Drought Indices
A recipe for computing SPEI
SPEI is based on a standardization of a simplified water balance for the climatology of a particular location. In this sense it would be good to associate some global reanalysis product/gridded product to be able to calculate this index everywhere, disregarding the user's data availability.
For a given point calculate monthly precipitation (P) and monthly potential evapotranspiration (PET) followed by the simplified water balance:
Di = Pi - PETi
Create several time series with different averaging windows based on the user's request (one month, 3 months, 6 months, 12 months, 24 months). These are the different time scales defined by the user considering her local conditions. The reference month for each window is the final month e.g. the water balance deficit of scale 6 for July 1990 is calculated with February-July data (could also be calculate with the expression in page 1702 of Begueria's paper).
A cdf will be later fitted to this time series.
Reference PET can be calculated with Penman-Monteith, Hargreaves of Thorthwaite equation. A good start is to use Hargreaves as in page 51 of this paper's supplement as it does not require too many input variables. The choice of PET method is not decisive on the final result. Hargreaves will need:
- monthly averages of daily maximum temperature
- monthly averages of daily minimum temperature
- monthly mean temperature
- extraterrestrial radiation
- latent heat of vaporization (2.45 MJ kg-1 at 20° C and normal pressure)
NB! maybe there is already a built-in function for fittig log-logistic in matlab!
We use the l-moments in order to fit the log-logistic distribution. The determination of the probability weighted moments (PWMs) is very clear (from page 1702 and following of Begueria's paper):
The log-logistic pdf is given by:
The parameters of the log-logistic are based on the probability weighted moments determined earlier:
Finally SPEI is given by the expression:
F(x) is the cdf of the log-logistic:
