Phenological Restriction of the Oryza (v3) Model

Restrição Fenológica do Modelo Oryza (v3)

Abstract

Photoperiod sensitivity affects the rice development cycle and its flowering. Crop simulation models, such as ORYZA (v3), use equations that depend on two main parameters calibrated by the user: sensitivity to photoperiod and minimum optimal photoperiod. Day length, determined by latitude and day of the year, also affects crop development. This study explores the interaction of these parameters in the ORYZA (v3) phenological model. When the optimum minimum photoperiod is shorter than the day length, photoperiod sensitivity delay or inhibit flowering. To ensure a proper simulation, these parameters need to be adjusted to avoid excessive prolongation of the vegetative phase. If calibrated incorrectly, or if let in constant low photoperiod conditions, the plant may remain in the vegetative state. The model presents challenges with cultivars that are highly sensitive to photoperiod in conditions where day length is constantly longer than the ideal minimum photoperiod. This situation may generate uninterpretable results and complicate the calibration of parameters via optimization algorithms. Therefore, it is crucial to properly adjust the optimal minimum photoperiod based on latitude and limit photoperiod sensitivity to ensure accurate and precise simulations of flowering.

Keywords
flowering; day length; photoperiod; parameter estimation; calibration

Resumo

A sensibilidade ao fotoperíodo influencia o ciclo de desenvolvimento do arroz, afetando o florescimento. Modelos de simulação de culturas, como o ORYZA (v3), utilizam equações que dependem de dois parâmetros principais, calibrados pelo usuário: sensibilidade ao fotoperíodo e fotoperíodo mínimo ideal. O comprimento do dia, determinado pela latitude e dia do ano, também influencia o desenvolvimento da cultura. Este estudo explora a interação desses parâmetros no modelo fenológico do ORYZA (v3). Quando o fotoperíodo mínimo ideal é menor que o comprimento do dia, a sensibilidade ao fotoperíodo pode atrasar ou inibir o florescimento. Para garantir a simulação correta, esses parâmetros precisam ser ajustados para evitar um prolongamento excessivo da fase vegetativa. Se calibrados incorretamente, ou em condições constantes de baixo fotoperíodo, a planta pode permanecer em estado vegetativo. O modelo apresenta dificuldades com cultivares altamente sensíveis ao fotoperíodo em condições onde o comprimento do dia é constantemente superior ao fotoperíodo mínimo ideal, o que pode gerar resultados não interpretáveis e complicar a calibração dos parâmetros via algoritmos de otimização. Portanto, é crucial ajustar adequadamente o fotoperíodo mínimo ideal com base na latitude e limitar a sensibilidade ao fotoperíodo para garantir simulações precisas e acuradas do florescimento.

Palavras-chave
florescimento; comprimento do dia; fotoperíodo; estimativa de parâmetros; calibração

1. Introduction

The network of genetic and biochemical processes that regulate flowering is complex. It depends on interactions between endogenous and environmental factors (Blümel et al., 2015), mainly air temperature and day length (Song et al., 2012), known as photoperiod (Runkle, 2002). Rice (Oryza sativa L.) mainly promotes its flowering through photoperiod (Lee and An, 2015; Song et al., 2012). Rice is a quantitative short-day plant, but sensitivity to photoperiod depends on the cultivar. However, when the plant is exposed to a photoperiod shorter the ideal minimum and is at the appropriate age, flowering accelerates (Shim and Jang, 2020; Lee and An, 2015; Tsuji et al., 2011).

Equations that calculate photoperiod for rice genotypes are widely used by process-based crop simulation models (CSM), such as CERES-Rice (Hoogenboom et al., 2019) and ORYZA (v3) (Li et al., 2017). Sensitivity to photoperiod affects the crop cycle, the end of the juvenile phase, and the continuity of its development stages, such as panicle formation, flowering and physiological maturity. These changes in crop cycle have significant effects on the physiological and morphological processes of the plant, including its structural growth and the allocation of resources to different plant parts. In the CSM ORYZA (v3), the equation that calculates the sensitivity of genotype to photoperiod has three parameters: photoperiod sensitivity (PPSE), minimum optimal photoperiod (MOPP), and day length (DL).

