https://orcid.org/0000-0002-2735-0778
Abstract
In this study, the power of 12 of the most widely used meteorological drought indices was compared. For this purpose, the datasets of 12 stations (from 1967 to 2021) with different climatic conditions in Iran were used. For statistical analysis, multiple linear regression based on the relative importance metric introduced by the Lindeman, Merenda, Gold (MLR-LMG) and data visualization (DV) models were used. In the temporal assessment, the relative importance metrics (RIM) between the drought severity based on the different drought indices and the annual yield of rain-fed winter wheat (AYW) based on the fitted MLR-LMG model was investigated at the annual timescale in the chosen stations. In the spatial evaluation, the RIM between the drought severity based on the different drought indices and the AYW were investigated each year (1967, … , 2021). The results showed that in temporal assessment, the modified standardized precipitation evapotranspiration index (MSPEI) was the most suitable (58.33% of selected stations). Also, in spatial evaluation, the MSPEI and Z-score were the most efficient drought indices (65.45% and 27.27% of the years, respectively). The validation results of the fitted MLR-LMG models showed that the models were trustworthy in all stations and all years.
HIGHLIGHTS
In this study, 12 drought indicators were evaluated and compared.
New statistical models (multiple linear regression based on the relative importance metric introduced by the Lindeman, Merenda, Gold and DV models) were used for comparing drought indices.
The relationship between drought and annual yield of rain-fed winter wheat was assessed in temporal and spatial forms.
The research findings are applicable in any region with any climatic conditions.
Results help to select the best drought index for assessing drought conditions.
INTRODUCTION
Meteorological drought is an undesirable phenomenon that results from a lack of precipitation and can occur in any area, even in humid climates (Sahana et al. 2021; Qiu et al. 2023). This phenomenon has direct and indirect adverse impacts on different sectors such as agriculture, environment, industry, and wildlife (Band et al. 2022; Li et al. 2023; Zarei et al. 2023a). Of course, according to the nature and conditions of each sector, its effectiveness level is different (Minea et al. 2022). For example, the effect of meteorological drought on rural areas, where the livelihood and economy of families are generally more dependent on water, is more than in urban areas (Savari et al. 2022; Bahiru et al. 2023). It seems the economic and social effects of drought such as immigration (Melville-Rea 2022), poverty (Yazdi et al. 2022), lack of food and social security (Shahpari et al. 2022; Prall & Scelza 2023), unemployment (Drugova et al. 2022), health (Mehdipour et al. 2022), water crisis (Tomasella et al. 2022), and so on are the most important effects of drought on human life. Therefore, a more accurate assessment of the drought severity has a vital role in better understanding the level of the crisis (especially by the managers). During the past years, various drought indicators have been presented worldwide. The standardized precipitation evapotranspiration index (SPEI) (Vicente-Serrano et al. 2010), modified SPEI (MSPEI) (Zarei & Moghimi 2019; Zarei & Mahmoudi 2020), modified reconnaissance drought index (MRDI) (Tigkas et al. 2016), and modified standardized precipitation index (MSPI) (Tigkas et al. 2019) are some of these indices. Naturally, choosing the best indicator is very important in increasing the accuracy of assessments of the drought severity in each region.
Many studies have been done to compare different drought indices. Elhoussaoui et al. (2021) compared the power of several drought indices to assess drought conditions in the northwest of Algeria. They showed the capability of the deciles index (DI) and Z-score index for assessing drought conditions was more than that of other indices. Liu et al. (2021) evaluated the ability of eight drought indicators in China. The results of this study revealed that the drought severity index and evaporation stress index had the more appropriate ability. Zarei et al. (2023a) compared six drought indices, including reconnaissance drought index (RDI), MRDI, standardized precipitation index (SPI), MSPI, SPEI, and MSPEI, to choose the best index for evaluating agricultural drought. This study was conducted using the datasets of ten stations in Iran on one-, three-, six- and 12-month timescales. They showed that the MSPEI and SPEI have a more suitable performance for evaluating agricultural drought. Javed et al. (2021) compared the ability of four drought indices in assessing agricultural drought in China. This study indicated that the performance of the multivariate standardized drought index to evaluate drought conditions was better than that of other indices. Askarimarnani et al. (2021) assessed the capability of 11 drought indices in three time periods during 1900–2018 in Australia. This research revealed that different indices (especially those that are only based on rainfall such as SPI) present different outputs about the duration, severity, frequency, start time, and end time of the drought. Senatilleke et al. (2023) in Sri Lanka, Zarei et al. (2023b) in Iran, Shyrokaya et al. (2022) in Central Europe, Zhang et al. (2022) in China, Araneda-Cabrera et al. (2021) in Mozambique, and Zarei et al. (2021) in Iran are some of the other studies related to the comparison of drought indices.
On the other hand, various studies worldwide have proved the direct and indirect impact of drought on the performance of agricultural products (especially wheat). Yu et al. (2018) assessed the effect of drought on annual yield of rain-fed winter wheat (AYW) in eastern China using the datasets of five provinces from 2001 to 2016. This study indicated that drought occurrence has a meaningful impact on AYW. Ray et al. (2018) assessed the effect of drought on rain-fed and irrigated crop production in Texas. They showed that drought has a significant effect on crop yield. Also, the impact of drought on reducing the yield of winter wheat was more than on the yield of corn, cotton, and sorghum. Hlavinka et al. (2009) evaluated the impact of drought events on the yield of eight crops in 77 regions in the Czech Republic. This study proved that the occurrence of severe droughts has adverse effects on crop yield (even in areas with humid climate conditions). Mokhtar et al. (2022) in China, Oleksiak et al. (2022) in Poland, and Schmitt et al. (2022) in Germany are some of the other studies that proved the effect of drought on AYW.
Finally, due to the adverse impacts of drought on various sectors as well as the vital role of selecting the appropriate drought index in controlling and reducing its adverse effects, the objective of this research is to compare the ability of 12 meteorological drought indices based on the relationship between their severity with the AYW in Iran using the data series of 12 stations with different climatic conditions (during 1967–2021). Temporal and spatial assessment of the relationship between drought severity and AYW, the large number and variety of investigated drought indices (12 indices), statistical methods used (multiple linear regression based on the relative importance metric introduced by the Lindeman, Merenda, Gold (MLR-LMG) and DV models), the length of the statistical period of the selected data (55 years) in each station, and also, the climatic diversity of the chosen stations are some of the innovative aspects of the presented research.
MATERIALS AND METHODS
Study area
in the northern and northwestern parts (such as Bandar Anzali) to less than 60 
in the central and southeastern parts (such as Yazd, Zahedan, and Zabol). Iran is located in the arid belt of the Earth (latitude 30°–45° north), so about 66% of its area has hyper-arid to semi-arid climate conditions (mainly the central and southern regions). The semi-humid to humid areas of the study area are located primarily in the northern and northwestern parts (Zarei & Bahrami 2016; Zarei et al. 2021). The long-term average rainfall (R), temperature (T), and potential evapotranspiration (PET) of Iran are 238.11 
, 19.21 °C, and 2,050 
, respectively (based on data series of 1967–2021). About 20% of Iran's active workforce works in the agricultural sector. Nearly one-third of Iran's land has the capability of farming activities. However, due to soil limitations (such as salinity) and inappropriate water conditions (quality and quantity), only 12% of the country's area is used for agriculture (about two-thirds of it is dry farmed). As a strategic product, winter wheat is the main agricultural product in Iran (Iran Agricultural Ministry 2016). Naturally, the occurrence of drought has many direct and indirect effects on rain-fed agriculture. Especially in Iran, underground water resources are also in unfavorable and critical conditions, and this issue intensifies the vulnerability to drought. 
