Estimation of Sugar Beet Yield and its Dry Matter Partitioning Under Different Irrigation and Nitrogen Levels

In this study, a simple logistic model was developed for estimating total dry matter of sugar beet under different irrigation and nitrogen levels. The experiment was conducted using line source sprinkler irrigation in 2013 and furrow irrigation in 2014. Irrigation treatments were from 44% to 130% of full irrigation and applied nitrogen treatments ranged from 0 to 240 kg N ha. Results showed that the model was more accurate in predicting total dry matter at harvest date with the Normalized Root Mean Square Error (NRMSE) amounting to almost 10 percent. After total dry matter estimation, a model was needed for dry matter partitioning between different organs of sugar beet. To achieve this goal, another logistic model was developed and was compared with three revised models. Finally, white sugar content of root dry matter was estimated using a quadratic equation as a function of applied water and nitrogen. Validation results indicated that total and root dry matters, and white sugar yield were estimated fairly well. Results showed that excessive water had negative effects on total dry matter and root dry matter. Also, excessive nitrogen affected root dry matter negatively too, but even the excess had positive effects on total dry matter. In contrast to common belief, our results showed that drought stress reduced both ratios of root to leaf, and root to shoot dry matter.


Introduction
Sugar beet (Beta vulgaris L.) is a biennial plant and is an economically important crop for its profound use in the production of sugar.It is harvested in the growing season of the first year of growth if it is to be used for sugar production, but will be kept in the ground until the second year if to be used for seed production.The plant has a large storage root that contains 14% to 20% sucrose in its fresh mass (Steduto, 2012).Its water management is of prime importance because of its high water requirement, especially in arid and semi-arid countries like Iran.Its water requirements depend on several factors such as the climate conditions, irrigation method, sowing date, water quality and soil properties.
The anatomy of sugar beet is divided into several parts such as: tap root (storage root), fibrous roots, blades and petioles.Total dry matter is considered to be comprised of these parts (Lukaszewska & Sliwinska, 2007).The partitioning of dry matter between the crop components is important in crop modeling.The patterns that are used for allocating the dry matter to the crop components have always been regarded as one of the most important challenges in crop modeling, since it plays an important role in the estimation of yield.Some models have been proposed to describe the term "assimilate partitioning" within the sugar beet plant (Webb et al., 1997).There have been descriptions of a dynamic model, specifically for partitioning the occurring assimilates between the shoot, storage root and fibrous roots.These were derived from observations dealing with the effect of soil nitrogen on crop growth.Werker et al. (1999) proposed allometric and logarithmic models which examine simple relationships between the sugar yield, total dry matter and soil nitrogen in rain-fed and irrigated sugar beet Dry matter partitioning is significantly affected by several environmental variables, i.e. soil water, soil nitrogen, weather conditions and genotype.In many cases, nitrogen is a limiting factor, because few soils contain sufficient amounts of nitrogen in a form available for the crop to absorb (Draycott, 2008).Water is vital for sugar beet growth, especially in arid regions such as Iran (Hassanli et al., 2010).It can be construed that the most important elements for sugar beet growth are water and nitrogen.
It is obvious that achieving efficient models for dry matter partitioning depends on the accurate estimation of total dry matter.Several models are proposed for sugar beet that can estimate the total dry matter.These models include AquaCrop (Stricevic et al., 2011), CERES (Baey et al., 2014;Jones et al., 1986;leviel, 2000), Greenlab (De Reffye & Hu, 2003), SUBEMOpo (Vandendriessche, 2000a;Vandendriessche, 2000b), the Broom's Barn sugar beet growth model (Qi et al., 2005) and a model for water and salt stress condition (Sepaskhah et al., 2006).Of all these mentioned, few consider different scenarios for irrigation and nitrogen conditions.On the other hand, mechanistic models need various ranges of inputs (Baey et al., 2014;Mahbod et al., 2015).This gives rise to some researchers becoming interested in empirical models.One of the practical approaches is the logistic model.Stagnari et al. (2014) proposed a logistic model for the estimation of red beet dry matter, its root diameter and leaf dry weight under water stress conditions.Another logistic model has been proposed by Sepaskhah et al. (2011), which can be applied to predict the yield of maize under specific managements of water and nitrogen.
The objectives of this study are (i) to develop a logistic model for predicting the total dry matter of sugar beet by considering the affected of water and nitrogen application, (ii) to validate the developed model along with another four selected models for the estimation of dry matter partitioning and sugar yield under different conditions of water supply and nitrogen availability.

