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http://agsys.cra-cin.it/tools/evapotranspiration/help/Hargreaves.html There is a link, to the original works there, and a derivative work from Allen. Both are used to estimate ET with missing information. You would need an ASCE login for access to the papers there, if you don’t want to pay for that, http://www.iwhr.com/download/li080827-yoder.pdf is a nice abstract comparing and defining the evolution of a standard ET calculation. If you work out the base equations with a bit of dummy data, you will see a trend that is close to what the zimmerman method provides with the same data and his base weighting of inputs.
Zimmerman uses 3 pieces of data: Mean humidity ( defined as (min+max)/2 ), mean temp, and precipitation.
They are weighted in the following manner:
30 – mean humidity
(mean temp – 70)*4
Precipitation * 200
Those are all divided by 100 and added together, then 100 is added for a scale, which is then bound to 0 to 200.
Scientifically it appears to have no direct supporting work, however, it works out close to a couple ET calculations for inland areas free of high humidity influence. It is quite close to Hargreaves formula using only temperature, the formula is in the first link provided.