Introduction

With the continuous emission of greenhouse gases, the global greenhouse effect has become more and more serious. It is estimated that by 2035, the global average surface temperature will increase by 0.3–0.7 \(^{\circ }\)C compared with that in 2016. By the end of this century it will increase by 0.3–4.8 \(^{\circ }\)C (Stocker et al., 2014). The warming trend in China is basically consistent with that in global changes in the past 100 years. By the end of this century, the temperature in China will increase by 2.2–4.2 \(^{\circ }\)C, and the amplitude of temperature increase in the northern is greater than that in the southern and coastal regions (Dong and Yu, 2007; Lang and Sui, 2013). Jilin Province is located between 122\(^{\circ }\)–131\(^{\circ }\) east longitude and 41\(^{\circ }\)–46\(^{\circ }\) north latitude which is located in the central part of northeast China. It has a temperate continental monsoon climate, with large temperature differences between autumn and summer, and large temperature differences between day and night. All rice fields are fallow from October to April of the following year and belong to cool region where rice grows.

Plant photosynthesis is extremely sensitive to temperature response (Berry and Bjorkman, 2003). Increasing ambient temperature has two main effects on plant photosynthesis. One is that when the ambient temperature is higher than the optimal temperature for photosynthesis, the photosynthetic rate decreases; the other is that when the ambient temperature is lower than the optimal temperature for photosynthesis, the photosynthetic rate of plants increases (Shiraishi et al., 1996; Takagaki et al., 2010). The previous research has shown that the photosynthesis of rice usually peaks at 30 \(^{\circ }\)C, and the assimilation capacity of CO\(_2\) may be decreased significantly after high temperature stress (Yamori et al., 2011; Xiong et al., 2017). Studies have shown that the decrease in photosynthetic rate caused by high temperature is the result of the combined effect of stomatal factors and non-stomatal factors (Song et al., 2011; Zhao et al., 2009). There are many non-stomatal factors that inhibit photosynthesis due to high temperature, such as increased gas diffusion resistance of mesophyll cells, decreased CO\(_2\) solubility, decreased affinity of Rubisco for CO\(_2\), and decreased thermal stability of key components of photosynthesis, etc. (Mathur et al., 2014; Sage and Kubien, 2010). Overall, the current research focuses on the impact of high temperature stress on rice, the mechanism of the positive effect of proper warming on rice is ignored.

The distribution of photosynthetic assimilates to rice grains during the grain-filling stage determines the yield. The suitable temperature during this stage is 21–22 \(^{\circ }\)C. When the temperature at the grain-filling stage is high (\(>26^{\circ }\)C), the grain shape and grain-filling process will be adversely affected that could result in smaller grains and decreased grain weight (Morita et al., 2005; Yonemaru and Morita, 2012). There have been many studies on the mechanism of the grain-filling differences between superior and inferior grains of rice in the past (Xu et al., 2013; Hao et al., 2009; Liang et al., 2001). However, there are few studies to distinguish the superior grains from the inferior grains to study the response and mechanism of the grain-filling process when the temperature increases. Especially in cool region, the whole grain-filling stage experiences a change from high temperature to low temperature. In this context, it has far-reaching significance to study the accumulation and distribution of dry matter of rice panicle.

Table 1 Summary of the weather and soil conditions in the experimental field
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In order to clarify the changes in yield and photosynthetic mechanism under warming at different growth stages of rice in cool region. Jiyang100, a high-yield and high-quality rice cultivar, was chosen for this study. Firstly, we studied the changes in yield and grain-filling process (refined to inferior grains and superior grains) under warming treatment at different stages. Then, we evaluated the effects of warming at each stage on the LAI and photosynthetic parameters. Finally, we clarified the effects of LAI and photosynthetic parameters on yield or grain-filling process under warming at different stages, and the relationship between photosynthetic parameters and \(A_\mathrm{max}\). Such information on the yield, grain-filling process, LAI and leaf photosynthesis parameters in response to the warming at different growth stages of rice in cool region will improve our understanding of the regulation of intra-plant partitioning of photosynthetic assimilates by warming.

