Introduction

The world's population is growing, and as a result, water resources per capita are shrinking (Dinar et al. 2019). The global water demand has been increasing at a rate of about 1% per year, and it will continue to grow significantly over the next two decades (UN-Water 2018). Although there is a fiercer competition for water between sectors, agriculture will remain the largest water consumer in the world (Pereira 2017; UN-Water 2018). Water scarcity is the main challenge, especially in arid and semi-arid regions. It is estimated that due to the growing world population, the amount of food production by the agricultural sector in 2050 should increase by 50% compared to 2013 (FAO 2017). Enhancing crop water productivity, which could be defined as the crop production per unit of (applied) water (Molden 1997), is a way to increase total food production (Kang et al. 2017). Deficit irrigation is a strategy to increase crop water productivity (Geerts and Raes 2009) in arid and semi-arid regions such as Iran. Soil characteristics and weather parameters are among the factors affecting crop yield (Hakojärvi et al. 2013; Merlos et al. 2015) and, subsequently, crop water productivity in the potential and water-limited conditions. Kukal and Irmak (2017) analyzed spatial and temporal dynamics of county-level crop yields of nine major crops in the USA (maize, soybeans, spring wheat, winter wheat, alfalfa, sorghum, cotton, barley, and oats) due to differences in management, environmental conditions, soils, and the applied policies. Due to spatial changes in soil characteristics and spatio-temporal variations in weather parameters, it can be expected that crop water productivity has spatial and temporal differences (Ahmad et al. 2004; Maestrini and Basso 2018). Kravchenko and Bullock (2000) studied the relationship between maize and soybean yield with topography and soil characteristics. According to their results, 30 and 20% of spatial differences in crop yields were due to soil characteristics and topographic conditions, respectively. Ahmed et al. (2004), using measured data from the farmers’ field in Punjab, Pakistan, have identified differences in water use, sowing date, fertilizer use, soil quality, socio-economic conditions, and rainfall as factors causing temporal and spatial variations in crop water productivity. Water productivity in their study was in the range of 0.17–0.38 and 0.78–2.03 kg m−3, respectively, for rice and wheat. Spatial variation of water productivity for cotton and rice in the Syr Darya basin in central Asia indicated a high potential to increase average values of water productivity within the basin (Abdullaev and Molden 2004). Cai Et al. (2014) stated that increasing air temperature had negative and positive effects in warm and cold regions on maize performance. However, the impact of rainfall on crop yield is more complex and is affected by irrigation. Van Wart et al. (2013) studied spatial and temporal variation in maize yield in the USA, rice in China, and wheat in Germany. According to their results, changes in the performance of these crops were influenced by weather factors. Moreover, regions with more regular topography had lower crop yield variations than areas with more irregular topography.

Crop growth simulation models that describe the relationship between soil, water, atmosphere, and crop are appropriate tools for estimating the impact of irrigation management on crop growth and its performance (Edreira et al. 2017; Lak et al. 2019; Motha 2011). These models have been used to estimate crop water requirement, yield, and consequently, water productivity in potential and limited situations (Ababaei et al. 2014). Pohanková et al. (2018) used WOFOST (WOrld FOod STudies) (Van Diepen et al. 1989), CERES-Barley (Otter-Nacke et al. 1991), HERMES (Kersebaum 2011), DAISY (Abrahamsen and Hansen 2000), and AquaCrop (Steduto et al. 2009) models to investigate water use efficiency of spring barley in three regions in the Czech Republic. Wu et al. (2008) used the WOFOST model to study the spatial and temporal variation of maize growth between 1961 and 2000 in northern China. According to their results, the growth of maize was affected by spatial and temporal variations of weather conditions. Moreover, changes in the soil water-holding capacity cause changes in the crop yield. Greaves and Wang (2016) employed the AquaCrop model to examine the effect of irrigation management on the maize yield. They have determined the best irrigation management strategy that led to the highest water productivity in their study. Ashraf Vaghefi et al. (2017) combined SWAT (Arnold et al. 1998) and MODSIM (Labadie 2006) models to examine water productivity for wheat and maize in the Karkheh catchment area. The accuracy of the combined model was increased by considering the amount of water allocation obtained from the MODSIM model. Considering the complexity, accuracy, and the number of required parameters (Abi Saab et al. 2015; López-Urrea et al. 2020; Quintero and Díaz 2020; Steduto et al. 2009), AquaCrop which is exclusively based on the water-driven growth module (Todorovic et al. 2009) was selected to simulate crop growth in this study. AquaCrop was developed by the Food and Agriculture Organization of the United Nations (FAO); is a relatively simple and user-friendly model; and its capability for the simulation of crop growth in a wide range of crops under a variety of climatic conditions have been reported (Steduto et al. 2009).

