In my previous post I noted that the summer temperatures inside the house were higher than I expected from my research and detailed in a much earlier post “Earth Sheltering Insulation - Southern Europe”.
Whilst the problems with the ventilation and the resulting lack of sufficient earth sheltering on the rear half of the house, mentioned in my previous post, are the probable causes of this overheating I decided to look again at some of the research material in this area. And to compare these theoretical earth temperature predictions with actual house temperatures. I am assuming that the high thermal mass of the walls will reflect these temperatures and affect the air temperature inside the house accordingly.
In June there was a sustained heatwave with outside temperatures at the house rising to over 36 degrees Celsius and daytime temperatures averaging around 31-32 degrees Celsius during this period. This was coupled with the fact that the overnight temperatures were not falling sufficiently (i.e. by about 7 degrees or more) to allow natural overnight cooling to occur by using cross ventilation to purge the hot stale air from the house. This meant that the house was totally dependent upon the temperature of the earth surrounding and covering it to provide a sufficient thermal mass to cool the uninsulated walls of the house. Over this period, in an attempt to explain the higher than expected temperatures inside the house I conducted many experiments using the conventional window vents in the southerly window wall and the light well north facing vent. (NB The passive venting installed in the three large vents was not fit for purpose and therefore could play no part in the cooling solution).
Not surprisingly, with the hot June air being significantly hotter than the earth some 2 - 3 metres down, the best solution for cooling the house was to shut all the vents and rely upon the high mass walls of the house, cooled by the earth, to provide the cooling. However, without the benefit of the non fuctioning passive ventilation system, there was a rise in the humidity level throughout the house with all the windows closed. This proved quite unpleasant and cancelled out the benefits of the cooling effect of the walls. For this fact alone, as well as all the general health benefits, the replacement passive ventilation system for the three large roof vents needs to provide 24/7 air flow in and out, ideally via a heat exchange mechanism to warm the input air in winter and, perhaps more importantly, cool the incoming summer air.
Given this experience I decided to revisit some of my earlier research in order to establish a base set of data for how the solar passive earth sheltered house should perform throughout the year and thus clarify my suspicions as to the factors contributing to the higher than expected in-house temperatures.
I had previously established that it was theoretically possible to predict the temperature of the soil surrounding the the house at various depths and hence the expected temperature of the high thermal mass walls.
The vertical temperature of the ground can be modelled based on the method developed by Kasuda  who found that the temperature of the ground is a function of the time of year and the depth below the surface that can be described by the following correlation:
The problem that I had with this approach, however, was that I did not have a Typical Meteorological Year (TMY) dataset for, say, central southern Crete, to provide the input to the above predictive equation.
From my earlier research, a paper by Mihalakakou et al [ 2 ] presented a complete model for the prediction of the daily and annual variation of ground surface temperature and validated this model against 10 years of hourly measured temperatures for bare earth and for short-grass covered soil in both Athens and Dublin.
Figure 1 below shows the annual variation in temperature for earth at a depth of 3 metres in Athens.
Whilst this was a reasonable approximation to southern Crete I sought some further evidence/confirmation that more reflected the island, all be it a large island, conditions here in Crete. In a very round about way, as is the nature of exploring particular areas of interest on the internet, I hit upon a paper that considered the annual ground temperature at various soil depths for Nicosia in Cyprus by Florides and Kalogirou. 
Whilst not directly applicable to Crete, Cyprus has meteorological similarities to Crete, with long hot dry summers, cloudless skies and, in winter, fairly frequent small depressions which cross the Mediterranean from west to east that give short periods, 1 - 3 days, of disturbed weather and produce most of the annual precipitation.
As noted in the paper by Florides and Kalogirou:
“The ground temperature is affected by meteorological, terrain and subsurface variables. Meteorological elements such as solar radiation and air temperature influence the surface and subsurface temperature by affecting the rate at which heat is exchanged between the atmosphere and the ground. Solar radiation is probably the single most important factor. Seasonal and daily changes in solar radiation impose a cyclical variation on both air and ground surface temperature."
“In addition to an annual cycle ground temperature undergoes both a daily cycle and a cycle associated with changes in the weather. These changes are confined to the near surface region, daily cycles penetrating about 0.5 m and weather cycles about 1 m below the surface."
