A Gaussian-Process-Based Global Sensitivity Analysis of Cultivar Trait Parameters in APSIM-Sugar Model: Special Reference to Environmental and Management Conditions in Thailand

: Process-based crop models are advantageous for the identiﬁcation of management strategies to cope with both temporal and spatial variability of sugarcane yield. However, global optimization of such models is often computationally expensive. Therefore, we performed global sensitivity analysis based on Gaussian process emulation to evaluate the sensitivity of cane dry weight to trait parameters implemented in the Agricultural Productions System Simulator (APSIM)-Sugar model under selected environmental and management conditions in Khon Kaen (KK), Thailand. Emulators modeled 30 years, three soil types and irrigated or rainfed conditions, and emulator performance was investigated. rue , green_leaf_no , transp_e ﬀ _cf , tt_emerg_to_begcane and cane_fraction were identiﬁed as the most inﬂuential parameters and together they explained more than 90% of total variance on the simulator output. Moreover, results indicate that the sensitivity of sugarcane yield to the most inﬂuential parameters is a ﬀ ected by water stress conditions and nitrogen stress. Our ﬁndings can be used to improve the e ﬃ ciency and accuracy of modeling and to identify appropriate management strategies to address temporal and spatial variability of sugarcane yield in KK.


Introduction
Sugarcane plays a critical role in Thailand's economy and has become one of the most important agricultural crops of the country [1]. Being the major sugarcane production region of Thailand, the Northeast is responsible for 43.2% of the total produced sugarcane and 44.2% of the total sugarcane harvesting area [2]. Recently, paddy fields that produce lower net value per hectare in the Khon Kaen (KK) area of the Northeast have been converted into sugarcane fields [3]. Increasing evidence indicates that global climate change could reduce sugarcane production. According to Preecha et al. [4], climate change is the most obvious factor responsible for spatial and temporal yield variability in the Northeast of Thailand. Thus, identification of suitable management strategies to cope with both temporal and mean daily maximum and minimum temperatures and mean daily solar radiation of each month between 1980-2010 in KK. We observed similar values of mean daily maximum and minimum temperatures and mean daily solar radiation among the years. However, mean monthly rainfall values were highly varied among years. Textural classes and physical and chemical properties of each selected soil type are shown in Table 1. Available water content varies as; S1 > S46 > S44 (Table  1).

APSIM Simulation
APSIM [30] is a modeling platform that can be used to simulate the performance of a single crop or a cropping system under different soil and climatic conditions and permits evaluation of management interventions via tillage, fertilization, irrigation and selection, timing and crop sequencing (in fixed or flexible rotations) [31]. For instance, Ojeda et al. [32] has used APSIM for forage crop by considering crop sequences. The APSIM 7.10 Sugar model was used for the simulations. APSIM-Sugar uses radiation use efficiency (rue) to simulate CDW accumulation by converting intercepted radiation into biomass [11]. On the basis of the crop phenological stage, biomass is partitioned among different plant components (sucrose, leaf, structural stem, cabbage and roots). It uses six different crop phenological stages to define sugarcane growth, i.e., "sowing (from sowing to sprouting), sprouting (from sprouting to emergence), emergence (from emergence to the beginning of cane growth), begin cane (from the

APSIM Simulation
APSIM [30] is a modeling platform that can be used to simulate the performance of a single crop or a cropping system under different soil and climatic conditions and permits evaluation of management interventions via tillage, fertilization, irrigation and selection, timing and crop sequencing (in fixed or flexible rotations) [31]. For instance, Ojeda et al. [32] has used APSIM for forage crop by considering crop sequences. The APSIM 7.10 Sugar model was used for the simulations. APSIM-Sugar uses radiation use efficiency (rue) to simulate CDW accumulation by converting intercepted radiation into biomass [11]. On the basis of the crop phenological stage, biomass is partitioned among different plant components (sucrose, leaf, structural stem, cabbage and roots). It uses six different crop phenological stages to define sugarcane growth, i.e., "sowing (from sowing to sprouting), sprouting (from sprouting to emergence), emergence (from emergence to the beginning of cane growth), begin cane (from the beginning of cane growth to flowering), flowering (from flowering to the end of the crop) and the end of the crop (crop is not currently in the simulated system)" [30]. The model is designed for the simulation of a uniform cane field using daily time-steps, and predicts cane yield, crop biomass, sucrose yield, commercial sucrose concentration, water use and crop nitrogen uptake on an area basis [33]. Cultivar-specificity, plant/ratoon and environmental conditions (climate and soil) are the factors that control this simulation process [27,33,34].
