The Standardized Precipitation Drought Evapotranspiration Index (SPEI) requires a Di term of the difference between precipitation and potential evapotranspiration (PET) on a weekly or monthly basis. I have Di for my 17-year time series, where each day of the time series represents ~1,000,000 30x30 meter squares in a city.
The formula for SPEI is attached and is straightforward. This should be easy to calculate in Matlab. W is -2ln(P), and P is 1-F(x). I don't understand how to calculate F(x). I read that to calculate F(x) I could fit the log-logistic distribution to the Di time series, but when I tried in Matlab this didn't work due to negative values (which are common since Di is Precipitation-PET).
Since the whole purpose of the math I attached is to standardize Di, would it be appropriate for me to detrend the time series and then to find the z-score? I could do that very quickly.
Any input on how to calculate F(x) would be appreciated.
http://spei.csic.es/home.html
In quantifying the SPEI is needed to used a three parameter distribution, since in two
parameter distributions the variable (x) has a lower boundary of zero (0> x x
Dear Dion,
I have just came accross this R package called "SPEI" at https://cran.r-project.org/web/packages/SPEI/SPEI.pdf by S.M. Vicente-Serrano, S. Beguería, J.I. López-Moreno. 2010. A Multi-scalar drought index sensitive to global warming: The Standardized Precipitation Evapotranspiration Index – SPEI. Journal of Climate 23: 1696, DOI: 10.1175/2009JCLI2909.1.
I hope it will be helpful.
For the rest of people looking into the SPEI calculation, the methodology for the log-logistic distribution calculation can be found in this article: Article SPEI-Based Spatiotemporal Analysis of Drought in Haihe River...
This manuscripts mentions how to estimate alpha, beta and gamma parameters from the distribution using probability-weighted moments.
The other alternative is to use the gamma distribution as in spi. However, an offset needs to be set to make your values positive as it can be seen when studying the code of climate_indices using python, in which the authors just add 1000 to the subtraction between rainfal and ETr:
https://github.com/monocongo/climate_indices/blob/master/climate_indices/indices.py
Hi
Why we calculate difference between precipitation and potential evapotranspiration?
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