Field and Climate Description
This study was conducted during the growing seasons in 2013 and 2014 at the Experimental Station of Agricultural College, Shiraz University, at 29 • 56΄_N, 52 • 02΄_E and at 1810 m above sea level, in the southwest of Iran, where the climate is semi-arid, with an annually average air temperature of 13.4 • C, a relative humidity of 52.2%, and a precipitation value of 387 mm.The typical soil at the experimental site is silt-clay loam, which is consistent down to 1.2 m beneath the ground surface (Table 1).The chemical properties of the irrigation water are shown in Table 2. Meteorological data were obtained from the weather station at the Agricultural College, located near the experimental field.Figure 1 shows the maximum and minimum of daily air temperatures (Tmax and Tmin), the mean daily relative humidity (RHavg) and the daily reference evapotranspiration (ETo) during the growing seasons in 2013 and 2014.The reference evapotranspiration (ETo) was calculated by using a modified FAO-Penman-Monteith method (Razzaghi & Sepaskhah, 2012).

Treatm
The exper nitrogen fe (I5) and 44 In the first thinned on via sprinkl area of eac ha -1 .Nitro order to m Figure 2.

Description of the Logistic Model
A logistic model was fitted against GDD for the estimation of total dry matter as follows: where W is the total dry matter (Mg ha -1 ), W m is the maximum total dry matter (Mg ha -1 ), A is the values corresponding to the maximum total dry weight, B is a parameter describing the rate of the increases in growth and GDD is the accumulative growing degree days that stands for elapse time.
The values of W m , A and B pertained to the applied water and nitrogen as: where * = , * = , IR is the amount of water being irrigated, ET o is the reference evapotranspiration, N is the amount of applied and soil residual nitrogen and N r is the soil residual and fertilizer nitrogen for no deficiency (kg ha -1 ).The optimal values of W 1 to W 6 , A 1 to A 6 and B 1 to B 6 were estimated using the multiple linear regression method.
It is better to consider the amount of total nitrogen as the amount of residual soil nitrogen plus the amount of nitrogen fertilizer.In the present study, we consider this point of view accordingly: Where N s is the residual soil nitrogen (kg ha -1 ), N f is the amount of applied nitrogen (kg ha -1 ) and N fr is the nitrogen fertilizer amount for no deficiency (kg ha -1 ).After estimating the total dry matter, a dry matter partitioning model is needed to estimate the dry matter weights of the root and shoot.Therefore, another logistic model is developed in the present study in order to estimate the root dry matter.Root dry matter is calculated when the total dry matter is multiplied by the dry matter partition coefficient (P r ): where R is the root dry matter, S is the shoot dry matter, P r is the fraction of the total dry matter which is considered to be the storage root, P m is the maximum fraction of root dry matter, a is the values corresponding to the maximum fraction of root dry matter and b is a parameter which describes the increase in growth.Optimal values of P 1 to P 6 , α 1 to α 6 and b 1 to b 6 were estimated using the multiple linear regression method.

