Evaluating Growth and Photosynthesis of Kimchi Cabbage According to Extreme Weather Conditions

: The aim of this study was to develop and validate growth and photosynthetic models of Kimchi cabbages under extreme temperature conditions at di ﬀ erent growth stages. Kimchi cabbage plants were subjected to low and high air temperatures 7–10 days after transplanting (DAT) and 40–43 DAT using extreme weather simulators. Except during these periods, the air temperature, relative humidity, solar radiation, and precipitation were set according to previous meteorological data. The experiments were performed over two years: in the ﬁrst year, data were used to develop the models; the second-year experimental data were used for validation. The growth parameters and relative growth rate of Kimchi cabbage decreased due to low and high air temperature treatments. Photosynthetic CO 2 response curves, which were measured using a portable gas exchange system, were used to calculate three biochemical parameters from measured data: photochemical e ﬃ ciency, carboxylation conductance, and dark respiration. These parameters were used to develop the photosynthetic models (modiﬁed Thornley’s models) representing predictions of net photosynthetic rate by CO 2 concentration and growth stage. The simulated photosynthetic rate with extreme high temperature treatment (35 / 31 ◦ C) was 19.7 µ mol m − 2 s − 1 which was evaluated approximately 3% deduction compared with control. Results of this study indicate that the growth and photosynthetic models developed here could be applied to evaluate retarded growth and net photosynthetic rate under extreme temperature conditions.


Introduction
Kimchi cabbage (Brassica rapa L. ssp. pekinensis) is a primary vegetable crop in Korea given that it is the main ingredient of Kimchi, one of the nation's leading foods. Because of its agricultural and economic importance, Kimchi cabbage is widely cultivated in Asia, especially in Korea and China. It is classified as a cool-season crop, and most cultivars will not form heads when the daily mean air temperature is >25 • C [1]. In general, the harvest period for Kimchi cabbage, i.e., when full head formation has occurred, varies from 50 to 100 days after sowing, depending on cultivars and the prevailing environmental conditions.
Previous studies have suggested that when Kimchi cabbage is exposed to a combination of elevated temperature and CO 2 , its leaf dry weight decreases [2]. Relevant studies have also indicated that increased air temperature reduces the growth, photosynthetic rate, PSII activity, and yield of Kimchi cabbage and can lead to severe soft rot disorder [3,4]. The interacting effects of elevated CO 2 and air temperature on the growth and physiological responses of vegetables have been reported.
Science, located in Wanju, Korea (35 • 16 N, 127 • 02 E, and 32 m altitude). The air temperatures were set at 20 • C for the light period and 18 • C for the dark period during the transplant production phase. The average photo-and dark-periods each growing season, spring (14/10 h) and autumn seasons (11/13 h), were set respectively. Full irrigation was applied every day, and Mulpure nutrient solution (Daeyu Co., Seoul, Korea) for seedlings was applied at 3-4 day intervals. The plants were transplanted 28 days (spring season) and 35 days (autumn season) after sowing in approximately 22 m 2 extreme weather growth-chambers (EWGCs; Modified Controlled Environment Extreme Weather Simulator (CEEWS) model, EGC, Chagrin Falls, OH, USA). The soil bin was 3 × 1 × 1 m (length × width × depth) in size and plant density was 7.7 plants/m 2 . Fertilizer was applied based on the results of soil tests performed during the spring and autumn seasons, following regional recommendations (920 kg/ha; 361 kg/ha for N, 263 kg/ha for P 2 O 5 , and 9.0 kg/ha for K 2 O).
The weather profiles were programmed into the eight EWGCs using an advanced environmental control program (SIMATIC WinCC Runtime Advanced V13 SP1; Siemens, Munich, Germany) and weather data were collected. Changes in air temperature are shown in Figure 1. The soil type was clay loam and soil moisture were maintained at 30-40% after transplanting until harvest. Irrigation was via a drip irrigation system. The irrigation amount and frequency were 500 mL/plant and 2-3 times per week, respectively.