Materials and Methods

Site Description and Experimental Design

The experiment was set up in the experimental field of Jiyang Academy of Agricultural Sciences, Wanlong Town (125\(^{\circ }\) 45\(^{\prime }\) E, 42\(^{\circ }\) 36\(^{\prime }\) N), Meihekou City, Jilin Province in 2019 and 2020, where annual average frost-free period was 141 days. The weather of rice growth stage, soil and basic fertility conditions in the experimental field are shown in Table 1.

In the field, we set the warming scaffolding of each warming treatment, with the size of 8 m \(\times \) 6 m \(\times \) 2.5 m, in a north-south direction, and 6 m between each treatment as the isolation belt. During the warming stage, the transparent film was covered, in which the south and north sides were above 1.2 m from the ground, and the transverse distance was 1.8 m without film, so as to ensure ventilation and the south side of the sun was not blocked. In addition, the central part of the shed was equipped with a blast heating device and connected with a ventilation pipe. The ventilation pipe used small holes to uniformly release heat. During the day, the sun was used to passively increase the temperature, while in cloudy days and at night, the heating wind was used to help increase the temperature. The experimental rice varieties were planted in an unshaded area on the south side. Warming at six growth stages after transplanting: T1, the before heading stage (BBCH 16–51); T2, the whole growth stage (BBCH 16–92); T3, the grain-filling stage (BBCH 65–92); T4, the early grain-filling stage (BBCH 65–76); T5, the middle grain-filling stage (BBCH 77–86); T6, the late grain-filling stage (BBCH 87–92). Each treatment adopted continuous warming during the corresponding growth stage. Warming time and air temperature changes of each treatment in the experimental field are shown in Table 2.

Table 2 Warming time and air temperature changes of each treatment in the experimental field
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Crop Variety and Field Management

Jiyang100, a high-quality and high-yield japonica rice cultivar broadly cultivated in Jilin Province, was chosen for this study. This variety was bred from the cross of Jijing88 and Tong98–56, and its economic characteristics were in line with the trend of widely cultivated rice varieties in cool regions. The heading date of Jiyang100 in Meihekou area was around August 4th. It happened to be mature during the frost-free period in the Meihekou area and can make the most of the effective accumulated temperature to grow in the experimental area.

The field management methods were the same in 2019– 2020. The pre-germinated seeds were sown on April 13. Rice seedlings were transplanted with three seedlings in each hill (spacing 20 cm \(\times \) 30 cm) on May 25 in both years. The ratio of nitrogen, phosphorus and potassium fertilization was 2:1:1, of which the total amount of nitrogen fertilizer was 0.15 t hm\(^{-2}\). 50% of the total of N fertilizer, the total of P fertilizer and 90% of the total of K fertilizer were used as base fertilizer on May 20 (before harrowing). 30% of the total of N fertilizer was used as a top dressing at the early tillering stage on June 15. 20% of the total of N fertilizer and 10% of the total of K fertilizer were used as a top dressing at the panicle initiation stage on July 11.

Leaf Photosynthetic Parameter Measurements

Assayed the photosynthetic parameters at the panicle initiation stage (PI), heading stage (HD), early grain-filling stage (EF), mid-grain-filling stage (MF) and late grain-filling stage (LF), with a portable photosynthesis system (Li-Cor 6400XT). Light response curves measurement: the photosynthetically active radiation gradient was set to 0, 25, 50, 100, 150, 200, 300, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000 \(\upmu \)mol \(\mathrm m^{-2}\) \(\mathrm s^{-1}\). CO\(_2\) response curve measurement: CO\(_2\) concentration was set to 400, 350, 300, 250, 200, 150, 100, 50, 25, 0, 400, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000 \(\upmu \)mol \(\mathrm mol^{-1}\). The stomatal conductance (g\(_\mathrm{s}\)) was the measured value of a fixed red and blue light source with an optical quantum density of 1400 \(\upmu \)mol \(\mathrm m^{-2}\) \(\mathrm s^{-1}\) from 10:00 to 11:00. The mesophyll conductance (g\(_\mathrm{m}\)) was measured by the method of chlorophyll fluorescence and gas exchange measurement (Harley et al., 1992).

