Guoqing LEIWenzhi ZENGYonghua JIANGChang AOJingwei WU and Jiesheng HUANG

1 State Key Laborator y of Water Resources and Hydropower Engineering Science，Wuhan University，Wuhan 430072(China)

2 School of Remote Sensing and Information Engineering，Wuhan University，Wuhan 430079(China)

3 State Key Laborator y of Infor mation Engineering in Sur veying，Mapping and Remote Sensing，Wuhan University，Wuhan 430079(China)

ABSTRACT Sensitivity analysis is important for determining the parameters in the model calibration process.In our study，a variance-based global sensitivity analysis(extended Fourier amplitude sensitivity test，EFAST)was applied to an agro-hydrological model(the SWAP(Soil-Water-Atmosphere-Plant model)model).The sensitivities of 20 parameters belonging to 4 categories(soil hydraulics，solute transport，root water uptake，and environmental stresses)for the simulated accumulated transpiration，dry matter(DM)，and yield of sunf lowers were analyzed under three nitrogen application rates(N1，N2，and N3)，four salinity levels(S1，S2，S3，and S4)，and three root distributions(R1，R2，and R3).The results indicated that for predominantly loamy soils，the high-impact parameters for accumulated transpiration，DM，and yield were the soil hydraulic parameters(αand n)，critical stress index for compensatory root water uptake(ωc)，the salt level at which salt stress starts(Pi)，the decline of root water uptake above Pi(SSF)，residual water content(θr)，saturated water content(θs)，and relative uptake of solutes by roots(TSCF).We also found that nitrogen application did not change the order of the parameter impacts on accumulated transpiration，DM，and yield.However，TSCF replacedαas the highest-impact parameter for the accumulated transpiration，DM，and yield at high salinity levels(S2 and S3).Furthermore，αwas also the highest-impact parameter for DM and yield under different root distributions，but the highest-impact parameters for transpiration wereωc，α，andθs under R1，R2，and R3，respectively.Nitrogen application could be neglected when considering the interactive effects of nitrogen application，salinity level，and root distribution on the transpiration，DM，and yield.Additionally，the mean values and uncertainties of the transpiration，DM，and yield were similar in all scenarios，except S3，which showed a sharp decrease in the mean values.We suggest determining the above eight parameters(α，n，ωc，Pi，SSF，θr，θs，and TSCF)and the saturated vertical hydraulic conductivity(K s)based on rigorous calibrations with direct or indirect local measurements using economical methods(e.g.，a literature review)，with limited observations for other parameters when using the SWAP model and other similar agro-hydrological models.

Key Words: accumulated transpiration，agro-hydrological model，dry matter，hydraulic parameter，sunf lower，yield

INTRODUCTION

Crop modeling has played an important role in agriculture for maximizing crop yields and minimizing the adverse environmental impacts(Ezuiet al.，2018;Tribouilloiset al.，2018;Wanget al.，2018;Zenget al.，2018a，2018b;Lecerfet al.，2019).Over the past decades，crop models have been signif icantly developed and diversely applied.In general，all crop models need to simulate soil water movement(SWM)，which is crucial for crop growth modeling(Singhet al.，2017;Sinnathambyet al.，2017).There are two main methods for simulating SWM in present crop models.One is the tipping bucket method(TB)，which calculates SWM based on the f ield capacity and the permanent wilting point，without considering the SWM between soil layers(Connolly，1998;Ritchieet al.，2009).Related crop models include DSSAT(Joneset al.，2003)，WOFOST(Van Diepenet al.，1989)，and HERMES(Hlavinkaet al.，2014).The other method uses the Richards equation to determine the spatial and temporal SWM(Maet al.，2011;Nooryet al.，2011;Zhouet al.，2012).In principle，the Richards equation is processbased and more accurate in identifying and representing SWM.The SWAP(Soil-Water-Atmosphere-Plant)model is a typical numerical simulation model that allows the def inition of a layered soil prof ile and considers SWM by Richards equation(Kroeset al.，2017).Moreover，the SWM that is considered in the SWAP model，is also related to the pressure head，water content，and hydraulic conductivity per soil layer，by respective soil hydrodynamic parameters.In addition to SWM，the crop growth module(CGM)is another important component for describing crop growth processes，such as the phenology，specif ic leaf area，assimilation，and dry matter(DM)allocation，in almost all crop models(Chipanshiet al.，1999;Zenget al.，2016，2018a，2018b).Therefore，many excellent crop/hydrological models，e.g.，SWAP，are combinations of hydrological and agricultural models and can be named agro-hydrological simulation models.Due to the high number of parameters included，it is always cumbersome to calibrate an agro-hydrological model.Furthermore，modelers of crop growth are often not aware of the parameters of hydrological processes.Therefore，determining appropriate parameters for calibration is usually the f irst but difficult step before applying an agro-hydrological model.

