The Effects of Climate Change on Heading Type Chinese Cabbage ( Brassica rapa L. ssp. Pekinensis) Economic Production in South Korea

: Since Chinese cabbage is consumed fresh, its wholesale price varies with the total amount supplied on the market. However, in these days, climate variability presents a large threat to sustainable Chinese cabbage production in South Korea. To manage Chinese cabbage production well under unexpected weather conditions, it is important to study the impacts of climate variability on Chinese cabbage economic yields in South Korea. In this study, 2-year ﬁeld trials were conducted in multiple locations across seven provinces in South Korea. The collected morphological data from 24 different varieties were used to develop a yield prediction model using a machine learning technique. Three Chinese cabbage groups were carried out through the clustering analysis, and a yield model was developed for each cluster group. The developed model was used to predict the cabbage economic yields under different combinations of climate change and cropping management plans. According to simulation results, Group 1 had the shortest growing degree days and produced higher yields than the other two groups. However, the overproduction of Group 1 led to a price reduction in the market of (USD(0.04–0.08) per kg), which suggested that producing Group 2 of (USD(0.31–0.96) per kg) is more beneﬁcial to farmers. Based on the production results of the groups, their revenue varied by location and cropping management. The results of this study provide farmers with a better understanding of the relationship between production and economic beneﬁts in future climate change scenarios.


Introduction
The heading-type Chinese cabbage, also well known as napa cabbage (Brassica rapa L. ssp.Pekinensis), is one of most important fall vegetables in South Korea.Since the Chinese cabbage is the major ingredient for Korean cuisine, it is one of the most consumed vegetables in Korea [1].With a total production of 2,555,876 tons, Korea has remained the world's fourth largest Brassica cabbage-producing nation over the past decades [2].The Chinese cabbage is a cool season crop, and it is grown during fall and winter.The cabbage is usually cultivated in open fields; thus, its production is highly affected by weather conditions.Among weather factors, temperature is the most important growth factor for the Chinese cabbage.During early growing stages, it grows well at relatively high temperatures, while during boot stages (head formation stage), the plant becomes susceptible to high temperatures [3].Although the Chinese cabbage can tolerate light frost in the fall, cold stress (<10 • C) can negatively affect its growth and development, resulting in yield loss [4,5].
Korea has been experiencing wide temperature fluctuations with increasing frequencies of severe extreme events, such as extremely hot [6] and cold [7] air temperatures during summer and winter, respectively.These extremes in weather conditions are associated with negative cabbage yield anomalies, which can directly affect cabbage price and increase the risks of farm-level crop revenues [8].For example, in 2021, Chinese cabbage produced 14% less than in the 2020 year of production due to increases in the rate of emergence of infectious diseases under warmer weather conditions.This led to an approximate 32% cabbage price increase between August 2020 and August 2021 [9].Shin et al. [10] projected that climate variability between years will continuously increase, with the expectation of more heat stress conditions in future periods.The development of efficient cabbage management strategies is critical to maintain sustainable cabbage production that can ensure farmers' profits and food security.There are many varieties of Kimchi cabbage that have different tolerance ranges for abiotic environmental conditions (e.g., drought and cold).Therefore, to decide optimal crop management strategies for certain environmental conditions, it is important to select the appropriate cabbage variety that can maintain high yield and production at the cultivated condition.
Chinese cabbages only take 50 to 85 days to mature, and their optimal growth temperatures range from 18 to 20 • C with a base temperature of 4-5 • C [11].Due to their quite short growing season and moderate cold tolerance abilities, it is possible to produce fresh cabbage throughout the year in open field conditions.Since high temperature and heavy rainfall negatively affect cabbage yields during the summer [12], most production of cabbage occurs in the fall, winter, and spring months throughout South Korea [9].However, since the growing season of Chinese cabbage differs by region and variety, it is critical to select the appropriate variety and to plan the planting time for the selected cultivar at the cultivated location.Because temperature and light radiation are the primary drivers of the crop lifecycle, a successful planting cabbage strategy requires accurate prediction of the growth and development of various Chinese cabbage varieties in the growing region.Growing degree days (GDD), also known as heat units or growth units, are often used to determine plant growth, development, and maturation stages in their growing regions [13].
The GDD can be calculated using some climatic features, such as maximum and minimum air temperatures.At temperatures above base temperature, the amount of plant growth is directly related to the amount of heat or temperature accumulated [13].The GDD plays a key role in the prediction of developmental stages and in evaluating the growth potential of cabbage varieties of interest at the location [14].Accurate calculation of GDD is very helpful in selecting cabbage varieties appropriate to different farming areas and in scheduling the planting dates of different varieties in different locations.Additionally, insect and disease emergence and development are highly related to temperature; thus, heat sums can also be used to predict epidermic outbreaks of insects and disease that can significantly lead to the yield loss of Chinese cabbage.
In this study, we investigated various morphological characteristics of different fall Chinese cabbage varieties grown in multiple years in different locations throughout South Korea.Fall Chinese cabbage varieties were selected in this study because their production plays an important role in price stability in the Korean agricultural market.Chinese cabbage is a primary ingredient for Kimchi, which is an essential stable side dish that is eaten at most mealtimes in South Korea [15].Among the total domestic cabbage production, 56% of the total production is consumed by private households and small-scale users, while 34% is used by restaurants and other commercial entities [15].November is kimchi-making season, also termed "kimjang".Most Korean families consume Chinese cabbage in the beginning of November.Thus, with high demands of cabbage during the kimchi-making season, the production of fall Chinese cabbage varieties is crucial for price stability in the Korean agricultural market.After analyses of various morphological characteristics of a number of Chinese cabbage varieties, machine learning (ML) approaches, including multivariate polynomial regression (MPR) and k-means clustering with the Elbow method, were used to identify the similar patterns of morphological characteristics among the number of Chinese cabbage commercial varieties in South Korea.Optimal base temperatures for each variety clustering group were determined.The determined optimal base temperatures were used to select the appropriate variety in future climate change conditions.Based on the analysis of data, we investigated the economic impacts of abnormal weather on the production of Chinese cabbage fall varieties in South Korea.For economic analysis, we used the partial equilibrium model of Chinese cabbage price between supply and demand [16].The model was calibrated with production and sales price data collected by Statistics Korea [17] and the Korea Agro-Fisheries and Food Trade Corporation [18] from 2010 to 2020.As a result of this study, optimal cropping management strategies under various climate conditions that provide the best economic benefits to farmers are suggested.

