Determination of Growth Stage-specific Crop Coefficients (k C ) of Sunflowers (helianthus Annuus L.) under Salt Stress

Crop coefficients (K c) are important for the development of irrigation schedules, but few studies on K c focus on saline soils. To propose the growth-stage-specific K c values for sunflowers in saline soils, a two-year micro-plot experiment was conducted in Yichang Experimental Station, Hetao Irrigation District. Four salinity levels including non-salinized (EC e = 3.4–4.1 dS·m –1), low (EC e = 5.5–8.2 dS·m –1), moderate (EC e = 12.1–14.5 dS·m –1), and high (EC e = 18.3–18.5 dS·m –1) levels were arranged in 12 micro-plots. Based on the soil moisture observations, Vensim software was used to establish and develop a physically-based water flow in the soil-plant system (WFSP) model. Observations in 2012 were used to calibrate the WFSP model and acceptable accuracy was obtained, especially for soil moisture simulation below 5 cm (R 2 > 0.6). The locally-based K c values (LK c) of sunflowers in saline soils were presented according to the WFSP calibration results. To be specific, LK c for initial stages (K c1) could be expressed as a function of soil salinity (R 2 = 0.86), while R 2 of LK c for rapid growth (K c2), middle (K c3), and mature (K c4) stages were 0.659, 1.156, and 0.324, respectively. The proposed LK c values were also evaluated by observations in 2013 and the R 2 for initial, rapid growth, middle, and mature stages were 0.66, 0.68, 0.56 and 0.58, respectively. It is expected that the LK c would be of great value in irrigation management and provide precise water application values for salt-affected regions.


Introduction
Sunflower (Helianthus annuus L.) is one of the four most important oil crops in the world [1].Based on data from the National Sunflower Association, more than 25 million hectares of global croplands are planted in sunflowers.The Hetao Irrigation District, which is located in northern China, is the largest sunflower-growing region in China, and sunflower seeds are the main source of income for local farmers [2].However, due to high rates of evaporation and low levels of precipitation, the significance of irrigation in attaining and sustaining optimum productivity of major crops in the Hetao Irrigation District or other regions with similar climate conditions is important and has been documented [3,4].Demir et al. [1] reported that the seed and oil yield of oil sunflowers increased by 82.9% and 85.4% with irrigation as compared to the treatment without irrigation at three growth stages of sunflowers in Turkey; Ertek and Kara [5] also conducted a series of deficit irrigation experiments, and concluded that maize fresh ear yield was affected by water stress.Furthermore, between yield and water use, a positive linear relationship has been recognized by various researchers [6][7][8][9][10].However, because of the limited knowledge of crop water use in this region, flood irrigation without scheduling is still the main irrigation practice, which is not only a non-efficient use of water resources but also has the possibility for increasing the risk of groundwater contamination because a large number of solutes could be leached below the root zone using this irrigation practice [11].Therefore, it is necessary to determine an efficient and representative irrigation scheduler to improve the crop productivity and water resource management for the region.
Crop evapotranspiration (ET c ), which represents the combined processes of water loss through evaporation from soil surface and transpiration from crop surface, has a potential advantage to attain proper irrigation scheduling [12,13].Although there are few traditional technologies (e.g., weighting lysimeters, sap-flow sensors) that can assist scientists with determining ET c [14], it is still laborious, time-consuming and costly to apply these technologies in large regions [15].As recommended by Food and Agricultural Organization (FAO) [16], the approach of the crop coefficient (K c ) is widely used to estimate crop water use and to schedule irrigations.The concept of K c was introduced by Jensen [17] and further developed by the other researchers [16,18,19].Generally speaking, K c is defined as the ratio between ET c and reference evapotranspiration (ET 0 ) which is based on the evapotranspiration (ET) rate from a well-water (not limiting) reference surface.As discussed and summarized in the FAO document, the single crop coefficient approach is used for most applications related to irrigation planning, design, and management due to its simplicity.Values of K c for most agricultural crops increase from a minimal value at planting to a maximum K c value near full canopy cover or pollination.FAO provides details on the development and use of generalized K c values for different crops in different regions of the world [16].However, few methods available to attain crop coefficients for site-specific values have been determined experimentally for different growth stages of sunflowers.What data is available is considerably different from that listed in the FAO-56 paper [20].Meanwhile, approximately 70% of the cultivated land in the Hetao Irrigation District is contaminated by soil salinity, which has been proven to be a vital factor affecting crop growth [3,21].Based on our previous works, soil salinity affects sunflower growth elements such as the photosynthesis [22] and dry matter formation [23], which indicates that there may be a direct relationship between soil salinity and K c .However, as far as we know, almost no published studies focus on this correlation.Therefore, it is important to determine local-based K c values for more precise crop ET c estimation, especially for crops growing in saline soils.However the traditional method for estimating K c is usually via weighting lysimeters [24], which is both costly and time consuming.Due to the lack of research-based information on sunflower water use in saline soils and the inconvenience of directly experimental K c determination, the objectives of this study were to (1) construct a physically-based model to determine local growth-stage-specific K c values for sunflowers in different levels of saline soils, and (2) to ascertain the relationship between K c values and soil salinity (K c -S).Also, evaluations for both model performance and the K c -S relationship were performed based on field experiments.

