## Wednesday, March 6, 2013

### 60 degrees of Confusion.

There is a lot to consider in climate.  Internal heat transfer is the toughest since at the top of the atmosphere there is not much going on.  So while waiting this morning I though I would toss out a simple example of internal potential energy difference due to solar orbital variation.

Since the Earth is a sphere not a flat disc, you should allow for curvature when calculating surface irradiance.  At the nadir or the point on the Earth facing the center of the Sun, you could receive 100% of the energy emitted.  At 60 degrees, due to the angle of the surface relative to the Sun, that energy would be spread over an area twice as large.  Since the annual orbit of the Earth around the Sun is an ellipse, not purely circular, in winter the maximum energy is ~1410 Wm-2 and in summer it is ~1315 Wm-2.

At latitude 60S, since the Earth tilts ~23.5 degrees, the effective angle is closer to 45 degrees than the 60 degrees used to reference to Earths rotational axis.  Instead of 50%, 60S would receive closer to 70% of the maximum 1410 Wm-2 or 987 Wm-2.  At 60N, there is the same tilt impact but with the lower 1315 Wm-2 producing a maximum possible irradiance of 920 Wm-2.  The difference is ~67 Wm-2.  Since the length of day is longer in local summer, also due to our axial tilt, a smaller percentage of the globe would be able to gain more energy, think of it as pulse width modulation, adding a small but significant amount to the seasonal impact.

If you consider the range of peak values at the Equator, the maximum irradiant is 1293 in winter and minimum is 1205 in summer.  A difference of 87 Wm-2 between those seasons, but in spring and fall the maximum is roughly 1366 Wm-2 (it could be as low as 1360 Wm-2, so there is some uncertainty). That would produce a Southern Hemisphere imbalance wrt the Equator of roughly 70 to 67 Wm-2 and a Northern Hemisphere imbalance of roughly 155 to 161 Wm-2.

The axial tilt of the Earth is not fixed.  It drifts over a period of roughly 44 thousand years which would change the Equatorial imbalance by about 10 Wm-2.  Depending on what the actual absolute surface temperature is, that could produce a roughly a two degree C range of temperature.

The precession of the Equinoxes also changes in an irregular period averaging roughly 21,500 years.  The impact of that change requires considering surface albedo which would impact the percentage of solar energy absorbed and emitted, which can get complicated.  The point of this short post is that there is more than enough internal energy imbalance to offset a significant portion of a radiant impact dependent near isothermal or at least relatively stable conditions.  Speaking of which, Venus has the closest to a purely circular orbit with a day nearly equal to its year.  With no significant orbital or hemispherical imbalances, it has the conditions needed for a maximum radiant impact.  More on that later, right now I have to meet a man about a Tarpon.