Standardized Precipitation Index (SPI)
The SPI is calculated according to Edwards and McKee (1997) using the Gamma Distribution with maximum likelihood as shown in Guenang and Kamga (2014).
The fit parameters for the distribution are determined using the estimation defined in Thom (1958).
The cumulative distribution is calculated using the Python SciPy package Gamma CDF function, which uses the same integration process found in MATLAB.
The distribution is standardized according to Abramowitz and Stegun (1965) and limited to the range of -3.0 to 3.0
The grid size for the SPI is 1/24° x 1/24° (4km x 4km).
The SPI data are calculated by the National Drought Mitigation Center.
Standardized Precipitation Evapotranspiration Index (SPEI)
The SPEI is calculated according to Vincente-Serrano and Begueria (2010, 2014) using the 3-parameter Log Logistic Distribution (LLD3) with unbiased probability weighted moments.
The PWMs and L-Moments are calculated according to the methods described in Greenwood et al. (1979) and Hosking (1990).
The fit parameters and cumulative distribution are determined using methods described in Hosking (1990, 1997) following Hosking’s FORTRAN routines.
Code for the distribution process was verified using the R-language “lmomco” package and the following functions:
The distribution is standardized according to Abramowitz and Stegun (1965) and limited to the range of -3.0 to 3.0
The grid size for the SPEI is 1/24° x 1/24° (4km x 4km).
The SPEI data are calculated by the National Drought Mitigation Center.
References
- Abramowitz, M. and I.A. Stegun, 1965: Handbook of Mathematical Functions. Dover Publications, New York.
- Beguería, S., Vicente-Serrano, S.M., Fergus Reig, Borja Latorre. Standardized Precipitation Evapotranspiration Index (SPEI) revisited (2014): parameter fitting, evapotranspiration models, kernel weighting, tools, datasets and drought monitoring. International Journal of Climatology, 3 4: 3001-3023.
- McKee, T. B., Doesken, N. J. and j. Kleist, 1993: The Relationship of Drought Frequency and Duration to TIme Scales, Eighth Conference on Applied Climatology, 17–22 January 1993, Anaheim, California [Available online at https://climate.colostate.edu/pdfs/relationshipofdroughtfrequency.pdf.]
- Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979, Probability weighted moments—Definition and relation to parameters of several distributions expressable in inverse form: Water Resources Research, v. 15, pp. 1,049–1,054.
- Guenang, G. M., & Kamga, F. M. (2014). Computation of the Standardized Precipitation Index (SPI) and Its Use to Assess Drought Occurrences in Cameroon over Recent Decades, Journal of Applied Meteorology and Climatology, 53(10), 2310-2324.
- Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.
- Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.
- Thom, H. C. S., 1958: A note on the gamma distribution. Mon. Wea. Rev., 86, 117–122.
- Vicente-Serrano S.M., Santiago Beguería, Juan I. López-Moreno, (2010) A Multi-scalar drought index sensitive to global warming: The Standardized Precipitation Evapotranspiration Index - SPEI. Journal of Climate 23: 1696-1718.
Funding