Multi-Objective Co-Optimization of Parameters for Sub-Models of Grain and Leaf Growth in Dryland Wheat via the DREAM-zs Algorithm

Response to Reviewer 1 Comments

Drear Reviewer:

We sincerely appreciate your valuable feedback and expert guidance. Your insights have substantially enhanced the academic rigor and clarity of our manuscript. In accordance with your suggestions and requirements, all necessary revisions have been incorporated into the revised draft, with the corresponding changes highlighted in yellow.

Comments 1: The abstract contains extensive methodological detail but gives insufficient attention to the scientific relevance and innovation of the work.

Response 1: We sincerely appreciate your time in reviewing this manuscript and providing valuable constructive suggestions. Following your guidance, we have revised the abstract, streamlined the Methods section by removing redundant details, and emphasized the scientific significance and core innovations of the study. The revised full abstract is as follows:

Page 1, Line 13 to 28:

The simulation accuracy of crop models is highly dependent on the proper calibration of key parameters. To enhance the applicability of the Next-Generation agricultural production systems sIMulator (APSIM NG) in dryland wheat production within the Loess hilly region, this study proposes a crop model parameter calibration framework that deeply integrates Morris and DREAM-zs methodologies. Morris was employed to conduct a global sensitivity analysis on parameters related to the APSIM NG dryland wheat grain and leaf growth submodels. The DREAM-zs algorithm was then utilized for multi-objective collaborative optimization of key parameters. Results indicate Morris excels at capturing nonlinear and coupled relationships among model parameters. Optimized key parameters include maximum grain size (0.055 g), radiation use efficiency (1.540 g·MJ^-1), and extinction coefficient (0.443). Post-optimization, the root mean square error (RMSE) and mean absolute error (MAE) for wheat yield decreased by 24.1% and 23.2%, respectively, while those for LAI decreased by 16.9% and 19.2%. This framework conserves computational resources and accelerates convergence when handling nonlinear internal model parameters and complex coupling relationships, providing technical support for the localized application of APSIM NG in the Loess Hills region of Northwest China.

Comments 2: A clearer statement of the study’s contribution, particularly how the combined DREAM-zs and sensitivity-analysis framework advances parameter optimization in crop models, is needed.

Response 2: We sincerely appreciate the reviewer for raising this critical point. The original manuscript lacked focus in summarizing the research contributions, failing to sufficiently highlight the methodological significance of combining sensitivity analysis with DREAM-zs for optimizing crop model parameters. In response to this suggestion, we have further refined and clarified the core contributions of this study at the end of the abstract. Specifically:

Page 1, Line 25 to 28: This framework conserves computational resources and accelerates convergence when handling nonlinear internal model parameters and complex coupling relationships, providing technical support for the localized application of APSIM NG in the Loess Hills region of Northwest China.

Comments 3: Although improvements in RMSE and MAE are mentioned, specific numerical gains or validation statistics are absent. Please include these.

Response 3: We sincerely appreciate the reviewer's valuable suggestion. We agree that reporting only the trend of error metrics without providing specific quantitative values is indeed insufficient to intuitively reflect the model optimization effect. In response to this feedback, we have revised the abstract and results section accordingly, explicitly adding the specific numerical changes and relative improvement rates of RMSE and MAE before and after model optimization. The revised abstract now quantitatively states the following:

Page 1, Line 23 to 25: Post-optimization, the root mean square error (RMSE) and mean absolute error (MAE) for wheat yield decreased by 24.1% and 23.2%, respectively, while those for LAI de-creased by 16.9% and 19.2%.  

Comments 4: The introduction reviews major crop-modeling tools but does not adequately position the study within recent developments in multi-objective optimization. A brief gap analysis explaining the limitations of current approaches would better highlight the study’s contribution.

Response 4: We sincerely appreciate your valuable feedback. We acknowledge that the initial draft placed excessive emphasis on crop modeling tools and sensitivity analysis in the introduction, failing to adequately clarify the study's position within recent advances in multi-objective optimization. Accordingly, we have substantially revised the introduction to include a clear analysis of the gap in multi-objective optimization for crop model calibration. Key points include: (1) Existing calibration studies for complex crop models still predominantly rely on single-objective optimization (e.g., focusing solely on yield or LAI), which fails to adequately reflect trade-offs between coupled growth processes; (2) Although multi-objective optimization algorithms like NSGA-II, MOCOM-UA, CMOPSO, and genetic algorithms have been applied in agricultural modeling, their high computational cost, slow convergence, and sensitivity to parameter coupling limit their practical application in structurally complex models such as APSIM NG; (3) Although the DREAM-zs algorithm converges faster and exhibits stronger global exploration capabilities compared to the aforementioned algorithms, its application has thus far been primarily confined to single-objective calibration. Its potential for multi-objective parameter optimization within crop models remains largely unexplored.

Addressing these gaps, the revised introduction explicitly states that this study aims to establish an efficient and stable multi-objective calibration framework by integrating global sensitivity analysis for parameter screening with a multi-objective optimization strategy based on DREAM-zs. The revised full introduction is as follows:

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In arid and semiarid regions, the frequent occurrence of extreme weather events and sustained population growth have intensified pressures on the food supply [1]. As one of the primary staple crops, wheat plays a vital role in ensuring global food security. The wheat growth process is relatively complex, requiring a balance of interactions among factors such as genotype, environment, and management practices. Mechanistic crop growth models can dynamically simulate the physical growth and development of crops [2]. The APSIM model stands as one of the leading mechanistic models, widely adopted for agricultural ecosystem simulation and management strategy optimization due to its modular structure, high flexibility, and systematic approach [3,4]. The APSIM model comprises a classic version and a Next-Generation iteration (APSIM NG). The classic version suffers from issues such as code redundancy, whereas APSIM NG enables plant model construction through component libraries, allowing users to assemble organs and physiological processes without programming [5,6]. The accuracy of crop model simulations depends on efficient and precise parameter calibration. However, APSIM NG parameters have not undergone localized calibration, making it difficult to accurately reflect regional environmental characteristics and thus limiting the model's effectiveness in China's northwestern Loess Hills region. Well-adapted models provide reliable data sources. Therefore, enhancing the localized adaptability of APSIM NG holds significant implications for intelligent decision-making in dryland wheat production across China's northwestern Loess Hills.

Traditional model calibration often focuses on single objectives, such as yield or leaf area index (LAI) alone. However, 90–95% of wheat's biological yield originates from crop photosynthetic products [7]. LAI is a key indicator of collective photosynthetic capacity, where higher LAI signifies greater photosynthetic area [8]. However, excessively high LAI can cause shading, which conversely reduces yield [9]. The non-linear trade-off between LAI and yield makes it challenging to simultaneously improve the simulation accuracy of both indicators through single-objective calibration. In contrast, multi-objective cooperative optimization seeks balance among different objectives [10], continuously refines crop models to more accurately reflect their performance under real-world field conditions and better guides future intelligent agricultural production. Scholars have applied multi-objective optimization to agriculture and crop models. For instance, Tatsumi combined the MOCOM-UA algorithm with the Erosion-Productivity Impact Calculator (EPIC) model, effectively improving maize yield simulations [11]. Additionally, multi-objective optimization algorithms include the improved multi-objective particle swarm optimization (CMOPSO), non-dominated sorting genetic algorithm II (NSGA-II), and genetic algorithm (GA) [12–14]. These algorithms demand substantial computational resources for multi-objective optimization problems, exhibit slow convergence rates, and are susceptible to parameter coupling effects, rendering them less suitable for the structurally complex APSIM NG model. In contrast, the DREAM algorithm proposed by Vrugt et al. (2009) integrates multi-chain parallel Markov chain Monte Carlo with adaptive differential evolution strategies. It exhibits strong global exploration capabilities and rapid convergence, enabling robust sampling in highly nonlinear, strongly coupled, high-dimensional parameter spaces [15]. Cui et al. (2023) demonstrated in yield simulation optimization studies that the DREAM-zs algorithm converges more rapidly [16]. However, its application in multi-objective parameter calibration remains limited and warrants further validation.

Multi-objective optimization involves numerous parameters, and direct calibration increases complexity and uncertainty [17]. Therefore, this study introduces sensitivity analysis prior to optimization to identify key parameters significantly influencing the model. Sensitivity analysis serves as the foundation for evaluating how changes in input factors affect model outputs [18]. By quantifying the relative influence of various parameters on simulation outputs, it identifies key parameters contributing significantly to output variations and reveals potential interactions arising from different parameter combinations [19,20]. Sensitivity analysis is categorized into local and global sensitivity analysis. Local sensitivity analysis is computationally simple and cost-effective but ignores parameter interactions, making it applicable only to linear or additive models [21]. Global sensitivity analysis explores the entire parameter space by simultaneously varying all parameter values and typically accounts for parameter interactions [22]. Common global sensitivity analysis methods include Morris, Sobol, and EFAST. Morris performs global sensitivity analysis based on differential basic effects with low computational cost; the Sobol method employs variance-based global sensitivity analysis; EFAST combines the advantages of FAST and Sobol methods, yielding more robust results [23–25]. Although Morris and EFAST have been widely applied in crop model calibration, studies applying these methods to the APSIM NG model re-main scarce.

Therefore, to enhance the effective application of the APSIM NG model in dryland wheat production within China's northwestern Loess hilly regions, this study employs a strategy integrating global sensitivity analysis with multi-objective optimization to conduct multi-objective synergistic optimization of dryland wheat yield and LAI. Key parameters significantly influencing wheat yield and LAI were identified in the grain and leaf growth submodels through Morris and EFAST screening, ensuring optimization focused on parameters likely to yield substantial changes. The DREAM-zs algorithm was then employed for multi-objective parameter optimization.