Chinese Cabbage Morphological Data Collection
A total of thirteen field studies were conducted during 2020-2021 throughout the six provinces of Gangwon, Chungcheonbuk, Chungcheongnam, Gyeongsanbuk, Jeollabuk, and Jeollanam in South Korea (Figure 1).In each province, at least three different field sites were investigated (Figure 1).
of a number of Chinese cabbage varieties, machine learning (ML) approaches, including multivariate polynomial regression (MPR) and k-means clustering with the Elbow method, were used to identify the similar patterns of morphological characteristics among the number of Chinese cabbage commercial varieties in South Korea.Optimal base temperatures for each variety clustering group were determined.The determined optimal base temperatures were used to select the appropriate variety in future climate change conditions.Based on the analysis of data, we investigated the economic impacts of abnormal weather on the production of Chinese cabbage fall varieties in South Korea.For economic analysis, we used the partial equilibrium model of Chinese cabbage price between supply and demand [16].The model was calibrated with production and sales price data collected by Statistics Korea [17] and the Korea Agro-Fisheries and Food Trade Corporation [18] from 2010 to 2020.As a result of this study, optimal cropping management strategies under various climate conditions that provide the best economic benefits to farmers are suggested.

Chinese Cabbage Morphological Data Collection
A total of thirteen field studies were conducted during 2020-2021 throughout the six provinces of Gangwon, Chungcheonbuk, Chungcheongnam, Gyeongsanbuk, Jeollabuk, and Jeollanam in South Korea (Figure 1).In each province, at least three different field sites were investigated (Figure 1).Due to limited land areas, not all varieties were planted at the same time and same location.Each province had multiple field sites, and 24 different commercial varieties were planted in all field sites.The number of varieties planted at each field site ranged from 1 to 3. The experiment plot was laid out as a randomized completed design, with variety being the only treatment factor.Seeds were sown in pots in greenhouses at different times according to planting sites, and seedling plants in the stage of 3-4 true leaves Due to limited land areas, not all varieties were planted at the same time and same location.Each province had multiple field sites, and 24 different commercial varieties were planted in all field sites.The number of varieties planted at each field site ranged from 1 to 3. The experiment plot was laid out as a randomized completed design, with variety being the only treatment factor.Seeds were sown in pots in greenhouses at different times according to planting sites, and seedling plants in the stage of 3-4 true leaves were transplanted in open fields from late August to early September.The seedling plants were transplanted at a spacing of 50 cm × 40 cm.The plant density was 3-4 plants per m 2 .Inorganic fertilizer was applied before planting at a rate of 100, 60, and 60 kg K ha −1 and 2 weeks after planting at a rate of 100, 60, and 60 kg K ha −1 .All field data collection was supported by the Korea Rural Economic Institute (KREI).
At harvest, samples were collected from three random small sizes of plots (about 3.3 m 2 size of plot) in each field trial.A range of morphological characteristics of various Chinese cabbage varieties was collected.The morphological characteristic traits collected were fresh head weight (g), root weight (g), root diameter, number of inner leaves (no.), number of outer leaves (no.), leaf blade width (cm), and plant height (cm).Table 1 shows the measurement method for each morphological trait.