Dry Matter Determination

The full heading stage of rice was recorded as the beginning of grain-filling (0 day), and the panicle of representative rice in six holes were taken every 7–8 days, which was weighed after being dried, and the end at 45 days. The grain number of the half of distance from the neck to the tip of panicle was defined as the inferior grains (IG), and the remaining half was the superior grains (SG). When harvesting, parts of the plot were harvested separately according to superior and inferior grains, and calculated the yield of superior and inferior grains based on the total yield of the plot. In this study, yield referred to dry matter weight of the grains after drying.

Data Analysis

Statistical package SPSS 20.0 and Rstudio were used to analyze data. Image software of Origin2018 was used to perform graphing. Light response curve fitting combined the results of non-right-angle hyperbolic model (Thornley, 1976) and right-angle hyperbolic modified model (Ye, 2010). The fitting of the CO\(_2\) response curve needed to be achieved with the fitaci function of the R package ‘plantecophys’ (Duursma, 2015). The fitaci function fitted the measured data of the A–Ci curve according to the FvCB model (Farquhar, 1980), and estimated \(J_\mathrm{max}\), \(V_\mathrm{c,max}\), \(R_\mathrm{d}\) and their standard deviations, and considered the influence of temperature according to the method of Medlyn et al. (2010). The g\(_\mathrm{m}\) formula is as follows : 

$$\begin{aligned} \textit{g}_{m}=\frac{A_{n}}{C_{i}-\displaystyle {\frac{\varGamma ^*{}\left[ J_{f}+8\,\left( A _{n}+R_{d} \right) \right] }{J_{f}-4\,\left( A_{n}+R_{d} \right) }}} \end{aligned}$$

where \(A_{n}\) is the net assimilation rate, \(C_{i}\) is the CO\(_2\) within the internal sub-stomatal air-spaces, \(\varGamma ^*{}\) is the CO\(_2\) compensation point in the absence of mitochondrial respiration, \(J_{f}\) is the photochemical electron transport rate determined from Chl-Flr parameters, \(R_\mathrm{d}\) is the rate of mitochondrial respiration in the light.

Results and Discussion

Yield and Grain-Filling Process

Fig. 1
figure 1

The grain-filling process of CK (a), T1 (b), T2 (c), T3 (d), T4 (e), T5 (f) and T6 (g) of Jiyang100

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Table 3 Yield of Jiyang100 under warming treatments (2019–2020)
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The yield of rice in cool region showed a trend of \(\hbox {T}1>\,\hbox {T}2>\,\hbox {T}3>\,\hbox {T}5>\,\hbox {T}6>\,\hbox {CK}>\,\hbox {T}4\). Compared with CK, T1, T2, T3, and T5 increased significantly yield by 13.2%, 9.4%, 6.9%, and 6.3% respectively on the average from 2019 to 2020 (Table 3). T4 only had a significant level in 2019, but it showed a downward trend for two years, decreasing by 4.8% (Table 3). Although T6 did not reach a significant level, it showed an upward trend for two years, increasing by 2% (Table 3). Regarding the effect of warming on yield, the results of previous research were different. Yang (2018) increased the temperature by 1–2 \(^{\circ }\)C based on the air temperature in 2016 and 2017, which significantly decreased the yield of rice. Warming would increase the dry matter weight of rice compared with the control, and also promoted the increase of rice yield (Yang, 2020). The experiment site of the former was in Hubei Province (30\(^{\circ }\) 50\(^{\prime }\) N), while the latter was in Liaoning Province (41\(^{\circ }\) 49\(^{\prime }\) N). The average annual temperature was 17.7 \(^{\circ }\)C, 8.8 \(^{\circ }\)C respectively. The environmental temperature was different in different regions, and the changes in yield caused by warming were different. This experiment was set in Jilin Province (42\(^{\circ }\)36\(^{\prime }\)N), with an average annual temperature of 6.2 \(^{\circ }\)C, and the average daily temperature increased at each stage did not exceed 3 \(^{\circ }\)C (Table 2). Jiang et al. (2021) found that warming at the whole growth stage, the jointing stage, the heading stage, and the grain-filling stage had a positive effect on the yield accumulation of two varieties of rice with different heat tolerance in cold regions, which is similar to our conclusion.