Growth Environment Factors and Extreme Weather Treatments
The climate values were adjusted to the existing weather conditions. Daegwanryeong (37°30′ N, 128°43′ E, and 800 m altitude) region data from June 1st to August 10th, 2013, 2014, and 2015 were used for the spring season experiment. Haenam (34°32′ N, 126°34′ E, and 15 m altitude) region data from September 1st to November 10th, 2013, 2014, and 2015 were used for the autumn season experiment as a control. Kimchi cabbages were subjected to extreme weather treatments at two times, in spring at 7-10 days after transplanting (DAT), and in fall at heading (40)(41)(42)(43) The weather profiles were programmed into the eight EWGCs using an advanced environmental control program (SIMATIC WinCC Runtime Advanced V13 SP1; Siemens, Munich, Germany) and weather data were collected. Changes in air temperature are shown in Figure 1. The soil type was clay loam and soil moisture were maintained at 30-40% after transplanting until harvest. Irrigation was via a drip irrigation system. The irrigation amount and frequency were 500 mL/plant and 2-3 times per week, respectively.

Growth Parameter Analysis
Growth parameters, including maximum leaf length and width, number of leaves, leaf area, and fresh and dry weight, were measured 4 and 18 days after commencing extreme weather treatment (at the early transplanting stage). The leaf area was measured using a leaf area meter (LI-3100; Li-Cor Co., Inc., Lincoln, NE, USA). Three randomized samples were harvested to measure the fresh weight of Kimchi cabbage at five growth stages for the spring season experiment (0, 14, 28, 42, and 56 DAT) and at six growth stages for the autumn season experiment (0, 14, 28, 42, and 70 DAT). All fresh weights in each cultivation season with extreme weather treatment were applied to a regression

Growth Parameter Analysis
Growth parameters, including maximum leaf length and width, number of leaves, leaf area, and fresh and dry weight, were measured 4 and 18 days after commencing extreme weather treatment (at the early transplanting stage). The leaf area was measured using a leaf area meter (LI-3100; Li-Cor Co., Inc., Lincoln, NE, USA). Three randomized samples were harvested to measure the fresh weight of Kimchi cabbage at five growth stages for the spring season experiment (0, 14, 28, 42, and 56 DAT) and at six growth stages for the autumn season experiment (0, 14, 28, 42, and 70 DAT). All fresh weights in each cultivation season with extreme weather treatment were applied to a regression analysis in Agronomy 2020, 10, 1846 4 of 16 a sigmoidal curve model (Equation (1)). In addition, a curve of the relative growth rate (Equation (2)) of Kimchi cabbage was calculated based on the fresh weight of each growth stage and those were validated: y = a where y: fresh weight; x: days after transplanting; a: maximum value of growth; b: relative growth rate is equal to maximum growth; x 0 : predicts the time of inflection.
where y: relative growth rate (RGR); x: days after transplanting; y 0 : the constant that affects the degree of kurtosis; a: the constant that affects the point at which the RGR maximum; b: the constant that affects the peak of RGR.

Measurement of Photosynthetic Rate for Developing Photosynthetic Rate Models
The CO 2 assimilation rate (An) response to the intercellular CO 2 concentration (C i ) (An-C i ) curve of cabbage leaves was measured using a portable photosynthesis system (Li 6400XT; Li-Cor Co., Inc., Lincoln, NE, USA) in the morning time. The curve data were collected at four growth stages for spring season experiment (16,29,43, and 59 DAT) and at five growth stages for autumn season experiment (16,29,43,59, and 70 DAT). Each measurement was performed with three replicates per extreme weather treatment. The fully expanded leaf was clamped onto a 6 cm 2 leaf chamber, and light was provided by a sensor head (6400-02B LED; Li-Cor Co., Inc., Lincoln, NE, USA). Relative humidity in the leaf chamber was 70-80% and the block temperature was maintained at 25 • C. For the An-C i curve, gas exchange responses to various CO 2 concentrations ranging from 50 to 1500 µmol/mol were measured at 500 µmol/m 2 /s photosynthetic photon flux. Each CO 2 concentration level was measured for 300 s after an equilibrium time of 120 s. This is slightly less than the light saturation points for photosynthesis in Kimchi cabbage, with a 10% ratio of blue light required to maximize the stomatal aperture [24].