K-Means Clustering with the Elbow Method for Chinese Cabbage Segmentation
In ML, k-means clustering [19] is a well-kwon clustering method of assigning an element to a certain cluster that has the minimum distance between an element and a cluster.Although it is based on x and y coordinates on a map [20], it is not limited to the two-dimensional coordinate system.In fact, Yoon et al. [21] showed that the k-means clustering could be applied to segment soybean cultivars based on their morphological characteristics (e.g., lodging, height, number of pods per plant).In this study, the k-means clustering was applied with the Elbow method [22], which determines the number of clusters (k) based on within-cluster sums of squares (WSS).Figure 2  Notice that m morphological characteristics should be normalized via Equation 1, because they have different scale units (see Table 1).The normalization makes values between 0 and 1 so that the proposed k-means clustering can identify clusters (or cultivar groups) without causing skewness on a certain morphological characteristic with large scale values.Notice that m morphological characteristics should be normalized via Equation ( 1), because they have different scale units (see Table 1).The normalization makes values between 0 and 1 so that the proposed k-means clustering can identify clusters (or cultivar groups) without causing skewness on a certain morphological characteristic with large scale values.
In Figure 2, each normalized data d j ∈ D involving m morphological characteristics of Chinese cabbage are assigned to k clusters.However, since the number of clusters (k) is not determined, the k-means is conducted under different k values (i.e., k = 2 to k max , which is the maximum number of potential clusters in the segmentation process).Each clustering process is completed when the clustering result is less than or equal to the given threshold (θ centriod ).On the other hand, only cluster information satisfying WSS k ≤ θ elbow is selected as the final outcome with k.The proposed clustering was used to organize multivariate datasets collected from field research into isolated groups of similar Chinese cabbage varieties.The head weight, number of inner leaves, number of outer leaves, plant height, leaf blade width, root length, and root diameter were used to identify groups of similar Chinese cabbage varieties (i.e., m = 7).
Figure 3 represents the WSS values under different k from 1 to 10 (i.e., k max = 10).Initially, the WSS value is 5.60 (k = 1), but as the value of k increases, its value decreases.After k = 3, the difference between WSS k and WSS k+1 is smaller than θ elbow = 0.5.Thus, this study selected 3 as the number of clusters (k) according to the Elbow method.

Determination of GDD for Each Chinese Cabbage Group
The weather data, including the daily maximum and minimum air temperature and precipitation, were obtained from the nearest meteorological station from the study site.All weather data are available from the KREI Outlook and Agricultural Statistics Information System.The maximum and minimum temperatures were used to calculate GDDs for each variety grown in different locations and years.Table 2 lists the mean temperatures and total rainfall averaged over 2020-2021 in different provinces over the Chinese cabbage growing season (September-November).
Climate features varied by geographic location in South Korea (Table 2).For example, Gangwon province, which is surrounded by high mountains, had the lowest air mean temperatures across all locations, while Jeollanam province, which is in the southern area, had the highest mean air temperatures during the Chinese cabbage growth seasons.In general, high rainfall was received until September in Korea, and the precipitation decreased in both fall and winter to 30-50 mm (Table 2).In September, the highest total precipitation amount in September was observed in Gangwon province, while Jeollanam had the lowest values in total precipitation amount.

Determination of GDD for Each Chinese Cabbage Group
The weather data, including the daily maximum and minimum air temperature and precipitation, were obtained from the nearest meteorological station from the study site.All weather data are available from the KREI Outlook and Agricultural Statistics Information System.The maximum and minimum temperatures were used to calculate GDDs for each variety grown in different locations and years.Table 2 lists the mean temperatures and total rainfall averaged over 2020-2021 in different provinces over the Chinese cabbage growing season (September-November).
Climate features varied by geographic location in South Korea (Table 2).For example, Gangwon province, which is surrounded by high mountains, had the lowest air mean temperatures across all locations, while Jeollanam province, which is in the southern area, had the highest mean air temperatures during the Chinese cabbage growth seasons.In general, high rainfall was received until September in Korea, and the precipitation decreased in both fall and winter to 30-50 mm (Table 2).In September, the highest total precipitation amount in September was observed in Gangwon province, while Jeollanam had the lowest values in total precipitation amount.The values of cumulative GDDs for each cultivar can be calculated by the following equation [23]: In Equation ( 2), T max is the maximum temperature; T min is the minimum temperature; T avg = (T max + T min )/2; T b is the base temperature (T b = 5 • C, Park et al. 2019); and T u is the upper temperature.The cumulative GDDs for each Chinese variety were calculated by adding the GDD values from planting date to harvesting date at the planting location.The value of the GDDs for each cluster was calculated by averaging the values of the GDDs of varieties within each cluster.

