Predictive Modeling Study on the Critical Nitrogen Concentration and Nitrogen Accumulation in Cut Chrysanthemum Based on the Cumulative Photo-Thermal Effect

doi:10.21203/rs.3.rs-4955190/v1

Download PDF

Research Article

Predictive Modeling Study on the Critical Nitrogen Concentration and Nitrogen Accumulation in Cut Chrysanthemum Based on the Cumulative Photo-Thermal Effect

https://doi.org/10.21203/rs.3.rs-4955190/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

Background and aims

Critical nitrogen (N) concentration (N_c) and critical accumulation (N_a) are essential for N status diagnosis and precise N fertilization in crops. However, efficient prediction models for N_c and N_a in cut Chrysanthemum remains scarce, limiting precision N management.

Methods

Five experiments with varying N gradients were conducted from May 2021 to August 2022 using the ‘Nannong Xiaojinxing’ cultivar. We developed and validated dry matter prediction models with various growth and developmental driver variables, established N_c and N_a models using dry matter as model driving variable, and created N_c and N_a models using optimal driving variable identified from dry matter predictions.

Results

Among the dry matter prediction models for cut Chrysanthemum, the model incorporating cumulative photo-thermal effect (PTE) demonstrated superior accuracy and stability. We established the N_c and N_a models using dry matter as the driving variable. When the above-ground dry matter was 1 g·plant^− 1, the N_c and N_a were 4.5295% and 45.30 mg·plant^− 1, respectively. At the flower picking stage, the N_a reached 236.50 mg·plant^− 1. The PTE-driven N_c and N_a prediction models demonstrated high accuracy, with R² at 0.9687 and 1.0019, RMSEs at 0.2105% and 17.47 mg·plant^− 1, and n-RMSEs at 7.31% and 12.72%, respectively.

Conclusions

These models can dynamically predict N_c and N_a based on light and temperature factors, providing a scientific basis for efficient N diagnostics and precise N fertilizer management for cut chrysanthemum. Moreover, the methodology developed herein could be extrapolated to other crops, contributing to sustainable agriculture and mitigating excessive N fertilizer application.

Critical nitrogen concentration

nitrogen accumulation

dry matter prediction model

cumulative photo-thermal effect

cut chrysanthemum

Cut chrysanthemum (Chrysanthemum morifolium Ramat.) is one of the four prominent cut flowers in the world, which plays an essential role in the world flower industry (Aliniaeifard and van Meeteren, 2016; Teixeira da Silva et al., 2013). In China, the production area of cut chrysanthemum covers about 6800 hectares, with annual sales reaching at least 2.5 billion branches, demonstrating its vast scale. Nitrogen (N) is one of the most crucial elements for the growth, development, and formation of the external quality of cut chrysanthemum (Albornoz, 2016; Ding et al., 2009). Applying insufficient or excessive N fertilizer at any growth stage can potentially impact the final crop yield and quality (Sinclair and Rufty, 2012). To achieve accurate N diagnosis and precise control of N fertilizers throughout all growth stages of cut chrysanthemums, it is essential to understand the dynamics of the critical N concentration (N_c) and critical nitrogen accumulation (N_a).

The N_c is the minimum N concentration required for the crop to reach maximum dry matter during a specific growth stage (Greenwood et al., 1991; Greenwood et al., 1990; Lemaire et al., 2008; Ulrich, 1952). Similarly, N_a is the minimum N concentration needed when the crop reaches maximum dry matter. Determining the crop's N_c and N_a is crucial for accurately diagnosing crop N nutrition (Lemaire et al., 1984; Lemaire et al., 2019) and making informed decisions about N fertilizer application. Currently, predictive models for crop N_c and N_a primarily use crop dry matter as the driving variable of the model (Gao et al., 2022; Li et al., 2022). However, measuring crop dry matter was a cumbersome and time-consuming process (Minghui et al., 2022), limiting the practical application of N_c and N_a for efficient N nutrition diagnosis in actual production(Li et al., 2024).

The N_c in crops decreases progressively with the accumulation of dry matter (DM) (Lemaire et al., 1984; Li et al., 2022). The "Nc dilution curve" describes this relationship, which can be expressed by the power function equation N_c=a·DM-b (Greenwood et al., 1990; Justes, 1994). Since the concept of N_c dilution curve model was proposed, many scholars have established N_c dilution curves for several crops, such as rice (Oryza sativa L.), wheat (Triticum aestivum L.), corn (Zea mays L.), cotton (Gossypium hirsutum L.), cauliflower (Brassica oleracea var. botrytis L.), and chrysanthemum (Chrysanthemum morifolium Ramat.) (Ata-Ul-Karim et al., 2013; He et al., 2022; He et al., 2017; Kage et al., 2002; Lu et al., 2022; Tei et al., 2002; Zhou et al., 2021). In addition to the classical form of the plant N_c – plant DM, the N_c dilution model also includes organ N_c – organ DM (Bi et al., 2022; Josefina et al., 2023; Lemaire et al., 2007) and plant N_c - organ number indicators (leaf area index, LAI) (Cheng et al., 2022; Fernandez et al., 2022). Whether the increase in crop DM weight or the LAI, both are driven by crop growth and developmental progress (Ceglar et al., 2011). Therefore, is an N_c model based directly on the crop growth and developmental driver variables feasible? To provide a real-time and efficient diagnostic tool for managing crop N nutrition, research has shown that the N_c in wheat has a significant nonlinear relationship with developmental stages (Zhao et al., 2014). A diagnostic curve based on time series (growing degree days, GDD) was established, demonstrating that a time-series-based N_c model exhibits increased robustness and is more readily applicable to crop growth modeling and cultivation (Fu et al., 2024). The growth and development process of greenhouse horticultural crops includes GDD, physiological development time (PDT), product of thermal effectiveness and photosynthetically active radiation (PAR) (TEP), and cumulative photo-thermal effects (PTE) (Hidén and Larsen, 1994; Lin et al., 2011; Liu et al., 2013; Zhang and Tao, 2013; Zheng and Zhang, 2023; Yang et al., 2011). Based on the Logistic model, we can build the prediction model of crop DM using the crop growth and developmental driver variables as the driving variables (Lee, 2002; Mohammad Rafie and Mehdi, 2020; Shabani et al., 2013; Zhou et al., 2023). This provides theoretical support for establishing a dynamic model of N_c based on crop growth and developmental driver variables.

In this study, we carried out several batches of cut chrysanthemum greenhouse cultivation experiments with different N fertilizer gradients. We aimed to construct a high-precision, quickly applied dynamic prediction model for N_c and N_a. This model would provide a scientific basis for N nutrition diagnosis and fertilizer decision-making throughout the whole growth stage of cut chrysanthemums. The specific research methods are as follows: Initially, variables such as GDD, PDT, TEP, and PTE were adopted as the driving variables for the model, and a prediction model for DM of cut chrysanthemums was established using the Logistic model. Through model validation and comparison, the optimal model driving variables were determined. Subsequently, the relationship between DM and N_c in cut chrysanthemums was investigated to establish models for both N_c and N_a. Finally, prediction models for cut chrysanthemum N_c and N_a were established based on the optimal driving variables. These models were tested using independent experimental data.

Summary of the pilot area

The experiment was conducted from May 2021 to July 2022 in the continuous thin film greenhouse of Yunnan Kaiyuan Tianhua Biological Industry Co.Ltd. The location is at 23^°43^′N latitude and 103^°27^′E longitude, with an altitude of 1300 m. The area has an average annual temperature of 19.8 ℃, average annual precipitation between 843–877 mm, and average annual evaporation of 2039 mm. Each polyethylene film greenhouse is 20 m long, 9.6 m in span, and 4.5 m high, covered with polyvinyl chloride film. The greenhouses are equipped with 1-meter wide vents at the top and bottom and are listed inside and around with a fully closed black film for short-day treatment.

Experimental design

In the greenhouse, cultivation experiments of cut chrysanthemum with different planting periods and N fertilizer gradients were carried out. The tested chrysanthemum variety was 'Nannong Xiaojinxing,' using the direct cottage planting method. The standard for cuttings was: stem length 6.80 cm, stem thickness 3.30 mm, with four leaves and one bud. After planting, the plants were supplemented with light each night from 8:00 p.m. to 2:00 a.m. using 200 W incandescent bulbs for 6 hours. When the plant height reached 40 cm, short-day treatment began. The blackout curtains was closed from 6:00 p.m. until 8:00 a.m. to ensure night length exceeded 14 hours, continuing until the end of the harvesting period. A total of five batches of experiments were conducted. The amount of N applied per plant was the standard for N application (Table 1).