Comments 5: The research objectives appear repetitive and dispersed; they should be consolidated into a concise research question and hypothesis.

Response 5: Thank you for your constructive feedback. We agree that research objectives should be concise and clear. Based on your suggestions and requirements, we have made significant revisions to the introduction. The revised introduction consolidates the previously scattered research objectives into a single, focused research question. The core inquiry centers on whether integrating global sensitivity analysis with multi-objective optimization can enhance the calibration efficiency and regional adaptability of the APSIM NG arid wheat model in the Loess Hills region. The complete revised introduction is provided in Response 4.

Comments 6: The field experiment description is useful but lacks details required for reproducibility, such as replication strategy, control of environmental variability, statistical design, and soil-property measurement procedures.

Response 6: Thank you for your valuable feedback! We have supplemented the Materials and Methods section of the manuscript with the details required for reproducibility testing, as per your request and suggestions. Below is a detailed response to the supplementary content.

Page 3, Line 108: Supplemented with “the district has geographical coordinates of 104°38′E, 35°35′N”

Page 3，Line 109 to 110: Supplemented with “The annual accumulated temperature ≥0°C is 2933.5°C, the annual accumulated temperature ≥10°C is 2239.1°C, and the frost-free period lasts 140 days ”

Page 3, Line 112: Supplemented with “annual evaporation of 1531 mm”

Page 4, Line 130 to 139: Supplemented with “cultivated via the locally customary traditional farming method of three plowings and two harrows. The three plowings were conducted as follows: the first plowing after the previous crop harvest before August, the second plowing at the end of August, and the third plowing in September, with plowing depths of 200 mm, 100 mm, and 50 mm, respectively. Two harrows: One harrowing after the third tillage in September, and another before soil freezing in October. Crops were sown according to the normal planting schedule. Due to interannual variations in meteorological conditions, sowing and harvesting dates were slightly adjusted in different years (generally mid-March sowing and late July harvesting annually).”

Page 4, Line 141 to 142: Supplemented with “using a no-till machine seeding”

Page 4, Line 153 to 156: The calculation formula for LAI Supplemented with:

(1)

(2)

where L_area denotes leaf area; L_length denotes leaf length, referring to the distance from the leaf base to the leaf tip; L_width denotes leaf width, referring to the width at the broadest part of the leaf; L_tarea denotes total leaf area; S_area denotes land area.

Page 4, Line 157 to 164: Supplemented with “Soil physicochemical properties data for the experimental area (Table 1) represent actual measurements taken during the trial period. Soil moisture measurements were conducted every 15 days, concurrently determining field capacity and the lower limit of available water. Nine measurement layers were established: 0–50 mm, 50–100 mm, 100–300 mm, 300–500 mm, 500–800 mm, 800–1100 mm, 1100–1400 mm, 1400–1700 mm, and 1700–2000 mm. The 0-100mm layer was determined using the air-drying method. Soil samples were air-dried, sieved through a 1mm mesh, and stored in bags. Layers below 100mm were measured using a neutron moisture analyzer.”

Page 5, Line 174 to 180: Supplemented with “In this study, long-term district-level annual yield data (1971 to 2021) primarily served as background input for model operation, characterizing the interannual variability of the study area under different climatic years, rather than being directly used to construct the parameter optimization objective function. Model parameter calibration and performance evaluation were conducted using contemporaneous district-level yearbook yield and LAI measurements from the periods 2002 to 2005 and 2015 to 2017, ensuring temporal consistency between the two optimization objectives.”

Comments 7: The DREAM-zs algorithm is described mathematically, yet the rationale for selected parameter ranges, sample sizes, and iteration numbers is not provided. A justification of these choices is needed to support methodological rigor.

Response 7: Thank you for pointing this out. We agree with this comment. This study implemented parameter optimization based on the DREAM-zs algorithm in the R optimization program by calling the CroptimizR package. We have supplemented the manuscript with the rationale for the internal parameter settings of the DREAM-zs algorithm as per your request and suggestion. The specific additions are as follows:

Page 8, Line 290 to 292: Supplemented with “the DREAM-zs algorithm is invoked via the CroptimizR package to drive the APSIM NG-Wheat model for parameter optimization”

Page 8, Line 306 to 309: Supplemented with “The iteration count for the DREAM-zs algorithm was empirically set to 500 and run multiple times to ensure stability. The number of Markov chain members was set to 3 based on Vrugt et al. (2009) [15]. The random seed was set to 1234.”

Comments 8: The sensitivity-analysis figures identify key parameters but provide no statistical measures (e.g., confidence intervals) to convey the reliability of the results.

Response 8: We sincerely appreciate the reviewer's constructive feedback regarding the reliability of the sensitivity analysis results. We fully concur with these points. Following the reviewer's suggestions, we have systematically revised the sensitivity analysis workflow, encompassing both Morris and EFAST global sensitivity analysis methods. First, prior to re-conducting the sensitivity analysis, both output variables—yield and LAI—were uniformly normalized to eliminate the impact of differing dimensions and magnitudes on the comparability and stability of sensitivity metrics. This normalization effectively prevents overestimation of sensitivity or ranking bias caused by output scale differences, enhancing the interpretability of sensitivity results across different outputs. Second, for the Morris method, the revised version redraws sensitivity analysis plots. Beyond presenting mean sensitivity indices (μ*), it explicitly includes corresponding standard deviations (σ) to characterize the dispersion of parameter disturbance effects across multiple samples. Standard deviation reflects the stability of parameter influences and potential nonlinear and interactive effects, providing supplementary uncertainty information for parameter screening results. For the EFAST method, the revised version recalculates first-order sensitivity indices and total effect indices based on normalized outputs. Since EFAST inherently employs variance decomposition, its sensitivity indices reflect the proportional contribution of parameters to output variance, implicitly incorporating uncertainty metrics at the methodological level. To enhance result robustness, multiple sampling is applied, and consistency tests are conducted on sensitivity indices to ensure stable ranking of key sensitive parameters across different sampling conditions. Due to the introduction of normalization prior to sensitivity analysis, both the numerical values and relative rankings of the sensitivity indices have been updated accordingly. Consequently, the sensitivity analysis results have been comprehensively revised. Based on the above content, the specific modifications are as follows:

Page 5, Line 202 to 207: The global sensitivity method introduced a supplementary normalization process, namely “In conducting sensitivity analysis for this study, the yield data and LAI from the model simulations were first subjected to Min-Max normalization to prevent dimensional differences from affecting the sensitivity analysis results. The Min-Max normalization formula is:

                              (3)

where X represents the raw simulation data output by the model, while min(X) and max(X) denote the minimum and maximum values of the raw simulation data, respectively”.

Page 10 to 12, Line 327 to 375: Revise the sensitivity analysis results and redraw the sensitivity analysis chart. The content is as follows:

The results of the parameter sensitivity analysis based on the Morris method are shown in Figures 2 and 3. According to the sensitivity parameter criteria, the parameters sensitive to yield and LAI are maximum grain size (G3), radiation use efficiency (L2), and extinction coefficient (L3). Regarding yield (Figure 2), parameter L3 exhibits the highest mean sensitivity and largest standard deviation, indicating its dominant role in yield formation, alongside significant parameter interactions. This parameter primarily in-fluences yield formation by regulating the canopy's radiation interception efficiency, thereby affecting the fundamental supply of photosynthetic products. Parameters G3 and L2 exhibited medium-level sensitivity means with relatively pronounced standard deviations, indicating they exert a stable yet relatively minor influence on yield. In contrast, parameters G1, G2, G4, G5, G6, G7, L1, and L4 cluster near the origin with low mean sensitivity and standard deviation, suggesting limited direct contribution to yield and stable parameter responses. For LAI (Figure 3), the overall sensitivity ranking resembles that for yield, though relative importance shifts. L3 remains the most sensitive parameter, underscoring its pivotal role in regulating canopy growth structure. L2 maintains moderate sensitivity, while L1 and G3 exhibit heightened sensitivity to LAI compared to yield, reflecting their close association with leaf expansion and leaf area formation processes. The remaining parameters demonstrate weaker sensitivity.

The results of the parameter sensitivity analysis obtained using the EFAST method are shown in Figure 4. Figure 4a and Figure 4b represent the first-order sensitivity in-dices for yield and LAI, respectively, while Figure 4c and Figure 4d show the corresponding full-order sensitivity indices. According to the sensitivity parameter criteria, only parameter L3 exhibited significant sensitivity for both yield and LAI objectives, while the remaining parameters failed to meet the sensitivity thresholds. In the first-order sensitivity analysis (Figures 4a and 4b), parameter L3 demonstrated significantly higher first-order sensitivity indices for both yield and LAI compared to other parameters, indicating the strongest response characteristics of model outputs to variations in this parameter. Parameters G3 and L2 exhibit relatively higher first-order sensitivity indices among the non-sensitive parameters, with slightly greater direct in-fluence on yield and LAI than others, though their overall sensitivity remains markedly lower than L3. The full-order sensitivity analysis results (Figures 4c and 4d) further confirm that parameter L3 maintains the highest full-order sensitivity index, highly consistent with the first-order findings. This indicates that the interaction effects be-tween this parameter and others contribute relatively little to model outputs. Sensitivity indices for other parameters in the full-order analysis remain low, indicating their limited combined contribution to yield and LAI.

