I am using CRU TS global gridded dataset for climate impacts on crop yields. The data has monthly mean values for temperature (min and max) and precipitation. Literature suggests that instead of averages, using degree days is more appropriate ( better RMS). However, the studies I have read so far, use daily temperature data to derive degree day derivations. For example, Schlenker and Roberts (2009) uses synodal function to approximate daily data into hourly and then derive the degree days. I have the STATA codes for these.

Since I have monthly and not daily observations, I cannot use these codes.

Can someone please help me figure out how I can use monthly data to derive degree days. I am looking for codes or alternative ideas.

Options I found through research:

1. Schlenker and Roberts (2009) suggests using Thom's formula to approximate daily values from monthly. I do not know how to code for that, any ideas?
2. Another author suggests using MARS and hinges function with the monthly data and use them instead of degree days.