Study Site Characteristics and Field Experiment Design
This experiment was conducted at the Yichang Experimental Station in the Hetao Irrigation District (40  1a).The Hetao Irrigation District has the largest gravity irrigation area (~1.05 × 10 6 ha) in China and is representative of the continental climate.The mean annual precipitation and mean annual Plants were harvested on 24 September 2012 and 16 September 2013.More details for the micro-plot experiments can be found in [21].Sunflower growth periods were divided into four stages including initial stage, rapid growth stage, middle stage, and mature stage [25].Soil samples at different depths were taken at sowing stage and four times for each subsequent growth stage.Soil samples were taken at depths of 0-5, 5-10, 10-20, 20-40, 40-60, 60-80, and 80-100 cm on 10 June, 13 July, 2 August, 9 August, and 24 September in 2012 and at depths of 0-10, 10-20, 20-30, 30-40, 40-60, 60-80, 80-100 cm on 30 May, 10 July, 24 July, 14 August, and 16 September in 2013, respectively.After sampling, soil moisture was determined using the oven-dry method.Soil texture was analyzed using the pipette method [26,27] and the bulk density was measured by the cutting-ring method [27,28] (Table 1).September in 2013, respectively.After sampling, soil moisture was determined using the ovendry method.Soil texture was analyzed using the pipette method [26,27] and the bulk density was measured by the cutting-ring method [27,28] (Table 1).

Model Descriptions
System Dynamics (SD) was firstly proposed by Forrester [29] and widely applied to analyze the change of a modeling system based on the linkage and response mechanism among models, which can represent complex systems and analyze their dynamic behavior [30].Vensim software (http://vensim.com/)has been shown to be an adequate tool to depict system dynamics [31][32][33].Vensim™, the Ventana ® Simulation Environment, is an interactive software environment that allows the development, exploration, analysis and optimization of simulation models.It was created to increase the capabilities and productivity of skilled modelers and has the functionality that improves the quality and understanding of models [34].In this study, Vensim software was used to establish a physically-based model to consider the water flow in the soil-plant system (WFSP model).Vensim is designed to simultaneously solve a series of material held within a stock and its depletion or replenishment by flow into and out of the stock [35,36], and its open version Vensim PLE is freely available to the academic community for use in education and research.Here, stocks represent the mass of water within a given soil layer; while the flows represent the fluxes of water among stocks, model runs were conducted using a one-day time step, with state variables at each interval.All storage terms were given in millimeters; also, flow terms were given in millimeters per day.More details about this model, including the equations used to calculate the stocks and the flows are shown in following sections.

Model Descriptions
System Dynamics (SD) was firstly proposed by Forrester [29] and widely applied to analyze the change of a modeling system based on the linkage and response mechanism among models, which can represent complex systems and analyze their dynamic behavior [30].Vensim software (http://vensim.com/)has been shown to be an adequate tool to depict system dynamics [31][32][33].Vensim™, the Ventana ® Simulation Environment, is an interactive software environment that allows the development, exploration, analysis and optimization of simulation models.It was created to increase the capabilities and productivity of skilled modelers and has the functionality that improves the quality and understanding of models [34].In this study, Vensim software was used to establish a physically-based model to consider the water flow in the soil-plant system (WFSP model).Vensim is designed to simultaneously solve a series of material held within a stock and its depletion or replenishment by flow into and out of the stock [35,36], and its open version Vensim PLE is freely available to the academic community for use in education and research.Here, stocks represent the mass of water within a given soil layer; while the flows represent the fluxes of water among stocks, model runs were conducted using a one-day time step, with state variables at each interval.All storage terms were given in millimeters; also, flow terms were given in millimeters per day.More details about this model, including the equations used to calculate the stocks and the flows are shown in following sections.For the layer 1, layers 2-6, and layer 7, we can describe the water movement by Equations ( 1)-( 3) respectively.

