Effect of different timescales of drought on water productivity of rain-fed winter wheat in arid and semi-arid regions

To achieve sustainable agriculture and food security in arid and semi-arid regions, rainfed cultivation is a major key. In rainfed cultivation, rainwater is the only source of water supply for plants. In arid and semi-arid regions, rainfall shows strong spatiotemporal variations. Drought is a temporary severe decrease of water availability due to a decrease in the amount of rainfall (Tigkas & Tsakiris 2015). Several indices are presented to characterize and monitor the drought (Zhao et al. 2018; Shamshirband et al. 2020; Zarei et al. 2021). Reconnaissance drought index (RDI) is one of the most widely used to characterize drought (Moghimi & Zarei 2019; Zarei et al. 2019a; Moghimi et al. 2020). RDI can be used to assess the effects of meteorological parameters on drought severity because it is based on precipitation and evapotranspiration (Mohammed & Scholz 2017). Numerous studies have proved the capabilities of the RDI (Tsakiris et al. 2007; Khalili et al. 2011; Zarei et al. 2016; Merabti et al. 2018). This is rather important, since, if the drought analyses are for agricultural applications, the utilization of the RDI capabilities would seem to serve a better purpose (Khalili et al. 2011). There are two views (hydrological and agricultural) in defining effective precipitation (EP). In the hydrological view, EP is the percentage of rainfall that drains out of the basin as runoff (Mahdavi 2002), and in the agricultural view, it is the percentage of rainfall that can be used productively by the plants (Tigkas et al. 2016, 2019) to meet the water requirement. Tigkas et al. (2016) presented a modified version for RDI (MRDI) by replacing the observed precipitation (OP) with EP. For calculating EP, methods of the Food and Agriculture Organization of the United Nation (FAO), US Bureau of Reclamation (USBR), the Simplified version of Soil Conservation Service of the US Department of Agriculture (USDA-SCS-simplified), and the CROPWAT version of USDA-SCS (USDA-SCS CROPWAT) were used. According to the results, MRDI in an area with agricultural activities has better performance in studying the impacts of drought.

In countries like Iran where most water resources are used for agriculture and most of their areas are arid and semi-arid, these analyses are of much more importance. For the evaluation of water utilization in rainfed cultivation, water productivity (WP) is a very important tool (Guan et al. 2015). WP is calculated as the ratio of the amount or value of crop yield to the amount of water consumed by crop (Wakil et al. 2018). WP can be increased by an increase in crop yield per the unit water consumption or a decrease in water consumed to produce the unit crop yield (Grassini et al. 2015; Gang et al. 2019; Srivastava et al. 2019). Crop models can be used to simulate WP. AquaCrop, as a popular crop model, was used by many investigators for modeling climate change impacts on the yield of rainfed crops (Qin et al. 2015; Bird et al. 2016). In this study, an open-source version FAO AquaCrop model was used. This model simulates efficiently water-limited crop production across diverse environmental and agronomic conditions (Foster et al. 2017). Several studies have been conducted in the field of drought analyses for agricultural applications.