Table 1

Basic information about the experimental design
Experiments	Cutting date	Harvesting date	N level (mg N·plant^− 1)		Plant spacing (cm × cm)
Exp. 1	2021-5-30	2021-9-2	80, 160, 230, 310, 390	substrate	10 × 10
Exp. 2	2021-8-2	2021-11-5	47, 175, 315, 455	soil	12 × 12
Exp. 3	2021-9-24	2022-1-16	14, 62, 179, 311, 442, 574	substrate	10 × 10
Exp .4	2022-3-9	2022-6-14	20, 336, 532	soil	12 × 12
Exp. 5	2022-4-11	2022-7-10	28, 139, 236, 310, 390	substrate	10 × 10
Note: Three plots were set for each nitrogen level, and 120 plants were planted in each plot.

A proportional fertilizer was used for precise N quantification in this experiment. The N supply was divided into four stages: seedling stage, vigorous growth stage, flower bud differentiation stage, and bud emergence to membrane-breaking stage (Table S1, see online supplementary material). The N supply at each stage was 30%, 40%, 20%, and 10% of the total N amount, respectively, with fertilization occurring every three days during each stage. By controlling the quantities of fertilizers in the fertilizing solution, such as urea (N 46%), diammonium phosphate (N 11.8%, P₂O₅ 60.8%), dipotassium phosphate (K₂O 34%, P₂O₅ 52%), potassium chloride (K₂O 60%), calcium and magnesium mixture, different gradients of N supply were achieved. Additionally, the soil or substrate’s water potential was maintained above − 20 Kpa (Lin et al., 2011) to ensure that cut chrysanthemums were free from water stress. The nutritional status of the substrate or soil at the time of planting for each experiment is shown in Table 2.Pictures of the growth status at each growth stage in Exp.4 were shown in Fig. 1.

Table 2

Nutrient status of the substrate or soil at the time of cutting insertion for each batch
Experiment	Available nitrogen (mg·Kg^− 1)	Available phosphorus (mg·Kg^− 1)	Available kalium (mg·Kg^− 1)	Organic matter (g·Kg^− 1)	Volume weight (g·cm^− 3)	EC (ms·cm^− 1)	pH
Exp. 1, 3 and 5	313.51	60.96	2805.34	110	0.083	1.12	6.52
Exp. 2	113.02	179.25	47.2	6.8	1.059	0.91	6.52
Exp. 4	80.41	206.14	55.04	5.2	1.065	0.92	6.45
Note: The growing medium of Exp. 1, 3, and 5 were the substrate composed of coconut bran: perlite (3:1); the growing medium of Exp. 2 and 4 were local laterite cultivation in Kaiyuan, Yunnan.
Greenhouse environmental data collection

Greenhouse environmental data were automatically collected by a data logger (CR1000X, Campbell Scientific Inc., USA) equipped with various sensors. These included a photosynthetically active radiation sensor (PQS1, Kipp & Zonen, Netherlands) and an air temperature and humidity sensor (HMP60, Vaisala, USA). The parameters collected were photosynthetically active radiation (PAR), air temperature, and humidity at 1.5 m above ground level inside the greenhouse. Data were collected every 30 seconds and the average value stored over 30 minutes.

Measurement of organ dry matter and nitrogen content

Measurement of organ dry matter: Measurement began after the cut chrysanthemum cuttings survive. Destructive sampling was carried out every seven days, with three plants taken from each plot, totaling nine sampled plants, and the sampling time was recorded. After sampling, the fresh matter of the aboveground stems, leaves, and flowers was weighed. The samples were then fixed at 105°C for 15 minutes, dried at 75°C to a constant weight, and the dry matter of each organ was measured.

Measurement of organ N concentration: Organ dry matter was sampled every 14 days, ground with a small grinder, and further crushed with a high-throughput grinder. The plant samples were digested using the H₂SO₄-H₂O₂ method, and the total N concentration in the digestion solution was measured by AA3 flow analyzer (Brian + Luebbe, Norderstedt, Germany) (Lu et al., 2022), based on the Kjeldahl N determination method.

The N accumulation in each organ (mg·plant^-1) = organ N concentration (%) × organ dry matter (g·plant^-1) × 1000. The N accumulation in the stems, leaves, and flowers was summed to obtain the N accumulation in the plant's aboveground parts. The N concentration in the aboveground parts (%) = N accumulation in the aboveground parts (g·plant^-1) / dry matter mass of the aboveground parts (g·plant^-1) × 100%.

Crop growth and developmental driver variables

The driving variables for the growth and development process of greenhouse horticultural crops include GDD, PDT, TEP, and PTE(Gómez and Soriano, 2020; Zhang and Tao, 2013; Zheng and Zhang, 2023; Liu et al., 2018; Lin et al., 2011; Cheng et al., 2023; Hidén and Larsen, 1994; Jiang et al., 2023; Yang et al., 2011).

Growing degree day (GDD)

GDD is the earliest method for quantifying thermal effect (McMaster and Wilhelm, 1997). Currently, there are multiple calculation models. This study uses the average temperature every half hour as the input variable, with the specific calculation equations provided in formulas (1) to (3).

$$\:{ET}_{i,j}=\left\{\begin{array}{c}0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{T}_{i,j}<{T}_{min}\\\:{T}_{i,j}-{T}_{min}\:\:\:\:\:\:\:\:\:{T}_{min}\le\:{T}_{i,j}<{T}_{\text{m}\text{a}\text{x}}\\\:{T}_{\text{m}\text{a}\text{x}}-{T}_{min}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{T}_{i,j}\ge\:{T}_{\text{m}\text{a}\text{x}}\end{array}\right.$$

$$\:GD{D}_{j}=\frac{1}{48}{\sum\:}_{i=1}^{48}{ET}_{i,j}$$

$$\:GDD={\sum\:}_{j=1}^{n}GD{D}_{j}$$

Where $\:{T}_{i,j}$ represents the average temperature for the i-th (i = 1 ~ 48) half-hour of the j-th day; $\:{T}_{min}$ represents the biological lower limit temperature (℃); $\:{T}_{max}$ represents the biological upper limit temperature (℃);$\:\:i$ represents the $\:i$-th ($\:i$=1~48) half-hour period; $\:{ET}_{\text{i},\text{j}}$ represents the effective temperature for the j-th day’s i-th (i = 1 ~ 48) half-hour (℃); $\:GD{D}_{j}$ represents the GDD for the j-th day (℃); $\:j$ represents the $\:j$-th day after the rooting and survival of cut chrysanthemum.

Physiological development time (PDT)

PDT is a time scale under the most suitable developmental environment (Liu et al., 2018; Liu et al., 2013; Zhang et al., 2020), which is the product of the daily relative thermal effect (RTE) and the daily relative photo-period effectiveness (RPE). The daily RTE is defined as the ratio of the growth of cut chrysanthemum in actual temperatures to their growth in optimal temperatures for a day.

$$\:{RTE}_{i,j}=\left\{\begin{array}{c}0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{T}_{i,j}<{T}_{min}\\\:({T}_{i,j}-{T}_{min})/({T}_{ob}-{T}_{min})\:\:{\:T}_{min}\le\:{T}_{i,j}<{T}_{ob}\\\:\:\:\:\:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{T}_{ob}\le\:{T}_{i,j}<{T}_{ou}\\\:({T}_{\text{m}\text{a}\text{x}}-{T}_{i,j})/(\:{T}_{max}-{T}_{ou})\:\:{\:T}_{ou}\le\:{T}_{i,j}\le\:{T}_{max}\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{T}_{i,j}>{T}_{max}\end{array}\right.$$

$$\:{RTE}_{j}=\frac{1}{48}\sum\:_{i=1}^{48}{RTE}_{i,j}$$

Where T_ob represents the lower limit of the most suitable temperature for growth and development (℃); T_ou represents the upper limit of the most suitable temperature for growth and development (℃); $\:{RTE}_{i,j}$ represents the RTE for the i-th (i = 1 ~ 48) half-hour of the j-th day; $\:{RTE}_{j}\:$represents RTE for the j-th day.