Overall, only a few parameters exhibit high sensitivity toward both yield and LAI simultaneously, and their response characteristics display certain nonlinearity and uncertainty. The sensitivity results for yield and LAI show both overlaps and differences, reflecting potential trade-offs among different physiological processes during multi-objective synergistic calibration.

Figure 2. The Morris sensitivity analysis results (Yield).

Figure 3. The Morris sensitivity analysis results (LAI).

Figure 4. The EFAST sensitivity analysis results. (a) Results of first-order sensitivity analysis of parameters on wheat yield; (b) Results of first-order sensitivity analysis of parameters on LAI; (c) Results of global sensitivity analysis of wheat yield; (d) Results of global sensitivity analysis of parameters on LAI.

Comments 9: The optimization results are presented numerically without linking them to agronomic meaning.

Response 9: Thank you for your comments. We fully agree with this point. Following your suggestion, we have explicitly articulated the agronomic significance of the optimized parameters in the Discussion section, rather than limiting it to numerical descriptions in the Results section. In the Discussion section, we have linked the numerical variations in maximum grain size, radiation use efficiency, and extinction coefficient to the grain filling process, canopy light interception, and drought stress adaptation mechanisms, respectively. We also evaluated whether the optimized parameter values possess physiological plausibility for wheat growth in the Loess hilly region. Specific modifications are as follows:

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Based on the sensitivity analysis results, the parameters to be optimized were determined to be maximum grain size, radiation use efficiency, and extinction coefficient. Their optimization ranges were referenced from previous studies and align with the growth and development patterns of wheat in loess hilly dryland areas. Optimization results indicate that the maximum grain size and radiation use efficiency increased compared to default values, while the extinction coefficient showed a decreasing trend. Within the APSIM NG-Wheat model module, grain size directly influences yield calculations [16], and grain size is determined by the degree of grain filling from flowering to grain filling stage [43], concurrently with the continuous accumulation of dry matter through photosynthesis and other processes. Fisher (2011) and Wang et al. (2023) noted that water stress directly impacts agronomic traits like photosynthesis and dry matter accumulation. Under water deficiency, wheat yield formation relies more on grain filling capacity than on grain number per spike [44,45]. Dryland wheat often exhibits grain number limitation compensated by enhanced grain weight [46]. Therefore, increasing maximum grain size enhances the potential for dry matter accumulation per grain during the grain filling stage, partially offsetting the adverse yield effects of reduced grain number. Photosynthesis is a primary driver of dry matter accumulation, and leaf area directly influences the photosynthetic capacity of wheat populations [47]. LAI is closely correlated with the extinction coefficient [48]. The extinction coefficient indicates light transmittance within the crop canopy [34], influencing light energy distribution and use efficiency. Under rainfed conditions, water and high-temperature stress induce leaf stomatal closure and reduced photosynthetic rates, leading to de-creased extinction coefficients [49]. This physiological response aligns with the optimization trend of extinction coefficient parameters observed in this study. Radiation use efficiency reflects a crop's ability to convert available light energy into biomass through photosynthesis and is highly sensitive to environmental conditions. Under water stress, dryland wheat often maintains population productivity by enhancing the conversion efficiency of dry matter per unit of intercepted light energy [50]. Thus, the increase in radiation use efficiency parameters observed in this study demonstrates the model's adaptive regulation of light energy utilization efficiency under dryland conditions.

Comments 10: The discussion largely restates results rather than comparing them critically with previous work using similar optimization or machine-learning calibration methods.

Response 10: We sincerely appreciate your valuable feedback. Your observation that “the discussion section primarily reiterates the research findings without critically comparing them to prior studies employing similar optimization or machine learning calibration methods” is exceptionally insightful and crucial for enhancing the paper's depth and academic value. We fully concur with your perspective and have incorporated additional content into the Discussion section based on your feedback. This section now includes a critical comparison of multi-objective optimization algorithms, contrasting the DREAM-zs algorithm employed in this study with commonly used methods in crop model parameter optimization, such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Non-Dominated Sorting Genetic Algorithm II (NSGA-II). By citing relevant literature, we elucidate the limitations of algorithms like GA and PSO when handling complex mechanism model parameters characterized by high dimensionality, nonlinearity, and strong coupling. These include sensitivity to hyperparameter settings, susceptibility to local optima, slow convergence rates, and high computational costs. This comparison highlights the unique advantages of the DREAM-zs algorithm in convergence stability and computational efficiency, demonstrating its particular suitability for the complex multi-objective cooperative optimization problem addressed in this study. Beyond these core additions, we have also revised the structure and content of the entire “Discussion” section to ensure it no longer serves as a mere restatement of the “Results” section. The revised discussion is presented below, with revised content indicated by underlining:

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This study employs the APSIM NG to perform multi-objective cooptimization of parameters related to the grain and leaf growth sub-models for dryland wheat. The model features numerous complex internal parameters and relatively computationally intensive operations. To enhance calibration efficiency, sensitivity analysis methods such as Morris and EFAST were employed to screen critical model parameters. Under the two global sensitivity analysis methods described above, the key parameters influencing wheat yield and LAI were not entirely consistent between the grain and leaf growth sub-models. The Morris method identified sensitive parameters, including maximum grain size, radiation use efficiency, and extinction coefficient, while the EFAST method selected the extinction coefficient as the sensitive parameter. The discrepancy primarily stems from differing emphases in process analysis between the two methods. Both methods effectively capture overall trends in parameter influences on model outputs and exhibit high sensitivity to nonlinear effects and parameter interactions [23]. The Morris method, with its heightened sensitivity to nonlinear effects and parameter interactions [23], can thus identify parameters like maximum grain size and radiation use efficiency that exhibit stage-dependent or scenario-dependent effects. The EFAST method characterizes total effect indices while also focusing on the stable contribution of individual parameters to the overall variance in model outputs [25]. In this study, EFAST analysis revealed that the extinction coefficient exerts a dominant in-fluence on yield and LAI across the entire parameter space, mitigating the impact of the interaction between maximum grain size and radiation use efficiency. The Morris method's advantage in multi-objective parameter screening lies in its ability to uncover potentially critical parameter sets and their interactions, thereby providing more comprehensive parameter space information for subsequent optimization. The sensitivity analysis results of this study are consistent with those of Li et al. (2011) [42], Wei and Nie (2023) [34], and Zhao et al. (2014) [36], indicating reasonable findings.

Based on the sensitivity analysis results, the parameters to be optimized were determined to be maximum grain size, radiation use efficiency, and extinction coefficient. Their optimization ranges were referenced from previous studies and align with the growth and development patterns of wheat in loess hilly dryland areas. Optimization results indicate that the maximum grain size and radiation use efficiency increased compared to default values, while the extinction coefficient showed a decreasing trend. Within the APSIM NG-Wheat model module, grain size directly influences yield calculations [16], and grain size is determined by the degree of grain filling from flowering to grain filling stage [43], concurrently with the continuous accumulation of dry matter through photosynthesis and other processes. Fisher (2011) and Wang et al. (2023) noted that water stress directly impacts agronomic traits like photosynthesis and dry matter accumulation. Under water deficiency, wheat yield formation relies more on grain filling capacity than on grain number per spike [44,45]. Dryland wheat often exhibits grain number limitation compensated by enhanced grain weight [46]. Therefore, increasing maximum grain size enhances the potential for dry matter accumulation per grain during the grain filling stage, partially offsetting the adverse yield effects of reduced grain number. Photosynthesis is a primary driver of dry matter accumulation, and leaf area directly influences the photosynthetic capacity of wheat populations [47]. LAI is closely correlated with the extinction coefficient [48]. The extinction coefficient indicates light transmittance within the crop canopy [34], influencing light energy distribution and use efficiency. Under rainfed conditions, water and high-temperature stress induce leaf stomatal closure and reduced photosynthetic rates, leading to de-creased extinction coefficients [49]. This physiological response aligns with the optimization trend of extinction coefficient parameters observed in this study. Radiation use efficiency reflects a crop's ability to convert available light energy into biomass through photosynthesis and is highly sensitive to environmental conditions. Under water stress, dryland wheat often maintains population productivity by enhancing the conversion efficiency of dry matter per unit of intercepted light energy [50]. Thus, the increase in radiation use efficiency parameters observed in this study demonstrates the model's adaptive regulation of light energy utilization efficiency under dryland conditions.

Optimizing crop model parameters is fundamentally a complex problem of finding global optimal solutions within a high-dimensional, nonlinear parameter space. When the optimization objective expands from a single goal to multiple goals, such as the synergistic optimization of yield and LAI, the uncertainty and complexity of model parameters increase accordingly [51]. The modular design of the APSIM NG model and its complex system simulation requirements demand precise parameterization to ensure simulation reliability. The DREAM-zs algorithm employed in this study features straightforward parameter configuration. By running multiple Markov chains in parallel and utilizing adaptive sampling strategies, it achieves higher efficiency and stability when addressing multi-objective optimization problems. In contrast, GA and PSO typically rely on iterative adjustments of empirical parameters such as crossover probability, mutation rate, or inertia weight in practical applications. When parameter dimensions are high or strong nonlinear couplings exist, their optimization performance becomes highly sensitive to hyperparameters, often leading to reduced search efficiency or premature convergence [12,14]. Although the NSGA-II algorithm excels in constructing Pareto frontiers, its function evaluation count is typically the product of population size and iteration count [13], often consuming substantial computational resources in computationally intensive applications like crop modeling. In this study, the DREAM-zs algorithm was set to 500 iterations, with a maximum total runtime of 2887.5 seconds. This demonstrates that, while balancing multi-objective optimization accuracy and computational resources, DREAM-zs can provide a computationally efficient and stable parameter optimization solution for complex crop models like APSIM NG.