The SWAP model has been widely applied in agricultural simulations.For example，Xue and Ren(2017b)applied the SWAP model to simulate saline and non-saline water irrigation in the Hetao Irrigation District(HID)，China.Hassanliet al.(2016)simulated maize yields with saline water irrigation using the SWAP model.In addition，Kumaret al.(2015)applied the SWAP model to simulate salt dynamics in the root zone and yield of wheat.To calibrate the SWAP model well，it is necessary to understand the sensitivities of parameters for various model outputs.Many scientists have conducted related studies.For example，Shaf ieiet al.(2014)demonstrated that the predictive uncertainty in soil moisture during the maize and wheat growing seasons was relatively low.Baroni and Tarantola(2014)applied a general probabilistic framework to estimate the sensitivity of the SWAP model，but mainly focused on the effects of weather data.Importantly，in recent decades，the SWAP model has been updated several times to respond to issues in both practical and scientif ic areas(Kroesetal.，2017).Nitrogen is a major limiting factor of crop growth and yield production in most areas of the world(Zenget al.，2016a，2016c).The latest version of the SWAP model implemented the nitrogen module(NM)to simulate nitrogen mineralization and immobilization，in relation to fertilizer application and the organic matter cycle(Groenendijket al.，2016).However，these updates involved more intrinsic and complicated coupling processes between the SWM，CGM，and NM modules，such as the improvements of crop growth resulting from nitrogen application could enhance the root water uptake in SWM，while affect SWM and aggravate the drought stress in CGM.Further，whether the interactive effects increase the uncertainty of model parameters is not clear.

The complexity of environmental stress factors also obstructs model application and parameter calibration.Soil salinization has been one of the most critical factors in land degradation，which reduces crop production and affects food security(FAO，2008).However，the interactive effects of crop salt tolerance and salt stress usually exist simultaneously，which raises doubts about the changes of sensitive parameters when applying the SWAP model to soils with different salinity levels.The existence of salt ions increases the stress heterogeneity in the soil prof ile for root water uptake，which will increase the calculation complexity of the root water uptake due to the further stimulation of compensatory root water uptake(CRWU).In addition，root distribution(RD)is one of the main inputs for almost all agro-hydrological models，including the SWAP model.Presently，RD is determined based on limited measurements or experience.Therefore，even for the same crop in the same region，different scientists often use different RDs(Assenget al.，1997;Camargo and Kemanian，2016;Fanet al.，2016).In this situation，would it be necessary to modify RD for the same crop in different regions，even though the model has been calibrated?Conversely，does RD affect the parameter sensitivity for the specif ic model outputs?Moreover，agricultural management，such as irrigation or fertilization，also affects crop growth.Statistical data from FAO indicates that irrigated land constitutes approximately one-f ifth of the total arable area in developing countries but produces two-f ifths of all crops and close to three-f ifths of cereal production(http://www.fao.org/3/Y4683E/y4683e07.htm).Our previous studies proved that nitrogen fertilizer could alleviate crop salt stress in saline soils.One important application for agro-hydrological models is to simulate various scenarios after calibration to benef it decision-making and agricultural development.However，few studies have focused on the effects of agricultural management on model calibration，and it is unknown whether parameter sensitivity would vary among different agricultural management strategies(e.g.，nitrogen application and irrigation)(Zenget al.，2018a).

Therefore，the main objective of this study is to explore the parameter sensitivity of an agro-hydrological model(i.e.，the SWAP model)under different salinity levels，RDs，and nitrogen applications.The sensitivity analysis(SA)can be classif ied into two schools:the local SA school and the global school.The local SAapproach usually changes one parameter at a time around a basis point，while other parameters are kept at nominal values.Although the local SA has a low computational cost and is relatively easily implemented，it has the limitations of linearity and normality assumptions along with local variations(Baroni and Tarantola，2014;Xuet al.，2016).Therefore，for complex nonlinear models，such as the SWAP model and other hydrological and crop models，only global SA(GSA)methods are able to provide useful information about parameter sensitivity.In this study，the extended Fourier amplitude sensitivity test(EFAST)，one of the well-known GSA methods(Vanuytrechtet al.，2014;Zengetal.，2018a)，was applied for sensitivity analysis of the SWAP model under different scenarios.Moreover，the uncertainties of the crop yield，DM，and accumulated transpiration，simulated by the SWAP model in each scenario，were also analyzed.

MATERIALS AND METHODS

Study site

Experimental data from a f ield experiment in the HID(40°19′—41°18′N，106°20′—109°19′E)in North China was chosen to study the effects of RD，nitrogen application，and soil salinity level on the sensitivity of the SWAP model.The potential evapotranspiration and annual precipitation of HID are approximately 2 200—2 400 mm and 139—222 mm，respectively(Liet al.，2010).The strong evapotranspiration and low precipitation result in the upward transportation of groundwater and salt accumulation on the soil surface，which causes the HID to be one of the most salt-affected regions in China.Hetao Irrigation District is also the largest sunf lower growing region in China，and selling sunf lower seeds is the major source of income for the local farmers.This study selected sunf lower as an indicator crop.Initial soil conditions and crop parameters were determined based on our previous subplot experiments at the Yichang Experimental Station in HID.