Models that Describe the Dry Matter Partitioning
In this study, three models were used to compare the validity of the logistic model for dry matter partitioning.The first models were proposed by Webb et al. (1997), while the second and third were proposed by Werker et al. (1999).Meanwhile, (Webb et al., 1997) described a quadratic model for the partitioning of assimilates between the shoot, storage root and fibrous roots, which was estimated based on observations regarding the effect of soil nitrogen on crop growth as follows: Where Q s , Q k and Q r are the partitioning of assimilates to the shoot, storage root and fibrous root, respectively; P is a partitioning variable being described by using the following logistic function: Where t is time (days from January 1); α, σ and μ are constant parameters, while β illustrates the nitrogen content in the soil.The optimal values of α, σ, μ and β were obtained using the solver menu of Excel as α = 0.48, σ = 0.364 (d -1 ), μ = 209.52(d) and β = 0.15, 0.18, 0.22, 0.23, 0.24, 0.26 and 0.27 for different nitrogen applications of 0, 30, 60, 90, 120, 150 and 180 (kg N ha -1 ), respectively.Werker et al. (1999) proposed simple relationships between sugar yield, total dry matter and soil nitrogen under rain-fed and irrigated conditions.They proposed two models for the dry matter partitioning, the first of which was named the allometric growth function and the second was named a logarithmic model.The first function is based on the assumption that the relative growth rates of plant components are proportional to each other and remain constant.After solving some equations, the allometric growth function was proposed as follows: where W is the total dry matter (W=Y+G), Y is the storage dry matter (sugar), G is the structural dry matter, W 0 is the initial total dry matter, Y 0 is the initial storage dry matter (sugar), and α 0 is the initial partitioning fraction of total dry matter set against Y.
Another model proposed by Werker et al. (1999) is a logarithmic model.They simplified the model with some assumptions, and finally presented the model as follows: Where k is a constant parameter that shows the speed of the partitioning function (g -1 m 2 ).The effects of drought and nitrogen deficiency were estimated by two separate equations.The effect of drought was estimated for the purpose of harvesting the dry matter and evaluating the effect of nitrogen on the partitioning.These were analyzed by allowing the parameter k to vary with respect to the nitrogen supply.
As it was expected, these three models for dry matter partitioning could not reasonably estimate the dry matter partitioning under different water and nitrogen conditions.Therefore, they were modified in the present study so as to consider the water and nitrogen being used therein.

The Revised Quadratic Model
As mentioned earlier, in the alternative model constructed by Webb et al. (1997), the amount of water for irrigation was not to be considered in the dry matter partitioning and α was a fixed parameter, while β showed the effect of nitrogen content in the soil.But in this study, we had α and β as being related to the nitrogen added to the soil and the irrigated water in dimensionless formulas as follows: ) Where σ and μ are constant parameters, while α and β show the effects of water and nitrogen.Optimal values of σ, μ, α 1 to α 6 and β 1 to β 6 were estimated using a multiple linear regression method.

The Revised Allometric Model
The second model was extracted from the allometric growth function previously described according to Equation 15.In this model, R represents the storage root dry matter, S is the shoot dry matter, λ is the initial partitioning fraction of total dry matter to the storage root (R) as follows: ) Optimal values of λ 1 to λ 6 were estimated using the multiple linear regression method.

The Revised Logarithmic Model
The third model is derived from Equation 16.In this model, K is considered to indicate the effects of drought and nitrogen on dry matter partitioning --the dry matter that is divided between the root and shoot.The equation is as follows: The optimal values of k 1 to k 6 were estimated using the multiple linear regression method.

Sugar Yield Estimation
White sugar yield is estimated when the root dry matter is multiplied by the sugar content (Sc) as a function of IR * and N * as follows: Where SY is sugar yield, Sc 1 to Sc 5 are constant coefficient and their values are estimated using the multiple linear regression method.All the equations were calibrated via experimental data of the second year and were validated via experimental data of the first year.

Criteria for Evaluating the Models
Part of the assessments included a process to evaluate the results of the models in order to predict the fractions of dry matter allocation to the root and shoot.Accordingly, three statistical parameters were defined.These are the coefficient of determination (R 2 ), the Normalized Root Mean Square Error (NRMSE) (Loague & Green, 1991) and the index of agreement Willmott (1982).The parameters comprise the following equations: Where P i and O i are the i th estimated and measured values, respectively, O represents the mean measured values, ′ = − , ′ = − , and n is the total number of observations.The normalized root mean square error (NRMSE) gives information on the relative error based on the comparison between the measured and predicted values.The simulation is considered excellent, good, fair and poor if the values of NRMSE are, respectively, less than 0.1, greater than 0.1 but less than 0.2, greater than 0.2 but less than 0.3, and greater than 0.3 (Jamieson et al., 1991).
According to the d-index, values that are closer to one indicate a better agreement between the two variables that are being compared.The index (d) is intended to be a descriptive measure, and it is both a relative and a bounded measure which can be widely applied in order to make cross-comparisons between models (Willmott, 1982).