Study area, selected stations, chosen random points, and their geographical distribution maps.
Study area, selected stations, chosen random points, and their geographical distribution maps.
Data collection
In this research, climatic datasets and the datasets of the AYW wheat of 12 stations over Iran from 1967 to 2021 were used (provided by Iran Meteorological Organization and Iran Agricultural Ministry). The stations consisted of Babolsar, Esfahan, Gorgan, Kerman, Mashhad, Ramsar, Rasht, Sanandaj, Shahre Kord, Shiraz, Tehran, and Zanjan (Table 1). The reasons for choosing the stations were their suitable spatial distribution and climatic diversity. In all selected stations, the run-test method, the Mockus equation, and the fuzzy regression method were used to assess the homogeneity of meteorological data, adequacy of time duration, and reconstruction of missing data (Shamshirband et al. 2020; Mahmoudi & Zarei 2023; Zarei et al. 2023a).
Selected stations and some of their spatial and climatic (from 1967 to 2021) characteristics
| Station | Eastern longitude (DD) | Northern latitude (DD) | Altitude (msl) | Rainfall ( ) | ET0 ( ) | Climate condition |
|---|---|---|---|---|---|---|
| Babolsar | 52.65 | 36.72 | −21.1 | 912.89 | 1,145.81 | H |
| Esfahan | 51.71 | 32.52 | 1,550.4 | 127.67 | 1,709.61 | A |
| Gorgan | 54.41 | 36.91 | 0.00 | 557.79 | 1,272.66 | Se |
| Kerman | 56.96 | 30.26 | 1,754.2 | 134.68 | 2,130.22 | A |
| Mashhad | 59.63 | 36.24 | 999.2 | 252.86 | 1,651.81 | A |
| Ramsar | 50.68 | 36.90 | −19.8 | 1,235.52 | 1,030.10 | H |
| Rasht | 49.65 | 37.20 | 24.8 | 1,314.34 | 1,088.34 | H |
| Sanandaj | 47.01 | 35.25 | 1,373.4 | 435.36 | 1,004.38 | Se |
| Shahre Kord | 50.84 | 32.29 | 2,048.9 | 322.22 | 1,460.87 | Se |
| Shiraz | 52.60 | 29.56 | 1,487.6 | 316.80 | 1,937.04 | A |
| Tehran | 51.31 | 35.69 | 1,190.8 | 238.86 | 1,891.94 | A |
| Zanjan | 48.52 | 36.66 | 1,659.4 | 302.07 | 978.85 | Se |
| Station | Eastern longitude (DD) | Northern latitude (DD) | Altitude (msl) | Rainfall () | ET0 () | Climate condition |
|---|---|---|---|---|---|---|
| Babolsar | 52.65 | 36.72 | −21.1 | 912.89 | 1,145.81 | H |
| Esfahan | 51.71 | 32.52 | 1,550.4 | 127.67 | 1,709.61 | A |
| Gorgan | 54.41 | 36.91 | 0.00 | 557.79 | 1,272.66 | Se |
| Kerman | 56.96 | 30.26 | 1,754.2 | 134.68 | 2,130.22 | A |
| Mashhad | 59.63 | 36.24 | 999.2 | 252.86 | 1,651.81 | A |
| Ramsar | 50.68 | 36.90 | −19.8 | 1,235.52 | 1,030.10 | H |
| Rasht | 49.65 | 37.20 | 24.8 | 1,314.34 | 1,088.34 | H |
| Sanandaj | 47.01 | 35.25 | 1,373.4 | 435.36 | 1,004.38 | Se |
| Shahre Kord | 50.84 | 32.29 | 2,048.9 | 322.22 | 1,460.87 | Se |
| Shiraz | 52.60 | 29.56 | 1,487.6 | 316.80 | 1,937.04 | A |
| Tehran | 51.31 | 35.69 | 1,190.8 | 238.86 | 1,891.94 | A |
| Zanjan | 48.52 | 36.66 | 1,659.4 | 302.07 | 978.85 | Se |
Note: DD is decimal degrees; msl is the mean sea level; ET0 is potential evapotranspiration (calculated based on the FAO-56 Penman–Monteith model); H, Se, and A are humid, semi-arid, and arid, respectively, based on the UNEP (United Nations Environment Programme) aridity index.
Drought indices
In this study, 12 meteorological drought indices were compared. Based on the literature review, these indicators are among the most widely used and newest meteorological indices, which can be generally used quantitatively on different timescales.
SPI
are calculation coefficients, and 
is the gamma function (fitted on datasets of R variables on different timescales).RDI
and 
are the average and the standard deviation of 
, and 
and 
are the amount of R and PET in month j of the ith year during the whole N years.SPEI
and 
parameters will be calculated for the month i:
. This is based on the L-moments and helps in considering the negative values of 
. Then, to determine the SPEI, estimated values of 
are converted into Z-standardized normal values:
are scale factors.MSPI, MRDI, and MSPEI
The calculation methods of MSPI, MRDI, and MSPEI are similar to those of SPI, RDI, and SPEI, respectively, but in MSPI (Tigkas et al. 2019), MRDI (Tigkas et al. 2016), and MSPEI, the R variable is replaced by effective R or ER. The developed model by the US Bureau of Reclamation (USBR) was used for calculating the ER. This model was recommended by Tigkas et al. (2016) and Zarei et al. (2023a).
CZI and MCZI
are the skewness coefficient and coefficient of variation of the rainfall data series on the chosen timescales.The calculation method of the modified CZI (MCZI) (Wu et al. 2001) is similar to that of the CZI, but in MCZI, for calculating Cs and 
, the average of R is substituted by the median of R.
Z-score (Z)
and 
are the rainfall, the average rainfall, and the standard deviation of the rainfall, respectively.EDI
is effective daily rainfall, MER is a long-term mean of the effective rainfall (at least 30 years), and 
is the standard deviation of calculated 
in the long-term (at least 30 years).Drought classification based on the SPI, MSPI, RDI, MRDI, SPEI, MSPEI, Z-score, CZI, MCZI, and EDI indices is presented in Table 2.
Drought classification based on the chosen drought indices (Khanmohammadi et al. 2022; Laimighofer & Laaha 2022; Piri et al. 2022; Singh et al. 2022; Tigkas et al. 2022; Zarei et al. (2023a).
| Range of drought index values | ||||
|---|---|---|---|---|
| Drought class | Symbol | RDI, MRDI, SPI, MSPI, SPEI, MSPEI, EDI, Z-Score, CZI and MCZI indices | PNPI index (%) | DI index (%) |
| I | E-We | More than 2 | More than 130 | More than 90 |
| II | V-We | 1.5–1.99 | 120–130 | 80–90 |
| III | M-We | 1–1.49 | 110–120 | 70–80 |
| IV | Norm | −0.99 to 0.99 | 80–110 | 30–70 |
| V | M-Dr | −1.49 to −1 | 55–80 | 20–30 |
| VI | S-Dr | −1.99 to −1.5 | 40–55 | 10–20 |
| VII | E-Dr | Less than −2 | Less than 40 | Less than 10 |
| Range of drought index values | ||||
|---|---|---|---|---|
| Drought class | Symbol | RDI, MRDI, SPI, MSPI, SPEI, MSPEI, EDI, Z-Score, CZI and MCZI indices | PNPI index (%) | DI index (%) |
| I | E-We | More than 2 | More than 130 | More than 90 |
| II | V-We | 1.5–1.99 | 120–130 | 80–90 |
| III | M-We | 1–1.49 | 110–120 | 70–80 |
| IV | Norm | −0.99 to 0.99 | 80–110 | 30–70 |
| V | M-Dr | −1.49 to −1 | 55–80 | 20–30 |
| VI | S-Dr | −1.99 to −1.5 | 40–55 | 10–20 |
| VII | E-Dr | Less than −2 | Less than 40 | Less than 10 |
Note: The E-We, V-We, and M-We are extremely, very, and moderately wet classes, respectively. Norm is normal class. The E-Dr, V-Dr, and M-Dr are extremely, very, and moderately dry classes, respectively.