For cultivars less sensitive to photoperiod, air temperature determines phenological development in the ORYZA (v3) model. However, for more sensitive cultivars, the crop development rate (DVS) between the end of the basic vegetative development stage (DVS = 0.40) and the beginning of panicle formation (DVS = 0.65) is calculated by the accumulation of heat units over time (TT), PPSE, MOPP (Bouman et al., 2001).

The PPSE ranges from 0 to 1, reflecting sensitivity to photoperiod. A value equal to 0 indicates that the plant is insensitive to photoperiod, while a value equal to 1 indicates that the MOPP must be shorter than or very close to DL for flowering to occur. Therefore, when applying the CSM ORYZA (v3), it is necessary to adjust the PPSE and MOPP (Bouman et al., 2001). In most cases, PPSE is assigned values very close to 0, regardless of the genotype, environmental conditions, or management. This is partially justified in subtropical rice production regions in Latin America, where it is assumed that genotypes are insensitive or only slightly sensitive to photoperiod (Lorençoni et al., 2010; Santos et al., 2017; Duarte et al., 2021). In some tropical regions, such as Southwest Asia, the use of photoperiod-sensitive genotypes as a management strategy is common. In this case, the PPSE is adjusted to values very close to 1 (Boling et al., 2011; Sujariya et al., 2023). Many studies omit information about the values and calibration methods of these parameters, or fix default values (Li et al., 2020; Tan et al., 2022, Yu et al., 2023). Despite being a strategy to simplify parameterization in CSM depending on the purpose of its use, it is important to optimize the parameters that guide the calculation of photoperiod (van Oort et al., 2011). PPSE adjustment is usually empirical and performed through trial and error so that simulated panicle beginning dates correspond as closely as possible to observed dates (Boling et al., 2011). Empirical methods are useful, but they are hardly effective in optimizing hyperparameters of an equation in which there is a combinatorial analysis, for example. Due to advances in computational capacity, advanced techniques that use modern and efficient optimization algorithms for model parameterization can be applied easily (Tan et al., 2022). However, it is necessary that the combinations of parameter values are appropriate to the model's assumptions and that their interactions allow the crop cycle to be completed.

This study aims to understand how PPSE, MOPP, and DL interact and affect the functioning of the ORYZA (v3) phenological model, especially under unfavorable photoperiodic conditions. We seek to describe the limitations of CSM photoperiod calculation equations and propose an efficient method to establish a range of values for these parameters, ensuring the simulation of flowering for Brazilian conditions.

2. Methodology

2.1. Model

In the CSM ORYZA (v3), potential DVS is calculated as a function of air temperature and photoperiod. However, in this CSM, water deficit is a limiting factor that affects DVS (Bouman et al., 2001). In this study, which focuses on irrigated rice, we assume that there are no biotic and abiotic limitations to crop development. Thus, only air temperature and photoperiod affect DVS.

Thermal time (TT) is calculated based on daily temperatures considering that development linearly increases above a minimum basal temperature (TBD) up to an optimum temperature (TOD) and decreases up to reaching the maximum development temperature (TMD), beyond which development ceases.

Eq. (1) through Eq. (5) describe how TT is calculated:

(1)$$\begin{array}{l}{T}_d=\frac{T_{\mathrm{m}\mathrm{i}\mathrm{n}}+T_{\mathrm{m}\mathrm{a}\mathrm{x}}}{2}+\frac{T_{\mathrm{m}\mathrm{a}\mathrm{x}}-T_{\mathrm{m}\mathrm{i}\mathrm{n}}}{2}\cos (0.2618(h-14)),\end{array}$$

(2)$$\mathrm{S}\mathrm{e} T_d\le TBD \mathrm{e} T_d\ge TMD:HUH=0$$

(3)$$\begin{array}{l}\mathrm{S}\mathrm{e} TBD<T_d\le TOD:\text{H}\text{U}\text{H}=\frac{T_d-TBD}{24}\end{array}$$

(4)$$\begin{array}{l}\mathrm{S}\mathrm{e} TOD<T_d<TMD:\text{H}\text{U}\text{H}=\frac{TOD-(T_d-TOD)\times \frac{TOD-TBD}{TMD-TOD}}{24}\end{array}$$

(5)$$\begin{array}{l}TT={\sum }_{h=1}^{24}HU{H}_h\end{array}$$

where T_d is the daily temperature, T_min and T_max are the minimum and maximum temperature, respectively, h is the time of day and HUH is the hourly increase of air temperature.

According to daily weather conditions and rice variety characteristics, the CSM ORYZA (v3) assigns specific values of TT required to complete each phenological phase. This is done through a specific correction factor for each phenological phase and genotype over the TT accumulated on a given day. Thus, the vegetative phase requires a certain amount of TT to be completed. At this phase, the TT is corrected by the specific factor, called DVRJ (development rate during the juvenile phase), as follows:

(6)$$\begin{array}{l}DV{R}_{DAYJ}=T{T}_{DAYJ}\times DVRJ\end{array}$$

where DAYJ is the Julian day and DVR is the crop development rate, which is added to the DVS on each simulation day. Thus, the phase change occurs when DVS reaches the specific value for the given phase. For the juvenile vegetative phase, the established DVS value is 0.4. From this value, the vegetative phase begins, which is sensitive to the photoperiod.

The most important phenological change is the transition from the vegetative to the reproductive phase. Between these two phases is the photoperiod-sensitive phase (DVS from 0.40 to 0.65). This phase determines the moment when the plant is sufficiently mature and prone to stimulation by photoperiod. At this point, the model simulates the DL from the astronomical day length (DAYL) plus 0.90 to consider the effect of low levels of solar radiation after sunset and before sunrise.

The DL is calculated as follows:

(7)$$DEC=-{\sin }^{-1}(\sin (23.45\times 0.017453292)\times \cos \left(\frac{2\pi \times (DAYJ+10)}{365}\right)),$$

(8)$$AOB=\tan (0.017453292\times LAT)\times \tan (DEC),$$

(9)$$DAYL=12\times (1+\frac{2\times {\sin }^{-1}(AOB)}{\pi }),$$

(10)$$\begin{array}{l}DL=DAYL+0.9\end{array}$$

where DEC is the sun's declination angle, AOB is an auxiliary variable, and LAT is the latitude of the location.

The CSM compares the MOPP to the DL under analysis. If it is short, a factor called PPFAC assumes the value 1. If the DL is longer than the MOPP, the model applies the PPSE parameter on the difference of MOPP and DL to calculate the PPFAC:

(11)$$PPFA{C}_{DAYJ}=1-(D{L}_{DAYJ}-MOPP)\times PPSE$$

(12)$$PPFA{C}_{DAYJ}=min(1,max(0,PPFA{C}_{DAYJ}))$$

PPFAC, now modulated between 0 and 1, is used as a correction to calculate the DVR. A specific development rate for panicle initiation (DVRI) is also applied to it. Therefore, at this stage, the DVR is calculated as follows:

(13)$$\begin{array}{l}DV{R}_{DAYJ}=DVRI\times T{T}_{DAYJ}\times PPFA{C}_{DAYJ}\end{array}$$

Finally, for flowering to occur, the DVR is added to the DVS, adjusting the calculations for each day until the DVS is greater than 0.65.

(14) $$\begin{array}{l}DVS=DVS+DV{R}_{DAYJ}\end{array}$$

2.2. Implementation

The phenology calculation equations from the CSM ORYZA (v3) PHENOL subroutine were implemented in R to simulate only phenology and simplify analyses, focusing on functions related to photoperiod. Henceforth, these equations are called the photoperiod model. The photoperiod model in the R language was assessed for several parameters compared with its original versions in Fortran with the aim of verifying whether there is any inconsistency in the script in the R language.

