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"The Warming Papers" edited by David Archer and Raymond Pierrehumbert is good for historical context. It is basically a collection of classic journal papers, starting with Fourier and Tyndall, but it also covers key papers on climate modelling, ice cores and the carbon cycle etc.

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I don't know if ERA5 data has some weird format, as I'm really not familiar with working with such data directly. But it's vital to realize that the greatest hourly temp is rarely the daily max, and the same idea with mins. Orlando's data today: The max today was 87°F and the min 63°F (found from this using the 6 hour max\mins... there can be rare issues ...

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Yes, daily minima, maxima and precipitation totals are calculated simply as you suggested in your question. Take care that there aren't missing values,, but that's more of an issue calculating means. Also check whether the reported values for precipitation are in fact a null value, it's unlikely that it could be measured in such small units.

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Model data seta can vary in several ways from a reference data set. Taylor diagrams visually compare multiple datasets output to a reference dataset (e.g., model experiments to observations). This is done by exploiting the geometric relationship between centered RMS, correlation, and standard deviation when computing differences between datasets. Several ...

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You are looking to do some sort of regression analysis on two-dimensional data. The $r^2$ coefficient of determination value is often used for one dimensional data. $r^2=1$ means a perfect match and $r^2=0$ means no correlation. $r^2$ may be used for two-dimensional data as well; I don't know. Another example is the Kolmogorov–Smirnov test. Neither of these ...

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