About SPEI

Overview

The Standardized Precipitation Evapotranspiration Index (SPEI)¹ is a drought index which measures the difference between precipitation (P) and potential evapotranspiration (PET), i.e., the water loss from evaporation and vegetation combined. SPEI speaks only to relative drought, i.e., the difference between future and historical conditions, and is not an absolute measure of water availability. Negative (positive) values indicate water deficit (surplus), while zero indicates no change relative to historical conditions.

CMIP5 SPEI Projections

The CMIP5 SPEI projections² on ClimateData.ca are from a 29-member climate model ensemble and are provided at 1° x 1° (100x100km) resolution for three emissions scenarios, RCPs 2.6, 4.5 and 8.5 for 1950-2100. Projections are provided in summarized format using the 10th, 50th (median) and 90th percentiles. Prior to calculating SPEI,  monthly mean maximum and minimum temperature and monthly total precipitation data were bias-adjusted and downscaled using the multivariate MBCn method with the CanGRD dataset as the target. See below for more details and an example of interpretation:

• SPEI is available here as a three month (SPEI-3) or twelve month (SPEI-12) drought index, labeled by the final month of the period.

• SPEI is presented as a standard deviation from a reference baseline period (1950-2005) Interpretation is important (see example below)

Technical Details and Interpretation

At the core of the calculation of the SPEI is the simple climate water balance equation, precipitation (P) minus potential evapotranspiration (PET):

 D = P – PET 

This can be calculated over various time scales, e.g., over 3 months, 6 months, a year etc., and SPEI accumulates the difference (D) over the time scale in question. So, for example, if we are interested in seasonal (i.e., 3-month) SPEI, a time series is constructed by summing the D values from two months before to the current month. For summer SPEI, this would mean totalling June, July and August values.

However, there are strong spatial and temporal differences in precipitation amount and potential evapotranspiration, so to obtain an SPEI series which can be compared across space and time, the D series are transformed into standardized units. This is done by fitting the D values to a probability distribution for the time scale under consideration (e.g., 3 or 6 months), over a reference historical time period, e.g., 1950-2005. SPEI values are then obtained as standardized values with a mean of zero and standard deviation of 1. This means that the values correspond to a standard normal distribution which can be used to aid their interpretation (Table 1). These standardized values have been used to classify the SPEI values into general water surplus/deficit categories as shown in Table 2:

Example SPEI interpretation

Table 3 shows some sample CMIP5 SPEI values for a location in Canada. The three percentile values represent the range (10^th and 90^th percentiles) and median (50^th percentile) of the future projections for each emissions scenario (RCP) and time period. Table 4 indicates how these values can be interpreted. For example, the 10th percentile SPEI value for the 2041-2070 summer season for the moderate emissions scenario, RCP 4.5, is -1.00, i.e., one standard deviation below the average value. This indicates moderate dry conditions compared to the 1950-2005 historical reference period. If we look at Table 1, we can see that -1.00 corresponds to about 85% of the values being greater than this amount. This can be interpreted as shown in Table 4, “the average summer [in 2041-2070] could be drier than about 85% of summers in the historical reference period”. The median value for the same emissions scenario and future time period is -0.51, so roughly -0.5. Again looking at Table 1, we can see that in this case about 70% of the values are greater than -0.5, and interpreted as “the average summer could be drier than about 70% of summers in the past” (Table 4).