### Tuesday Aug 11, 2009 at 23:23

# Using TPE, Part 3: Geodesy

Here’s the third in a series of tutorials on The Photographer’s Ephemeris.

We covered the basics of using the program in Part 1. In Part 2, we covered the Twilight information and the Details View (most of it at least). You’ll need to have understood the material in those tutorials before tackling this one.

This tutorial is based on Beta 0.9.6. Click on any screenshot for a full-size expanded view.

## Geodesy?

Geodesy? Geodetics? What’s that all about? I’ll admit that until I started really getting into writing TPE, I didn’t have a clue. However, it turns out that there are whole class of questions a landscape photographer might legitimately ask that can only be answered accurately by use of the science of geodesy.

I’ll leave it to Wikipedia to explain the details, but in essence, geodesy deals with the measurement and mathematical representation of the earth.

The earth is round. Sort of. In fact, it’s sufficiently not round that measuring point-to-point distances on the surface of the earth is only poorly approximated by assuming a sphere. You wouldn’t want your airline pilot navigating this way.

An ellipsoid is a much better assumption to make, but the maths gets hard. So hard, in fact, that a decent solution for calculating point-to-point distances between points on the surface of an ellipsoid was only devised in 1975 by Thaddeus Vincenty.

The Geodetics panel and the accompanying Secondary Map Marker included in v0.9.5 of TPE and later use Vincenty’s algorithms to enable some new functionality that will help you plan shoots in greater detail.

## Our destination for this tutorial: the Macey Lakes

Colorado’s Sangre de Cristo Wilderness contains some of the most spectacular peaks in the whole of the Rockies. There are around 18 drainages within the wilderness boundaries, many with stunning alpine lakes surrounded by jagged mountainous cirques.

1. Type ‘Macey Lakes’ into the search box, and press Enter
2. The primary map marker in red will (should) be positioned over the Macey Lakes in Colorado, USA
3. For the purposes of this tutorial, set your date to July 5th 2009

We’re zoomed out a bit too far as is, so let’s fix that:

1. Drag and drop the primary marker to the north east of the lower lake, as shown
2. Zoom in around 3 clicks or so (you may prefer to zoom in before dragging the marker – do whatever works for you)
3. Click the Details button to show the details view for July 5th
4. Notice that we now have a Secondary Map Marker in light grey

Using that secondary marker is what this tutorial is all about.

A few things about it:

- It’s optional – you don’t have to use at all if you don’t want to
- By default, it will always appear to eastern side of the map
- If you don’t drag and drop it, it stays light grey
- Moving it won’t (by default – check back for the next tutorial) change your sun/moon rise/set/phase or twilight times

However, we won’t learn much by leaving it alone, so let’s see what useful information this could provide us.

### When will I lose direct sunlight on Lower Macey Lake?

Looking at the map, you can see that the sun will set to the north west at this time of year. It’s also easy to make out the high ridge-line in the same direction, with the summit of Little Baldy Mountain clearly marked. Just eyeballing the contour lines, it seems likely that the sun will disappear behind the ridge well before it actually sets below the true horizon. But when?

We can use the secondary marker to find out.

1. Start by dragging and dropping the secondary marker on the summit of Little Baldy. You’ll notice that when you do, the colour changes to a darker grey, indicating that you have activated the geodetics information
2. In the Geodetics panel, you’ll now see three numbers displayed. The most significant for our purposes is the apparent altitude of 18.5°

What do they tell us? Firstly, notice the icon to the left. It shows an arrow from primary to secondary marker. This indicates that all the data displayed in the panel is referenced in terms of travel from the primary location to the secondary. Let’s look at the three data items in reverse order from the bottom up:

- Distance and bearing: distance is the point-to-point as-the-crow-flies distance from primary to secondary marker; bearing is the map bearing from primary to secondary in degrees (note: this is map bearing, not compass bearing – the same comment applies to all azimuths and bearings in v0.9.6, although I will likely add a compass bearing option in a later version)
- Change in elevation: elevation refers to height above mean sea level. The change in elevation is measured from primary to secondary. In this case, it’s 1,391ft from the lower lake to the summit of Little Baldy
- Apparent altitude: the units of degrees give away that this is altitude in the astronomical sense. If you had a sextant and took a sighting to the peak, this is angle you would measure. ‘Apparent’ means that this measurement is adjusted for refraction, the bending of light caused by passage through the atmosphere.

