TAC 39 Index
"SOME FOLK," said the Ed to me, the other day, "swear blind that they have seen the mountains of Norway from the Cairngorms." And then, being the man he is, he added reflectively, "Or maybe 'swear 20:20 vision' would be more appropriate."
At this point I made a sort of strangled snorting noise, compounded of appreciation for the editorial bon mot and disdain for the folk who might have made such a lunatic claim.
But the thought lingered, and soon the urge to do a bit of pointless spherical trigonometry proved too strong for flesh and blood to withstand. (Although I accept that my flesh and blood may well differ from yours in this respect.)
There's an easy bit and a hard bit to the "Can I see it from here?" question. The easy bit is: "Is it above the horizon?" The hard bit is: "Does anything closer stick up in front of it?"
People have been thinking about this stuff for a while. On the topic of the easy bit, James Parker (Munroist number three) produced an article and a gorgeous fold-out diagram for the SMC Journal of 1935(1). And in 1956 Guy Barlow demonstrated why the hard bit is so hard - he reported on what must have been weeks of his life spent superimposing contour profiles of Glen Shiel and the Cuillin, trying to work out whether Sgurr na Banachdich could be seen from Cairn Toul(2).
Reading Barlow's article, and looking at his laboriously produced hand-drawn diagrams, makes me appreciate the advent of the pocket calculator and computer graphics. These days, Jonathan de Ferranti in Newburgh is producing computer-generated Viewfinder panoramas based on Ordnance Survey digital contour data - sixteen quid buys you a custom viewfinder for any spot you care to name(3). Amazing.
But what about Norway?
Well, let's take the Cairngorm viewpoint to be Cairn Gorm itself (1245m, 57.12║N 3.64║W). The only Norwegian mountains that seem even a remote possibility are the Jotunheim, which include Norway's highest mountain, Galdh°piggen (2469m, 61.62║N 8.28║E). These two peaks are separated by a daunting 839km.
A little na´ve horizon calculation, based on a spherical Earth of radius 6378km, gives Cairn Gorm a sea-level horizon of 130km, and Galdh°piggen 182km. The two are 527km short of being intervisible, even if nothing else gets in the way!
Hmm. But what about atmospheric refraction? Because the air is denser at the Earth's surface, light rays tend to curve downwards. Effectively, you can see over the geometrical horizon. But by how much?
Well, astronomers will tell you that light rays from stars on the horizon are refracted by an average of 0.6║. Doesn't seem like much, does it? But it means that when the Sun's disk appears to touch the horizon at sunset, the Sun has actually, in pure geometric terms, already set. It's only visible because of atmospheric refraction.
So refraction seems worth a look. Parker and Barlow, in their SMC articles, give figures for average light-ray curvature at Scottish latitudes, and suggest a cunning way of simulating refraction effects. Refraction makes the Earth look bigger. Because we can see over the "real" horizon, we treat the Earth as if it is a bit bigger than it really is, so that the calculated horizon matches what we can actually see. The jigger factor suggest by Barlow is a 20% increase in the Earth's radius, taking it up to 7654km. This increases the effective sea-level horizon for Cairn Gorm to 143km, and for Galdh°piggen to 199km - but still leaves us with a deficit of 497km.
Is all hope lost? Not quite. Notice that atmospheric refraction is always quoted as an average value. The atmosphere being the unpredictable thing it is, there are occasions when unusual refraction can occur. The condition we want is called a superior mirage, which appears when there is a steeper-than-usual density gradient in the atmosphere. It can make distant objects look vertically distorted or levitated into the air, and can even bring things into view that usually lie over the horizon.
At its best, the superior mirage can work some marvellous effects - like the fata morgana, in which some distant object is smeared vertically until it resembles the towers and battlements of a mediaeval castle, with bits of detached landscape fluttering in and out of sight here and there, like flags and banners. Given that the whole lot appears to float magically in the air, and tends to vanish unexpectedly, it's no wonder that folk used to think they were catching a glimpse of a fairy citadel.