2.3. Model calibration

The cardinal temperatures for the BRS 7 Taim cultivar were previously calibrated (da Conceição et al., 2018). The DVRI was self-calibrated according to the observed data, described in sub-item 2.4, based on the genetic parameters. To this end, the accumulated TT was calculated in the interval of days between the vegetative phase V6 and the observed panicle initiation (R0). The daily TT value was corrected by PPFAC, normalized, and adjusted to the range between 0.40 and 0.65. This range refers to the DVS of the photosensitive phase and represents the relative variation range for the DVRI. In short:

(15) $$DVRI=(0.65-0.40)\times \left(\frac{1}{\sum _{i=V6}^{R0}(T{T}_{DAY}\times PPFA{C}_{DAY})}\right)$$

2.4. Experimental data

A phenological database of the cultivar BRS 7 Taim was used. It was created for the 2005/06 agricultural season in Capão do Leão, RS, Brazil (latitude -31.79, longitude -52.51), as described by Steinmetz et al. (2009). The field trial had a spacing of 17.5 cm between rows and a sowing density of 80 suitable seeds per meter. The development of ten plants (main stem) was monitored by sampling throughout the cycle, characterizing each stage according to the scale proposed by Counce et al. (2000).

2.5. Site

In this study, there were two extreme locations in relation to photoperiod: the municipalities of Pelotas (latitude -31.61, longitude -52.33) in Rio Grande do Sul and Cantá (latitude 2.41, longitude -60.67) in Roraima. To calculate the day length (DL), Eq. (1) to Eq. (5) were used, applied to the respective latitudes of Pelotas and Cantá. Figure 1 shows the variation in day length (DL) for both locations.

Figure 1.
Variation in day length (DL) throughout the year calculated using Eq. (1) to Eq. (5) for the latitudes -31.61 (Pelotas-RS) and 2.41 (Cantá-RR).

2.6. Climate data

Climate data were obtained from the Infoclima system database (Embrapa, 2024), covering the period from 1991 to 2009. The dataset includes the maximum and minimum air temperatures for Pelotas and were used to calculate the TT.

3. Results and Discussion

For PPSE equal to 0, the value of MOPP is irrelevant. This denotes insensitivity to the photoperiod. Some studies have ignored this, assigning MOPP values to insensitive genotypes (Poulton et al., 2015; Biswas et al., 2021). This calculation process is shared by several CSM (Bai et al., 2019).

For a MOPP greater than DL, 1 is assigned to PPFAC since the plant's photoperiodic needs were met. In this case, the PPSE value becomes irrelevant because Eq. (10) and Eq. (11) are not executed (Bouman et al., 2001). Although the plant is sensitive to photoperiod, the location and growing season of the simulation may not allow the expression of this characteristic. On the other hand, if the MOPP is lower than the DL, the PPSE value becomes decisive, and the PPFAC value is calculated daily since DL varies between days (Fig. 1) but not between years. Thus, if the relationship between PPSE, MOPP and DL, in Eq. (11), returns consecutive values close to 0, the plant extends its cycle. If PPFAC is greater than 0, flowering occurs as long as the thermal gain corrected by PPFAC and DVRI (Eq. (13)) is sufficient for this, respecting the amount of temperature data available.

As the DL varies throughout the year (minimum in July for Pelotas and in December for Cantá; Fig. 1), the sowing date should consider, in terms of photoperiod, whether the PPSE and MOPP sets are suitable for the DL of the estimated flowering period. If the MOPP is lower than the minimum DL of the region, flowering is still viable. For this to occur, PPSE needs to be close to 0 or MOPP should be close to DL values. As the MOPP approaches the DL, the PPSE may be slightly larger, as Fig. 2 shows.

Figure 2.
Photoperiod sensitivity (PPSE) values as a function of the minimum optimal photoperiod (MOPP) for the factor PPFAC to be greater than 0, given a day length (DL) in Pelotas of (A) 10.84 h, (B) 11.84 h, (C) 12.84 h, (D) 13.84 h, and (E) 14.84 h.

In the case of the municipality of Pelotas, whose minimum DL is 10.84 h, highly sensitive cultivars (PPSE = 1) can flower in July when the MOPP is longer than 9.85 h, resulting in a PPFAC of 0.01 (Fig. 2A). However, PPFAC increases to values to close to 1 as MOPP approaches DL (Fig. 2). This is in line with the fact that most rice genotypes are quantitative short-day plants (Shim and Jang, 2020; Lee and An, 2015; Tsuji et al., 2011).