Tigkas & Tsakiris (2015) used AquaCrop to simulate the wheat yield under rainfed conditions for 50 years in the Mediterranean climate. Then, they determined the relationship between simulated yield by model and various periods of RDI and monthly average minimum temperatures of winter months. Their results showed that RDI can be used to estimate the effects of drought on the rainfed winter wheat yield. Mustafa et al. (2017) used RDI to determine the time of drought occurrence in the drought-prone area of Bangladesh and applied the AquaCrop model to recommend irrigation water management strategies for coping with drought. They concluded that deficit irrigation during the most water-sensitive stages could increase the interannual yield stability and the grain yield compared to rainfed conditions for different soil fertility levels on loamy and sandy soils by 21–136 and 11–71%, respectively, while it could increase WP compared to full irrigation strategies. Pirmoradian & Davatgar (2019) used the AquaCrop model to simulate the climatic fluctuation impacts on the rice irrigation water requirement for Guilan province, which is located in the north of Iran. They used the validated model to estimate the irrigation water requirement of rice for 33 years (1982–2014). Their results showed that the calculated RDI based on timescales of 3 months had the best correlation with irrigation water requirement of rice (R = −0.89). Due to changes in precipitation and temperature in Iran under the influence of various factors, especially human factors, the incidence of different droughts has intensified at different timescales (Zarei et al. 2020, 2021). On the other hand, this issue has affected the performance of winter wheat as a strategic product in the field of food security in Iran. Also, the production of this product is a priority in some areas (study stations). Due to limited water resources in these arid and semi-arid regions, rainfed cultivation was selected. Therefore, the aim of this study was to investigate the effect of different periods of drought on the WP of rainfed winter wheat. Zarei et al. (2019b) compared the accuracy of UNEP and MDM indices to assess climate conditions, based on the correlation between mentioned indices and the percent of annual yield loss in rainfed winter wheat using simple and multiple generalized estimating equation (GEE) methods. Results showed that, in all stations, the accuracy of UNEP aridity index was more than the MDM index. Zarei & Moghimi (2019a) suggested a modification for standardized precipitation evapotranspiration index (SPEI) using EP to evaluate drought, with an emphasis on the consideration of drought effects on the agricultural section. To calculate EP, FAO, USBR, USDA-SCS-simplified, and the USDA-SCS CROPWAT methods were used. To compare the calculated original and modified SPEI, the correlation coefficients (CCs) between these indices and annual winter wheat yield loss (%) were used in four synoptic stations in the suitable reference periods. Results showed that, in stations studied in this research, the CC between modified SPEI using the USBR method and annual yield loss had the highest values. Zarei et al. (2020) assessed the influence of occurrence time of drought on the annual yield of rainfed winter wheat using backward multiple GEE using the climatic data series of eight synoptic stations from 1967 to 2016 over Iran in 27 reference time periods. The results of this paper revealed that the stem extension and heading growth stages of rainfed winter wheat are the most sensitive stages of plant growth to drought occurrence which confirms the results of the present study. Zarei et al. (2021) investigated the susceptibility of winter wheat, barley, and rapeseed to drought (based on SPEI) using GEE and cross-correlation function in Iran. In this research, the climatic data series of 10 stations during 1968–2017 in selected constant and progressively increasing reference time periods, including 1-, 3-, 6-, and 12-month timescales (27 reference time periods) starting in October, were used. The results of this paper indicated that in all stations, the susceptibility of rapeseed to drought was more than that of wheat, and the susceptibility of wheat was more than that of barley.

In the literature, the effect of drought in moving different timescale on WP has not been considered. Investigating how different timescales of drought affect water utilization in the rainfed cultivation leads to increased decision-making power on how to manage this cultivation to decrease the damage reduction of drought through operations such as single irrigation and mulching. This study has focused on the WP of winter wheat affected by drought. Following subjects were considered in this study: (I) variations of meteorological indices (original RDI (ORDI) and MRDI) in seven meteorological synoptic stations over 50 years (from 1967 to 2017) in Iran, (II) determining the WP of rainfed winter wheat and its variation during the study period, using the AquaCrop model, and (III) identification of the relationship between the WP of rainfed winter wheat and meteorological indices (ORDI and MRDI) by determining CC (R) and applying the GEE method.

In this research, the calculations were performed in three stages: (I) Calculation of the WP of winter wheat, using the AquaCrop model after calibration for the time period of 1967–2017. (II) Calculation of RDI and MRDI indices in different timescales (1, 3, and 6 months and annually) for the time period of 1967–2017. (III) Consideration of drought effects on WP, using CC and the GEE model. The flowchart of methodology is presented in Figure 2.

The difference in the calculation of ORDI and MRDI is only related to the precipitation parameter (P_ij in Equation (2)) that in ORDI, P_ij is OP and in the MRDI, P_ij is EP. The classification of MRDI is the same as RDI.

There are two views (hydrological and agricultural) in defining EP. In the hydrological view, EP is the percentage of rainfall that drains out of the basin as runoff (Mahdavi 2002), and in the agricultural view, it is the percentage of rainfall that can be used productively by the plants (Tigkas et al. 2016, 2019) to meet the water requirement. In this research, the approach of EP in the fields of water consumptive use in plant development (EP in agricultural science) was considered. Different nonempirical methods, such as monitoring of soil moisture in the root zone of plants that introduced to estimate EP, require data that may not be available. Regarding this fact, empirical methods include the FAO method (MRDI-1), USBR method (MRDI-2), USDA-SCS-simplified method (MRDI-3), and USDA-SCS CROPWAT method (MRDI-4), which were used in this study.

