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# Q_day to mu

I'm in the process of writing some code to compute $\bar{Q}_{day}$ as defined at [[Insolation]]. Once I'm done, I hope to use this as the input $\mu$ to the temperature evolution illustrated here.

However, there is probably going to be some unit conversions (at a minimum) required to go from $\bar{Q}_{day}$ to $\mu$. In the meantime, if someone reading this could have a look and try to figure out the correct conversion, that would be very helpful.

Source Text:hoidle

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1.

I don't think there need to be any unit conversions. Insolation will have units of watts per square meter, which is correct for the ZG10 formula. However, the EBM they use is designed to take spatially-averaged insolation as an input. Your code will calculate insolation at a given latitude. (There are also issues of time-of-year vs. annually averaged insolation; the latter may be more appropriate for an EBM that assumes an instantaneous temperature response to forcing.)

Source Text:I don't think there need to be any unit conversions. Insolation will have units of watts per square meter, which is correct for the ZG10 formula. However, the EBM they use is designed to take spatially-averaged insolation as an input. Your code will calculate insolation at a given latitude. (There are also issues of time-of-year vs. annually averaged insolation; the latter may be more appropriate for an EBM that assumes an instantaneous temperature response to forcing.)
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2.

Thanks Nathan. Yeah, I agree. I've been thinking about this sporadically throughout the day as time allows. So to connect the two, we can either

1. Take some kind of average of $\bar{Q}_day$ over latitude (and maybe averaged over the year as well)
2. Develop a latitude dependent EBM (not sure what EBM stands for though :))

Not sure if 2.) is possible, but it sounds like it would be fun to try.

In the meantime, I think it would be a good exercise (for me) to continue trying to compute $\bar{Q}_{day}$, so I'll keep staring at it for a bit longer. Plus, this is a good warm up to give some rudimentary python skills.

PS: $\mu$ in the paper is unitless, but it is clear what to do now, e.g. $\bar{Q}_{day} = \mu Q_0$ (or similar).

Source Text:Thanks Nathan. Yeah, I agree. I've been thinking about this sporadically throughout the day as time allows. So to connect the two, we can either 1. Take some kind of average of $\bar{Q}_day$ over latitude (and maybe averaged over the year as well) 1. Develop a latitude dependent EBM (not sure what EBM stands for though :)) Not sure if 2.) is possible, but it sounds like it would be fun to try. In the meantime, I think it would be a good exercise (for me) to continue trying to compute $\bar{Q}_{day}$, so I'll keep staring at it for a bit longer. Plus, this is a good warm up to give some rudimentary python skills. PS: $\mu$ in the paper is unitless, but it is clear what to do now, e.g. $\bar{Q}_{day} = \mu Q_0$ (or similar).
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3.

It's not hard to make an energy balance model (EBM) latitude-dependent. You just have to make the albedo of the Earth depend on latitude, and integrate the heat flux over latitude. The Roe and Baker paper on Snowball Earth, "Notes from a catastrophe", has details of these Budyko-Sellers type models. However, Snowball Earth models (like the ZG10 EBM) aren't entirely suited to studying glacial-interglacial dynamics. Since they have instantaneous response, they're suited to situations in which the climate responds much faster than the forcing (variations in insolation). But in the glacial cycle, the response time of ice sheets is comparable to the periodicity in Milankovitch cycles. Ultimately, a Saltzman-type model would be better suited for studying Quaternary dynamics.

Source Text:It's not hard to make an energy balance model (EBM) latitude-dependent. You just have to make the albedo of the Earth depend on latitude, and integrate the heat flux over latitude. The Roe and Baker paper on Snowball Earth, "Notes from a catastrophe", has details of these Budyko-Sellers type models. However, Snowball Earth models (like the ZG10 EBM) aren't entirely suited to studying glacial-interglacial dynamics. Since they have instantaneous response, they're suited to situations in which the climate responds much faster than the forcing (variations in insolation). But in the glacial cycle, the response time of ice sheets is comparable to the periodicity in Milankovitch cycles. Ultimately, a Saltzman-type model would be better suited for studying Quaternary dynamics.
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4.

Nathan wrote:

Ultimately, a Saltzman-type model would be better suited for studying Quaternary dynamics.

And perhaps not so ultimately: now that you mention it, my whole idea of coupling the Zaliapin-Ghil model to changes in insolation at 65° N is sort of dumb. I suggest that Eric hold off on any program like this until I (or we) think more what's going on.

But having a program that computes the insolation at 65° N (or an arbitrary latitude) is a good thing.

One big issue with $\overline{Q}day$ is that it rises in some latitudes and times of year while it decreases in others: I don't think any of the Milankovitch cycle changes in the Earth's orbit make it bigger or smaller _on average! So, if we use a naive averaging procedure, we might get no effect at all.

I want to say more about this, but it's my bed-time!

