The need for accurate and up-to-date space-time information on crop needs based on a specific region climate for water resources managing and agricultural decision-making is undeniable (Shelia et al., 2019). Traditionally, estimating agriculture parameters carried out through field sampling measurement (Wellens et al., 2017). However, as the traditional estimation is costly and time-consuming (Mohamed Sallah et al., 2019), there is a need to use crop models for agriculture planning and irrigation scheduling (Midingoyi et al., 2021).
Several significant crop models have been developed in the last few decades to understand the relationship between the soil-crop-atmosphere system and their main controlling factors (Bouman et al., 1996; Droutsas et al., 2019; Yu et al., 2021). Crop models are practical tools in research and management for different purposes such as ecology, environment, agronomy (Jin et al., 2018). They quantify the analysis of the growth and production of crops. These models can be helpful for irrigation scheduling, climate change impact evaluating, field managing, and crop yield predicting (Hossard et al., 2017; Huang et al., 2020).
Crop models represent the mathematics of agricultural processes based on theory and empirical research; thus, the representation entails different assumptions and simplifications of reality that make the output variables uncertain and inaccurate (Han et al., 2019; Andrea Saltelli et al., 2008). On the other hand, too many parameters (up to hundreds) must be specified to describe the properties of the soil-crop-atmosphere system (Ganot & Dahlke, 2021; Thorp et al., 2020). Estimating every parameter in the model needs significant field measurements, which is costly and time-consuming. To reduce the costs and time-saving, there is a need to find fewer parameters that affect crop growth most than others (Kelly & Foster, 2021; Poulose et al., 2021; X. Xu et al., 2016).
The AquaCrop model is a water-driven model developed by FAO, which simulates the crop's parameters under different management conditions. This model makes a good balance between robustness, simplicity, and output accuracy (Raes et al., 2009; Steduto et al., 2009; Vanuytrecht et al., 2014). The model is based on the concepts of crop yield response to water developed by Doorenbos and Kassam (Delgoda et al., 2016; Doorenbos et al., 1980). There have been several research-tested using the AquaCrop model to simulate yields for various crops under normal and different stress situations (e.g., wheat (Jalil et al., 2020; Ruane et al., 2016; XING et al., 2017); maize (Elbeltagi et al., 2020; Jalil et al., 2020; Sandhu & Irmak, 2019), barley (Hellal et al., 2019; López-Urrea et al., 2020), potato (Montoya et al., 2016; Razzaghi et al., 2017), rice (Er-Raki et al., 2021; J. Xu et al., 2019; Zhai et al., 2019), grape (Er-Raki et al., 2021), date (Nunes et al., 2021), soybeans (Adeboye et al., 2019), cotton (Tsakmakis et al., 2019). Although the results proved the AquaCrop model's accuracy, the need for extensive data is not desirable. So, there is a need to reduce the number of input, find the most influential ones, and understand the relations between different parameters and their best-fitted values to calibrate the model more efficiently (Hamby, 1994; Shirazi et al., 2021; Zhang et al., 2022).
To quantifying and comparing the impact of various parameters on a model's output, the sensitivity analysis (SA) can be used (Green & Whittemore, 2005). SA is an uncertainty analysis technique that characterizes the impact of the input factors on the output of a model (Sarrazin et al., 2016), which considers as a prerequisite step in the model-building process (Campolongo et al., 2007). This diagnostic tool suggests considering high-impact parameters while neglecting the low-impact ones (Stella et al., 2014) by identifying parameters that have a significant impact on model simulations for specific regions (van Griensven et al., 2006). The modeling domain and the specific applications aim control the type of approach, level of complexity, and purposes of SA (Pianosi et al., 2016).
SA methods are classified as local SA (LSA) and global SA (GSA) methods. In the local SA method, only one input factor varies at a time, while others are fixed at a nominal value (Wang et al., 2013). Although this method is efficient, quick, and easy to use (X. Xu et al., 2016), it cannot be used to study the effects of several input parameters on the model output responses (DeJonge et al., 2015). So to check the interactions of several factors and to evaluate the varying input parameters simultaneously, the global SA algorithms were developed considerably (Hamm et al., 2006).