The crop growth simulation models which, are point models, could be coupled with Geographic Information System (GIS) to execute at multiple spatial locations. Ines et al. (2002), by coupling the crop growth model of CERES and GIS, have studied spatio-temporal changes in crop water productivity in the Laoag River catchment area, Philippines. They concluded that the spatio-temporal analysis of water productivity could provide important information for water-saving opportunities. Thorp and Bronson (2013) have developed a geospatial toolbox named GeoSim that can be used to manage input files of AquaCrop and DSSAT for execution at multiple spatial locations. As weather data are recorded at meteorological stations, weather data interpolation is a common method for estimating the spatial variation of weather data. Chaudhari et al. (2010), using generated weather data in the grids of 25 * 25 km, estimated spatial changes in the wheat yield by the WOFOST model. In the framework of the Monitoring Agriculture with Remote Sensing (MARS) project which was initiated by the European Commission, an agro-meteorological model was developed which was later called the Crop Growth Monitoring System (CGMS) (Van Diepen and Boogaard 2009). Sargordi et al. (2013) and Ahmadi et al. (2014) used this system for spatial and temporal analysis of crop yield and water requirements in Iran. In this system, the study area was divided into homogenous units in terms of soil and weather. For each grid weather, weather parameters were generated based on available data in the weather stations using the inverse distance weighting method. The weight of each station is calculated based on the concept of equivalent distance, which is calculated based on the distance and changes in elevation between the weather station and the center of grid weather. One of the advantages of the grid weather generator in this system is the interpolation of the weather data based on the concept of equivalent distance. The equivalent distance is calculated based on the differences between the elevation of the weather station and the average of elevation in the grid, as well as the horizontal distance between the weather station and grid weather center (Savin et al. 2004).

Kermanshah Province, with fertile lands, is one of the agricultural hubs in Iran. Agricultural activities are the most important means of livelihood for many people in Kermanshah Province (Keshavarz et al. 2016). Maize is a major crop in Kermanshah Province (Choukan and Shirkhani 2010). Single Cross 704 cultivar, which is the most common maize variety in Iran, is also cultivated in this region (Khavari Khorasani et al. 2008). This study aimed at proposing a combined method for estimating the spatial and temporal variation of crop yield, seasonal evapotranspiration, and water productivity under deficit irrigation conditions. The proposed method was implemented in a case study in the Gavoshan irrigation network, Iran.

Materials and methods

Study area

The efficiency of the proposed method was investigated for estimating crop yield, water requirement, and water productivity of maize under different irrigation scenarios in the Gavoshan irrigation and drainage network, located in Kermanshah and Kurdistan Provinces, Iran (Fig. 1). The irrigation network includes 6910 hectares of agricultural lands in the Miandarband and Bile-var plains. This irrigation network includes 9 and 4 irrigation zones, respectively, in Miandarband and Bile-var plains. Irrigation zones located in Bile-var and Miandarband plains are called by the acronyms B and D, respectively, along with the index number of that area. The study area has a relatively temperate climate and is cold in the winter months. The average annual rainfall in Miandarband and Bile-var plains is 463 and 444 mm, respectively, and the average annual pan evapotranspiration in these plains is almost three times of annual rainfall (1377 and 1310 mm, respectively).

Fig. 1
figure 1

Location of the study area

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AquaCrop model

AquaCrop is a canopy-level and water-driven model which simulates crop biomass and harvest index as constrained by water availability (Steduto et al. 2009). The AquaCrop model is based on the FAO approach, which estimates a decrease of crop yield in response to water stress (Doorenbos and Kassam 1979) (Eq. 1).

$$\left( {1 - \frac{{Y_{{\text{a}}} }}{{Y_{{\text{m}}} }}} \right) = K_{y} *\left( {1 - \frac{{{\text{ET}}_{{\text{a}}} }}{{{\text{ET}}_{{\text{c}}} }}} \right)$$
(1)

where Ya: actual crop yield (corresponding to ETa) (kg ha−1), Ym: maximum theoretical crop yield (corresponding to ETc) (kg ha−1), ETa: actual crop evapotranspiration (mm), ETc: potential crop evapotranspiration (mm), Ky: crop yield response factor to water deficit (–).

