Determination of Growth Stage-Specific Crop Coefficients (Kc) of Sunflowers (Helianthus annuus L.) under Salt Stress

Abstract

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 (R² > 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 (R² = 0.86), while R² 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 R² 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.

1. 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 (ET₀) 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.

2. Materials and Methods

2.1. Study Site Characteristics and Field Experiment Design

This experiment was conducted at the Yichang Experimental Station in the Hetao Irrigation District (40°19′ to 41°18′ N, 106°20′ to 109°19′ E), Inner Mongolia, China (Figure 1a). The Hetao Irrigation District has the largest gravity irrigation area (~1.05 × 10⁶ ha) in China and is representative of the continental climate. The mean annual precipitation and mean annual potential evapotranspiration are 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 (Figure 1b,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 = 5.5–8.2 dS·m^–1), moderate (EC_e = 12.1–14.5 dS·m^–1), and high (EC_e = 18.3–18.5 dS·m^–1), 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. 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. Soil physical properties of experimental area.

Depth (cm)	Soil Particle Size Distribution/Mean ± S.D.* (%)			Bulk Density (g/cm3)
	Sand (0.05–2.0 mm)	Silt (0.002–0.05 mm)	Clay (< 0.002 mm)
0–10	12.58 ± 4.30	54.94 ± 12.13	32.48 ± 13.86	1.35
10–20	11.79 ± 3.97	52.81 ± 13.53	35.40 ± 14.67	1.35
20–30	12.02 ± 4.24	52.32 ± 12.43	35.66 ± 14.05	1.35
30–40	12.27 ± 6.86	53.77 ± 12.10	33.96 ± 15.49	1.44
40–60	8.91 ± 12.96	69.77 ± 11.41	21.32 ± 12.29	1.48
60–80	12.48 ± 13.91	70.57 ± 11.80	16.95 ± 10.61	1.51
80–100	16.69 ± 16.69	69.59 ± 13.28	13.72 ± 6.17	1.51

Note: * S.D. indicates standard deviation.

).

2.2. 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.

2.2.1. Basic Principles

Figure 2 indicates the water movement in the root zone of sunflowers for our model. Based on our soil sampling design, we considered a 100-cm depth soil profile and divided it into seven layers (0–5, 5–10, 10–20, 20–40, 40–60, 60–80, and 80–100 cm, for 2012 and for 2013, 0–10, 10–20, 20–30, 30–40, 40–60, 60–80, and 80–100 cm).

For the layer 1, layers 2–6, and layer 7, we can describe the water movement by Equations (1)–(3) respectively.

$$\mathrm{\Delta }{\mathrm{S}}_1={\mathrm{S}}_{1,\mathrm{t}}-{\mathrm{S}}_{1,\mathrm{t}-1}=\mathrm{P}+{\mathrm{C}}_1-\mathrm{RO}-{\mathrm{U}}_1-{\mathrm{I}}_1-\mathrm{E}$$

(1)

$$\mathrm{\Delta }{\mathrm{S}}_{\mathrm{i}}={\mathrm{S}}_{\mathrm{i},\mathrm{t}}-{\mathrm{S}}_{\mathrm{i},\mathrm{t}-1}={\mathrm{C}}_{\mathrm{i}}+{\mathrm{I}}_{\mathrm{i}-1}-{\mathrm{C}}_{\mathrm{i}-1}-{\mathrm{U}}_{\mathrm{i}}-{\mathrm{I}}_{\mathrm{i}}$$

(2)

$$\mathrm{\Delta }{\mathrm{S}}_7={\mathrm{S}}_{7,\mathrm{t}}-{\mathrm{S}}_{7,\mathrm{t}-1}=\mathrm{I}+\mathrm{RW}-\mathrm{FW}-{\mathrm{U}}_7-{\mathrm{C}}_6$$

(3)

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 ΔS 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).