GSA investigates the impact of input variation of a numerical model on output variations by a set of mathematical techniques. GSA has been used for different purposes, such as apportion output uncertainty to different sources of uncertainty of a model (e.g., unknown parameters, measurement errors in input data) (Pianosi et al., 2015), model calibration, verification, diagnostic evaluation, or simplification (Sieber & Uhlenbrook, 2005), uncertainty reduction (Hamm et al., 2006), analysis the dominant controls of a system (Pastres et al., 1999), and robust decision-making (Anderson et al., 2014).
There have been several GSA methods developed (Morris, 1991; Pappenberger et al., 2008; A. Saltelli et al., 1999; Sobol, 1993; Yang, 2011), which are commonly used as auxiliary tools for different purposes (e.g., hydrology (Mehdi Ahmadi et al., 2014) Ecology (Ciric et al., 2012), and crop models (Vazquez-Cruz et al., 2014)). Although GSA is an essential tool for developing and calibrating models, its techniques are rather limited in some domains (Pianosi et al., 2015). There are some freely available GSA tools such as a repository of Matlab and Fortran functions maintained by the Joint Research Centre, the GUI-HDMR Matlab package, the C + + based PSUADE software, Python Sensitivity Analysis Library SALib, and Matlab Sensitivity Analysis For Everybody (SAFE) (Pianosi et al., 2015). The last one, SAFE, is used in this study.
In recent years, there has been a surge in the number of ways for calculating meaningful uncertainty boundaries on the model predictions, such as classical Bayesian (Kuczera & Parent, 1998; Z. Liu et al., 2021; J.A. Vrugt et al., 2001; Yin et al., 2021), pseudo-Bayesian (Beven & Binley, 1992; Freer et al., 1996; Freni et al., 2009), set-theoretic (Klepper et al., 1991; Van Straten & Keesman, 1991; Jasper A. Vrugt et al., 2003), multiple criteria (Gupta et al., 1998; H. Madsen, 2000; Henrik Madsen, 2003; Yapo et al., 1998), sequential data assimilation (Blasone et al., 2008; Fan et al., 2016; Moradkhani et al., 2005; Jasper A. Vrugt et al., 2005), and multi-model averaging methods (Jasper A. Vrugt & Robinson, 2007). Despite the different advantages and disadvantages of each of these models, the main difference between them is their assumptions and the kind of different errors that are treated and made explicit (Blasone et al., 2008). In this study, Generalized Likelihood Uncertainty Estimation (GLUE) is used to study different input parameters of the AquaCrop model. This method, which was introduced in 1992 (Beven & Binley, 1992), is one of the first attempts of Beven and Binley to represent prediction uncertainty.
The Monte-Carlo simulations can be used to combine probability distributions and examine the relationships between model input and outcome variables (Nash & Hannah, 2011). Monte-Carlo simulations have been used in different studies, such as flood zoning (Natale & Savi, 2007), agriculture (Baranyai & Zude, 2009; Nash & Hannah, 2011; Qin & Lu, 2009), environmental modeling (Jasper A. Vrugt, 2016), hydrology modeling (Jeremiah et al., 2012), groundwater modeling (Hassan et al., 2009), rivers (Berends et al., 2018), wastewater managing (Piri et al., 2021), and coastal lands (Cooper et al., 2019).
Recently, Adabi et al. (2020) studied on LSA of the AquaCrop model for wheat and maize in two plains in Iran. They studied 47 crop parameters on five output variables on this closed-source crop model. The relative Nash-Sutcliffe Efficiency Index was used to evaluate the sensitivity of these parameters. They found out that around half of the selected parameters in the Qazvin plain were ineffective, and calibrating the AquaCrop model would be more efficient and simpler than different GSA methods (Adabi et al., 2020). In this study, we continued this research on GSA and GLUE methods of wheat, for the Qazvin plain to find efficient domains of every 47 parameters to calibrate the AquaCrop model with the highest accuracy output. Five outputs were studied in this research as soil evaporation, crop transpiration, evapotranspiration, crop biomass at maturity, and grain yield. For this purpose, the model was calibrated by the two-years observed data, then ran for 36-years data from the synoptic station in the Qazvin plain. After that, 3000 random runs based on the Monte-Carlo method were conducted. Then a new domain of each parameter was introduced with a 5% error with the real data. Finally, the probabilistic behavior of each parameter on five outputs was introduced.