The daily RPE represents the ratio of the growth of cut chrysanthemum under actual light conditions to their growth under optimal light conditions for a day. Cut chrysanthemum are short-day plants; during the bud differentiation period, when the actual day length is less than the optimal day length, the RPE is 1. When the actual day length is between the optimal and critical days, the RPE decreases linearly as the day length increases. When the actual day length exceeds the critical day length, the RPE is 0, as shown in Formula (6).

$$\:{\text{R}\text{P}\text{E}}_{j}=\left\{\begin{array}{c}1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{DL}_{j}\le\:{DL}_{\text{o}}\\\:\frac{({DL}_{c}-{DL}_{j})}{({DL}_{c}-{DL}_{\text{o}})}\:\:\:\:\:\:\:\:\:{DL}_{\text{o}}<{DL}_{j}\le\:{DL}_{c}\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{DL}_{c}<{DL}_{j}\end{array}\right.$$

Where $\:{DL}_{j}$ represents the actual day length for the $\:j$-th day, $\:{DL}_{c}$ represents the critical day length, $\:{DL}_{0}$ represents the optimal day length, and $\:{\text{R}\text{P}\text{E}}_{j}\:$represents the RPE for the $\:j$-th day.

For a particular variety of cut chrysanthemum, the PDT needed to complete its developmental stages is constant and can be calculated using formulas (7) to (8).

$$\:{\text{P}\text{D}\text{T}}_{j}=\left\{\begin{array}{c}{RTE}_{j}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:PDT<GER\\\:{RTE}_{j}\times\:{RPE}_{j}\:\:\:\:\:\:\:\:GER\le\:PDT<FLO\\\:{RTE}_{j}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:PDT\ge\:FLO\end{array}\right.$$

$$\:\text{P}\text{D}\text{T}={\sum\:}_{j=1}^{n}{\text{P}\text{D}\text{T}}_{j}$$

Where $\:{\text{P}\text{D}\text{T}}_{j}$ represents the PDT for the $\:j$-th day; GER is the PDT required from rooting to the initiation of bud differentiation; $\:\text{F}\text{L}\text{O}$ is the PDT required from rooting to the appearance of buds; In order to meet the demand for light length in the growth and development of the chrysanthemum, the corresponding light filling or shading field management was conducted during the experiment. In the short-day treatment stage, the daily length was less than 10 H, so the PRE in this stage was always 1.

Product of thermal effect and PAR (TEP)

TEP is the product of relative thermal effect and the daily total photosynthetically active radiation (PAR)(Lin et al., 2011; 程陈 et al., 2023). The specific calculation formula is as follows.

$$\:{RTE}_{i,j}=\left\{\begin{array}{c}0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\text{T}}_{\text{i},\text{j}}<{\text{T}}_{\text{m}\text{i}\text{n}}\\\:\text{\:sin}\left(\frac{{\pi\:}}{2}\times\:\frac{\:{\text{T}}_{\text{i},\text{j}}-{\text{T}}_{\text{m}\text{i}\text{n}}}{{\text{T}}_{\text{o}}-{\text{T}}_{\text{m}\text{i}\text{n}}}\right)\:\:\:\:\:\:\:\:{\text{T}}_{\text{m}\text{i}\text{n}}\le\:\:{\text{T}}_{\text{i},\text{j}}<\:{\text{T}}_{\text{o}}\\\:\text{sin}\left(\frac{{\pi\:}}{2}\times\:\frac{{\text{T}}_{\text{m}\text{a}\text{x}}-\:{\text{T}}_{\text{i},\text{j}}}{{\text{T}}_{\text{m}\text{a}\text{x}}-{\text{T}}_{0}}\right)\:\:\:\:\:{\:\:\:\:\text{T}}_{\text{o}}\le\:\:{\text{T}}_{\text{i},\text{j}}\le\:{\text{T}}_{\text{m}\text{a}\text{x}}\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\text{T}}_{\text{i},\text{j}}>{\text{T}}_{\text{m}\text{a}\text{x}}\end{array}\right.$$

$$\:\text{P}\text{A}{\text{R}}_{\text{j}}=\sum\:_{\text{i}=1}^{48}{(\text{P}\text{A}\text{R}}_{\text{i},\text{j}}\times\:0.0018)$$

$$\:{\text{R}\text{T}\text{E}}_{j}=\frac{1}{48}\sum\:_{\text{i}=1}^{48}{\text{R}\text{T}\text{E}}_{i,j}$$

$$\:{\text{T}\text{E}\text{P}}_{\text{j}}={\text{R}\text{T}\text{E}}_{j}\times\:{\text{P}\text{A}\text{R}}_{\text{j}}$$

$$\:\text{T}\text{E}\text{P}=\sum\:{\text{T}\text{E}\text{P}}_{\text{j}}$$

Where T_o is the optimal temperature (℃);$\:{\text{P}\text{A}\text{R}}_{\text{j}}$ is the daily total PAR for the j-th day (MJ·m^− 2);$\:{\:\text{P}\text{A}\text{R}}_{\text{i},\text{j}}\:$represents the average PAR for the the i-th (i = 1 ~ 48) half-hour of the j-th day (µmol·m^− 2·s^− 1); in the formula, 0.0018 is the unit conversion coefficient from µmol·m^− 2·s^− 1 to MJ·m^− 2·(30min)⁻¹; $\:{\text{T}\text{E}\text{P}}_{\text{j}}$ represents the TEP for the j-th day (MJ·m^− 2).

Cumulative photo-thermal effect (PTE)

PTE, defined as the product of daily relative thermal effect and daily cumulative relative light effect, is derived by transforming PAR into relative light effect (RLE) through a negative exponential model (Jiang et al., 2023; Karlsson et al., 1989; Yang et al., 2023; Yang et al., 2011). The relative light effect for cut chrysanthemum refers to the proportion of cut chrysanthemum's growth and development rate under actual radiation conditions compared to light-saturated radiation conditions. The calculation of RPE uses half-hour intervals as the time unit. When the average PAR for each half-hour period reaches or exceeds the saturation light intensity for cut chrysanthemum leaves, the RLE value is 1; if it falls below the saturation light intensity, the RLE value is quantified using a negative exponential function. The method for calculating the PTE is as follows.

$$\:{RLE}_{i,j}=\left\{\begin{array}{c}1-{exp}^{-b\times\:{(\text{P}\text{A}\text{R}}_{\text{i},\text{j}}-{PAR}_{0})}\:\:\:\:\:\:\:{PAR}_{i,j}>{PAR}_{0}\\\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{PAR}_{i,j}\le\:{PAR}_{0}\end{array}\right.$$

$$\:{\text{R}\text{L}\text{E}}_{\text{j}}=\sum\:_{\text{i}=1}^{48}{RLE}_{i,j}$$

$$\:{\text{P}\text{T}\text{E}}_{\text{j}}={\text{R}\text{T}\text{E}}_{j}\times\:{\text{R}\text{R}\text{E}}_{\text{j}}$$

$$\:\text{P}\text{T}\text{E}=\sum\:{\text{D}\text{P}\text{T}\text{E}}_{\text{j}}$$

Where $\:{PAR}_{0}$ is the light compensation point of photosynthesis (µmol·m^− 2·s^− 1); b is a constant parameter of photosynthesis;$\:{\:RLE}_{i,j}$ represents the RLE for the i-th (i = 1 ~ 48) half-hour of the j-th day;$\:{\:\text{R}\text{L}\text{E}}_{\text{j}}$ is the cumulative RLE of the j-th day;$\:{\:\text{P}\text{T}\text{E}}_{\text{j}}$ is the PTE of the j-th day (MJ·m^− 2);$\:{\:\text{R}\text{T}\text{E}}_{j}$ is calculated in the same way as formula (9). By measuring the light response of photosynthesis in healthy chrysanthemum leaves using Li-6400 (LI-COR, USA), the light compensation point $\:{PAR}_{0}$ of chrysanthemum photosynthesis was found to be 31.02 µmol·m^− 2·s^− 1; the parameter b equals 0.004096.

Base temperature and critical day length at different stages of cut chrysanthemum

Based on previous studies(Larsen and Persson, 1999; Lee, 2002; Lin et al., 2011; Nothnagl et al., 2004; Ding et al., 2009; Zhou et al., 2009), the temperature and daylight hours for different growth stages of chrysanthemum were determined as follows (Table 3).