SWAP model

The SWAP model is a one dimensional physically-based f ield-scale agro-hydrological model that simulates the vertical transport of water，solutes，heat，and plant growth in both unsaturated and variably saturated soils.It simulates soil water movement using the well-known Richards equation:

whereθis the soil water content，tis the time(d)，his the soil matric head(cm)，zis the vertical coordinate，which is positive in the upward direction(cm)，Kis the hydraulic conductivity(cm d-1)，andSis the water extraction by plant roots(1/d).The relationships betweenθ，h，andKin Eq.1 are described by Van Genuchten(1980)and Mualem(1976)，as shown in Eqs.2—3.

whereKsis the soil saturated hydraulic conductivity，Seis the relative soil water saturation，θrandθsare the soil residual and saturated volumetric water content(cm3cm-3)，respectively，andα(cm-1)，n，andλare the empirical parameters.

Solute transport is simulated by a convective-dispersive equation(CDE)as follows(Eq.4):

whereqis vertical f low(cm-2d-1)，cis the solute concentration in soil water(mg cm-3)，DDIF is the diffusion coefficient(cm2d-1)，DDIS is the dispersion coefficient(cm2d-1)，ρbis the dry soil bulk density(g cm-3)，Qis the amount of solute absorbed on organic matter or clay(mg g-1)，andSsis the solute sink term(mg cm-3d-1)accounting for decomposition(not considered in this study)and uptake by roots.

In our study，the solute concentration in the soil water(c)was obtained from the saturated electrical conductivity(ECe)(Rhoadeset al.，1992)as follows:

whereλis an empirical coefficient obtained experimentally.In this study，λis equal to 0.432 4.

The Feddes-Jarvis model is used in the SWAP model for root water uptake(RWU)(Eqs.S1—S8 in File S1，see Supplementary Material for File S1).The Feddes-Jarvis model considers RWU in three steps(Jarvis，1989，2010).First，the potential root water uptake(PRWU)is calculated by the Penman-Monteith function and is allocated to each soil depth based on the root length distribution.Second，the reduction coefficients(RCs)of the RWU caused by water and salt stresses are calculated based on the soil matrix and solute potential using piecewise linear functions.Third，the weighting stress index(ω)is determined according to the RC and RD at the whole-plant scale.Moreover，ωwas compared with the critical stress index(ωc，0＜ωc≤1)for CRWU to identify whether CRWU would occur.Specif ically，complete CRWU occurred(no reduction of transpiration)whenωwas greater thanωc.Furthermore，incomplete CRWU occurred whenωwas smaller thanωc，and consequently，the actual RWU was determined as(PRWU×ω/ωc).Therefore，no CRWU occurred whenωwas equal to 1，and a smallerωcvalue indicated a stronger CRWU capacity.More details can be found in File S1.

Crop growth can be simulated using either a simple crop module or a detailed crop growth module in the SWAP model.In the simple crop module，the user only needs to specify the leaf area index(LAI)，crop height，and root depth as functions of the development stage.The detailed crop module is the WOFOST model，which is a generic crop model integrated into the SWAP model to simulate the growth and development of most crops.This study used the detailed crop growth module，and more details on crop growth simulation by the SWAP model can be found in Kumaret al.(2015)，Hassanliet al.(2016)，Kroeset al.(2017)，and Mokhtariet al.(2018).

Synthetic scenarios

Our study considered four soil salinity levels(Fig.1)，three RDs，and three nitrogen application rates.The subplot with the lowest salt content and highest sunf lower yield in the experiments in 2012 was selected as the controlled salinity treatment(CST)(Zenget al.，2015，2016b，2016c).The electrical conductivity with a soil-to-water ratio of 1:5(EC1:5)was measured in CST，and then the EC1:5was converted into ECeto indicate the soil salinity level(Eq.5)using Eq.6(Hachichaet al.，2005):

Fig.1 Initial soil moisture(a)and four soil salinity levels(b).S1 is the initial soil salt content used in the SWAP model(base value);S0，S2，and S3 represent the base value times of 0.5，2，and 4，respectively.

The initial soil salt content at 0—100 cm depth of the four salinity levels was determined using the initial salt content in CST，with multiplication by specif ic factors.The factors of the four soil salinity levels were 0.5，1，2，and 4，marked as S0，S1，S2，and S3，respectively(Fig.1).Furthermore，the initial soil salt content in the subplot experiment was only measured from 0 to 100 cm at depths of 10，20，30，40，80 and 100 cm.We assumed that the soil salt content below 100 cm was the same as that at the 100-cm depth.

The three typical RDs were categorized as uniform，linear，and empirical and marked as R1，R2，and R3，respectively(Fig.2)(Albashaet al.，2015;Soyluet al.，2017).The empirical RD was based on our previous experimental study in this f ield(Leiet al.，2019).In addition，three nitrogen application rates were applied:N1(0 kg ha-1)，N2(135 kg ha-1)，and N3(270 kg ha-1).Our previous studies found that a nitrogen application rate of 135 kg ha-1was the most suitable for the experimental areas in the HID(Zenget al.，2015;Maet al.，2017)，so we doubled this amount(N3)to represent a high nitrogen application rate.

Fig.2 Uniform(R1)，linear(R2)，and empirical(R3)root distributions.EC e=saturated electrical conductivity.

