Standardized precipitation evapotranspiration index (SPEI) for Canada: assessment of probability distributions

Candidate probability distributions for the Standardized Precipitation Evapotranspiration Index (SPEI) for Canada were examined using the Canadian Gridded (CANGRD) temperature and precipitation dataset and CMIP5 projections. The probability distribution is a core component to the calculation of standardized values. For SPEI, a continuous probability distribution is fitted to the water balance time series so that the resulting transformed index follows a standard normal distribution. Selection of an appropriate distribution is therefore important as an inappropriate distribution may lead to biased values and subsequently affect the interpretation of SPEI results. Candidate distributions considered for SPEI included the generalized logistic (GLO), generalized extreme value (GEV), Pearson Type III (PE3) and normal (NOR) distributions. A range of goodness of fit tests were used to assess how well the distributions fit SPEI. Differences in CANGRD SPEI time series between three pairs of distributions, GLO-GEV, GLO-PE3, and GEV-PE3, showed that there were larger differences in SPEI values between GLO and the other two distributions than the difference between GEV and PE3. SPEI results fitted with GLO resulted in lower threshold exceedances of extreme SPEI (-/+2) than GEV and GLO. A comparison between CMIP5 SPEI values fitted with GLO (SPEI-GLO) and PE3 (SPEI-PE3) showed that there were seasonal and spatial variations in results, although the use of multi-model ensembles reduced these differences. As was the case for CMIP5 SPEI-GLO projections, projected annual changes in CMIP5 SPEI-PE3 show an increase in drying at the surface in central/southern Canada. Overall, the study recommends using PE3 or GEV for SPEI analysis for Canada.