DI
The DI index was suggested by Gibbs & Maher (1967). In this method, the rainfall data series of each station are sorted from small to large; then the sorted data are categorized into 10 deciles. Finally, based on the placement of each data in each decile, its drought class is determined based on the presented classification in Table 2.
PNPI
are rainfall and the long-term average of rainfall, respectively.Drought classification based on the PNPI is presented in Table 2.
Statistical models
MLR-LMG
:
are the model's coefficients, and 
is the model's error; 
are estimated using the dataset, and we have:
are the estimations of 
, and 
is the predicted value of Y.It can be seen that the MLR technique considers the linear impacts of 
. However, because of colinearity among 
, in applications, the relative importance of 
is usually studied based on standard coefficients. Using standard coefficients may have the following issues:
Standard coefficients are not interpretable when facing with multicolinearity.
High multicolinearity can lead to reversals of the signs of the impacts of the predictors.
Standard coefficients are not interpretable and are not reliable indicators of relative importance when facing multicolinearity.
There are several reliable ways to decompose R2. Lindeman et al. (1980) introduced the Lindeman, Merenda, Gold (LMG) measure as one of the recommended metrics. The LMG relative importance is available through the R package ‘relaimpo’ (Grömping 2007). In this work, the MLR-LMG model is applied to consider the effects of the predictors on the response variable. The most important advantage of the above method is in helping to better and more accurately understand the relationship between variables. In this study, the AYW was the dependent variable, and the drought indices were the independent variables.
DV
The primary purpose of data visualization (DV) is to construct a new schema to recognize outliers, trends, and patterns in different datasets, especially in big data. When data are collected and analyzed, DV, as a powerful tool, helps scientists to make better conclusions. DV can be used in every field of science. It can be used by computer experts tracking developments in artificial intelligence or by data scientists in big-data processing. Generally, visualizations of complicated algorithms are usually more effective than explaining numerical outputs. DV provides an effective and fast tool to discuss information in a generic procedure using visual information. In other words, the DV model can help to provide a better visual representation of the obtained results. This can make it easier for readers to understand the results.
Further advantages of DV can be summarized as follows:
The competency to attract information fast develop visions, and construct faster decisions.
A better conception of the following stages that should be derived to develop the structure.
A simple dispensation of information that increases the chance to share visions with others.
Lower need for data scientists, because of more availability and comprehension.
A quick way to take actions that result in greater success and fewer mistakes.
Temporal and spatial assessment of the ability of drought indices
Interpolated maps of the drought indices and yield over the study area in 2010 and 2020 (in a radius of 50 km around each station).
Interpolated maps of the drought indices and yield over the study area in 2010 and 2020 (in a radius of 50 km around each station).
The study steps (flowchart).
RESULTS
Calculated drought indices
Calculated drought classes based on different drought indices in Tehran station from 1967 to 2021.
Calculated drought classes based on different drought indices in Tehran station from 1967 to 2021.
AYW
(Figure 5). Based on the results, the AYW in each station is highly dependent on the climate conditions of the region. In other words, in stations with more humid climate conditions, such as Ramsar, Rasht, and Babolsar, the long-term average AYW is higher than the stations with drier climate conditions, such as Shiraz, Esfahan, and Kerman. In addition, the AYW fluctuations in more humid stations are less than in drier stations. The maximum AYW compared with its minimum in more humid stations shows an increase of about two times during chosen years, while it is up to 18 times in drier stations. The main reason for this issue is the more regular climatic regime (especially precipitation) in more humid stations. It should be noted that the coefficient of variation of climatic variables (with emphasis on rainfall and temperature) in humid regions is lower than in arid areas (Zarei et al. 2023a). 
AYW in some of the selected stations from 1967 to 2021.
Temporal assessment of the ability of drought indices
Ability assessment of selected drought indices based on the fitted MLR-LMG model in each station (in temporal form) indicated that in Babolsar (with RIM equal to 26.5936%), Esfahan (with RIM equal to 18.7502%), Kerman (with RIM equal to 33.8596%), Mashhad (with RIM equal to 24.0321%), Ramsar (with RIM equal to 26.7526%), Shahre Kord (with RIM equal to 32.1076%), and Zanjan (with RIM equal to 21.0894%) the MSPEI had the best ability to assess drought conditions in Gorgan (with RIM equal to 28.3805%) and Shiraz (with RIM equal to 18.7573%) it was the RDI, in Rasht (with RIM equal to 39.9057%) it was the MCZI, in Sanandaj (with RIM equal to 15.9686%) it was the CZI, and in Tehran (with RIM equal to 16.4188%) it was the MSPI that had the best ability to assess drought conditions (Table 3). In other words, the MSPEI in 58.33% of the chosen stations and the RDI in 16.66% of stations were the most suitable indices for evaluating drought situations. Table 3 shows that in Babolsar, Esfahan, Gorgan, Kerman, Mashhad, Ramsar, Rasht, Sanandaj, Shahre Kord, Shiraz, Tehran, and Zanjan, the EDI, RDI, PNPI, RDI, CZI, MSPI, EDI, EDI, DI, MRDI, MSPEI, and PNPI were the most inefficient indicators respectively.