Table 3

Base temperature and critical day length at different stages of cut chrysanthemum
Growth stage	Temperature/℃					Day length/h
Growth stage	T_min	T_max	T_o	T_ob	T_ou	DLc	DLo
Vegetative growth stage	10	36	24	18	26	/	/
Flower bud differentiation stage	12	34	24	20	26	14	10
Bud emergence-flower picking stage	10	36	24	18	26	14	10

The methods for constructing models

Prediction model for maximum dry matter of cut chrysanthemum

This study uses variance analysis to determine the maximum aboveground dry matter of cut chrysanthemum for each sampling period. The dynamic changes in aboveground dry matter are quantitatively described using the Logistic model. A dry matter prediction model was constructed using crop growth and developmental driver variables as the driving variable for the dry matter prediction model:

$$\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}={\text{D}\text{M}}_{0}/(1+\text{a}\times\:\text{E}\text{X}\text{P}(-\text{b}\times\:\text{T}\left)\right)$$

Where $\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}$ represents the maximum aboveground dry matter of cut chrysanthemum, g·plant^− 1; $\:{\text{D}\text{M}}_{0}$ represents the maximum value of aboveground dry biomass at harvest time, g·plant^− 1; T represents the crop growth and developmental driver variable, which in this study could be GDD, PDT, TEP, or PTE; a and b are coefficients to be determined.

Prediction model for N_c of cut chrysanthemum

To construct a critical N concentration (N_c) dilution model based on crop dry matter, it is first necessary to determine the N_c value. This is the N concentration in plants that is not limited by N nutrition and does not involve luxury N consumption (Justes, 1994). Following the N_c calculation method and integrating the modeling ideas from various scholars on N_c dilution curve models (Josefina et al., 2023), the steps to construct a N_c dilution curve based on dry matter for cut chrysanthemum are as follows: (1) Measure the aboveground dry matter and their corresponding N concentration values for each sampling; (2) Perform variance analysis on the aboveground dry matter of cut chrysanthemum, and based on whether the growth is restricted by N nutrition, divide the data into a N-restricted group and a non-restricted group; (3) The relationship between the aboveground dry matter and N concentration values in the N-restricted group is fitted with a linear curve, while for the non-restricted group, the average value of the aboveground dry matter is taken to represent the maximum dry matter. The theoretical N_c for each sampling is determined by the ordinate of the intersection point between the curve mentioned above and a vertical line, where abscissa is the maximum dry matter. The formula for the N_c dilution model based on aboveground dry matter is:

$$\:{N}_{C}=\text{a}\text{c}\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{-b}$$

where N_c is the critical N concentration value, in %; ac represents the N_c when the aboveground dry matter (DM) is 1 g·plant^− 1, in %; DM_max is the maximum aboveground DM, g·plant^− 1; b is the statistical parameter determining the slope of the N_c dilution curve.

Prediction model for N_a of cut chrysanthemum

The relationship between the N accumulation ($\:{N}_{a}$) of cut chrysanthemums and the $\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}$ can be expressed by the following formula:

$$\:{N}_{a}=10\times\:{N}_{C}\times\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}$$

By substituting Eq. (19) into Eq. (20), the critical N_a model for cut chrysanthemum is obtained as follows:

$$\:{N}_{a}=10\times\:ac\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{(1-b)}$$

Where N_a represents the nitrogen accumulation under N_c conditions, mg·plant^− 1; (1-b) is a growth parameter that is the relative N absorption rate ratio to aboveground dry matter accumulation rate.

Prediction model for N_c and N_a driven by the crop growth and developmental driver variables

Using the dry matter of cut chrysanthemum as a medium, substituting Eq. (18) into Eq. (19) yields a prediction model for the N_c based on the crop growth and developmental driver variables as follows:

$$\:{N}_{\text{c}}=\text{a}\text{c}\times\:{\left(\frac{{\text{D}\text{M}}_{0}}{1+\text{a}\times\:\text{E}\text{X}\text{P}\left(-\text{b}\ast\:\text{T}\right)}\right)}^{-b}$$

By substituting Eq. (18) into Eq. (21), the result is a N_a model for cut chrysanthemum based on the crop growth and developmental driver variables:

$$\:{N}_{a}=10\times\:ac\times\:{\left(\frac{{\text{D}\text{M}}_{0}}{1+\text{a}\times\:\text{E}\text{X}\text{P}\left(-\text{b}\ast\:\text{T}\right)}\right)}^{(1-b)}$$

Model evaluation

According to international common standards, the model's prediction accuracy is evaluated using the root mean square error (RMSE) and the normalized RMSE (n-RMSE).

$$\:\text{R}\text{M}\text{S}\text{E}=\sqrt{\frac{\sum\:_{i=1}^{n}{(Si-Mi)}^{2}}{n}}$$

$$\:\text{n}-\text{R}\text{M}\text{S}\text{E}=\frac{\text{R}\text{M}\text{S}\text{E}}{\text{S}}\times\:100\text{\%}$$

Where $\:Si$ and $\:Mi$ refer to the measured and simulated values, respectively, n is the sample number, and S is the average of the observed data. If n-RMSE < 10%, the model stability is excellent; if 10% ≤ n-RMSE < 20%, the model stability is good; if 20% ≤ n-RMSE < 30%, the model stability is average; if n-RMSE ≥ 30%, the model stability is considered poor(Willmott, 1982; Yang et al., 2000).

Data statistics and analysis

This study employs Excel 2019 (Microsoft Corporation, Redmond, WA, USA) for data organization, SPSS 25.0 (IBM Corporation, Armonk, NY, USA) for variance analysis, and Origin 2021 (OriginLab Corporation, Northampton, MA, USA) for chart creation and model fitting.

Construction and comparison of predictive models for dry matter of cut chrysanthemum

Using the maximum aboveground dry matter of cut chrysanthemum at each sampling period of Exp.1, 3, and 4 as the modeling values and taking GDD, PDT, TEP, and PTE as the driving variables of the model, the growth curve of the maximum aboveground dry matter of cut chrysanthemum was established (Fig. 2). The growth curves derived from the four different driving variables exhibited a characteristic slow-fast-slow "S" type growth trend, aligning well with the modeling prerequisites of the Logistic growth model. In addition, PTE were the optimal driving variable for the DM_max model (Table 4), followed by PDT, TEP, and GDD.

Table 4

Predictive models of cut chrysanthemum dry matter driven by different crop growth and developmental driver variables.
Driver variables	Formula	R²	Number of data pairs	P value
GDD	$\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+30.311\times\:\text{E}\text{X}\text{P}(-0.00461\times\:\text{G}\text{D}\text{D}\left)\right)$	0.861	N = 42	P < 0.001
PDT	$\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+31.288\times\:\text{E}\text{X}\text{P}(-0.08782\times\:\text{P}\text{D}\text{T}\left)\right)$	0.944	N = 42	P < 0.001
TEP	$\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+30.085\times\:\text{E}\text{X}\text{P}(-0.02542\times\:\text{T}\text{E}\text{P}\left)\right)$	0.915	N = 42	P < 0.001
PTE	$\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+30.916\times\:\text{E}\text{X}\text{P}(-0.00644\times\:\text{P}\text{T}\text{E}\left)\right)$	0.974	N = 42	P < 0.001

Validation and comparison of the dry matter prediction model

The DM prediction models based on four different driving variables were tested using the maximum aboveground dry matter (DM_max) of cut chrysanthemum sampled in Exp.2 and 5 at each sampling period as the model verification values (Fig. 3). The accuracy (RMSE) and stability (n-RMSE) of the four models ranked as follows, from best to worst: PTE > PDT > TEP > GDD. Therefore, using the PTE as the driving variable to establish a predictive model for cut chrysanthemum dry matter yielded the best result.

Predictive model construction of the Nc and Na based on dry matter

Figure 4 showed the N concentration dilution curves across five experiments under different N gradient treatments. Results showed that as the dry matter increased, the aboveground N concentration of the cut chrysanthemum gradually decreased. Each N-level treatment was associated with its distinct dilution curve. Moreover, higher N treatment levels correspond to the cut chrysanthemum's higher initial aboveground N concentration. However, the difference between different treatments diminished as the dry matter increased. Using the N_c calculation method (Justes, 1994), significant difference analysis and linear fitting of dry matter and N concentration for different N treatments were carried out at each Exp1, 3, and 4 sampling period. This aimed to determine the N_c value at each sampling period and establish the N_c dilution curve (Fig. 5). The curve was fitted using the inverse power function model from formula (19), yielding the result: $\:{\text{N}}_{\text{C}}=4.5295\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{-0.309}$ with the R² of 0.9276. According to the model, when the aboveground dry matter was 1 g·plant⁻¹, the N_c value was 4.5295%.