The increase in the yield of T1, T2, T3 and T6, the contribution of IG was greater than that of SG; the increase in the yield of T5, the contribution of SG was slightly greater than that of IG; and the decrease of T4 was mainly affected by SG (Table 3). Cai et al. (2016) and Wang et al. (2018) found that rising temperature decreased panicle number per unit area and spikelet number per panicle. The proportion of DM allocated to the panicle was significantly decreased because of infertile spikelets caused by high temperature (Kim, Lim, et al., 2011). This phenomenon may be attributed to the higher background environmental temperature (Wang et al., 2019). Investigating the SG and IG yield, and the grain-filling process can clarify the reasons for the changes in yield caused by warming. Compared with CK, the increase in T1 yield was due to the increase in the grain-filling rate of SG and IG at EF stage and the grain-filling rate of IG at LF stage (Fig. 1b); the increase in T2 yield was due to the increase in the filling rate of IG at the grain-filling stage (Fig. 1c); the increase in T3 yield was due to the increase in the grain-filling rate of SG and IG at LF stage (Fig. 1d); the decrease in T4 yield was due to the shortening in grain-filling time of SG (Fig. 1e); the increase in T5 yield was due to the increase in the grain-filling rate of SG at MF stage and the increase in the grain-filling rate of IG at LF stage (Fig. 1f); the increase in T6 yield was due to the increase in the grain-filling rate of IG at LF stage (Fig. 1g). Kim, Shon, et al. (2011) and Ahmed et al. (2015) believed that although high temperature would increase the grain-filling rate at the grain-filling stage, it would significantly shorten the grain-filling time and resulted in a decrease in grain weight. However, this study found that T1, T2, T3 or T4 could all increase the grain-filling rate at the early stage, but the overall grain-filling time did not been shortened. Among them, T1 and T4 shortened the grain-filling time of SG, but did not shorten the grain-filling time of IG. The SG grain-filling time of T2 and T3 was not shortened, which may be an adaptive mechanism for plants to be continuously warmed. It had a positive effect on DM accumulation when the temperature increased to slightly above the optimal level but did not reach the threshold (Sánchez et al., 2014). Otherwise, high temperature would obstruct rice growth by reducing DM accumulation (Chaturvedi et al., 2017). In the present study, the increase in yield caused by warming treatments at different stages of rice in cool region was mostly caused by increasing the grain-filling rate of IG and the IG yield. The change of IG yield was closely related to the yield, and there was a strong positive correlation (Fig. 4). But not all stages of warming treatments would increase the yield, which was closely related to the environmental temperature during SG and IG grain-filling. Warming in the higher environmental temperature at the early grain-filling stage, leaving the warming would have a negative effect on SG yield which resulted in a decrease in yield.

Fig. 2
figure 2

The leaf area index (LAI) (a) and maximum photosynthesis rate (\(\mathrm A_{max}\)) (b) under warming treatments Different letters indicate significant differences at the P \(< 0.05\) level. The box boundaries indicate the 25th and 75th percentiles; the black line in the box marks the median; whiskers below and above the box indicate the minimum and maximum values, respectively; \(\circ \) indicates outlier

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LAI and Photosynthetic Parameters at Different Stages

Fig. 3
figure 3

The maximum carboxylation rate (\(\mathrm V_{c,max}\)) (a), maximum electron transport rate (\(\mathrm J_{max}\)) (b), day respiration rate (\(\mathrm R_d\)) (c), mesophyll conductance (\(\mathrm g_m\)) (d), stomatal conductance (\(\mathrm g_s\)) (e) under warming treatments

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Warming was not only beneficial to the accumulation of LAI before grain-filling stage, but also delayed the decline of LAI at the grain-filling stage. However, warming only at the early grain-filling stage would cause the accelerated decline of LAI at MF and LF stages, which may be triggered by stress reaction caused by the plant’s sudden transition from high temperature to low temperature (Fig. 2a). Scafaro et al. (2010) found that the third leaf of a heat-tolerant wild variety stretched 47% under high temperature. On the contrary, Fahad et al. (2016) pointed out that the significant increase of temperature decreased the leaf area index of rice, thereby affecting the canopy apparent photosynthetic rate (CAP) of rice. The results of this study were closely related to the characteristics of parabolic changes in temperature of the whole growth stage of rice in cool region.