CDW of sugarcane plant-crop at harvest was simulated for 30 years (1980-2010) for three selected soil types under Ir or Rf conditions to study soil and climate interactions on trait parameters. Management criteria used for the APSIM simulation setup are indicated in Table 2. Planting date was selected as 28 November of each year in accordance with the previous simulation study [4] to represent realistic management practices in the region. Soil data (Table 1) and daily weather data for KK from 1980 to 2010 collected by Preecha et al. [4] were used for the simulations. * The irrigation schedule was manually induced; a to ensuring the crop establishment, b based on the actual management practices. The amount of irrigation (24 mm) was assumed with the purpose of avoiding water stress and to confirm the difference between Ir and Rf conditions in the simulation. Therefore, Irrigation efficiency is considered as one.

Preparation of Training Design Points
Parameters which control the underlying biophysical process of sugarcane growth in APSIM-Sugar are categorized into cultivar specific parameters, plant and ratoon class parameters and soil and climate parameters [11]. Table 3 shows the cultivar-specific parameters implemented in APSIM-Sugar which we used in this study. Leaf development (leaf size, green_leaf_no, tiller leaf size), phenological development based on thermal time (tt_emerge_to_begcane, tt_begcane_to_flowering, tt_flowering_to_crop_end) and partitioning of assimilates (cane_fraction, sucrose_fraction_stalk, stress_factor_stalk, sucrose_delay, min_sstem_sucrose, min_sstem_sucrose_redn) are controlled by cultivar specific parameters. Parameters such as green_leaf_no are directly related to express the cultivar traits [11]. Some of the traits are expressed via a parameter combination. For instance, parameters such as leaf_size and leaf_size_no (position of the leaf along stalk) together control canopy development [35]. Although, parameters which are related to later phenological development stages such as tt_begcane_to_flowering and tt_flowering_to_crop_end included in APSIM-sugar, they remain deactivated until a better physiological basis for prediction is available [33,35]. Both rue and transp_eff_cf are not considered as cultivar specific parameters in APSIM-Sugar [11]. However, rue and transp_eff_cf were included in the analysis. In APSIM, dry matter assimilation is governed by radiation interception and rue in the conditions which soil water availability is not limited. If the soil water supply is not enough to meet the transpiration demand, dry matter assimilation is governed by water supply, transp_eff_cf and the vapor pressure deficit. Moreover, results of SA studies conducted by Sexton et al. [11,35], Gunarathna et al. [27] and Sexton and Everingham [26] have indicated that both rue and transp_eff_cf may improve simulations based on cultivar differences. Initially, 500 parameter combinations were generated based on the parameter ranges indicated in Table 3 using APSIM package [37] of R software [38]. These training design points were generated as uniform random numbers distributed between the minimum and maximum values of selected cultivar trait input parameters (listed in Table 3). Minimum and maximum values of parameters were selected based on available literature on previous research and APSIM-Sugar documentation ( Table 3).
According to Sinclair [39], transp_eff_cf ranges between 0.009-0.010 kg kPa/kg for C4 plants like sugarcane. A recent research conducted by Jackson et al. [40] has reported that under water stressed conditions, higher transpiration efficiency could be identified for sugarcane cultivars. Therefore, in order to represent the response of sugarcane to water stressed conditions, the present study has used the range of transp_eff_cf as 0.008-0.014 kg kPa/kg following Gunarathna et al. [27].
In the APSIM-Sugar model, rue parameter is fixed as 1.8 g/MJ for plant crops and 1.65 g/MJ for ratoon crops [36]. It is reported that a considerable variation in rue could be occurred due to temperature variations, soil water deficit or excess [33], crop class and age, lodging, soil fertility (Nitrogen deficit) and culm death [41]. Considering the intercepted photosynthetically active radiation, Ferreira et al. [42] have found that rue of sugarcane in single and combined spacing as 2.73 (±0.09) and 2.78 (±0.25) g/MJ, respectively. Further, Olivier et al. [43] have reported rue value of 1.75 g/MJ for N19 sugarcane variety. Meki et al. [44] have obtained rue value of 2.06 g/MJ for their study on modeling of specific crop parameter attributes of two-year sugarcane growth cycle. Hence, by considering values of previous studies, we have used 1.2-2.5 g/MJ as the range for rue.
Above mentioned parameter combinations were then simulated in APSIM-Sugar for 30 years under three selected soil types and Ir or Rf conditions (described in Section 2.2). APSIM output values (CDW) corresponding to each parameter combination and environmental and management condition (180 APSIM output files and each file including 500 outputs) were obtained from the simulations. Both parameter combination files and corresponding APSIM output files were used as training design points for emulator generation and validation during the GSA.

Gaussian-Process-Based Global Sensitivity Analysis
To conduct SA for complex simulation models, an increasing number of studies have focused on model emulation. According to Villa-Vialaneix et al. [45], it is a common approach to use GP when generating emulators [20,46], even though other options are available as well. GP can be defined as a distribution for a function. According to O'Hagan et al. [46], each value of a function has a normal distribution, and a set of function values has a multivariate normal distribution. Therefore, GPs and the normal distribution both have equal mathematically convenient properties. During emulator building, the original model is described by assigning a GP prior, and then the prior is updated using a series of model runs by applying the Bayes theorem. The emulator is the resulting posterior distribution [47].
SA was conducted by using GP-based emulation implemented in the Gaussian emulation machine for sensitivity analysis (GEM-SA) software package [47]. A more detailed description of the mathematics underlying GEM-SA can be found in Kennedy and O'Hagan [7] and Oakley and O'Hagan [22]. The GEM-SA package calculates two variance-based sensitivity indices, the main-effect index (S i ) and the total-effect index (ST i ).
Equation (1) defines the main-effect index as: where "Var{f (X)} is the total variance in the output given variations of all parameters and Var{E(f (X)|x i )} is the variance in the expected output of f (X) given x i . Therefore, S i represents the expected reduction in output variance if parameter x i is known" [22]. Equation (2) defines the total-effect index as: where "Var{E(f (X)|x i )} is the variance in the expected output of f (X) if all parameters except x i are known. Therefore, TS i represents the total effect of the parameter x i and all its interactions. If parameters are linearly additive (i.e., no strong interactions), S i and ST i should be equal" [22]. Prepared training design points for the outputs of the APSIM-Sugar and the parameter combinations (described in Section 2.3.1) were run in GEM-SA. 300 training points of APSIM outputs and corresponding parameter combinations were used to generate emulators. 180 emulators (30 × 3 × 2) for combinations of each year (30), each soil type (3) and Ir or Rf condition were generated. While developing the emulators, remaining 200 parameter combinations were used in GEM-SA to obtain emulator predictions (emulator predicted CDW). These predictions were graphed with remaining APSIM-output training design points and coefficient of determination (R 2 ) were calculated to evaluate how well emulator can predict the APSIM simulator outputs. R 2 range between 1 to 0 and emulators with higher accuracy can be identified with R 2 values close to one.
When running the GEM-SA, linear term for each input was set as the prior mean option for the outputs, as it allows us to observe the output trend in response to input changes. Leave-one-out cross-validation was selected to evaluate the accuracy of emulators built by GEM-SA. GEM-SA calculated S i and TS i values for each parameter corresponding to each emulator were recorded. Further, GEM-SA calculates leave-one-out cross-validated RMSSE (Equation (3)) and sigma-squared value (σ 2 ) for each emulator [48]; these values were used to represent the performance of model emulators with reference to environmental and management conditions in addition to R 2 .
Equation (3) defines cross-validated RMSSE as: where, "y i is the true output for the ith training run,ŷ is the corresponding emulator approximation, s i is the standard deviation calculated with the ith training point removed and n is the number of runs" [48].
The cross-validated RMSSE is close to 1 if the actual error variance is accurately estimated by the emulator variance [49], while lower and higher values indicate overestimation and underestimation, respectively [50].
The σ 2 value is an effective measure that indicates an emulator's non-linearity by expressing emulator variance after output standardization [51]. The values of σ 2 ranges near 0 for a linear model and has greater values (without a defined cutoff value) for moderately to highly nonlinear models [49].
The sensitivity of the model outputs to cultivar parameters was explored using stacked column bar chart with S i indices. Parameters with the strongest effects on simulated CDW were identified from S i values and were further examined with reference to environmental and management conditions in KK by using main effect plots.

Results and Discussion
3.1. Emulator Accuracy R 2 calculated by using the APSIM simulated CDW and emulator predicted CDW, and GEM-SA internally calculated σ 2 and cross-validated RMSSE values were used to evaluate the performances of generated emulators. Scatter plots of Figure 2 indicate the linear relationship between the APSIM simulated CDW and emulator predicted CDW. As it is complicated to show all the graphs, here we present only some examples to represent all the conditions. However, calculated R 2 for all conditions were ranged between 0.85 to 0.99 and closer to one indicating that all emulators can successfully approximate the APSIM simulators.
The calculated σ 2 values of all emulators ranged between 0.08 and 0.89 (Figure 3a). Petropoulos et al. [51] obtained σ 2 values ranging from 0.13 to 1.6 for their emulators and concluded that their parameters deviated only moderately from linearity. Gunarathna et al. [27] obtained σ 2 values ranging from 0.10 to 1.43 and concluded that their models showed good to moderate linearity. Hence, we can conclude that our emulators showed good linearity in each environmental and management condition. internally calculated σ 2 and cross-validated RMSSE values were used to evaluate the performances of generated emulators. Scatter plots of Figure 2 indicate the linear relationship between the APSIM simulated CDW and emulator predicted CDW. As it is complicated to show all the graphs, here we present only some examples to represent all the conditions. However, calculated R 2 for all conditions were ranged between 0.85 to 0.99 and closer to one indicating that all emulators can successfully approximate the APSIM simulators. The calculated σ 2 values of all emulators ranged between 0.08 and 0.89 (Figure 3a). Petropoulos et al. [51] obtained σ 2 values ranging from 0.13 to 1.6 for their emulators and concluded that their parameters deviated only moderately from linearity. Gunarathna et al. [27] obtained σ 2 values ranging from 0.10 to 1.43 and concluded that their models showed good to moderate linearity. Hence, we can conclude that our emulators showed good linearity in each environmental and management condition. S1_Ir_Y 10 S1_Ir_Y 20 S1_Rf _Y 10 S1_Rf _Y 20  Computed cross-validated RMSSE values of emulators ranged between 0.82 and 1.21 ( Figure  3b). These values were lower than the values reported by Kennedy et al. [47] and Petropoulos et al. [51], and were close to one in all the SA experiments, suggesting that the true model can be well represented by the generated emulators.  and were close to one in all the SA experiments, suggesting that the true model can be well represented by the generated emulators.

Determination of Parameter Sensitivity
Studying the sensitivity of model outputs to cultivar parameters under different environmental and management conditions would help to improve the calibration efficiency of the model. Moreover, when determining the appropriate management practices for sugarcane cultivation, it is important to consider parameters that strongly affect sugarcane yield. Therefore, to determine parameter sensitivity across environmental and management conditions, we examined S i and ST i computed by GEM-SA. However, we disregard the ST i values because of the observation of less difference among S i and ST i values and a greater fraction of variability being explained by S i . The S i values of each parameter for all simulated conditions are shown in Figure 4. In order to explain the differences of S i among each condition APSIM simulated CDW was included (Figure 4).   Table 3). However, our results are evidence that Si  , TLS5, LS2 and 3, TLS4, SF1, BF, MSSR, MSS, FC, SD, TLS2, TLS1, TLS3, LS1, SF2 were identified as the insensitive parameters (each parameter explained <1% of the variability of CDW)(Parameters were defined in Table 3). However, our results are evidence that S i values of influential parameters are widely differed across simulated years under selected environmental and management conditions (Figure 4).
For CDW, RUE was the most influential parameter under each environmental and management condition in KK except in few years (Figure 4). Ojeda et al. [52] has also found similar results for SA of APSIM-Sugar. In APSIM-Sugar, CDW accumulation is largely governed by intercepted radiation via RUE. Higher sensitivity of RUE is not surprising because as a tropical country, Thailand receives high solar radiation throughout the year (Figure 1).
Nitrogen stress arise due to higher rainfall affects to reduce the sensitivity of RUE and cause for the reduction of CDW. Under Ir conditions, we could observe lower S i of RUE and lower CDW only for year 1982 than the other years of Ir ( Figure 4). For this condition under S1, RUE became the lowest and CF and EB became more sensitive than RUE. In APSIM-Sugar RUE is affected from temperature extremes, excess or shortage of available water or nitrogen deficit for photosynthesis [11]. Therefore, we analyzed these factors using APSIM and could find that nitrogen deficit for photosynthesis (nfact_photo) in the year 1982 between April to November. Figure 5 indicates APSIM simulated nfact_photo under S1 and Ir as this condition represents the most severe nitrogen stress during the period (Y2 in Figure 5). Though we simulated similar urea application among all conditions, the nitrogen stress occurred due to higher rainfall prevailing during these months. Nitrogen stress arise due to higher rainfall affects to reduce the sensitivity of RUE and cause for the reduction of CDW. Under Ir conditions, we could observe lower Si of RUE and lower CDW only for year 1982 than the other years of Ir ( Figure 4). For this condition under S1, RUE became the lowest and CF and EB became more sensitive than RUE. In APSIM-Sugar RUE is affected from temperature extremes, excess or shortage of available water or nitrogen deficit for photosynthesis [11]. Therefore, we analyzed these factors using APSIM and could find that nitrogen deficit for photosynthesis (nfact_photo) in the year 1982 between April to November. Figure 5 indicates APSIM simulated nfact_photo under S1 and Ir as this condition represents the most severe nitrogen stress during the period (Y2 in Figure 5). Though we simulated similar urea application among all conditions, the nitrogen stress occurred due to higher rainfall prevailing during these months. Moreover, results prove that severity of nitrogen stress arise due to higher rainfall, varies with the soil type. When compared to S1 under Ir of year 1982, Si of RUE became higher under S46 and the highest under S44 (Figure 4). This is because soil water content in selected soil types are varied according to textural properties; S1 (clay 68%, silt 29%, sand 3%) > S46 (clay 29.2%, silt 29%, sand 41.8%) > S44 (clay 1%, silt 9.5%, sand 89.5%) ( Table 1). As indicated in Figure 4 this will largely reduce the CDW and therefore it is crucial to manage nitrogen application when molding higher rainfall periods to reduce the nitrogen stress specially in S1 soil type.
It is observed that sensitivity of RUE reduced with available water content. Sensitivity of RUE became lower in Rf condition than in Ir condition (Figure 4). Under Rf, sensitivity of RUE was the highest in S1 and weakened in S46 and S44 soils. This is because the available soil water content in Moreover, results prove that severity of nitrogen stress arise due to higher rainfall, varies with the soil type. When compared to S1 under Ir of year 1982, S i of RUE became higher under S46 and the highest under S44 (Figure 4). This is because soil water content in selected soil types are varied according to textural properties; S1 (clay 68%, silt 29%, sand 3%) > S46 (clay 29.2%, silt 29%, sand 41.8%) > S44 (clay 1%, silt 9.5%, sand 89.5%) ( Table 1). As indicated in Figure 4 this will largely reduce the CDW and therefore it is crucial to manage nitrogen application when molding higher rainfall periods to reduce the nitrogen stress specially in S1 soil type.
It is observed that sensitivity of RUE reduced with available water content. Sensitivity of RUE became lower in Rf condition than in Ir condition ( Figure 4). Under Rf, sensitivity of RUE was the highest in S1 and weakened in S46 and S44 soils. This is because the available soil water content in selected soil types are varied; S1 > S46 > S44 (Table 1). This was more evident in years which represent lower annual rainfall (year: 1981, 1984, 1991, 1992, 1993 and 2006 in Figure 4) than the other years during the study period.
For CDW, TEC was the second most influential parameter under each environmental and management condition in KK based on average S 1 values across study period. However, the sensitivity of TEC is higher in Rf than Ir (Figure 4) indicating that TEC is highly sensitive to water stressed conditions. Sexton and Everingham [26] has also found similar results for their study. This is because in APSIM, dry matter assimilation is governed by radiation interception and RUE in the conditions which soil water availability is not limited. However, in case the soil water supply is not enough to meet the transpiration demand, dry matter assimilation is governed by water supply, TEC and the vapor pressure deficit.
GLN is highly influential under water stressed conditions. GLN indicated higher S i under Rf than Ir. Although GLN was the third most influential parameter based on the average S i values, it became the second most influential one in the year of 1981, 1984, 1991, 1992, 1993 and 2006 (Figure 4). These years indicated lower rainfall compared to other years and under Rf condition water stress becomes more sever. Higher water stresses may create leaf emergence rate reduction and leaf senescence rate increment, causing significant reduction in GLN and reduce CDW [53]. This was more evident in our results of year 1991, 1992 and 1993 (the years with lowest rainfall) ( Figure 4) under S44 (soil type with lowest water availability) and Rf.
For CDW, CF was the fourth most influential parameter and EB was the fifth most influential parameter. Both indicated higher S i values for Rf than Ir indicating high sensitivity for water stresses (Figure 4). In addition, they indicated high sensitivity for year 1982 under S1 and Ir which we previously identified as nitrogen stressed condition. This is not surprisingly because in APSIM, water deficit and nitrogen deficit both cause for limiting the biomass partitioning in the stem (CF) and phenological development based on thermal time (EB).
Computed S i indicated that sensitivity of RUE, GLN, TEC, EB and CF explains more than 90% of total variance for most of the simulator outputs across all simulated years, while other parameters had much weaker effects ( Figure 4). Similar studies on cultivar-by-environment interactions conducted by Sexton et al. [11] and Gunarathna et al. [27] also found these parameters among highly influential parameters under their selected environmental and management conditions. Therefore, when modeling CDW using APSIM-Sugar those influential parameters can be used to calibrate the model. When such calibrations are streamlined, non-influential (low S i ) parameters could be fixed to default values. Parameters such as RUE and TEC are ideal for statistical calibration of APSIM-Sugar as they are difficult in measuring. By measuring comparatively simple-to-obtain parameters like GLN, it can be reduced the number of parameters used for calibration.

Sensitivity of Highly Influential Parameters
Knowledge of sensitive parameters is needed for the improvement of simulations of sugarcane growth under various environmental and management conditions. Therefore, we further analyzed the response of outputs to selected environmental and management conditions. The response of CDW to the highly influential parameters (CF, EB, GLN, TEC and RUE) was visualized by plotting the mean of the emulator's main effects from 6000 randomly selected iterations ( Figure 6). Agronomy 2020, 10, x FOR PEER REVIEW 13 of 17 Figure 6. Parameter main effect of highly influential parameters under soil types (S1, S44 and S46), and Ir (blue) and Rf (orange) conditions for CDW.
Statistical calibration of RUE and TEC parameters would improve the simulation of cultivar differences in CDW. When parameter value of RUE increased from 1.2 g/MJ to 2.5 g/MJ we could observe high increment in CDW ( Figure 6). This relationship was stronger in Ir condition when compared with Rf condition and the strongest in soil types with the highest available water content (S1, S46) and weakened with the lowest available water content (S1 > S46 > S44). These results confirm that CDW is highly sensitive to RUE, which is directly connected with the availability of moisture for plants. In addition, when increasing the TEC parameter value from 0.008-0.014 kg kPa/kg, CDW tends to increase slightly in all conditions, however this was more evident in Rf conditions than in Ir conditions ( Figure 6). In APSIM, both RUE and TEC do not differ by default [36,54]. Therefore, statistical calibration of highly influential RUE and TEC parameters are crucial to achieve higher accuracy when modeling the CDW in KK.
Cultivars with higher GLN and lower CF values will be more beneficial when modeling CDW under any of the environmental and management conditions in KK. This is because under all simulated conditions, the influence of GLN on CDW shows an increasing trend while CF indicting the declining trend when increasing the parameter values from 9 to 14 and 0.65 to 0.8 g/g, respectively ( Figure 6). However, it seems that increasing the parameter value from 1200 to 1900 °C day of EB may cause lower increment in CDW compared to other parameters ( Figure 6). These results are very important when parameterizing the crop model for KK because they are useful in reducing the number of parameters to be calibrated and avoiding over-parameterization.
We could study the sensitivity of model outputs to cultivar parameters under different environmental conditions of tropical sugarcane production in KK, Thailand. Determination of Figure 6. Parameter main effect of highly influential parameters under soil types (S1, S44 and S46), and Ir (blue) and Rf (orange) conditions for CDW.
Statistical calibration of RUE and TEC parameters would improve the simulation of cultivar differences in CDW. When parameter value of RUE increased from 1.2 g/MJ to 2.5 g/MJ we could observe high increment in CDW ( Figure 6). This relationship was stronger in Ir condition when compared with Rf condition and the strongest in soil types with the highest available water content (S1, S46) and weakened with the lowest available water content (S1 > S46 > S44). These results confirm that CDW is highly sensitive to RUE, which is directly connected with the availability of moisture for plants. In addition, when increasing the TEC parameter value from 0.008-0.014 kg kPa/kg, CDW tends to increase slightly in all conditions, however this was more evident in Rf conditions than in Ir conditions ( Figure 6). In APSIM, both RUE and TEC do not differ by default [36,54]. Therefore, statistical calibration of highly influential RUE and TEC parameters are crucial to achieve higher accuracy when modeling the CDW in KK.
Cultivars with higher GLN and lower CF values will be more beneficial when modeling CDW under any of the environmental and management conditions in KK. This is because under all simulated conditions, the influence of GLN on CDW shows an increasing trend while CF indicting the declining trend when increasing the parameter values from 9 to 14 and 0.65 to 0.8 g/g, respectively ( Figure 6). However, it seems that increasing the parameter value from 1200 to 1900 • C day of EB may cause lower increment in CDW compared to other parameters ( Figure 6). These results are very important when parameterizing the crop model for KK because they are useful in reducing the number of parameters to be calibrated and avoiding over-parameterization.
We could study the sensitivity of model outputs to cultivar parameters under different environmental conditions of tropical sugarcane production in KK, Thailand. Determination of variability in the influence of model input parameters on model output could have a considerable impact on studies of cultivar-by-environment interactions. Such studies would improve the efficiency and accuracy of crop modeling, which is computationally expensive, and will be ultimately important for identification of appropriate management strategies to cope with both temporal and spatial variability of crop yield. Therefore, we encourage future research focused on a range of soil types, climate interactions and different water regimes.

Conclusions
Our study focused on the use of GP-based emulators to analyze parameter sensitivity in the APSIM-Sugar model under different environmental and management conditions in KK, Thailand. The emulators we obtained, which corresponded to each environmental and management condition across simulated years showed satisfactory results, as evidenced by R 2 , σ 2 and cross-validated RMSSE values, indicate that these emulators can successfully replace the simulators. rue (RUE), green_leaf_no (GLN), transp_eff_cf (TEC), tt_emerg_to_begcane (EB) and cane_fraction (CF) were the most influential parameters regardless of soil type, Ir or Rf conditions. Other analyzed parameters had little influence on the simulator output. Outcomes of our study are beneficial in enhancing the efficiency and accuracy of crop modeling. Further, findings can be used to identify appropriate management strategies to address temporal and spatial variability of sugarcane yield in KK.