Predictive model construction of the N_a

Table 5 presented the results of the significant difference analysis of the aboveground N accumulation under different N gradient treatments across five experiments. Results indicated that aboveground N accumulation of cut chrysanthemum significantly increased with higher N fertilizer application. When the N application rate reached between 230–310 mg·plant^− 1, the increase in N accumulation significantly slowed. However, with continued increases in N application, N accumulation continues to rise, indicating the phenomenon of luxurious N absorption. This suggested that measured N accumulation may have limited practical significance in guiding precise N management for cut chrysanthemums. To calculate the N_a at each sampling period, we mimicked the N_c calculation method. Model fitting was conducted based on dry matter and N accumulation in Exp. 1, 3, and 4 for each sampling period. As shown in Fig. 6, the results established a power function-based N_a model for cut chrysanthemum based on dry matter: $\:{\text{N}}_{\text{a}}=45.295\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{0.703}$ R²=0.9680. Using Formula (21), the N_a model based on dry matter as follows:$\:{\:\text{N}}_{\text{a}}=45.295\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{0.691}$. Both models showed similar simulation results, indicating that when the aboveground dry matter of cut chrysanthemum was 1 mg·plant-1, the aboveground N_a was 45.295 mg·plant⁻¹.

Validation of the N_c and N_a models based on dry matter

We used data from Exp. 2 and 5, which were independent of the model establishment process, to validate the performance of N_c (Fig. 7A) and N_a (Fig. 7B) models. The RMSE for the N_c and N_a models in cut chrysanthemum based on dry matter were 0.2105% and 17.47 mg·plant^− 1, respectively. The n-RMSE values were 7.31% and 12.72%, respectively. The stability of the models was classified as excellent and reasonable.

Predictive model construction of the N_c and N_a based on PTE

Based on the verification and comparison results of the dry matter prediction model for cut chrysanthemum in section 3.1, where PTE was identified as the optimal model driving variable, the predictive model for the N_c was established using Eq. (22) as follows.

$$\:{\text{N}}_{\text{C}}=4.5295\times\:{\left(\frac{12.50}{1+30.916\times\:\text{E}\text{X}\text{P}\left(-0.00644\times\:\text{P}\text{T}\text{E}\right)}\right)}^{-0.309}$$

The predictive model for the N_a based on the PTE was established using Eq. (23) as follows:

$$\:{\text{N}}_{\text{a}}=45.295\times\:{\left(\frac{12.50}{1+30.916\times\:\text{E}\text{X}\text{P}\left(-0.00644\times\:\text{P}\text{T}\text{E}\right)}\right)}^{0.691}$$

We used the data from Exp. 2 and 5 as the model validation dataset to test the performance of predictive models for N_c and N_a of cut chrysanthemum based on PTE. Results indicated that both models achieved a good level of stability (Fig. 8)

Table 6

Aboveground N accumulation of cut chrysanthemum under different N gradient treatments in each experiment.
Experiment	N levels (mg/plant)	Nitrogen accumulation(mg·plant^− 1)
Experiment	N levels (mg/plant)	Slow growth stage	Vigorous growth stage	The flower bud differentiation stage	Bud emergence stage	Membrane breaking stage	Flower picking stage
Exp.1	80	/	31.46 ± 2.38 b	56.3 ± 7.24 c	53.14 ± 2.68 c	/	71.00 ± 9.22 b
	230	/	86.58 ± 17.7 a	101.78 ± 5.97 b	125.23 ± 7.42 b	/	241.19 ± 42.36 a
	310	/	96.36 ± 11.49 a	147.99 ± 9.49 a	167.46 ± 7.87 a	/	264.00 ± 30.23 a
Exp.2	47	/	33.88 ± 1.89 b	102.73 ± 16.86 c	113.54 ± 23.15 c	/	138.13 ± 5.73 c
	345	/	55.90 ± 10.36 a	137.05 ± 10.08 ab	199.35 ± 42.71 ab	/	223.95 ± 22.43 ab
	455	/	54.76 ± 10.06 a	163.56 ± 39.87 a	217.50 ± 54.94 a	/	273.91 ± 22.40 a
Exp.3	14	7.54 ± 0.92 cd	9.54 ± 1.55 cd	26.16 ± 0.89 e	25.23 ± 7.82 e	29.19 ± 8.61 f	29.42 ± 1.08 e
	69	10.91 ± 2.05 c	17.14 ± 0.98 d	38.79 ± 7.60 d	48.98 ± 5.98 d	46.44 ± 10.56 e	40.28 ± 3.85 d
	179	18.92 ± 1.91 b	48.54 ± 1.65 c	102.15 ± 16.11 c	111.06 ± 12.06 c	97.37 ± 29.98 d	102.52 ± 38.71 c
	311	47.63 ± 1.67 a	71.99 ± 7.81 a	139.32 ± 21.96 ab	195.07 ± 19.96 ab	210.64 ± 22.15 c	236.95 ± 24.60 b
	442	49.23 ± 5.26 a	78.46 ± 7.06 a	150.68 ± 15.75 a	227.77 ± 14.53 ab	233.15 ± 29.94 b	272.96 ± 9.92 a
	574	50.58 ± 4.87 a	69.61 ± 3.09 b	146.81 ± 6.71 ab	281.87 ± 21.97 a	268.04 ± 34.3 a	294.21 ± 27.72 a
Exp.4	20	/	25.47 ± 3.16 c	82.05 ± 1.94 c	109.23 ± 14.45 c	/	172.53 ± 11.47 c
	336	/	47.15 ± 2.33 b	122.75 ± 14.97 ab	176.33 ± 2.44 b	/	242.21 ± 34.29 ab
	532	/	61.32 ± 10.44 a	135.32 ± 5.63 a	242.56 ± 26.04 a	/	295.91 ± 27.72 a
Exp.5	28	17.53 ± 0.18 d	19.93 ± 1.40 d	22.00 ± 1.73 d	29.21 ± 3.88 d	32.1 ± 4.88 e	32.77 ± 4.80 e
	139	24.49 ± 1.21 c	35.71 ± 8.36 c	51.88 ± 8.87 c	58.38 ± 9.82 c	63.19 ± 5.47 d	85.92 ± 7.10 d
	236	29.31 ± 2.73 ab	80.12 ± 10.03 ab	122.63 ± 16.39 b	140.3 ± 3.55 b	151.7 ± 16.32 c	162.49 ± 19.19 c
	310	33.34 ± 2.31 a	90.08 ± 2.33 a	142.97 ± 16.73 a	210.16 ± 15.25 a	237.47 ± 10.92 ab	256.25 ± 10.04 ab
	390	36.77 ± 4.94 a	102.89 ± 8.64 a	156.79 ± 11.86 a	227.16 ± 9.95 a	250.39 ± 16.44 a	277.56 ± 24.33 a
Note: The data are the means of nine replicates (± standard deviations (SDs). The means denoted with different lowercase letters differed significantly at P < 0.05.

Application of the predictive model for the N_c and N_a based on PTE

Using Eq. (22) and incorporating the PTE of each experiment, we can predict the N_c of cut chrysanthemum during each sampling period (Fig. 9). When the measured N concentration exceeded the predicted N_c, it indicated that the cut chrysanthemum was undergoing luxury N absorption. Conversely, if the measured N concentration was below the predicted N_c, it suggested that the cut chrysanthemum was experiencing N deficiency. Similarly, by using Eq. (23), we can predict the N_a of cut chrysanthemum based on the same PTE (Fig. 10). By comparing the measured N accumulation with the predicted N_a, we can accurately diagnose the N accumulation status of cut chrysanthemum. This method provides a precise theoretical basis for N fertilization as needed, ensuring optimal N management throughout growth stages.