Development and Validation of Photosynthetic Rate Models
The photosynthetic rate at all CO 2 concentrations was obtained using Equation (3) [20]: where PPF and C i represented photosynthetic photon flux and intercellular carbon dioxide concentration, respectively. P is the photosynthetic rate (µmol CO 2 /m 2 /s), while a, b, and c are the photochemical efficiency (µmol CO 2 /µmol), carboxylation conductance (/s), and dark respiration (µmol CO 2 /m 2 /s), respectively. Values for a, b, and c were obtained by regression analysis with photosynthetic rates at each growth stage from An-C i curve data. A decrease in P with growth stage could be expressed as shown in Equation (4) because light use efficiency was exponentially reduced with leaf size and growth stage [24]: where p and q are regression parameters. A simple multiplication model (Equation (5)) was developed by multiplying Equations (3) and (4) as follows:  (6)) was described as follows: all the regression parameters in the simple multiplication model and the Thornley model were analyzed using the statistical program SPSS (IBM, New York, NY, USA). These models were then validated using the An-C i curve data at each growth stage and extreme weather treatment.

Experiment Design and Statistical Analysis
In total, 40 Kimchi cabbage plants were placed in each EWGC treatment condition. Each EWGC condition was an independent treatment and was part of a randomized block design. The experiments were performed over two years with the same conditions each year in terms of plant materials, treatment methods, and growth and photosynthetic rate measurements. The first-year data were used to develop models or formulate curves; the second-year data were used to validate the developed models and equations. ANOVA was used to assess differences in growth parameters via SAS (SAS 9.2, SAS Institute Inc., Cary, NC, USA). Mean separation was analyzed using LSD tests (p < 0.05).

Growth Parameter Analysis
Four days after commencing low air temperature treatment, the fresh weight of control Kimchi cabbage was 108.2 g/plant. Comparatively, the fresh weight of cabbage treated at 9 • C/6 • C was 54.0 g/plant, approximately 50% that of the control (Table 1). Eighteen days after commencing the low air temperature treatment, the growth of Kimchi cabbage differed significantly. The fresh weight of the control was 1158 g/plant, while that of Kimchi cabbage treated with moderate (15 • C/16 • C) and extreme (12 • C/9 • C and 9 • C/6 • C) low air temperatures was 79%, 62%, and 51% of the control. In contrast, 4 days after commencing moderate and extreme high air temperature treatments, the fresh weight of control Kimchi cabbage was the lowest among all treatments at 93.9 g/plant, while that of Kimchi cabbage treated at 25 • C/22 • C (moderate high air temperature treatment) was 147.9 g/plant (the highest value among all treatments). However, 18 days after commencing moderate and extreme high air temperature treatments, the fresh weight and leaf area of Kimchi cabbage did not differ significantly among treatments (Table 2). Indeed, 16 days after commencing the extreme high temperature treatment (at the heading formation period), fresh weight decreased by 41.4% in cabbage treated with extreme high temperatures (35 • C/31 • C) (data not shown). Extreme high air temperatures severely affected heading formation and development; however, low extreme air temperature treatments did not produce such effects.