Two fundamental principles separate this water-driven “growth engine” from other cropping models. AquaCrop predicts green canopy cover (CC) instead of the leaf area index (LAI). It calculates evapotranspiration (ET) from the flowing water in and out of a system on a daily basis and partitions it into evaporation (E) and transpiration (T) (Araya et al. 2010; Toumi et al. 2016). AquaCrop estimates daily biomass production using Eq. 2:

$$B_{i} = {\text{WP}}^{*} *\sum \left( {\frac{{{\text{Tr}}_{i} }}{{{\text{ET}}_{{{\text{oi}}}} }}} \right)$$
(2)

where Bi is the daily aboveground biomass, Tri is the daily crop transpiration, EToi is the daily reference evapotranspiration, and WP* is the water productivity of the crop species normalized for both evaporative demand and atmospheric CO2. The normalization of WP for climate makes AquaCrop applicable to diverse locations and seasons, including future climate scenarios (Karunaratne et al. 2011). Crop yield was obtained by multiplying aboveground biomass and specified harvest index (HI) using Eq. 3 (Steduto et al. 2009).

$$Y = {\text{HI}}*B$$
(3)

where Y is the main yield (kg ha−1), B is aboveground biomass (kg ha−1), and HI is the harvest index (%).

The AquaCrop model distinguishes four water stress effects on leaf expansion, stomatal conductance, canopy senescence, and harvest index (Steduto et al. 2009). Except for the harvest index, these effects are expressed through their stress coefficient, Ks, an indicator of the relative intensity of the impact. The Ks values are a function of soil water depletion and are reflected in the canopy growth of the crop. The model requires the estimation of the total available water (TAW) of the soil and adjusts the Ks values based on the fraction of the TAW, which has been depleted (p). Water stress affecting leaf expansion begins when the fraction of TAW depleted exceeds an upper threshold (pupperexp), and leaf expansion ceases when the fractional depletion exceeds a lower threshold (plowerexp). Likewise, there are upper thresholds for water stress affecting stomatal conductance and canopy senescence, and the corresponding lower thresholds are defined by the permanent wilting point of the soil (Geerts and Raes 2009; Steduto et al. 2009). In this model, transpiration (Tr) is calculated using Eq. 4:

$$T = K_{{\text{s}}} *{\text{CC}}*K_{{{\text{c}}_{{{\text{Trx}}}} }} *{\text{ET}}_{0}$$
(4)

where Ks is the soil water stress coefficient including waterlogging, stomatal closure and soil salinity stress, CC* is the actual canopy cover adjusted for micro-adventive effects, KcTr,x is the coefficient for maximum crop transpiration (well-watered soil and complete canopy, canopy cover = 100%), and ET0 is the reference evapotranspiration which is calculated in this study using the FAO Penman–Monteith method (mm day−1) (Allen et al. 1998).

Research methodology

The main steps in this study are: (1) delineation of homogeneous units, (2) generation of grid weather data, (3) generation of irrigation scenarios, (4) simulation of the crop growth of maize, based on 28-year (1988–2015) weather data in all homogeneous units, and (5) analysis of the results (Fig. 2).

Fig. 2
figure 2

Main steps of the study

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Soil characteristics and weather conditions are principal environmental factors which have impacts on crop growth and subsequently crop yield and water requirement. Therefore, the study area was divided into homogenous units in terms of soil and weather characteristics. According to the previous studies and available soil reports, 19 soil units were identified in the study area (Fig. 3). Soil physical characteristics of these units, which are required for the AquaCrop model, are presented in “Appendix 1”.