Development of Chinese Cabbage Yield Prediction Model Using GDD and Other Weather Variables
The Chinese cabbage economic yield model was developed using the calculated GDD with a base temperature of 5 • C and the two most important weather variables of total precipitation and average air relative humidity [24,25] that significantly affect Chinese cabbage yields.Let X 1 , X 2 , and X 3 be the GDD, precipitation, and humidity, respectively.According to the correlation analysis between Chinese cabbage yield and weather data mentioned in Section 2.3, the coefficients of correlation of GDD, precipitation, humidity, and temperature are −0.24(weak correlation), −0.37 (weak correlation), −0.28 (weak correlation), and 0.01, respectively.Thus, the absolute coefficient of correlation of temperature of less than 0.2 (unrelated) is disregarded as an independent variable for the MPR modeling.Notice that the correlation analysis only shows the linear correlation between variables [26].From the three selected independent variables, the crop yield (Y) prediction model was developed via the multivariate polynomial regression (MPR) proposed by Kim et al. [27].The MPR is a popular supervised machine learning model that explains the relationship between independent variables (or predictors) and a response variable [28].In particular, unlike the traditional regression modeling approaches, it consists of polynomial functions for multiple independent variables so that the nonlinear relationship between variables can be captured [29].Equation (3) depicts the general form of MPR: where , and the error term (ε) follows a normal distribution with a mean of 0 and variance of ∑ n i=1 σ 2 i .Similar to the linear regression (LR) model, coefficient β ij for X i represents the relationship between X i and the response variable Y (i.e., the crop yield).The Moore-Penrose pseudoinverse can be utilized to compute coefficient β ij [30].Thus, by analyzing the absolute value of the coefficient, the significance of each variable on crop yield can be identified.Figure 4 describes an algorithm used to develop an MPR model from cultivar clusters (i.e., C 1 , C 2 , . . ., C K ) given by the k-means clustering with the Elbow method addressed in Section 2.2.In Figure 4, the algorithm enables the most appropriate L for X i to be identified in terms of R 2 , which is greater than or equal to the given estimation accuracy (θ accuracy ).

Determination of the Appropriate Chinese Cabbage group under Various Climate Change Conditions
To project the climate change weather conditions, the MIROC6 model from the Coupled Model Intercomparison Project Phase 6 (CMIP6) was used to downscale climate change scenario information.The MIROC6 model was developed by the Center for Climate System Research, University of Tokyo, National Institute for Environmental Studies (NIES), and the Japan Agency for Marine-Earth Science technology [31].Eleven locations were selected to cover the land surface of all study sites shown in Figure 1.Historical weather data (1986-2005) from 11 locations were used to predict future climate conditions.Future climate conditions, including maximum, minimum temperatures, total precipitation, wind speed, and humidity, were projected under two climate change scenarios through the combination of shared socioeconomic pathways (SSPs) and representative concentration pathways (RCPSSPs), namely SSP245 (SSP2 + RCP4.5, an intermediate development pathway) and SSP585 (SSP5 + RCP8.5, a high development pathway).SSP585 represents a high-emission scenario that is based on the emission scenario considering SSP5 and radiative forcing of 8.5 W/m 2 at the end of the 21st century [32].The MIROC6 model was bias-corrected and downscaled for a near future period (2030-2050) using empirical quantile mapping methods based on the reproducibility of minimum temperature and precipitation-related extreme climate indices for the past.
To make projections for climate change scenarios, GDDs, total precipitation, and relative humidity under SSP245 and SSP585 climate pathways were calculated for all simulation sites from 2030 to 2050.The calculated GDDs, total precipitation, and relative humidity values were added to the Chinese cabbage yield models created in Section 2.4.In this study, a total of six climate change scenarios were analyzed: two climate pathways (SSP245 and SSP585) times three growing day values of 60, 70, and 80 days.We decided to use three different vegetable growing day values, since the growing days of Chinese cabbage varieties analyzed in this study ranged from 60 to 80 days (data not shown).For all simulations, the transplanting dates were 1 September, and the plant density was 3 plants/m 2 .Seven provinces of Gyeonggi, Gangwon, Chungcheonbuk, Chungcheonnam, Gyeongsangbuk, Jeollabuk, and Jeollanam, where most Chinese cabbages are produced, were selected for the simulation, and in the seven provinces, a total of 10 study sites were simulated.When multiple sites for Gangwon, Chungcheonbuk, and Jeollanam were simulated, the prediction values were averaged over the sites within the province.Total Chinese cabbage production was calculated using the average values of Chinese cabbage harvested areas in 2017-2021 [9].Total production for the historical period (2020-2021) was calculated using the average total harvested areas (2017-2021) in the seven provinces, and the measured yield data in Section 2.1.