Assessment of Growth Curves and Relative Growth Rate
In fresh weight regression analysis including moderate and extreme low air temperature treatments, the DAT on which the fresh weight of Kimchi cabbage increased exponentially was as follows: 31 (control), 32 (15 • C/12 • C), 35 (12 • C/9 • C), and 39 (9 • C/6 • C) ( Figure 2). Thus, growth was retarded by extreme low air temperature in the early stage of transplanting. A predictive model for growth inhibition by daily average temperature was developed, and the growth inhibition of Kimchi cabbage according to low air temperature levels in the early stage of transplanting was assessed. The root means square error (RMSE) was calculated between simulated and measured fresh weight values. The RMSE for the control, moderate, and two extreme low air temperature treatments were 321, 303, 575, and 418 g/plant, respectively. Prediction errors can be reduced by using additional statistical data and physiological responses with photosynthetic model-applied data.
The regression analysis of fresh weight for moderate and extreme high air temperature treatments according to DAT is shown in Figure 3. The time of exponential increase of fresh weight at moderate high air temperature was accelerated relative to the control, although fresh weight did not increase rapidly at extreme high air temperatures (30 • C/27 • C and 35 • C/31 • C) at the beginning of the growth stage. Indeed, fresh weight significantly decreased by approximately 7% and 34% with these extreme high air temperatures, respectively, compared to the control.
According to estimations of the decrease in Kimchi cabbage weight by average daily temperature via the predictive model equation, a 21.9% decrease in Kimchi cabbage weight was expected at 28 • C for 4 days during the constituency period (data now shown). It would be possible to estimate the yield of Kimchi cabbage production when abnormally high air temperature occurs during cultivation periods. In addition, it would be possible to apply practical cultivation techniques to retard growth and reduce yield when extreme high air temperature occurred in the cultivation area of Kimchi cabbage.  The regression analysis of fresh weight for moderate and extreme high air temperature treatments according to DAT is shown in Figure 3. The time of exponential increase of fresh weight at moderate high air temperature was accelerated relative to the control, although fresh weight did not increase rapidly at extreme high air temperatures (30 °C/27 °C and 35 °C/31 °C) at the beginning of the growth stage. Indeed, fresh weight significantly decreased by approximately 7% and 34% with these extreme high air temperatures, respectively, compared to the control. The relative growth rate (RGR) in fresh weight with extreme air temperature treatment is shown in Figure 4. The control had the highest RGR at 0.1861 g/g/day 5 days after the moderate and extreme low air temperature treatment. That was the highest at 26 DAT by the RGR equation. With an extreme low air temperature, the number of days at which the RGR reached a peak was one day later, which represented a~6.7% reduction compared to the control (Figure 4a). Given RMSE analysis, there was an average difference of 0.047 g/g/d (Figure 4b). The RGR of the control was 0.1441 g/g/day on 27 days after commencing the extreme high air temperature treatment, while that of the extreme high air temperature treatment (35 • C/31 • C) was highest at 0.1396 g/g/day. The number of days at which the RGR reached a peak with extreme high air temperature treatment was 2 days earlier, which represented a~3.1% decrease compared to the control (Figure 4c). According to RMSE analysis, there was an average difference of 0.044 g/g/d (Figure 4d). After correlating the predicted and measured values, the growth and development of head formation in Kimchi cabbage with moderate and extreme weather events could be analyzed.  According to estimations of the decrease in Kimchi cabbage weight by average daily temperature via the predictive model equation, a 21.9% decrease in Kimchi cabbage weight was expected at 28 °C for 4 days during the constituency period (data now shown). It would be possible to estimate the yield of Kimchi cabbage production when abnormally high air temperature occurs during cultivation periods. In addition, it would be possible to apply practical cultivation techniques to retard growth and reduce yield when extreme high air temperature occurred in the cultivation area of Kimchi cabbage.
The relative growth rate (RGR) in fresh weight with extreme air temperature treatment is shown in Figure 4. The control had the highest RGR at 0.1861 g/g/day 5 days after the moderate and extreme low air temperature treatment. That was the highest at 26 DAT by the RGR equation. With an extreme low air temperature, the number of days at which the RGR reached a peak was one day later, which represented a ~6.7% reduction compared to the control (Figure 4a). Given RMSE analysis, there was an average difference of 0.047 g/g/d (Figure 4b). The RGR of the control was 0.1441 g/g/day on 27 days after commencing the extreme high air temperature treatment, while that of the extreme high air temperature treatment (35 °C/31 °C) was highest at 0.1396 g/g/day. The number of days at which the RGR reached a peak with extreme high air temperature treatment was 2 days earlier, which represented a ~3.1% decrease compared to the control (Figure 4c). According to RMSE analysis, there was an average difference of 0.044 g/g/d (Figure 4d). After correlating the predicted and measured