(Note that the apparent altitude is not exactly what you’d get by dividing the elevation change by the distance and calculating the inverse tangent: the calculation accounts for the curvature of the earth’s surface and adjusts the result for refraction.)

OK, now we know what we’re looking at, let’s find out the altitude of the sun when it passes through the same bearing:

1. Use the time of day slider to drag forward to around 18:15.
2. You’ll see the azimuth line for the sun move around during the course of the day and line up with the grey line to the secondary marker. We already have learned something: the sun will pass through the line of the peak of Little Baldy at 18:16 on July 5th 2009. But will it be visible?
3. Looking at the sun’s altitude in the Details panel, you can see that it lies at 23.4° some 5° above the peak of Little Baldy

So, the sun should still be visible at 18:15. We need to look a little further:

1. Drag the time of day slider a little later in the day until the time is around 18:40. The sun is setting in the sky, so the altitude decreases to 18.8°
2. Drag the secondary marker a little farther to the north-east along the ridge line to match the azimuth line to the setting sun.
3. Note that the apparent altitude to the ridge line is now 18.8°

With a little trial-and-error, you can establish that the sun is likely to drop out of sight around 18:40, some time before actual sunset. You’ll need to apply some judgement here and look at the contours of the topological map (don’t try this in other map views) and see where the sensible test points should be. We’ll look at this in more detail below.

As an exercise, you may wish to try to determine how high on the north west flank of Colony Baldy will you observe direct light in the moments before sunset. Hint 1: you’ll need to relocate both markers. Hint 2: you may need to move the secondary marker farther than you think. Answers at the end.

### Will the rising sun strike Point 13,200’?

Let’s look at a different question. You want to make a sunrise image of Upper Macey Lake, and you’d like to take in the cirque to the south of the lake. However, the image will likely only work if the tops of the cirque catch the rising sun. You can use TPE to determine if the rising sun will be obstructed or not:

1. Use the skip backward button to move the timeline back to the moment of sunrise, 05:47
2. Move the primary marker to the top of the peak near the contour label 13,200’ on the map. Next, move the secondary marker to the first ridge line to east north east as shown
3. Notice the apparent altitude and change of elevation figures

So far, so good: the first ridge line lies below our peak by some margin, so we should get some direct light. However, to be sure, let’s check to see if Colony Baldy, farther to the east will cause us any problems:

1. Move the secondary marker out towards the direction of sunrise and drop it on the high point of the flank of Colony Baldy
2. Note the apparent altitude: it is still negative, indicating that the sun will clear Colony Baldy and strike our peaks

Good news. We should be able to make the shot. We can already see from the basic sun rise line that we should get good light over the lake itself at the moment of sunrise. Now that we know our rugged mountain ridge will also receive some direct light, we can hope for a good shot:

Upper Macey Lake

## Can we really see the ridge line?

Let’s look once more at the ridge line visibility question. This time, let’s say we want to determine the angle of view to the ridge line to the west of the upper lake:

1. Move the secondary marker to the ridge line west south west of Upper Macey Lake, opposite where the sun will rise (you’ll need to reposition the primary marker too)
2. The apparent altitude is 23.5°

OK. But this is where some trial and error and map reading skills come in.

1. Move the secondary marker down the slope a little to where the contours appear a little steeper
2. Note the increased apparent altitude – it’s now some 3 degrees greater

It might be that we’ll be looking at a false summit from our position on the lake shore. Probably won’t impact our images significantly in this case, but it’s important to be on the look out for these details in some situations.

## Why can’t the computer just work all this out for me?

Reasonable question. The main reason is that the computer would have to check out elevation data at every point along the path to the sun or moon and infer what was significant for your image and what was not. There are certainly some possibilities for taking this approach, but for now, I’ve opted for the simpler manually placed marker. That approach avoids too much second guessing by the program, avoids me having to pull too much elevation data and covers all scenarios, albeit potentially with more trial and error on occasions.

