Developing a nitrogen fertilizer management model for wheat in calcareous soils using the critical nitrogen dilution curve

The critical nitrogen (N) dilution curve, which expresses whole-plant critical N concentration as a function of shoot biomass, can be used as a N management diagnostic tool for cereals. The objectives of this research were to develop a critical N dilution curve for wheat grown in calcareous soils and to formulate a model for estimating N fertilizer requirement of wheat crop at different growth stages. Six N fertilization rates (0–250 kg N ha−1) were used to induce variability in plant growth throughout six site-years (three locations at West Delta of Egypt and two seasons [2020/21-2021/22]). Aboveground shoot biomass (W; Mg DM [dry matter] ha−1) and N concentration (Nc; g kg−1 DM) were determined on five sampling dates during the growing season. A critical N dilution curve was developed as: Nc=50.141W-0.424\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{\mathrm{c}}=50.141 {\mathrm{W}}^{-0.424}$$\end{document}. The Nc dilution curve was then used to develop a N fertilizer topdressing strategy. The study relied on N nutrition index inferred from the Nc based on N uptake, and instead of relying on a single N recovery efficiency coefficient, a variable N recovery efficiency was developed. This approach increased the hypothetical N requirements at low N application rates while decreased requirements at high N application rates, implying that the Nc dilution curve can be used successfully to estimate the rates of supplemental N application. The developed strategy will provide a solid basis for precisely managing N fertilizer, though challenge ahead at the farm level will be in determining the actual shoot biomass and N concentration.


Introduction
Nitrogen (N) is crucial to crop production since it is required for photosynthesis-driven energy creation and plant growth. High yield levels of wheat (Triticum aestivum L.) can be achieved only through accumulation of more substantial aboveground dry matter, whereas adequate N absorption is essential for dry matter accumulation (Damisch and Wiberg 1991;Song et al. 2016). Excessive N applications, on the other hand, result in not only reduced yield and quality, but also a significant loss of N fertilizer, resulting in greater production costs and environmental pollution (Raun and Johnson 1999;Fageria and Baligar 2005;Bijay-Singh 2018;Bijay-Singh and Craswell 2021). The global N use efficiency of cereal crops 1 3 Vol:. (1234567890) has remained alarmingly low at around 42% (Zhang et al. 2015), causing a variety of detrimental effects. Wheat crop used 22.8% of total fertilizer N consumption in Egypt (Heffer et al. 2017), indicating that considerable amounts of N are lost from the soil to the environment.
The future of N management is unclear (Lemaire et al. 2019), since historical patterns show considerable differences in N application and N use efficiency among cropping systems (Dobermann and Cassman 2005;Bijay-Singh 2022). Because of variances in N application and crop capacity to consume N, some cropping systems have excess N while others have a deficiency of N Bouwman et al. 2013). The critical value approach, diagnosis and recommendation integrated system, and compositional nutrient diagnosis are some diagnostic approaches that have been developed to evaluate the appropriateness of N supply to N demand of a crop (Bates 1971;Walworth and Sumner 1987;Parent and Dafir 1992). However, being focused on estimating N in a specific organ of the plant during a particular growth stage, these approaches are greatly depended upon phenological phases of the crop. Also, these approaches do not account for the dynamics of N in the soil-plant system at various stages of crop growth. Therefore, prediction of N status which can assist farmers in timely altering N fertilizer topdressing strategy is fundamental for improving N management (Cassman et al. 2003;Diacono et al. 2013;Bijay-Singh and Ali 2020;Ali et al. 2020).
A crop diagnostic approach based on the allometry between the dynamics of N concentration and biomass accumulation in crops is the critical N (Nc) dilution curve hypothesis. The Nc is the minimum N concentration required for maximum crop growth rate (Ulrich 1952). The concept of the N dilution curve is based on the notion that plant N concentration declines during the course of the growth cycle even when there is an ample supply of N. As illustrated below, Lemaire et al. (1984) described the Nc as a negative power function known as the "dilution curve": where N c is the total N concentration in shoot expressed in g kg −1 DM (dry matter), W is the total shoot biomass expressed in Mg DM ha −1 , and a N c = aW −b and b are the model's coefficients. For most cereal crops including wheat, rice (Oryza sativa L.), and maize (Zea mays L.), the Nc dilution curves have been developed in different parts of the world (Justes et al. 1994;Colnenne et al. 1998;Plénet and Lemaire 2000;Herrmann and Taube 2004;Li et al. 2012;Ata-Ul-Karim et al. 2013;Zhao et al. 2017;Zhang et al. 2020). The Nc dilution curve can be utilized to generate its N nutrition index (NNI), a useful function that has been used to successfully assess actual crop yield, quality, and N requirement (NR) (Ziadi et al. 2010;Ata-Ul-Karim et al. 2017;Wang et al. 2020). Greenwood et al. (1990) suggested two broad Nc-shoot biomass relationships: one for C 3 species (a = 57.0 and b = -0.50) and one for C 4 species (a = 41.0 and b = -0.50). Nonetheless, according to Lemaire and Gastal (1997), each species has its own critical N dilution curve. In wheat, the parameters for this allometric function were estimated by Lemaire and Gasal (1997), Ziadi et al. (2010), and Yue et al. (2012) to be a = 48 and b = -0.34, a = 38.8 and b = -0.57, and a = 41.5 and b = -0.38, respectively. Numerous studies have demonstrated that due to variable histological, morphological, and eco-physiological traits, the parameters of the dilution curves vary among different crops. In addition, variations in the N c curve across species (Justes et al. 1994;Bélanger et al. 2001;Du et al. 2020;Fabini et al. 2020;Wang et al. 2020) and between experimental sites have also been frequently observed (Katsura et al. 2010;Wang et al. 2020). Several recent studies have, in fact, suggested that comparing dilution curves developed at different locations without understanding the uncertainty surrounding the values of the critical parameters of the curves is risky (Makowski et al. 2020;Yao et al. 2021). To the best of our knowledge, no comparable research to establish or validate these parameters in Egypt have been carried out.
Farmers in the West Delta of Egypt and other comparable places have a tendency to apply more N fertilizer than is necessary for wheat due to the lack of N status diagnostic tools. Farmers would considerably benefit from an efficient indicator capable of identifying deficiency or excess N in order to optimize N fertilization and lower the environmental hazards, especially given the substantial losses of N fertilizer in calcareous soils. The objectives of the present study were: (1) to develop and validate a critical N dilution curve for wheat in calcareous soils of Egypt; (2) to determine whether it would be feasible to estimate the level of NNI in wheat using the established critical N dilution curve; and (3) to assess the possibility of using the curve to estimate NR at different growth stages of wheat.