Results and Conclusion
The precipitation during the growing periods in 2013 and 2014 were 75 mm and 26 mm, respectively, and the relative humidity was greater during the first growing season.The air temperature averaged nearly the same during the two years.
The root dry matter, relating to the different irrigation levels and nitrogen supplements of fertilizer, resulted in different values (Tables 3 & 4).The amount of yield was observed to increase parallelly to increasing irrigation; however, in some treatments, the excessive supply of water served to reduce the root dry matter due to nitrogen leaching.
In the second season, the static (I 3 ) and dynamic (I 4 ) treatments had no considerable difference in the root dry matter.In the dynamic treatment, a severe drought occurred in the late period of the growing season, hence, soil water content of the root zone declined and the root dry matter portion decreased in this period.Moreover, in the dynamic treatment, greater irrigation occurred in the early and middle periods of the growing season, as compared to the static treatment, hence, dry matter production was increased.In the static treatment, the occurrence of early drought caused the root system and canopy cover to shrink and reduced solar radiation interception and water uptake, compared to the occurrence of late drought (Brown et al., 1987).

Estima
The param follows: The results Figure 5. observed a of NRMSE in estimat estimated treatments

White Sugar Yield Estimation
The sugar yield is estimated using the multiplication of root dry matter and its sugar content (Sc) (Equations 21 and 22).The value of Sc is estimated as a function of IR * and N * as follows: = 0.361 + 0.301 ( * ) − 0.111 ( * ) − 0.021 ( * ) − 0.005 ( * × * ) = 0.89, = 20 (26) The measured and predicted sugar yield at 2013 (calibration) and 2014 (validation) are compared with the measured values in Figure 7 with good accuracy.Although the measured data are scattered along the 1:1 line, the slope of regression line is very close to one and NRMSE is less than 0.1.However, using nitrogen causes decreasing root sugar content, but increasing root dry matter causes increasing in white sugar yield.Also excess applied water decrease SP.
The relationship between root sugar content (Sc) with IR * and N * is shown in Figure 8 that shows with increasing in N * , sugar content of the root is decreased.This Figure also shows that with increasing IR * , the value of SP increases and.
The decreasing root sugar content with increasing nitrogen supply agrees with Milford and Watson (1971).Several experiments have been conducted to study the effect of water stress on sugar content, but still, skepticism persists among specialists.Although there is a common belief that water stress increase sugar content, results of some researches (Kiymaz & Ertek, 2015;Yonts et al., 2003) do not show significant effect of water stress on sugar content.In some other researches, the results show increasing root sugar content with increasing applied water (Cole, 1976;Woolley, 1956).It seems that the effect of water cannot be easily separated from the effect of nitrogen.Sugar content may be improved by applying less irrigation and reducing leached N, where excess water leaches N from the soil in the growing season (Hills, 1990).

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Discussion
On the one hand, the logistic model can be a good candidate if the production of root dry matter is of prime importance.On the other hand, when the objective turns to harvesting a more a more proliferative shoot dry matter, the logistic and revised quadratic models become more reasonable.The prediction of shoot dry matter can be useful in crop modeling, especially for estimating the leaf area index (LAI).
The results showed that fertilizers with excessive nitrogen caused increases in the shoot to root ratio as Milford et al. (1985) noted the general concept that nitrogen fertilizers encouraged the growth of shoot, possibly more than any other treatment.The effect of nitrogen on shoot growth was more prominent than the effect on root production, as Draycott (2008) indicated that crops growing on nitrogen-rich soils participate in the majority of their biomass to the growth of tops, in which case the root and sugar yield dwindled.
Moreover, logistic model shows that excessive irrigation could reduce the total dry matter and root dry matter.This may happen due to the leaching of nitrate (Gholamhoseini et al., 2013;Jégo et al., 2008).
Results showed that drought stress made a negative effect on the ratio of root to shoot.This implied that when water is scarce, the crop tends not to send dry matter to the root, but tends to send it to the shoot.

Figure
Figure 1.D reference

Figure
Figure 5 during Figure 8

Table 1 .
Physical and chemical properties of soil at the experimental site

Table 6 .
Effect of water scarcity on the root to shoot dry matter ratio and root to foliage dry matter ratio (Results pertain to the post-maturity stage of the plant)