The RIM of each index based on the fitted the MLR-LMG model in each station (temporal assessment)
| Stations | Relative importance metrics (%) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SPI | MSPI | RDI | MRDI | SPEI | MSPEI | CZI | MCZI | Z-score | EDI | DI | PNPI | |
| Babolsar | 4.8519 | 2.6633 | 15.9815 | 5.0495 | 10.1044 | 26.5936 | 3.0766 | 9.8806 | 5.9215 | 2.3175 | 3.3202 | 10.2394 |
| Esfahan | 13.7522 | 5.7290 | 2.6963 | 3.0708 | 10.8430 | 18.7502 | 3.8568 | 16.6124 | 5.1990 | 2.8803 | 10.7358 | 5.8743 |
| Gorgan | 5.8132 | 8.2240 | 25.3805 | 9.1454 | 11.2467 | 6.1659 | 5.3014 | 5.2974 | 6.7656 | 6.1631 | 6.6373 | 3.8595 |
| Kerman | 1.8048 | 2.5389 | 1.2077 | 1.5473 | 14.1858 | 33.8596 | 1.8164 | 3.3247 | 2.4209 | 4.4778 | 10.9112 | 21.9050 |
| Mashhad | 3.5345 | 8.0235 | 4.6492 | 10.0132 | 14.7318 | 24.0321 | 2.7619 | 3.8441 | 2.9391 | 11.9089 | 7.9530 | 5.6088 |
| Ramsar | 5.3835 | 2.0354 | 6.2169 | 12.0902 | 11.2820 | 26.7526 | 4.9863 | 4.2879 | 14.7107 | 2.1775 | 5.9050 | 4.1721 |
| Rasht | 5.6431 | 1.8637 | 2.6382 | 5.3448 | 5.9722 | 2.5569 | 14.0319 | 39.9057 | 7.9177 | 1.3924 | 5.1503 | 7.5832 |
| Sanandaj | 7.8623 | 2.5840 | 14.9192 | 2.6736 | 12.3794 | 4.3913 | 15.9686 | 11.9736 | 6.8008 | 2.3969 | 10.5963 | 7.4540 |
| Shahre Kord | 1.9264 | 6.5871 | 6.3711 | 8.5384 | 23.9884 | 32.1076 | 1.6378 | 6.4397 | 2.0401 | 7.9978 | 1.0786 | 1.2870 |
| Shiraz | 5.8114 | 4.0381 | 18.7573 | 2.3621 | 16.4394 | 9.8253 | 6.9585 | 9.6003 | 2.5673 | 3.8598 | 5.3027 | 14.4777 |
| Tehran | 7.7016 | 16.4188 | 12.6615 | 12.8359 | 4.4336 | 3.0097 | 3.9430 | 4.6825 | 13.4025 | 13.6120 | 3.5281 | 3.7705 |
| Zanjan | 6.3577 | 10.7674 | 11.7749 | 8.4403 | 13.7977 | 21.0894 | 4.8656 | 5.3115 | 5.8136 | 6.8381 | 2.6418 | 2.3020 |
| Stations | Relative importance metrics (%) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SPI | MSPI | RDI | MRDI | SPEI | MSPEI | CZI | MCZI | Z-score | EDI | DI | PNPI | |
| Babolsar | 4.8519 | 2.6633 | 15.9815 | 5.0495 | 10.1044 | 26.5936 | 3.0766 | 9.8806 | 5.9215 | 2.3175 | 3.3202 | 10.2394 |
| Esfahan | 13.7522 | 5.7290 | 2.6963 | 3.0708 | 10.8430 | 18.7502 | 3.8568 | 16.6124 | 5.1990 | 2.8803 | 10.7358 | 5.8743 |
| Gorgan | 5.8132 | 8.2240 | 25.3805 | 9.1454 | 11.2467 | 6.1659 | 5.3014 | 5.2974 | 6.7656 | 6.1631 | 6.6373 | 3.8595 |
| Kerman | 1.8048 | 2.5389 | 1.2077 | 1.5473 | 14.1858 | 33.8596 | 1.8164 | 3.3247 | 2.4209 | 4.4778 | 10.9112 | 21.9050 |
| Mashhad | 3.5345 | 8.0235 | 4.6492 | 10.0132 | 14.7318 | 24.0321 | 2.7619 | 3.8441 | 2.9391 | 11.9089 | 7.9530 | 5.6088 |
| Ramsar | 5.3835 | 2.0354 | 6.2169 | 12.0902 | 11.2820 | 26.7526 | 4.9863 | 4.2879 | 14.7107 | 2.1775 | 5.9050 | 4.1721 |
| Rasht | 5.6431 | 1.8637 | 2.6382 | 5.3448 | 5.9722 | 2.5569 | 14.0319 | 39.9057 | 7.9177 | 1.3924 | 5.1503 | 7.5832 |
| Sanandaj | 7.8623 | 2.5840 | 14.9192 | 2.6736 | 12.3794 | 4.3913 | 15.9686 | 11.9736 | 6.8008 | 2.3969 | 10.5963 | 7.4540 |
| Shahre Kord | 1.9264 | 6.5871 | 6.3711 | 8.5384 | 23.9884 | 32.1076 | 1.6378 | 6.4397 | 2.0401 | 7.9978 | 1.0786 | 1.2870 |
| Shiraz | 5.8114 | 4.0381 | 18.7573 | 2.3621 | 16.4394 | 9.8253 | 6.9585 | 9.6003 | 2.5673 | 3.8598 | 5.3027 | 14.4777 |
| Tehran | 7.7016 | 16.4188 | 12.6615 | 12.8359 | 4.4336 | 3.0097 | 3.9430 | 4.6825 | 13.4025 | 13.6120 | 3.5281 | 3.7705 |
| Zanjan | 6.3577 | 10.7674 | 11.7749 | 8.4403 | 13.7977 | 21.0894 | 4.8656 | 5.3115 | 5.8136 | 6.8381 | 2.6418 | 2.3020 |
Note: Bold characters are maximum values of the RIM in each station.
The estimated coefficients for each index based on the fitted MLR-LMG models in each station, also, confirmed the earlier obtained results. Table 4 shows that the estimated coefficients for the MSPEI, MSPEI, RDI, MSPEI, MSPEI, MSPEI, MCZI, CZI, MSPEI, RDI, MSPI, and MSPEI in the fitted MLR-LMG models in Babolsar, Esfahan, Gorgan, Kerman, Mashhad, Ramsar, Rasht, Sanandaj, Shahre Kord, Shiraz, Tehran, and Zanjan, respectively, were more than estimated coefficients for the other indices. Table 5 shows that in all stations, the calculated values of the P-value of the estimated coefficients for each index based on the fitted MLR-LMG model in the more appropriate indices are less than in the other indices. For instance, the calculated P-values for the MSPEI, MSPEI, RDI, MSPEI, MSPEI, MSPEI, MCZI, CZI, MSPEI, RDI, MSPI, and MSPEI in Babolsar, Esfahan, Gorgan, Kerman, Mashhad, Ramsar, Rasht, Sanandaj, Shahre Kord, Shiraz, Tehran, and Zanjan, respectively, were less than the estimated P-values for the calculated coefficients for the other indices. In Kerman, Mashhad, Rasht, and Tehran, the calculated P-values were significant at the 5% level.