Site description
A field experiment in calcareous soils was carried out at three sites in West Delta of Egypt (El-Tahrir, Bangar El-Sokar, and El-Nobaria) over two wheat seasons (2020/21 and 2021/22). The average annual rainfall in this area is about 75 mm and most of it falls during the growing season of wheat in winter. The average temperature fluctuated between 10 and 20 °C during winter. Before sowing of wheat, soil samples from 0 to 0.15 m depth were collected from all experimental sites and analysed for various properties (Table 1). Soil texture was measured using the pipette method (Page et al. 1982). Soil pH and electrical conductivity (EC) were determined in saturated soil paste and extract, respectively. The Walkely and Black method, as reported by Page et al. (1982) was used to assess soil organic carbon. The total calcium carbonate content was determined using a calcimeter (Nelson 1983). The cation exchange capacity (CEC) of soil was measured using the ammonium acetate-saturation method (Page et al. 1982). According to Dahnke and Johnson (1990), available N was extracted using a 2 M potassium chloride (KCl) solution and then measured using the micro-Kjeldahl method (Bremner 1965). Available phosphorus (P) and potassium (K) were determined by extracting the soil samples with 1 M ammonium bicarbonate (NH 4 HCO 3 ) and 0.005 M DTPA (pH 7.6), respectively (Soltanpour 1991). While ascorbic acid and ammonium molybdate were used to estimate P colorimetrically in the soil extracts, K was estimated flamephotometerically.

Treatments and experimental design
The treatments included six N application rates of 0, 50, 100, 150, 200, and 250 kg N ha −1 in four equal split doses as ammonium nitrate at 0, 30, 45, and 60 days after sowing (DAS). The range of N fertilizer application rates used to cause significant variations in shoot DM and N concentration in shoot. The treatments were applied in randomized complete block design with three replications. Before sowing wheat, the experimental field was ploughed twice and divided into 15 m 2 plots. Spring wheat is the type of wheat cultivated in Egypt. Giza 171 wheat cultivar was manually sowed in early November at a sowing rate of 155 kg ha −1 and harvested in mid-April. Phosphorus and K fertilizers, weeds, and diseases were managed following the general recommendations for the region. At maturity, wheat was harvested from an area of 3 m 2 from each plot. Grain and straw yields were recorded at 12% moisture content and on dry weight basis, respectively.

