The plot looks very close to Diviner, but perhaps with the surface conductivity a bit high.

rhoda. if you email me I will send you the Vasavada data (Apollo & Diviner data). You need this for your calcs. roger(dot)longstaff(at)live(dot)co(dot)uk

I haven't made the changes to the mass of the sand as suggested by Jeremy, more mass with the same area will change the heat loss... let me run it with 10x mass.... 218K.

I think it is the surface layer that dominates, because it is a very good insulator. You can simulate this by lowering the density to reduce the heat loss - this is of course not physically correct, but it should give you a closer approximation to the Diviner curve.

All of this contains errors of course - the Earth's radiation is nor accouted for, or seasons. However, I think you are the first person to do this - respect!! You should publish, when you are happy with it.

As for making the model available online..... I'd need to get some webspace for that, my personal space only runs Perl and PHP. Anyone know of any .Net webspace going cheap or preferably free?

BigYin, The next time you show a plot, please include max and min temps. Thanks.

Sorry, got confused.

Was the plot you showed @ 2.45 the mean temperature integrated over all latitudes vs. time? Again, if you could include max/min temps, or even a temp scale, it would be v. interesting!

Not yet Roger.... it's still just that little slab of sand on the equator.

I found some webspace, so put the model as-is on there, with some params to twiddle.

http://www.heatmodels.somee.com/

I only have 5GB monthly allowance so don't hit it TOO hard! If this becomes a successful project we can move it to proper paid hosting.

Is this still for 1 point? Why is the curve such an odd shape? It warms sort of exponentially for 4 hours and than suddenly stops with a definite knee in the graph. What could cause that? Nothing happens suddenly in a rotating moon.

Yeah it's still 1 point so far, on the equator.

The knee is where heating reaches the maximum temperature the incoming insolation will allow, before that it has been heating according to the heat capacity of the solid, i.e quite fast. At that point, it can no longer heat because it is in thermal equilibrium, and the temperature is governed by the amount of insolation.

As daft as it looks, you do see such knees in the records

http://www.ncdc.noaa.gov/paleo/ctl/images/diurnal.gif
http://www.oneonta.edu/faculty/baumanpr/geosat2/Urban_Heat_Island/FIGURE3.GIF

But those are smooth, yours is sharp. Does the temperature-rise suddenly reach a limit, or would it will slow down as it neared the limit? Maybe a sampling thing?

A good start. Now, may I suggest ways to make it more like Diviner (where there in no "knee", and more like your plot @ 2.45)? I think your surface conductivity is way too high.

Why not fix the default albedo at 0.12 (for the Moon) and also add a variable for surface conductivity (with a default value such as the one you used for your 2.45 graph)?

You must have spent all day on this?

It's a good question BB... I can't think of a mechanism that would tell the solid to stop heating as fast as it can as it approached solar insolation.

One thought : This is not in an atmosphere, so the night time temperature is low, so it is having to heat from a very low value, whereas the real earth ones are only rising from a value just under thermal crossover, so the gradient of the thermal rise is close to the gradient of the sine-based insolation at that point, so the 'knee' is shallower. The moon gets away with this because it has slow rotation, so the insolation near sunrise is small, making the thermal crossover very quickly - if you make the rotation 0.1 and fiddle with the days and horizontal scale, you see the knee effect is much less.

Not all day, I already had the model from yesterday, I only had to add a few parameters. I am my own boss, so it's only my own business which is suffering, and I can make that up :)

Replied to you rhoda.

Intuitively, it seems wrong that the max temperature can be reached at around 10AM, before maximum insolation. With heat capacity providing a drag, it would be logical to expect max temperature after midday. If you look at the plots at SoD from before, the heating phase is pretty sinusoidal until heat capacity is large.

BB, I followed your SoD link on my new laptop (you are right about my old desktop).

I think the answer is in the Vasavada paper (if you email I will send it to you). The regolith has a thin insulating layer of powder, that rapidly reaches SB temps with a large temp drop to the more conductive stuff underneath. This is in agreement with Apollo 15 measuremenrs (and samples) and the Diviner results. So it seems it is not just a question of bulk heat capacity (at least on the Moon).

Roger, thanks. Is that E00H18 you refer to? Fig 4 shows nice curves, no knobbly knees.

It's not reaching 'maximum' temperature at 10am, it's only reached the point where it's thermal equilibrium governing its maximum temperature. The temperature still goes up, but now follows insolation as it peaks and declines in the afternoon.

My model, being the result of about 45 minutes coding, is surely wrong in many, many respects, but it's already thrown up this interesting nugget to discuss.

Think of it this way.... at dawn, the insolation is accelerating at its maximum value (sine curve) so it's first derivative is large, meanwhile, the temperature of the sand, heating according to heat laws, is an exponential... which has a low first derivative near zero. Insolation outpaces temperature for a while.... but sine slackens off as the morning progresses....exponential heating is accelerating, at a certain point, they cross (thermal crossover).

The model is heating the ground according to the joules that the insolation gives it. The curves are intrinsically related. I'll put the calculation code up tomorrow see if you can spot any howlers in it.

BB - yes - that is the paper I was referring to.

What really happens when you heat the surface periodically is that the temp in the layers below also varies periodically but the amplitude of the oscillation decreases exponentially with depth, and there is a phase lag with depth. So at some depth it is warmest at night and coolest at mid day! If you do a simulation with say 10 layers of sand you should see an effect like this.

For what it is worth, here is my simulation. It looks reasonably similar to the SoD plots and to Figure 4 of the Vasavada paper (suitably shifted) although the drop-off on mine is less steep. But take it with a pinch of salt - I have no experience in these matters.