The USBR method that is recommended to use for arid and semi-arid regions (Tigkas et al. 2019) was first introduced by the US Bureau of Reclamation. In this method, the range of monthly effective rainfall varies with the monthly rainfall changes that this range of changes is presented in Table 2.

Winter wheat (Triticum sativum), as a strategic plant, is affected by drought in arid and semi-arid climate conditions significantly. To investigate the impacts of drought, changes in winter wheat WP influenced by the severity of drought were used. WP calculation was performed using the AquaCrop model. The simulation was performed for the entire study period, based on precipitation, maximum and minimum temperatures, and potential evapotranspiration data of each station. In the stations selected for this study, winter wheat was planted in the period of October–November and harvested in the period of June–July. For mentioned investigation, the constant and moving timescales, including 1, 3, 6, and 12 months, were selected (reference periods in 1-month timescale were October, November, December, January, February, March, April, May, June, July, and August; in 3-month timescale were October–December, November–January, December–February, January–March, February–April, March–May, April–June, May–July, and June–August; in 6-month timescale were October–March, November–April, December–May, January–June, February–July, and March–August; and in 12-month timescale were October–September in each year). In this research, the main reasons for considering different timescales are (a) difference in the sensitivity of different growth stages of winter wheat to drought stress and (b) comparison of the impacts of drought occurrence and its changes in different timescales, on winter wheat WP. According to considering precipitation and evapotranspiration in the calculation of RDI, by considering different RDI timescales, in fact, the simultaneous effect of changes of these two parameters on WP in different timescales is considered.

CCs between the ORDI and MRDI values and winter wheat WP values in each station at different reference periods were used to compare and assess the calculated ORDI and MRDI. Then to calculate CCs, in normal drought indices data series, Pearson's test and in non-normal drought indices data series, Spearman's rho test were utilized. Determining the normality of ORDI and MRDI data series was evaluated using the Kolmogorov–Smirnov test.

Annual variations of the OP and EP values calculated with different methods are presented in Figure 3. Results showed that using the USDA-SCS CROPWAT and FAO methods in the calculation of monthly EP led to the most and least amount of annual EP in all of the stations studied in this research. This indicates the low amount of rainfall in the studied stations and the approximate uniformity of rainfall in the rainy months. According to the effective rainfall calculation relationships in different methods used in this research, for the amount of monthly rainfall less than 131, the USDA-SCS CROPWAT method leads to the maximum values, and for monthly rainfall less than 101, the FAO method leads to the minimum values. Between methods of USBR and USDA-SCS-simplified, in stations of Arak, Sanandaj, and Shiraz, the method of USBR and in stations of Tabriz, Zanjan, and Kerman, the method of USDA-SCS-simplified lead to the higher amount of EP. In Ghazvin station, in 6 months, the USBR method and in the other 6 months, the USDA-SCS-simplified method lead to higher values. It seems that the nature of the procedures and the equation of methods to estimate EP led to differences in the amount of calculated EP using different methods of EP calculation.

Annual variations of the WP values estimated with the AquaCrop model (WP_e) are presented in Figure 4. According to the results, in Tabriz station, the values of WP_e vary between 0.01 and 0.07, in Zanjan station vary between 0.01 and 0.15, in Ghazvin station, vary between 0.01 and 0.66, in Arak station, vary between 0.01 and 0.48, in Sanandaj station, vary between 0.01 and 0.74, in Shiraz station, vary between 0.01 and 0.95, and in Kerman station vary between 0.01 and 0.11. The reason for the low values of WP_e at Tabriz and Zanjan stations is the minimum rainfed grain yield and at Kerman station is the low rainfed grain yield and the high value of evapotranspiration. The WP values predicted using different GEE models (WP_p) are presented in Figure 5. The results indicated that at Tabriz and Zanjan stations, the GEE model of MRDI-1, at Ghazvin, Arak, and Kerman stations, the GEE model of MRDI-2, at Sanandaj station, the GEE model of ORDI, and at Shiraz station, the GEE model of MRDI-3 were more accurate because of more similarity between predicted and estimated values of WP. These results show the different effect of rainfall on rainfed winter wheat production in different regions. In Sanandaj and Shiraz stations, rainfall had the most effect (due to the results of the GEE model of ORDI and MRDI-3, which have led to more EP, lead to the most similarity) and in Tabriz and Zanjan stations had the least effect (due to the results of GEE model of MRDI-1, which has led to less EP, lead to the most similarity) on rainfed winter wheat WP improvement. These results can be used by agricultural managers to manage rainfed crops including winter wheat in these areas.