2.2.2. Infiltration

Infiltration is described based on Kostiakov [37] model (Equation (4)).

$${\mathrm{i}}_{\mathrm{t}}={\mathrm{i}}_1{\mathrm{t}}^{-\mathrm{p}}$$

(4)

where i_t is the infiltration rate at time t (h) and expressed using the infiltration depth at unit time (cm·h⁻¹); i₁ 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)).

$$\mathrm{K}={\mathrm{K}}_{\mathrm{s}}{\left(\frac{\mathsf{\theta }-{\mathsf{\theta }}_{\mathrm{r}}}{{\mathsf{\theta }}_{\mathrm{s}}-{\mathsf{\theta }}_{\mathrm{r}}}\right)}^{0.5}{\left\{1-{\left[1-{\left(\frac{\mathsf{\theta }-{\mathsf{\theta }}_{\mathrm{r}}}{{\mathsf{\theta }}_{\mathrm{s}}-{\mathsf{\theta }}_{\mathrm{r}}}\right)}^{\frac{1}{\mathrm{m}}}\right]}^{\mathrm{m}}\right\}}^2$$

(5)

$$\mathrm{m}=1-\frac{1}{\mathrm{n}}$$

(6)

where K_s is the saturated hydraulic conductivity (mm·d⁻¹); θ is the soil moisture (cm³·cm⁻³); θ_r and θ_s are the residual and saturated soil moistures (cm³·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. Parameters of Equations (5) and (6) for the model. θ_r: residual soil moisture; θ_s: saturated soil moisture.

Depth	θr	θs	α	n	Ks
	cm3·cm−3	cm3·cm−3	1/cm	-	mm/d
0–10 cm	0.0883	0.4691	0.0082	1.5057	121.9
10–20 cm	0.0919	0.4774	0.0093	1.4737	125.4
20–30 cm	0.0921	0.4776	0.0094	1.4702	125.9
30–40 cm	0.0901	0.4733	0.0087	1.4893	123.5
40–60 cm	0.0763	0.4540	0.0058	1.6156	131.2
60–80 cm	0.0687	0.4477	0.0051	1.6582	176.0
80–100 cm	0.0616	0.4431	0.0046	1.6903	235.6

Notes: θ_r and θ_s are the residual and saturated soil moistures (cm³·cm⁻³) respectively; K_s is the saturated hydraulic conductivity (mm·d⁻¹); α and n are dimensionless empirical parameters.

).

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.

2.2.3. 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].

$$\frac{{\mathrm{W}}_{\mathrm{g}}}{{\mathrm{W}}_{\mathrm{c}}}=-0.54742\mathrm{H}+1.66494$$

(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)).

$${\mathrm{w}}_{\mathrm{i}+1}^{\mathrm{t}}={\mathrm{W}}_{\mathrm{g}}\frac{\left({\mathsf{\theta }}_{\mathrm{i}+1}^{\mathrm{t}}-{\mathsf{\theta }}_{\mathrm{w}\mathrm{i}+1}\right){\mathrm{h}}_{\mathrm{i}+1}-\left({\mathsf{\theta }}_{\mathrm{i}}^{\mathrm{t}}-{\mathsf{\theta }}_{\mathrm{w}\mathrm{i}}\right){\mathrm{h}}_{\mathrm{i}}}{0.5\left({\mathrm{h}}_{\mathrm{i}}+{\mathrm{h}}_{\mathrm{i}+1}\right)}$$

(8)

where ${\mathrm{w}}_{\mathrm{i}+1}^{\mathrm{t}}$ is water flux moving upward from layer i + 1 to layer i by capillarity at time t (mm); ${\mathsf{\theta }}_{\mathrm{i}+1}^{\mathrm{t}}$, ${\mathsf{\theta }}_{\mathrm{i}}^{\mathrm{t}}$, ${\mathsf{\theta }}_{\mathrm{w}\mathrm{i}+1}$, and ${\mathsf{\theta }}_{\mathrm{w}\mathrm{i}}$ are soil moisture and wilting point of layer i + 1 and layer i at time t (cm³·cm⁻³); h_i and h_i+1 are the thicknesses of layer i + 1 and layer i (cm).

2.2.4. Root Distribution

Root distribution was determined according to the researches of Gale and Grigal [45] and Jackson et al. [46] (Equation (9)).

$$\mathrm{Y}\left(\mathrm{z}\right)=1-{\mathsf{\beta }}^{\mathrm{z}}$$

(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.