Plant sampling and analysis
Whole plants were sampled from each plot from a net area of 1 m 2 at 20, 40, 55, 70, and 85 DAS, avoiding the border rows. Whole plants were cut at ground level and weighed fresh in the field. Subsamples were collected for dry matter determination and analysis of total N. At maturity, samples of both grain and straw were collected for N analysis. After drying to a consistent weight in a hot air oven set to 70 °C, all samples were powdered. After digesting the samples in an H 2 SO 4 -H 2 O 2 mixture, total N was measured using the micro-Kjeldahl method (Kalra 1998).

Data analysis
Fitting a critical N curve requires the selection of data points at which N is neither limiting shoot growth nor it is in excess. These data points represent a N rate at which shoot biomass does not significantly increase. The technique proposed by Greenwood et al. (1990) and Ata-Ul-Karim et al. (2017) for identifying these data points was employed. For each site-year and sample date, the significantly highest shoot biomass (P ≤ 0.05) produced with any rate of N fertilization as well as the related N concentration were identified and selected for further analysis. These data points were used to develop the relationship between critical N concentration and shoot biomass using an allometric function. Data points not included for defining the allometric function, were used to validate the critical N dilution curve by discriminating between the limiting and nonlimiting N conditions (Ata-Ul-Karim et al. 2017). For validation, the significant shoot biomass (P ≤ 0.10) differences higher and lower than the selected critical points were selected. Data points with significantly lower shoot biomass than the selected critical points were regarded as limiting, whereas points with significantly higher shoot biomass than the selected critical points were considered as non-limiting N conditions. For validation of the critical N dilution curve, the NNI was calculated at the Feekes 6 growth stage (55 DAS) as: where Na is the actual N concentration in the shoot biomass and Nc is the critical N concentration. Data from an independent wheat experiment, other than those used to develop the allometric function of this study, was used for this purpose. This experiment was sown in 2021/22 at site #2, using the same treatments, sampling dates, and management practices. The relative grain yield was calculated by dividing the maximum grain yield by the grain yield obtained at a certain N rate. The relationship between NNI and NNI = Na Nc relative grain yield was expressed using a quadratic function. Nitrogen requirements (kg N ha −1 ) at different growth stages of wheat in the independent experiment were determined using the equation: where NR is N requirement, Nac is the plant N accumulation under the Nc, Naa is the actual plant N accumulation at different N rates, and NRE is the N recovery efficiency. The value of NR equal to zero represents an optimal N supply, whereas NR > zero (positive values) and NR < zero (negative values) values represent the surplus and deficit N supply, respectively.
Because NRE is not same at different crop stages, a relationship between NRE and growth stage was developed using the difference method and the equation: where N uf is N uptake in the fertilized plot and N u0 is the N uptake in the unfertilized plot.
Another approach for determining NR was proposed based on the relationship between NNI and NR. The following equation was used to calculate NNI based on N uptake rather than concentration at different growth stages: where NNIu is the N nutrition index based on N uptake, Nau is the actual N uptake in the shoot biomass, and Ncu is the critical N uptake as derived from the Nc dilution curve.
Excel software (as part of the Microsoft Office program, Pullman, WA) and Statistical Product and Service Solutions (SPSS 18.0 software; SPSS Inc., Chicago, IL) were used for computations, statistical data analysis, and curve fittings.

Results
Response of wheat grain yield to increasing rate of N fertilizer Figure 1 shows the effect of N fertilizer application rates on relative grain yield of wheat averaged over six site-years. Increasing N fertilizer rate increased relative grain yields steadily until it reached a plateau at which further additions resulted in a slight decrease in grain yield. This relationship was best described by a second-degree polynomial function with an R 2 value of 0.94. By setting the first derivative dy dx = 0 revealed that N fertilizer rate to achieve maximum grain yield of wheat was 207 kg ha −1 .
Influence of N fertilizer rate on shoot dry matter and N concentration The average shoot biomass during the growing season ranged from 1.65 to 16.96 Mg DM ha −1 , depending on the N application rate and sampling date (Fig. 2). In general, independent of N fertilizer application rate, there was an increase in shoot biomass with time. However, it was apparent that shoot biomass increased gradually from 20 to 55 DAS, following which a sharp increase was observed. The N concentration decreased during the growing season (Fig. 2). Depending on the rate of N application and growth stage, N concentrations ranged from 41.0 to 15.7 g kg −1 DM.
Parameters estimation of a critical N dilution curve for wheat The criterion that shoot N declines as plant biomass increases was fulfilled by 15 points from all site-years experiments ( Table 2). Each of these points reflects a critical N concentration point for a specific shoot biomass. Using shoot biomass as the independent factor and N concentration as the dependent factor, a scatter plot was formed. When the inverse power function was employed to describe this relationship, the R 2 value was 0.94 (Fig. 3). Based on the shoot biomass, following equation was fitted to determine the critical N concentration: where N c denotes the critical N concentration in the shoot expressed in g kg −1 DM and W denotes total shoot biomass expressed in Mg DM ha −1 .