Fig. 3
figure 3

Location of soil units (coordinate system: UTM, Zone 38 N)

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To define homogenous units in terms of weather conditions, the study area was divided into 37 grids with a size of 5 by 5 km. By overlaying the soil units and grid weather, 94 homogenous units were created. Grid weather data were generated using weather data interpolation tools in the CGMS package software (Savin et al. 2004). For this purpose, daily weather data (minimum temperature, maximum temperature, wind speed at the height of 2 m, vapor pressure, and sunshine hours) from 1988 to 2015 and the geographical coordinates (longitude, latitude, and altitude) of 24 weather stations located in the study area and its adjacent areas (Fig. 4) were stored in the appropriate tables in CGMS software. In the rain gauge and evaporation stations, only rainfall and temperature are measured. The weather data were provided by the Iranian meteorological organization. The list of weather stations is presented in “Appendix 2”.

Fig. 4
figure 4

Location and type of weather stations

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In this package, the weather data (except rainfall) in the center of each grid are interpolated using the inverse distance weighting method. The score of each weather station in each grid is calculated considering the horizontal distance between the location of the weather station and the center of grid weather as well as differences between the altitude of the weather station and average altitude in the grid (Savin et al. 2004). In the CGMS, it is assumed that the weather parameters of temperature, sunshine hours, relative humidity, and wind speed change gradually, while the rainfall changes abruptly. For each grid, the CGMS model retrieves rainfall data from the most similar weather station (highest score). The rest of the weather parameters were interpolated in each grid by interpolating weather data, in the four weather stations with the highest score. This software does not require the reconstruction of missing weather data and, in this case, uses the average of long-term data. Reference evapotranspiration (ETo) is required as the input file for AquaCrop. It was calculated based on generated grid weather using the FAO Penman–Monteith formula (Allen et al. 1998). The ETo calculation was performed in a Microsoft Excel spreadsheet.

The AquaCrop model requires input files such as climate (temperature, ETo, and CO2 files), crop, soil (soil profile and groundwater files), and management (irrigation and field files). For each grid temperature, ETo files were created. The default file of CO2 was used for all grids. A soil file was created for each soil unit based on measured soil physical parameters in the available reports. Given that the depth of groundwater in the study area was more than 30 m, it was assumed that the depth of groundwater in this area does not affect crop growth. The crop file is one of the most important input files of this model, which should be calibrated. In this study, the calibrated crop file of maize in Kermanshah was used (Ahmadpour 2013).

To investigate the effect of irrigation management on crop water productivity, four irrigation scenarios (S40, S60, S80, and S100) were defined as 40, 60, 80, and 100% of irrigation requirement (Penman method, FAO modified). “Determination of net irrigation water requirement” is an optional irrigation management mod in the AquaCrop software. The net daily irrigation requirement for each year and homogeneous unit under non-water stress conditions (considered as irrigation requirement in the S100 scenario) were determined using this option. Then, for each year and scenario, an irrigation file was created with irrigation interval of seven days. In all scenarios, to ensure crop establishment, the water deficit was not considered in the first three weeks of the growth period.

In total, AquaCrop should be run 10,528 times to simulate the growth of maize in 94 homogeneous units, 28-year weather data, and four irrigation scenarios. Although it was initially decided to use the AquaCrop-GIS (Lorite et al. 2015) for this large number of model simulations, in practice, it did not meet the expectations of researchers. Therefore, the plug-in version of AquaCrop 6.0 was used for simulations. For this purpose, a list of (multiple runs) project files was created based on the reference manual of AquaCrop plug-in program (Raes et al. 2011), and all 10,528 runs were executed simultaneously.

The model outputs, including crop yield (grain and biomass) and crop water use for all 10,528 runs, were stored in a Microsoft Access database. It should be mentioned that in this paper, biomass and grain yield are reported in terms of dry matter. Crop water productivity in each run was calculated as the ratio of crop yield over the seasonal crop water use. Due to the relatively large volume of data, it was difficult to analyze all the results simultaneously. Therefore, the results were analyzed from two perspectives (temporal and spatial analysis). For temporal analysis, the weighted average of studied parameters (biomass, grain yield, evapotranspiration, and water productivity) in the whole study area was calculated for each year and scenario (averaging over space). The analysis was carried out graphically and statistically. The minimum, maximum, and mean of each parameter during the study period (1988–2015) were determined for each scenario. The coefficient of variation (CV), which is defined as the ratio of standard deviation to the mean of the data, was consulted to examine the range of annual changes in the studied parameters. To investigate the effect of irrigation scenarios, the percentage reduction of the mean of the studied parameters compared to the S100 scenario was also calculated.

