How to evaluate the trend of Standardized Precipitation Evapotranspiration Index (SPEI) in a specific class of drought risk?

We present the code used for the computation of SPEI time series at a global scale as well as that for the trend analysis. The part of the code regarding the SPEI computation starts from that proposed by (Beguería et al. 2014) and it is based similarly on the precipitation and evapotranspiration time series of the CRU dataset (Harris et al. 2014). It differs from that released by (Beguería 2017): 1) because it is based on the raster (Hijmans 2018) instead of ncdf4 R package and 2) it is possible to set the time window for the reference period to be used in the parameter estimation phase. The SPEI dataset resulting from our computation is comparable in principle with the SPEI global database released by (Beguería et al. 2014), however, the comparison is not feasible since the code released by these authors does not allow to set reference period and, moreover it seems to contain a bug in the part regarding the expansion of potential evapotranspiration from the mm/day scale to mm/month.

The trend test for the different classes of drought risk is based on the Poisson process. In fact, when a truncation level is imposed, a time series of climatological extreme phenomena become counting processes. Generally, the arrival rate of events of a counting process follows a Poisson distribution and, furthermore, if the arrival rate does not remain constant through time, then it follows a nonhomogeneous Poisson process (Nhpp). We consider the use of a special case of Nhpp's: the power law process defined in (Crow 1974). The power law approach suggests the use of the \chi^2 test for time-trend analysis.

We use R software (R Core Team 2018), and SPEI (Beguería and Vicente-Serrano 2017) package for SPEI calculation. We use the modifiedmk R package for the computation of Mann-Kendall test significance and of the trend Sen's slope (Patakamuri and O’Brien 2019).

Please, cite this work as .

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Needed directories

You should have 3 subdirectories of the main one, that is where you put the sources: * Data (where to download CRU data) * Outputs * Plots

The Sequence of scripts to be launched:

1. DroughtIndexGenerator.sh (parent)
   • look for the last CRU version among those in /Data then launch the childs DryMask.sh and *.R to compute SPI and SPEI for each grid cell (the outputs is a NetCDF file)
   • the default SPEI time scales are set to 3,4,6,12,24, if needed change them in CRU_SPEI_calculation.R file
   • needed functions are in TrendFunctions.R

• DryMask.sh (child) set to NA the whole values of time series where yearly average precipitation is lesser than 73 mm (0.2mm per day by 365 days) to guarantee the presence of missing values in the SPEI computation

2. DroughtTrendTest-Generator.sh (parent) (ONLY FOR SPEI)

• check in /Outputs/../ if time series of SPEI have been generated
• launch CRU_SPEI_TrendAnalysis.R to compute the trend analysis
• the outputs is a NetCDF file composed of 4 layers (Nhpp, MK, MK-classic, Difference Nhpp-MK), each one having -1, 0, +1 values. Notice that an increasing trend of drought events is marked by -1 fo M-K whilst 1 for Nhpp.
• another output is composed of the maps of the trend results (in /Plots)

WARNING: if using an UBUNTU machine, one should follow these steps:

1. include ./ in the PATH
2. add the bash command to call for the correspondent shell before the file name: e.g. nohup bash DroughtIndexGenerator.sh &

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REFERENCES

Beguería, Santiago. 2017. “Sbegueria/SPEIbase: Version 2.5.1,” July. doi:10.5281/zenodo.834462.

Beguería, Santiago, and Sergio M. Vicente-Serrano. 2017. SPEI: Calculation of the Standardised Precipitation-Evapotranspiration Index.

Beguería, Santiago, Sergio M. Vicente-Serrano, Fergus Reig, and Borja Latorre. 2014. “Standardized Precipitation Evapotranspiration Index (SPEI) Revisited: Parameter Fitting, Evapotranspiration Models, Tools, Datasets and Drought Monitoring.” International Journal of Climatology 34 (10): 3001–23. doi:10.1002/joc.3887.

Crow, Larry H. 1974. “Reliability Analysis for Complex, Repairable Systems.” In Reliability and Biometry, edited by F. Proschan and R. G. Serfling, 379–410. SIAM.

Harris, I., P. D. Jones, T. J. Osborn, and D. H. Lister. 2014. “Updated High-Resolution Grids of Monthly Climatic Observations the CRU TS3.10 Dataset.” International Journal of Climatology 34 (3): 623–42. doi:10.1002/joc.3711.

Hijmans, Robert J. 2018. Raster: Geographic Data Analysis and Modeling.

Patakamuri, Sandeep Kumar, and Nicole O’Brien. 2019. Modifiedmk: Modified Versions of Mann Kendall and Spearman’s Rho Trend Tests.

R Core Team. 2018. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.