The decrease in PPSE may also compensate for the mismatch between MOPP and the minimum DL. A PPSE below 0.101 still allows flowering, even when MOPP tends to 0. However, very low values for MOPP do not reflect reality. Restricting the MOPP range to values close to reality is interesting, as it increases the amplitude of the PPSE. Nevertheless, most combinations between PPSE and MOPP lower than DL resulted in PPFAC equal to 0 (Fig. 2).

When PPFAC is equal to 0, the product of Eq. (13) is 0. The CSM ORYZA (v3) simulates plant growth day by day. When the combination of parameter values results in constant zeros at PPFAC, growth stagnates. The DVR generated daily under this condition, when added to the DVS (Eq. (14)), does not result in any change. Therefore, there is no change in phenological phase, and the calculation remains in this cycle until there is no more daily climate data available for calculation. This reveals a limitation of the model to adequately deal with cultivars highly sensitive to photoperiod under unfavorable conditions, when DL is constantly higher than MOPP, resulting in outputs without a logical interpretation (“-10000”).

To elucidate the functioning of the CSM, Fig. 3 illustrates a hypothetical highly sensitive genotype grown in unfavorable environments. Considering that genotypes sensitive to photoperiod generally have a PPSE close to 0.7 (Boling et al., 2011), a PPSE of 0.8 was adopted to represent high sensitivity. The MOPP value was set at 11.5, as it is commonly used (Tan et al., 2022; Yu et al., 2023). If this hypothetical genotype were cultivated in Pelotas-RS, it would only flower during the period when the MOPP approaches the DL (Fig. 3A). In contrast, this same cultivar does not flower in Cantá-RR, as the PPFAC remains constantly at 0 (Fig. 3B).

Figure 3.
Response to photoperiod (DL) according to the ORYZA model (v3) for a fictitious genotype with photoperiod sensitivity (PPSE) of 0.8 and minimum optimal photoperiod (MOPP) of 11.5 h, grown in (A) Pelotas-RS and in (B) Cantá-RR.

The permanence in the vegetative phase observed for this genotype in Cantá (Fig. 3B) does not suggest an inconsistency in the ORYZA (v3) model, but rather a limitation of it. There are records of highly sensitive genotypes cultivated in continuously long photoperiods that remained in the vegetative phase for more than ten years (Yoshida, 1981). For Pelotas-RS, the sowing date for this supposed genotype must consider the coincidence of the photosensitive phase with the reduction in day length. If the photosensitive phase occurs after this period of shorter DL, the vegetative phase may be longer, flowering only in the following year, which is also predicted in the literature. Dore (1959), in studies conducted in Malaysia, where the DL is very close to that of Cantá (RR), recorded the response of a genotype with high sensitivity to the photoperiod in January (increasing DL), in which situation it flowered at 329 days due to a small difference in the annual amplitude of DL (only 14 minutes). When grown in September (decreasing DL), it flowered at 161 days. However, a positive PPFAC does not necessarily lead to flourishing either. Thus, the speed of flowering onset depends on its relationship with TT and DVRI (Eq. (13)). Regarding PPFAC, for the DVS to reach the value necessary to change the phenological phase from V6 to R0 (0.65), it needs to be close to 1 so that the DVR generated on each day of simulation, when added to the DVS (Eq. (14)), increases its value at a speed that allows flowering before the simulation period ends.

When calculating the DVR, the factor related to the climate condition may increase the degree of complexity in the relationship between parameters. Figure 4A2 and B2 show this scenario. It is similar to that Fig. 3A shows for Pelotas. The PPFAC value does not change between years, but the DVR value does. For the DVR calculation, the DVRI is relative to the genotype (fixed). The TT, on the other hand, varies according to the climatic conditions of the year (Figs. 4A1 and B1) and is calculated considering cardinal temperatures (Eq. (1) to Eq. (5)), which also do not change during the simulation. DVRI, TOD, TBD, and TMD are reported by users and considered fixed by the ORYZA (v3) model. These factors affect the DVR value, which varies daily (Figs. 4A2 and B2).