For spatial analysis, the average of studied parameters (biomass, grain yield, evapotranspiration, and water productivity) in the study period (1988–2015) for each homogenous unit and scenario was calculated (averaging over time). Grain yield, biomass, seasonal water use, and crop water productivity maps were generated for each scenario. Finally, results were analyzed graphically and statistically as was performed for spatial analysis.

Analysis of the results

Quality assessment of results

Although the crop file was calibrated based on the data of the research farm in Kermanshah (Ahmadpour 2013), the model outputs were also compared with the real data of farmers in the region. The yield of the simulated crop in scenario S100 was compared with the yield of the top corn producers in the region. Maize yields recorded by these farmers are 12,000, 12,200, 12,000, 12,400, 12,500, 12,800, and 13,000 kg ha−1, respectively, in the years 2002, 2003, 2005, 2008, 2010, 2013, and 2015. The simulated crop yield by the AquaCrop model is dry matter, multiplied by 1.14 (14% grain moisture) to calculate fresh grain yield. The maximum difference between the average simulated grain yield at the S100 scenario and the best maize producers in the region was less than 8% (Fig. 5). This difference was lower in recent years.

Fig. 5
figure 5

The average of simulated grain yield and measured yield at farms of best maize producers in the region

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The minimum, average, and maximum simulated seasonal crop water requirements (S100 scenario) in the study area were 686, 760, and 816 mm. To assess the accuracy of calculated crop water requirement by the model, in the absence of no measured data, results were compared against literature. Barati et al. (2019) calculated the crop water requirement of maize, based on 30-year weather data (1986–2015) in Kermanshah plain, which is close to the study area. The average calculated crop water requirement of maize in that study was 784 mm, which is almost the same as that in this study (760 mm). It should be mentioned that the period of both studies was almost the same.

Temporal analysis

The annual average of simulated crop parameters (biomass, grain yield, evapotranspiration, and water productivity) of maize in the study area between 1988 and 2015 for various irrigation scenarios is presented in Fig. 6.

Fig. 6
figure 6

Temporal changes in biomass (a), grain yield (b), seasonal crop evapotranspiration (c), and crop water productivity (d) in 1988–2015

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Results showed that the crop yield (biomass and grain), crop evapotranspiration, and crop water productivity have been affected by water stress and weather conditions. Also, the impact of water stress (irrigation scenario) on studied parameters is much more than yearly variations in weather conditions. Summary statistics of studied parameters also show the same results (Table 1).

Table 1 Statistical summary of the studied parameters in the temporal analysis for the whole study area
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With increasing water stress in irrigation scenarios, the crop yield (grain and biomass) decreases further. Grain yield under S40 and S60 scenarios was significantly lower than S80 and S100 scenarios (Fig. 6). The average of simulated biomass reduced 8.4, 36.4, and 77.8% for the scenarios of S80, S60, and S40 relative to the full irrigation scenario (S100), respectively (Table 1). The percentage of grain yield reduction for S80, S60, and S40 scenarios was estimated at 8.8, 38.0, and 82.0%, respectively (Table 1).

The annual crop yield variation was affected by irrigation scenarios. In the scenarios with higher water stress, the coefficient of variation (CV) for crop yield (biomass and grain) was higher. The CV values of biomass yield for S100 and S40 scenarios were 4.1% and 10.1%, respectively. Almost the same results were obtained for the grain yield.

In this study, it is assumed that soil and crop characteristics are constant during the study period. So, the same crop and soil files have been used to simulate crop growth in each year and homogeneous unit. Therefore, it can be concluded that for each scenario, the difference between crop yields in different years is related to annual changes in weather parameters. In semi-arid regions such as the study area, by increasing water stress intensity, there are more adverse effects of climatic parameters on crop yield. Machado et al. (2002), Ahmadi et al. (2014), Ara et al. (2016), Grassini et al. (2014), Ababaei et al. (2014), Merlos et al. (2015), Cai et al. (2014), Van Wart et al. (2013), Wu et al. (2008) and Hakojärvi et al. (2013) are among the studies confirming the effect of weather conditions on temporal changes in crop yield.

