The Bubbling Barometer - Soil Temperature Profile

Using the small temperature logger I purchased from Jaycar, I established that the soil temperature at a depth of 1.0m was very constant, with no indication of a diurnal variation, but showing a slow rise in temperature of around ≈1/6 °C per day (see left).  Given that these measurements were made in the Austral springtime, it's perhaps not surprising that soil temperatures are generally on the rise.  But although the diurnal temperature variation is immeasurably small (the logger has a measurement resolution of ±0.5°C) I was curious to know how quickly the surface temperature variations reduced with soil depth, so I again used the logger for a series of test measurements.

By progressively burying the logger at depths of 0, 0.05, 0.1, 0.2, 0.5 and 1.0 metres, and leaving the logger at each depth for 24 hours, data were obtained (see lefthand plot - click on plot for full-sized version).  The logger was repositioned to a new depth at 7am each morning.  This plot shows that diurnal temperature variations of the soil decrease very quickly with depth, and by a depth of 0.5m the daily temperature variation is less than than the measuring accuracy of the logger, ±0.5°C.  By comparing the daily maximum and minimum figures from this plot, with the daily ambient air temperatures recorded at a nearby automatic weather station I noticed that they were closely logarithmically related, within the first 0.2m of soil depth at least.

Consider a scale factor by which soil temperature compares with the daily air temperature variation, and which we will call the 'Diurnal Temperature Scale Factor' (or DTSF), where...

DTSF = daily-range-in-soil-temperature ÷ daily-range-in-air-temperature.

So for example, if the daily air temperature varied by a range of 20°C and the soil temperature correspondingly ranged by 10°C, then the DTSF woud be 10÷20=0.5.  By analysing the plot above, I found that the DTSF is well modelled by...

log10(DTSF) = −(4.6 ± 1.0) × depth-in-metres

...or...

DTSF ≈ 10**( −4.6 × depth-in-metres )    (note that '10**' means "ten to the power of")

So for example, if the daily air temperature varied by 20°C, the daily variation of the soil temperature at 0.2m depth woud be the DTSF×20 or...

10**(−4.6×0.2) × 20 = 2.5°C

If this temperature-depth relationship continues to be valid for depths greater than 0.2m, then at a depth of 0.5m a daily air temperature variation of 20°C would cause a corresponding soil temperature variation of 0.1°C.  This suggests that for our burial of the Water Cylinder, a soil-covering of 0.5m would have been sufficient for the required temperature stability of ±0.1°C per day.  In fact the mean soil depth of our buried Water Cylinder is 1.0m, at which depth a 20°C daily air temperature variation would cause a 0.005°C (1/200th °C) variation in soil temperature... a figure which is vanishingly small and consistent with our observation of absolutely zilch measured daily variation.

The plot above also shows a vertical temperature profile of around 5°C per metre.  I decided it would be interesting to measure this profile more accurately, and to chart its variation throughout the year.  These data will be presented as they become available.

 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Depth/m 0 19.0 20.5 14.0 12.0 8.0 5.5 4.5 3.0 6.0 14.5 14.5 17.0 0.2 23.5 25.5 20.5 17.5 13.0 9.0 8.0 7.0 6.0 17.0 18.0 21.0 0.4 24.5 25.5 21.5 19.0 15.0 10.5 10.0 9.0 6.5 17.5 18.5 21.5 0.6 24.0 24.5 21.5 19.0 16.0 11.5 11.0 9.5 8.0 17.5 18.5 21.0 0.8 23.5 24.0 21.5 19.5 17.0 12.0 11.5 10.0 9.5 17.0 18.0 21.0 1.0 23.0 23.5 22.0 19.5 17.5 13.0 12.5 11.0 11.0 16.5 17.5 20.0
* temperature profile measurements made at 7am, during the middle of the month.