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Sand is granular in nature, which allows air columns to trap in between them. As we know that air is an insulator of heat. So here are my questions:

Does sand maintain its temperatures close to its surface? (Like a conducting shell distributes charge on its surface)

If there were layers of sand, is it possible that in the deeper layers the temperatures remain constant? And only the temperatures of the upper layers changes as the surrounding environment changes?

P.S. If all of this is true is there a particular formula or a study I can use to figure out the temperature difference between the surface and at a depth in a desert?

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Yes sand is, on average, quite insulative with the temperature at the surface being rather higher than that at depth when the surface is being actively heated, as by sunlight. The actual degree of insulation depends on at least three factors;

  1. Moisture content, wetter sand is less insulative than dry sand because the water in it's pore spaces conducts heat better than air filled pores would.
  2. Average grain size, courser sand has more pore spaces and thus more of it's total volume is made of air so it's more insulative at a given water content.
  3. Grain size distribution and sorting, sand composed of grains that are all of a similar size will have more pore spaces than sand composed of many sizes of grain. Grains of the same size act like stacked ball-bearings leaving a lot of empty spaces but with larger and smaller grains the pores between the large grains are filled by the small ones leaving little space for insulative air pockets.

Due to the complexity of the processes involved it is very difficult to have any single formula that gives you a measure of sand in general. You may be able to find, or create, data sets that allow you to predict the insulative value and thus temperature at depth of a particular sand under a particular set of circumstances. Generally speaking it's easier to take field measurements, unless there's a really long-term project involved.

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    $\begingroup$ I suspect that grain size doesn't matter much: The void fraction will be about the same regardless of the size. However fine sand with smaller spaces will hold water more easily, and also have slower air exchange with the surface. The distribution of grain size will be a big thing however. $\endgroup$ – Sherwood Botsford Jun 23 '18 at 12:44
  • $\begingroup$ @SherwoodBotsford I think it's on the order of a couple of percent total pore space difference from the biggest to the smallest sand grains so it's contribution will likely be dwarfed by other differences in a non-laboratory setting. $\endgroup$ – Ash Jun 24 '18 at 10:17
  • $\begingroup$ But a mix of sizes will have less pore space. The classic example is putting putting a pail of pea gravel in a bucket of rocks, then a few cups of sand between the pea gravel. Road crush is screened carefully to get a pore space that allows for drainage, but keeps the larger rocks touching so that overall layer is stable. $\endgroup$ – Sherwood Botsford Jun 25 '18 at 12:37
  • $\begingroup$ @SherwoodBotsford Absolutely, there are riverbeds in a couple of countries that have stopped draining to groundwater because their once gravel beds are full of silt and clay discharged by deforestation etc... that blocks their drainage pores. $\endgroup$ – Ash Jun 25 '18 at 12:39

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