BIT Numerical Mathematics

, Volume 7, Issue 2, pp 145–155

# Seasonal temperature variation of soil

• Harry v. Nordén
• Ilari Seppä
Article

## Abstract

The surface temperature of the ground is a periodic function of time. The summer temperature of the surface can be approximated by a harmonic function, and the winter temperature, due to an insulating layer of snow, can be assumed constant. In this paper the temperature of the ground was determined as a function of depth and time.

The ground temperature variation was solved by means of the Laplace transformation; the analytic solution was calculated numerically for different soil types and air temperatures. The results are presented numerically and graphically.

## Keywords

Surface Temperature Temperature Variation Soil Type Computational Mathematic Harmonic Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## List of symbols

a

thermal diffusivity

a1,a2,a3

thermal diffusivities for different soil types

F, FW

dimensionless temperatures

F0

asymptotic expansion of the result function for large values of time forp = 0

F1,F2, ...Fn

residues for polesp = 2πni

f

Laplace transformed dimensionless temperature

k

constant

p

Laplace transform variable

Re

real part

T

temperature

TA

half amplitude of air temperature variation near the ground surface

TM

annual mean temperature of air near the ground surface

TW

ground surface temperature under the snow cover

t

time variable

t0

1 year

t00

time in spring when air temperature reaches average temperature

t1

beginning of snow-free period

t2

beginning of winter

y

dimensionless time variable

y1

dimensionless time value, beginning of the snow-free period

X0

constant = √a·t0

x

dimensionless depth

ϕ

phase shift

ω

2π

## References

1. 1.
Vuorelainen, Olavi,Thermal Conditions in the Ground from the Viewpoint of Foundation Work, Heating and Plumbing Installations and Draining, The State Institute for Technical Research, Finland, Publication 51, Helsinki 1960.Google Scholar
2. 2.
Kolkki, Osmo,Temperaturkarten und Tabellen von Finnland für den Zeitraum 1921–50, Beilage zum Meteorologischen Jahrbuch für Finnland, Band L, Teil I-1950, Helsinki, 1959.Google Scholar