The estimated coefficients for each index based on the fitted MLR-LMG model in each station (temporal assessment)
| Stations | Coefficient | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SPI | MSPI | RDI | MRDI | SPEI | MSPEI | CZI | MCZI | Z-score | EDI | DI | PNPI | |
| Babolsar | 0.3526 | 0.0245 | 0.0915 | −0.0055 | 0.0529 | 0.3930 | 0.0764 | −0.3265 | −0.2664 | 0.0110 | 0.0129 | −0.2197 |
| Esfahan | 0.5948 | −0.3423 | 0.2420 | −0.2762 | −0.0692 | 0.3521 | −0.1575 | −0.2035 | −0.1316 | 0.1349 | −0.0115 | −0.0521 |
| Gorgan | 0.3651 | −0.8185 | −0.6319 | 0.2819 | −0.2472 | 0.0441 | −0.5955 | 0.4522 | 0.2473 | 0.5219 | −0.0788 | −0.0605 |
| Kerman | 0.0270 | −0.0963 | −0.0460 | 0.1202 | 0.1854 | 0.2430 | 0.0952 | −0.1042 | −0.0314 | −0.0387 | −0.0779 | −0.2497 |
| Mashhad | 0.2696 | 0.1604 | −0.0529 | −0.0388 | −0.2717 | −0.6573 | −0.0143 | 0.1797 | −0.1941 | 0.0793 | 0.2577 | −0.1531 |
| Ramsar | −0.2484 | 0.0728 | −0.3997 | −0.0020 | 0.4699 | 0.4733 | 0.1232 | 0.1250 | −0.4762 | −0.1208 | 0.2633 | −0.1840 |
| Rasht | 0.2436 | −0.3545 | 0.1362 | 0.3068 | −0.4446 | −0.0937 | −1.8448 | 1.9403 | 0.7290 | 0.2182 | 0.0120 | −0.2287 |
| Sanandaj | 0.5441 | −0.1935 | −0.3429 | −0.0714 | 0.3743 | −0.0425 | −1.5469 | 0.8761 | 0.1373 | 0.2511 | −0.0795 | −0.0627 |
| Shahre Kord | −0.0532 | 0.0910 | −0.0243 | 0.0556 | 0.0151 | −0.1816 | −0.0203 | 0.1165 | −0.0605 | −0.0932 | 0.0147 | −0.0076 |
| Shiraz | 0.4273 | 0.5155 | −0.7256 | −0.1264 | −0.2557 | 0.0259 | −0.8851 | 0.6173 | −0.2691 | −0.3866 | −0.3030 | 0.4150 |
| Tehran | −0.9347 | 0.9484 | −0.4284 | −0.2811 | −0.2560 | 0.2254 | −0.1264 | 0.3907 | 0.7880 | 0.1902 | −0.0585 | −0.0921 |
| Zanjan | 0.0799 | −0.0593 | −0.0808 | 0.0376 | 0.0579 | −0.0898 | 0.0528 | −0.0821 | 0.0295 | −0.0126 | 0.0236 | −0.0227 |
| Stations | Coefficient | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SPI | MSPI | RDI | MRDI | SPEI | MSPEI | CZI | MCZI | Z-score | EDI | DI | PNPI | |
| Babolsar | 0.3526 | 0.0245 | 0.0915 | −0.0055 | 0.0529 | 0.3930 | 0.0764 | −0.3265 | −0.2664 | 0.0110 | 0.0129 | −0.2197 |
| Esfahan | 0.5948 | −0.3423 | 0.2420 | −0.2762 | −0.0692 | 0.3521 | −0.1575 | −0.2035 | −0.1316 | 0.1349 | −0.0115 | −0.0521 |
| Gorgan | 0.3651 | −0.8185 | −0.6319 | 0.2819 | −0.2472 | 0.0441 | −0.5955 | 0.4522 | 0.2473 | 0.5219 | −0.0788 | −0.0605 |
| Kerman | 0.0270 | −0.0963 | −0.0460 | 0.1202 | 0.1854 | 0.2430 | 0.0952 | −0.1042 | −0.0314 | −0.0387 | −0.0779 | −0.2497 |
| Mashhad | 0.2696 | 0.1604 | −0.0529 | −0.0388 | −0.2717 | −0.6573 | −0.0143 | 0.1797 | −0.1941 | 0.0793 | 0.2577 | −0.1531 |
| Ramsar | −0.2484 | 0.0728 | −0.3997 | −0.0020 | 0.4699 | 0.4733 | 0.1232 | 0.1250 | −0.4762 | −0.1208 | 0.2633 | −0.1840 |
| Rasht | 0.2436 | −0.3545 | 0.1362 | 0.3068 | −0.4446 | −0.0937 | −1.8448 | 1.9403 | 0.7290 | 0.2182 | 0.0120 | −0.2287 |
| Sanandaj | 0.5441 | −0.1935 | −0.3429 | −0.0714 | 0.3743 | −0.0425 | −1.5469 | 0.8761 | 0.1373 | 0.2511 | −0.0795 | −0.0627 |
| Shahre Kord | −0.0532 | 0.0910 | −0.0243 | 0.0556 | 0.0151 | −0.1816 | −0.0203 | 0.1165 | −0.0605 | −0.0932 | 0.0147 | −0.0076 |
| Shiraz | 0.4273 | 0.5155 | −0.7256 | −0.1264 | −0.2557 | 0.0259 | −0.8851 | 0.6173 | −0.2691 | −0.3866 | −0.3030 | 0.4150 |
| Tehran | −0.9347 | 0.9484 | −0.4284 | −0.2811 | −0.2560 | 0.2254 | −0.1264 | 0.3907 | 0.7880 | 0.1902 | −0.0585 | −0.0921 |
| Zanjan | 0.0799 | −0.0593 | −0.0808 | 0.0376 | 0.0579 | −0.0898 | 0.0528 | −0.0821 | 0.0295 | −0.0126 | 0.0236 | −0.0227 |
The P-value of the estimated coefficients for each index based on the fitted MLR-LMG model in each station (temporal assessment)
| Station | The P-value of the estimated coefficients | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SPI | MSPI | RDI | MRDI | SPEI | MSPEI | CZI | MCZI | Z-score | EDI | DI | PNPI | |
| Babolsar | 0.6840 | 0.9650 | 0.7130 | 0.9840 | 0.1850 | 0.1480 | 0.8420 | 0.2820 | 0.6900 | 0.9820 | 0.9320 | 0.3650 |
| Esfahan | 0.0730 | 0.2174 | 0.3326 | 0.2803 | 0.7649 | 0.0574 | 0.4203 | 0.0710 | 0.5017 | 0.3622 | 0.9595 | 0.3287 |
| Gorgan | 0.6490 | 0.4390 | 0.1080 | 0.5670 | 0.5600 | 0.9000 | 0.6210 | 0.5780 | 0.7770 | 0.5630 | 0.8220 | 0.8640 |
| Kerman | 0.9124 | 0.7393 | 0.8995 | 0.7312 | 0.2792 | 0.0329* | 0.6641 | 0.4311 | 0.8760 | 0.8470 | 0.2648 | 0.1304 |
| Mashhad | 0.6658 | 0.6635 | 0.8783 | 0.9140 | 0.2721 | 0.0497* | 0.9872 | 0.5391 | 0.7627 | 0.7471 | 0.1311 | 0.3755 |
| Ramsar | 0.7950 | 0.9130 | 0.2550 | 0.9940 | 0.2210 | 0.1740 | 0.8920 | 0.7810 | 0.2350 | 0.8620 | 0.2520 | 0.4350 |
| Rasht | 0.7825 | 0.5574 | 0.7305 | 0.3603 | 0.3611 | 0.5104 | 0.1169 | 0.0108* | 0.2629 | 0.6448 | 0.9564 | 0.4831 |
| Sanandaj | 0.3540 | 0.7193 | 0.1580 | 0.7511 | 0.0925 | 0.8020 | 0.0698 | 0.1198 | 0.8444 | 0.6410 | 0.6952 | 0.7704 |
| Shahre Kord | 0.5054 | 0.2430 | 0.5884 | 0.1983 | 0.8086 | 0.1684 | 0.8846 | 0.2160 | 0.6960 | 0.2354 | 0.6845 | 0.8377 |