Figure 4.
(A1) Thermal time (TT) calculated using a minimum basal temperature of 9 °C, an optimum temperature of 25 °C, and a maximum development temperature of 36 °C, calibrated for the BRS 7 Taim cultivar, and (B1) considering an increase in minimum basal temperature to 14 °C from 1991 to 2009 for Pelotas-RS. Crop development rate (DVR) was calculated for minimum, average, and maximum temperatures, considering (A2 and B2) a minimum optimal photoperiod (MOPP) of 11.5 h and (A3 and B3) a MOPP of 10.0 h, both with photoperiod sensitivity (PPSE) of 0.8 and a development rate at panicle initiation (DVRI) of 0.0008709396.

Figure 4 shows the period before day 100, and the DVR is 0, reflecting a null PPFAC. This repeats after day 250, where the DL is increasing and longer than MOPP again. Figure 3 shows that as PPFAC approaches 1, the DVR increases. The magnitude of the increase depends on the TT accumulated on the day and the DVRI. This was not demonstrated for Cantá, as the constantly null PPFAC does not allow flowering (Fig. 3B).

The increase in TBD causes a reduction and even nullification of TT in low temperature scenarios (Fig. 4B1). Coincidentally, the minimum temperatures occur in the same shortest photoperiods in Pelotas. This means that, even under good photoperiods, there is no TT in extremely cold conditions. This reflects on the DVR, assigning 0 to it. However, with too many consecutive days below TBD, the CSM kills the plant and ends the simulation. The slightest reduction in the MOPP value may also lead to large reductions in the DVR value (Figs. 4A3 and B3), especially when associated with low TT values.

Table 1 shows the sum of annual DVR and the number of years required for flowering to occur based on the parameters shown in Fig. 4, whose DVRI is not self-calibrated. The 1.5-h reduction in MOPP, combined with the increase in TBD from 9 °C to 14 °C, increases the need from 8.6 simulated years to 1,276.8 years for flowering to occur, which is undesirable. This shows that the DVR is very sensitive to any of its direct or indirect parameters.

Table 1
Sum of the annual crop development rate (DVR) and number of years simulated for flowering to occur under the conditions shown in Fig. 4.

MOPP* (hours)	TBD* (°C)	TT* (Degree-days)	DVR Annual Sum	Time to flowering (years)
10.0	9	minimum	0.009813662	25.5
10.0	14	minimum	0.0001958052	1276.8
10.0	9	average	0.05355447	4.7
10.0	14	average	0.01881494	13.3
10.0	9	maximum	0.1100469	2.3
10.0	14	maximum	0.06096323	4.1
11.5	9	minimum	0.1701145	1.5
11.5	14	minimum	0.0290618	8.6
11.5	9	average	0.5540252	0.5
11.5	14	average	0.2231328	1.1
11.5	9	maximum	1.006132	0.2
11.5	14	maximum	0.5750299	0.4

• *MOPP is the minimum optimal photoperiod; TBD is the minimum basal temperature; TT is the thermal time.

The reducing effect on TT is not exclusive to TBD. All three cardinal temperatures can reduce TT and affect flowering ability. With TOD ranging from 15 to 32 °C, TBD and TMD fixed at 14 and 33 °C, respectively, Fig. 5A shows the effect of TOD on TT under average temperature conditions. As after TOD the thermal gain starts to decrease as it approaches TMD, and with a high TBD, low TOD values suppress the TT, which drastically affects the DVR. Similarly, high TOD allows for higher TT.

Figure 5.
(A) Thermal time (TT) and (B) self-adjustment of the development rate at panicle initiation (DVRI) as a function of the optimum development temperature (TOD).

In summary, MOPP, PPSE, TBD, TOD, and TMD directly affect the DVR. Indirectly, it is influenced by the day and latitude, which make up the DL, and by the climatic characteristics of the region. The combination of these parameters must ensure that:

(16)$$\sum _{i=1}^{DAYJ}(DVRI\times T{T}_{DAYJ}\times PPFA{C}_{DAYJ})=0.25$$

where the number of Julian days simulated between V6 and R0 (DAYJ) should be close to the number of observed days.