Differentiation of limiting and non-limiting N conditions
Data points that were not used to determine the parameters of the function were used to assess the suitability of the developed critical curve. These points for the various N application rates were categorized as limiting or non-limiting growing N conditions. As shown in Fig. 4, all the points labelled as limiting N growing conditions were below the developed critical curve, whereas 93% of the points labelled as non-limiting N growing conditions were above it. Although this is a preliminary validation, it indicates that the critical N dilution curve developed in this study effectively differentiates between limiting and non-limiting N growing conditions. More testing in a variety of environmental conditions, particularly with other cultivars or under different growing conditions will be needed.
Prediction of grain yield using NNI derived from the Nc dilution curve As Feekes 6 growth stage is considered to be critical for N nutrition of wheat, the Nc from the developed model at this growth stage was used to estimate NNI using data from the independent experiment on wheat Relative grain yield N fertilizer rate (kg ha -1 ) Fig. 1 Relationship between N fertilizer application rate and wheat relative grain yield averaged across the six site-years with comparable N fertilizer rates and sampling dates. Figure 5 shows the relative grain yield from this experiment plotted against the NNI at the Feekes 6 growth stage. Grain yields were gradually increased in relation to NNI until a plateau was reached (relative grain yield close to 1). The NNI at the curve's maximum point was calculated to be 1.06 according to a derivative analysis of the function. The hypothesis suggests that crops are in non-limiting N conditions when NNI values > 1.0, but NNI values < 1.0 suggest N deficiency. According to the relationship, when NNI was close to 1.06, the relative grain yield was close to 1.0, whereas when NNI was considerably lower than 1.06, the relative grain yield was reduced. As a result, the developed Nc model and inferred NNI accurately predicted relative grain yield and can thus be utilized to diagnose deficient and non-deficient N nutrition status in wheat.

Estimation of N requirements depending on the Nc dilution curve
Estimating in-season NR during wheat vegetative growth is critical for achieving high production levels as well as for maximizing N fertilizer use efficiency.
In the current study, in-season NR at different growth stages was estimated using Nc computed from the dilution curve. To eliminate bias, the Nc was estimated using data from an independent experiment on wheat that was not used to develop the Nc critical curve. Figure 6 represents the highest significant shoot biomass of the independent experiment at different times. The difference between actual N accumulation under different fertilizer N application rates and the Nc divided by the N recovery efficiency parameter provides an estimate of the amount of N required to optimize N uptake. Therefore, recovery efficiency of N fertilizer was calculated at 20, 40, 55, and 70 DAS (after the application of N fertilizer at 0, 30, 45, and 60 DAS) by difference method in the six site-years experiments used to develop the Nc model (using the 150 and 200 kg N ha −1 treatments). The difference in total N uptake between sampling times was used to calculate N recovery efficiency for a certain interval. Figure 7 shows that the average recovery efficiency at 20, 40, 55, and 70 DAS was 29.4, 39.2, 53.1, and 69.8%, respectively. This relationship was described as a linear function predicting the N recovery efficiency from number  The N requirements of wheat at various growth stages were estimated hypothetically using the Nc computed from the established equation and predicted N recovery efficiency. Figure 8 demonstrates the evolution of NR in different growth stages under different N fertilizer rates from the independent experiment. Negative values of NR indicate that the actual N accumulation is greater than the Nc accumulation, and so N application is not required. At 20 DAS, the hypothetical NR for treatments of 0, 50, 100, 150, 200, and 250 kg N ha −1 were 38.9, 34.3, 18.6, 14.1, 1.7, and -1.2 kg N ha −1 , respectively. At 40 DAS, the requirements were 53.5, 44.9, 24.2, 16.8, 3.7, and -2.0 kg N ha −1 , respectively. At 55 DAS, the NR were 60.9, 48.6, 25.8, 20.5, 12.1, and -6.0 kg N ha −1 , respectively. At 70 DAS, the requirements were 66.7, 50.5, 27.9, 22.9, 22.2, 15.5, and -16.6 kg N ha −1 , respectively. In general, wheat response to application of N fertilizer after Feekes 6 growth stage (around 55 DAS) is low (Bijay-Singh et al. 2011;Ali 2020;Ali et al. 2021), although the hypothetical N fertilizer requirement used at 70 DAS was only for comparison.
The NNIu (the ratio between actual N uptake in shoot biomass and critical N uptake based on the Nc dilution curve) divided by recovery efficiency can be computed based on N uptake using the target uptake determined from the Nc dilution curve. At different growth stages of wheat, the NR were expressed as a function of NNIu, and scatter plots were created. Inverse linear functions describing the relationships between NR and NNIu, suggested that N requirement increased as NNIu decreased (Fig. 9). When NNIu was about 1, the NR were zero, indicating an optimal N supply, and vice versa. The relationships presented in the Fig. 9 between NNIu and NR for 20, 40, 55, and 70 DAS satisfactorily explained the variation in wheat NR linearly.

