title: Undisturbed Ground Temperature Model: Xing¶

Undisturbed Ground Temperature Model: Xing¶

Approach¶

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.

\[T(z,t) = \bar{T}_{s} - \sum_{n = 1}^{2} \Delta\bar{T}_{s,n} \cdot e^{-z \cdot \sqrt{\frac{n\pi}{\alpha\tau}}} \cdot cos\left[ \frac{2 \pi n}{\tau} \left(t - \theta_{n} \right) - z \sqrt{\frac{n \pi}{\alpha \tau}} \right]\]

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

\(\bar{T}_{s}\) is the average annual soil surface temperature, in deg C

\(\Delta\bar{T}_{s,n}\) is the n-th amplitude of the soil temperature change throughout the year, in deg C

\(\theta_{n}\) is the n-th phase shift, or day of minimum surface temperature

\(\alpha\) is the themal diffusivity of the ground

\(\tau\) is time constant, 365.

References¶

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