The average seasonal crop evapotranspiration in the study area was estimated as 760, 713, 558, and 377 mm, respectively in S100, S80, S60, and S40 scenarios. This means that seasonal crop evapotranspiration in S80, S60, and S40 scenarios would be 6.2, 26.6, and 50.4% less than S100, respectively (Table 1). Minimum and maximum seasonal crop evapotranspiration for S100, in the study period, was calculated as 686 and 816 mm in the years 1988 and 2008, respectively. Annual changes in seasonal crop evapotranspiration have not been significantly affected by deficit irrigation scenarios (Fig. 6c). The annual CV of this parameter was 4.3, 4.6, 4.7, and 4.2% for the S100, S80, S60, and S40 scenarios, respectively. The low values of CV for seasonal crop evapotranspiration could be related to the fact that temperature has two opposite impacts on this parameter. The seasonal crop evapotranspiration is a function of two factors, daily crop evapotranspiration and growth period. Higher temperatures reduce the growing season while increasing the daily evapotranspiration of the crop. Therefore, the effect of temperature on seasonal crop evapotranspiration is not great. The same results are also reported by Grassini et al. (2014) on soybean in the United States, Ara et al. (2016) on rice in Bangladesh, Sargordi et al. (2013) on wheat and forage maize in Iran, and Cai et al. (2014) on maize in the United States.

As water stress increases, water productivity (WP) decreases. The average WP of maize in the studied period was estimated to be 1.5, 1.4, 1.2, and 0.5 kg m−3, respectively, in S100, S80, S60, and S40 scenarios. This indicates a decrease of 2.7, 15.8, and 64.4%, respectively, for S80, S60, and S40 compared to the S100 scenario (Table 1). The amount of WP in the S100 and S80 scenarios was close to each other (Fig. 6d). Since the rate of reduction of grain yield and seasonal crop water requirement in S80 compared to S100 is almost the same (Fig. 6b, c), there was no significant difference between the water productivity of S100 and S80 scenarios. These findings agreed with those of Abdullaev & Molden (2004) and Ashraf Vaghefi et al. (2017). It should be mentioned that the findings were different from those of Ahmadi et al. (2014) in Iran. Due to the low WP of severe deficit irrigation scenarios (S40 and S60), these scenarios are not recommended in the study area. Results indicated that the S80 scenario can be used to reduce water consumption instead of S100 without significantly decreasing WP and production revenues of grain yields. Overall, for irrigation scenarios, the temporal CV values of WP were estimated to be higher than the crop yield and seasonal crop evapotranspiration (Table 1, Fig. 9). The temporal CV values of WP for scenarios S100, S80, S60, and S40 were determined as 6.1, 7.0, 8.4, and 8.8, respectively, indicating greater CV values by increasing water stress.

Spatial analysis

The long-term average of simulated parameters (biomass and grain yield, crop evapotranspiration, and water productivity) was calculated for each homogeneous unit and irrigation scenario. The maps of these parameters were produced. Although these maps are created for all scenarios, only the maps of the S100 scenario are presented in Fig. 7, and the information from the maps in other scenarios is presented in the form of tables and text.

Fig. 7
figure 7

Average spatial changes of biomass yield (a), grain yield (b), and seasonal evapotranspiration (c) of maize in S100 scenario

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Results showed that by increasing water stress, the average crop yield (grain and biomass) in each homogeneous unit is lowered. The simulated crop yield in homogeneous units was different, and these differences widened by higher water stress intensity. The average simulated biomass and grain yield in the S100 scenario were in the range of 22.2–30.4 and 9.3–12.8 tons per hectare, respectively (Fig. 7a, b). Yield differences between homogeneous units are due to differences between soil properties and weather conditions of these units. The spatial CV in biomass and grain yield was 5.4 and 5.5 percent under the S100 scenario respectively and increased to 30.1 and 33.6 percent under the S40 scenario (Table 2). It was also observed that spatial CVs in maize yield were more than temporal CVs (Fig. 9). Results also indicated that the spatial CV of crop yield rises by increasing water stress intensity.