Comparative Assessment of the Developed Photosynthetic Rate Model
The Thornley model was applied to develop a photosynthetic model of Kimchi cabbage. The constants used in the model equation included photochemical efficiency (µmol CO 2 /mol), carboxylation conductance (/s), and dark respiration (µmol CO 2 /m 2 /s). Constant values were obtained by regressing the An-C i curves, and the constants p and q were calculated by regressing from these values in Kimchi cabbage growth stages (Tables 3 and 4 Agronomy 2020, 10, 1846 9 of 16 Agronomy 2020, 10    The developed photosynthetic models were simulated with DAT and the concentration of intercellular CO 2 and then validated with data from the second-year experiments (Figures 5 and 6). The simulated net photosynthetic rates (s-An) differed according to extreme weather treatment: the s-An from the extreme high temperature treatment was 19.7 µmol/m 2 /s, which was approximately 3% lower than that of the control. Biochemical models can be simulated by growth stage and levels of CO 2 concentration in mesophyll cells; the parameters were estimated through regression analysis with the measured data by creating An-C i curves for each growth stage. According to the RMSE of the photosynthetic rate at each growth stage and validation with data measured in the second year, there were differences of 3.1 (spring season cultivation) and 4.7 (autumn season cultivation) µmol/m 2 /s. Correction is likely to be possible due to the high coefficient of determination (R 2 = 0.92) of the correlation analysis results; however, the predicted values for photosynthetic rate were estimated to be lower or higher than the measured values.
The developed photosynthetic models were simulated with DAT and the concentration of intercellular CO2 and then validated with data from the second-year experiments (Figures 5 and 6). The simulated net photosynthetic rates (s-An) differed according to extreme weather treatment: the s-An from the extreme high temperature treatment was 19.7 μmol/m 2 /s, which was approximately 3% lower than that of the control. Biochemical models can be simulated by growth stage and levels of CO2 concentration in mesophyll cells; the parameters were estimated through regression analysis with the measured data by creating An-Ci curves for each growth stage. According to the RMSE of the photosynthetic rate at each growth stage and validation with data measured in the second year, there were differences of 3.1 (spring season cultivation) and 4.7 (autumn season cultivation) μmol/m 2 /s. Correction is likely to be possible due to the high coefficient of determination (R 2 = 0.92) of the correlation analysis results; however, the predicted values for photosynthetic rate were estimated to be lower or higher than the measured values. (c) (d) Figure 5. Pn of Kimchi cabbage leaf simulated by Equations (7)-(10) and the closed circle dot represented the measured Pn for validation: (a) control (normal weather data); (b,c) applied the moderate weather scenarios (photo-/dark-periods; 15/12 °C and 12/9 °C, respectively); (d) applied extreme weather scenarios (9/6 °C). Ci: intercellular carbon dioxide concentration.

Growth of Kimchi Cabbage during Extreme Weather Events
Kimchi cabbage is a well-known cool-season crop; the optimal average daily temperature is 20 • C-22 • C for growth and 16 • C-18 • C for proper formation of the Kimchi cabbage head [1,7,16,17,[26][27][28][29][30][31][32]. However, given that Kimchi cabbage is a material for raw Kimchi, it must be produced stably throughout the year. Thus, in Korea, Kimchi cabbage is planted in late June in alpine areas (>700 m elevation) and harvested in August (the summer season cultivation). For autumn season cultivation, Kimchi cabbage is transplanted at the end of August in the South West area of Korea (Haenam) with the harvest being conducted in mid-or late-November. Due to climate change, abnormally low air temperatures now occur during the summer planting season in the highland regions, which cause damage to production. In the autumn season, extremely high air temperature in early autumn affects the growth and physiological responses of planted Kimchi cabbage [4,33]. The present study was performed using cutting-edge climate change research apparatus (EWGCs) capable of realizing extreme weather events; thus, a precisely controlled study of weather conditions was conducted. Results showed that the initial growth stage of Kimchi cabbage was delayed by low air temperature. Kimchi cabbage is particularly sensitive to weather and environmental stress; indeed, physiologically active substances in Kimchi cabbage can be reduced even under low temperature stress [11,22,23]. In contrast, high-temperature stress decreases growth and physiological reaction activity [2,6,16,30,[34][35][36].
In the present study, the fresh weight and relative growth rate of Kimchi cabbage rapidly decreased with high air temperature in the early growth stage and continuum period (leaf elongation and heading stage) after commencing treatments; this resulted in significantly retarded head formation and development. These results were similar to those reported in previous studies [4,33]. They were also similar to the results of studies of Kimchi cabbage productivity according to climate change scenarios and the decreased physiological activity of cabbage due to long-term high-temperature stress [34,37]. The growth curves and relative growth in the present study will enable the evaluation of crop damage due to extreme weather (high or low temperatures) in certain crop types. This sort of study could be used in other research studies on climate change or environmental stress.