Model performance was evaluated via the RMSE and MAE, with the optimized model demonstrating improved adaptability. Since this study employed dual objectives of minimizing simulation errors for both yield and LAI with equal weighting (weight coefficient of 1), yield optimization achieved relatively more significant improvements despite the substantial difference in dimensionality between the two objectives, whereas LAI showed smaller improvements. This finding indicates that differences in the magnitude of different indicators may lead to uneven responses of optimization objectives during collaborative search.

Although this study optimized the results of model simulations, certain limitations remain. First, measurement errors in input data, such as meteorological and soil parameters, may affect simulation accuracy. Under complex terrain conditions, accurately obtaining spatial distribution information of wheat is crucial for yield estimation and model spatial scale validation [52]. In the future, the quality of model input data can be further enhanced through multi-source data fusion, such as multi-temporal remote sensing data. Additionally, while this study treated growth stage parameters as fundamental crop variety attributes, subsequent research could incorporate growth stage phase parameters to analyze their influence.

Comments 11: Some statements overgeneralize the findings and imply broad applicability without supportive evidence.

Response 11: Thank you for your professional review. We fully agree and have revised the conclusions based on your suggestions. The complete revised conclusions are as follows:

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This study established a calibration framework for crop model parameters by deeply integrating Morris global sensitivity analysis with DREAM-zs multi-objective optimization. The key parameters identified for the APSIM NG-based dryland wheat grain and leaf growth submodels are maximum grain size, radiation use efficiency, and extinction coefficient. Post-optimization, the RMSE and MAE for yield decreased by 24.1% and 23.2%, respectively, while those for LAI decreased by 16.9% and 19.2%. This framework achieves synergistic optimization of dryland wheat yield and LAI, enhancing the localized adaptability of the APSIM NG model in China's northwestern Loess hilly region.

Comments 12: Performance improvements should be quantified, and claims about wider relevance moderated.

Response 12: Thank you for bringing this issue to our attention. We have quantified the performance improvements based on your requirements and suggestions, and standardized the broader related statements. The revised conclusions are provided in Response 11.

Response to Reviewer 2 Comments

Drear Reviewer:

We sincerely appreciate your valuable feedback and expert guidance. Your insights have substantially enhanced the academic rigor and clarity of our manuscript. In accordance with your suggestions and requirements, all necessary revisions have been incorporated into the revised draft, with the corresponding changes highlighted in yellow.

Comments 1: The abstract states “synergistic optimization” and “significantly improved accuracy” but never quantifies how much improvement in relative/percent terms, nor whether improvements are statistically meaningful rather than just numerically smaller errors.

Response 1: We sincerely thank you for taking the time to provide your expert review of this manuscript and for offering numerous constructive suggestions. Following your guidance, we have refined the abstract: we have condensed and removed redundant details from the Methods section while emphasizing the scientific significance and core innovations of the study. The revised full abstract is as follows:

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The simulation accuracy of crop models is highly dependent on the proper calibration of key parameters. To enhance the applicability of the Next-Generation agricultural production systems sIMulator (APSIM NG) in dryland wheat production within the Loess hilly region, this study proposes a crop model parameter calibration framework that deeply integrates Morris and DREAM-zs methodologies. Morris was employed to conduct a global sensitivity analysis on parameters related to the APSIM NG dryland wheat grain and leaf growth submodels. The DREAM-zs algorithm was then utilized for multi-objective collaborative optimization of key parameters. Results indicate Morris excels at capturing nonlinear and coupled relationships among model parameters. Optimized key parameters include maximum grain size (0.055 g), radiation use efficiency (1.540 g·MJ^-1), and extinction coefficient (0.443). Post-optimization, the root mean square error (RMSE) and mean absolute error (MAE) for wheat yield decreased by 24.1% and 23.2%, respectively, while those for LAI decreased by 16.9% and 19.2%. This framework conserves computational resources and accelerates convergence when handling nonlinear internal model parameters and complex coupling relationships, providing technical support for the localized application of APSIM NG in the Loess Hills region of Northwest China.

Comments 2: The introduction spends much space on ML, Bayesian optimization, and MCMC overall, whereas the actual implementation of the paper is a small DREAM-zs model with a highly simplistic squared-error objective. The story is written as a survey that does not narrow down to a definite methodological contribution until the end.

Response 2: We sincerely appreciate the reviewer for pointing out this structural issue. We have systematically rewritten the introduction as suggested, removing discussions on machine learning model performance and scalability that were not directly related to high-dimensional generalization and the Bayesian optimization framework. We have supplemented the literature review on multi-objective optimization, analyzed the limitations of existing multi-objective optimization methods applied to agricultural or crop models, and highlighted the advantages of the DREAM-zs method used in this study through comparative analysis. The introduction's logic has been reorganized to emphasize the methodological contributions of this paper. Following revisions, the introduction now structures as follows: Problem Background (complex yield formation mechanisms in dryland wheat, critical importance of localized model calibration for arid zone agricultural management); Research Gap in Crop Model Calibration (limited multi-objective optimization research on crop models); Solution Approach (rapid, accurate parameter estimation via sensitivity analysis and multi-objective optimization for crop models with numerous parameters and strong interactions); Introduction to Research Work. The revised full introduction is as follows:

Page 1 to 3, Line 33 to 103: Underlined text indicates modified content:

In arid and semiarid regions, the frequent occurrence of extreme weather events and sustained population growth have intensified pressures on the food supply [1]. As one of the primary staple crops, wheat plays a vital role in ensuring global food security. The wheat growth process is relatively complex, requiring a balance of interactions among factors such as genotype, environment, and management practices. Mechanistic crop growth models can dynamically simulate the physical growth and development of crops [2]. The APSIM model stands as one of the leading mechanistic models, widely adopted for agricultural ecosystem simulation and management strategy optimization due to its modular structure, high flexibility, and systematic approach [3,4]. The APSIM model comprises a classic version and a Next-Generation iteration (APSIM NG). The classic version suffers from issues such as code redundancy, whereas APSIM NG enables plant model construction through component libraries, allowing users to assemble organs and physiological processes without programming [5,6]. The accuracy of crop model simulations depends on efficient and precise parameter calibration. However, APSIM NG parameters have not undergone localized calibration, making it difficult to accurately reflect regional environmental characteristics and thus limiting the model's effectiveness in China's northwestern Loess Hills region. Well-adapted models provide reliable data sources. Therefore, enhancing the localized adaptability of APSIM NG holds significant implications for intelligent decision-making in dryland wheat production across China's northwestern Loess Hills.

Traditional model calibration often focuses on single objectives, such as yield or leaf area index (LAI) alone. However, 90–95% of wheat's biological yield originates from crop photosynthetic products [7]. LAI is a key indicator of collective photosynthetic capacity, where higher LAI signifies greater photosynthetic area [8]. However, excessively high LAI can cause shading, which conversely reduces yield [9]. The non-linear trade-off between LAI and yield makes it challenging to simultaneously improve the simulation accuracy of both indicators through single-objective calibration. In contrast, multi-objective cooperative optimization seeks balance among different objectives [10], continuously refines crop models to more accurately reflect their performance under real-world field conditions and better guides future intelligent agricultural production. Scholars have applied multi-objective optimization to agriculture and crop models. For instance, Tatsumi combined the MOCOM-UA algorithm with the Erosion-Productivity Impact Calculator (EPIC) model, effectively improving maize yield simulations [11]. Additionally, multi-objective optimization algorithms include the improved multi-objective particle swarm optimization (CMOPSO), non-dominated sorting genetic algorithm II (NSGA-II), and genetic algorithm (GA) [12–14]. These algorithms demand substantial computational resources for multi-objective optimization problems, exhibit slow convergence rates, and are susceptible to parameter coupling effects, rendering them less suitable for the structurally complex APSIM NG model. In contrast, the DREAM algorithm proposed by Vrugt et al. (2009) integrates multi-chain parallel Markov chain Monte Carlo with adaptive differential evolution strategies. It exhibits strong global exploration capabilities and rapid convergence, enabling robust sampling in highly nonlinear, strongly coupled, high-dimensional parameter spaces [15]. Cui et al. (2023) demonstrated in yield simulation optimization studies that the DREAM-zs algorithm converges more rapidly [16]. However, its application in multi-objective parameter calibration remains limited and warrants further validation.

Multi-objective optimization involves numerous parameters, and direct calibration increases complexity and uncertainty [17]. Therefore, this study introduces sensitivity analysis prior to optimization to identify key parameters significantly influencing the model. Sensitivity analysis serves as the foundation for evaluating how changes in input factors affect model outputs [18]. By quantifying the relative influence of various parameters on simulation outputs, it identifies key parameters contributing significantly to output variations and reveals potential interactions arising from different parameter combinations [19,20]. Sensitivity analysis is categorized into local and global sensitivity analysis. Local sensitivity analysis is computationally simple and cost-effective but ignores parameter interactions, making it applicable only to linear or additive models [21]. Global sensitivity analysis explores the entire parameter space by simultaneously varying all parameter values and typically accounts for parameter interactions [22]. Common global sensitivity analysis methods include Morris, Sobol, and EFAST. Morris performs global sensitivity analysis based on differential basic effects with low computational cost; the Sobol method employs variance-based global sensitivity analysis; EFAST combines the advantages of FAST and Sobol methods, yielding more robust results [23–25]. Although Morris and EFAST have been widely applied in crop model calibration, studies applying these methods to the APSIM NG model re-main scarce.

