Statistical Analysis of Subsurface Diffusion of Solar Energy with Implications for Urban Heat Stress


Analysis of hourly underground temperature measurements at a medium-size (by population) US city as a function of depth and extending over 5+ years revealed a positive trend exceeding the rate of regional and global warming by an order of magnitude. Measurements at depths greater than ~2 m are unaffected by daily fluctuations and sense only seasonal variability. A comparable trend also emerged from the surface temperature record of the largest US city (New York). Power spectral analysis of deep and shallow subsurface temperature records showed respectively two kinds of power-law behavior: 1) a quasi-continuum of power amplitudes indicative of Brownian noise, superposed (in the shallow record) by 2) a discrete spectrum of diurnal harmonics attributable to the unequal heat flux between daylight and darkness. Spectral amplitudes of the deepest temperature time series (2.4 m) conformed to a log-hyperbolic distribution. Upon removal of seasonal variability from the temperature record, the resulting spectral amplitudes followed a log-exponential distribution. Dynamical analysis showed that relative amplitudes and phases of temperature records at different depths were in excellent accord with a 1-dimensional heat diffusion model.

Share and Cite:

Silverman, M. (2014) Statistical Analysis of Subsurface Diffusion of Solar Energy with Implications for Urban Heat Stress. Journal of Modern Physics, 5, 751-762. doi: 10.4236/jmp.2014.59085.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Tollefson, J. (2011) Nature News.
[2] Cook, J., et al. (2013) Environmental Research Letters, 8, Article ID: 024024.
[3] Rohde, R., et al. (2013) Geoinformatics & Geostatics: An Overview, 1, 1.
[4] IPCC (2013) Climate Change 2013: The Physical Science Basis.
[5] McMichael, A.J., Woodruff, R.E. and Hales, S. (2006) The Lancet, 367, 859-869.
[6] Hajat, S., Vardoulakis, S., Heaviside, C. and Eggen, B. (2014) Journal of Epidemiology & Community Health, 68, 641-648.
[7] Centers for Disease Control and Prevention: Climate and Health Program.
[8] Robine, J.-M., et al. (2008) Comptes Rendus Biologies, 331, 171-178.
[9] Stone Jr., B. (2007) International Journal of Climatology, 27, 1801-1807.
[10] Union of Concerned Scientists (2006) Climate Change in the US Northeast. UCS Publications, Cambridge, MA, 10.
[11] Committee on America’s Climate Choices (2011) America’s Climate Choices. National Academy Press, Washington DC, 15.
[12] Silverman, M.P. (2014) A Certain Uncertainty: Nature’s Random Ways. Cambridge University Press (to be published), Cambridge.
[13] NYC Temperature Data.
[14] Shannon, C. (1949) Proceedings of the IRE, 37, 10-21.
[15] Silverman, M.P., Strange, W., Bower, J. and Ikejimba, L. (2012) Physica Scripta, 85, Article ID: 065403.
[16] Fieller, N.R.J., Flenley, E.C. and Olbricht, W. (1992) Applied Statistics, 41, 127-146.
[17] Bibby, B.M. and Sorensen, M. (1997) Finance and Stochastics, 1, 25-41.
[18] Barndorff-Nielsen, O. (1977) Proceedings of the Royal Society of London. Series A, 353, 401-419.
[19] Evett, S.R., et al. (2012) Advances in Water Resources, 50, 41-54.
[20] Wu, J., et al. (2014) Environmental Health Perspectives, 122, 10-16.
[21] Meehl, G. and Tebaldi, C. (2004) Science, 305, 994-997.
[22] Turcotte, D.L. (1997) Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge, 148-149.
[23] Hergarten, S. (2002) Self-Organized Criticality in Earth Systems. Springer, Heidelberg, 48-66.
[24] Silverman, M.P. and Strange, W. (2009) Europhysics Letters, 87, Article ID: 32001.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.