"Applying the above equation for the Nicosia-Cyprus environment the Typical Meteorological Year data for Nicosia developed by Petrakis et al [ 4 ] were used. The mean surface temperature, which by definition should correspond to the temperature of the ground at an infinite depth, showed a discrepancy and although it should have been about 22 degrees celsius as indicated by actual measurements was only 18.5 degrees celsius as calculated from the TMY data.
Adjusting these variables to fit the experimental results the graph below was obtained."
Figure 2 Temperature distribution with respect to time for various depths of Nicosia, Cyprus
The paper further noted:
“As it is observed the temperature of the ground surface remains almost in phase with that of the air temperature. Below the surface, however, the maximum or minimum occurs later than the corresponding values at the surface, the time lag increasing with the depth as shown by the cosine term in Equation 1 (above).
At a depth of 2 to 3 metres the maximum ground temperature occurs about 6 months later than the average maximum temperature of the surface in summer."
Interpretation of results
From Figure 2 it can be seen that, for Nicosia, Cyprus, at a depth of 2 m the earth is at its hottest on approximately day 330 of the year and should be around 25 degrees Celsius at that time. Similarly it is at its coldest on day 150 and at that time should be around 18 degrees Celsius.
Similarly at a depth of 4 m the earth should be hottest at 23 degrees Celsius around day 0 and coldest at 19.5 degrees Celsius around day 200.
From Figure 1 above for the bare soil option at a depth of 3 m in Athens it is at its hottest in mid-October (say, day 273) at around 25 degrees Celsius and at its coldest in mid-April (say, day 105) at 17 degrees Celsius.
Whilst the maximum and minimum earth temperatures for both Athens and Cyprus, at a depth of 2-3 m, therefore, appear fairly consistent there is a notable difference of some one and a half to two months in the timing of the thermal lag.
With the earth temperatures at various depths for Nicosia confirming the earlier data for Athens, albeit with differing thermal lags, I now feel confident that this data can form the basis for testing the performance of the earth sheltering and the high thermal mass properties of the house.
From Figure 2, above, for the heatwave period in June the earth/high thermal mass walls at between 2 and 4 metres depth should have been around 20 degrees Celsius. Indeed when the house had been shut up and unoccupied for short periods of time upon entering the air felt much cooler than the outside temperature and the walls themselves were very pleasantly cool to the touch. i.e. The design was working as expected.
Given this the experience over this summer of higher than expected/predicted temperatures inside the house was therefore undoubtedly due to a number of other factors.
Formost of these is the not fit for purpose design of the passive ventilation system which itself resulted in insufficient earth covering being in place across the rear half of the house. In addition the settlement of a loosely packed earth covering on the east end of the house resulted in a significant area of wall being exposed to the hot morning sunshine thoughout the long summer.
Furthermore, last winter was very mild and sunny and this, coupled with the fact that the house is “buried” into a south facing, extremely rocky, hillside would have combined to produce higher than average ground temperatures throughout the winter thus causing the cooling effect of the thermal lag to be less effective in the June/July period than usual.
For futher investigations, when a new ventilation system incorporating a heat/cool exchanger is installed and the earth sheltering completed, I will use a portable surface themometer to measure the surface temperature of the walls and compare these results with corresponding air temperatures inside and outside the house and the predicted values as described above.
 Kasuda, T., and Archenbach, P.R. "Earth Temperature and Thermal Diffusivity at Selected Stations in the United States", ASHRAE Transactions, Vol. 71, Part 1, 1965.
 Mihalakakou G., Santamouris M., Lewis O., Asimakopoulos D. "On the application of the energy balance equation to predict ground temperature profiles". Solar Energy, Vol. 60, No. 3/4 pp. 181-190,1997.
 Florides, G. and Kalogirou, S., "Measurements of Ground Temperature at Various Depths, Proceedings of the SET 2004, 3rd International Conference on Sustainable Energy Technologies on CD-ROM, Nottingham, UK, 2004.
 Petrakis M, Kambezides HD, Lykoudis S, Adamopoullos AD, Kassomenos P, Michaelides IM, Kalogirou SA, Roditis G, Chrysis I, Hadjigianni A. "Generation of a typical meteorological year for Nicosia, Cyprus". Renewable Energy, 13(3):381–8, 1998.