Therefore, to enhance the effective application of the APSIM NG model in dryland wheat production within China's northwestern Loess hilly regions, this study employs a strategy integrating global sensitivity analysis with multi-objective optimization to conduct multi-objective synergistic optimization of dryland wheat yield and LAI. Key parameters significantly influencing wheat yield and LAI were identified in the grain and leaf growth submodels through Morris and EFAST screening, ensuring optimization focused on parameters likely to yield substantial changes. The DREAM-zs algorithm was then employed for multi-objective parameter optimization.

Comments 3: The parameters of the soil profile appear to be partly copied-in/generic (e.g., hydraulic conductivity is always 0.60), and there is no explanation that these are the two experimental sites. This nullifies arguments of local adaptability.

Response 3: The soil physicochemical parameters employed in this study derive from field measurements collected during long-term experiments conducted by our team in Mazichuan Village, Lijiabao Town, from 2002 to 2005. These parameters underwent multiple rounds of calibration using an exhaustive trial-and-error approach, resulting in a regionalized soil parameter set refined through iterative modifications. This parameter set was initially established and validated by Li et al. (2009) in their study “Applicability of the APSIM Model to Different Tillage Practices in the Loess Hilly and Gully Region” [1]. Validation results showed that the NRMSE between simulated soil water storage and measured values was below 20%, with a correlation coefficient exceeding 0.7, indicating that this parameter set effectively characterizes soil moisture properties in the study area.

Given the high similarity between Mazichuan Village in Lijiabao Town and Anjiagou Village in Fengxiang Town in terms of topography, parent material, soil texture composition, and cropping systems, previous studies have classified them as the same type of dryland wheat production area. Therefore, this study adopts the same set of regionalized soil parameters. Team member Nie et al. (2018) also employed this soil parameter set during their dryland wheat model parameter optimization research [2], achieving favorable simulation results at both test sites: The RMSE of yield in Mazichuan Village decreased from 64.21 kg·hm^-2 to 33.64 kg·hm^-2, while the NRMSE decreased from 4.33% to 2.27%. The yield RMSE for Anjiagou Village decreased from 94.05 kg·hm^-2 to 36.88 kg·hm^-2, while the NRMSE decreased from 7.61% to 2.99%. These results further validate the applicability and robustness of this parameter set within the study area.

Although we cannot entirely eliminate minor variations between sites, the soil data used in this study were repeatedly validated based on long-term experiments, and their applicability has been confirmed through multiple studies. Additionally, in the discussion section of the original revised manuscript, we have identified the potential impact of uncertainty in soil input data on model simulation accuracy as a limitation of this study.

References:

[1] Li G. Huang G.B., Bellotti W., Chen W. Applicability of the APSIM Model to Different Tillage Practices in the Loess Hilly and Gully Region. Acta Ecologica Sinica, 2009, 29(05): 2655-2663.

[2] Nie Z., Li G., Luo C., Ma W., Dai Y. Optimization of Parameters in an APSIM-Based Dryland Wheat Yield Formation Model Using a Hybrid Frog-Jump Algorithm. Acta Agronomica Sinica, 2018, 44(08): 1229-1236.

Comments 4: The article confounds multisite, multiphase field experiments with district-level yield based on statistical yearbooks, which are essentially different scales of measurement (plot vs administrative statistics). The connection between these sources is not described and may cause structural bias in calibration/validation.

Response 4: Thank you for your highly constructive review. Your comment regarding “the article confounding multi-point phased field trials with district-level yield data from statistical yearbooks (essentially field-scale versus administrative statistical scale)” is both expertly raised and critically important. This is indeed a crucial distinction that must be clearly defined in cross-scale modeling. We fully acknowledge the risk that mixing data from different scales may introduce structural bias. In our study, we strictly separated these scales and did not combine data from different scales during either the optimization or validation phases. Specifically: (1)The long-term district-level yearbook yield data from 1971 to 2021 served as background climate-production scenario inputs for model runs. This approach allowed the model to operate within the framework of long-term climate variability, enhancing parameter robustness to interannual climate fluctuations; (2)Multi-objective parameter optimization and model validation were conducted exclusively using synchronized data from two periods: 2002 to 2005 and 2015 to 2017. This included contemporaneous field-measured LAI and annual wheat yields from the same period in the stable zone. This approach ensured temporal consistency between the yield and LAI optimization targets.

We recognize that the core concern may lie in whether “district-level statistical yields” can effectively represent “experimental plot” yield levels—specifically, differences in spatial scale and statistical methods. To address this, we emphasize that the statistical scope of the Anding District Yearbook selected for this study overlaps with the specific experimental sites (Lijiabao Town and Fengxiang Town), both located within the core rain-fed agricultural zone of the Loess Hills. These areas share similar climate types and soil textures, employing uniform cropping systems and crop varieties. Furthermore, the statistical yields for Anding District are aggregated from production units within its jurisdiction, employing statistical estimation methods that are conceptually identical to those used for measuring yields in experimental plots. Through extensive field investigations and comparative analyses, we found that the discrepancy between district-level yields and experimental plot yields is minimal and falls within an acceptable, reasonable range. Of course, we do not deny the existence of differences in absolute scale.

Following your suggestion, we have supplemented the revised manuscript's “Data collection” section with explanations regarding the use of different data sources to present the data utilization logic more transparently. In the discussion section, we have also included the impact of uncertainty in model input data on model accuracy as a research limitation. In future work, we will utilize remote sensing data to enhance the precision of model input data. Specific additions are as follows:

Page 5, Line 173 to 179: Supplemented with “In this study, long-term district-level annual yield data (1971 to 2021) primarily served as background input for model operation, characterizing the interannual variability of the study area under different climatic years, rather than being directly used to construct the parameter optimization objective function. Model parameter calibration and performance evaluation were conducted using contemporaneous district-level yearbook yield and LAI measurements from the periods 2002 to 2005 and 2015 to 2017, ensuring temporal consistency between the two optimization objectives.”

Page 16, Line 506 to 514: Supplemented with ”Although this study optimized the results of model simulations, certain limitations remain. First, measurement errors in input data, such as meteorological and soil parameters, may affect simulation accuracy. Under complex terrain conditions, accurately obtaining spatial distribution information of wheat is crucial for yield estimation and model spatial scale validation [52]. In the future, the quality of model input data can be further enhanced through multi-source data fusion, such as multi-temporal remote sensing data.”

Comments 5: LAI estimation via “length-width ratio method” is stated with no equation, correction factor, or sampling protocol detail (leaf shape coefficient, which leaves included, senescent leaves, etc.).

Response 5: Thank you for bringing this issue to our attention. We have added the formula and explanation for the long-length coefficient method at the corresponding location. The specific additions are as follows:

Page 4, Line 153 to 156: The calculation formula for LAI Supplemented with:

                           (1)

                                 (2)

where L_area denotes leaf area; L_length denotes leaf length, referring to the distance from the leaf base to the leaf tip; L_width denotes leaf width, referring to the width at the broadest part of the leaf; L_tarea denotes total leaf area; S_area denotes land area.

Comments 6: The meteorological data are of a bureau station of Dingxi/Anding (1971-2021) but the experiments are carried out in two villages that are approximately 30 km apart; the paper does not comment on representativeness, gap filling, and station-to-site corrections.

Response 6: We sincerely appreciate the reviewers' critical feedback. We understand and acknowledge that the spatial distance between different experimental sites and meteorological stations may influence the model simulation results. The meteorological data used in this study were sourced from the Gansu Provincial Meteorological Bureau, specifically the multi-year (1971–2021) historical meteorological records for Dingxi City's Anding District. These records include daily maximum temperature, daily minimum temperature, daily precipitation, and daily solar radiation. Daily solar radiation was calculated using the sunshine duration conversion method. Both study sites (Mazi Village, Lijiabao Town, and Anjiagou Village, Fengxiang Town) and the Anding District meteorological station are located within the Loess Hills region, sharing relatively consistent topography, elevation, and climatic background.

Regarding the regional representativeness of the meteorological data, team member Nie et al. (2017) conducted a systematic assessment of its applicability within the study area using the APSIM diagnostic analysis method [1]. Results indicate that when solar radiation is calculated using the sunshine duration conversion method, the model-simulated key crop growth process indicators align with regional climate suitability classifications and comprehensive evaluation results at a rate of 86%–90%. This demonstrates the meteorological data's good representativeness and validity at the study area scale. Therefore, to maintain consistency in data sources and processing methods, this study employs the same solar radiation calculation method.

Regarding data integrity, the meteorological records used were continuous daily data compiled by meteorological departments, with no significant missing values. Thus, no additional interpolation or reanalysis data were introduced for supplementation. We acknowledge that data from a single meteorological station may not fully capture microclimate variations at the local scale, potentially introducing uncertainty into model simulations. We have incorporated this uncertainty into the study limitations as follows:

Page 16, Line 506 to 511: Although this study optimized the results of model simulations, certain limitations remain. First, measurement errors in input data, such as meteorological and soil parameters, may affect simulation accuracy. Under complex terrain conditions, accurately obtaining spatial distribution information of wheat is crucial for yield estimation and model spatial scale validation [52]. In the future, the quality of model input data can be further enhanced through multi-source data fusion, such as multi-temporal remote sensing data.

References:

[1] Nie Z., Ren X., Li G., Dong L., Ma W., Tang J., Liu X., Luo Y. Evaluation of Climate Suitability for Dryland Wheat in Loess Hilly Areas Based on APSIM. Chinese Journal of Agricultural Meteorology, 2017, 38(06): 369-377.

