By Dan Smeal located at NMSU Agriculture Science Center Farmington New Mexico.
A simple frost depth gage was designed by D. K. McCool and Myron Molnau (1984) and installed at Farmington New Mexico. http://snow.ag.uidaho.edu/Publications/frost/frost.html

The tube was filled with fluid used in irrometer tensiometers.
The maximum frost depth of 10 inches occurred on February 5- 7 in 2001.
| Table 1 FROST DEPTH DATA FROM FARMINGTON - Winter 2001 | ||||
| Date | Frost Depth, inches | |||
| 18-Jan | 2.5 | |||
| 19-Jan | 5 | |||
| 22-Jan | 8 | |||
| 23-Jan | 9.5 | |||
| 24-Jan | 9 | |||
| 26-Jan | 8.5 | |||
| 29-Jan | 8 | |||
| 1-Feb | 7.5 | |||
| 2-Feb | 9 | |||
| 5-Feb | 10 | |||
| 6-Feb | 10 | |||
| 7-Feb | 10 | |||
| 8-Feb | 8 | |||
| 9-Feb | 7 | Snow cover | ||
| 12-Feb | 1.5 | Snow cover | ||
Campbell 1985 wrote a finite difference solution to predict temperature in the soil profile based on air temperature. This can be used to predict a first approximation of the soil temperature profile with no snow cover. It has been modified to include a change in daily air temperature.
Reference
D. K. McCool and Myron Molnau (1984) , Measurement of Frost depth. published in the Proceedings Western Snow Conference 52:33-42.1984 Sun Valley, Idaho James Meiman, General Chairman
Campbell. G. S. Soil Physics with basic. Transport models for soil-plant system Elservier p1-150