up before the sunrise is my normal operating mode.

I knew that plotting the points of the sunrises thru the year should yield a sine wave, with the high and low points being at the solstices.  What didn't occur to me for some time was that your local, personal sunrise time would vary with objects on your horizon.  And, sure enough, I found that sunrise/sunset charts are calculated only by the flat-earth longitude and latitude values for any given location.

Given the two concepts: the difference between actual and theoretical sunrise times and that the sunrise point is different each day, I figured that I should be able to get a plot which would be representative of my horizon within the sweep of the sun's path as the seasons passed.

Data Sources

Next I downloaded the data from the U.S. Naval Observatory Astronomical Applications Department.  On that page I clicked on Table of Sunrise/Sunset, Moonrise/Moonset, or Twilight Times for an Entire Year and filled in the form for my area.  Pulling the files I found there into Microsoft Word, I first fixed the bottom of the columns, where there was a problem with spacing due to shorter months.  Next I used the "Alt" key to select and copy the columns for each month into MS Excel.  I added a column for day of the year and filled that with the series function.  Now I could plot the data and see that there was also a sine wave representing the change in sunrise times.  There was a problem in this plot, however:  the data was given as "658" for 6:58 A.M.  Of course when the time got to 659, the next number is 700 for a 40 unit jump in the curve.

But for my purposes I simply entered the actual sunrise time and subtracted the USNO values so the offset was not a factor.  If you are in a fairly flat area you may get negative numbers as a result of your subtractions.  These will plot equally well, but if this is bothersome simply add or subtract a constant from either your data or the USNO data.  [Please note the footnote on the USNO page: "Add one hour for daylight time, if and when in use."  Don't worry, once you get going on this you will adjust automatically to the time you put on the paper, what will be difficult will be getting up earlier in the morning to catch the sunrise!]

I wasn't looking for this in the first two years of data collection so the plot wasn't highly accurate, but I did, indeed, get two high points which represented Mt. Diablo (the highest point on my horizon) and another hill nearby. 

More refinement came when I did a proper interpolation of the USNO times.   When the changes are fastest the change in sunrise time is one minute per day.   So from day 267 (Sept 23) thru day 337 (Dec 2) - and equivalent period in spring - there is at least one full minute change.  But up to and after that period there is a "rollover" about every few days, where you'll see the chart giving the same sunrise time for two days.   That means that the change was not one minute per day, but something less and even that amount is constantly changing as a sine function.

So, if you want to try this plotting adventure and if you want a better representation of your horizon, you'll need to take this "discrepancy" into account.  I took short periods (~20 days) and plotted the changes in MS Excel and printed them out.  On these I drew a straight line between the end points and took the values for each day from that line.

Added 10/18/00: here is a better curve, based on using the techniques described above.  The resolution has improved greatly and the match to the photos is much closer.  The circle with "apparent inconsistency" may be due to trees on the hill making it appear bigger in the picture, where the sunrise time was based on the appearance of the sun thru the trees.

Things come into focus

Added 2/25/01. It is early in 2001 and I have begun to set up my data collection pages again.  I had been bothered by the fact that there was a strangeness about the curve linked above.  The curve matches the two mountains OK, but the line on the left goes right up the summer solstice point (a round-looking tree above the "s" of the hand-written "Minutes of delay") and keeps right on a-goin'.  It finally struck me that the original data I was looking for (the sine wave of the sun's apparent rise points along the horizon) was missing from the data and that my curve was off by that factor.

So I collected 2001 sunrise/sunset data for Walnut Creek, California from the USNO, as above, but this time I did a right proper job which yielded a good working set of data to fix everything. Well, almost!  You can download my sunrise file (for .csv) or sunset file (for .csv) if you want an example.   As a matter of fact, if you live not too far north or south of my parallel (38 degrees north) you can use my very data and merely add or subtract enough time to keep your data around your local horizon. Note "xx.csv" files are comma-separated variable files that can be read into other data bases.

