Standardized Precipitation-Evapotranspiration Index (SPEI)#

Overview#

Droughts can be separated into three main types: meteorological, hydrological, and agricultural drought. Common for all types is that a drought needs to be put in context of local and seasonal characteristics, i.e. a drought should not be defined with an absolute threshold, but as an anomalous condition.

Meteorological droughts are often described using the Standardized Precipitation Index (SPI; McKee et al., 1993), which in a standardized way describes local precipitation anomalies. It is calculated on monthly mean precipitation, and is therefore not accounting for the intensity of precipitation and the runoff process. Because SPI does not account for evaporation from the ground, it lacks one component of the water fluxes at the surface and is therefore not compatible with the concept of hydrological droughts.

A hydrological drought occurs when low water supply becomes evident, especially in streams, reservoirs, and groundwater levels, usually after extended periods of meteorological drought.

ESMs normally do not simulate hydrological processes in sufficient detail to give deeper insights into hydrological drought processes. Neither do they properly describe agricultural droughts, when crops become affected by the hydrological drought. However, hydrological drought can be estimated by accounting for evapotranspiration, and thereby estimate the surface retention of water. The standardized precipitation-evapotranspiration index (SPEI; Vicente-Serrano et al., 2010) has been developed to also account for temperature effects on the surface water fluxes. To consider evapotranspiration and plant water stress, potential evapotranspiration (PET) is calculated based on atmospheric variables. Different methods to derive PET are described below.

This page documents a set of R diagnostics based on the SPEI.R library. recipes/roughts/recipe_spei.yml is an example how to calculate and plot SPEI using diag_scripts/droughts/pet.R and diag_scripts/droughts/spei.R.

pet.R#

The potential evapotranspiration (PET) is a measure of the evaporative demand of the atmosphere. It represents the amount of water that would evaporate from a reference surface, i.e. fully watered grass land. pet.R is able to calculate PET based on a method of the users choosing (pet_type) using the SPEI.R library. The approximations require different input variables. To control which variables are available to which diagnostic script in a more complex recipe, they can be set explicitly as ancestors.

  • Thornthwaite: tas

  • Hargreaves: tasmin, tasmax, (rsdt, pr)

  • Penman: tasmin, tasmax, sfcWind, ps, rsds, (rsdt, clt, hurs)

The Thornthwaite equation (Thornthwaite, 1948) is the simplest one based solely on temperature. Hargreaves (1994) provides an equation based on daily minimum (tasmin) and maximum temperature (tasmax) and external radiation (rsdt). If precipitation data (pr) is provided and use_pr: TRUE it will be used as a proxy for irradiation to correct PET following Droogers and Allen (2002). The Penman-Monteith formula additionally considers surface windspeed (sfcWind), pressure (ps), and relative humidity (hurs). Some of these variables can be approximated if not available (for example by providing clt instead of rsds). There are further modifications to the Penman-Monteith equation, that can be selected using the method key for pet_type: Penman. Details about the different methods can be found in the SPEI.R package documentation (Beguería and Vicente-Serrano, 2011).

User settings#

pet_type: str

The method used to calculate the potential evapotranspiration. Some settings and required variables depend on the calculation method. Options are: Penman, Thornthwaite, Hargreaves

use_pr: boolean, optional

Use precipitation as proxy for irradation to correct PET. Only used for pet_type: Hargreaves. By default FALSE.

method: str, optional

Method used for PET calculation. Only used for pet_type: Penman. Options are: "ICID" (Allen et al., 1994), "FAO" (Allen et al., 1998), "ASCE" (Walter et al. 2002). By default: "ICID".

crop: str, optional

Crop type for PET calculation. Only used for pet_type: Penman. Options are: "short", "tall". By default: "tall".

spei.R#

The Standardized Precipitation-Evapotranspiration Index (SPEI) is calculated by fitting a probability distribution to the accumulated water budget (pr-PET) for each grid cell and month of the year. The accumulation period is configurable using the smooth_month setting. The PDF is transformed to a normal distribution. Based on given percentiles, index values from -2 (extreme droughts) to 2 (extreme wet spells) are assigned. The distribution used to fit the water budget can be configured through the distribution setting. The required PET can be provided by setting the pet.R diagnostic as an ancestor or adding an evspsblpot variable. To use alternative variables (i.e. actual evapotranspiration) change the short_name setting accordingly.