Study on the prediction model of dry matter in cut chrysanthemum

Crop dry matter reflects its biomass accumulation and is one of the crucial bases for assessing crop growth and quality(Gao et al., 2022; Yang et al., 2023). The dry matter of cut chrysanthemum showed an “S” shaped growth pattern in response to all four driving variables, consistent with the findings of previous studies(Mohammad Rafie and Mehdi, 2020; Shabani et al., 2013). Prediction models for cut chrysanthemum dry matter constructed through these driving variables achieved an R² of over 85%, showing excellent predictive capability. The accuracy and stability of the models, ranked from best to worst, are as follows: PTE > PDT > TEP > GDD. The GDD method primarily focuses on temperature factors, directly accumulating the effective temperature for calculations. Studies have shown it performed poorly in modeling crop growth and development in both field and greenhouse crops (McMaster and Wilhelm, 1997; Zhang and Tao, 2013; 程陈 et al., 2023). PDT not only considers temperature changes but also converts them into thermal effects while accounting for the impact of photo-period. This method has shown promising results in phenology simulation for field crops such as wheat and rice (Liu et al., 2018; Liu et al., 2013). Similarly, the cut chrysanthemum dry matter prediction model driven by physiological development time performed well in this study. Research indicates that cut chrysanthemum growth and development are affected by the combined effects of temperature, photo-period, and light intensity (Hidén and Larsen, 1994). Many studies have constructed growth and development simulation models for cut chrysanthemums using integrated radiation accumulation indices, with good predictive results(Lee, 2002; Lin et al., 2011; Nothnagl et al., 2004; Ding et al., 2009; Zhou et al., 2009). However, in this study, the model driven by TEP performed poorly. This may be due to the high altitude of the experiment site, where the light intensity during spring and summer seasons often exceeds the light saturation point of cut chrysanthemum(Larsen and Persson, 1999). The TEP method accumulates the total daily photosynthetic effective radiation, resulting in the excessive accumulation and surplus of light intensity effect. The PTE method improves upon this by quantifying light intensity as a photo-thermal effect using a negative exponential model (Karlsson et al., 1989; Larsen and Persson, 1999; Yang et al., 2011). This approach provides a more accurate quantification of light intensity’s impact on cut chrysanthemum growth by multiplying the thermal and light intensity effect, essentially functioning as a simple photosynthetic accumulation model (Yang et al., 2023). Consequently, the PTE-driven prediction model for cut chrysanthemum dry matter demonstrated the highest accuracy and stability in this study.

Study on the prediction model of the Nc and Na based on dry matter

In this study, spanning 16 months and encompassing five comprehensive cultivation experiments, we established a prediction model for N_c of cut chrysanthemum driven by dry matter: $\:{N}_{C}=4.5295\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{-0.309}$ with an R² of 0.9276. This model was consistent with the N_c dilution curve model $\:{N}_{C}=4.53\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{-0.327}$for processed tomatoes(Tei et al., 2002), showing only slight parameter differences. The N_a represents the minimum N accumulation required for optimal crop growth (Fernandez et al., 2022; Li et al., 2022) and can be considered the plant’s minimum N requirement (Albornoz, 2016; Fu et al., 2023; Lacasa et al., 2023). Determining the dynamic N_a during crop growth provides a basis for on-demand nitrogen supply. According to the relationship between the dry matter, N_c, and N_c dilution model(Lacasa et al., 2023; Lemaire et al., 2019), we established the prediction model for N_a as follows: $\:{N}_{a}=45.295\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{0.691}$. Additionally, based on the N_c calculation method(Justes, 1994; Plénet and Lemaire, 1999), we calculated each sampling period's N_a using the dry matter and measured N accumulation. Then, the power function fitting model is used to obtain the N_a model of cut chrysanthemum as follows:$\:{\:N}_{a}=45.295\times\:{{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}}^{0.703}$, with an R² of 0.9680. Both models could directly predict the cut chrysanthemum N_a, having identical ‘a’ values and slightly different ‘b’ values, which were considered negligible for practical applications.

Study on the prediction model of the N_c and N_a based on PTE

In recent years, crop N_c and N_a have been widely used for efficient N nutrition diagnosis and N fertilizer decision-making (Guo et al., 2023; Li et al., 2022; Maltese et al., 2023; Yao et al., 2021b). However, measuring crop dry matter was cumbersome and time-consuming (Cheng et al., 2022), limiting the application of prediction models based on dry matter-driven N_c and N_a (Lemaire et al., 2019). To address this issue, researchers have developed non-destructive methods for measuring crop N using chlorophyll meters, hyperspectral imaging, and remote sensing techniques (Bi et al., 2022; Jiang et al., 2023; Lu et al., 2022). Despite these advancements, the application of these methods for continuous dynamic monitoring of crop N still needs improvement. The N_c model driven by the crop growth and developmental driver variables had demonstrated greater robustness. For example, Zhao et al. used wheat models to establish N_c prediction model based on developmental stages, finding that N_c determined by developmental stage showed less variation than by dry matter (Zhao et al., 2014). N diagnosis curves for wheat and rice were developed based on time series (GDD), enabling dynamic N diagnosis throughout the entire developmental stages of the crops (Fu et al., 2024). In this study, we successfully established prediction models for the N_c and N_a of cut chrysanthemum based on PTE, which takes temperature, light intensity, and photo-period effects into account(Matsui and Mochida, 2024). This allows for real-time prediction of N_c and N_a of cut chrysanthemum using environmental data monitored during its growth. When combined with non-destructive N diagnostic technologies such as hyperspectral imaging, this approach enables immediate and efficient diagnosis of N status in cut chrysanthemum. Furthermore, by integrating the N utilization efficiency of cut chrysanthemum (Albornoz, 2016; Yao et al., 2021a), the optimal N fertilization amount can be estimated using the N_a prediction model, allowing for real-time, on-demand N supply for cut chrysanthemum.

This study, drawing upon data from five batches of greenhouse cut chrysanthemum cultivation experiments under different N gradient treatments, yields several key findings: (1) The prediction model was established based on four crop growth and developmental driver variables methods, with the PTE emerging as the most effective driving variable, as confirmed through model validation and comparison; (2) The N_c and N_a prediction models for cut chrysanthemum were established using dry matter as the driving variable. When the aboveground dry matter was 1 g plant^-1, the cut chrysanthemum N_c and N_a were 4.5295% and 45.295 mg plant^-1, respectively; (3) The N_c and N_a prediction models for cut chrysanthemum were established employing the PTE as the driving variable. This approach facilitates real-time and efficient N diagnosis in cut chrysanthemum, while simultaneously providing a theoretical framework for dynamically supplying N fertilizer to optimize their growth.

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author contributions

Huahao Liu: Data curation, formal analysis, writing of the draft paper. Yin Wu: Data collection and data curation. Jinshan Lu: Study design, writing of the draft paper, review of the paper. Tingyu Gou: Data curation. Shuang Zhao: Review and editing. Fadi Chen: Review and editing. Sumei Chen: Review and editing. Weimin Fang: Study design, review of the paper. Zhiyong Guan: Study design, formal analysis, review and editing.

Acknowledgements

This work was financially supported by the National Key Research and Development Program of China (2020YFD1000400) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

Data Availability

All data generated or analyzed during this study are included in this published article (and its supplementary information fles).