Warming before grain-filling of rice had a negative effect on \(A_\mathrm{max}\) at PI and HD stages. In addition, the \(A_\mathrm{max}\) of all warming treatments was higher than that of CK to varying degrees at grain-filling stage (Fig. 2b). Previous studies have shown that rising temperature decreased \(A_\mathrm{max}\) but increased \(R_\mathrm{d}\) (Cai et al., 2018; Ziska and Teramura, 1992; Long, 1991). Wang et al. (2019) believed that only increasing the temperature had no significant effect on \(A_\mathrm{max}\), but slightly increased \(R_\mathrm{d}\). The differences of \(A_\mathrm{max}\) result were related to the environmental temperature characteristic of the continuous decrease in the temperature during the grain-filling stage of rice in cool region. Rising temperature can stimulate the enzyme activity rate, which may result in an immediate effect on leaf \(R_\mathrm{d}\) in moderate thermal environments (5–40 \(^{\circ }\)C for C\(_3\) species) (Arcus et al., 2016; Eric et al., 2018). Under the influence of warming at different stages, \(R_\mathrm{d}\) was increased significantly in most stages, which was consistent with previous studies (Fig. 3c). Wang et al. (2019) believed that when warming alone, \(V_\mathrm{c,max}\) was decreased slightly, while \(J_\mathrm{max}\) was increased. The changing law of \(V_\mathrm{c,max}\) in this study was more complicated, and the influence of warming on \(V_\mathrm{c,max}\) was closely related to the environmental temperature and the duration of warming. Warming at the before PI stage (T1 or T2) and the LF stage (T6) which the environmental temperature was relatively low had a positive effect on \(V_\mathrm{c,max}\) (Fig. 3a). When the environmental temperature was high, warming (T2, T3 or T4) had a certain negative effect on \(V_\mathrm{c,max}\) (Fig. 3a). The long-term warming (T1, T2 and T3) had a positive effect at the MF or LF stages (Fig. 3a). T4 and T5 had a certain negative effect when warming and had a positive effect after leaving the warming (Fig. 3a). However, \(J_\mathrm{max}\) was increased rapidly when warming, which should be caused by the sensitivity of the \(J_\mathrm{max}\) regulation process to the temperature and this positive effect had a certain continuity after leaving the warming (Fig. 3b). Previous studies have shown that the response of g\(_\mathrm{m}\) of plant leaves to temperature may be closely related to the enzymatic reaction, and there was an optimal temperature (Yamori et al., 2006; Diaz-Espejo et al., 2010). g\(_\mathrm{m}\) was a highly complex trait with unpredictable sensitivity to temperature that varies between species, between genotypes within a single species, with growth environment, between replicate leaves, and even with age for an individual leaf (Shrestha et al., 2019). There was a negative correlation between g\(_\mathrm{m}\) and leaf ABA content (Qiu et al., 2017). In our research, warming at the grain-filling stage could delay the decrease of g\(_\mathrm{m}\) which caused by leaf senescence, and this positive effect had a certain continuity. In addition, although warming before grain-filling had a negative effect on g\(_\mathrm{m}\), it would have a positive effect for a longer time after leaving the warming (Fig. 3d). Zhang et al. (2012) believed that g\(_\mathrm{s}\) was risen sharply when the temperature increased from 36 to 38 \(^{\circ }\)C, and we found that warming generally had a positive effect on g\(_\mathrm{s}\), but this positive effect would quickly disappear leaving the warming (Fig. 3e).