Parameters，outputs，and model settings

Parameters for the soil hydraulics，solute transport，and root water uptake in the SWAP model were considered in this study(Table I).We assumed a 330-cm soil column，and divided it into six depths:0—10，10—20，20—40，40—80，and 80—330 cm(Fig.1).The initial soil hydraulic parameters were determined by the Rosetta model(Schaapet al.，2001)based on soil particle analysis(Table II).The base values of the solute transport and root water uptake parameters are listed in Table I.For the solute transport and root water uptake parameters，we used uniform distributions with the parameter ranges from the studies of Jianget al.(2011)，Xue and Ren(2017a)，Renet al.(2016)，and Xuet al.(2016).For the soil hydraulic parameters，since they were intrinsically linked for the same soil type，we proposed a multiplication factor(MF)for each layer and used uniform distributions for all f ive MFs(Xuet al.，2017).The MFs ranged only from 0.9 to 1.1 to ensure that the soil texture would not change too much with the generation of the soil hydraulic parameters.Meanwhile，the MFs reduced the number of soil hydraulic parameters for calibration and avoided overf itting of the model.Three outputs，DM，yield，and accumulated transpiration of sunf lowers，were selected for this study.

The parameters for sunf lowers(variety:LD5009)were calibrated based on the observations in CST in 2012(Table III).The coefficient of determination(R2)of LAI and plant height were 0.73 and 0.98，respectively.The simulated and observed DM(18 607vs.18 648 kg ha-1)and yield(6 436vs.6 150 kg ha-1)were comparable.Therefore，the calibrated SWAP model accurately simulated sunf lower growth in CST in 2012(Fig.3).

Fig.3 Calibration of the SWAP model for leaf area index(LAI，a)，plant height(b)，dry matter(c)，and yield(d).

TABLE I Soil hydraulic，solute transport，and root water uptake parameters a)in the SWAP model

TABLE II Soil hydraulic parameters a)determined by the Rosetta model

TABLE III Crop parameters in the SWAP model

In the calibration and further SA and uncertainty analysis(UA)，the upper boundary condition(BC)was the atmospheric BC.The potential soil evaporation was calculated by transforming the reference ET，and we set the soil factor(CFBS，0.5)as the recommended value in the SWAP model，which means that the potential soil evaporation was equal to 0.5×reference ET.Then，the actual evaporation was calculated based on Black’s reduction function.The lower BC was set as the calculated bottom f lux from the hydraulic head of the deep aquifer，which was the groundwater table depth of the subplot(CST)in the HID in 2012(Fig.S1 in File S2，see Supplementary Material for File S2).The soils(0—330 cm)below the groundwater depth were regarded as saturated，and the pressure heads were positive and equal to the difference between 330 cm and the groundwater depth.In addition，because of the absence of measurements of solute concentrations in both precipitation and groundwater，these concentrations were assumed to be zero in this study.

Sensitivity and uncertainty analyses

The EFAST method was used for SA in our study.It is a variance-based method using a variance ratio to estimate the importance of parameters with the foundation of variance decomposition.It can calculate two sensitivity indices，the main sensitivity(MS)and total sensitivity(TS)indices，for each parameter.The difference between MS and TS can be regarded as a measure of the interactions of one parameter(noted as parameteri)with others.Because the interactions increase with the number of parameters，as well as their variation range，previous studies have proven that variance decomposition methods are suitable for models with numerous parameters.

Our study considered 36 scenarios(four soil salinity levels，three RDs of sunf lowers，and three nitrogen application rates)for the year 2012.The climate data were measured by an agricultural weather station located 10 m from the subplots.The sample size was set asn=10 000 to attain stable convergence for SA.The parameter generation and index calculation of EFAST were performed using SIMLAB software based on the studies of Vazquez-Cruzet al.(2014)，Sunet al.(2015)，Dimovet al.(2012)and He and Yang(2013).

Considering the physical processes of root water uptake，rules were added to UA to conf irm the order of the parameters ash1＜h2＜h3h＜h3l＜h4(absolute values)(Table I).Box plots were used in UA for outputs derived from the variation in the considered parameters.

RESULTS

Considering the main effects of all treatments，the inf luential parameters for crop DM，transpiration，and yield，wereα，n，ωc，Pi，SSF，θr，θs，and TSCF.From the view of the mean of the main effect，ωchad a higher impact thanθr，θs，and TSCF on transpiration.However，ωchad a very weak effect on DM and yield(Fig.4a).In contrast，αhad the highest impact on DM，accumulated transpiration，and yield at the same time.The eight high-impact parameters for the main effect also had greater effects on DM，accumulated transpiration，and yield(Fig.4b).For the mean of the total effect，αhad the highest impact on DM and yield，whileωchad the greatest effect on accumulated transpiration.In addition，the effects of TSCF，α，Pi，SSF，andωchad higher variability than those ofθrandθs.Except forθs，the effects on accumulated transpiration ofθrandθshad low variability with respect to the total effect of all three outputs of the SWAP model.