Source Text:Nathan wrote: > Ultimately, a Saltzman-type model would be better suited for studying Quaternary dynamics. And perhaps not so ultimately: now that you mention it, my whole idea of coupling the Zaliapin-Ghil model to changes in insolation at 65&deg; N is sort of dumb. I suggest that Eric hold off on any program like this until I (or we) think more what's going on. But having a program that computes the insolation at 65&deg; N (or an arbitrary latitude) is a good thing. One big issue with $\overline{Q}_day$ is that it rises in some latitudes and times of year while it decreases in others: I don't think any of the Milankovitch cycle changes in the Earth's orbit make it bigger or smaller _on average_! So, if we use a naive averaging procedure, we might get no effect at all. I want to say more about this, but it's my bed-time!
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5.

No worries and no need to hold off on anything. I'm still developing basic coding skills in Python, so even a few dead ends here and there is no big deal. They'll just make me better prepared for when we do find the right path.

One thing I like about these EBM models is they reduce things down to a few variables (3). To me, modeling geometry is fun, so I also want to learn enough Python to be able to model a tessellation of a sphere and couple this EBM stuff to something like FEM, which seems like something like a coarse low dimensional type of GCM.

For example, in ZG10, we're looking at incident radiation, reflected radiation, absorbed radiation, and re-radiation. With a triangulation of the surface of the earth, with the same variables, we can start looking at conduction and convection as well.

For geometric visualization, I've installed ParaView.

Source Text:No worries and no need to hold off on anything. I'm still developing basic coding skills in Python, so even a few dead ends here and there is no big deal. They'll just make me better prepared for when we do find the right path. One thing I like about these EBM models is they reduce things down to a few variables (3). To me, modeling geometry is fun, so I also want to learn enough Python to be able to model a tessellation of a sphere and couple this EBM stuff to something like FEM, which seems like something like a coarse low dimensional type of GCM. For example, in ZG10, we're looking at incident radiation, reflected radiation, absorbed radiation, and re-radiation. With a triangulation of the surface of the earth, with the same variables, we can start looking at conduction and convection as well. For geometric visualization, I've installed [ParaView](http://www.sandia.gov/ParaView/).
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6.

I think eccentricity does alter the annual average insolation, but only as the square of eccentricity, so it's a small variation (since eccentricity itself is a small forcing even at a specific time of year).

Source Text:I think eccentricity does alter the annual average insolation, but only as the square of eccentricity, so it's a small variation (since eccentricity itself is a small forcing even at a specific time of year).
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7.

I think eccentricity does alter the annual average insolation, but only as the square of eccentricity, so it's a small variation...

Right - and nobody seems to claim that's the cause of the ice ages. I'm trying to find an article I read which reviewed this issue. A lot of first-order effects cancel so something subtler is at work. Some people argued that less sunshine in the Northern hemisphere in the winter brings on an ice age, while others argued that less sunshine in the Northern hemisphere in the summer is what does it. Or something like that.

Source Text:> I think eccentricity does alter the annual average insolation, but only as the square of eccentricity, so it's a small variation... Right - and nobody seems to claim _that's_ the cause of the ice ages. I'm trying to find an article I read which reviewed this issue. A lot of first-order effects cancel so something subtler is at work. Some people argued that less sunshine in the Northern hemisphere in the _winter_ brings on an ice age, while others argued that less sunshine in the Northern hemisphere in the _summer_ is what does it. Or something like that.
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8.

I think less sunshine in the summer at 65 N is the most commonly accepted theory.

Source Text:I think less sunshine in the summer at 65 N is the most commonly accepted theory.
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9.
edited April 2011

John: I also hold off model programming for some days but it's available at the same demo.sagenb.org.

I will finish some more Azimuth experiments and tutorials.

Eric: Paraview has always attracted me but I never got a chance to use it. How is it compared to MayaVi?

Source Text:John: I also hold off model programming for some days but it's available at the same [demo.sagenb.org](http://demo.sagenb.org/home/pub/92). I will finish some more Azimuth experiments and tutorials. Eric: Paraview has always attracted me but I never got a chance to use it. How is it compared to MayaVi?
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10.
edited April 2011

I also read in Everett's book "Critical transitions in Nature and Society" pp 152ff see [[Recommended reading]]

In spite of the apparent ...link between variation in radiation and ice ages, the response of the Earth to to the Milankovitch cycles appear rather difficult to explain after a closer look

and he refers to a Nature 409(6817), 147 2001 article by D. Paillard and continues as Nathan that the incoming due to all M-cycles radiation is small:

Even when all the orbital parameter favours glaciation the increase in winter snowfall and decrease in summer melt seems not enough too grow large ice sheets. This happens only because of amplification of the forcing by positive feedback. The most obvious amplifying feedbacks...

I left a climate cliffhanger there :-)

Source Text:I also read in Everett's book "Critical transitions in Nature and Society" pp 152ff see [[Recommended reading]] > In spite of the apparent ...link between variation in radiation and ice ages, the response of the Earth to to the > Milankovitch cycles appear rather difficult to explain after a closer look and he refers to a Nature 409(6817), 147 2001 article by D. Paillard and continues as Nathan that the incoming due to all M-cycles radiation is small: > Even when all the orbital parameter favours glaciation the increase in winter snowfall and decrease in > summer melt seems not enough too grow large ice sheets. This happens only because of amplification > of the forcing by positive feedback. The most obvious amplifying feedbacks... I left a climate cliffhanger there :-)