James Hansen has a new paper (a draft for review), “Paleoclimate Implications for Human-Made Climate Change.” We’ll discuss it in a future post. There’s a so-called “review” by Martin Hertzberg at WUWT in which he claims that Hansen fails to understand the Milankovitch cycles. But it’s Hertzberg whose understanding is a failure.



Hertzberg quotes Hansen:



Earth orbital (Milankovic) parameters have favored a cooling trend for the past several thousand years, which should be expected to start in the Northern Hemisphere (NH). For example, Earth is now closest to the sun in January, which favors warm winters and cool summers in the Northern Hemisphere.



Then Hertzberg says:



Those statements are typical of the misunderstanding in the popular literature of the Milankovic cycles. Since we are now further from the sun in the NH summer, he argues that the NH should get less solar insolation in the NH summer thus “favoring the growth of glaciers and ice-caps in the NH”. So why then we may ask are we now in an Interglacial Warming? What Hansen fails to realize is that when we are further from the Sun in NH summer we move more slowly in orbit, and are therefore exposed to the summer sun for a longer period of time.



Sorry, Martin, Hansen is right and you’re wrong.

First let’s examine the issue of further-during-summer and longer-duration-summer.

The energy received from the sun at any moment is inversely proportional to the square of the distance from the sun

.

The total energy received throughout the year is the integrated momentary energy over time

.

One of the properties of planetary orbits is that the planet’s longitude in its orbit increases at a rate which is also inversely proportional to the square of the distance

,

where is a constant, the specific angular momentum of the planet in its orbit (the angular momentum per unit mass). This is an equivalent statement of Kepler’s second law of planetary motion.

This means that the infinitesimal change in longitude is related to the infinitesimal change in time

.

If we substitute this expression for in our annual-total energy integral we get

.

When we integrate time over an entire year, that’s the same as integrating longitude over a full circle. But the longitude integral is of , which is a constant. So the integral itself is a constant. In other words, it doesn’t depend at all on whether the earth is closest to the sun during northern hemisphere winter, or summer, or spring or fall or whenever. It’s always the same. And that’s true not only for the earth as a whole, but for any specific location on earth. If your location is further from the sun during summer (so a summer day gets less solar energy), summer also lasts longer (you have more summer days), and those two competing factors cancel each other out. Exactly.

The changing relationship between the seasons and when we’re closest to the sun is the precession cycle, one of the Milankovitch cycles. We’ve just seen that this particular Milankovitch cycle has no effect at all on total annual solar insolation, either for the planet or any single location on it. If that were the whole story, then this particular Milankovitch cycle would have no effect on ice sheet growth or decay.

But it’s not the whole story. Suppose you live in the extreme north, at latitude 65 deg.N. Suppose further that the precession cycle is such that you’re further from the sun during your summer, and closer during winter. Then midsummer day won’t be as warm as it would otherwise — so you can expect less ice melting. Also, midwinter day won’t be as cold as otherwise, so you can expect the warmer winter air to hold more moisture and produce more snowfall. Less midsummer melt, more midwinter snowfall, both tend to increase ice accumulation and make ice sheets grow. If the precession cycle is reversed, you’ll have warmer midsummer and more ice melt, colder midwinter and less snowfall, both of which tend to decrease ice accumulation and make ice sheets shrink. That’s why the precession cycle actually does affect ice sheet growth and decay. Even though you get exactly the same total solar energy over the entire year, the precession cycle affects when you get that energy during the year.

Right now, in the northern hemisphere we’re closer to the sun in winter and further in summer — just the right conditions to increase ice growth and cool the planet. The situation is opposite in the southern hemisphere, but since there’s so little land (compared to ocean) in the southern hemisphere there’s a lot less land-based ice as well. So the present condition of the precession cycle favors the increase of glacial ice, especially in the northern hemisphere, just as Hansen said.

Hertzberg reveals his failure to understand when he asks, “why then we may ask are we now in an Interglacial Warming?” We’re not. We’re in an interglacial warm but not warming. And we’re in that interglacial warm because 12,000 years ago, when we came out of the last glaciation, the precession cycle was opposite its present condition — the northern hemisphere was closest to the sun during summer and furthest during winter, exactly the condition which tends to make ice sheets waste away. The present state of the precession cycle is tending to reverse that, just as Hansen said.

Hertzberg also said “What Hansen fails to realize is that when we are further from the Sun in NH summer we move more slowly in orbit, and are therefore exposed to the summer sun for a longer period of time.” On the contrary, I’m confident that Hansen is fully aware of that, and fully aware of the fact that it’s through the timing of incoming solar energy, not its yearly total, that the precession cycle affects the growth and decay of ice sheets. But apparently, Hertzberg is not so aware.

In fact Hertzberg is so confused about the whole issue that he says:



So 10,000 years ago the earth was further from the sun during NH winter and it spent a longer time on the winter half of the orbit, thus both effects re-enforced each other to give us a marked Glacial Cooling. (Actually the peak in that Glacial Cooling occurred several thousand years earlier than 8,000 BC.)



On the contrary, 10,000 years ago the precession cycle so tended to warm the earth that that was near the peak of interglacial warmth. Until now … but the present warmth isn’t due to Milankovitch cycles.

When it comes to the influence of Milankovitch cycles on glaciation, Hertzberg couldn’t be more confused. His assertion that it’s Hansen who is confused about the issue is just an example of the Dunning-Kruger effect.

UPDATE:

I’ve posted about Milankovitch cycles before. Those who want more detail can find some in these posts:

Wobbles, part 1

Wobbles, part 2