Fig.4 Box plots of the main(a)and total(b)effects of different parameters in the SWAP model on crop actual dry matter(DM)，yield(Yi)，and accumulated transpiration(AT).The 25th percentile(Q1)，mean value，and 75th percentile(Q3)of the estimation objects are represented by the upper edges，middle bold lines，and lower edges of the boxes，respectively，and the vertical lines of the boxes indicate the estimation objects extended to 1.5×(Q3-Q1).See Table I for detailed description of each parameter.

The three nitrogen application rates(N1，N2，and N3)did not change the effect order of the parameters for crop DM，transpiration，and yield(Fig.5).For the mean main effect，αhad the highest impact for all three outputs.The second most inf luential parameter for DM and yield wasn，but for transpiration，it wasωc.The effects ofα，TSCF，θs，θr，andnhad higher variability with respect to the main effect compared with other parameters.Moreover，the parameter effect with the highest variability with respect to the main effect wasαfor DM and yield，and TSCF for accumulated transpiration.The total effect was similar to the main effect for N1，N2，and N3，in terms of the parameter sensitivity.However，in terms of effect variability，Pi was similar to TSCF with respect to DM and yield，and the effects of these parameters had higher variability than those ofα.Moreover，the effects of TSCF had the highest variability with respect to the total effect，while the variability of Pi，α，and SSF was similar.

Fig.5 Box plots of the main(ME)and total(TE)effects of different parameters in the SWAP model on crop actual yield(Yi)，dry matter(DM)，and accumulated transpiration(AT)under low(N1)，moderate(N2)，and high(N3)nitrogen application rates.The 25th percentile(Q1)，mean value，and 75th percentile(Q3)of the estimation objects are represented by the upper edges，middle bold lines，and lower edges of the boxes，respectively，and the vertical lines of the boxes indicate the estimation objects extended to 1.5×(Q3-Q1).See Table I for detailed description of each parameter.

Considering the main effect，the four most inf luential parameters for crop DM and yield wereα，n，θr，andθs，as salinity levels increased from S0 to S2(Fig.6).However，the most inf luential parameter for Crop DM and yield was TSCF under S3.Furthermore，the most effective parameter for accumulated transpiration wasαunder S0 and S1，but TSCF under S2 and S3.In addition，soil salinity decreased the effect variability of the main effects for almost all parameters，such asωc，α，θs，θr，andn.Similar phenomena were found for the total effects.

For crop yield，the RDs of R1 and R2 had similar inf luential parameters considering the main effect，and the four highest-impact parameters wereα，n，θr，andθs(Fig.7).Althoughαhad the highest effect under R3，its main effect(Si)decreased from 0.40 to 0.28.The sensitivity of DM toward the input parameters under R1，R2，and R3 was similar to that of the yield.However，the parametersωc，α，andθshad greater impacts on the accumulated transpiration in R1，R2，and R3，respectively.Furthermore，the effects ofαandnhad the largest variability，with respect to the main effect for DM and yield under all three RDs.However，for accumulated transpiration，the largest effect variability of the main effect was observed forωc，αandθs，under R1，R2，and R3，respectively.The main and total effects indicated similar phenomena with regard to parameter effects.However，the effect of Pi had higher variability with respect to the total effect compared with the main effect for DM，yield，and accumulated transpiration under R1，R2，and R3.In addition，R3 increased the variability of the total effect of TSCF on accumulated transpiration.

Fig. 6 Bo x p lot s of the ma in (ME) and to tal (TE) effect s o f d iffe ren t par ame ter s i n the SWAP mod el on cr op act ual yi el d (Yi)， d ry mat te r (DM)， a nd ac cum ula ted tr ans pi rat ion (AT) und er th e S 0， S1， S2， and S3 sal ini ty lev els. The 25 th per cen ti le (Q1)， mea n v al ue， an d 7 5th pe rc ent ile (Q 3) of th e e sti mat ion o bje cts ar e r epr es ent ed by the up pe r e dge s， mid dl e b old li nes， a nd lo wer ed ges of t he box es， re spe ct ive ly， an d t he ver tic al lin es of th e b oxe s i ndi ca te the es tim ati on ob jec ts ext end ed to 1.5 × (Q 3 - Q 1). Se e Fig. 1 fo r d eta ile d d es cri pti ons of S0， S1， S2， a nd S3.

Fig.7 Box plots of the main(ME)and total(TE)effects of different parameters in the SWAP model on crop actual yield(Yi)，dry matter(DM)，and accumulated transpiration(AT)under the R1(a)，R2(b)，and R3(c)root distributions.The 25th percentile(Q1)，mean value，and 75th percentile(Q3)of the estimation objects are represented by the upper edges，middle bold lines，and lower edges of the boxes，respectively，the vertical lines of the boxes indicate the estimation objects extended to 1.5×(Q3-Q1)，and the solid point indicates the outlier.See Fig.2 for detailed descriptions of R1，R2，and R3.See Table I for detailed description of each parameter.