Comments 7: The Morris method is introduced, although the sensitivity indices that are reported subsequently have outrageously varying scales among outputs (yield vs LAI). In the absence of normalization (e.g. relative change, standardized output), the comparison of the importance is arbitrary and can be misleading to screening.

Response 7: We sincerely appreciate the reviewer for highlighting this critical issue. We fully agree that without normalization, directly comparing sensitivity indices across output variables with significant differences in physical dimensions and numerical scales—such as yield and LAI—can lead to interpretive biases in results, thereby compromising the reliability of parameter selection. Following the reviewer's suggestion, we have normalized the yield and LAI outputs and re-implemented the Morris global sensitivity analysis to eliminate the influence of dimensional differences on the magnitude of sensitivity metrics. Specifically, during the sensitivity analysis phase, model outputs were first converted to a dimensionless form, and corresponding Morris mean and standard deviation metrics were then calculated. This ensures comparability of sensitivity results across different output variables. Following normalization, the relative importance of parameters for different outputs became more stable and physically interpretable, effectively avoiding potential misinterpretations caused by output scale differences. The relevant methodological explanations and results have been supplemented and updated in the revised manuscript. Detailed responses are provided below:

Page 5, Line 202 to 207: The global sensitivity method introduced a supplementary normalization process, namely “In conducting sensitivity analysis for this study, the yield data and LAI from the model simulations were first subjected to Min-Max normalization to prevent dimensional differences from affecting the sensitivity analysis results. The Min-Max normalization formula is:

                              (3)

where X represents the raw simulation data output by the model, while min(X) and max(X) denote the minimum and maximum values of the raw simulation data, respectively”.

Page 10 to 12, Line 327 to 375: Revise the sensitivity analysis results and redraw the sensitivity analysis chart. The content is as follows:

The results of the parameter sensitivity analysis based on the Morris method are shown in Figures 2 and 3. According to the sensitivity parameter criteria, the parameters sensitive to yield and LAI are maximum grain size (G3), radiation use efficiency (L2), and extinction coefficient (L3). Regarding yield (Figure 2), parameter L3 exhibits the highest mean sensitivity and largest standard deviation, indicating its dominant role in yield formation, alongside significant parameter interactions. This parameter primarily in-fluences yield formation by regulating the canopy's radiation interception efficiency, thereby affecting the fundamental supply of photosynthetic products. Parameters G3 and L2 exhibited medium-level sensitivity means with relatively pronounced standard deviations, indicating they exert a stable yet relatively minor influence on yield. In contrast, parameters G1, G2, G4, G5, G6, G7, L1, and L4 cluster near the origin with low mean sensitivity and standard deviation, suggesting limited direct contribution to yield and stable parameter responses. For LAI (Figure 3), the overall sensitivity ranking resembles that for yield, though relative importance shifts. L3 remains the most sensitive parameter, underscoring its pivotal role in regulating canopy growth structure. L2 maintains moderate sensitivity, while L1 and G3 exhibit heightened sensitivity to LAI compared to yield, reflecting their close association with leaf expansion and leaf area formation processes. The remaining parameters demonstrate weaker sensitivity.

The results of the parameter sensitivity analysis obtained using the EFAST method are shown in Figure 4. Figure 4a and Figure 4b represent the first-order sensitivity in-dices for yield and LAI, respectively, while Figure 4c and Figure 4d show the corresponding full-order sensitivity indices. According to the sensitivity parameter criteria, only parameter L3 exhibited significant sensitivity for both yield and LAI objectives, while the remaining parameters failed to meet the sensitivity thresholds. In the first-order sensitivity analysis (Figures 4a and 4b), parameter L3 demonstrated significantly higher first-order sensitivity indices for both yield and LAI compared to other parameters, indicating the strongest response characteristics of model outputs to variations in this parameter. Parameters G3 and L2 exhibit relatively higher first-order sensitivity indices among the non-sensitive parameters, with slightly greater direct in-fluence on yield and LAI than others, though their overall sensitivity remains markedly lower than L3. The full-order sensitivity analysis results (Figures 4c and 4d) further confirm that parameter L3 maintains the highest full-order sensitivity index, highly consistent with the first-order findings. This indicates that the interaction effects be-tween this parameter and others contribute relatively little to model outputs. Sensitivity indices for other parameters in the full-order analysis remain low, indicating their limited combined contribution to yield and LAI.

Overall, only a few parameters exhibit high sensitivity toward both yield and LAI simultaneously, and their response characteristics display certain nonlinearity and uncertainty. The sensitivity results for yield and LAI show both overlaps and differences, reflecting potential trade-offs among different physiological processes during multi-objective synergistic calibration.

Figure 2. The Morris sensitivity analysis results (Yield).

Figure 3. The Morris sensitivity analysis results (LAI).

Figure 4. The EFAST sensitivity analysis results. (a) Results of first-order sensitivity analysis of parameters on wheat yield; (b) Results of first-order sensitivity analysis of parameters on LAI; (c) Results of global sensitivity analysis of wheat yield; (d) Results of global sensitivity analysis of parameters on LAI.

Comments 8: The assertion that bounds are ±50% of default value is not always consistent with the ranges displayed (e.g. some N concentration bounds are very narrow and do not appear like ±50%). At least, the defaults that are used to build bounds should be reported.

Response 8: We sincerely appreciate the reviewers' detailed comments regarding the parameter boundary setting. This study centers on multi-objective optimization, with sensitivity analysis primarily employed to screen critical parameters and enhance optimization efficiency. The scope of parameter sensitivity analysis references the research by Wei and Nie (2024) [1], who noted that a 50% fluctuation in parameter ranges can objectively identify sensitive parameters. Verman et al. (2021) further emphasized that when specific parameter ranges are unavailable [2], a broad range should be adopted to prevent underestimating parameter sensitivity due to overly narrow constraints. Consequently, a uniform ±50% perturbation range was applied throughout the sensitivity analysis phase.

Regarding the reviewer's comment that “some parameter ranges appear narrow and default values are not explicitly reported,” we have supplemented the original parameter table in the revised manuscript by listing the model default values for each parameter. This clearly demonstrates the specific implementation of the ±50% range principle. Detailed responses are as follows:

Page 7, Line 256 to 259: For the “Default” column of parameters in Tables 2 and 3:

Table 2. Range of values for sensitivity analysis of 7 parameters for the APSIM NG-Wheat dryland wheat grain growth sub-model.

Table 3. Range of values for sensitivity analysis of 4 parameters for the APSIM NG-Wheat dryland wheat leaf growth sub-model.

References:

[1] Wei X., Nie Z. Sensitivity Analysis and Optimization of Parameters Related to LAI in Dryland Wheat Based on APSIM Model. Chinese Journal of Ecological Agriculture, 2024, 32(01):119-129.

[2] Verman R.A., Geenen J.W., Knies S., Mantel-Teuwisse A.K., Leufkens H.G.M., Goettsch W.G. The Application and Implications of Novel Deterministic Sensitivity Analysis Methods. Pharmacoeconomics. 2021, 39(1):1-17.

Comments 9: DREAM-zs is characterized as Bayesian/MCMC (posterior sampling), although the likelihood/error model, priors, or the construction of the posterior distribution based on the equation of (10) are not defined anywhere in the paper.

Response 9: We appreciate the reviewers' valuable corrections. The application of the DREAM-zs algorithm in this paper emphasizes its adaptive multi-chain parallel search and differential evolution mechanism to achieve efficient parameter calibration for complex crop models, rather than strictly adhering to Bayesian inference or posterior distribution estimation. In the specific implementation, the objective function defined in Equation (10) is based on the squared errors of yield and LAI, serving as the fitness function for parameter space search. It does not explicitly construct a probabilistic likelihood function or prior distribution. To avoid conceptual confusion, the description of DREAM-zs in the revised manuscript's discussion section has been modified to explicitly state that it is employed herein as an adaptive global optimization algorithm based on MCMC principles, rather than for posterior distribution inference. Additionally, the methodology section now includes supplementary clarification on the role of the objective function and error metrics in parameter updates, enhancing the clarity and consistency of the model description. The supplementary content is as follows:

Page 8, Line 282 to 287: Revise the multi-objective function formula:

where x denotes the parameter vector of the calibration model, and k represents the number of parameters in the vector; N denotes the number of samples; Y_S(x_i), Y_O(x_i), L_S(x_i), and L_O(x_i) represent the simulated wheat yield, observed wheat yield, simulated LAI, and observed LAI for the i-th sample corresponding to parameter vector x, respectively; and  denote the minimum and maximum values of parameter x.

Page 15, Line 483 to 486: Modified the description of DREAM-zs:

The DREAM-zs algorithm employed in this study features simple parameter settings. By running multiple Markov chains in parallel and adopting adaptive sampling strategies, it achieves higher efficiency and stability when addressing multi-objective optimization problems.

Comments 10: The values of Morris mean sensitivity index that is reported (173.695 on yield at L3) cannot be interpreted without indicating the step size, scaling, and whether the outputs were standardized. The paper considers them as directly comparable measures of importance, which is not justified.