Spatial distribution of RDI in selected stations for two greenest (1968 and 1992) and two driest (1973 and 2008) years are presented in Figure 6. Annual variations of ORDI and MRDI in Tabriz, Arak, Shiraz, and Kerman stations are presented in Figure 6 (for example) for different EP calculation methods. Frequency analysis of ORDI and MRDI drought classes indicated that the normal class of drought severity had the most frequency of occurrence in all stations and all timescales. According to the results, in stations of Tabriz, Zanjan, and Kerman, the order of the EP calculation methods from the highest to the lowest was 4, 3, 2, and 1. In stations of Arak, Sanandaj, and Shiraz, the order of the EP calculation methods from the highest to the lowest was 4, 2, 3, and 1. Methods resulted in maximum and minimum values of EP in all stations and all reference periods.

Spearman's rho test was used to estimate CCs between ORDI and MRDI and WP values, in each station at all reference periods because of the abnormality of data series in all of them at 0.05 significant level according to the Kolmogorov–Smirnov test. For each of the under-study stations, the timescales, in which the CCs were significant at 0.01 or 0.05 significance level, are presented in Table 3.

Considering 1-month timescale, in Tabriz station, the month February, in Zanjan, Shiraz, and Kerman stations, the month December, and in Ghazvin, Arak, and Sanandaj stations, the months November, January, and April resulted in the highest CCs (R), respectively. At 3-month timescale, in Tabriz, Ghazvin, Sanandaj, Shiraz, and Kerman stations, the time period of October–December and in Zanjan and Arak stations, the time periods of December–February and February–April resulted in the highest value of R, respectively. Considering 6-month timescale, in Tabriz, Zanjan, and Kerman stations, the time period of October–March, in Ghazvin, Sanandaj, and Shiraz stations, the time period of November–April, and in Arak station, the time period of February–July resulted in the highest values of R. Correlation of the 12-month timescale with WP was significant only in Zanjan, Sanandaj, and Shiraz stations. Meanwhile, in Tabriz, Ghazvin, Arak, and Sanandaj stations, using the MRDI-4 resulted in the highest R values, especially in time periods of 3, 6, and 12 months. In Zanjan, Shiraz, and Kerman stations, using the MRDI-2, MRDI-1, and MRDI-3 resulted in the highest R values, respectively. According to the results of Zarei & Moghimi (2019a), the CCs between modified SPEI using the USBR method and annual yield loss had the highest values.

According to the results, the values of drought indices of early month of the growing season (October–February) have the greatest impact on WP values. These impacts may be positive or negative. The CCs were positive in all cases with the exception of month February in Tabriz station and months January and July in Arak station. In the 3-months scale, at all stations, the 3-month periods (October–December, November–January, and December–February) prior to tillering and stem elongation growth stages have the greatest impact on WP values. This shows the greater impact of the drought situation of the early 3-month periods of the growing season on WP. This is because of the more useful use of rainfed winter wheat from the mentioned 3-month rainwater. For reference periods of longer than 3 months, growth stages of lower sensitivity to water stress are added to sensitive stages, which reduces the CC or makes the relationship meaningless. For reference periods of less than 3 months, not all stages of growth sensitive to water stress are considered, which in turn reduces the CC or makes the relationship meaningless. At Arak and Sanandaj stations, the periods of February–April and March–May were also effective on WP values. In these stations, due to the climatic conditions of these areas, these 3-month periods have shifted forward. Between 6-month periods, the periods prior stem elongation and flowering have the most effect on WP values.

Agricultural operations at most effective timescales of drought that improve soil condition to retain more rainwater help the plant in the face of drought and achieve greater WP.

In the GEE model used in this research (Equation (10)), the dependent variable was WP_e that estimated using the AquaCrop model, and independent variables were RDI values in different timescales. In this model, the combined effect of independent variables (RDI at different timescales) on WP was investigated. Significant coefficients of Equation (10) are presented in Tables 4–8.

