Technical documentation: CMIP5 standardized precipitation evapotranspiration index (SPEI)

On this page

• Overview
• Data and processing
  • Multi-model data
  • Bias correction and observational target
  • SPEI parameters and calibration
    • Potential evapotranspiration estimates
    • Probability distribution
    • SPEI time scales
• Equal model weighting
• Model range through the use of ensemble percentiles
• Best practice
• Interpreting SPEI results
• Use limitation
• Contact information
• References

Overview

Standardized Precipitation Evapotranspiration Index (SPEI) calculated using global climate model projections from the Coupled Model Intercomparison Project Phase 5 (CMIP5) are provided. SPEI is a multiscalar index frequently used to quantify drought and is based on a climate water balance. As opposed to some existing indices of climatological drought, SPEI incorporates multiple climatological factors including precipitation and temperature, which is imperative for assessing the influence of climate change on drought (Vicente-Serrano, Begueria, and Lopez-Moreno, 2010^{Footnote 1}).

Multi-model SPEI datasets for historical simulations and three emission scenarios, RCP2.6, RCP4.5 and RCP8.5, are available at a 1x1 degree grid resolution. Both multi-model ensembles and individual model SPEI output are available for download.

The projected SPEI using the present approach should be interpreted as a relative measure of surface water surplus (for positive values) or deficit (negative SPEI values) with respect to hydroclimate of the reference period. Specifically, SPEI at a location gives the number of standard deviations from which the transformed precipitation (P) − potential evapotranspiration  (PET) departs from mean values over the reference period.

Projections among climate models can vary because of differences in their underlying representation of earth system processes. Thus, the use of a multi-model ensemble approach has been demonstrated in recent scientific literature to likely provide better projected climate change information.

Please also see Tam et al. (2023)^{Footnote 2} for further details of SPEI calculation and analysis.

Data and processing

Multi-model data

An ensemble of 29 models was used for SPEI analysis to allow some quantification of projection uncertainty (Tam et al. 2019) ^{Footnote 3} .

Bias correction and observational target

A multivariate bias correction (MBC) algorithm that corrects marginal distributions and Pearson correlation dependence structure (MBCp) were applied on all GCM data (minimum and maximum temperature and precipitation) prior to SPEI calculation (Cannon 2016^{Footnote 4}).

Monthly gridded minimum and maximum temperature and precipitation data, i.e. the Canadian Gridded Dataset (CANGRD) – a gridded climate dataset based on interpolated data from Adjusted and Homogenized Canadian Climate Data (AHCCD) (Vincent et al. 2015^{Footnote 5}) – was used as the observational target over the reference period of 1950–2005.

Bias correction was applied to the full time period of each GCM simulation (1900–2100).

SPEI parameters and calibration

Potential evapotranspiration estimates
The modified Hargreaves method was used to calculate PET. The original Hargreaves method was modified by Droogers and Allen (2002)^{Footnote 6} to include a precipitation variable and to require only monthly data input. Droogers and Allen (2002)^{Footnote 6} found that the results based on the modified approach were comparable to those obtained by the Penman–Monteith formulation. See Droogers and Allen (2002)^{Footnote 6} for full details.

Probability distribution
For SPEI, water balance is transformed into a standard normal variable based on an equi-probability transformation. Vicente-Serrano et al. (2010) ^{Footnote 1} recommends using the three-parameter log-logistic, also known as generalized logistic (GLO), as the probability distribution to fit water balance to yield SPEI values. While GLO is a valid probability distribution for fitting water balance values, Tam et al. (2023) ^{Footnote 2} recommends using Pearson Type 3 (PE3) or generalized extreme value (GEV) distributions for SPEI studies in Canada.

SPEI datasets fitted with GLO and PE3 are therefore available for download. In terms of estimating distribution parameters, an unbiased probability weighted moments (PWM) method was used.

Since the CMIP5 historical simulations end at 2005, 1950–2005 was selected as the reference period for fitting the probability distributions and parameter estimation. These parameters were then applied to the full time series.

SPEI time scales
SPEI was calculated for time scales of 1, 3 and 12 months (also referred to as SPEI-1, SPEI-3 and SPEI-12, respectively). SPEI-24 is also available for the SPEI dataset fitted with Pearson Type 3. SPEI-3 corresponds to SPEI of one month and the previous 2 months, while SPEI-12 corresponds to SPEI of one month and the previous 11 months. The occurrence of multi-year droughts may be assessed from the SPEI-12 results.

For SPEI-3 and SPEI-12, an unshifted rectangular kernel (i.e. equal weighting for previous n time steps) was applied.

Equal model weighting

The different CMIP5 models used for the projections are all considered to give equally likely projections in the sense of 'one model, one vote'. Models with variations in physical parameterization schemes are treated as distinct models.

Model range through the use of ensemble percentiles

As local projections of climate change are uncertain, a measure of the range of model projections is provided (i.e., 25th and 75th) in addition to the median response (50th percentile) of the model ensemble interpolated to a common 1x1 degree grid. For more information on managing uncertainty in climate projections.

It should again be emphasized that this range does not represent the full uncertainty in the projection. The distribution combines the effects of natural variability and model spread.

Best practice

Given the range of natural climate variability and uncertainties regarding future greenhouse gas emission pathways and climate response, SPEI projected by one climate model should not be used in isolation. Rather, it is good practice to consider a range of projections from multiple climate models (ensembles) and emission scenarios.

While likelihoods are not associated with particular climate change scenarios, the use of a range of scenarios may help convey to users the potential spread across a range of possible emission pathways.

Interpreting SPEI results

Projected changes in SPEI in Canada under various forcing scenarios are presented. SPEI results should be interpreted as a relative measure of surface water surplus or deficit with respect to hydroclimate conditions of the reference period, 1950–2005. Thus, results of surface water deficit may be interpreted as dryness or, in other words, an indicator of drought conditions. Further, SPEI at a location gives the number of standard deviations by which the transformed P-PET is deviated from the mean values assessed for the reference period. As SPEI is a normalized index, an SPEI value of zero would indicate no change relative to historical values. The results presented herein are aimed at informing assessments of drought based on relative changes to SPEI with respect to observed conditions.

Further, a range of drought indices have been developed over the years to understand climatological drought, varying from each other in theoretical methodology, application and formulation. SPEI is one of many indices to quantify drought. Each index has its own utilities; the choice of an index to quantify drought would therefore depend on context or application as well as data availability. SPEI serves as a reasonable metric for meteorological or climatological drought conditions, but it should be noted that index may not be adequate for gauging surface water availability of cold regions, including most parts of Canada. This is because the formulations of the aforementioned indices do not take into account snow and glaciers, which play a critical role in governing the supply and availability of surface water of such regions.

Use limitation

Multi-model ensembles made available through Environment and Climate Change Canada websites are provided under the Open Government Licence - Canada.

In addition to these terms and conditions, individual model datasets are subject to the terms of use of the source organization.

Contact information

Email: f.ccds.info-info.dscc.f@ec.gc.ca