Solar Angles, Aspects, and Topographic Shading

Motivated by the previous post, I thought we would dig a bit more deeply into solar angles, terrain aspects, and topographic shading, which are critical for understanding mountain meteorology and microclimates.

Although Fox News might argue differently, the Earth is round (technically it is an oblate spheroid), orbits the sun, and has a axis of rotation that is presently at about a 23.5˚ angle relative to its orbital plane.  Its orbit is not perfectly circular, but is slightly eccentric, so that the distance from the Sun to the Earth varies by about 3% (5 million kilometers) during the year.  All of these affect the path of the sun through sky and/or the amount of solar energy received by the Earth's surface.  Although nearly constant for the recent past or immediate future, slow variations in the orbital characteristics and angle of rotation have caused large variations in the Earth's climate, including cycles from ice age to interglacial periods (see this NASA article).

Because the Earth is nearly round, we use spherical geometry to deal with calculations related to sun angle.  Representing these spherical perspectives in two dimensions is challenging!

First, let's talk about how the sun's angle changes during the day and during the year.  The graphic below was developed for Atlantic City, New Jersey, but works reasonably well for Salt Lake because they are nearly the same latitude (subtract a degree for Salt Lake City - see addendum at end of this post discussing how the solar paths in this image should be parallel).  On January 1st, shortly after the winter solstice, the sun rises just south of east and sets just south of west, reaching a maximum elevation of 28 degrees relative to the horizon at solar noon.  As we move through the first part of the calendar year, sunrise and sunset shift northward and the maximum elevation angle increases.

Source: pressofatlanticcity.com

Ignore the shading in the image above, which is fixed.  In reality, shadows change during the day but also during the year.  At our latitude, your shadow is longer at solar noon in January than in June.

The amount of solar energy received by the Earth's surface depends on the location of the sun in the sky, the aspect of the terrain, the steepness of the terrain, and the surrounding topography.  At our latitude at solar noon on a clear day, a south aspect that is illuminated by the sun receives more solar radiation per unit area than a north aspect that is illuminated by the sun since the sunlight hits the north aspect more obliquely, as illustrated below.

Source: https://www.eoas.ubc.ca/courses/atsc113/snow/met_concepts/07-met_concepts/07h-aspect-effects/

At the extreme, if the sun angle is low or the terrain is steep, the north aspect might not receive any direct sunlight.  Ski High Rustler at Alta on noon on a clear day in late December and you know exactly what I mean.  It's in the shade.  In contrast, in April at noon, High Rustler receives direct sunlight.  At that time, however, the slopes across the canyon that face south receive far more solar energy per unit area than High Rustler.  This is true for most (but not all) of the day, which is the primary reason why south facing slopes at our latitude melt faster than north facing slopes.

Much depends, however, on latitude, time of day, time of year, and slope angle.  In Utah in June, just after sunrise and just before sunset, a north aspect actually receives more radiation per unit area than a south aspect.  There can be a brief period during which High Rustler receives more solar energy per unit area than the slopes on the other side of the canyon.  But integrated throughout the day, it receives less, regardless of time of year.

Elsewhere, your mileage may vary.  If you were on a mountain near the equator, the north slopes receive more energy per unit area than the south slopes in June, but less in December.

Aspect is great, but there is another concern and that is topographic shading.  Topography can cast shadows.  Extreme examples are created by high peaks, such as the triangular shadow cast by K2 pictured below.

Source: https://i.imgur.com/1mAzNUY.jpg?

 If one does not consider this effect, then a solar radiation calculation in the shadowed area would be incorrect.  Both aspect and topographic shading often need to be considered in areas of complex terrain.

With a little playing around, one can examine what sites are exposed to the sun or shadowed at caltopo.com.  Below is an example for upper Lake Blanche Fork in the central Wasatch at 3PM in December.  The drop-down menu at upper-right allows you to specify sun exposure, along with month and time of day.  I'm not sure if we're looking at a first of month or middle of month calculation, but for our purposes, two weeks or so is good enough.  I do think they are considering topographic shading.  For instance, you can see the shadow cast by Sundial Peak extends up the southwest facing aspect on the other side of the canyon to its northeast.

Let's test my comments about High Rustler above.  Top image below is the sun exposure at noon in January and the bottom is noon in April.  Bingo!  In fact, very little at Alta is in the shade at noon in April.

We tend to think about how all of this affects snow, but it also affect soil moisture and vegetation.  At our latitude, south aspects receive a great deal more solar energy than north aspects.  This leads to greater water stress on south aspects than north aspects and resulting contrasts in vegetation.  You'll notice these even when the snow is gone.

Addendum

Professor Phil Dennison of the University of Utah Geography Department pointed out to me that the solar paths in the top figure above for Atlantic City are angled and not parallel.  He provided the schematic below showing the solar paths over Salt Lake City on the solstices and the equinoxes (middle path) to illustrate the correct paths.

Courtesy Dr. Phil Dennison