According to the results, in Tabriz station, when ORDI was the independent variable, considering the combined effect of variables, the May–July timescale had the most incremental impact on WP, and the 1-month timescale of May had the most decreasing effect on WP. For ORDI, 33% of all different timescales were significant in the model at 0.05 level. While considering MRDI as an independent variable, for MRDI-1, MRDI-2, and MRDI-3, the February–July timescale had the most incremental impact on WP, and the timescale of February–April had the most decreasing effect on WP. For these methods of RDI calculation, 41, 52, and 41% of all different timescales were significant in the model at 0.05 level. In MRDI-4, the timescales of May–July and May had the most incremental and decreasing effect on WP, respectively. For this method, 33% of all different timescales were significant in the model at 0.05 level. According to the results of CCCCs and GEE models in Tabriz station, 1-month timescales of December and February, 3-month timescales of October–December and November–January, and 6-month timescales of October–March have the highest impact on WP.

In Zanjan station, the timescale of October–March had the most incremental effect on WP for the independent variable of ORDI and MRDI (all methods). The 3-month timescale of March–May had the most decreasing effect on WP for the independent variable of ORDI, MRDI-3, and MRDI-4. For MRDI-1 and MRDI-2, the timescales of May–July and December–May had the most decreasing effect on WP, respectively. In this station, when ORDI, MRDI-1, MRDI-2, MRDI-3, and MRDI-4 were independent variables, 59, 63, 52, 44, and 59% of all different timescales were significant in the model at 0.05 level, respectively. According to the results of CCs and GEE models in Zanjan station, 1-month timescales of November, December, and June, 3-month timescales of October–December, November–January, and December–February, and 6-month timescale of October–March have the highest impact on WP. At this station, the effect of the annual timescale effect was also significant.

In Ghazvin station, for the independent variable of ORDI and MRDI (all methods with the exception of MRDI-1), the timescale of March–August had the most incremental impact on WP. For MRDI-1, the 1-month timescale of May had the most incremental impact. On the other hand, for ORDI and MRDI-4, the timescale of February–July, for MRDI-1, the timescale of May–July, and for MRDI-2 and MRDI-3, the timescale of March–May had the most decreasing effect on WP. For ORDI, 59%, MRDI-1, 33%, MRDI-2, 70%, MRDI-3, 59%, and MRDI-4, 59% of all different timescales were significant in the model at 0.05 level. According to the results of CCs and GEE models in Ghazvin station, 1-month timescales of November and 6-month timescale of November–April have the highest impact on WP.

In Arak station, the timescales of May–July for independent variables of ORDI and MRDI-4 and February–July for MRDI-1, MRDI-2, and MRDI-3 had the most incremental impact on WP. On the other hand, the 1-month timescale of May for independent variables of ORDI and MRDI-4, the timescale of February–April for MRDI-1 and MRDI-3, and October–March for MRDI-2 had the most decreasing effect on WP. In this station, when ORDI, MRDI-1, MRDI-2, MRDI-3, and MRDI-4 were independent variables, 30, 37, 52, 37, and 30% of all different timescales were significant in the model at 0.05 level, respectively. According to the results of CCs and GEE models in Arak station, 1-month timescales of January and July, 3-month timescales of February–April, and 6-month timescale of February–July have the highest impact on WP.

In Sanandaj station, the timescales of June–August, November, November–April, May–July, and March–May had the most incremental impact on WP for independent variables of ORDI, MRDI-1, MRDI-2, MRDI-3, and MRDI-4, respectively. In this station, for ORDI and MRDI-4, the timescale of December–May and timescales of July, December, and May had the most decreasing effect on WP for MRDI-1, MRDI-2, and MRDI-3, respectively. In this station, when ORDI, MRDI-1, MRDI-2, MRDI-3, and MRDI-4 were independent variables, 44, 11, 7, 15, and 41% of all different timescales were significant in the model at 0.05 level, respectively. According to the results of CCs and GEE models in Sanandaj station, 1-month timescale of November, 3-month timescales of October–December, November–January, and March–May, and 6-month timescales of November–April and March–August have the highest impact on WP. At this station, the effect of the annual timescale effect was also significant.