## Gotchas

The Geodetics calculation can determine distance and bearing quite happily just from the map marker positions (which we always know by definition – you placed the markers). However, to do anything more, we need to know the elevation above sea level for both marker positions. Some potential gotchas:

- The program may be unable to obtain an elevation for extreme latitudes (the Shuttle Radar Topography Mission only covered latitudes from around 60°N to 56°S)
- Sometimes, there is no data available for very steep terrain, as you might find in mountainous areas (for example, try the summit of Longs Peak, Colorado – no data, even though it’s a famous local fourteener)
- The elevation data points are spaced every 90 metres (3 arc-seconds), so relying on this for high precision, short distance work is not recommended

That said, for most landscape uses, this will work well. However, if you have a shot that requires critical planning, I highly recommend that you

- Consult multiple reliable sources for sun/moon information (I highly recommend Jeff Conrad’s Sun/Moon Calculator)
- Obtain a large-scale topographical map of the area from a reputable publisher of your shoot and take careful measurements of distance and elevation
- Consult the online tools from the National Geodetic Survey and perform your own geodetic calculations
- Maintain your sanguine disposition when, even though the clouds cooperated, the sun or moon did not appear quite where or when your expected: even if all your preparation and calculation was perfect, the vagaries of atmospheric refraction may result in an unexpected outcome

## Answer to the exercise

I make it 13,350ft. The ridge line of Little Baldy isn’t the limiting factor – you need to look at the next ridge line farther north west which lies higher. Place the secondary marker there, and then adjust the primary marker up and down the north west flank of Colony Baldy until you obtain an apparent altitude of around zero. From that point upwards, you should see direct light from the setting sun. More or less.

The next tutorial will cover Elevation at the horizon. If you’re shooting in high places, this could be significant…

You might also enjoy “Understanding Light with The Photographer’s Ephemeris” co-authored with renowned landscape photographer Bruce Percy. It’s available through Bruce’s web-site

Posted in TPE

Stephen · Tuesday, August 11, 2009, 23:23 · Permalink

## 5 comments on this post

1

13:39 12 Sep 2010

ted leeming said:

Fantastic app. Downloading to my iphone now too.

As a matter of interest, are you thinking of adding a option where you can link to google maps sun feature so that from dawn til dusk on any given day you can plot shadows on hills. I can approximate to this and a mate has some software that can do this accurately but it is a business application and v expensive. to do this on your app and see what is and is not in sun in 3D would be AWESOME (even more).
thanks for a great tool, I’ll recommend it in my workshops.
best
ted

2

06:27 29 Sep 2010

Stephen said:

Hi Ted – would be possible to do this, but the amount of elevation data required to do it dynamically would be a lot more (likely would need to download in advance). When I retire from the day job I’ll probably take a look at doing this! Until then, Google Earth is there to help…

3

20:29 27 Nov 2010

Dewey said:

As a person who was an instrument man on a survey crew for ten years, and did more than my share of “ Sun Shots “ to estabish bearings, etc., I see something lacking in this program , and it’s H-U-G-E. Where is the compensation for Refraction due to the Earth’s atmosphere ? Which , by the way , is variable. We always had to take temeprature readings and presume altitude ASL to compute air density and allow for refraction for shots requiring precise ranging over distance. For instance, the disk of the rising Sun can actually be about 1.5 degrees BELOW the horizon point when you see it, if refraction has it’s way with you and bends the light path. That’s three full Sun diameters away from calculated. Not to mention the time offset.

Just curious. A friend of mine showed me this program. I personally could make good use of it , and used to do these sorts of calculations the long way …HP calculator and lots of time and paper. But I refuse to load Adobe AIR on my MACs till it gets much , MUCH more secure. It’s worse than Flash for security and hackability.

Great work . Keep it up nevertheless

4

20:37 27 Nov 2010

Stephen said:

Hi Dewey

Compensation for refraction is built in to all the calculations used in the program. The program uses variable correction for refraction based on elevation above sea level at the selected location. The US Standard Atmosphere model is used, in conjunction with Saemundsson’s values as described in Meeus book (see the About page for details).

So, other than being able to correct for actual atmospheric condition on the day, which as you point out can cause varying results, I think the program does cover the points you raise.

5

14:20 15 Dec 2011

Tim Zukas said:

“An ellipsoid is a much better assumption to make, but the maths gets hard. So hard, in fact, that a decent solution for calculating point-to-point distances between points on the surface of an ellipsoid was only devised in 1975 by Thaddeus Vincenty.”

Don’t think Vincenty would have claimed that his formulas were a huge improvement on Rainsford’s formulas from 1955. I’ve never looked at Helmert’s 1880 book (in German) but I gather everything you need is in there, just in a less convenient form. I’m guessing ellipsoid formulas that were plenty good enough for our purposes existed decades before that.

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