# A Calculation Tool for Analyzing Nitrogen Use Efficiency in Annual and Perennial Crops

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Assessment of NUE and Its Components

^{−1}) is the N accumulation capacity from the initial perennial plant parts (e.g., seed grain in cereals, winter shoots in woody perennials) to the harvested plant parts (grain or shoot yield), and decomposed into the following three components, according to Weih et al. [6]:

_{y}is the yield N content (g N) and N

_{p}is the N content in the perennial plant parts (seed grain or winter shoots) (g N); for cereals the N

_{p}is equivalent to the N

_{s}by Weih et al. [6]; U

_{N}is the N uptake efficiency (g g

^{−1}):

_{N,y}is the yield-specific N efficiency (g g

^{−1}):

_{y}being the yield biomass; C

_{N,y}is the yield N concentration (g g

^{−1}):

_{N}and E

_{N,y}(Equations (2) and (3)) and is consequently most critical in analyzing NUE. In cereals, the main growth period can be defined as the period from the start of accelerated plant N uptake and growth in spring (BBCH 11 to 13 according to Lancashire et al. [11]) to the beginning of anthesis (BBCH 61), where major plant N uptake and growth ceases and factors other than nutrients limit plant growth and development. The corresponding phenology stages can be defined also for other crops. For example in willow, the start and end of the main growth period is defined by the bud break and bud set, respectively.

#### 2.2. Assessment of the Mean Plant N Content during the Main Growth Period (N’)

_{H}

_{1}) and the second harvest (N’

_{H}

_{2}), the mean relative N accumulation rate (R

_{N}) between the two sampling occasions is calculated according to classical growth analysis [12]:

_{H}

_{1}and t

_{H2}being the days of the first and second harvest.

_{N}represents the slope of the line connecting the plant N contents (log

_{e}transformed) between the first and second harvest. Based on that slope and a fixed point at time t

_{H}

_{1}, the constant c of the corresponding linear equation can be derived:

_{t}) can be calculated:

_{N’i}) and the time point of the phenology stage terminating the main growth period (t

_{N’f}), although no sampling has been performed at the exact dates of those stages. The mean N during the main growth period is then calculated as the mean of the plant N contents at the start and end of the main growth period, as defined by the dates of the critical phenology stages.

#### 2.3. Data Material Used for the Case Study

## 3. Results and Discussion

_{H}

_{1}), because that harvest was made when the first leaves were unfolded (BBCH 11), which here occurred on days (after planting) 9 to 11 across all varieties and treatments. This means that N’

_{H1}is similar to N’

_{i}in this experiment (Table 1, Figure 1a). In contrast, the phenology stage terminating the main growth period (BBCH 61) varied greatly across the varieties and treatments (range: day 45 to 64), and the second plant harvest was made on day 40, when most plants had not reached the critical anthesis stage (BBCH 61). This means that N’

_{H}

_{2}differed considerably from N’

_{f}for most of the plants in this experiment, and accurate values of N’

_{f}must be calculated to accommodate the genetic and treatment variation in phenology. The calculations of N’

_{i}and N’

_{f}are here illustrated with two scenarios representing the extreme values observed in the wheat experiment [9], i.e., BBCH 11 at day 9 and 11 for N’

_{i}, and BBCH 61 at day 45 and 64 for N’

_{f}(Figure 1a). Thus, the fictional variety here called “Wheat 1” represents an early-starting, fast-growing and early-flowering variety, whilst “Wheat 2” combines the characteristics late starting, slow growing and late flowering. The construction of fictional varieties is indeed based on true observations from real experiments, and an illustrative attempt to clarify the methodology proposed here.

_{i}is bud burst and the critical phenology stage for N’

_{f}is bud set [14]. Also in the willow data, the calculations of N’

_{i}and N’

_{f}are based on two scenarios with the extreme values covering the observed genetic and treatment variation in the critical phenology stages (early phenology in “Salix 1” and late phenology in “Salix 2”). Among the genotypes and treatments, bud burst varied from day (of year) 77 to 115, and the first destructive plant harvest was carried out on day 125 (Figure 1b). The second harvest was made on day 250, and bud set occurred from day 252 to 283 depending on variety and treatment. The similar slopes of the two willow scenarios indicate similar relative N accumulation rate (R

_{N}), despite great differences in total plant N pools and thus the mean N during the main growth period (N’).

**Figure 1.**The increase of total plant N content during the main growth period for two scenarios in wheat (

**a**) and willow (

**b**) (scenario description see main text); note the log

_{e}scale for the plant N pool; BBCH 11 and BBCH 61 indicate the critical phenology stages in wheat; bud burst and bud set are the corresponding stages for willow; the symbols (squares for wheat and circles for willow) indicate the plant N contents at two destructive plant harvests; data from [9] for wheat and [13,14] for willow.