Albornoz F (2016) Crop responses to nitrogen overfertilization: A review. Sci Hort 205:79–83. https://doi.org/10.1016/j.scienta.2016.04.026
Aliniaeifard S, van Meeteren U (2016) Stomatal characteristics and desiccation response of leaves of cut chrysanthemum (Chrysanthemum morifolium) flowers grown at high air humidity. Sci Hort 205:84–89. https://doi.org/10.1016/j.scienta.2016.04.025
Ata-Ul-Karim ST, Yao X, Liu X, Cao W, Zhu Y (2013) Development of critical nitrogen dilution curve of Japonica rice in Yangtze River Reaches. Field Crops Res 149:149–158. https://doi.org/10.1016/j.fcr.2013.03.012
Bi K, Gao S, Xiao S, Zhang C, Bai J, Huang N, Sun G, Niu Z (2022) N distribution characterization based on organ-level biomass and N concentration using a hyperspectral lidar. Comput Electron Agric 199:107165. https://doi.org/10.1016/j.compag.2022.107165
Ceglar A, Crepinsek Z, Kajfez-Bogataj L, Pogacar T (2011) The simulation of phenological development in dynamic crop model The Bayesian comparison of different methods. Agric For Meteorol 151:101–115. https://doi.org/10.1016/j.agrformet.2010.09.007
Cheng MH, He JY, Wang HD, Fan JL, Xiang YZ, Liu XQ, Liao ZQ, Tang ZJ, Abdelghany AE, Zhang FC (2022) Establishing critical nitrogen dilution curves based on leaf area index and aboveground biomass for greenhouse cherry tomato: A Bayesian analysis. Eur J Agron 141:126615. https://doi.org/10.1016/j.eja.2022.126615
Fernandez JA, van Versendaal E, Lacasa J, Makowski D, Lemaire G, Ciampitti IA (2022) Dataset characteristics for the determination of critical nitrogen dilution curves: From past to new guidelines. Eur J Agron 139:126568. https://doi.org/10.1016/j.eja.2022.126568
Fu Z, Zhang J, Jiang J, Zhang Z, Cao Q, Tian Y, Zhu Y, Cao W, Liu X (2024) Using the time series nitrogen diagnosis curve for precise nitrogen management in wheat and rice. Field Crops Res 307:109259. https://doi.org/10.1016/j.fcr.2024.109259
Fu Z, Zhang R, Zhang J, Zhang K, Cao Q, Tian Y, Zhu Y, Cao W, Liu X (2023) Potential of Establishing the Universal Critical Nitrogen Dilution Curve for Japonica Rice. Plant Phenomics 5:36–49. https://doi.org/10.34133/plantphenomics.0036
Gao H, Zhang C, van der Werf W, Ning P, Zhang Z, Wan S, Zhang F (2022) Intercropping modulates the accumulation and translocation of dry matter and nitrogen in maize and peanut. Field Crops Res 284:108561. https://doi.org/10.1016/j.fcr.2022.108561
Gómez JA, Soriano M-A (2020) Evaluation of the suitability of three autochthonous herbaceous species as cover crops under Mediterranean conditions through the calibration and validation of a temperature-based phenology model. Agric Ecosyst Environ 291:106788. https://doi.org/10.1016/j.agee.2019.106788
Greenwood DJ, Gastal F, Lemaire G, Draycott A, Millard P, Neeteson JJ (1991) Growth rate and % N of field grown crops: theory and experiments. Ann Botany 67:181–190. https://doi.org/10.1093/oxfordjournals.aob.a088118
Greenwood DJ, Lemaire G, Gosse G, Cruz P, Draycott A, Neeteson JJ (1990) Decline in percentage N of C3 and C4 crops with increasing plant mass. Ann Botany 66:425–436. https://doi.org/10.1093/oxfordjournals.aob.a088044
Guo R, Qian R, Naseer MA, Han F, Zhang P, Jia Z, Chen X, Ren X (2023) Estimation of in-season nitrogen requirement for drip-irrigated spring maize without or with straw incorporation using critical nitrogen dilution curve. Plant Soil 490:555–572. https://doi.org/10.1007/s11104-023-06099-z
He J, Ma J, Cao Q, Wang X, Yao X, Cheng T, Zhu Y, Cao W, Tian Y (2022) Development of critical nitrogen dilution curves for different leaf layers within the rice canopy. Eur J Agron 132:126414. https://doi.org/10.1016/j.eja.2021.126414
He ZY, Qiu XL, Ata-Ul-Karim ST, Li YD, Liu XJ, Cao Q, Zhu Y, Cao WX, Tang L (2017) Development of a critical nitrogen dilution curve of double cropping rice in south China. Front Plant Sci 8:638. https://doi.org/10.3389/fpls.2017.00638
Hidén C, Larsen RU (1994) Predicting flower development in greenhouse grown chrysanthemum. Sci Hort 58:123–138. https://doi.org/10.1016/0304-4238(94)90133-3
Jiang J, Atkinson PM, Chen C, Cao Q, Tian Y, Zhu Y, Liu X, Cao W (2023) Combining UAV and Sentinel-2 satellite multi-spectral images to diagnose crop growth and N status in winter wheat at the county scale. Field Crops Res 294:108860. https://doi.org/10.1016/j.fcr.2023.108860
Josefina L, David M, Trevor H, Javier F, Emmanuela vV, Gilles L, Ignacio C (2023) Comparison of statistical methods to fit critical nitrogen dilution curves. Eur J Agron 145:126770. https://doi.org/10.1016/j.eja.2023.126770
Justes E (1994) Determination of a critical nitrogen dilution curve for winter wheat crops. Ann Botany 74:397–407. https://doi.org/10.1006/anbo.1994.1133
Kage H, Alt C, Stützel H (2002) Nitrogen concentration of cauliflower organs as determined by organ size, N supply, and radiation environment. Plant and Soil 246, 201–209. https://Doi10.1023/A:1020627723616
Karlsson MG, Heins RD, Erwin JE, Berghage RD, Carlson WH, Biernbaum JA (1989) Irradiance and Temperature Effects on Time of Development and Flower Size in Chrysanthemum. Sci Hort 39:257–267. https://doi.org/10.1016/0304-4238(89)90138-6
Lacasa J, Makowski D, Hefley T, Fernandez J, van Versendaal E, Lemaire G, Ciampitti I (2023) Comparison of statistical methods to fit critical nitrogen dilution curves. Eur J Agron 145:126770. https://doi.org/10.1016/j.eja.2023.126770
Larsen RU, Persson L (1999) Modelling flower development in greenhouse chrysanthemum cultivars in relation to temperature and response group. Sci Hort 80:73–89. https://doi.org/10.1016/s0304-4238(98)00219-2
Lee JH (2002) Simulation of leaf area development based on dry matter partitioning and specific leaf area for cut chrysanthemum. Ann Botany 91:319–327. https://doi.org/10.1093/aob/mcg015
Lemaire G, Jeuffroy M-H, Gastal F (2008) Diagnosis tool for plant and crop N status in vegetative stage. Eur J Agron 28:614–624. https://doi.org/10.1016/j.eja.2008.01.005
Lemaire G, Salette J, Sigogne M, Terrasson J-P (1984) Relation entre dynamique de croissance et dynamique de prélèvement d'azote pour un peuplement de graminées fourragères. II. - Etude de la variabilité entre génotypes. Agronomie 4:431–436. https://doi.org/10.1051/agro:19840504
Lemaire G, Sinclair T, Sadras V, Bélanger G (2019) Allometric approach to crop nutrition and implications for crop diagnosis and phenotyping. A review. Agron Sustain Dev 39:27–44. https://doi.org/10.1007/s13593-019-0570-6
Lemaire G, van Oosterom E, Sheehy J, Jeuffroy MH, Massignam A, Rossato L (2007) Is crop N demand more closely related to dry matter accumulation or leaf area expansion during vegetative growth? Field Crops Res 100:91–106. https://doi.org/10.1016/j.fcr.2006.05.009
Li W, Gu X, Fang H, Zhao T, Yin R, Cheng Z, Tan C, Zhou Z, Du Y (2024) Optimizing nitrogen application rate by establishing a unified critical nitrogen dilution curve for maize under different mulching planting patterns. Eur J Agron 152:127026. https://doi.org/10.1016/j.eja.2023.127026
Li X, Ata-Ui-Karim ST, Li Y, Yuan F, Miao Y, Yoichiro K, Cheng T, Tang L, Tian X, Liu X, Tian Y, Zhu Y, Cao W, Cao Q (2022) Advances in the estimations and applications of critical nitrogen dilution curve and nitrogen nutrition index of major cereal crops. A review. Comput Electron Agric 197:106998. https://doi.org/10.1016/j.compag.2022.106998
Lin L, Li W, Shao J, Luo W, Dai J, Yin X, Zhou Y, Zhao C (2011) Modelling the effects of soil water potential on growth and quality of cut chrysanthemum (Chrysanthemum morifolium). Sci Hort 130:275–288. https://doi.org/10.1016/j.scienta.2011.06.008
Liu L, Wallach D, Li J, Liu B, Zhang L, Tang L, Zhang Y, Qiu X, Cao W, Zhu Y (2018) Uncertainty in wheat phenology simulation induced by cultivar parameterization under climate warming. Eur J Agron 94:46–53. https://doi.org/10.1016/j.eja.2017.12.001
Liu L, Wang E, Zhu Y, Tang L, Cao W (2013) Effects of warming and autonomous breeding on the phenological development and grain yield of double-rice systems in China. Agric Ecosyst Environ 165:28–38. https://doi.org/10.1016/j.agee.2012.11.009
Lu J, Nie W, Song J, Zhan Q, Wang M, Chen F, Fang W, Chen S, Zhang F, Zhao S, Guan Z (2022) Estimation of nitrogen nutrition index in chrysanthemum using chlorophyll meter readings. Ind Crops Prod 187:115459. https://doi.org/10.1016/j.indcrop.2022.115459
Maltese NE, Maddonni GA, Melchiori RJM, Ciampitti IA, Caviglia OP (2023) The allometric relationships between biomass and nitrogen of vegetative organs affect crop N status in maize at silking stage. Field Crops Res 294:108861. https://doi.org/10.1016/j.fcr.2023.108861
Matsui H, Mochida K (2024) Functional data analysis-based yield modeling in year-round crop cultivation. Hortic Res hr uhae144. https://doi.org/10.1093/hr/uhae144
McMaster GS, Wilhelm WW (1997) Growing degree-days: one equation, two interpretations. Agric For Meteorol 87:291–300. https://doi.org/10.1016/s0168-1923(97)00027-0
Minghui C, Jiaoyang H, Haidong W, Junliang F, Youzhen X, Xiaoqiang L, Zhenqi L, Zijun T, Elsayed AA, Fucang Z (2022) Establishing critical nitrogen dilution curves based on leaf area index and aboveground biomass for greenhouse cherry tomato: A Bayesian analysis. Eur J Agron 141. https://doi.org/10.1016/j.eja.2022.126615
Mohammad Rafie R, Mehdi M (2020) Application of logistic model to estimate eggplant yield and dry matter under different levels of salinity and water deficit in greenhouse and outdoor conditions. Water SA 46:8652. https://doi.org/10.17159/wsa/2020.v46.i3.8652
Nothnagl M, Kosiba A, Larsen RU (2004) Predicting the effect of irradiance and temperature on the flower diameter of greenhouse grown Chrysanthemum. Sci Hort 99:319–329. https://doi.org/10.1016/s0304-4238(03)00096-7
Plénet D, Lemaire G (1999) Relationships between dynamics of nitrogen uptake and dry matter accumulation in maize crops.: Determination of critical N concentration. Plant Soil 216:65–82. https://doi.org/10.1023/a:1004783431055
Shabani A, Sepaskhah AR, Kamgar-Haghighi AA (2013) Estimation of yield and dry matter of rapeseed using logistic model under water salinity and deficit irrigation. Arch Agron Soil Sci 60:951–969. https://doi.org/10.1080/03650340.2013.858807
Sinclair TR, Rufty TW (2012) Nitrogen and water resources commonly limit crop yield increases, not necessarily plant genetics. Global Food Secur 1:94–98. https://doi.org/10.1016/j.gfs.2012.07.001
Tei F, Benincasa P, Guiducci M (2002) Critical nitrogen concentration in processing tomato. Eur J Agron 18:45–55. https://doi.org/10.1016/s1161-0301(02)00096-5
Teixeira da Silva JA, Shinoyama H, Aida R, Matsushita Y, Raj SK, Chen F (2013) Chrysanthemum Biotechnology:Quo vadis? Crit Reviews Plant Sci 32:21–52. https://doi.org/10.1080/07352689.2012.696461
Ulrich A (1952) Physiological bases for assessing the nutritional requirements of plants. Annu Rev Plant Physiol 3:207–228. https://doi.org/10.1146/annurev.pp.03.060152.001231
Willmott CJ (1982) Some comments on the evaluation of model performance. Bull Am Meteorol Soc 63:1309–1313. https://doi.org/10.1175/1520-0477(1982)063
Yang J, Greenwood DJ, Rowell DL, Wadsworth GA, Burns IG (2000) N_ABLE Agricultural Syst 64:37–53. https://doi.org/10.1016/s0308-521x(00)00010-x. Statistical methods for evaluating a crop nitrogen simulation model
Yang K, Mo J, Luo S, Peng Y, Fang S, Wu X, Zhu R, Li Y, Yuan N, Zhou C, Gong Y (2023) Estimation of rice aboveground biomass by UAV imagery with photosynthetic accumulation models. Plant Phenomics 5:0056. https://doi.org/10.34133/plantphenomics.0056
Yao B, He H-b, Xu H-c, Zhu T-z, Liu T, Ke J, You C-c, Zhu D-q, Wu L-q (2021a) Determining nitrogen status and quantifying nitrogen fertilizer requirement using a critical nitrogen dilution curve for hybrid indica rice under mechanical pot-seedling transplanting pattern. J Integr Agric 20:1474–1486. https://doi.org/10.1016/s2095-3119(21)63622-5
Yao B, Wang X, Lemaire G, Makowski D, Cao Q, Liu X, Liu L, Liu B, Zhu Y, Cao W, Tang L (2021b) Uncertainty analysis of critical nitrogen dilution curves for wheat. Eur J Agron 128:111017. https://doi.org/10.1016/j.eja.2021.126315
Zhang L, Xu Z, Xu D, Ma J, Chen Y, Fu Z (2020) Growth monitoring of greenhouse lettuce based on a convolutional neural network. Hortic Res 7:124. https://doi.org/10.1038/s41438-020-00345-6
Zhang S, Tao F (2013) Modeling the response of rice phenology to climate change and variability in different climatic zones: Comparisons of five models. Eur J Agron 45:165–176. https://doi.org/10.1016/j.eja.2012.10.005
Zhao Z, Wang E, Wang Z, Zang H, Liu Y, Angus JF (2014) A reappraisal of the critical nitrogen concentration of wheat and its implications on crop modeling. Field Crops Res 164:65–73. https://doi.org/10.1016/j.fcr.2014.05.004
Zheng J, Zhang S (2023) Improving rice phenology simulations based on the Bayesian model averaging method. Eur J Agron 142:126646. https://doi.org/10.1016/j.eja.2022.126646
Zhou H, Kang S, Genard M, Vercambre G, Chen J (2023) Integrated model simulates bigger, sweeter tomatoes under changing climate under reduced nitrogen and water input. Hortic Res 10:uhad045. https://doi.org/10.1093/hr/uhad045
Zhou L, Feng H, Zhao W (2021) Plastic film mulching affects the critical nitrogen dilution curve of drip-irrigated maize. Field Crops Res 263:55–63. https://doi.org/10.1016/j.fcr.2021.108055
Cheng C, Li C, Li W et al (2023) Trans Chin Soc Agricultural Eng 39:158–167 (in Chinese). https://doi.org/10.11975/j.issn.1002-6819.202303028. Optimal simulation path of the developmental period and harvest period simulation model for horticultural crops
Ding Q, Dai J, Luo W et al (2009) Simulation of the effect of nitrogen on the appearance quality of ‘Shenma’ single-stem chrysanthemum in solar greenhouses. Scientia Agricultura Sinica 42:363–369 (in Chinese). https://doi.org/10.3864/j.issn.0578-1752.2009.01.047
Yang Z, Huang H, Jin Z et al (2011) Establishment and validation of a bayberry growth period model based on photo-thermal effects. Acta Horticulturae Sinica 38:1259–1266 (in Chinese). https://doi.org/10.16420/j.issn.0513-353x.2011.07.007
Zhou Y, Dai J, Lin L et al (2009) Simulation of water impact on the appearance quality of Chrysanthemum in a solar greenhouse. Trans Chin Soc Agricultural Eng 25:204–209 (in Chinese). https://doi.org/10.3321/j.issn:1002-6819.2008.11.035

