Lu Xing and Jeff Spitler have developed a two-harmonic analytical model for the estimation of undisturbed ground temperatures for engineering applications that is described in three companion papers:

1. papers: 1. Xing and Spitler 2017. Prediction of undisturbed ground temperature using analytical and numerical modeling. Part I: Model development and experimental validation. Science and Technology for Built Environment 23:787-808.

2. 23:787-808. 2. Xing and Spitler 2017. Prediction of undisturbed ground temperature using analytical and numerical modeling. Part II: Methodology for developing a world-wide dataset. Science and Technology for Built Environment 23:809-825.

3. 23:809-825. 3. Xing, Spitler, and Bandyopadhyay 2017. Prediction of undisturbed ground temperature using analytical and numerical modeling, Part III: Experimental validation of a world-wide dataset. Science and Technology for Built Environment 23:826-842.

(excerpt 23:826-842. (quoting from the abstract for Paper 2): "... a two-harmonic analytical model which is used for the estimations of undisturbed ground temperatures for engineering applications has been developed. This model relies on a second-order harmonic relationship and five weather-related constants - annual average ground temperature, two temperature amplitudes, and two phase lags to predict the ground temperatures. These parameters are estimated using temperature results calculated from the numerical method developed by Xing and Spilter (2017). The two -harmonic model is validated using measured ground temperature data at 19 sites in the US... in three different climates - arid, warm, and snow... The model... relies on inputs such as soil diffisivity, vegetation density, and snow depth to estimate the ground temperatures...paper 2):