Response 10: We sincerely appreciate the reviewer's professional and critical comments regarding the interpretability of the Morris sensitivity index. We concur with the reviewer's perspective. This study implemented the Morris sensitivity analysis using SimLab software. In accordance with your requests and suggestions, we have supplemented the settings for Morris-related parameters in SimLab and made significant revisions to the sensitivity analysis methodology. We first standardized the model outputs (yield and LAI) to eliminate differences in dimensionality and numerical scale between output variables. Subsequently, we reran the Morris global sensitivity analysis, recalculated the Morris mean and standard deviation metrics for each parameter individually, revised the sensitivity analysis results, and redrew the sensitivity analysis plots, as detailed in Response 7. The supplementary content regarding Morris-related parameter settings in SimLab is as follows:

Page 7, Line 250 to 253: Supplemented with “In the Morris, the model is executed r×(k+1) times. Here, r represents the number of trajectories, typically ranging from 4 to 10; in this study, it was set to 10. k denotes the number of model input factors, with a total of 120 groups sampled.”

Comments 11: The EFAST outcomes suggest that L3 accounts for the first-order/global yield variance (96-98%) and this is extremely large considering that there are grain growth parameters (G3, etc.). This does not indicate sample convergence/stability of indices, which makes it look fragile.

Response 11: We sincerely appreciate the reviewers' professional feedback. To address this concern, we have re-normalized the model outputs and conducted sensitivity analyses based on this adjusted data to eliminate differences in dimensionality and numerical scale between yield and LAI. During the sensitivity analysis, we maintained the EFAST sampling parameters unchanged while running the model multiple times in independent replicates to ensure robustness of the results. The results indicate that under normalized conditions, the rankings of first-order effects and total effects for each parameter remain highly consistent across multiple runs. Notably, the L3 parameter consistently exhibits a dominant influence on both yield and LAI. From a mechanistic perspective, L3 (canopy extinction coefficient) directly governs light interception and canopy biomass accumulation processes. Its significant influence on the coordinated variation of yield and LAI under drought conditions, coupled with its high contribution in sensitivity analysis, holds physiological plausibility. Sensitivity analysis results are provided in Response 7.

Comments 12: The analysis seems to be based on a limited number of years (as illustrated in Figure), although the paper also presents long time-series yield and met data (1971-2021). What was used where and whether any actual out of sample validation was performed is not clear.

Response 12: We sincerely appreciate the reviewer's important comments regarding the unclear use of time scales and insufficient out-of-sample validation. We acknowledge that the original manuscript did not clearly specify the specific roles of different time series data during the model-driving, parameter optimization, and validation stages, which could lead to misunderstandings. In this study, data from different time scales served distinct functional roles and were not mixed during the same stage. (1) The 1971 to 2021 meteorological data and annual production data were primarily used to provide long-term climate background inputs for the APSIM NG model. This enabled the model to capture environmental fluctuations under different climatic years within the study area, thereby enhancing its representativeness and robustness to climate interannual variability during model runs. This long-term dataset did not directly participate in parameter optimization or objective function construction. (2) Multi-objective parameter optimization and model validation were conducted using data from 2002 to 2005 and 2015 to 2017. LAI was derived from contemporaneous field measurements, while yield was sourced from corresponding yearbook data for the same periods. This approach ensured temporal consistency between the two optimization objectives, thereby preventing additional bias from temporal mismatches. Additionally, this study did not further allocate additional samples independent of the aforementioned two periods for strictly out-of-sample validation. Both model parameter optimization and performance evaluation were completed using data from the 2002 to 2005 and 2015 to 2017 periods. The primary focus of this research is to evaluate the improvement achieved by multi-objective synergistic optimization relative to default parameter conditions, rather than constructing a completely independent prediction model. However, we fully agree with the reviewer's suggestion that incorporating fully independent out-of-sample validation data would further validate the generalization capability of the optimized parameters. Unfortunately, due to the limited availability of long-term, continuous plot-scale LAI and yield synchronous observation data in the study area, this extension was not feasible in the current study. This will be an important direction for our future research.

We have incorporated the reviewers' suggestions into the revised manuscript with the following specific modifications:

Page 5, Line 173 to 179: Supplemented with “In this study, long-term district-level annual yield data (1971 to 2021) primarily served as background input for model operation, characterizing the interannual variability of the study area under different climatic years, rather than being directly used to construct the parameter optimization objective function. Model parameter calibration and performance evaluation were conducted using contemporaneous district-level yearbook yield and LAI measurements from the periods 2002 to 2005 and 2015 to 2017, ensuring temporal consistency between the two optimization objectives.”

Comments 13: It is more of a discussion that is skewed towards mechanistic explanations (light interception, canopy structure) but never links them to the scale of parameter changes or their physiological plausibility to the cultivar/region.

Response 13: Thank you very much for this insightful comment. We fully agree with your perspective that the discussion section would lose depth and persuasiveness if it merely offered general explanations of mechanisms like light interception and canopy structure without closely linking the specific magnitude of parameter changes to their physiological plausibility under specific cultivar/regional conditions. We fully concur with your suggestions and have made targeted revisions to the discussion section. When analyzing the optimization results of key parameters, we have strengthened the argument linking “magnitude of change –physiological mechanism–regional adaptability.” The revised discussion is presented in full below:

Page 14 to 16, Line 421 to 514: Underlined text indicates modified content:

This study employs the APSIM NG to perform multi-objective cooptimization of parameters related to the grain and leaf growth sub-models for dryland wheat. The model features numerous complex internal parameters and relatively computationally intensive operations. To enhance calibration efficiency, sensitivity analysis methods such as Morris and EFAST were employed to screen critical model parameters. Under the two global sensitivity analysis methods described above, the key parameters influencing wheat yield and LAI were not entirely consistent between the grain and leaf growth sub-models. The Morris method identified sensitive parameters, including maximum grain size, radiation use efficiency, and extinction coefficient, while the EFAST method selected the extinction coefficient as the sensitive parameter. The discrepancy primarily stems from differing emphases in process analysis between the two methods. Both methods effectively capture overall trends in parameter influences on model outputs and exhibit high sensitivity to nonlinear effects and parameter interactions [23]. The Morris method, with its heightened sensitivity to nonlinear effects and parameter interactions [23], can thus identify parameters like maximum grain size and radiation use efficiency that exhibit stage-dependent or scenario-dependent effects. The EFAST method characterizes total effect indices while also focusing on the stable contribution of individual parameters to the overall variance in model outputs [25]. In this study, EFAST analysis revealed that the extinction coefficient exerts a dominant in-fluence on yield and LAI across the entire parameter space, mitigating the impact of the interaction between maximum grain size and radiation use efficiency. The Morris method's advantage in multi-objective parameter screening lies in its ability to uncover potentially critical parameter sets and their interactions, thereby providing more comprehensive parameter space information for subsequent optimization. The sensitivity analysis results of this study are consistent with those of Li et al. (2011) [42], Wei and Nie (2023) [34], and Zhao et al. (2014) [36], indicating reasonable findings.

Based on the sensitivity analysis results, the parameters to be optimized were determined to be maximum grain size, radiation use efficiency, and extinction coefficient. Their optimization ranges were referenced from previous studies and align with the growth and development patterns of wheat in loess hilly dryland areas. Optimization results indicate that the maximum grain size and radiation use efficiency increased compared to default values, while the extinction coefficient showed a decreasing trend. Within the APSIM NG-Wheat model module, grain size directly influences yield calculations [16], and grain size is determined by the degree of grain filling from flowering to grain filling stage [43], concurrently with the continuous accumulation of dry matter through photosynthesis and other processes. Fisher (2011) and Wang et al. (2023) noted that water stress directly impacts agronomic traits like photosynthesis and dry matter accumulation. Under water deficiency, wheat yield formation relies more on grain filling capacity than on grain number per spike [44,45]. Dryland wheat often exhibits grain number limitation compensated by enhanced grain weight [46]. Therefore, increasing maximum grain size enhances the potential for dry matter accumulation per grain during the grain filling stage, partially offsetting the adverse yield effects of reduced grain number. Photosynthesis is a primary driver of dry matter accumulation, and leaf area directly influences the photosynthetic capacity of wheat populations [47]. LAI is closely correlated with the extinction coefficient [48]. The extinction coefficient indicates light transmittance within the crop canopy [34], influencing light energy distribution and use efficiency. Under rainfed conditions, water and high-temperature stress induce leaf stomatal closure and reduced photosynthetic rates, leading to de-creased extinction coefficients [49]. This physiological response aligns with the optimization trend of extinction coefficient parameters observed in this study. Radiation use efficiency reflects a crop's ability to convert available light energy into biomass through photosynthesis and is highly sensitive to environmental conditions. Under water stress, dryland wheat often maintains population productivity by enhancing the conversion efficiency of dry matter per unit of intercepted light energy [50]. Thus, the increase in radiation use efficiency parameters observed in this study demonstrates the model's adaptive regulation of light energy utilization efficiency under dryland conditions.

Optimizing crop model parameters is fundamentally a complex problem of finding global optimal solutions within a high-dimensional, nonlinear parameter space. When the optimization objective expands from a single goal to multiple goals, such as the synergistic optimization of yield and LAI, the uncertainty and complexity of model parameters increase accordingly [51]. The modular design of the APSIM NG model and its complex system simulation requirements demand precise parameterization to ensure simulation reliability. The DREAM-zs algorithm employed in this study features straightforward parameter configuration. By running multiple Markov chains in parallel and utilizing adaptive sampling strategies, it achieves higher efficiency and stability when addressing multi-objective optimization problems. In contrast, GA and PSO typically rely on iterative adjustments of empirical parameters such as crossover probability, mutation rate, or inertia weight in practical applications. When parameter dimensions are high or strong nonlinear couplings exist, their optimization performance becomes highly sensitive to hyperparameters, often leading to reduced search efficiency or premature convergence [12,14]. Although the NSGA-II algorithm excels in constructing Pareto frontiers, its function evaluation count is typically the product of population size and iteration count [13], often consuming substantial computational resources in computationally intensive applications like crop modeling. In this study, the DREAM-zs algorithm was set to 500 iterations, with a maximum total runtime of 2887.5 seconds. This demonstrates that, while balancing multi-objective optimization accuracy and computational resources, DREAM-zs can provide a computationally efficient and stable parameter optimization solution for complex crop models like APSIM NG.