But hang on, we're dealing with reported sightings of Norway, not TÝr na n-Og. We want an undistorted view - the sort of thing that sailors call looming, when the sea surface seems to curve upwards and bring distant land into plain sight. It's rare though, because it requires uniform, stable atmospheric conditions over a wide area. Can we really believe that this sort of thing could happen over 500 kilometres of North Sea?
Well, the longest-distance, more-or-less undistorted, confirmed mirage I know of was seen from Grand Haven, Michigan. On April 26th 1977, city lights became visible to the west, out across Lake Michigan. One of the lights was red, and blinked on and off. Someone smart decided to phone a friend in Milwaukee, across the lake. The red flashes matched the frequency of the beacon in Milwaukee harbour, 120km from Grand Haven(4).
But mirages may travel farther than that. When Erik the Red discovered Greenland, he sailed directly from Iceland to the nearest point on the Greenland coast, around 300km away, along a bearing that was difficult to maintain, given the prevailing winds and currents. Perhaps Iceland was treated to rare views of something cold and mountainous, out there to the northwest - enough to give a Erik a hint as to where he should be going.
And in Arctic Novaya Zemlya, in 1596, an overwintering expedition claimed to have seen the Sun rise, briefly, two weeks ahead of schedule. If this happened at all, then it was probably a highly distorted image that had travelled for 400km in a "light duct" formed by a band of cold air sandwiched between two warm layers.
Someone once told me that ninety percent of all golden eagles are buzzards. In that case at least 99.99% of Norway must be clouds. But perhaps, under truly extraordinary conditions, Norwegian mountains may come into sight from Cairn Gorm. It's going to be impossible to be sure, but there are some observations that would make Norway more likely.
First of all, the bearing of Galdh°piggen from Cairn Gorm is 481/2░ true. Digging out my Viewfinder for Cairn Gorm, and making due allowance for the difference between grid and true north, I find that the Jotunheim should swim into view in the notch between Knock Hill and Corryhabbie Hill. (Knock Hill protrudes a mere seven minutes of arc above the sea-level horizon, so it's not demanding too much more of our already extraordinary mirage for Galdh°piggen to pop into view across its southern shoulder.)
Secondly, our angle of view should line up with the broad strath that separates Hestbrepiggane from Galdh°piggen. I've used the GTOPO30 database(5) to generate the above view of the Jotunheim from the appropriate direction: 239║ true. (Not the reciprocal bearing of 481/2░ - the angles of spherical triangles don't add up the way you think they should.) The vertical scale is a bit exaggerated: a) for clarity, b) because it looks nice, c) because mirages do that sort of thing. Galdh°piggen is in the centre, with the main mass of the Jotunheim trailing away to the right. Hestbrepiggane and Liabre protrude to the left of the deep valley. The whole view is about 80km across, which would subtend around 51/2░ when seen from Cairn Gorm - the width of three fingers at arm's length.
So - if you're on top of Cairn Gorm some day, and something that looks like my little picture shows up on the right bearing, then maybe you've seen Norway.
But don't hold your breath.
1) James A Parker: Curvature and Visibility. Scottish Mountaineering Club Journal, Vol.20, No.119, April 1935, pp317-324.
2) Guy Barlow: On the possibility of seeing the Cuillin from the Cairngorms. Scottish Mountaineering Club Journal, Vol.26, No.147, May 1956, pp16-24. (Thanks are due here to Dave Hewitt, for finding these two pieces, and to Ken Crocket, for letting Dave borrow the relevant bound volumes long enough to make photocopies for me.)
3) Jonathan de Ferranti, Lochmill Farm, Newburgh, Fife, KY14 6EX.
4) This, and other mirage stories, from Robert Greenler: Rainbows, Halos and Glories. Cambridge University Press 1980.
5) Visit http://edcwww.cr.usgs.gov/landdaac/gtopo30/gtopo30.html The USGS used to distribute this database for free - five CD ROMs containing elevation data at one kilometre resolution for the whole land surface of the Earth. Nowadays it'll cost you $10 per CD.
TAC 39 Index