Basic Principles
where S is soil water storage within every soil layer (subscript i represents a soil layer) (mm), P is precipitation (mm); C is the capillary water movement into the soil layer (mm); I is the seepage movement out of the soil layer (mm); E is soil evaporation (mm); and U is root water uptake from the soil layer (mm).RO is the surface runoff (mm), and because of the scarce precipitation in Hetao District, RO equals zero; RW is the groundwater recharge (mm); FW is the water flow out of the whole root zone (mm) and ∆S is the change of water storage for the specific soil layer (mm) during the time interval.Subscript t indicates the current moment (day) and t − 1 indicates the last moment (day).Subscript i indicates the layer number (from 2 to 6).
where i t is the infiltration rate at time t (h) and expressed using the infiltration depth at unit time (cm•h −1 ); i 1 is the infiltration rate for the first unit time; p is the empirical index which ranges from 0.3 to 0.8 and is based on the soil properties and moisture, and p is initially determined as 0.5 in this study.Unsaturated hydraulic conductivity (K, mm•d −1 ) is calculated by van Genuchten [38] and van Genuchten and Nielsen [39] (Equations ( 5) and ( 6)).
where K s is the saturated hydraulic conductivity (mm•d −1 ); θ is the soil moisture (cm 3 •cm −3 ); θ r and θ s are the residual and saturated soil moistures (cm 3 •cm −3 ) respectively; and m, n are dimensionless empirical parameters.Parameters for Equation (5) were predicted using the Rosetta module [40] based on soil particle size and bulk density (Table 2).
Table 2. Parameters of Equations ( 5) and ( 6) for the model.θ r : residual soil moisture; θ s : saturated soil moisture.If soil moisture in the upper layer (θ) is larger than θs, I (Figure 2, Equations ( 1)-( 3)) from the upper layer to the lower layer is equal to θ − θs; if θ ranges from θr to θs, I is equal to K; otherwise, I = 0.

Groundwater Recharge
Groundwater table (GWT) depths were obtained according to the local water resources bulletin and Liang et al. [41].More exactly, the GWT depths of study area ranged from 1.14 m (November) to 2.59 m (March) and averaged at 1.82 m in 2012.In 2013 the lowest, deepest and average GWTs were 1.45 m (November), 2.33 m (March) and 1.91 m, respectively.
Groundwater recharge (RW) was calculated based on empirical formula proposed by Li [42] and Du et al. [25].
W g W c = −0.54742H+ 1.66494 (7) where W g is available groundwater (mm); W c is the crop water requirement (mm); and H is the GWT (m).Distribution of RW in the soil profile was calculated based on Feng and Liu [43] and Chen et al. [44], which was also to be used in the CERES-Wheat model (Equation ( 8)).
where w t i+1 is water flux moving upward from layer i + 1 to layer i by capillarity at time t (mm); θ t i+1 , θ t i , θ wi+1 , and θ wi are soil moisture and wilting point of layer i + 1 and layer i at time t (cm 3 •cm −3 ); h i and h i+1 are the thicknesses of layer i + 1 and layer i (cm).

Root Distribution
Root distribution was determined according to the researches of Gale and Grigal [45] and Jackson et al. [46] (Equation ( 9)).
where Y(z) is the accumulated root percentage with soil depth (%) and z is the soil depth (100 cm) calculated from surface and the positive direction is downward (cm).β is an empirical parameter affected by plant types, soil and climate conditions.Jackson et al. [46] indicated that β ranges from 0.913 to 0.978; in our study, β was defined as 0.95.
where RWU is the root water uptake rate (mm•d −1 ); L is the root depth (100 cm); T p is the potential transpiration rate (mm•d −1 ); z is the coordinate axis and positive downward (cm); and α(h) is the function about the soil water potential (SWP) (Equation ( 11)).
In Equation (11), h is the soil water potential (cm).h 1 , h 2 , and h 3 are three threshold values of soil water potential.To be specific, if soil is very wet and has poor ventilation when SWP is higher than h 1 , then RWU decreases with SWP.h 2 is the SWP when plant suffers from water stress and h 3 is the SWP at the wilting point.
Due to the SWP measurements being costly and time consuming, Feddes et al. [48] also proposed that SWP could be replaced by soil moisture (Equation ( 12)).
In Equation ( 12), θ is soil moisture (cm 3 •cm −3 ); θ wilt is the wilting point expressed by moisture (cm 3 •cm −3 ); θ stress is the soil moisture when plant is under water stress (cm 3 •cm −3 ).The details about parameters in Equation ( 12) are shown in Table 3.More exactly, the ranges of parameters in Equations ( 10)-( 12) were determined according to previous studies [32,49] and the exact parameters value were calibrated based on the soil moisture observations in non-saline treatments using a trial-and-error method, which is a fundamental method of problem solving, characterized by repeated, varied attempts until acceptance of results [50].By considering the root distribution (Section 2.2.4) together, the rate of RWU can be expressed as Equation (13).
where ET 0 is the reference evapotranspiration (mm•d −1 ); R n is net radiation at the crop surface ; T is mean daily air temperature at 2-m height ( • C); u 2 is wind speed at 2 m height (m•s −1 ); e s is saturation vapor pressure (kPa); e a is actual vapor pressure (kPa); e s − e a is saturation vapor pressure deficit (kPa); ∆ is slope vapor pressure curve (kPa Since sunflowers were sown below plastic films (reducing surface evaporation), the single crop coefficient (K c ) method was used to calculated the crop water requirement (ET c ) (Equation ( 15)).
In Equation ( 15), E p and T p are potential soil evaporation and potential transpiration, respectively (mm•d −1 ).Considering the plastic films that could reduce evaporation and regarding its coefficient as an adjustable parameter (values ranging from 0 to 0.5) [51], and through calibration we chose 0.1 for an appropriate value; thus E p was determined as in Equation ( 16).