Determination of the Appropriate Chinese Cabbage group under Various Climate Change Conditions
To project the climate change weather conditions, the MIROC6 model from the Coupled Model Intercomparison Project Phase 6 (CMIP6) was used to downscale climate change scenario information.The MIROC6 model was developed by the Center for Climate System Research, University of Tokyo, National Institute for Environmental Studies (NIES), and the Japan Agency for Marine-Earth Science technology [31].Eleven locations were selected to cover the land surface of all study sites shown in Figure 1.Historical weather data (1986-2005) from 11 locations were used to predict future climate conditions.Future climate conditions, including maximum, minimum temperatures, total precipitation, wind speed, and humidity, were projected under two climate change scenarios through the combination of shared socioeconomic pathways (SSPs) and representative concentration pathways (RCPSSPs), namely SSP245 (SSP2 + RCP4.5, an intermediate development pathway) and SSP585 (SSP5 + RCP8.5, a high development pathway).SSP585 represents a high-emission scenario that is based on the emission scenario considering SSP5 and radiative forcing of 8.5 W/m 2 at the end of the 21st century [32].The MIROC6 model was bias-corrected and downscaled for a near future period (2030-2050) using empirical quantile mapping methods based on the reproducibility of minimum temperature and precipitation-related extreme climate indices for the past.
To make projections for climate change scenarios, GDDs, total precipitation, and relative humidity under SSP245 and SSP585 climate pathways were calculated for all simulation sites from 2030 to 2050.The calculated GDDs, total precipitation, and relative humidity values were added to the Chinese cabbage yield models created in Section 2.4.In this study, a total of six climate change scenarios were analyzed: two climate pathways (SSP245 and SSP585) times three growing day values of 60, 70, and 80 days.We decided to use three different vegetable growing day values, since the growing days of Chinese cabbage varieties analyzed in this study ranged from 60 to 80 days (data not shown).For all simulations, the transplanting dates were 1 September, and the plant density was 3 plants/m 2 .Seven provinces of Gyeonggi, Gangwon, Chungcheonbuk, Chungcheonnam, Gyeongsangbuk, Jeollabuk, and Jeollanam, where most Chinese cabbages are produced, were selected for the simulation, and in the seven provinces, a total of 10 study sites were simulated.When multiple sites for Gangwon, Chungcheonbuk, and Jeollanam were simulated, the prediction values were averaged over the sites within the province.Total Chinese cabbage production was calculated using the average values of Chinese cabbage harvested areas in 2017-2021 [9].Total production for the historical period (2020-2021) was calculated using the average total harvested areas (2017-2021) in the seven provinces, and the measured yield data in Section 2.1.

Analysis of Impacts of Cropping Management and Various Weather Conditions on Economic Production
The total production change under two different climate pathways (SSP245 and SSP585) with three growing days of 60, 70, and 80 days resulted in the price change of Chinese cabbage.For accurate estimation of the price change, this study adopted the partial equilibrium model of crop price between supply and demand [16].In other words, this study did not consider other factors, such as the impact of the import and export of crops on price.Suppose that Q is the production quantity of Chinese cabbage, and P is its price.This study adopted a log-linear function used to compute the price from the production quantity [33].This relationship was proven by the historical avocado price data in San Francisco from 2015 to 2018 [34].Similarly, Sim [35] observed that watermelon supply followed the log-linear supply curve.Unlike the communities, crop production takes a longer production period (at least several weeks or months) and is heavily influenced by available farmland (or land-use type), which is restricted by government agency [36].This implies that the price elasticity of supply cannot be consistent on the supply curve.Equation ( 4) represents the general form of the log-linear curve: The assumed log-linear curve is calibrated with the production and sales price data collected by Statistics Korea [17] and the Korea Agro-Fisheries and Food Trade Corporation [18] from 2010 to 2020.According to the historical data, the total demand of Chinese cabbage in South Korea is quite stable.Annually, 2707 ± 410 thousand tons of Chinese cabbage have been consumed since 2000.Although the total demand of Chinese cabbage has decreased by approximately 32,789 ton/year, this is only 1.12 % of 2707 thousand ton [37].Because Koreans eat Kimchi as their common side dish, there exists consistent demand for Chinese cabbage [38].Regarding this condition, Equation (4) was calibrated, and its result is depicted as the log-linear curve: Q = 84.7986− 21.2766 ln(P) (5) Equation ( 5) can be transformed to compute the price P from the production quantity Q.