Here is what my Excel file looks like:

Explanation: Day is the day of the week; Min is the minutes after the hour; Conv is the conversion to decimal; Sunrise is the 2-decimal point rounded resultant; Run Avg is a - and + 2 day average (replaces ruler work above); Position is the calculated amount above the "zero" of the winter solstice; Actual s/r is the observed sunrise and Difference will be the actual plotable (Y-axis) data.

Calculations:

Date and Day - I used the fill function in Excel.  You can use my 2001(rise/set) data.xls files and save some work. 

Min - using the alt-highlighting function of MS Word as above I selected only the minutes portion of the columns, then pasted them into MS Excel.

Conv - I applied the formula =SUM(7+(C2/60)) - C2 is column C row 2 in the Excel worksheet and 7 (or 17 for setting chart data) is the hour which must be added back in.  To copy a formula to another cell (or bunch of cells) merely select the cell with the formula and use either the control C to copy or right click with your mouse and select "copy" from the menu.  Next select the area you want to copy to - in this case I highlighted the D column down to row 46, Feb. 14 - and paste.  The cell numbers will be adjusted automatically.  Next I went to Feb. 14 and modified the formula to 6+ instead of 7+.  I continued the copy/modify until June, where the earth reverses its oscillation.  In this process I also got rid of the problem I had last year of the offset where 59 minutes jumped to 0 when the next hour came up.  For your chart you will need to do this same routine for what ever day the time rolls over to the next hour.

Sunrise (or set) - the actual flat-earth decimal time that the sun would rise in my area if I weren't looking at hills and mountains while sipping on my morning coffee.  I used: =TRUNC(D2,2) to round the decimal time to only two digits.

Run Avg - I used the formula =AVERAGEA(E7:E11), but I didn't apply it until 1/9 because all of the times up to that point were the same.  For your area you should start the averaging two days before the first change in time after the winter solstice.   This will vary considerably with your latitude: at the equator you will already find daily changes on Jan. 1, and will have to get a couple of days from the previous year, or graph the data, or change the formula, or just ballpark it.

Position - this will be your X axis.  The actual starting number here is not important.  I used =SUM(-1*(E28-7.4)) because I don't want my X axis to have negative numbers.  The main point is that this will give you the actual horizontal displacement of the sun between the two solstices.

Recording your observation time.  OK, you have all of these weird conversions done so that you can get really quite a nice representation of your horizon without surveyors' tools, cameras, etc.  You don't even  need a computer.  With this article you could take a pad to the library and collect the required sun times and convert as it is convenient for you, and daily plot the results on graph paper as I did above. Another trick is to get the next day's info from your newspaper.  I only thought of this belatedly because I don't take a newspaper.  :-)

But, if you do use MS Excel and have all of these very accurate manipulations of data performed, you will find that your clock time does not have decimal seconds either,  which - of course - you knew all along!  So you can either record the real time on your sheets and then enter the data using a pre-formatted cell that will convert the minutes and seconds for you, or use the handy chart which I just made up and have included here (.csv) for your use.  Simply write down the time, look at the chart, change the second value and put it in your log.  By the way, this is a "universal" converter: it will work on any hour, anywhere. An easier way might be to just look over in the Min and Conv columns on the data sheets and find the seconds you want from the minutes conversion. 

Not quite a sine wave.  Here I made another discovery which some kind reader might enlighten me about:  The sun-rise -set times make a sine-looking curve with a strange flat ramp on their rising slopes.   Subtracting the rise from the set times, however, yields a pretty nice sine wave, indicating that the change in the length of the day does result in a sine function.  Here is a chart (.csv) showing sunrise, sunset and the difference.

By the way:  I have never heard of this concept before.  I was thinking of calling the resulting curve The Jardine Horizon Curve, in honor of myself, of course (humble smile.)  However, if anyone out there has seen or heard of this concept elsewhere please let me know so that I can link to a site or quote a publication, give proper credit, etc.

Some precautions and techniques.

Do not look directly at the sun!  Yes, it is true that the rising or - especially - the setting sun's rays are travelling thru hundreds of miles of atmospheric haze and human-generated pollution.  It is also true that the adepts in certain philosophical teachings stare at the sun.  But why take a chance with your eyesight?

