# Undisturbed Ground Temperature Model: Xing[LINK]

This model uses the correlation developed by Xing, 2014 to predict undisturbed ground temperature. The correlation parameters for 4000+ international locations can be found in Xing, 2014. The parameters were first determined by creating and validating a finite difference numerical model which used local weather data for boundary conditions. From the numerical model, the correlation parameters were determined to provide for this simplified design model.

T(z,t)=¯Ts−2∑n=1Δ¯Ts,n⋅e−z⋅√nπατ⋅cos[2πnτ(t−θn)−z√nπατ]

T(z,t) is the undisturbed ground temperature as a function of time and depth

¯Ts is the average annual soil surface temperature, in deg C

Δ¯Ts,n is the n-th amplitude of the soil temperature change throughout the year, in deg C

θn is the n-th phase shift, or day of minimum surface temperature

α is the themal diffusivity of the ground

τ is time constant, 365.

Xing, L. 2014. Estimations of Undisturbed Ground Temperatures using Numerical and Analytical Modeling. Ph.D. Diss. Oklahoma State University, Stillwater, OK.

## Undisturbed Ground Temperature Model: Xing[LINK]

## Approach[LINK]

This model uses the correlation developed by Xing, 2014 to predict undisturbed ground temperature. The correlation parameters for 4000+ international locations can be found in Xing, 2014. The parameters were first determined by creating and validating a finite difference numerical model which used local weather data for boundary conditions. From the numerical model, the correlation parameters were determined to provide for this simplified design model.

T(z,t)=¯Ts−2∑n=1Δ¯Ts,n⋅e−z⋅√nπατ⋅cos[2πnτ(t−θn)−z√nπατ]

T(z,t) is the undisturbed ground temperature as a function of time and depth

¯Ts is the average annual soil surface temperature, in deg C

Δ¯Ts,n is the n-th amplitude of the soil temperature change throughout the year, in deg C

θn is the n-th phase shift, or day of minimum surface temperature

α is the themal diffusivity of the ground

τ is time constant, 365.

## References[LINK]

Xing, L. 2014. Estimations of Undisturbed Ground Temperatures using Numerical and Analytical Modeling. Ph.D. Diss. Oklahoma State University, Stillwater, OK.

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