In Shiraz station, for independent variables of ORDI, MRDI-3, and MRDI-4, the timescale of November–April and for MRDI-1 and MRDI-2, the timescale of February–July had the most incremental impact on WP. On the other hand, the timescale of March–August had the most decreasing effect on WP for ORDI, MRDI-2, and MRDI-4. For MRDI-1 and MRDI-3, the timescales of February and December–May had the most decreasing effect on WP. In this station, when ORDI, MRDI-1, MRDI-2, MRDI-3, and MRDI-4 were independent variables, 41, 22, 26, 37, and 44% of all different timescales were significant in the model at 0.05 level, respectively. According to the results of CCs and GEE models in Shiraz station, 3-month timescales of October–December and November–January and 6-month timescale of November–April have the highest impact on WP. At this station, the effect of the annual timescale effect was also significant.

In Kerman station, the timescale of October–March had the most incremental effect On WP for ORDI and all methods of MRDI. In this station, for ORDI, MRDI-1, and MRDI-3, the timescales of March–August, February–April, and August had the most decreasing effect on WP, respectively. For MRDI-2 and MRDI-4, the timescale of January–March had the most decreasing effect on WP. In this station, when ORDI, MRDI-1, MRDI-2, MRDI-3, and MRDI-4 were independent variables, 59, 22, 63, 33, and 59% of all different timescales were significant in the model at 0.05 level, respectively. According to the results of CCs and GEE models in Kerman station, 6-month timescale of October–March has the highest impact on WP.

As can be seen in the results, in all stations, at timescales when the CC was significant, the coefficients of the GEE model were greater than the others. However, in the GEE model, the effect of more timescales was significant because of the simultaneous evaluation of the impact of variables. In GEE models, the timescales that were prior to or coincident with the different growth stages of winter wheat had the most significant effects. The difference in different methods is related to how effective rainfall is calculated in these methods. The reason for the difference in effective timescales at different stations is the difference in the time distribution of rainfall during water year and the difference in the occurrence time of winter wheat growth stages. This difference is due to the difference in the average monthly temperature at different stations, which determines the time of occurrence of different stages of growth based on the growing degree days concept.

As mentioned earlier, the drought of timescales with positive coefficients had an incremental impact on WP. In other words, with increasing RDI (decreasing drought), WP was increased. On the other hand, the drought of timescales with negative coefficients had a decreasing effect on WP. In other words, with increasing RDI (decreasing drought), WP was decreased. The incremental effect of RDI increasing on WP may be due to the increasing effect of increasing precipitation on grain yield value during the growth stage. The decreasing effect of RDI increasing on WP may be due to the decreasing effect of increasing precipitation on grain yield value (such as waterlogging and inappropriate time distribution) during the growth stage. The results of this research confirm the results of Tigkas & Tsakiris (2015) and Zarei et al. (2020). According to the results, Tigkas & Tsakiris (2015) show that the RDI, for reference periods that represent the critical development stages of the crop, is highly correlated with the wheat yield. According to Zarei et al. (2020), the stem extension and heading growth stages of rainfed winter wheat are the most sensitive stages of plant growth to drought occurrence.

A satisfactory prediction of the drought impacts on wheat yield 2–3 months before the harvest can be achieved. This indicates that the management of drought effects may be necessary to adopt water conservation practices such as mulching to control soil evaporation in highly correlated timescales with WP.

To evaluate the accuracy of GEE models, different criteria of the goodness of fit (NSE, RMSE, MAE, and R²) were used. The results of this evaluation are presented in Table 8. High values of NSE and CC (R² value) and small values of RMSE, MAE, and standard error indicate a good model. As can be seen in Table 8, in Tabriz and Zanjan stations, according to all of the goodness-of-fit parameters, the best model was obtained when MRDI-1 was the independent variable. In Ghazvin and Arak stations, according to all of the goodness-of-fit parameters, the best model was obtained when MRDI-2 was the independent variable, with the exception of the MAE parameter in Arak station, that according to this parameter, the best model was obtained when MRDI-3 was the independent variable. In Sanandaj station, according to all of the goodness-of-fit parameters, the best model was obtained when ORDI was the independent variable, with the exception of the MAE parameter, that according to this parameter, the best model was obtained when MRDI-4 was the independent variable. In Shiraz station, according to all of the goodness-of-fit parameters, the best model was obtained when MRDI-3 was the independent variable. In Kerman station, according to all of the goodness-of-fit parameters, the best model was obtained when MRDI-2 was the independent variable.