| Shiraz | 0.3916 | 0.3452 | 0.0901 | 0.7555 | 0.3097 | 0.8999 | 0.3466 | 0.1047 | 0.6778 | 0.4094 | 0.2729 | 0.0616 |
| Tehran | 0.2362 | 0.0295* | 0.4091 | 0.4711 | 0.3012 | 0.2996 | 0.8661 | 0.3169 | 0.0341* | 0.5879 | 0.7520 | 0.4962 |
| Zanjan | 0.4594 | 0.7541 | 0.4302 | 0.7154 | 0.2988 | 0.2529 | 0.7220 | 0.4510 | 0.8401 | 0.9480 | 0.6077 | 0.6946 |
| Station | The P-value of the estimated coefficients | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SPI | MSPI | RDI | MRDI | SPEI | MSPEI | CZI | MCZI | Z-score | EDI | DI | PNPI | |
| Babolsar | 0.6840 | 0.9650 | 0.7130 | 0.9840 | 0.1850 | 0.1480 | 0.8420 | 0.2820 | 0.6900 | 0.9820 | 0.9320 | 0.3650 |
| Esfahan | 0.0730 | 0.2174 | 0.3326 | 0.2803 | 0.7649 | 0.0574 | 0.4203 | 0.0710 | 0.5017 | 0.3622 | 0.9595 | 0.3287 |
| Gorgan | 0.6490 | 0.4390 | 0.1080 | 0.5670 | 0.5600 | 0.9000 | 0.6210 | 0.5780 | 0.7770 | 0.5630 | 0.8220 | 0.8640 |
| Kerman | 0.9124 | 0.7393 | 0.8995 | 0.7312 | 0.2792 | 0.0329* | 0.6641 | 0.4311 | 0.8760 | 0.8470 | 0.2648 | 0.1304 |
| Mashhad | 0.6658 | 0.6635 | 0.8783 | 0.9140 | 0.2721 | 0.0497* | 0.9872 | 0.5391 | 0.7627 | 0.7471 | 0.1311 | 0.3755 |
| Ramsar | 0.7950 | 0.9130 | 0.2550 | 0.9940 | 0.2210 | 0.1740 | 0.8920 | 0.7810 | 0.2350 | 0.8620 | 0.2520 | 0.4350 |
| Rasht | 0.7825 | 0.5574 | 0.7305 | 0.3603 | 0.3611 | 0.5104 | 0.1169 | 0.0108* | 0.2629 | 0.6448 | 0.9564 | 0.4831 |
| Sanandaj | 0.3540 | 0.7193 | 0.1580 | 0.7511 | 0.0925 | 0.8020 | 0.0698 | 0.1198 | 0.8444 | 0.6410 | 0.6952 | 0.7704 |
| Shahre Kord | 0.5054 | 0.2430 | 0.5884 | 0.1983 | 0.8086 | 0.1684 | 0.8846 | 0.2160 | 0.6960 | 0.2354 | 0.6845 | 0.8377 |
| Shiraz | 0.3916 | 0.3452 | 0.0901 | 0.7555 | 0.3097 | 0.8999 | 0.3466 | 0.1047 | 0.6778 | 0.4094 | 0.2729 | 0.0616 |
| Tehran | 0.2362 | 0.0295* | 0.4091 | 0.4711 | 0.3012 | 0.2996 | 0.8661 | 0.3169 | 0.0341* | 0.5879 | 0.7520 | 0.4962 |
| Zanjan | 0.4594 | 0.7541 | 0.4302 | 0.7154 | 0.2988 | 0.2529 | 0.7220 | 0.4510 | 0.8401 | 0.9480 | 0.6077 | 0.6946 |
*P-value is significant at the 0.05 level.
The visual output of the comparison of drought indices based on the DV model in selected stations (temporal assessment based on 1967–2021 data series). Note: Selected index had the greatest ability to assess drought conditions in each station.
The visual output of the comparison of drought indices based on the DV model in selected stations (temporal assessment based on 1967–2021 data series). Note: Selected index had the greatest ability to assess drought conditions in each station.
Spatial assessment of the ability of drought indices
The RIM of each index based on the fitted MLR-LMG model in some of the chosen years (spatial assessment)
| Drought index | Relative importance metrics (%) | |||||
|---|---|---|---|---|---|---|
| 1970 | 1980 | 1990 | 2000 | 2010 | 2020 | |
| SPI | 0.082479 | 0.079230 | 0.079210 | 0.095564 | 0.096712 | 0.091662 |
| MSPI | 0.101975 | 0.087728 | 0.087628 | 0.095562 | 0.096732 | 0.091681 |
| RDI | 0.080480 | 0.079230 | 0.079230 | 0.095561 | 0.096702 | 0.091648 |
| MRDI | 0.089728 | 0.085229 | 0.085229 | 0.055101 | 0.096732 | 0.091688 |
| SPEI | 0.078480 | 0.084229 | 0.089229 | 0.095566 | 0.096733 | 0.091682 |
| MSPEI | 0.078480 | 0.075231 | 0.075231 | 0.095567 | 0.096734 | 0.091689 |
| CZI | 0.082229 | 0.079230 | 0.079230 | 0.042402 | 0.016338 | 0.041560 |
| MCZI | 0.082979 | 0.088728 | 0.088828 | 0.095560 | 0.016339 | 0.091638 |
| Z-score | 0.110977 | 0.089978 | 0.069958 | 0.095563 | 0.096712 | 0.041559 |
| EDI | 0.075481 | 0.083729 | 0.084729 | 0.042400 | 0.096702 | 0.091628 |
| DI | 0.078980 | 0.085979 | 0.085969 | 0.095561 | 0.096731 | 0.091608 |
| PNPI | 0.077731 | 0.081480 | 0.081490 | 0.095560 | 0.096732 | 0.091683 |
| Drought index | Relative importance metrics (%) | |||||
|---|---|---|---|---|---|---|
| 1970 | 1980 | 1990 | 2000 | 2010 | 2020 | |
| SPI | 0.082479 | 0.079230 | 0.079210 | 0.095564 | 0.096712 | 0.091662 |
| MSPI | 0.101975 | 0.087728 | 0.087628 | 0.095562 | 0.096732 | 0.091681 |
| RDI | 0.080480 | 0.079230 | 0.079230 | 0.095561 | 0.096702 | 0.091648 |
| MRDI | 0.089728 | 0.085229 | 0.085229 | 0.055101 | 0.096732 | 0.091688 |
| SPEI | 0.078480 | 0.084229 | 0.089229 | 0.095566 | 0.096733 | 0.091682 |
| MSPEI | 0.078480 | 0.075231 | 0.075231 | 0.095567 | 0.096734 | 0.091689 |
| CZI | 0.082229 | 0.079230 | 0.079230 | 0.042402 | 0.016338 | 0.041560 |
| MCZI | 0.082979 | 0.088728 | 0.088828 | 0.095560 | 0.016339 | 0.091638 |
| Z-score | 0.110977 | 0.089978 | 0.069958 | 0.095563 | 0.096712 | 0.041559 |
| EDI | 0.075481 | 0.083729 | 0.084729 | 0.042400 | 0.096702 | 0.091628 |
| DI | 0.078980 | 0.085979 | 0.085969 | 0.095561 | 0.096731 | 0.091608 |
| PNPI | 0.077731 | 0.081480 | 0.081490 | 0.095560 | 0.096732 | 0.091683 |
Note: Bold characters are maximum values of the RIM in each station.