Two tricks to avoid looking directly at the sun:

• Use a piece of darkened glass or plastic as you would to look at a solar eclipse.   I have an old (1960) piece of Kodak Wratten Gelatin filter (# 89B.)  It is 3 inches square and, held at an angle, covers both of my eyes.
• Next, the times given by the USNO are the times that the sun's disk should just clear the horizon.  I don't know how they came upon this, but it certainly is not a convenient method for the hobbyist, for a few more reasons:

• More potential danger to your eyes!  It means sitting and watching for the detail of exactly when the bottom of the sun's disk is perfectly round.
• Lost time and tedious waiting.
• Unless you are close to the equator the sun rises at an angle, so it is constantly angling north or south as it rises.  You will have to select a point on the horizon just below the center of the bottom of the sun's disk.

The technique I have found that is quick, safer and easier is to simply watch the point where the sun should be rising.  Looking thru my filter I see the increasing glow take on a slight "twinkle" as the first of the sun's disk appears.  I look down at my watch, note the time on the chart and spot on my horizon sheet.  Then I move out of the sunlight to do any further work.

For sunsets you have the opposite problem, but I have found that once you know the general pattern you can be at your "station" within a minute of the actual last glitter, thereby avoiding a long stare while the disk sets.

Setting your watch.  There are several on-line methods of getting a really accurate time reference to set your watch.  I find it easiest to call the local phone number.  These time sources will vary slightly in absolute time, but all you should be interested in for purposes of this experiment is consistency.

More of a problem will come from the drift of your watch.  This is easily overcome by setting it as close as you can and then checking it in a week.  Divide the time difference between your standard and your watch by seven and you know the daily drift.   Now you can go back and correct those seven rise/set times.  In the future you can simply add or subtract your accumulating error, and reset your watch when it gets far enough out to make the calculations a chore instead of a hobby.

If your watch is digital and drifting much more than a second per day you might try either a new battery or wearing it.  Sound silly?  I don't wear a watch.  I stopped "watching" a couple of years ago.  So my cheapie digital hangs in the binder where I log my results.  It gains about a second per day.

As far as this rather detailed attention to the time goes, I got my initial results by simply turning around and looking at the time on the microwave clock.  I got great results.  Now I simply want to see more definition in the data so I am refining the techniques.

Plotting the horizon.  At first I just made a sketch and marked the points.  After two years it got kind of cluttered.  I also was fretting how I could put some reference numbers on the sketch.  I even devised a rifle-like mechanism made of my backpacker's compass and a rather long stick with a 3x5 card on the other end.  I was going to move the stick around the horizon, marking the degrees on my sketch.  Fortunately I never got to it.  The resolution would have been pretty poor.

Instead I took a couple of the several photos of our morning view, taped them together and then did a blowup in a copy machine to 11 x 17.  Then I marked it off in tenths of inches - furlongs don't have enough resolution for this application!  How linear will this be?  I'll find out at the vernal equinox when I have the first quarter of the sine wave to plot.  Well, if I had all of the answers I wouldn't need to experiment!

Missed days.  I missed a lot of days when I was still working at UC Berkeley.  I had to leave at the same clock time and the earth-sun interaction is relentless.  Now I work at home and can indulge in these weird experiments.  But you can still pick up data on weekends, days off, etc.  You could even plan your vacation to get a couple of missed points!  You could also relax and just collect what you can.  There is always next year when Thursday and Friday are Friday and Saturday.  In five or six years your curve is complete!

Weather will interfere a bit, but not as much as you might think.  Just recall how many rainy days begin or end with a bit of sunshine.  The sun is peeping under the edge of the cloud cover, many miles away, when it is close to the horizon.   I also get fog in the valley between me and Mt. Diablo on some mornings.  It's great because it dampens the noise from the freeway in the valley, but at times the tendrils will work their way north and right into the area of the sunrise.  But I sit and finish my coffee and wait and - most times - there will still be the glitter of first light penetrating the thin wisps of fog.

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Last update: May, 2008 . Comments or questions?