Identifying the most effective timescales related to the impact of drought on WP at different regions was one of the main objectives of this study. By using goodness-of-fit criteria, the best GEE models were recognized that these models considered the effects of all predictors (x₁, …, x₂₇). In practical cases, the effects of one or more predictors may not be significant (P > 0.05). In this research, the backward multiple GEE step by step removes the noneffective variables. The final GEE model contains minimum variables and has acceptable accuracy. According to the final GEE model obtained in different stations and also the CC related to the most effective method of estimating EP, the timescales in which drought had the most significant impact on WP were identified. The significant timescales in Tabriz station were 3-month timescale of October–December and 6-month timescale of October–March, and in Zanjan station were 1-month timescale of December, 3-month timescales of November–January and December–February, 6-month timescale of October–March, and annual timescale. In Ghazvin station, 6-month timescale of March–August and in Arak station, 1-month timescale of January and 6-month timescale of February–July had a significant effect. The significant timescales in Sanandaj station were 3-month timescales of October–December and March–May and 6-month timescale of November–April, and in Shiraz station was 6-month timescale of November–April. In Kerman station, 6-month timescale of October–March had a significant effect. These results indicate the most significant effects of timescales that were prior to or coincident with the different growth stages of winter wheat, which confirms the results of Zarei et al. (2020).

The sector most affected by drought, especially in arid and semi-arid regions, is agriculture. If more effective timescales of water year are identified, they can be helpful in managing drought damage to the agricultural sector. Rainfed cultivation suffers the most because its source of water supply is rainfall. For this study, winter wheat crop, which is a strategic crop in the field of food security, was selected. Determining effective rainfall is very important in rainfed crop management. In this study, the well-known index of RDI was used to quantify the drought, and a modified version of this index (MRDI) was used to take into account the effective rainfall. To investigate the effect of drought at different time periods in the wet year, this index was calculated at different timescales (fixed and moving) (27 reference periods). For investigating the impact of drought on agriculture, a performance measure of WP, which is a comprehensive measure, was used which simulated with the AquaCrop model for rainfed winter wheat.

The results indicated that the timescales prior to or coincident with the critical growth stages of winter wheat had the most significant effects, especially 3- and 6-month timescales. The values of drought indices of early months of the growing season (October–February) have the greatest impact on WP values. The CCs were positive in all cases with the exception of month February in Tabriz station and months January and July in Arak station. The highest value of R was obtained in Shiraz station for a 1-month scale and the MRDI-1 method.

In all stations, the higher coefficients of the GEE model were obtained at timescales with a significant CC. However, in the GEE model, because of the simultaneous evaluation of the impact of variables, the effect of more timescales was significant. In GEE models, the timescales that were prior to or coincident with the different growth stages of winter wheat had the most significant effects (positive or negative). The smaller timescales (1 and 3 months), generally, resulted in negative effects, and the larger timescales resulted in positive effects. According to the goodness-of-fit parameters, in Tabriz and Zanjan stations, the best GEE model was obtained when MRDI-1 was the independent variable. In Ghazvin, Arak, and Kerman stations, the best GEE model was obtained when MRDI-2 was the independent variable. In Shiraz and Sanandaj stations, the best GEE model was obtained when MRDI-3 and ORDI were the independent variables, respectively. The results of this research confirm the results of Tigkas & Tsakiris (2015) and Zarei et al. (2020). Zarei et al. (2020) assessed the influence of the occurrence time of drought on the annual yield of rainfed winter wheat using GEE. The results of this paper revealed that the stem extension and heading growth stages of rainfed winter wheat are the most sensitive stages of plant growth to drought occurrence, which confirms the results of the present study. The proposed methodology can be useful to the authorities and stakeholders for facing drought events and mitigating losses in rainfed agriculture. Finally, the results of the presented paper are proper for areas with arid and semi-arid climates (according to the climate of selected stations). Therefore, it should be noted that to use the GEE model in different climate conditions, the model requires calibration and adaptation. It is also suggested to use daily data in the AquaCrop model to increase the accuracy of work, which in this study was not possible due to lack of access to daily data.

The data used in this research are available from the corresponding author upon reasonable request.