A way to get around the difficulty posed by the complexity of this relationship is the self-calibration of the DVRI. DVRI is fixed during simulation and compensates for low PPFAC and TT values. Auto-adjustment forces its value to increase so that flowering occurs within the observed period. Figure 5B shows its adjustment as a function of TOD. Very restrictive cardinal temperatures require a higher DVRI to flourish (Fig. 6); this also occurs for the other parameters. This is a point of attention, as very high development rates and very restrictive parameters may not reflect reality. If the DVRI is not self-adjusted, restrictive combinations in cardinal temperature parameters can also prevent flowering.

Figure 6.
Relationship between development rate at panicle initiation (DVRI) and days after the start of the photosensitive phase (V6) for panicle initiation, setting PPFAC at 0.032 and thermal time at 1 °C day^-1.

However, this approach is error-prone. DVRI can override an error in the values of the TBD, TOD, TMD, MOPP, and/or PPSE. Similarly, cardinal temperatures can compensate an error in photoperiod response variables. Thus, there are several sets of parameters that provide identical simulations of phenology, making it impossible to determine which parameters reflect the true values of a cultivar (van Oort et al., 2011). Based on the sensitivity of the ORYZA (v3) model to DVRI, many studies have disregarded the other phenological parameters, setting them at the default values for the IR72 genotype and calibrating only the development rates (Tan et al., 2022; Yu et al., 2023). This creates a gap in accuracy of the phenological model when applied to other locations, as it depends on specific characteristics of the experiment location (van Oort et al., 2011).

When using inferential statistical techniques for parameter optimization, it is necessary to make assumptions about the range of parameter values. DVRI's self-adjustment reduces the need to worry about the parameter space of cardinal temperatures to nothing more than biological coherence. This simplifies the choice of parameter values by allowing the necessary constraints to be applied only to the MOPP and PPSE parameters. Therefore, it is essential to ensure that at some point in the simulation, and for a sufficient time, the following condition is met:

(17) $$(DL-MOPP)\times PPSE<1$$

Similarly:

(18)$$\begin{array}{l}DL-MOPP<PPS{E}^{-1}\end{array}$$

(19)$$\begin{array}{l}DL-PPS{E}^{-1}<MOPP\end{array}$$

The determination of MOPP and PPSE can be conducted experimentally, involving different sowing times throughout the year (Sujariya et al., 2023) or in controlled environments with regulated photoperiod (Pennisi et al., 2020). Some authors choose to calibrate this parameter empirically after adjusting the other parameters (Boling et al., 2011), giving it less importance. Although experimental determination is ideal, it is not always feasible due to the high cost and time required.

Assuming that the MOPP is unknown but higher than 8, to flower at any time of the year in Pelotas the PPSE parameter needs to be lower than 0.146 (Fig. 2E) or, at most, 0.352 when photosensitivity occurs in July (Fig. 2A). The closer to the equator, the shorter the DL amplitude (Fig. 1). This reduces the influence of sowing date on DL and on the choice of the MOPP and PPSE parameters (Fig. 7). However, for genotypes with high sensitivity, even a small variation in DL may drastically change flowering dates (Dore, 1959).

Figure 7.
Photoperiod sensitivity (PPSE) values as a function of the minimum optimal photoperiod (MOPP) for PPFAC to be greater than 0, given day lengths (DL) in Cantá-RR of (A) 12.76 h, (B) 12.86 h, and (C) 12.96 h.

As mentioned above, as the MOPP value increases or DL decreases, the maximum PPSE limit can expand (Fig. 4). Since in a calibration process the sowing date is fixed, the DL is known and must be considered when choosing the maximum PPSE limit. Forsythe et al. (1995) discuss differences in approaches to calculating DL. In the phenological calibration process, the angle of the sun at which twilight still affects day length must also be estimated. This angle can reach up to -6°, resulting in up to 1.5 h more light than when the sun was below the horizon (0°). The CSM ORYZA (v3) considers 0.90 h of light beyond the 0° angle. The inconsistency between the methods used to estimate the observed DL and the approach adopted by the ORYZA (v3) model may systematically under- or overestimate the effects of photoperiod, requiring transparency and methodological consistency (van Oort et al., 2011).