Fig. 4
figure 4

Correlation of yield, superior grains (SG) yield, inferior grains (IG) yield, maximum photosynthesis rate (\(\mathrm A_{max}\)), leaf area index (LAI), maximum carboxylation rate (\(\mathrm V_{c,max}\)), maximum electron transport rate (\(\mathrm J_{max}\)), day respiration rate (\(\mathrm R_d\)), mesophyll conductance (\(\mathrm g_m\)) or stomatal conductance (\(\mathrm g_s\))

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The Relationship Between LAI and Leaf Photosynthesis Parameters with Yield

The yield and IG yield had a significant positive correlation with LAI at each stage (Fig. 4). It showed that the change in yield of rice under warming in cool region was mainly due to the change of LAI. The increase in yield of T1, T2, T3 and T5 was mainly due to the positive effect of warming on LAI to varying degrees. And the decrease in T4 yield was due to the negative effect of warming on LAI at MF and LF stages (Table 3, Fig. 2a). Under higher temperature and elevated CO\(_2\) conditions, the increase in \(A_\mathrm{max}\) did not result in a high biomass accumulation or grain yield, and LAI was the main factor that restricted DM accumulation under rising temperature alone (Wang et al., 2019). In the present study, although the results of the correlation between photosynthetic parameters and yield could not explain the reasons for the changes in yield among the treatments, the significant difference in \(A_\mathrm{max}\) at the grain filling stage showed that the \(A_\mathrm{max}\) of T1, T2, T3, T4, T5 and T6 was higher than that of CK to varying degrees at grain-filling stage (Figs. 2b, 4). The results of T4 and T6 yields showed that the \(A_\mathrm{max}\) at the grain-filling stage had a positive effect on yield, but the effect of LAI was greater than that of \(A_\mathrm{max}\) (Fig. 2). 80% of the grain-filling material of rice grains came from the photosynthetic assimilates after heading (Venkateswarlu and Visperas, 1987). Therefore, compared with CK, the advantage of T1 yield came from the significant increase of LAI at PI-LF stage and \(A_\mathrm{max}\) at MF stage; the advantage of T2 yield came from the significant increase of LAI at PI-LF stage and \(A_\mathrm{max}\) at MF and LF stages; the advantage of T3 yield came from the significant increase of LAI and \(A_\mathrm{max}\) at EF-LF stage; the advantage of T5 yield came from the significant increase of LAI at the LF stage and the \(A_\mathrm{max}\) at the MF stage; the advantage of T6 yield came from the significant increase of \(A_\mathrm{max}\) at the LF stage. However, the decrease in yield of T4 was due to the significant decrease of LAI at the MF and LF stages.

The Relationship Between \(A_\mathrm{max}\) and Photosynthetic Parameters at Different Stages

