In ERA5, "2 metre temperature" is an instantaneous parameter and is available hourly, from both the analyses and the forecasts. The parameters "Maximum temperature at 2 metres since previous post-processing" and "Minimum temperature at 2 metres since previous post-processing" are the maximum and minimum in the last hour, and are available from the forecasts only.
The sub-set of ERA5 data on the CDS disks contains analysed parameters, if available, otherwise it contains forecast parameters. Therefore, on the CDS disks, the "2 metre temperature" is an analysed parameter, whereas the "Maximum temperature at 2 metres since previous post-processing" and "Minimum temperature at 2 metres since previous post-processing" are forecast parameters.
The forecast model in the version (CY41R2) of the ECMWF Integrated Forecasting System (IFS) used in ERA5, has a cold bias in the lower regions of the troposphere over most parts of the globe, which is at least partially corrected by the analysis system. This forecast cold bias means that the analysed "2 metre temperature" can be larger than the "Maximum temperature at 2 metres since previous post-processing".
Given this inconsistency in these three parameters on the CDS, we recommend, in general, that the hourly (analysed) "2 metre temperature" be used to construct the minimum and maximum over longer periods, such as a day. However, be aware that with the "2 metre temperature" being an instantaneous parameter, it is given by the time step value on the hour, whereas the "Maximum temperature at 2 metres since previous post-processing" and "Minimum temperature at 2 metres since previous post-processing" are calculated from all the time steps during the hour (3 hours for the ensemble). In ERA5, the time step is 12 minutes (20 minutes for the ensemble), so there are five time steps (three time steps for the ensemble) per hour.