Discussion
Wheat grain yield increased with increasing N fertilizer rate up to a point According to the study, the N fertilizer rate required to attain maximum wheat grain yield was 207 kg ha −1 . The general recommendation for N fertilizer for wheat grown on calcareous soils of Egypt is approximately 240 kg ha −1 , although studies on wheat in the same region have suggested that lower N fertilizer rates can be used without compromising grain yield (Ali 2020;Ali et al. 2021. Optimal N fertilizer rate for cereals is generally fixed to be 10% less than that to obtain maximum grain yield because when operating in the curvilinear portion of the second-degree response functions it requires application of large amount of N fertilizer to reach the plateau. Increasing N applications above optimum rates will result in minor increases in grain yield along with increased production costs and the possibility of negative environmental implications (Ju et al. 2009;Guo et al. 2010;Ciampitti and Vyn 2013;Bijay-Singh 2018, Bijay-Singh andCraswell 2021). For example, based on ratio of per kg grain price and cost of per kg fertilizer N, Ali and Habib (2022) calculated the economic optimal rate of N fertilizer for maize on a calcareous soil in Egypt to be 39.9 to 27.8 kg N ha −1 lower than the fertilizer N rate at maximum yield but with no significant loss in grain yield. Therefore, the current study paves the way for the development of field-specific N fertilizer management strategies that account for the spatial and temporal variability that governs optimal N fertilizer rates for wheat.
Variation in shoot dry matter and N concentration induced by varying N fertilizer rate The finding of a sharp increase in shoot biomass after 55 DAS, which coincides with the Feekes 6 growth stage, suggests that this phase is critical in wheat and requires adequate supply of N fertilizer. Zhang et al. (2019) observed similar trend in biomass accumulation and reported that leaf dry matter in wheat during Feekes stages 4-7 was more variable than other. In fact, several researchers have concluded that the Feekes 6 stage is appropriate for determining the amount of site-specific N fertilizer for wheat in order to achieve high yield while also maximizing N fertilizer use efficiency (Bijay-Singh et al. 2011;Varinderpal-Singh et al., 2017;Ali 2020;Ali et al. 2021). The concept of N dilution curves, which is based on the assumption that shoot N declines as plant biomass increases, supports the decline in N concentrations during the growth stages of wheat. Caloin and Yu (1984) and Ziadi et al. (2010) attributed this decline to a decrease in the relationship with a concurrent increase in the N fraction of structural and storage constituents.
The parameters of the developed wheat critical N dilution curve differ from those developed in other studies The biomass at the selected points was generally greater than 1 Mg DM ha −1 , as lower shoot biomass is unsuitable for developing a critical N dilution curve (Lemaire and Gasal 1997;Justes et al. 1994;Ziadi et al. 2010;Wang et al. 2020). Lemaire and Gasal (1997) explained that during these early growth stages, critical N concentration shows a constant value because of the minimal decline in Nc with increasing shoot biomass and the absence of competition for light among isolated plants. At different locations, researchers estimated the parameters for the function for wheat. These parameters were estimated by Lemaire and Gasal (1997), Ziadi et al. (2010), and Yue et al. (2012) to be a = 48 and b = -0.34, a = 38.8 and b = -0.57, and a = 41.5 and b = -0.38, respectively. In the current study, the coefficient 'a' was found to be higher than that reported in these studies. Higher values of 'a' may be associated with higher N concentrations in wheat shoots, possibly an attribute of the cultivar used in the present study. Several studies have indicated that N-efficient cultivars have a larger capacity to absorb N, resulting in a higher coefficient 'a' (Wang et al. 2017). Furthermore, Entz and Fowler (1991) found that protein yield, hence N concentration, is often higher in spring wheat (the wheat type cultivated in Egypt) than in winter wheat. The coefficient 'b', on the other hand, was higher than that reported by Lemaire and Gasal (1997) and Yue et al. (2012), but lower than that reported by Ziadi et al. (2010). Because it represents the decline in shoot N concentration with crop growth, the coefficient 'b' is dependent on N absorption relative to DM accumulation. The magnitude of 'b', according to Ma et al. (2017), is proportional to the ratio of N concentration to dry matter, with higher ratios resulting in higher 'b' values. The high 'b' value in the current study suggests that wheat growth was rapid and was strongly influenced by external N applications. Conversely, lower 'b' values indicate that the plant can extend the decline in N concentration that occurs as the biomass increases, allowing a steadier growth of the plant (Yang et al. 2015).