Considering the interactive effects of root distribution，salinity level and nitrogen application，the three highestimpact parameters were the same under all three nitrogen applications，andθrandθshad greater effects on the transpiration under S0R1 and S1R1(Tables SI—SIII in File S3，see Supplementary Material for File S3).Theωcdid not rank in the top three inf luential parameters for transpiration under R2 and R3，with S0 and S1 across all three nitrogen application levels.However，under S2R2 and S2R3，ωcranked as the third most inf luential parameter for transpiration.Furthermore，the effect ofθrbecame greater thanθsandnunder R2 and R3，coupled with S0 and S1 for DM.However，under S3，the most inf luential parameter for DM was TSCF.In terms of yield simulation，the top three inf luential parameters wereα，θr，andn，when the salinity level was lower than S3.Under S3，the top three inf luential parameters were TSCF，Pi，and SSF with R1 and R2，compared to TSCF，SSF，andθrin R3.

In addition，both nitrogen application rate and RD had almost no effects on the mean value and uncertainty of DM，yield，and accumulated transpiration.No signif icant difference was found in crop DM，yield，or accumulated transpiration among S0，S1，and S2;however，they were signif icantly decreased under S3(Fig.8).

Fig.8 Box plots of the uncertainties of crop yield(a)，dry matter(b)，and accumulated transpiration(AT，c)of the SWAP model under three nitrogen application rates(low(N1)，moderate(N2)，and high(N3))，four salinity levels(S0，S1，S2，and S3)，and three root distributions(R1，R2，and R3).The 25th percentile(Q1)，mean value，and 75th percentile(Q3)of the estimation objects are represented by the upper edges，middle bold lines，and lower edges of the boxes，respectively，the vertical lines of the boxes indicate the estimation objects extended to 1.5×(Q3-Q1)，and the symbol fork(×)indicates the outlier.

DISCUSSION

Effects of nitrogen application，salinity level，and root distribution on parameter sensitivity of the SWAP model

Soil hydraulic parameters，such asα，n，θrandθs，had greater effects on crop DM，accumulated transpiration，and yield simulations，when considering the entire scenario(Fig.4).The reason behind this result was that the above parameters were the main inputs for determining the relationships among soil moisture(θ)，soil matric potential(h)，and soil hydraulic conductivity(K)in the model of Van Genuchten(1980).Therefore，even slight perturbations ofα，n，θr，andθs，could effectively inf luencehand RWU，which participate directly in the calculations of accumulated transpiration，DM，and yield(Kroesetal.，2017).In addition toα，n，θr，andθs，ωchad signif icant effects on DM，accumulated transpiration，and yield simulations(Fig.4).This is becauseωcis the critical parameter of the Feddes-Jarvis model for determining whether CRWU can be triggered(Jarvis，1989，2010;Leiet al.，2019).However，when the weighting stress coefficient ofωwas smaller thanωc，the actual transpiration was inversely proportional toωc，which might indicate thatωcis more inf luential for the transpiration compared withθrandθswhen crops are under stress.The parameters of the water stress reduction functions(h1，h2，h3，andh4)had relatively low impacts on accumulated transpiration，DM，and yield(Fig.4).One possible reason is the inf luence of shallow groundwater during the experimental period in the study site(about 0.8—2.3 m，Fig.S1 in File S2)and the relatively high precipitation in 2012，which might have relieved the water stress to a certain degree.Furthermore，the setting of parameterωcfor CRWU also reduced the effects of water stress reduction parameters on RWU calculation，and this issue has been discussed by agricultural hydrologists several times(Skaggset al.，2006;Soyluet al.，2017).Additionally，although LDIS and DDIF affected the soil salt distribution through the CDE equation，they were not the direct inputs for determining the effect of salt stress on transpiration，and the main driving force of salt transport came from the convection effect related to soil water movement(Zhanget al.，1994).Therefore，the effects of LDIS and DDIF were insignif icant in the transpiration simulation in the SWAP model.Unexpectedly，the effect ofKswas limited on accumulated transpiration，DM，and yield，possibly because of the narrow f luctuation of the MF forKs(±10%，0.9—1.1 cm d-1)in our study.In fact，the range ofKsin a realistic soil medium changes by several orders of magnitude from heavy clay soil to sandy soil(Patil and Singh，2016;Di Primaet al.，2018);thus，modelers should calibrateKscarefully.

We obtained similar MS and TS for all parameters for crop accumulated transpiration，DM，and yield simulations under the three nitrogen application levels(N1，N2，and N3)(Fig.5).The primary reason is that the nitrogen application had no direct effect on accumulated transpiration，DM，and yield simulation processes，and the applied nitrogen could only affect the determination of daily assimilations when nitrogen stress occurred(Groenendijket al.，2016;Kroeset al.，2017).Another possible reason is the relatively high nitrogen applications of N2 and N3 in our simulation scenarios.Nitrogen stress is affected by the relationships between the crop nitrogen demand and nitrogen applications，(Zenget al.，2016a，2016c)，and applying more nitrogen than the crop nitrogen demand could reduce the nitrogen use efficiency as well as the DM and yield development sensitivities.However，a strange phenomenon was observed that nitrogen stress was still not obvious when no nitrogen was applied under N1.A possible reason could be that the initial nitrogen content was very high(about 100 kg ha-1nitrate nitrogen(NO-3-N)at the 0-40 cm soil depth)(Zenget al.，2014)，which reduced the nitrogen stress under N1.However，more observations about the nitrogen content in both soils and crops are needed for further analysis in the future.

In contrast to nitrogen application，crop accumulated transpiration，DM，and yield signif icantly reduced the salinity level of S3，compared with those of S0 and S1(Fig.6).The effect order of the parameters under S3 was also different from those under S0，S1，and S2.More precisely，the salt concentrations under S0 and S1 were lower than the salt tolerance threshold of sunf lower(ca.7.8 dS m-1)，and the effect of drought stress on crop growth was higher than that of salinity stress.Therefore，the hydraulic parameters had greater effects on accumulated transpiration，DM，and yield，compared to other parameters under S0 and S1.Under S2，the effects of TSCF and Pi increased with the soil salt concentration，but because the salt stress started with S2 and the stress degree was not high，the effect of SSF did not increase.Under S3，the salt stress became the main inhibitory factor for sunf lower growth，and the top three inf luential parameters were all related to soil salt concentration(TSCF，SSF，and Pi).Severe salt stress weakens the effects of hydraulic parameters andωc.In addition，the TS of Pi was much higher than the MS in the three nitrogen scenarios，but this result only occurred under S2 and S3，which indicated that the accumulated transpiration，DM，and yield were sensitive to the interactions between Pi and other parameters.Because Pi was the threshold for identifying salt stress and the main factor affectingω，this phenomenon further revealed the coupling effects of water and salt stresses on crop growth in the SWAP model.

Root distributions not only determine the range of RWU in the soil prof ile，but also inf luence the distributions of the potential RWU and CRWU(Dos Santoset al.，2017;Soyluet al.，2017).Therefore，RD also affected the parameter effects on transpiration calculation.For example，ωchad the greatest effect on transpiration under R1，while the effects of the hydraulic parameters were relatively small(Fig.7).The possible reason is that the capacity of CRWU was improved under R1，because more roots were distributed in deeper，wetter soil than R2 and R3，and higher CRWU in deep soils ensured that water stress occurred later under R1，which reduced the effects of hydraulic parameters on the transpiration in this situation.However，once water stress occurred under R1，the whole soil prof ile had a low water content，which abruptly decreased the transpiration，and produced strong effects fromωc.

The hydraulic parameters(e.g.，αandθr)under R2 and R3 had greater effects with respect to the accumulated transpiration compared with those in R1.This was because roots were densely distributed mainly at the 0—30 cm depth under R2 and R3，which caused water stress to occur more easily in this soil region compared with R1.Additionally，the effects ofωcon crop DM and yield were smaller than those on the accumulated transpiration across all RDs.The possible reason is thatωconly affected the transpiration under soil stress condition，while the DM and yield were inf luenced not only by RWU，but also by other factors，such as weather condition and nutrient application(Groenendijket al.，2016;Lecerfet al.，2019).

In addition，the increase of theθrandθseffects under R2 and R3 compared with those under R1 at low salinity levels(S0 and S1)indicated that root accumulation in the topsoil(e.g.，0—30 cm)increased the risk of water stress in this soil layer(Tables SI—SIII in File S3).Under R2 and R3，the accumulation of salt in the topsoil under high salinity levels caused a heterogeneous soil salt prof ile.In these scenarios，the determination of the parameterωcfor CRWU became more important.Furthermore，the effect of TSCF on DM under S2 and S3 with R2 and R3 also proved that salt stress was the main stress factor under high salinity levels.However，the effect ofθron yield increased under R3 and S3，which was different from the case for DM.The possible reason is that the biomass(yield)was formed in the late growth stages of sunf lowers，when soil moisture was signif icantly lower than that in the early growth stages，which might have increased the dependence of transpiration on the residual soil water content.

Limitations in the sensitivity analysis process of the SWAP model

The latest SWAP version effectively integrates soil water and solute movement through a detailed crop growth and nitrogen supply simulation module(Kroeset al.，2017)，making a great contribution to agricultural prediction and management.However，we found some limitations in the sensitivity analysis process.

First，uncertainty exists in the Feddes-Jarvis model for CRWU calculation.The simulations of DM and yield in the SWAP model are affected by the reduction of accumulated transpiration.The transpiration calculation in this study is based on the empirical Feddes-Jarvis RWUmodel.The compensation effect of RWU is considered by setting the critical compensatory factorωcin the Feddes-Jarvis model.Sensitivity analysis showed that the inf luence of theωcparameter value on the accumulated transpiration calculation exceeded that of the water stress reduction function parameters，which might result in two primary problems.One is the weakening of the physical meaning represented by the water stress reduction parameters，and the second is that the numerical values of these water stress parameters are bound to be different from those in the original Feddes model.In addition，how to determine the meanings and values of these parameters is confusing.On the other hand，becauseωcdetermines the compensation ability of root water absorption，which is correlated with the heterogeneous distribution of soil water as well as soil salt and stress degree，determining this parameter accurately is very important.Some studies have discussed this issue.Jarvis(2010)compared the Feddes-Jarvis model with the matric f lux potential model(macro physical root uptake model)and provided the calculation equations forωcusing the matric f lux potential，root morphological parameters，and potential transpiration.Leiet al.(2019)proposed the quantif ication ofωcby using the minimum stress index of the root zone and the weighted water-salt water stress of the whole root zone through correlation analysis between soil water and salt heterogeneity index andωc.However，the above methods lack sufficient verif ication and testing;thus，the quantif ication of theωcparameter still needs further discussion.

Second，incomplete salinity effects were considered in the crop growth and yield simulation.The salinity effects only participated in the transpiration calculation through the inhibition of root water uptake;however，the presence of soil salinity results in osmotic stress in root water absorption，and if the salt ions are absorbed by roots，toxic effects from ions will gradually appear，affecting the normal crop physiological metabolism，which may change the respiration and DM distribution of vegetative and reproductive organs(Munns and Tester，2008;Deinleinet al.，2014;Munzet al.，2014).Therefore，these inf luences of salinity stress need to be considered in a detailed crop module(WOFOST model).

Third，the secondary effects of nitrogen application were not considered.The reasons for the limited effects of nitrogen application on crop transpiration，DM and yield variations have been discussed above，but some possible inf luential processes of nitrogen application were not considered in the SWAP model，such as the effects on the soil hydraulic properties.Reasonable nitrogen application can improve soil microbial environment and soil structure，which may promote water transport in the soil prof ile(Marschneret al.，2003;Guet al.，2009).Nitrogen overuse may cause soil compaction and may impede soil water movement(Hamza and Anderson，2005).Thus，neglecting this process could decrease the sensitivity of the SWAP model to nitrogen application.

Fourth，previous studies also indicated that the soil texture was an important factor in sensitivity analysis(Nematiet al.，2002;Crescimanno and Garofalo，2005;Patil and Singh，2016;Zenget al.，2018a).However，the lower and upper boundaries of the soil hydraulic parameters(θr，θs，α，n，andKs)in our study were 0.9 and 1.1，respectively.Although the relatively narrow range(±10%)could benef it the convergence of iteration of the SWAP model，it restricted the scope of application of our results.More exactly，the f indings of the parameters which had high or low impacts on accumulated transpiration，DM，and yield are only applicable in regions with predominantly loamy soils.

To provide more useful information about the parameter calibration of the SWAP model，our study also applied different initial soil hydraulic parameters(Table SI in File S2).More specif ically，we assumed that the soil prof iles were uniform and considered the soil textures of sandy loam，loam，silt loam，silty clay loam，and sandy clay，respectively，with a nitrogen application rate of 270 kg ha-1and a uniform RD.The initial soil hydraulic parameters of these soils were also derived by the Rosetta model(Schaapet al.，2001).Similar to the parameter effects relative to the soil type in our study，the CRWU parameters(ωc)，salt uptake(TSCF)，and stress parameters(Pi and SSF)were also major inf luential parameters for all types of soil，and the effects of these parameters were relatively stable(Fig.S2 in File S2).However，the effects of the soil hydraulic parameters were different with different soil types，e.g.，the parameters ofθr，θs，andαhad greater impacts for sandy loam and loam soils，while for sandy clay soil，the most inf luential parameters werenandKs，which might have been inf luenced by the differences in the soil water retention capacity.Therefore，we conservatively suggest that the specif ic or all soil hydraulic parameters should be carefully selected and calibrated as to different soils before model simulation，thus more soil types need to be considered in future research to make the f indings of the sensitivity analysis more universal.In addition，this study was conducted through a one-location experiment and scenario modeling.In the next step，more experimental data from different locations are needed to further validate and improve the present f indings.

CONCLUSIONS

The present study revealed the parameter effects related to soil hydraulics，solute transport，plant root water uptake，and environmental stresses in the SWAP model，which could be useful not only for simplifying the calibration of agro-hydrological models，but also for improving model structures in the future.When considering the main effect，αwas the most inf luential parameter for crop accumulated transpiration，DM，and yield.However，when considering the total effect，ωchad the greatest effect on accumulated transpiration simulation.Importantly，nitrogen applications did not change the order of parameter sensitivity for accumulated transpiration，DM，or yield in our study.In contrast，the most inf luential parameter for accumulated transpiration，DM，and yield changed fromαat low salinity levels to TSCF at high salinity levels.Moreover，αhad the greatest effect on DM and yield simulations under all three RDs，but the most inf luential parameters for accumulated transpiration wereωc，α，andθsunder R1，R2，and R3，respectively.Additionally，the interactions between salinity level and RD also affected the parameter effects，while the effect of nitrogen application could be neglected in the interactions.Furthermore，both nitrogen application rate and RD had almost no effect on the mean value and uncertainty of DM，yield，and accumulated transpiration.However，S3 signif icantly decreased DM，yield，and accumulated transpiration when compared with S0，S1，and S2.In addition to the inf luential parameters mentioned above，we also suggest careful calibration ofKs，especially in heterogeneous soils.

ACKNOWLEDGEMENT

We are grateful for the f inancial support from the Major Programof the National Natural Science Foundation of China(Nos.51879196 and 51790533)，the China Postdoctoral Science Foundation Funded Project(No.2020M682475)，and the Fundamental Research Funds for the Central Universities，China(No.IWHR-SKL-KF201814).

SUPPLEMENTARY MATERIAL

Supplementary material for this article can be found in the online version.