Development of a simulation model for sugar beet growth under water and nitrogen deficiency

Abstract

Sustainable and profitable production of sugar beet requires information on knowing the effect of applied water and nitrogen (N), which is typically provided by simulation models. Considering limited information, it is essential to develop simulation models that can address irrigation water and N deficiencies for sugar beet production. The sugar beet simulation model (SSM) was developed for the simulation of storage root dry matter, plant-top dry matter, and the yield of white sugar under different applied N fertilizer and irrigation. The SSM simulates water, N, and soil heat flux under unsteady state conditions by applying numerical analysis in the root zone. Dry matter production and partitioning into plant top and root dry matter for different plant growth stages were simulated based on intercepted solar radiation, air temperature, and the amounts of N uptake. 2 years of field experiments data (2013 and 2014) were used to conduct model calibration and validation, respectively. In 2013, irrigation treatments were 130, 100, 85, 75, 66, and 44 percent of full irrigation, and N treatments were 0, 60, 120, and 180 kg N ha⁻¹ in the form of urea under line source sprinkler irrigation system. In 2014, irrigation treatments were 120, 100, 80, and 60 percent of full irrigation and N treatments were 0, 60, 120, 180, and 240 kg N ha⁻¹ in the form of urea under furrow irrigation system. Dry matter production was simulated according to radiation use efficiency (RUE) and was calibrated using the plant top and storage root dry matter production of treatment without water and N deficiency, which was 0.97 (g MJ⁻¹). The normalized root mean squared error (NRMSE) criterion was used to compare the simulation capability of the model with measured field data. White sugar yield, plant leaf area index, plant top dry matter, and storage root dry matter at harvest time and during the growing season showed acceptable NRMSE values. The values of the produced white sugar yield were simulated with NRMSE of 7.8% and 14.2% in calibration and validation data, respectively. The new and relevant information provided by the SSM was quite significant as it proved that possibility of management sugar beet under irrigation water and N deficiencies.

Appendices

Appendix 1

Description of the SSM model parameters and their default values.

Soil
Ks	Saturated hydraulic conductivity of soil (m s−1)	5.85 × 10–6
$n$	Coefficient of van Genuchten (1980) equation	1.386
$\alpha$	Coefficient of van Genuchten (1980) equation (m−1)	1.371
∆z	Soil layer thickness (m)	0.05
θr	Residual soil water content (m3 m−3)	0.1
θs	Saturated soil water content (m3 m−3)	0.415
frw	The ratio of wetted area	1.0
zr	Maximum soil depth (m)	1.8
Crop
rl	Stomatal resistance of well-illuminated leave (s m−1)	73
RootNpmax	Maximum concentration of nitrogen in storage root (kg kg−1)	Equation (60)
RootNpmin	Minimum concentration of nitrogen in storage root (kg kg−1)	Equation (61)
RUE	Radiation use efficiency (g MJ−1)	0.97
Sh	Extinction coefficient	0.58
TopNpmax	Maximum concentration of nitrogen in shoot (kg kg−1)	Equation (58)
TopNpmin	Minimum concentration of nitrogen in shoot (kg kg−1)	Equation (59)
Germination
RootD0	The sowing depth (m)	0.03
${ \alpha }_{1}\mathrm{and} {\alpha }_{2}$	Coefficients of Beta function	0.89
ß	Coefficient of Beta function	0.56
μ1	Coefficient of Beta function	− 4.8
μ2	Coefficient of Beta function	− 8.1
θbase	Soil water in the base conditions (m3m−3)	0.29
Tb	Base air temperature (℃)	2.6
Tc	Critical air temperature (℃)	30.0
Meteorological
$q$	A parameter that determines the shape of the temperature factor	1.2
Tn	Minimum air temperature for photosynthesis ($^\circ{\rm C}$)	0.0
Top	Temperature at which photosynthesis is maximum (℃)	24.5
Tx	Maximum air temperature for photosynthesis ($^\circ{\rm C}$)	45.0
A	Constant coefficient of Angstrom equation (Eq. 29)	0.31
B	Constant coefficient of Angstrom (Eq. 29)	0.55
Φ	Latitude (R)	0.521 $\mathrm{Rad}$
Lz	Longitude (R)	0.908 $\mathrm{Rad}$

Appendix 2

Root distribution function

The value of $\Gamma \left(z,t\right)$ in Eq. (5) was defined by Mathur and Rao (1999) as Eq. (6). In sugar beet, with potential transpiration, the absorption pattern of water was shown by Morillo-Velarde (2010), as Fig. 

Fig. 18

The values of measured $\Gamma \left( {z,t} \right)*0.3$ by Morillo-Velarde (2010) at different soil depths (a) and its estimated values using Eq. (6, $\frac{2.0}{{z_{{\text{r}}} }}\alpha_{{\text{r}}} \left( h \right)\left( {1 - \frac{z}{{z_{{\text{r}}} }}} \right)$ × 0.3) and Eq. (A1, $\frac{2.5}{{z_{{\text{r}}} }}\alpha_{{\text{r}}} \left( h \right)\left( {1 - \frac{z}{{z_{{\text{r}}} }}} \right)^{1.5}$ × 0.3)

18. This pattern was modified using the regression method for actual transpiration as follows:

$$\Gamma \left( {z,t} \right) = \frac{2.5}{{z_{r} }}\alpha_{r} \left( h \right)\left( {1 - \frac{z}{{z_{r} }}} \right)^{1.5}$$

(63)

As Fig. 18 shows, irrigated sugar beet preferentially extracts water near the soil surface (Brown et al. 1987; Draycott 2008; Vamerali et al. 2009), hence, in this research, we used Eq. (63) for estimating the value of $\Gamma \left( {z,t} \right)$.