Where can I download GIS data delimiting global climate types? For example mediterannean climate, temperate climate, etc.
Additionally, how similar are temperature profiles for various places in the same climate classification?
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NOAA has climate division files in netcdf and shapefile format, though they may be just CONUS:
The most promising link looks like this source with paper citation below. They have lots of freely available data in a variety of formats:
Rubel, F., and M. Kottek, 2010: Observed and projected climate shifts 1901-2100 depicted by world maps of the Köppen-Geiger climate classification. Meteorol. Z., 19, 135-141. DOI: 10.1127/0941-2948/2010/0430.
There's also the ArcGIS Online map service that has Koppen-Geiger Observed and Predicted Climate Shifts:
To answer your question about the types of temperature in a classification, I suggest you refer to the paper above and the ranges of expected temperatures for each Koppen climate type which can be found here: https://en.wikipedia.org/wiki/K%C3%B6ppen_climate_classification
For modeled and observed temperature, precipitation, etc. you might find the following resources helpful:
Also look at:
Peel, M. C., Finlayson, B. L. and McMahon, T. A. (2007) Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci. 11, 1633-1644. DOI: 10.5194/hess-11-1633-2007.
The GIS coverage is included in the supplemental materials.