Wheat N requirements vary with growth stage based on the Nc dilution curve Obviously, the variable recovery efficiency developed in this study serves better than using a single value because crop development changes N uptake capacity and consequently N recovery efficiency. Reduced N recovery efficiency at 20 and 40 DAS compared to 55 and 70 DAS should be due to lower N uptake rates caused by a lack of well-developed root and shoot biomass, which obstructs efficient N uptake. The reduced N uptake at these stages prolongs the time it takes for the applied N fertilizer to be absorbed, increasing the possibility for loss through different mechanisms in calcareous soils. Jiang et al. (2017) demonstrated that during early stages of wheat growth, root expansions are slow and N absorption capacity is limited, resulting in soil retention of applied N or loss of considerable amounts. Ali (2022) also found that N uptake rate in early growth stages of wheat was significantly lower than that in later stages, and that avoiding N fertilizer application in early growth stages leads to improved N recovery efficiency. In-season NR at different growth stages was estimated using Nc computed from the dilution curve developed in this study. The approach followed in this study in estimating in-season NR during wheat vegetative growth reveals that NR increases at low N application rates and decreases at high N application rates (Fig. 8). These findings suggest that the NR across the different growth stages based on the Nc dilution curve successfully detected events of N deficiency and excess N nutrition and could be used to estimate the rates of supplemental N application at important growth stages.
The NNI, which is derived from the Nc dilution curve, has emerged as a significant indicator for determining crop N status (Lemaire et al. 2008;Ziadi et al. 2010;Li et al. 2022). The challenge was to estimate the N topdressing rate using this concept. In the present study, a N fertilizer topdressing strategy for wheat based on the Nc dilution curve and the inferred NNI based on N uptake has been demonstrated. By establishing a functional relationship between NNI and NR at key growth stages, the rate of N fertilizer topdressing has been estimated. Although similar concept has been used in different crops and at different locations (Ata- UI-Karim et al. 2017;Wang et al. 2020;Li et al. 2022), but in this study NNI is based on N uptake (NNIu), and instead of depending on a single N recovery efficiency coefficient, a series of N recovery efficiency dependent on growth stage was developed. The relationships between NNIu and NR shown in Fig. 9 for different growth stages successfully explained the variation in wheat NR. Assessing crop NNIu quickly and non-destructively is required before using it to commercial crop production (Ziadi et al. 2008;Li et al. 2022). Tools such as chlorophyll meters and reflectance sensors may be used to connect their readings with the NNIu to make quick decisions. More research, however, is required to establish these relationships and put them into practice.

Conclusions
For wheat grown in calcareous soils, a critical N dilution curve relating above ground biomass (W) and N concentration (N c ) in it ( N c = 50.141W −0.424 ) was developed. The coefficients in the equation were influenced both by nature of the wheat cultivar and application of fertilizer N. The critical N dilution curve could differentiate between wheat grown under limiting and non-limited N conditions, and the NNI computed from it was found to be related with relative grain yield of wheat. The Nc dilution curve was used to develop a topdressing strategy for N fertilizer. The strategy formulated in the present study considered NNIu inferred from the Nc based on N uptake rather than concentration, and instead of relying on a single efficiency coefficient, a variable N recovery efficiency depending on growth stage. The challenge in using this technique practically at the farm level is in determining the actual shoot biomass and N concentration, which is time consuming. Non-destructive tools including chlorophyll meters and canopy reflectance sensors can be used to address this issue by connecting their readings to NNIu of the Nc dilution curve and it should be next step forward.