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Agreed, for the sunbeam element D units wide that strikes the earth's surface at near grazing incidence close to sunrise, at angle A° (say 1°), illuminating a corresponding surface area element S, the relative insolation D/S = sin A. The angle of incidence is usually defined, though, as the angle made relative to a radial line, therefore normal to the surface. Incident angle then would be (90-1)°, thereafter falling to 0°, if the sun were later to reach the zenith.
The dawn sunbeam is (almost) a tangent that is (90-A°) to the normal to the surface, so the angle of incidence as usually defined at that time would be (90-1) = 89°. So if you define the angle as usual as that made relative to the radius, not to the tangent line, it's cos(90-A°) = D/S = sin(A°). It's a cosine relationship if the incident angle is defined conventionally.
This ignores a large effect which is the absorbing and scattering effect of the thickness of the atmosphere, very large at the ends of the day and minimal at noon.
On an earlier question relating to the odd colour of a drake mallard's neck, someone asked what the effect of the seasons on light colour might be. The main effect on relative skylight composition is not seasonal, but is whether the sun happens to be contributing to the incident light, or whether illumination is solely from skylight, because of cloud cover or of occluding obstacles like mountains. It is discussed in terms of the effective 'equivalent colour temperature' ECT of the sky. With the sun in evidence, the ECT is usually below 5000K and more reddish, but without it, in northern latitudes, it can exceed 20,000K with a more steely blue cast, and a more even proportion of UV to Blue. As Planck first analyzed, when a perfectly black object is heated up, it radiates a well-defined, broad light/heat spectrum with a distribution that depends upon its absolute (K) temperature, peaking dull red to blue-white from hot to very hot. Skylight has extra glitches and doesn't exactly copy black body radiation, but colour specialists have made an equivalent scale (ECT), partly to allow creation of standard lighting conditions. This is important, for instance for matching cloth colour batches in the textile industry.
I checked the bible for this, 'Colour Science' (1972, 2nd ed) by G. Wyszecki (a Canadian) & W.S. Stiles, and they mention in passing that there may be minor variations throughout the season, but it doesn't sound that they think these are important. Speculating, presumably the reason is that contaminants in the atmosphere are generally more or less colour neutral in the visible, so act like grey 'neutral' filters, affecting intensity (irradiance) of course, but not much the spectral distribution. Particles from forest fires and volcanic emissions might provide partial exceptions, and water vapour is important in the infrared.
Steve
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of Hebda, Andrew J [Andrew.Hebda@novascotia.ca]
Sent: Sunday, February 28, 2016 10:54 PM
To: naturens@chebucto.ns.ca
Subject: RE: [NatureNS] Fw: Reconsideration; ground frost
David
I think I am missing something here.
I can see the relationship with the sine of the angle of incidence.. but until light strikes the surface, the effective angle of incidence is zero (as it is during the dark period), so am no sure how it can approach zero if it is there already.... or have I missed something fundamental here?
Andrew
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From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of David & Alison Webster [dwebster@glinx.com]
Sent: February-28-16 8:59 AM
To: NatureNS@chebucto.ns.ca
Subject: [NatureNS] Fw: Reconsideration; ground frost
Dear All, Feb 28, 2016
I overlooked another aspect to the question of frost shortly after sunrise; effective interception of solar radiation. This would apply to some extent year round in all terrain and locations given calm clear weather. On a global scale, the area of sunlight intercepted by the earth is a disk equal to the cross-sectional area of the globe. A portion of a recent private e-mail on this aspect is pasted below.
START OF PASTE\\\\\\\\\\\\
As one approaches the edge of this disk (sunrise) the effective area of insolation realtive to the area of earth insolated (the interception of radiation per unit area) approaches zero. Maximum insolation will be when the sun is directly overhead. Elsewhere the incoming radiation per unit area will be proportional to the sin of the angle of incidence.
An object will continue to cool until incoming radiation exceeds
outgoing radiation.
Sometimes it take a while to notice the obvious.
END OF PASTE
Yt, Dave Webster, Kentville
----- Original Message -----
From: David & Alison Webster<mailto:dwebster@glinx.com>
To: NatureNS@chebucto.ns.ca<mailto:NatureNS@chebucto.ns.ca>
Sent: Tuesday, October 13, 2015 7:15 AM
Subject: Reconsideration; ground frost
Hi Paul, Andrew & All Oct 13, 2015
This didn't get posted the first time; perhaps because it had become too large so I have pasted the original with several earlier exchanges clipped.
START OF PASTE\\\\\\\\\\
Hi Paul, Andrew & All, Oct 11, 2015
Having thought this over again, I suspect I overlooked the key factor which bears on both the value of air movement and the timing of greatest risk.
All bodies will radiate heat at rates (as I recall) which depend only on their temperature and at temperatures under consideration there will always be some heat lost by out radiation. Consequently thin or small organs (with consequently low heat content), such as leaves and flowers will continue to cool relatively rapidly by out radiation, and cool the adjacent air by conduction unless this heat loss is offset by heat gain. One possible way to replenish this heat loss, on a cloudless night, is in radiation from haze or nearby warm objects. But I suspect that air flow, provided the air is warmer than the sheath of cold air in the vicinity of the leaf or flower, is far more effective in general. Thus the value of air flow down a slope, wind machines and low aircraft.
Probably for much of NS the concepts of land breeze and sea breeze apply: land breeze at night, when land is cooling off faster than the sea, and sea breeze in the dayti