Once the DL is defined according to the observed flowering date and the assumed or already known minimum value of MOPP, the highest value of PPSE can be defined as:

(20)$$\begin{array}{l}PPSE<\frac{1}{DL-MOPP}\end{array}$$

Bai et al. (2019) described a similar approach for the CSM APSIM. This model, derived from ORYZA (v3), has a similar phenological subroutine. Different from that proposed in Eq. (20), Bai et al. (2019) incorporated the average effect of the photoperiod into the denominator to determine a specific value for the PPSE. This effect is estimated as a function of the TT accumulated until panicle initiation over the difference between stage V6 and flowering. Thus, errors in estimating the effects of photoperiod are related to errors in estimating cardinal temperatures.

In southern Brazil, rice can be cultivated between September and December, depending on the cultivar cycle (Steinmetz et al., 2019; Duarte et al., 2021). Especially when grown in September, the sensitivity range coincides with the period of maximum DL in Rio Grande do Sul, which occurs around December (14.84 h) (Steinmetz et al., 2022). Considering a minimum MOPP value of 10, for PPFAC to be greater than 0 in this period:

(21)$$PPSE<(14.84-10{)}^{-1}$$

(22)$$\begin{array}{l}PPSE<0.20\end{array}$$

(23)$$\begin{array}{l}PPFAC\hspace{0.17em}\approx \hspace{0.17em}0.032\end{array}$$

A low PPFAC value can impede the simulation if the TT and DVRI are not high enough to provide flowering. However, considering the measures proposed in this study, a PPFAC close to 0 is not an obstacle.

Boling et al. (2011) estimated photoperiod sensitivity parameters for a highly photoperiod-sensitive rice genotype (KDML105) grown in northeastern Thailand (latitude 18.73, longitude 98.94). The authors determined the MOPP value at 12.50 h, which was the maximum duration of the day when the panicle initiation stage occurred. PPSE was empirically estimated at 0.70 by pairing simulated panicle initiation dates with observed dates. However, this parameter estimation method dissociates MOPP from PPSE. Maintaining these values, flowering could occur up to a DL of 13.91 h. However, the maximum DL at which flowering occurred was 12.50 h. If the authors chose to simultaneously calibrate both parameters using automatic estimation techniques, the basic assumption about the value of MOPP should be at least 11.08 h for PPSE up to 0.70, or 11.60 h if they considered PPSE up to 1.00. The DVRI was adjusted similarly to Eq. (15).

4. Conclusion

There is a significant limitation of the ORYZA (v3) phenological model when photoperiod sensitivity is insufficient for flowering combined with finite meteorological data. This reflects a limitation in the model's ability to analyze highly photoperiod-sensitive cultivars under consistently unfavorable conditions.

We highlight the importance of carefully constraining genetic parameters, considering the specific conditions of the growing environment, to avoid uninterpretable responses. DVRI auto-adjustment simplifies this process by allowing necessary constraints to be applied to the MOPP and PPSE parameters to ensure flourishing.

By establishing minimum values for MOPP based on the observed DL for the flowering date, the maximum value of PPSE can be mathematically determined, thus facilitating the model calibration process. Eq. (20) offers a practical and accurate approach that simplifies this process and can be adopted for any latitude.

Acknowledgments

AB Heinemann acknowledges support from “Fundação de Amparo à Pesquisa do Estado de Goiás” (FAPEG - Processo: 202310267000216, CHAMADA PúBLICA: 03/2022 - Programa de Auxílio à Pesquisa Científica e Tecnológica) and “Conselho Nacional de Desenvolvimento Científico e Tecnológico” (CNPq N° 4/2021 - 310209/2021-8).

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Publication Dates

• Publication in this collection
  16 Dec 2024
• Date of issue
  2024

History

• Received
  24 Sept 2024
• Accepted
  5 Nov 2024