SPI is considered as a special case of the SPEI. Provide only precipitation as input variable or ancestor and set distribution="Gamma", to calculate SPI.

User settings#

smooth_month: int

The number of months (scale) to accumulate. Common choices are 3, 6, 9, 12.

write_coeffs: boolean, optional

Save fitting coefficients. By default FALSE.

write_wb: boolean, optional

Write water balance to netcdf file. By default FALSE.

short_name_pet: string, optional

Short name of the variable to use as PET. By default "evspsblpot".

distributionn: string, optional

Type of distribution used for SPEI calibration. Possible options are: “Gamma”, “log-Logistic”, “Pearson III”. By default "log-Logistic".

refstart_year: int, optional

First year of the reference period. By default null (first year of time series).

refstart_month: int, optional

First month of reference period. By default 1.

refend_year: int, optional

Last year of the reference period. By default null (last year of time series).

refend_month: integer, optional

Last month of reference period. By default 12.

References#

  • Allen, R. G., Pereira, L. S., Raes, D., and Smith, M.: Crop Evapotranspiration Guidelines for Computing Crop Water Requirements, no. 56 in FAO Irrigation and Drainage Paper, Food and Agriculture Organization of the United Nations, Rome, 1998.

  • Allen, Richard. G., Smith, M., Perrier, A. and P., Luis S., & others. (1994). An update for thedefinition of reference evapotranspiration. ICID Bulletin, 43(2), 1-34.

  • Beguería, S., & Vicente-Serrano, S. M. (2011). SPEI: Calculation of the Standardized Precipitation-Evapotranspiration Index (p. 1.8.1) [Dataset]. https://doi.org/10.32614/CRAN.package.SPEI

  • Droogers P., Allen R. G., (2002). Estimating reference evapotranspiration under inaccurate data conditions. Irrigation and Drainage Systems 16: 33-45.

  • Hargreaves G.H., (1994). Defining and using reference evapotranspiration. Journal of Irrigation and Drainage Engineering 120: 1132-1139.

  • McKee, T. B., Doesken, N. J., & Kleist, J. (1993). The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology (Vol. 17, No. 22, pp. 179-183). Boston, MA: American Meteorological Society.

  • Monteith, J.L., 1965. Evaporation and Environment. 19th Symposia of the Society for Experimental Biology, University Press, Cambridge, 19:205-234.

  • Thornthwaite, C. W., (1948). An approach toward a rational classification of climate. Geogr. Rev., 38, 55-94. https://doi.org/10.1097/00010694-194807000-00007

  • Vicente-Serrano, S. M., Beguería, S., & López-Moreno, J. I. (2010). A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. Journal of climate, 23(7), 1696-1718.

  • Walter I.A. and 14 co-authors, 2002. The ASCE standardized reference evapotranspiration equation. Rep. Task Com. on Standardized Reference Evapotranspiration July 9, 2002, EWRI-Am. Soc. Civil Engr., Reston, VA, 57 pp.

Example plots#

Note

To recreate figure 3 and 4 from Weigel et al. (2021) an older version of ESMValTool is required: Legacy Recipe: Standardized Precipitation-Evapotranspiration Index (SPEI).

../../_images/spi_example.png

Fig. 149 Example plot of SPI averaged over the year 2005. The reference period for index calibration is 2000-2005.#

../../_images/spei_example.png

Fig. 150 Example plot of SPEI averaged over the year 2005. The reference period for index calibration is 2000-2005.#