2.2.5. Root Water Uptake

The Feddes et al. [47] model was used to determine root water uptake (RWU) (Equation (10)).

$$\mathrm{RWU}=\frac{\mathsf{\alpha }\left(\mathrm{h}\right)}{{\displaystyle {\int }_0^{\mathrm{L}}\mathsf{\alpha }\left(\mathrm{h}\right)\mathrm{dz}}}{\mathrm{T}}_{\mathrm{p}}$$

(10)

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)).

$$\mathsf{\alpha }(\mathrm{h})=\left\{\begin{array}{ccc}\frac{{\mathrm{h}}_1}{\mathrm{h}}& ,\hfill & \mathrm{h}\ge {\mathrm{h}}_1\hfill \\ 1& ,\hfill & {\mathrm{h}}_2\le \mathrm{h}<{\mathrm{h}}_1\hfill \\ \frac{\mathrm{h}-{\mathrm{h}}_3}{{\mathrm{h}}_2-{\mathrm{h}}_3}& ,\hfill & {\mathrm{h}}_3\le \mathrm{h}<{\mathrm{h}}_2\hfill \\ 0& ,\hfill & \mathrm{h}<{\mathrm{h}}_3\hfill \end{array}\right\}$$

(11)

In Equation (11), h is the soil water potential (cm). h₁, h₂, and h₃ 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 h₁, then RWU decreases with SWP. h₂ is the SWP when plant suffers from water stress and h₃ 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)).

$$\mathrm{f}\left(\mathsf{\theta }\right)=\{\begin{array}{lll}0& ,\hfill & \mathsf{\theta }\le {\mathsf{\theta }}_{\mathrm{wilt}}\hfill \\ \frac{\mathsf{\theta }-{\mathsf{\theta }}_{\mathrm{wilt}}}{{\mathsf{\theta }}_{\mathrm{stress}}-{\mathsf{\theta }}_{\mathrm{wilt}}}& ,\hfill & {\mathsf{\theta }}_{\mathrm{wilt}}<\mathsf{\theta }<{\mathsf{\theta }}_{\mathrm{stress}}\hfill \\ 1& ,\hfill & \mathsf{\theta }>{\mathsf{\theta }}_{\mathrm{stress}}\hfill \end{array}$$

(12)

In Equation (12), θ is soil moisture (cm³·cm⁻³); θ_wilt is the wilting point expressed by moisture (cm³·cm⁻³); θ_stress is the soil moisture when plant is under water stress (cm³·cm⁻³). The details about parameters in Equation (12) are shown in

Table 3. List of Feddes model parameters.

Parameter	Units	Range	Value	Description	Reference
θwilt	cm3·cm−3	0.06–0.10	0.10	Wilting point	[49]
θfc	cm3·cm−3	0.32–0.42	0.39	Field capacity	[49]
θstress	cm3·cm−3	(0.45–0.9)·θfc	0.6·θfc	Stress point	[32]

. 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).

$$\mathrm{RWU}={\mathrm{T}}_{\mathrm{p}}\cdot \mathrm{f}\left(\mathsf{\theta }\right)\cdot \mathrm{Y}\left(\mathrm{z}\right)$$

(13)

2.2.6. Evapotranspiration and Crop Coefficients (K_c)

Reference evapotranspiration (ET₀) was calculated based on Penman–Monteith equations [16] (Equation (14)).

$$\mathrm{E}{\mathrm{T}}_0=\frac{0.408\mathrm{\Delta }\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+\mathsf{\gamma }\frac{900}{\mathrm{T}+273}{\mathrm{u}}_2({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}})}{\mathrm{\Delta }+\mathsf{\gamma }\left(1+0.34{\mathrm{u}}_2\right)}$$

(14)

where ET₀ is the reference evapotranspiration (mm·d⁻¹); R_n is net radiation at the crop surface (MJ·m⁻²·d⁻¹); G is soil heat flux density (MJ·m⁻²·d⁻¹); T is mean daily air temperature at 2-m height (°C); u₂ 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); Δ is slope vapor pressure curve (kPa·°C⁻¹); and γ is psychrometric constant (kPa·°C⁻¹).

