Begueria et al (2014) as well as Allen et al (1998) suggest Hargreaves as a better PET approximation method compared to Thornthwaite's when solar radiation, wind speed, and relative humidity data are unavailable.
The Hargreaves equation is spelled out in Droogers and Allen (2002), Allen et al (1998) and Hargreaves (1994).
There is R code for this, look into that and see what can be re-used.
Thanks/credit to Rebecca Ward for suggesting this.
Related to #101