Development of drought monitoring and analysis procedures has become an essential task, and increased research attention has been focused on this area. However, drought monitoring does not follow an exact procedure (Svoboda and Fuchs 2016; Mannocchi et al. 2005; Hayes 2000; Edwards 1997). Examining and elaborating the details and differences of various procedures can help improve our gained knowledge from drought analysis.
In this paper, the 3-month Jan SPI was calculated for Al-Mafraq governorate in Northern Jordan, using both the fixed mean and extending mean methods, and the resulting time series were compared (Table 2).
Table 2
Drought intensities for Al-Mafraq determined using calculation of SPI by Moving Mean and Fixed Mean methods
Time Series
|
Extending Mean method
|
Fixed Mean method
|
SPI value
|
Drought Category
|
SPI value
|
Drought Category
|
Jan 2011
|
-1.44
|
Moderate drought *
|
-1.56
|
Severe drought *
|
Jan 2012
|
0.68
|
Near Normal
|
0.67
|
Near Normal
|
Jan 2013
|
0.85
|
Near Normal
|
0.86
|
Near Normal
|
Jan 2014
|
-0.42
|
Near Normal
|
-0.43
|
Near Normal
|
Jan 2015
|
0.98
|
Near Normal
|
0.99
|
Near Normal
|
Jan 2016
|
0.09
|
Near Normal
|
0.09
|
Near Normal
|
Jan 2017
|
0.83
|
Near Normal
|
0.83
|
Near Normal
|
Jan 2018
|
-0.77
|
Near Normal
|
-0.77
|
Near Normal
|
Jan 2019
|
-0.52
|
Near Normal
|
-0.52
|
Near Normal
|
*different drought category obtained |
[Table 2]
The mean absolute error between SPI values produced was about 2%, which is not considerable by any measure, but it happens that the first time window in the record (Jan 2011) had different drought categories despite the small difference, this is in part due to the nature of how we assign drought categories for different SPI ranges (Table 1), and because the parameters calculated were not necessarily stable due to limited record available. Researchers may use different category ranges; for example, Bartczak et al. (2014) used a wide range of SPI (-1–1) to indicate near normal conditions, while Adnan et al. (2015) used narrower ranges of intensities (-0.5–0, 0–0.5, etc.) to differentiate between drought categories.
It is not suggested that one method is more accurate, as it is stated that calculation of the SPI does not follow an exact equation or formula, but it is “more of a process” (Hayes 2000; Edwards 1997), and researchers may develop or test different methods to quantify drought or calculate the SPI or characterize its distribution (Bartczak et al. 2014; Guttman 1999). However, we should have some understanding of how different drought analysis or communication approaches may result in differences. This is particularly true if an extending mean or a fixed mean method was selected by accident. If a meteorologist or a web app was monitoring and recording SPI for different time scales every year in real time, and documenting these values in a fixed archive, then every SPI value in such a record could be only based on the long-term mean (x̄) of its previous time, such that α and β may change for every subsequent time window (Fig. 2).
[FIGURE 2]
Meanwhile, a researcher interested in determining historical drought intensities in a given location may be inclined to calculate α and β only once for an entire precipitation time series and then determine all the SPI values based on those parameters (Fig. 3).
[FIGURE 3]
Of course, these concerns would be negligible for a researcher with an abundance of historical records (for example over 70 years of monthly data for all stations of interest), as the parameters would be somewhat stable either way (Svoboda et al. 2012; Hayes 2000; Guttman 1999), but researchers, hydrologists, or web applications with less than 40 years of times series may not have this luxury. Furthermore, when relying on satellite products in regions with no meteorological stations or sufficient coverage (Al-Kilani et al. 2021; Boluwade 2020; Zhao et al. 2018), the provided time series of precipitation may change its source over time (e.g. shifting satellite products due to expiration or other technical aspects), the NASA-POWER platform is one such example; shifting its source from GPCP to MERRA-2 recently. In such instances, the stability of the parameters would be in question, not only because of the possibility of shifting sources but due to relatively short coverage by many satellite products (Bai et al. 2020; Boluwade 2020). This shouldn’t mean that these data sources are worthless for drought analysis, but that procedures of data analysis should be more discussed and elaborated.
The same concept can be applied to many other distribution functions and their corresponding parameters that can be used to calculate the SPI, since they all require identifying the extent of the time series to identify the long term mean; such distributions can be found in Soľáková et al. (2014). The same concept can be also considered for calculating other drought indices such as the Standardized Precipitation Evapotranspiration Index (SPEI), which is an adjustment to the SPI devised by Vicente-Serrano et al. (2010), and considers the deviation of the water balance from a long term average.
One of the very common methods for calculating SPI and SPEI is the use of software packages such as the SPEI package in R studio (Silva et al. 2022; Mirgol et al. 2021), which strictly follows a fixed mean method. And so, the user should be cautioned on the reliability of drought intensities for years early in the record, as these will be relative to meteorological conditions of the subsequent years and not their own historical ranges. This may be a concern for applications such as drought impact analysis in hydrology, agriculture, socioeconomic, or other aspects in which we are examining the response of an aspect (e.g. crop productivity) to drought intensity, which is more likely to be related to adaptability or previous conditions and not to conditions in the future from its period (Budak et al. 2013; Zhang et al. 2009).