The estimated coefficients for each index based on the fitted MLR-LMG model in some of the chosen years (spatial assessment)
| Drought index | Coefficient | |||||
|---|---|---|---|---|---|---|
| 1970 | 1980 | 1990 | 2000 | 2010 | 2020 | |
| SPI | −2.1761 | −0.9486 | 3.0450 | 13.4786 | 0.2960 | 4.3616 |
| MSPI | 0.2094 | 5.1240 | 3.9192 | 3.1260 | 2.1048 | 2.8880 |
| RDI | 1.4437 | 5.3353 | −10.8211 | −4.4607 | 0.6198 | 0.2451 |
| MRDI | 9.1738 | −4.9223 | 1.8410 | 11.0354 | −0.6779 | −5.2939 |
| SPEI | −2.1370 | 1.4079 | −13.5927 | 2.6221 | 1.4269 | 3.0179 |
| MSPEI | 0.8447 | 0.4934 | 5.5101 | −26.1552 | 14.5753 | 3.3321 |
| CZI | 0.0503 | −0.0280 | 4.0366 | 11.0197 | −14.4730 | −20.2950 |
| MCZI | −4.1080 | −1.6890 | 11.6307 | −2.0330 | 0.2081 | 20.2055 |
| Z-score | −5.6593 | −6.2017 | 1.1253 | 15.9313 | 0.8832 | −4.3616 |
| EDI | 1.4300 | 0.9261 | −2.4910 | −11.0197 | −2.8642 | −3.7728 |
| DI | 1.0445 | 1.4776 | 1.5624 | −0.1234 | −0.4841 | −1.4950 |
| PNPI | 0.8837 | 0.0252 | −3.6405 | −1.3914 | −0.5131 | 2.1679 |
| Drought index | Coefficient | |||||
|---|---|---|---|---|---|---|
| 1970 | 1980 | 1990 | 2000 | 2010 | 2020 | |
| SPI | −2.1761 | −0.9486 | 3.0450 | 13.4786 | 0.2960 | 4.3616 |
| MSPI | 0.2094 | 5.1240 | 3.9192 | 3.1260 | 2.1048 | 2.8880 |
| RDI | 1.4437 | 5.3353 | −10.8211 | −4.4607 | 0.6198 | 0.2451 |
| MRDI | 9.1738 | −4.9223 | 1.8410 | 11.0354 | −0.6779 | −5.2939 |
| SPEI | −2.1370 | 1.4079 | −13.5927 | 2.6221 | 1.4269 | 3.0179 |
| MSPEI | 0.8447 | 0.4934 | 5.5101 | −26.1552 | 14.5753 | 3.3321 |
| CZI | 0.0503 | −0.0280 | 4.0366 | 11.0197 | −14.4730 | −20.2950 |
| MCZI | −4.1080 | −1.6890 | 11.6307 | −2.0330 | 0.2081 | 20.2055 |
| Z-score | −5.6593 | −6.2017 | 1.1253 | 15.9313 | 0.8832 | −4.3616 |
| EDI | 1.4300 | 0.9261 | −2.4910 | −11.0197 | −2.8642 | −3.7728 |
| DI | 1.0445 | 1.4776 | 1.5624 | −0.1234 | −0.4841 | −1.4950 |
| PNPI | 0.8837 | 0.0252 | −3.6405 | −1.3914 | −0.5131 | 2.1679 |
The P-value of the estimated coefficients for each index based on the fitted MLR-LMG model in some of the chosen years (spatial assessment)
| Drought index | The P-value of the estimated coefficients | |||||
|---|---|---|---|---|---|---|
| 1970 | 1980 | 1990 | 2000 | 2010 | 2020 | |
| SPI | 2.0 × 10−16* | 2.0 × 10−16* | <2 × 10−16* | 8.8 × 10−01 | 4.5 × 10−11* | 2.0 × 10−16* |
| MSPI | 9.4 × 10−01 | 1.0 | <2 × 10−16* | 9.1 × 10−01 | 2.1 × 10−01 | 1.3 × 10−01 |
| RDI | 2.0 × 10−16* | 7.2 × 10−01 | <2 × 10−16* | 5.5 × 10−01 | 5.1 × 10−16* | 5.6 × 10−05* |
| MRDI | 9.3 × 10−01 | 9.9 × 10−01 | <2 × 10−16* | 8.2 × 10−16* | 1.3 × 10−05* | 6.5 × 10−01 |
| SPEI | 2.0 × 10−16* | 4.9 × 10−01 | <2 × 10−16* | 8.8 × 10−01 | 5.9 × 10−06* | 2.0 × 10−16* |
| MSPEI | 1.1 × 10−12* | 8.4 × 10−01 | <2 × 10−16* | 2.0 × 10−16* | 2.0 × 10−16* | 2.0 × 10−16* |
| CZI | 1.1 × 10−05* | 1.2 × 10−02** | <2 × 10−16* | 8.6 × 10−01 | 5.0 × 10−04* | 2.0 × 10−16* |
| MCZI | 9.9 × 10−01 | 1.0 | <2 × 10−16* | 8.8 × 10−01 | 6.8 × 10−02 | 7.4 × 10−01 |
| Z-Score | 1.1 × 10−10* | 8.1 × 10−06* | <2 × 10−16* | 2.8 × 10−08* | 6.6 × 10−02 | 1.3 × 10−01 |
| EDI | 9.9 × 10−01 | 3.9 × 10−01 | 6.5 × 10−02 | 9.2 × 10−01 | 2.2 × 10−05* | 7.4 × 10−01 |
| DI | 1.5 × 10−10* | 6.4 × 10−05* | <2 × 10−16* | 8.8 × 10−01 | 2.0 × 10−16* | 1.7 × 10−07* |
| PNPI | 1.2 × 10−04* | 8.3 × 10−01 | <2 × 10−16* | 5.1 × 10−01 | 5.2 × 10−04* | 1.8 × 10−09* |
| Drought index | The P-value of the estimated coefficients | |||||
|---|---|---|---|---|---|---|
| 1970 | 1980 | 1990 | 2000 | 2010 | 2020 | |
| SPI | 2.0 × 10−16* | 2.0 × 10−16* | <2 × 10−16* | 8.8 × 10−01 | 4.5 × 10−11* | 2.0 × 10−16* |
| MSPI | 9.4 × 10−01 | 1.0 | <2 × 10−16* | 9.1 × 10−01 | 2.1 × 10−01 | 1.3 × 10−01 |
| RDI | 2.0 × 10−16* | 7.2 × 10−01 | <2 × 10−16* | 5.5 × 10−01 | 5.1 × 10−16* | 5.6 × 10−05* |
| MRDI | 9.3 × 10−01 | 9.9 × 10−01 | <2 × 10−16* | 8.2 × 10−16* | 1.3 × 10−05* | 6.5 × 10−01 |
| SPEI | 2.0 × 10−16* | 4.9 × 10−01 | <2 × 10−16* | 8.8 × 10−01 | 5.9 × 10−06* | 2.0 × 10−16* |
| MSPEI | 1.1 × 10−12* | 8.4 × 10−01 | <2 × 10−16* | 2.0 × 10−16* | 2.0 × 10−16* | 2.0 × 10−16* |
| CZI | 1.1 × 10−05* | 1.2 × 10−02** | <2 × 10−16* | 8.6 × 10−01 | 5.0 × 10−04* | 2.0 × 10−16* |
| MCZI | 9.9 × 10−01 | 1.0 | <2 × 10−16* | 8.8 × 10−01 | 6.8 × 10−02 | 7.4 × 10−01 |
| Z-Score | 1.1 × 10−10* | 8.1 × 10−06* | <2 × 10−16* | 2.8 × 10−08* | 6.6 × 10−02 | 1.3 × 10−01 |
| EDI | 9.9 × 10−01 | 3.9 × 10−01 | 6.5 × 10−02 | 9.2 × 10−01 | 2.2 × 10−05* | 7.4 × 10−01 |
| DI | 1.5 × 10−10* | 6.4 × 10−05* | <2 × 10−16* | 8.8 × 10−01 | 2.0 × 10−16* | 1.7 × 10−07* |
| PNPI | 1.2 × 10−04* | 8.3 × 10−01 | <2 × 10−16* | 5.1 × 10−01 | 5.2 × 10−04* | 1.8 × 10−09* |
*P-value is significant at the 0.01 level.
**P-value is significant at the 0.05 level.
The visual output of the comparison of drought indices based on the DV model in 1970, 1980, 1990, 2000, 2010, and 2020 (spatial assessment). Note: Selected index had the greatest ability to assess drought conditions in each year.
The visual output of the comparison of drought indices based on the DV model in 1970, 1980, 1990, 2000, 2010, and 2020 (spatial assessment). Note: Selected index had the greatest ability to assess drought conditions in each year.
