Dear Matteo, Thank you for pointing out this problem. As you mention, the documentation is incomplete for non-direct indices (SPI, SPEI, HD, CD) and needs to be updated providing further details on the calculation, such as exact definition/version of the index, input variables, code and version used, etc. We also need to update Table 4 including SPEI in tasmin and tasmax rows (used to calculate the PET component of SPEI6). We will update the documentation with the first update of the Atlas this month. In the meantime, I include here the requested information.
SPI and SPEI6 have been calculated using Python xclim software. The input for SPEI6 is precipitation - PET (potential evapotranspiration). PET is computed as explained below in the first version of the Atlas (will be changed to an updated version, Hargreaves, in the dataset v2 to align with EUCRA).
SPEI6: “The Standardised Precipitation Evapotranspiration Index (SPEI-6) is a monthly index that compares accumulated precipitation minus potential evapotranspiration (PET, Thornthwaite definition) for 6 months with the long-term distribution (reference period: 1971-2010) for the same location and accumulation period, as the number of standard deviations from the median"
PET (Potential Evapotranspiration): “Potential Evapotranspiration (PET) is the rate at which evapotranspiration would occur under ambient conditions from a uniformly vegetated area when the water supply is not limiting. The Thornthwaite (TW) version uses air temperature and latitude from meteorological observations to estimate radiation (Thornthwaite, 1948; An Approach toward a Rational Classification of Climate on JSTOR)”
IMPLEMENTATION: Python xclim using monthly precipitation and PET as input (PET is computed following the Thornthwaite version using tasmin and tasmax as input).
Note that part of this information (in particular the definition of SPEI, and note that there is an error with the method used, which is Thornthwaite in the first version –this will be corrected also in the first update of the Atlas–) is included in the information tool “I” of the Atlas, next to the title of the displayed figure.
Best regards and nice to talk to you through this forum.