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)).

$$\mathrm{E}{\mathrm{T}}_{\mathrm{c}}={\mathrm{K}}_{\mathrm{c}}·\mathrm{E}{\mathrm{T}}_0={\mathrm{E}}_{\mathrm{p}}+{\mathrm{T}}_{\mathrm{p}}$$

(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).

$${\mathrm{E}}_{\mathrm{p}}=0.1\cdot \mathrm{E}{\mathrm{T}}_{\mathrm{c}}$$

(16)

Then,

$${\mathrm{T}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}·\mathrm{E}{\mathrm{T}}_0-{\mathrm{E}}_{\mathrm{p}}$$

(17)

Sunflower growth periods were divided into four stages (noted as day after sowing (DAS)), initial stage (DAS: 1–36), rapid growth stage (DAS: 37–57), middle stage (DAS: 58–90), and mature stage (DAS: 90–109) according to the study of Du et al. [25] and Allen et al. [16]. Initial K_c values for each stage were 0.3, 0.75, 1.2, and 0.35, respectively [16].

2.2.7. 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., Table 2 and Table 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.

2.3. Statistical Analysis

The determination coefficient (R², Equation (18)) and the root-mean-square error (RMSE, Equation (19)) were used to evaluate the model performance.

$${\mathrm{R}}^2={\left[\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}-{\overline{\mathrm{Y}}}_{\mathrm{i}}^{\mathrm{obs}}\right)\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}-{\overline{\mathrm{Y}}}_{\mathrm{i}}^{\mathrm{sim}}\right)}}{\sqrt{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}-{\overline{\mathrm{Y}}}_{\mathrm{i}}^{\mathrm{obs}}\right)}^2}}\sqrt{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}-{\overline{\mathrm{Y}}}_{\mathrm{i}}^{\mathrm{sim}}\right)}^2}}}\right]}^2$$

(18)

$$\mathrm{RMSE}=\sqrt{\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}-{\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}\right)}^2}}{\mathrm{n}}}$$

(19)

where Y_i^obs is the ith observed value, Y_i^sim is the ith simulated value, and $\overline{{\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}}$ and $\overline{{\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}}$ are the means of the observed and simulated values, respectively.

3. Results

3.1. 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 ET₀ values in 2012 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.

3.2. 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., R² 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, R² 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 cm³·cm⁻³ respectively.

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.

3.3. 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 = 3.3–18.5 dS·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)).

$${\mathrm{K}}_{\mathrm{c}1}=0.0059\mathrm{E}{\mathrm{C}}_{\mathrm{e}}+0.2401$$

(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 0.11–0.73 for 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, R² 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 cm³·cm⁻³, respectively.

4. Discussion

4.1. 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 (Figure 4 and Figure 7, R² > 0.56, RMSE < 0.1 cm³·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.

4.2. 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 (R² = 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. Comparison of crop coefficients/K_c between different researchers and our model in moderately salinized soil (EC_e = 9.44 dS·m⁻¹).

Item	Initial Stage	Rapid Growth Stage	Middle Stage	Mature Stage	R2	Location	Reference
1	0.52	1.1	1.32	0.41	0.55	Karnal, India (29°43′ N, 76°58′ E)	[20]
2	0.697	0.751	0.804	0.35	0.55	Dengkou County, Hetao (40°24′ N, 107°02′ E)	[60]
3	0.194	0.779	1.26	0.315	0.67	Linhe County, Hetao (40°43′ N, 76°58′ E)	[25]
4	0.14	—	1.08	0.24	0.66	Yangchang, Hetao (40°48′ N, 107°05′ E)	[56]
5	0.35	—	1–1.15	0.35	0.64	California, US	[16]
6	Equation (20)	0.659	1.156	0.324	0.7	Wuyuan County, Hetao (41°04′ N, 108°00′ E)	WFSP model

). 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 R² 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 (R² = 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.

5. 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.