Cluster Analysis Based on Morphological Characteristics and GDD Evaluated on Nineteen Chinese Cabbage Varieties
Based on the clustering analysis, three Chinese cabbage groups were created.All groups include eight Chinese cabbage varieties.Table 3 lists the names of the varieties.The centroids of Group 1, Group 2, and Group 3 were C1 (0.73, 0.71, 0.40, 0.76, 0.75, 0.77, The R 2 of Equation ( 6) is 74.02% so that it can appropriately estimate the price (USD/kg) of Chinese cabbage under the given unit production quantity (ton/ha).

Cluster Analysis Based on Morphological Characteristics and GDD Evaluated on Nineteen Chinese Cabbage Varieties
Based on the clustering analysis, three Chinese cabbage groups were created.All groups include eight Chinese cabbage varieties.Table 3 lists the names of the varieties.The centroids of Group 1, Group 2, and Group 3 were C1 (0.73, 0.71, 0.40, 0.76, 0.75, 0.77, 0.71), C2 (0.43, 0.60, 0.45, 0.50, 0.58, 0.70, 0.51), and C3 (0.44, 0.39, 0.29, 0.41, 0.61, 0.57, 0.32), respectively.Seven normalized values of a centroid represent the height (cm), inner leaves (no.), outer leaves (no.), leaf blade width (cm), root length (cm), root diameter (cm), and head weight/plant (g).The groups were significantly different from each other at p < 0.0001.Table 4 shows the average values of morphological traits for each cluster group.Group 1 had the largest values for all morphological traits among all groups.The large values in height, number of inner leaves, and leaf blade width of Group 1 resulted in the highest head weight of 4302 g among all groups.Group 2 had the second largest values in most morphological variables.Group 3 showed the smallest values in most morphological traits, and its head weight was only 2516 g.Group 3 had only 61 inner leaves, while Groups 1 and 2 had 76 and 71 inner leaves, respectively.The number of outer leaves of Groups 1, 2, and 3 were 11, 9, and 6 leaves, respectively.Group 1 had the largest leaf blade width of 31.09cm, while Groups 2 and 3 had similar leaf blade widths of around 27 cm.The root lengths of Groups 2 and 3 were around 27 cm, while the root length of Group 1 was over 30 cm.The root diameters for Groups 1, 2, and 3 were 21.15, 20.38, and 18.98, respectively.Table 4 lists the values of GDDs and the number of growing days for each cluster.According to the results, Group 1 had the shortest value of GDDs of 765, while Group 2 had the largest GDD value of 873.Group 3 had the second largest value of GDDs of 814.From the three cultivar groups of Chinese cabbage, yield estimation models were developed via MPR, which is addressed in Section 2.4.Equations ( 7)-( 9) represent the yield estimation model of Group 1, Group 2, and Group 3, respectively.Note that these models use unnormalized data (i.e., original data) for practicality.Three independent variables of GDD (X 1 ), precipitation (X 2 ), and humidity (X 3 ) are considered in the models.
In Equations ( 7)-( 9), all three independent variables have nonlinear relationships with the yield (Y) of Chinese cabbage.In particular, precipitation (X 2 ) and humidity (X 3 ) have quadratic forms, while GDD (X 1 ) has a cubic form.The range of X 1 is 632-1009; the range of X 2 is 41.80 to 394.23 mm; and the range of X 3 is 69.33 to 78.55%.The R 2 values of MPR models for Groups 1, 2, and 3 are 93.35,99.92, and 95.71%, respectively.Although three independent variables (GDD, precipitation, and humidity) showed weak correlation with Chinese cabbage yield in Section 2.4, these high estimation accuracy values of Equations ( 7)-( 9) prove that there are nonlinear relationships between the independent variables and crop yield, and they are significant factors for yield estimation.As Senthilnathan (2019) mentioned, correlation analysis is not appropriate for identifying the nonlinear correlation between variables.

Chinese Cabbage Yields in Future Climate Climates
The developed Chinese cabbage yield models were used to predict Chinese cabbage yields in the near future period (2030-2050) in SSP245 and SSP585 pathways.Table 5 shows the future climate conditions in two pathways across all study locations in South Korea.In comparison with the weather conditions in 2020-2021, the maximum, minimum, and mean temperatures increased in future periods.According to the climate change simulation results, around 7-8 • C increases were observed in the minimum temperature in the future period, while the maximum temperatures were only increased by 1 • C or less than 1 • C. Between the two pathways, more temperature increases were observed in the SPS585 pathway.Extreme precipitation events were observed in September for both pathways.The maximum total precipitation in both SSP245 (905 mm) and SSP585 (1066 mm) pathways was more than triple the amount of total precipitation observed in 2020-2021 (331 mm).Mean values for relative air humidity did not change much in future periods, but an extreme drought air condition (around 59% humidity) was observed in each pathway.
Table 6 shows that the total harvested areas of seven provinces from 2017-2021 was 24,943 ha.Among the seven provinces, Jeollanam province had the largest harvested area (7582 ha), while Gangwon had the second largest harvested area (5712 ha).Chungcheonnam had the smallest harvested area for Chinese cabbage production (1663 ha).The calculated total Chinese cabbage production of Groups 1, 2, and 3 for the historical period 2020-2021 was 3219, 2550, and 1883 × 1000 tons, respectively.In climate change scenarios, Jeollanam province produced the highest Chinese cabbage production among all provinces, while Gangwon province had the second largest production.The Chinese cabbage total production for Group 1 increased under all combinations of climate change scenarios, while the total production for other groups varied by growing days and climate change pathways.In both climate change pathways, Group 1 had a higher production than the other two groups.In the SSP585 pathway, Group 1 produced the highest productions in the shortest growing period (60 days) for all provinces, but a different production pattern was observed in the SSP245 pathway.In Gyeonggi, Gangwon, and Gyeongsangbuk, Group 1 produced the highest yields in longer growing periods.The pattern of total productions of Group 2 varied by location.In northern regions, including Gyeonggi, Gangwon, Chungcheonbuk, and Chungcheonnam, Group 2 had the highest production in the shortest growing period, while Group 2 produced the highest production as it grew longer in southern regions.Group 3 showed a similar pattern to Group 1, while Group 3 increased its production when plants grew in a short growing period (60 growing days).Under the SSP585 pathway, Group 3 showed the highest production in Chungcheonnam province with the longest growing period.

Analysis of Impacts of Variable Weather Conditions on Chinese Cabbage Economic Production
As mentioned in Section 2.6, the prices of three groups (Group 1, Group 2, and Group 3) under two different climate pathways (SSP245 and SSP585) with three growing periods of 60, 70, and 80 days were estimated via Equation (6).The estimated yields illustrated in Table 6 were used, and Table 7 illustrates the estimated unit price of three groups of Chinese cabbage.
In Table 7, Group 1 has the lowest unit price due to its high production yield.Given that Chinese cabbage consumption in South Korea is almost consistent (see Section 2.6), it is possible that excess supply happens.The self-sufficiency rate of Chinese cabbage is about 84% on average; however, the yield of Group 1 is 26.53% higher (129.06ton/ha) than those of the existing Chinese cabbage cultivars (101.57ton/ha).Thus, this excess supply can cause a sales price reduction of Chinese cabbage, even if there is no exportation of the surplus quantity.Figure 5 illustrates this relationship between production quantity and sales price.On the other hand, Group 3 (75.49ton/ha) resulted in a short supply of Chinese cabbage; thus, its price will significantly increase.According to Ha et al. [39], the upper limit of the acceptable price of Chinese cabbage for Korean consumers is USD 0.90/kg.In fact, Ha et al. [39] conducted a survey of the price sensitivity of Chinese cabbage with 1000 subjects randomly selected regarding income, geological location, age, and number of household members (430 valid responses).In this case, there is an import of Chinese cabbage to resolve the short supply.Group 2 (102.23 ton/ha) had the most preferred price,