Modeling Process
Soil water flow and water uptake by sunflowers were computed for a soil profile with 100-cm depth.The simulation period extended from the early June to late September, and corresponded to the growth period of sunflowers.First, soil moisture observations in 2012 were used to calibrate the K c for each stage of sunflowers.In this step, only K c values were modified and other parameters (e.g., Tables 2 and 3) were not changed because we assumed that the effects of salinity on sunflower growth could be reflected by K c .Then the local-based K c values for sunflower growing in the saline soils involving a relationship between K c of initial stage and soil salinity were proposed.After that, soil moisture observations in 2013 were used to evaluate the proposed local-based K c values and the contrastive analysis between our K c values against previously reported research results.

Statistical Analysis
The determination coefficient (R 2 , Equation ( 18)) and the root-mean-square error (RMSE, Equation ( 19)) were used to evaluate the model performance.
where Y i obs is the ith observed value, Y i sim is the ith simulated value, and Y obs i and Y sim i are the means of the observed and simulated values, respectively.

Meteorological Conditions
The daily precipitation measured by the field meteorological station of the experiment station from April to October in 2012 and 2013 varied from 0-67.2 mm•d −1 to 0-20.8 mm•d −1 , respectively, with an accumulated precipitation of 254 mm for 2012 and 64.8 mm for 2013 (Figure 3), which indicated that the year 2012 was much wetter than 2013.Furthermore, the local water resources bulletin also confirmed that the 2012 was a wet year while 2013 was a drier one.Specifically, the total precipitation of 2012 in our experiment station is 400.6 mm (from April to October), which was about 127.6% higher than the historical mean precipitation (176 mm).Meanwhile, the total precipitation of 2013 was only about half of the historical mean precipitation.Inversely, calculated ET 0 values in 2012 were relative smaller than those in 2013 according to the accumulated ET 0 during the sunflower growth stages (Figure 3).The different weather conditions of 2012 and 2013 increased the challenge for model calibration and evaluation but could also prove an indication of the stability of the model, if it could perform accurately in both years.
were relative smaller than those in 2013 according to the accumulated ET0 during the sunflower growth stages (Figure 3).The different weather conditions of 2012 and 2013 increased the challenge for model calibration and evaluation but could also prove an indication of the stability of the model, if it could perform accurately in both years.

Calibration of the WFSP Model
Soil water flow and water uptake by sunflower were computed for a soil profile with 100-cm depth.The simulation period was from early June to late September, and conceded with the growth period of sunflowers.Model setup required specific daily precipitation and reference evapotranspiration as input data.The parameter calibration analysis was carried out using the main factors affecting the water regime (i.e., soil moisture, the cumulative values of actual transpiration and evaporation, capillary rise and other additional parameters) as the objective variables.After that, the above-mentioned sensitive parameters and some parameters introduced in Section 2.2 were calibrated using a trial-and-error method.An iterative calibration approach was adopted to account for the interactions between the measured soil moisture and simulated soil moisture.After proper calibration, the model was considered to be adequate for the evaluation of water movement in the soil-plant-atmosphere continuum (SPAC) system.The observed soil water contents in different soil layers relative to 2012 and 2013 were used to calibrate and validate the model, respectively.To assess the performance of the model, several goodness-of-fit indicators proposed in Section 2.3 were used as in the paper (e.g., R 2 and RMSE).Based on the parameter sensitivity analysis, many parameters were only slightly adjusted depending on the goodness-of-fit indicators.The root water uptake parameters, including Feddes' parameters and the basic soil parameters for sunflowers were calibrated and were shown in the former section.Some calibrated Kc values for sunflowers were slightly lower than those recommended in literature.This may due to the fact that the crop varieties planted in Hetao Irrigation District were more salt-tolerant than in the non-salinized area.
Soil moisture observed at different sunflower growth stages were well captured by the WFSP model except for the surface soil (0-5 cm) in the model calibration process (Figure 4, Year 2012).More exactly, R 2 in initial, rapid growth, middle, and mature stages for 5-100 cm depth were 0.60, 0.61, 0.66, and 0.72 respectively while RMSE were only 0.07, 0.04, 0.07 and 0.09 cm 3 •cm −3 respectively.

Calibration of the WFSP Model
Soil water flow and water uptake by sunflower were computed for a soil profile with 100-cm depth.The simulation period was from early June to late September, and conceded with the growth period of sunflowers.Model setup required specific daily precipitation and reference evapotranspiration as input data.The parameter calibration analysis was carried out using the main factors affecting the water regime (i.e., soil moisture, the cumulative values of actual transpiration and evaporation, capillary rise and other additional parameters) as the objective variables.After that, the above-mentioned sensitive parameters and some parameters introduced in Section 2.2 were calibrated using a trial-and-error method.An iterative calibration approach was adopted to account for the interactions between the measured soil moisture and simulated soil moisture.After proper calibration, the model was considered to be adequate for the evaluation of water movement in the soil-plant-atmosphere continuum (SPAC) system.The observed soil water contents in different soil layers relative to 2012 and 2013 were used to calibrate and validate the model, respectively.To assess the performance of the model, several goodness-of-fit indicators proposed in Section 2.3 were used as in the paper (e.g., R 2 and RMSE).Based on the parameter sensitivity analysis, many parameters were only slightly adjusted depending on the goodness-of-fit indicators.The root water uptake parameters, including Feddes' parameters and the basic soil parameters for sunflowers were calibrated and were shown in the former section.Some calibrated K c values for sunflowers were slightly lower than those recommended in literature.This may due to the fact that the crop varieties planted in Hetao Irrigation District were more salt-tolerant than in the non-salinized area.
Soil moisture observed at different sunflower growth stages were well captured by the WFSP model except for the surface soil (0-5 cm) in the model calibration process (Figure 4, Year 2012).More exactly, R 2 in initial, rapid growth, middle, and mature stages for 5-100 cm depth were 0.60, 0.61, 0.66, and 0.72 respectively while RMSE were only 0.07, 0.04, 0.07 and 0.09 cm 3 •cm −3 respectively.

Establishment and Evaluation of the Locally-Based Sunflower K c Values
Calibration of the WFSP model also indicates that K c values for sunflowers in saline soils (EC e = 3.3-18.5dS•m −1 ) ranged from 0.25-0.37,0.51-0.86,0.80-1.49,and 0.11-0.73 of initial (K c1 ), rapid growth (K c2 ), middle (K c3 ), and mature stages (K c4 ) respectively.Meanwhile, linear regression analysis indicated that all K c values except K c1 decreased with soil salinity levels (Figure 6).Furthermore, K c1 had a very good linear correlation with the initial salinity level of 0-20 cm depth (Equation ( 20)).
Therefore, we assume that sunflower's K c1 value in saline soils could be easily obtained through Equation ( 20) while the locally-based K c values for another three stages could be 0.51-0.86,0.80-1.49,and 0.11-0.73for use as reference values.To further simplify, we averaged the K c2 , K c3 , and K c4 values obtained in our model (0.659, 1.156, and 0.324, respectively) and applied the WFSP model to evaluate their accuracy with the calculated K c1 value (Equation ( 20)) using soil and weather conditions in 2013 (Figure 7).Similar to the model calibration process, higher accuracies for soil moisture simulations were also obtained for all four growth stages when the surface soils were ignored (0-10 cm in 2013).More exactly, R 2 in the initial, rapid growth, middle, and mature stages for 10-100-cm depth were 0.66, 0.68, 0.56, and 0.58, respectively, while RMSEs were only 0.04, 0.04, 0.08 and 0.11 cm 3 •cm −3 , respectively.

Establishment and Evaluation of the Locally-Based Sunflower Kc Values
Calibration of the WFSP model also indicates that Kc values for sunflowers in saline soils (ECe = 3.3-18.5dS•m −1 ) ranged from 0.25-0.37,0.51-0.86,0.80-1.49,and 0.11-0.73 of initial (Kc1), rapid growth (Kc2), middle (Kc3), and mature stages (Kc4) respectively.Meanwhile, linear regression analysis indicated that all Kc values except Kc1 decreased with soil salinity levels (Figure 6).Furthermore, Kc1 had a very good linear correlation with the initial salinity level of 0-20 cm depth (Equation ( 20)).Therefore, we assume that sunflower's Kc1 value in saline soils could be easily obtained through Equation ( 20) while the locally-based Kc values for another three stages could be 0.51-0.86,0.80-1.49,and 0.11-0.73for use as reference values.To further simplify, we averaged the Kc2, Kc3, and Kc4 values obtained in our model (0.659, 1.156, and 0.324, respectively) and applied the WFSP model to evaluate their accuracy with the calculated Kc1 value (Equation ( 20)) using soil and weather conditions in 2013 (Figure 7).Similar to the model calibration process, higher accuracies for soil moisture simulations were also obtained for all four growth stages when the surface soils were ignored (0-10 cm in 2013).More exactly, R 2 in the initial, rapid growth, middle, and mature stages for 10-100-cm depth were 0.66, 0.68, 0.56, and 0.58, respectively, while RMSEs were only 0.04, 0.04, 0.08 and 0.11 cm 3 •cm −3 , respectively.

Performance of the WFSP Model
Different from other models (e.g., HYDRUS) which use Richards equation to describe soil water flow [52,53], the WFSP model calculated water movement in the soil-plant system based on the water balance principle.The method is simpler than others and can overcome the iterative convergence issue when solving the Richards equation [54,55].In our study, the WFSP model could simulate soil water dynamics accurately in both 2012 and 2013 except for the surface soils (Figures 4 and 7, R 2 > 0.56, RMSE < 0.1 cm 3 •cm −3 ).Meanwhile, the AETc values for the different growth stages of the sunflower calculated by the WFSP model were also similar to those in research by Ren et al. [56], Du et al. [25], and Xin et al. [57].Therefore, the WFSP model could obtain reasonable simulations of soil water flow in the soil-plant system and could be used as a tool for analyzing the agro-hydrological processes and inverting the sunflower crop coefficient under salt stress.However, the poor accuracy for surface soil moisture simulation may be caused by the unusual weather conditions in 2012.In addition, the uncertainties of input data and field measurements such as groundwater table [58], the possible preferential flow [59] and even the observation errors might also bring adverse influences on the accuracy of the simulations for all four stages.

Performance of the WFSP Model
Different from other models (e.g., HYDRUS) which use Richards equation to describe soil water flow [52,53], the WFSP model calculated water movement in the soil-plant system based on the water balance principle.The method is simpler than others and can overcome the iterative convergence issue when solving the Richards equation [54,55].In our study, the WFSP model could simulate soil water dynamics accurately in both 2012 and 2013 except for the surface soils (Figures 4 and 7, R 2 > 0.56, RMSE < 0.1 cm 3 •cm −3 ).Meanwhile, the AETc values for the different growth stages of the sunflower calculated by the WFSP model were also similar to those in research by Ren et al. [56], Du et al. [25], and Xin et al. [57].Therefore, the WFSP model could obtain reasonable simulations of soil water flow in the soil-plant system and could be used as a tool for analyzing the agro-hydrological processes and inverting the sunflower crop coefficient under salt stress.However, the poor accuracy for surface soil moisture simulation may be caused by the unusual weather conditions in 2012.In addition, the uncertainties of input data and field measurements such as groundwater table [58], the possible preferential flow [59] and even the observation errors might also bring adverse influences on the accuracy of the simulations for all four stages.

Sunflower's K c Values in Saline Soils
Crop coefficient (K c ) is a key parameter for estimating crop water use and to schedule irrigations [12].In our study, K c in the initial stage (K c1 ) was determined by initial soil salinity of 0-20 cm depth due to a very high correlation (R 2 = 0.86, Figure 6a).For the rapid growth, middle and mature stages, sunflower's K c were 0.659, 1.156, and 0.324, respectively.However, locally-based K c values for sunflowers in saline soils proposed in our study (LK c ) were different to previous research (Table 4).FAO-56 reported K c values were 0.35, 1.0-1.15,and 0.35 for initial, middle and mature stages of sunflowers respectively [16].LK c used four growth stages and were adjusted a little (<8%) in middle and mature stages, which increased R 2 of soil moisture simulation (10-100 cm) for about 10% (Table 4) in moderately salinized soil (EC e = 9.44 dS•m −1 ).In India, Tyagi et al. [20] reported K c values for sunflowers as 0.52, 1.1, 0.32 and 0.41, estimating K c values 11.6%-74.2%higher than the values suggested by FAO-56, also different to our LK c values.Even for the same plants in close areas, K c values may also be extremely different.In Hetao Irrigation District, Dai et al. [60] reported K c values of 0.697, 0.751, 0.804, and 0.35, respectively for the four growth stages, with K c values over 100% higher than ours in the initial stage, and about 30% lower in the middle stage.Du et al. [25] also obtained different K c values for sunflowers compared to both Dai et al. [60] and our results (Table 4).The differences among K c values might be caused from both soil and climate conditions and one of the most important factors was soil salinity [61,62].Taking FAO-56 as an example, it deals with the calculation of crop evapotranspiration (ET c ) under standard conditions.The values for K c in FAO-56 are values for non-stressed crops cultivated under excellent agronomic and water management conditions and achieving maximum crop yield (standard conditions).Meanwhile, FAO-56 also ignores the difference among varieties.In addition, some specific agricultural practices such as plastic film covering the soil surface might also impact Kc determination.Therefore, FAO-56 strongly encouraged users to obtain appropriate local K c values for a specific crop variety based on local soil and weather conditions.By considering salinity effects, LK c values obtained the highest accuracy for soil moisture simulation (R 2 = 0.7) in moderately salinized soils when compared to previous research (Table 4).In general, higher soil salinity results in lower K c , which is also in accordance with our K c2 , K c3 , and K c4 (Figure 6b-d).However, a very high positive correlation was found between K c1 and salinity level (Figure 6a), which was unusual but also demonstrated that effects of salinity on K c1 were more pronounced than in other stages.Similar results also obtained by Grattan and Grieve [63], who indicated that the initial stage of the crop was generally more salt sensitive than later growth stages and that crop failures during initial stages are common on saline lands.However, Bernstein and Hayward [64] reported that salt accumulations at seed depths are often much greater than at lower levels in the soil profile and when response to actual ambient salinity is considered, the initial stage is generally no more salt sensitive than later stages.Meanwhile, sunflowers were classified as moderately salt-tolerant plants by Katerji et al. [65] and previous studies also proved that a certain extent of salinity level might enhance sunflower growth [66].Therefore, it is reasonable to believe that two or more of these processes with respect to the positive or negative effects of salinity on sunflowers may occur at the initial stage, but whether they ultimately affect K c value or crop yield depends upon the salinity level, composition of salts, the crop species, and some other environmental factors which need further research.

Conclusions
Crop evapotranspiration calculation (ET c ) plays a pivotal role in evaluating irrigation management strategies for improving agricultural water use, especially in saline regions.Appropriate irrigation schedules are of vital importance to adequately manage it.To determine ETc and make appropriate irrigation schedules, crop coefficients (K c ) have to be representatively determined.Based on soil moisture observations, a strong dynamics analysis tool (Vensim software) was used to establish and develop a physically-based model (WFSP model) for estimating the crop coefficients (K c ) of sunflowers in the Hetao Irrigation District.The two main findings were that firstly, only soil moisture data is needed for WFSP model, which makes this method more practical for developing an irrigation schedule.Meanwhile, the WFSP model could estimate reasonable simulations on the soil water flow in the soil-plant system and thus could be used as a tool for analyzing the agro-hydrological processes and deducing the sunflower crop coefficient under salt stress conditions.Secondly, our study indicates that the effects of salt stress on plant could be considered with K c determination.K c1 had a very good linear correlation with the initial salinity level of 0-20 cm depth (Equation ( 20)), and local-based K c values for rapid growth, middle, and mature stages are recommended as 0.659, 1.156, and 0.324, respectively.These local crop coefficients could be very useful in irrigation schedules for local agricultural water managers.
However, there are still several shortcomings of our study.Firstly, soil salt dynamics were not considered in the study and further work should focus on the effects of salt dynamics with respect to K c at the different crop stages.In addition, EC e was used to reflect the total salt content and the effects of salt composition on K c and would need further study.Meanwhile, the LK c values for sunflowers, especially Equation (20) also need to be evaluated in other saline soils to test their stability and applicability.
approximately 176 mm and 2056 mm, respectively, and 63%-70% of precipitation is from June to August[4].Micro-plot experiments were conducted on sunflowers (Helianthus) for two years, in 2012 and 2013.Each micro-plot covered an area of 1.8 m × 1.8 m and was surrounded by an impermeable plastic barrier to a depth of 1.5 m to prevent lateral drainage (Figure1b,c).Salt crusts on the surface of saline bare soils were collected and used to modify salinity from the 0-20 cm depth of the micro-plots.Saturated electrical conductivity (EC e ) was used to indicate soil salinity levels.Four different salinity levels were established, including non-salinized (EC e = 3.4-4.1 dS•m -1 ), low (EC e = 5.5-8.2dS•m -1 ), moderate (EC e = 12.1-14.5dS•m -1 ), and high (EC e = 18.3-18.5dS•m -1 ), respectively.Sunflowers (cv.LD5009) were planted on 7 June 2012 and 4 June 2013 in a grid of four rows (0.45 m × 0.4 m spacing) within each subplot (Figure 1d); the plant density was 4.94 plants m −2 , and soil was covered by plastic films in order to decrease soil evaporation.

Figure 1 .
Figure 1.The location site (a) of the experimental study area.The green dot is the location of subplots at the Yichang Experimental Station.The arrangement of the trial blocks are depicted in (b) with the schematic diagram of the block profile (c) and plant arrangement (d) within each block (units in cm) also being shown.

Figure 1 .
Figure 1.The location site (a) of the experimental study area.The green dot is the location of subplots at the Yichang Experimental Station.The arrangement of the trial blocks are depicted in (b) with the schematic diagram of the block profile (c) and plant arrangement (d) within each block (units in cm) also being shown.

Figure 2 .
Figure2.Basic model framework.P is precipitation (mm); C is the capillary water movement into the soil layer (mm); I is the seepage movement out of the soil layer (mm); E is soil evaporation (mm); and U is root water uptake from the soil layer (mm).RO is the surface runoff (mm).RW is the groundwater recharge (mm); FW is the water flow out of the whole root zone (mm).Subscript i indicates the layer number.

Figure 2 .
Figure2.Basic model framework.P is precipitation (mm); C is the capillary water movement into the soil layer (mm); I is the seepage movement out of the soil layer (mm); E is soil evaporation (mm); and U is root water uptake from the soil layer (mm).RO is the surface runoff (mm).RW is the groundwater recharge (mm); FW is the water flow out of the whole root zone (mm).Subscript i indicates the layer number.

Figure 3 .
Figure 3. Precipitation and potential evapotranspiration (ET0) of sunflower growing seasons in 2012 (a) and 2013 (b).Red curves are the parabolic fitting of the ET0.

Figure 3 .
Figure 3. Precipitation and potential evapotranspiration (ET 0 ) of sunflower growing seasons in 2012 (a) and 2013 (b).Red curves are the parabolic fitting of the ET 0 .

Figure 4 .
Figure 4. Soil moisture simulation of sunflowers at four different growth stages of model calibration using the observations in 2012 ((a): initial stage; (b): rapid growth stage; (c): middle stage; (d): mature stage; blue points indicate observations in 0-5 cm and red points indicate observations in 5-100 cm).RMSE: root-mean-square error Accumulative evapotranspiration (AETc) was also calculated, and the average AETc of the four growth stages were 77.1, 66.5, 156.2, and 44.3 mm respectively in 2012 (Figure 5a); and 60.0, 74.2, 123.6, and 19.7 mm respectively in 2013 (Figure 5b), indicating that the AETc of sunflowers was comparable in first two growth stages and achieved highest and lowest values in the middle and mature stages respectively.

Figure 5 .
Figure 5. Box plot of accumulative evapotranspiration (AETc) of the four growth stages of sunflowers in 2012 (a) and 2013 (b) respectively.The line in the box is the median, the edges of the box are the lower hinge (25%, Q1) and the upper hinge (75%, Q3), the up and low boundary lines out of the box indicate the maximum and minimum values and the cross symbols near the up and low boundaries are the 99% and 1% hinges respectively.

Figure 4 .
Figure 4. Soil moisture simulation of sunflowers at four different growth stages of model calibration using the observations in 2012 ((a): initial stage; (b): rapid growth stage; (c): middle stage; (d): mature stage; blue points indicate observations in 0-5 cm and red points indicate observations in 5-100 cm).RMSE: root-mean-square error.

Figure 4 .
Figure 4. Soil moisture simulation of sunflowers at four different growth stages of model calibration using the observations in 2012 ((a): initial stage; (b): rapid growth stage; (c): middle stage; (d): mature stage; blue points indicate observations in 0-5 cm and red points indicate observations in 5-100 cm).RMSE: root-mean-square error Accumulative evapotranspiration (AETc) was also calculated, and the average AETc of the four growth stages were 77.1, 66.5, 156.2, and 44.3 mm respectively in 2012 (Figure 5a); and 60.0, 74.2, 123.6, and 19.7 mm respectively in 2013 (Figure 5b), indicating that the AETc of sunflowers was comparable in first two growth stages and achieved highest and lowest values in the middle and mature stages respectively.

Figure 5 .
Figure 5. Box plot of accumulative evapotranspiration (AETc) of the four growth stages of sunflowers in 2012 (a) and 2013 (b) respectively.The line in the box is the median, the edges of the box are the lower hinge (25%, Q1) and the upper hinge (75%, Q3), the up and low boundary lines out of the box indicate the maximum and minimum values and the cross symbols near the up and low boundaries are the 99% and 1% hinges respectively.

Figure 5 .
Figure 5. Box plot of accumulative evapotranspiration (AETc) of the four growth stages of sunflowers in 2012 (a) and 2013 (b) respectively.The line in the box is the median, the edges of the box are the lower hinge (25%, Q1) and the upper hinge (75%, Q3), the up and low boundary lines out of the box indicate the maximum and minimum values and the cross symbols near the up and low boundaries are the 99% and 1% hinges respectively.

Figure 6 .
Figure 6.The relationship between the crop coefficient/Kc of sunflowers simulated by WFSP model and initial salinity level/ECe (dS•m −1 ) of 0-20 cm depth.

Figure 6 .
Figure 6.The relationship between the crop coefficient/K c of sunflowers simulated by WFSP model and initial salinity level/EC e (dS•m −1 ) of 0-20 cm depth.

Figure 7 .
Figure 7. Soil moisture simulation of sunflowers in four different growth stages for model evaluation using the observations in 2013 ((a): initial stage; (b): rapid growth stage; (c): middle stage; (d): mature stage; blue points indicate observations in 0-10 cm and red points indicate observations in 10-100 cm).

Figure 7 .
Figure 7. Soil moisture simulation of sunflowers in four different growth stages for model evaluation using the observations in 2013 ((a): initial stage; (b): rapid growth stage; (c): middle stage; (d): mature stage; blue points indicate observations in 0-10 cm and red points indicate observations in 10-100 cm).

Table 1 .
Soil physical properties of experimental area.

Table 1 .
Soil physical properties of experimental area.

Table 3 .
List of Feddes model parameters.

Table 4 .
Comparison of crop coefficients/K c between different researchers and our model in moderately salinized soil (EC e = 9.44 dS•m −1 ).