Prediction of Photosynthetic Rate of Kimchi Cabbage
A crop growth model is a mathematical description of the physiological response or growth process that occurs in the growth and development of a crop. The elements that comprise the growth model include weather parameters, such as temperature, relative humidity, radiation, wind speed, rainfall, and soil moisture, and state values of growth, including photosynthesis, respiration, and evaporation. The relationships of each parameter and the state values of growth and development are considered [20][21][22][23]29,[38][39][40][41][42][43][44][45].
In crop growth models, the instantaneous rate of change in terms of photosynthesis, respiration, elongation, and development of leaves is calculated according to changes in the environment to represent the overall system change numerically. Correction by calibration and validation is important for improving the accuracy of model prediction [20,25,[38][39][40]. The rate of photosynthesis of crops can be calculated from the assimilation rate of CO 2 , which can be accurately measured. Methods for modeling crop assimilation have changed gradually. For example, de Wit [46] calculated total dry matter production based on the photosynthetic reaction curve of leaves. However, this model underestimated CO 2 assimilation rate at the light saturation point. Therefore, Goudriaan and van Laar [47] produced a modified equation using exponential models. Another method for simulating photosynthesis was proposed by Monteith [48]. A clear linear relationship was revealed between dry weight and cumulative blocked radiation; this was expressed as an equation measuring how efficiently solar radiation blocked by the plant canopy is converted into dry weight.
On the other hand, according to the biochemical approach of Farquhar et al. [45], the photosynthetic properties of leaves can be expressed in terms of the Rubisco enzyme reaction and electron transfer rate. As the concentration of CO 2 outside the crop canopy increases, the speed of photosynthesis increases because the physical resistance is lowered, enabling rapid diffusion of CO 2 and inhibiting the combination of rubisco and oxygen, the cause of photorespiration. These theoretical concepts were developed as biochemical model equations and programmed to judge the efficiencies of the photosynthetic mechanism of crops [49,50]. Lee et al. [4] applied the model to evaluate the photosynthetic efficiencies of Kimchi cabbage according to climate change scenarios. In addition, Kim et al. [51] developed photosynthetic models of roses by combining Farquhar's leaf-level photosynthesis model and Ball-Berry's stomatal diffusion conductivity model. A plant gas exchange simulator has also been created and disseminated. However, use of Thornley's dynamic photosynthesis model is appropriate when measuring photosynthetic rates [52].
In the present study, using Thornley's photosynthesis model, we developed a model that can simulate photosynthesis during the growth stage of Kimchi cabbage according to extreme weather (low and high temperatures). Eight different equation models were determined for predicting photosynthetic rate. By repeating our experiment in a second year, the predicted values of photosynthetic rate were validated with the resultant data. Those models simulated by growth stage and carbon dioxide in mesophyll cells, and parameters can be inferred through regression analysis using the measured data by creating a carbon dioxide saturation curve for each cultivation period. Early after transplanting, the maximum photosynthesis rate of Kimchi cabbage decreased by 9.1% compared to the control by extreme low air temperate treatment, while the photosynthetic efficiency decreased by 36.1% compared to the control in the extreme high air temperature treatment during the autumn cultivation season. It was able to judge the inhibition of growth and biomass production. Although there were errors in this validation, we nevertheless developed a tool to evaluate the impact of extreme weather events due to climate change by using a photosynthetic model to predict the photosynthetic rate under CO 2 limiting conditions with air temperature stress for each Kimchi cabbage growth stage.

Conclusions
The growth parameters and relative growth rate of Kimchi cabbage decreased due to extreme low and high air temperature treatments. In particular, encountering extreme weather in a short period at the early growth stage severely affected growth, head formation, and development. Therefore, the Kimchi cabbage production is seriously vulnerable to climate change and tools to accurately calculate potential damage should be developed. Here, a modified Thornley model that predicts photosynthesis according to growth stage and the degree of damage from extreme weather was developed and validated. The developed photosynthetic model can predict the dynamic physiological response of Kimchi cabbage to extreme weather by cultivation region and crop type; thus, it could be used to evaluate practical damage-reducing cultivation methods prior to their application. In addition, rather than evaluating the vulnerability of crop productivity to long-term climate change, it can be used as the evaluation tools for rapid countermeasures and adaptation technology development for dynamic extreme weather.