The paper by Belda et Al (2014) is probably the best to date in reconstructing the Koppen-Trewartha climate classification map from modern datasets.
The Belda maps show the climate regions of the world (except Antarctica) for two periods, 1901-1931 and 1975-2005, based on a 30 minute grid, average area about 2500 km2, (About 50,000 grid cells cover 135 million km2, the land area of the Earth except Antarctica.)
Between the two periods separated by 75 years, 8% of the cells changed climate type. When you plot a scatter diagram of distributions for the two periods, you will find there is little divergence from the straight line passing through the origin and with slope unity. R-squared is 99.5.
The paper does not discuss error bars. However, the CRU (UK) has revised the climate data to remove wet bias, an adjustment that would increase R2, indicating even less change than these maps show.
Indeed you can do that, you can correlate the variability of climatic elements with crop productivity. But you have to consider that, other factors like irrigation support or other input of agriculture remain constant throughout the time period or taking care of those factors for your study. You can also increase your temporal scale, like climatic variability of a particular season and its relation with the crop grown in that particular season.
you can have a look at 20th century precipitation or temperature variability decomposed in 3 major time scales: year-to-year, decadal and climate change, for a season on your choice, with those Maprooms tools: