Sensitivity analysis of the AquaCrop model for wheat crop in Campos Gerais region, Paraná

ABSTRACT The use of crop modeling can be useful to understand the interactions between the soil-plant-atmosphere system. The objective of this study was to evaluate sensitivity analysis of the AquaCrop model parameters for wheat crop in the Campos Gerais Region. The varietie tested was TBIO Sinuelo in Castro, Ponta Grossa and Itaberá cities. The analyzed parameters refer to crop phenology, transpiration, biomass production, yield formation, stresses and soil management. The sensitivity analysis was realized varying individually each input parameter in the AquaCrop for the calculation of the Relative Sensitivity Index (SI). The most sensitive parameters of the AquaCrop were: reference harvest index (HIo); water productivity normalized for evapotranspiration and CO2 concentration (WP*); crop coefficient when canopy expansion is complete (KcTR,x); fertility levels; and maximum canopy cover (CCx). The higher sensitivity of HIo and WP* is because they are directly related to two main equations of AquaCrop, linked to the estimates of dry above-ground biomass and yield formation, respectively. The AquaCrop counts WP* reflecting directly on dry above-ground biomass production and on final grain yield. The canopy decline coefficient (CDC) presented considerable sensitivity only in Castro due to the longer duration of the phenological cycle. Fertility levels and saturated hydraulic conductivity (Ksat) in Castro was the least sensitive parameters in the analysis.


INTRODUCTION
The crop productivity evaluation with models simulations can help in the prediction of harvest and the understanding of the interactions resulting from the soil-plant-atmosphere continuum.The models consider the combination of the several factors that influence crop productivity (Gomes et al., 2014) and help in decision making and crop planning, predicting the crop potential productivity in different scenarios (Basso et al., 2013;Morell et al., 2016).Crop models are highly recommended for research in places with high agricultural production, such as the Campos Gerais, in Paraná and São Paulo States, which stand out for presenting grain yields above the national agricultural average (Shimandeiro et al., 2008).
The literature is rich in examples of mathematical models used to handle agricultural crops.Among them, the AquaCrop has been widely used (Raes et al., 2009;Steduto et al., 2012;Piekarski et al., 2017).The main advantage of the AquaCrop is due to the small number of required input parameters, being data easily obtainable.
The AquaCrop is viable in the yield simulation of Sensitivity analysis of the AquaCrop model for wheat crop in Campos Gerais region, Paraná different crops, under different soil and climatic conditions (Heng et al., 2009;Todorovic et al., 2009;Bitri & Grazhdani, 2015;Mirsafi et al., 2016;Bouazzama et al., 2017;Pareek et al., 2017).However, its application in Brazil is still scarce, especially for wheat, an important cereal cultivated in 2 million hectares, being the southern region of the country the traditionally producer (Conab, 2017).In Paraná State, wheat is the most important winter crop, reaching 934.527 hectares of planted area in the 2017 harvest, with a production of 2.3 million tons and an average yield of nearly 2.5 ton ha -1 .The Campos Gerais Region confirmed wide potential productivity in the 2017 harvest, once again yielding above the national average (IBGE, 2017).The model's accuracy depends largely on the parameters involved.It is important to identify the parameters that most influence the results, as well as what each parameter causes in the model, aiming to reduce the uncertainties in the final result (Salemi et al., 2011).However, the model parameters values are subject to variation and errors, being necessary for the investigation of the changes.For this, sensitivity analysis is performed, changing the value of a parameter in an individual way and verifying the influence of the variables in the results (Bouazzama et al., 2017).
The main functions present in AquaCrop are described in Raes et al. (2012) and Raes et al. (2018b).The authors recommend that the variables susceptible to penalization of crop potential productive should be submitted to the sensitivity analysis.
Simulations in models allow identifying confidence intervals for the parameters (Taconeli & Barreto, 2003).The most sensitive parameters of a model are mostly submitted to the calibration process (Cibin et al., 2010;Xing et al., 2017).After identifying the most sensitive parameters and performing their calibration, it is possible to obtain the maximum potential of the model, making it able to identify better planting dates and consequently resulting in higher yields.
A key goal of agriculture is to achieve the maximum crop yield while minimizing inputs and losses from cropping systems.In this regard, the use of models that predict crop yields becomes a fundamental tool in decision-making.
Considering the application of the AquaCrop model and the importance of the wheat crop for Brazilian agribusiness, the objective of this study was to perform the sensitivity analysis to identify the most sensitive parameters of the model for the wheat crop in the Campos Gerais Region.
The wheat crop data were obtained from the Fundação ABC database protocols (Table 2).Plant density per hectare 3411800 2338200 2337100 (1) Day After Planting.
With the parameters inserted, the AquaCrop derives and counts the evaporation of superficial soil layer, internal drainage, deep percolation, surface runoff, and capillary rise.To perform the analysis of the water balance in AquaCrop the initial soil water content was considered equal to the available water in the root zone.
The values attributed to the AquaCrop parameters related to the wheat crop were based on the literature (Raes et al., 2017) and protocol data from Fundação ABC.Salinity stress was not considered.Calibration for soil fertility stress was adjusted to the program options, being: i) Biomass production near optimal; ii) Maximum canopy cover close to the reference (no stresses); and, iii) Canopy decline in the season was considered small. (1)Volumetric water content at permanent wilting point; (2) Volumetric water content at field capacity; (3) Volumetric water content at saturation; (4) Saturated hydraulic conductivity.
Sensitivity analysis of the AquaCrop model for wheat crop in Campos Gerais region, Paraná The sensitivity analysis of the conservative and non-conservative AquaCrop parameters was performed by individually varying each input parameter, remaining the others fixed.As analysis criteria, it was adopting the Relative Sensitivity Index (SI), proposed by Silva et al. (2009): ) Where: SI is the model sensitivity index for the input parameters (dimensionless); R 1 is the result obtained with the model for the lowest input value; R 2 is the result obtained with the model for the highest input value; R 12 is the average of the results obtained with the lowest and highest input value; I 1 is the lower value of input parameter; I 2 is the highest value of input parameter; I 12 is the average value of input parameters.
The SI result indicates that as higher is the index obtained (in module) more sensitive the model is to the parameter.Values close to zero indicate that the model has no sensitivity (Silva et al., 2009).

RESULTS AND DISCUSSION
The sensitivity index of the AquaCrop parameters and respective rankings are shown in Table 4.In all locations evaluated, the highest sensitivity was found for the reference harvest index (HI o ).The parameters also strongly sensitive were: normalized water productivity for ETo and CO 2 (WP*); crop coefficient when the canopy is complete but before senescence (Kc TR,x ); maximum canopy cover (CC x ); and, fertility levels.The canopy decline coefficient (CDC) presented the highest sensitivity in Castro (Figure 1).The simulations were carried out for periods of no water deficit in the locations, to account the sensitivity under ideal conditions of crop development.

Crop phenology
The curve that represents the initial phase of canopy cover (CC) is equal to the canopy cover at 90% crop emergence (Figure 2: CCo).Posteriorly, in the second path, the curve has an exponential trend, and as the crop grows, the canopy cover becomes larger (Figure 2: Equation 1).Upon reaching maximum development the CC becomes equal to the maximum canopy cover (Figure 2: CC x ).In this phase, the radiation capture and photoassimilates production in the photosynthesis process tends to decrease due to the crop mutual shading, and the CC follows exponential decay function in the third stretch (Figure 2: Equation 2).
As the crop approaches maturity the CC declines, as a result of leaf senescence.The canopy decline coefficient (CDC) corresponds to the rate of canopy decay due to senescence.The CDC values are directly proportional to the rate of canopy decline (Figure 3: Equation 3).
The CC x is determined in AquaCrop based on the planting density, being dependent on the environment and the management adopted (Steduto et al., 2009;Raes et al., 2011;Steduto et al., 2012;Dalla Marta et al., 2016;Raes et al., 2018c).The sensitivity of this parameter is related to be part of two main equations that determine the crop canopy cover (Figure 2: Equation 2; and Figure 3: Equation 3).
The CC x was more sensitive in Castro (SI = 0.76; Ranking 4), followed by Ponta Grossa (SI = 0.72; Ranking 5) and Itaberá (SI = 0.58, Ranking 5) (Figure 1a).Razzaghi et al. (2017) when simulating the potato yield under different water stress conditions (irrigated, deficit irrigated, and not irrigated) in Denmark observed that the CC x is one of the most sensitive parameters to changes in AquaCrop.
The canopy decline coefficient (CDC) presented considerable sensitivity for the wheat crop only in Castro (IS = 0.74; Ranking 5; Table 4 and Figure 1b).The sensitivity of this parameter is related to being part of the equation responsible for the canopy decline by senescence (Figure 3: Equation 3).This parameter was also sensitive to wheat crop in studies involving other locations, as observed by Xing et al. (2017) when evaluating the sensitivity of the AquaCrop parameters for winter wheat with the Extended Fourier Amplitude Sensitivity Test (EFAST) in Beijing, China, under different water treatments, found that CDC was one of the most sensitive parameters under irrigated (normal and over irrigation) and no irrigated planting condition (rainfall only).Vanuytrecht et al. (2014), evaluating the EFAST method, also observed sensitivity for CDC parameter for maize and winter wheat in Belgium (north-western Europe), and for rice in Vietnam (south-east Asia).However, Silvestro et al. (2017), using MORRIS and EFAST methods to perform the sensitivity analysis in three sites, two in China and one in Italy, representing contrasting environments in terms of extreme temperatures and water availability, found that CDC showed low influence on final productivity when compared to other parameters.The sensitivity of CDC in Castro is due to the longer duration of the variety phenological cycle (Table 2).The time interval between senescence and maturity was longer (38 days) when compared to other localities.Thus, the program counted for longer the influence of this parameter in the final wheat crop yield.------------------------------Biomass production and yield formation ------------------------------WP*: Water productivity normalized for ETo e CO 2 (g m −2 ) (1) 0.98 2 0.98 2 0.98 3 Water productivity normalized for ETo e CO 2 during yield formation (%) (1) 0.00 18 0.00 21 0.00 20 Maximum possible increase of HI (%) (1) 0.00 23 0.00 23 0.01 14  (1) Conservative generally applicable; (2) Conservative for a given specie but can or may be cultivar specific; (3) Dependent on environment and/or management; (4) Cultivar specific.
Sensitivity analysis of the AquaCrop model for wheat crop in Campos Gerais region, Paraná   1) and the exponential decay (Equation 2) stages (Raes et al., 2018c).The other phenology parameters presented a negligible influence (Table 4).Significantly changes in the input values did not result in expressive differences on the program output data, mainly in the "Shape factor describing root zone expansion" and the "Minimum effective rooting depth" (Z min ).

Crop transpiration
The proportionality factor of crop transpiration in AquaCrop is known as Kc TR,x , being the coefficient that indicates when canopy expansion is complete (CC = 1) and without stresses condition.The Kc TR,x is a parameter considered conservative and approximately equivalent to the basal crop coefficient at mid-season, in cases of canopy complete expansion (Dalla Marta et al., 2016;Raes et al., 2018b;Raes et al., 2018c).The parameter Kc TR,x presented high sensitivity (Table 4, Figure 1c), being: SI = 1.00 in Ponta Grossa (Ranking 2), SI = 0.91 in Itaberá (Ranking = 4); and, SI = 0.88 in Castro (Ranking 3).
The crop transpiration (Tr) depends on the fraction of land area covered by the canopy (CC) when there is insufficient stress to limit stomatal opening.When the canopy fully covers the ground (CC is close and approaching 1.0), the program multiplies the value of Kc TR,x by the effective canopy cover adjusted for micro-advective effects and reference evapotranspiration (ETo), resulting in crop transpiration values (Tr) (Raes et al., 2009;Steduto et al., 2012).Raes et al. (2018c) remark that the Kc TR,x is proportional to the CC and for this reason is continuously adjusted throughout the crop cycle.When water stress occurs in the soil, besides the canopy development being affected, the program can also consider that there was stomatal closure (Equation 4and Figure 4).The whole mechanism occurs through the water stress coefficient for stomatal closure (Ks sto ), interfering in crop transpiration.5), determining the dry above-ground biomass.
The effect of canopy cover on reducing soil evaporation in the late season stage (Ke) did not present a considerable sensitivity in the analysis.

Biomass production and yield formation
The normalized biomass water productivity (WP*) presented high sensitivity, with SI = 0.98 for all localities, resulting in Ranking 2 in Castro and Itaberá (   6) reflecting directly on dry above-ground biomass production (Equation 5) and, consequently, on final grain yield (Equation 7).
As the Kc TR,x , the sensitivity of WP* occurs due to the participation in the equation that determines the dry above-ground biomass (Equation 5) being one of the main  4; Figure 1e).Considering the small and higher values adopted for the parameters during simulations, differences observed were above 30000 kg.The HI o presented high sensitivity for being part of the second main equation of AquaCrop.Together with the equation that determines the dry above-ground biomass (Equation 5), the HI o determines the grain yield formation (Equation 7).However, some varieties may require adjustments to obtain better results by the program (Silvestro et al., 2017).
AquaCrop is a crop water productivity model very sensitive to water stress.The effects of water scarcity directly interfere on reference harvest index (HI o ).One negative impact of drought on simulated productivity occurs in pollination and embryo formation.In the case of severe and long water stress, there is a reduction in HI o , and consequently yield drop (Steduto et al., 2012).

Stresses
The The effects of air temperature stress in AquaCrop are accounted in growing degree-day.Raes et al. (2017) consider that 5 °C is the minimum air temperature below which pollination starts to fail (cold stress) and 35 °C is the crop.It was submitted to the sensitivity analysis the TBIO Sinuelo variety, with medium to late characterization cycle, in three cities of Campos Gerais Region, cultivated in 2014 crop year: Castro and Ponta Grossa, in Paraná State; and, Itaberá, São Paulo State.All the experimental plots used have flat to gently undulating relief.The management practices in the areas were no-tillage with residual vegetation covered from the previous harvest.The edaphoclimatic characterization of the analyzed areas is shown in 10-0.25 m and 0.25-0.40m depths.The soil data inserted in the program was obtained in a previous study in the same areas, carried out by Piekarski et al. (2017) (Table

Figure 1 :
Figure 1: Variation of simulated productivity for wheat crop in AquaCrop, for the localities of Castro, Ponta Grossa and Itaberá, by adjusting the most sensitive parameters of the model, being: a) maximum canopy cover (CC x ; %); b) canopy decline coefficient (CDC; % day −1 ); c) crop coefficient when the canopy is complete (Kc TR,x ; dimensionless); d) normalized water productivity (WP*; g m -2 ); e) reference harvest index (HI o ; %); and, f) soil fertility levels (%).

Figure 3 :
Figure 3: Decline of green canopy cover during senescence for CDC values.

Figure 4 :
Figure 4: Depletion of root zone soil water (Dr), green canopy cover (CC) and transpiration (Tr) during the crop cycle, for Castro-PR, with the three water stress thresholds affecting: i) the canopy expansion (below the green line, bottom graph); ii) stomatal closure (below the red line) affecting Tr; and iii) triggering canopy senescence (below the yellow line).
equations of AquaCrop.Xing et al. (2017) andRazzaghi et al. (2017) also observed sensitivity for WP*.Vanuytrecht et al. (2014) noted a sensitivity of WP* only in rice crop, and Silvestro et al. (2017) for wheat, mainly in Yangling (China) and Viterbo (Italy).The sensitivity of WP* obtained by Salemi et al. (2011) was considered moderate.Bouazzama et al. (2017) at the National Institute of Research in Morocco found that WP* was highly sensitive in simulating the wheat final yield and, with the maximum effective rooting depth, were the most sensitive parameters to simulate AquaCrop biomass production.The reference harvest index (HI o ) was the most sensitive parameter in AquaCrop, with SI = 1.00 for all localities (Table Sensitivity analysis performed by Xing et al. (2017), considering simulations with water input only by rainfall, indicated the HI o in the third sensitivity position to estimate final grain yield.Silvestro et al. (2017) observed higher sensitivity of HI o in Viterbo, Italy.The HI o was also sensitive in the simulations performed by Bouazzama et al. (2017) and Razzaghi et al. (2017).Steduto et al. (2012) describe that HI o is considered a conservative parameter for most high-yielding varieties.
AquaCrop responses for water loss are indicated by stress depletion in the root zone, expressed as a p factor of available soil water.The stress coefficient (K s ) ranges from 0 (p lower − full stress) to 1 (p upper − no stress).The low Ranking values obtained for p factor in the analysis indicated that no calibration adjustments were necessary.Farahani et al. (2009) analyzing the sensitivity of some parameters in the AquaCrop, for the cotton crop, obtained low sensitivity for Ks sto .Ks sto has minor importance in the calibration since AquaCrop automatically adjusts its values, based on daily crop evapotranspiration in the localities evaluated.

Table 1 :
Edaphoclimatic characterization of Fundação ABC Experimental Stations, located in Castro, Itaberá and Ponta

Table 2 :
Wheat crop data, TBIO Sinuelo varietie, obtained from experiments at Fundação ABC, for Castro, Itaberá and Ponta Grossa cities, inserted in the AquaCrop program

Table 3 :
Soil physical-water atributes from the Experimental Stations of Fundação ABC, inserted in the AquaCrop for the sensitivity analysis of the parameters

Table 4 :
Parameters evaluated in the sensitivity analysis of AquaCrop, respective sensitivity indexes (SI), score in which each parameter becomes more or less sensitive (Ranking) for TBIO Sinuelo varietie, in the localities of Castro-PR, Ponta Grossa-PR and Itaberá-SP

Table 4
; Figure 1d), and Ranking 3 in Ponta Grossa (Table4).Sensitivity analysis of the AquaCrop model for wheat crop in Campos Gerais region, Paraná