Fitted models validation
Validation test of the fitted MLR-LMG models in the temporal and spatial assessment of the ability of drought indices showed that in all stations and in all years, the calculated T-statistics were less than 1.96, and also, the estimated correlation coefficients (R) were significant at the 1% level (Tables 9 and 10). In other words, in all stations and all years, the correlation between observed and estimated AYW (based on the fitted MLR-LMG model) was not different from the perfect reliability line (y = x). This result proves the appropriate ability of the fitted MLR-LMG models on the data series in the temporal and spatial assessment of the power of the drought indices.
T-statistics and correlation coefficients (R) between the real annual yield of rain-fed winter wheat and their simulated yield using the fitted MLR-LMG model in each station (temporal assessment)
| Station | T-statistics | R |
|---|---|---|
| Babolsar | 5.7 × 10−14* | 0.9936* |
| Esfahan | 5.7 × 10−12* | 0.8619* |
| Gorgan | 1.7 × 10−14* | 0.9816* |
| Kerman | 9.6 × 10−15* | 0.8270* |
| Mashhad | 8.1 × 10−17* | 0.8151* |
| Ramsar | 2.9 × 10−14* | 0.9936* |
| Rasht | 4.5 × 10−14* | 0.9898* |
| Sanandaj | 3.2 × 10−14* | 0.8277* |
| Shahre Kord | 4.4 × 10−15* | 0.8745* |
| Shiraz | 2.0 × 10−15* | 0.9422* |
| Tehran | 9.7 × 10−15* | 0.8923* |
| Zanjan | 1.6 × 10−15* | 0.6994* |
| Station | T-statistics | R |
|---|---|---|
| Babolsar | 5.7 × 10−14* | 0.9936* |
| Esfahan | 5.7 × 10−12* | 0.8619* |
| Gorgan | 1.7 × 10−14* | 0.9816* |
| Kerman | 9.6 × 10−15* | 0.8270* |
| Mashhad | 8.1 × 10−17* | 0.8151* |
| Ramsar | 2.9 × 10−14* | 0.9936* |
| Rasht | 4.5 × 10−14* | 0.9898* |
| Sanandaj | 3.2 × 10−14* | 0.8277* |
| Shahre Kord | 4.4 × 10−15* | 0.8745* |
| Shiraz | 2.0 × 10−15* | 0.9422* |
| Tehran | 9.7 × 10−15* | 0.8923* |
| Zanjan | 1.6 × 10−15* | 0.6994* |
*T-statistic or R is significant at the 0.01 level.
T-statistics and correlation coefficients (R) between the real annual yield of rain-fed winter wheat and their simulated yield using the fitted MLR-LMG model in some of the selected years (spatial assessment)
| Year | T-statistics | R |
|---|---|---|
| 1970 | 1.9 × 10−11* | 0.9999994* |
| 1980 | 1.63 × 10−12* | 0.9999987* |
| 1990 | 8.27 × 10−13* | 0.9999887* |
| 2000 | 1.13 × 10−11* | 0.9999993* |
| 2010 | 3.9 × 10−11* | 0.9999991* |
| 2020 | 1.23 × 10−11* | 0.9999991* |
| Year | T-statistics | R |
|---|---|---|
| 1970 | 1.9 × 10−11* | 0.9999994* |
| 1980 | 1.63 × 10−12* | 0.9999987* |
| 1990 | 8.27 × 10−13* | 0.9999887* |
| 2000 | 1.13 × 10−11* | 0.9999993* |
| 2010 | 3.9 × 10−11* | 0.9999991* |
| 2020 | 1.23 × 10−11* | 0.9999991* |
*T-statistic or R is significant at the 0.01 level.
DISCUSSION
Based on the results, in more humid stations, the AYW was higher than in the stations with drier climate conditions. It is natural that in more humid stations, the occurrence probability of the water stress on rain-fed winter wheat is lower than in the drier stations, so the AYW will be better (Hasan & Abed 2023; Javadi et al., 2023). Also, under the influence of the more regular climatic regime in humid stations, fluctuations of the AYW in these stations are less than in drier stations (Zarei et al. 2023a). The results of this study furthermore indicated that from 12 investigated indicators, the MSPEI has a better performance in temporal and spatial assessment of drought conditions. Zarei & Moghimi (2019) introduced the MSPEI and proved that the ability of the MSPEI to assess drought conditions is greater than that of the SPEI. The results of the study by Ramezani & Nazeri Tahroudi (2020) showed that in areas with diversity and changes in climatic conditions, the MSPEI has a better performance than the SPEI for assessing drought. Zarei et al. (2023a) showed that the MSPEI and SPEI have a more suitable performance for evaluating agricultural drought. Therefore, it can be stated that the results of the studies by Zarei & Moghimi (2019), Ramezani & Nazeri Tahroudi (2020), and Zarei et al. (2023a, 2023b) are similar to the results of the present study. The literature review to compare the results of this study with the previous research showed that to compare drought indicators, visual methods such as DV were used less. One of the most important advantages of this method is to make it easier for the reader to understand the results, and this point is one of the strengths of the present study. It seems that the main reasons for the greater efficiency of MSPEI include the following:
- (a)
More climatic variables are used in calculating the MSPEI. In other words, unlike some other indices such as SPI, MSPI, CZI, and so on, the MSPEI is not only based on rainfall. In MSPEI calculation, in addition to rainfall, other variables such as PET are also used. The PET also was calculated using several variables such as minimum temperature, maximum temperature, sunshine, and wind speed.
- (b)
Rainfall is replaced with effective rainfall in calculating the MSPEI.
- (c)
The MSPEI has a greater correlation with the yield of agricultural products (due to attention to the effective part of rainfall on agriculture, which has a direct role in crop yield).
The results of the study of Zarei & Mahmoudi (2017) showed that the number of used climatic variables in the calculation PET method has an effective role in the accuracy of the outputs. Also, Tigkas et al. (2022) showed that replacing the R with ER to calculate the drought indices has a positive role in increasing the correlation between the values of drought severity and AYW.
CONCLUSION
Considering the vital role of selecting the appropriate drought index for accurately assessing drought conditions (including drought severity, duration, and frequency), in this study, the ability of the 12 drought indicators for temporal and spatial evaluation of drought situations was evaluated and compared based on the relationship between drought severity with the AYW. For this purpose, meteorological datasets, as well as AYW data in 12 stations with diverse climatic conditions in Iran during the years 1967–2021, were used. Also, for assessing the relationship between drought severity with the AYW, MLR-LMG and DV models were used. The results indicated that:
In temporal evaluation, the MSPEI (in 58.33% of selected stations) was the most efficient drought index.
In spatial evaluation, the MSPEI and Z-score (in 65.45% and 27.27% of the years, respectively) were the most efficient drought indices.
The validation test of the fitted MLR-LMG showed that in all stations and all years, the fitted models were reliable in assessing the relationship between drought severity with the AYW.
In this research, meteorological drought indices have been compared using two new methods, but to be more complete with the results, it is suggested that the satellite drought indices should also be compared and investigated in future research. In addition, in the absence of data access restrictions, this research also can be done on a global scale.
ACKNOWLEDGEMENTS
The authors thank Iran Meteorological Organization and Iran Agricultural Ministry for providing necessary data series.
AUTHOR CONTRIBUTIONS
Abdol-Rassoul Zarei and Mohammad Reza Mahmoudi: data collection, analysis of the results, and writing the article. Yaser Ghasemi Aryan: analysis of the results.
ETHICS APPROVAL
The authors confirm that this article is original research and has not been published or presented previously in any journal or conference in any language (in whole or in part).
FUNDING STATEMENT
No funds, grants, or other support was received.
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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