I am not aware of your area of expertise and therefore can't suggest specific methods but there are hundreds out there. A distinguished field called 'Paleoclimatology' is specifically designed for climate reconstruction and thus obtain historical climate data. But if you want to generate past data based on present data temporal interpolation or trend analyses might help. Hope that helps.

To validate climate data you could compare it to sediment records(marine) there is a vast amount of validated data out there that has been created through marine sediment records. Look out for the fields of Paleoclimatology and Paleooceanography.

To create the data sediment sampling could also be used, through radioactive data you can determine the sediment age. And climate markers in the sediment cores will give you climate data (Carbon, nitrogen, algae, zoop etc).

I guess you mean to obtain climate data in areas without observations. In this case you coud use a method of spatial interpolation if there are data surrounding the areas.

I have provided the means, I have writen and documented and detailed described that, and discovered the mechanisms involved

https://www.researchgate.net/profile/Dimis_Poulos