Model performance was evaluated via the RMSE and MAE, with the optimized model demonstrating improved adaptability. Since this study employed dual objectives of minimizing simulation errors for both yield and LAI with equal weighting (weight coefficient of 1), yield optimization achieved relatively more significant improvements despite the substantial difference in dimensionality between the two objectives, whereas LAI showed smaller improvements. This finding indicates that differences in the magnitude of different indicators may lead to uneven responses of optimization objectives during collaborative search.

Although this study optimized the results of model simulations, certain limitations remain. First, measurement errors in input data, such as meteorological and soil parameters, may affect simulation accuracy. Under complex terrain conditions, accurately obtaining spatial distribution information of wheat is crucial for yield estimation and model spatial scale validation [52]. In the future, the quality of model input data can be further enhanced through multi-source data fusion, such as multi-temporal remote sensing data. Additionally, while this study treated growth stage parameters as fundamental crop variety attributes, subsequent research could incorporate growth stage phase parameters to analyze their influence.

Comments 14: The authors are encouraged to incorporate the following references to further strengthen their work.

Wang, N., Wu, Q., Gui, Y., Hu, Q., & Li, W. (2024). Cross-Modal Segmentation Network for Winter Wheat Mapping in Complex Terrain Using Remote-Sensing Multi-Temporal Images and DEM Data. Remote Sensing, 16(10), 1775. doi: https://doi.org/10.3390/rs16101775

Wang, Y., Yu, T., Wang, C., Wei, J., Zhang, S., Liu, Y., Xu, Z. (2023). Heat shock protein TaHSP17.4, a TaHOP interactor in wheat, improves plant stress tolerance. International Journal of Biological Macromolecules, 246, 125694. doi: https://doi.org/10.1016/j.ijbiomac.2023.125694

Yang, X., Xia, X., Zhang, Z., Nong, B., Zeng, Y., Wu, Y., Xiong, F., Zhang, Y., Liang, H., Pan, Y., Dai, G., Deng, G., & Li, D. (2019). Identification of anthocyanin biosynthesis genes in rice pericarp using PCAMP. Plant biotechnology journal, 17(9), 1700–1702. https://doi.org/10.1111/pbi.13133

Response 13: We sincerely appreciate your valuable feedback and are deeply grateful for your recommendations of these highly insightful papers. Their innovative research perspectives and rigorous argumentation frameworks have provided us with significant inspiration. After thorough review, we have incorporated the core findings from Wang et al. (2023) and Wang et al. (2024) into the Discussion section. Yang et al. (2019) focuses on crop gene functional identification (specifically rice pigment metabolism-related genes), which differs significantly from our research direction on crop model parameter calibration techniques. Therefore, this reference was not included. The other two references are discussed in the corresponding sections as follows:

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Response to Reviewer 3 Comments

Drear Reviewer:

We sincerely appreciate your valuable feedback and expert guidance. Your insights have substantially enhanced the academic rigor and clarity of our manuscript. In accordance with your suggestions and requirements, all necessary revisions have been incorporated into the revised draft, with the corresponding changes highlighted in yellow.

Comments 1: The study investigated a multi-criteria optimization problem with the goal of enhancing the localized adaptability of the model for dryland wheat production. Parameter optimization was conducted for both grain and leaf development sub-models. Sensitivity analysis identified three primary parameters influencing wheat yield and leaf area index: maximum grain size, radiation use efficiency, and the extinction coefficient. Optimization of these key parameters was shown to significantly improve not only wheat yield but also overall crop growth performance.

Response 1: Thank you very much for the reviewer’s careful summary and positive assessment of our study. We appreciate your recognition of the multi-criteria optimization framework and its role in enhancing the localized adaptability of the APSIM NG model for dryland wheat production.

Comments 2: However, the formulation of the multi-objective optimization model requires further clarification. Although the objective function is presented in Formula (10), the design variable vector and constraint vector are not explicitly defined in a mathematical form. Additionally, despite framing the task as a multi-criteria optimization problem, Formula (10) presents a single optimization function expressed as the sum of the minimum values of two sub-functions.

Response 2: We sincerely appreciate the reviewer's meticulous and professional corrections regarding the mathematical formulation of the multi-objective optimization model. In response to this feedback, we have systematically supplemented the mathematical structure of the multi-objective optimization problem in the revised manuscript. First, we have reformulated Equation (10) in the original manuscript, explicitly providing mathematical definitions for the design variable vector, objective function vector, and constraint vector. This ensures a more complete, standardized, and rigorous structural representation of the multi-objective optimization problem. Relevant supplementary content has been prominently marked in the revised manuscript. Additionally, regarding the reviewer's observation that “Equation (10) combines multiple objectives into a single scalar function, which is not entirely consistent with the multi-objective framework,” we provide further clarification here. This study employs the DREAM-zs algorithm for parameter optimization. This algorithm is fundamentally an efficient parameter search framework integrating parallel Markov Chain Monte Carlo (MCMC) sampling with an adaptive differential evolution strategy. Its implementation mechanism requires a single scalar objective function as the criterion for accepting or rejecting candidate samples. Therefore, to ensure the usability and numerical stability of the DREAM-zs algorithm during parameter search while fully leveraging its advantages in parallel sampling and adaptive step size updates, it is necessary to transform the multi-objective optimization problem into a single-objective optimization problem through scalarization. This approach represents a common and mature technical route in multi-objective optimization, widely adopted in existing research. For instance, Bazgan et al. (2022) systematically discussed the theoretical properties and approximation characteristics of weighted and scalarization methods in converting multi-objective optimization problems into single-objective problems [1]. This approach has been extensively applied in combinatorial optimization and related fields.

The modified multi-objective function formula is as follows:

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where x denotes the parameter vector of the calibration model, and k represents the number of parameters in the vector; N denotes the number of samples; Y_S(x_i), Y_O(x_i), L_S(x_i), and L_O(x_i) represent the simulated wheat yield, observed wheat yield, simulated LAI, and observed LAI for the i-th sample corresponding to parameter vector x, respectively; and  denote the minimum and maximum values of parameter x.

References:

[1] Bazgan, C., Ruzika, S., Thielen, C. et al. The Power of the Weighted Sum Scalarization for Approximating Multiobjective Optimization Problems. Theory Comput Syst 66, 395–415 (2022). https://doi.org/10.1007/s00224-021-10066-5

Comments 3: The root mean square error (RMSE) and mean absolute error (MAE) are used for model validation. It is also useful to include the root mean squared percentage error (RMSPE), which expresses the error as a percentage relative to the test data.

Response 3: We sincerely appreciate the reviewer's constructive suggestion. We fully agree that RMSPE holds significant reference value in model evaluation, as it provides complementary insights into model performance from the perspective of relative error. Following the reviewer's suggestion, we carefully evaluated the feasibility of introducing RMSPE. However, in this study, LAI often exhibits small observed values during the early growth stages of crops and under water-limited conditions. Under such circumstances, RMSPE is highly sensitive to the denominator, potentially amplifying errors and thereby compromising the stability and interpretability of model performance evaluation to some extent. Considering the above, this study ultimately selected RMSE and MAE as primary evaluation metrics to ensure consistency and robustness in error assessment across different growth stages and variables. We once again express our gratitude for the reviewer's valuable suggestions.

Comments 4: The optimization program was developed in R (version 4.2.3) using RStudio, but a detailed description of the algorithmic steps used to solve the optimization problem should be included in the appendix.

Response 4: We sincerely appreciate the valuable suggestions provided by the reviewers. In Section 1.8 of the original manuscript, we have outlined the overall parameter optimization workflow, including model initialization, setting observation targets, determining parameter ranges, configuring DREAM-zs parameters, and the basic process of iterative optimization by calling the APSIM model via CroptimizR. However, we acknowledge that the manuscript's description of relevant steps remains insufficient, with certain technical details presented less clearly. Based on the reviewers' feedback, we have further supplemented and refined the optimization workflow in Section 1.8 of the manuscript to enhance the clarity and reproducibility of the method description. The specific additions are as follows:

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The DREAM-zs algorithm is invoked via the CroptimizR package to drive the APSIM NG-Wheat model for parameter optimization. The crop variety optimized was Dingxi Spring Wheat No. 35. The parameter optimization steps are illustrated in Figure 1. The specific steps are as follows:

Step 1: Initialize the model. Download and load the packages required for the optimization program, including: CroptimizR, CroPlotR, ApsimOnR, dplyr, ggplot2, gridExtra, and tidyr.

Step 2: Set the simulator and observation targets. The observation targets in this study are yield and LAI.

Step 2: Run the model to evaluate initial results. Extract the simulator name and observed target values from the output data.

Step 3: Define the optimization range for target parameters. The parameters to be optimized in this study are those identified through sensitivity analysis as having significant synergistic effects on yield and LAI.

Step 4: Configure optimization algorithm parameters. Use the CroptimizR package to invoke the DREAM-zs algorithm for optimization. The iteration count for the DREAM-zs algorithm was empirically set to 500 and run multiple times to ensure stability. The number of Markov chain members was set to 3 based on Vrugt et al. (2009) [15]. The random seed was set to 1234.

Step 5: Drive the model to run iteratively and evaluate the output results for plausibility until the optimization termination criteria are met.