Ground Response to Global Warming

Abstract

Owing to the awareness of the impact of global warming, there has been a growing interest in studying the relationship between the climatic changes and human activities. An increased global mean air temperature leads to an increase of the ground temperature. Therefore the analysis of borehole temperature depth profile (BTDP) has become an accepted method for detecting the past climatic changes. Mathematical models have been suggested to simulate deviation of BTDP in order to detect the warming level and time elapsed since warming started. Unlike previous studies, the aim of the current study was to derive a new equation that gives the ground temperature increase in areas where the warming is identified. A comparison of the solution suggested in the current study with other solutions established in other studies shows excellent agreement. The suggested solution is characterized by the fact that it is more user-friendly compared to other solutions. Furthermore, the obtained solution was used to get a very simple expression for the heat retained by a column of earth during the warming event. In addition it was used to determine the average change of ground temperature over a particular depth. This average change of ground temperature is of great importance in the borehole system.

Nomenclature

C:

Volumetric heat capacity (J/m³ k)

H:

Reference depth (m)

L:

A certain depth that is of interest to calculate the ΔT_ave (m)

Q(t):

Heat retained by a column of earth surface due to the climatic changes (J/m²)

t:

Time elapsed since start-up warming (s)

T(z,t):

Ground temperature anomaly (°C)

T_s :

Air temperature at the surface level (°C)

z:

Depth below ground surface (m)

α = λ/C:

Thermal diffusivity (m²/s)

γ:

Temperature gradient due to geothermal heat flux (°C/m)

δ:

Temperature change at the ground surface (°C)

ΔT_m(L,t):

Average change of ground temperature over a certain depth L (°C)

ε:

Warming rate of air (assumed to be constant over time) (°C/s)

θ(z,t):

The transient ground temperature at depth z and time t

λ:

Thermal conductivity (W/m K)