SupplementalTable.xlsx

Download PDF

Reviewers agreed at journal
16 Sep, 2024
Reviewers invited by journal
05 Sep, 2024
Editor invited by journal
29 Aug, 2024
Editor assigned by journal
29 Aug, 2024
First submitted to journal
29 Aug, 2024

You are reading this latest preprint version

Predictive Modeling Study on the Critical Nitrogen Concentration and Nitrogen Accumulation in Cut Chrysanthemum Based on the Cumulative Photo-Thermal Effect

Status:

Version 1

Abstract

Background and aims

Methods

Results

Conclusions

Figures

Introduction

Materials and methods

Results

Discussion

Conclusion

Declarations

Author contributions

Acknowledgements

Data Availability

References

Supplementary Files

Status:

Version 1

Driver variables	Formula	R²	Number of data pairs	P value
GDD	\(\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+30.311\times\:\text{E}\text{X}\text{P}(-0.00461\times\:\text{G}\text{D}\text{D}\left)\right)\)	0.861	N = 42	P < 0.001
PDT	\(\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+31.288\times\:\text{E}\text{X}\text{P}(-0.08782\times\:\text{P}\text{D}\text{T}\left)\right)\)	0.944	N = 42	P < 0.001
TEP	\(\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+30.085\times\:\text{E}\text{X}\text{P}(-0.02542\times\:\text{T}\text{E}\text{P}\left)\right)\)	0.915	N = 42	P < 0.001
PTE	\(\:{\text{D}\text{M}}_{\text{m}\text{a}\text{x}}=12.50/(1+30.916\times\:\text{E}\text{X}\text{P}(-0.00644\times\:\text{P}\text{T}\text{E}\left)\right)\)	0.974	N = 42	P < 0.001