**Table 1.**The calculation of the mean N content during the main growth period (N’) according to Equations (5)–(7) for two wheat and two Salix scenarios (scenario description see main text); shaded background indicates input variables, and light background indicates the calculated output; t = time (day after seeding in wheat, day of year in Salix); N’

_{i}and N’

_{f}= initial and final plant N contents with respect to the main growth period; H1 and H2 = destructive harvest 1 and 2; R

_{N}= relative N accumulation rate during the main growth period; data from [9] for wheat and [13,14] for Salix.

Variable (unit) | Wheat 1 | Wheat 2 | Salix 1 | Salix 2 |
---|---|---|---|---|

t_{N’i} (day) | 9 | 11 | 77 | 115 |

t_{N’f} (day) | 45 | 64 | 252 | 283 |

t_{H}_{1} (day) | 11 | 11 | 125 | 125 |

t_{H2} (day) | 40 | 40 | 250 | 250 |

N’_{H}_{1} (g N m^{−2}) | 0.4 | 0.3 | 4.6 | 0.9 |

N’_{H}_{2} (g N m^{−2}) | 9.1 | 1.8 | 15.9 | 3.2 |

R_{N} (day^{−1}) * | 0.1095 | 0.0681 | 0.0099 | 0.0102 |

Constant c ^{§} | −2.172 | −2.135 | 0.286 | −1.374 |

N’_{i} (g N m^{−2}) | 0.3 | 0.3 | 2.9 | 0.8 |

N’_{f} (g N m^{−2}) | 15.7 | 9.2 | 16.2 | 4.5 |

N’ (g N m^{−2}) | 8.0 | 4.7 | 9.5 | 2.6 |

N’_{H}_{1H2} (g N m^{−2}) | 4.7 | 1.0 | 10.3 | 2.1 |

_{N}values represent the slopes of the lines connecting the plant N pools in Figure 1;

^{§}cf. Equation (6).

_{H}

_{1H2}in Table 1). For example in the wheat scenarios, the R

_{N}is much greater than in the willow scenarios, which results in greater differences between the two ways of N’ calculation in the wheat. The scenario comparison reveals that any comparison of N’ (and thus the NUE components U

_{N}and E

_{N,y}; Equations (2) and (3)) among different crops is sensitive to the method of N’ calculation. Therefore, fair NUE comparisons among different crops should be based on the procedure proposed here or similar methods that consider the exact timing of the critical phenology stages for the main growth period.

_{N}is similar during the period between the two destructive harvests and the short time period(s) before and/or after, i.e., the days between the critical phenology stages and the destructive harvests. That assumption can be regarded valid as long as the environmental conditions are normal in the sense that no exceptional weather events in terms of temperature and precipitation occur during the short time period(s) over which the R

_{N}is extrapolated. In addition, as a rule, the accumulated duration of the extrapolated period should not be longer than approximately one third of the length of the whole main growth period. If exceptional weather conditions do occur and/or the accumulated length of the extrapolated period exceeds the above limit, additional destructive harvest(s) should be considered to ensure correct estimates of the N’.

_{N}and E

_{N,y}) also in situations in which genotypes and treatments produce great variation in the timing of the critical developmental stages for the main growth period. The present paper provides the required method improvement. Judged from the scenarios presented here, it appears likely that the U

_{N}values in Asplund et al. [9] are generally underestimates, and the E

_{N,y}values are overestimates, because they are based on inaccurate (under)estimates of N’ (i.e., N’

_{H}

_{1H2}). The inaccurate estimate of N’ has no effect on the overall NUE (cf. Equation (1)), but is still important since the NUE components U

_{N}and E

_{N,y}are often most interesting in terms of crop NUE comparisons and evaluation.

_{N,y}) as was previously discussed [6,9]. The use of the here introduced method improvement for the accurate assessment of N’ (e.g., Equations (5)–(7)) is especially important when crops with high N acquisition rates (i.e., high R

_{N}) are to be evaluated and/or when destructive plant harvests, e.g., for feasibility reasons, cannot be carried out exactly at the time points of the critical phenology stages for the main growth period.

_{Soil}in the calculation tool), which indicates the net N accumulation over the whole growing season per soil N and requires an estimate of soil N content as an additional input.

## 4. Conclusions

## Acknowledgments

## Conflict of Interest

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**MDPI and ACS Style**

Weih, M.
A Calculation Tool for Analyzing Nitrogen Use Efficiency in Annual and Perennial Crops. *Agronomy* **2014**, *4*, 470-477.
https://doi.org/10.3390/agronomy4040470

**AMA Style**

Weih M.
A Calculation Tool for Analyzing Nitrogen Use Efficiency in Annual and Perennial Crops. *Agronomy*. 2014; 4(4):470-477.
https://doi.org/10.3390/agronomy4040470

**Chicago/Turabian Style**

Weih, Martin.
2014. "A Calculation Tool for Analyzing Nitrogen Use Efficiency in Annual and Perennial Crops" *Agronomy* 4, no. 4: 470-477.
https://doi.org/10.3390/agronomy4040470