Table 4 Stepwise regression analysis and path analysis between photosynthetic characteristics and \(\mathrm A_{max}\) at different stages
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The increase in leaf net photosynthesis at high temperature was due to the changes in leaf biochemical characteristics such as \(V_\mathrm{c,max}\) and \(J_\mathrm{max}\) (Adachi et al., 2014; Ruiz-Vera et al., 2015). With a given g\(_\mathrm{s}\), the leaf photosynthetic rate would increase dramatically with \(V_\mathrm{c,max}\) or \(J_\mathrm{max}\) increase (Huang et al., 2021). Sun et al. (2013) found that \(V_\mathrm{c,max}\) was more sensitive to g\(_\mathrm{m}\) than \(J_\mathrm{max}\). Our results showed that the direct influence of \(J_\mathrm{max}\) at the PI stage was greater than that of g\(_\mathrm{m}\), but \(J_\mathrm{max}\) played a negative role, and the indirect path coefficient showed that g\(_\mathrm{m}\) had a relatively large influence on \(A_\mathrm{max}\) through \(J_\mathrm{max}\) (Table 4). This showed that although warming (T1 or T2) caused an increase in \(J_\mathrm{max}\) at the PI stage, it did not increase \(A_\mathrm{max}\) and the decrease of g\(_\mathrm{m}\) was the main reason for the decrease of \(A_\mathrm{max}\) at the PI stage. The direct influence of g\(_\mathrm{m}\) at HD stage was greater than that of \(V_\mathrm{c,max}\), while the indirect path coefficient indicated that \(V_\mathrm{c,max}\) had a relatively large influence on \(A_\mathrm{max}\) through g\(_\mathrm{m}\) (Table 4). It showed that the significant decrease in g\(_\mathrm{m}\) caused by warming (T2) was the main reason that affected the decrease in \(A_\mathrm{max}\) at HD stage, and the significant decrease in \(V_\mathrm{c,max}\) also had a certain extent of impact. This was also the reason why the average value of \(A_\mathrm{max}\) was still lower than that of CK even though g\(_\mathrm{m}\) increased significantly after leaving the warming of T1. \(J_\mathrm{max}\) was the main factor affecting \(A_\mathrm{max}\) at the EF stage (Table 4). At this time, warming (T2, T3 or T4) increased \(J_\mathrm{max}\), so that the gap between \(A_\mathrm{max}\) of T2 and CK was significantly reduced at the EF stage compared with that at the HD stage, while the \(A_\mathrm{max}\) of T3 or T4 was increased significantly at the EF stage. The direct influence of g\(_\mathrm{m}\) at the MF stage was greater than that of g\(_\mathrm{s}\), and the indirect path coefficient indicated that g\(_\mathrm{s}\) had a relatively large influence on \(A_\mathrm{max}\) through g\(_\mathrm{m}\) (Table 4). It showed that the positive effects of warming (T2, T3 and T5) or leaving the warming treatments (T1 and T4) on g\(_\mathrm{m}\) and g\(_\mathrm{s}\) all promoted the increase of \(A_\mathrm{max}\) at the MF stage. The g\(_\mathrm{m}\) at LF stage was the main factor that affected \(A_\mathrm{max}\) (Table 4), the positive effect of warming (T2, T3 and T6) and leaving the warming treatment (T5) on g\(_\mathrm{m}\) was the reason for the increase of \(A_\mathrm{max}\) at the LF stage. Previous studies have pointed out that \(J_\mathrm{max}\)/\(V_\mathrm{c,max}\) and the CO\(_2\) concentration at the carboxylation sites were two determines for the photosynthetic limiting steps (Yamori et al., 2011). The influence of mesophyll on stomatal movement was related to the balance between light harvesting and carboxylation in photosynthesis (Mott and David, 2018). Among the photosynthetic parameters, g\(_\mathrm{m}\) and \(J_\mathrm{max}\) played a major role, \(V_\mathrm{c,max}\) and g\(_\mathrm{s}\) played a minor role, and \(R_\mathrm{d}\) had no effect on \(A_\mathrm{max}\). In addition, g\(_\mathrm{m}\) mainly affected \(A_\mathrm{max}\) at most growth stages of rice and had a strong positive correlation with \(A_\mathrm{max}\) (Fig. 4). Therefore, g\(_\mathrm{m}\) was the most important factor that affected \(A_\mathrm{max}\) under warming treatments in cool region.

Conclusions

Temperature has potential positive or negative effects on plant growth. In this study, the yield of rice in cool region showed a trend of \(\hbox {T}1> \hbox {T}2> \hbox {T}3> \hbox {T}5> \hbox {T}6> \hbox {CK} > \hbox {T}4\). The change of IG yield was closely related to the yield and there was a strong positive correlation. The increase in yield was mostly caused by the increase in the grain-filling rate of IG and the IG yield. The decrease in T4 yield was due to the shortening in grain-filling time of SG, resulted in a decrease in SG yield. In addition, the yield and IG yield had a significant positive correlation with LAI at each stage. Although warming before grain-filling of rice had a negative effect on \(A_\mathrm{max}\) at PI and HD stages, all the warming treatments had a positive effect on \(A_\mathrm{max}\) to varying degrees at the grain-filling. Among the photosynthetic parameters, g\(_\mathrm{m}\) was the most important factor that affected \(A_\mathrm{max}\) under warming treatments. These results suggested warming at most growth stages of rice in cool region would be beneficial to photosynthesis and promote the yield accumulation. However, it was adversely affected by the short-term warming at the early grain-filling stage of rice.