Table 2 Statistical summary of the studied parameters in the spatial analysis for the study area
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The average seasonal evapotranspiration of maize under S40, S60, S80, S100 scenarios is calculated as 377, 558, 713, and 760 mm, respectively. Seasonal crop evapotranspiration also had spatial changes, although these changes were less than crop yield spatial variation (Table 2). The long-term (1988–2015) average of seasonal crop evapotranspiration was in the range of 719–818 mm over the study area. The spatial variation of seasonal crop evapotranspiration was less than the crop yield. The minimum and maximum spatial CVs for seasonal crop evapotranspiration in irrigation scenarios were 2.3% and 3.6% (Table 2). There were no significant differences between the spatial CV of the studied scenarios. In the central and western parts of the Miandarband plain, which have a relatively colder climate than other regions, the seasonal crop evapotranspiration values of maize for all irrigation scenarios were higher than other areas in the plain (Fig. 7c).

Results showed that crop water productivity, which is calculated as the ratio of crop yield over the seasonal crop evapotranspiration, has a spatial variation (Fig. 8). In the area with a colder climate, crop yield and seasonal crop evapotranspiration increased but at different rates. As in these units, the rate of increasing crop yield was higher than seasonal crop evapotranspiration, and the WP was higher than other regions. In general, the average WP of maize in the Miandarband plain was higher than the Bile-var plain. The simulated crop water productivity under the S100 scenario varied from 1.2 to 1.6 kg m−3 over the study area (Table 2). By increasing the water stress, the spatial CVs of WP of maize increase. The CV of crop water productivity was increased from 6.0% in the S100 scenario to 30.1% in the S40 scenario. The spatial CVs of this parameter, such as other studied parameters, were higher than the temporal CVs (Fig. 9). According to the results of Ahmadi et al. (2014), Abdullaev & Molden (2004), and Ashraf Vaghefi et al. (2017), changes in weather parameters (temperature, precipitation, and solar radiation) as well as spatial changes in soil physical properties (water-holding capacity, topography, and hydraulic conductivity) form one zone to another can explain spatial changes in the WP.

Fig. 8
figure 8

Average spatial changes of water productivity for scenarios S40 (a), S60 (b), S80 (c), and S100 (d)

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Fig. 9
figure 9

Comparison of spatial and temporal CVs of studied parameters under irrigation scenarios

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Conclusion

In this study, a combined method was developed for analyzing the spatio-temporal variation of yield (grain and biomass), seasonal crop evapotranspiration, and water productivity under various irrigation scenarios. In this method, a GIS system-based software was used to display and analyze spatial data; the Reference Weather tool of the CGMS was employed for interpolating and generating daily meteorological data; and the calibrated AquaCrop model was adopted to simulate the potential yield, crop evapotranspiration, and WP under various irrigation scenarios. Given that the model needed 10,528 runs in this study, the use of AquaCropGIS was considered an option to run the simulation, but the current version of this software (version 2.1) had several deficiencies. The preparation of project files and automatic execution of the model using the plug-in version of AquaCrop software were among the challenges in this research. The codes developed for this issue facilitated the execution of the simulation. Storing model outputs in a geodatabase and joining them to homogeneous units in the GIS environment allows the mapping of studied parameters in order to study their spatial variation. The developed method was implemented in a case study in the west of Iran. The simultaneous impacts of water stress and spatio-temporal variations in weather parameters and soil characteristics over the 94 homogenous units and 28 years of daily weather data on studied parameters were simulated by the developed model. The model showed the capability of calculating spatial and temporal variations of studied parameters (crop yield, seasonal crop evapotranspiration, and crop water productivity) as the results of soil and weather variations over the region. Results indicated that all the studied parameters have spatial and temporal variations. The spatial variations of the crop yield were higher than temporal variations. According to this result, it can be said that the effect of spatial changes in soil properties on the crop yield in the study area is greater than the annual changes in weather parameters. The results also showed that deficit irrigation enhances spatial and temporal changes in crop yield and crop water productivity and at a lower rate the seasonal crop evapotranspiration. The variations of seasonal crop evapotranspiration were calculated less than crop yield and water productivity. Considering the results of this study, it is recommended to apply 20% deficit irrigation for maize in the study area. Finally, the results showed that the proposed method in this study was a method with appropriate speed for examining the spatial and temporal variation of water productivity in irrigation and drainage networks. This approach can be used as a tool to enhance agricultural management and irrigation planning.