Discussion
Approximately 70% of Korea is covered with mountainous areas; thus, the climate features can vary with elevation and location [41].Since most Chinese cabbage is produced in open field sites, its production is highly affected by the weather conditions, such as temperature [42,43].According to the report from Statistics Korea [9], the total harvested area for fall Chinese cabbages grown in an open field was 13,854 ha, while the harvested area for greenhouse Chinese cabbage was only 2008 ha.Although Chinese cabbage is the most important vegetable in South Korea, the price fluctuations of Chinese cabbage were higher than those of other vegetables due to unstable yield production.Increases in frequencies of extreme weather conditions significantly affect Chinese cabbage yields [44,45].Thus, to maintain sustainable Chinese cabbage production under unpredicted weather conditions, it is crucial to study how various weather conditions obtained from different locations affect Chinese cabbage production and which cabbage variety performs well at the harvest site.
The sustainable production of Chinese cabbage during 'kimjang' season in late fall is crucial for stabilizing its price in the market.This study is the first attempt to group multiple Korean fall Chinese cabbage varieties by similar morphological characteristics.The results obtained in this study indicate the yield patterns of three types of Chinese cabbage varieties varied by location and cropping management (different harvest time).From an economic perspective, the results indicate that when demand is lower than the excessive amount of supply, producing high yields is not always the answer for the best Chinese cabbage supply plan.
There is an abundance of Chinese cabbage varieties (about 100) in the South Korean market.In this study, we selected only the 23 most popular varieties in the market in South Korea.Based on the similarities of morphological characteristics measured in field studies from 2020-2021, a total of twenty-four Chinese cabbage varieties were grouped into three clusters.Group 1 had higher values in all morphological variables, such as head weight, resulting in greater economic yields than the other two groups.Group 2 had the second largest values in morphological characteristics, resulting in the second largest yield among all groups.Similar values of morphological characteristics for Group 2 were observed in Sim et al. [46].Sim et al. [46] had similar results of morphological characteristics from the 'Chungwang' variety, which, in this study, belonged to Group 2. Most varieties in Groups 1 and 2 were products from large Korea seed companies, such as Monsanto Korea, Sakata Korea, and NH seed company [47].Even though Group 3 had the smallest yield values, some varieties in Group 3 had strong tolerances to biotic (insect and disease) stresses [47].Group 1 had the lowest GDD values compared to the other two groups.This result is supported by Sim et al. [46], who reported that the varieties with shorter GDDs produced higher yields than those with longer GDDs.
Chinese cabbage prediction models for Group 1, Group 2, and Group 3 were successfully developed.Despite only three weather variables, of the calculated GDDs, precipitation, and relative humidity, being considered in the models, the three models were very accurate, as shown in the values of R 2 for all three models being over 0.93.According to simulation results, the highest Chinese cabbage productions were observed in Jeonnam province.This result was supported by Statistics Korea [9], who reported that Chinese cabbage is mainly grown in Jeonnam province in South Korea, accounting for 30 percent of the total production in Korea.Under climate change scenarios, the growth patterns of groups varied by location and cropping management.The growth pattern of Group 2 was very different from Groups 1 and 3, while Groups 1 and 3 had similar growth patterns.Group 2 had higher yields in the northern region for a shorter growing period, while it had higher yields in the southern region for a longer growing period.
The economic production under various weather conditions with three different crop management scenarios (growing periods of 60, 70, and 80 days) was analyzed via the log-linear curve, as addressed in Section 2.6.Unlike crop yield estimation, increased production yield by Group 1 caused excess supply; thus, the sales price was reduced.To maintain the existing sales price (USD 0.48/kg) of Chinese cabbage in South Korea, an export of excessive quantity should be considered in the future.Notice that the export policy should be devised by considering the sales price change in SSP245 and SSP585 under three different crop management scenarios (see Table 7).Moreover, although Group 3 was selected as the case with the highest total revenue, it is not the recommended strategy because the sales price increase was caused by supply shortage.This may threaten food security for South Korea.Additionally, regarding the upper limit of the acceptable price of Chinese cabbage for Korean consumers (i.e., USD 0.90/kg), the sales price of Group 3 was too high for Korean consumers.In fact, similar to summer Chinese cabbage, which has a high sales price of USD 0.89/kg due to unstable production under climate change conditions [48], the import of Chinese cabbage should be considered for food security and society in South Korea.Thus, this study recommends either Group 1 or Group 2 as an alternative cultivar in the future.To maintain or increase the existing self-sufficiency rate under the upper limit of acceptable price, both cultivar groups are appropriate options in South Korea.
In summary, three Chinese cabbage groups were created from the 23 most popular varieties in the market in South Korea, and they showed different growth patterns under different climate change scenarios.Group 1 always showed the highest yield among the three groups, while Group 2 showed the second largest yield.Most varieties in Groups 1 and 2 were products from large seed companies in Korea.The developed models predicted large yield increases in Group 1 under climate change scenarios.However, increased yields in the future period resulted in excessive supply in the market, which led to a large price reduction.As a result, alternative ways, such as exporting or producing Group 2, were suggested under future weather conditions.
Although the findings from this study provide useful information to farmers, there should be additional tasks in the future.Further greenhouse or growth chamber studies that study the effects of extreme weather conditions, such as heavy rainfall and heat stress, on Chinese cabbage are needed to improve model accuracy.Because the machine learning models were created using historical weather conditions, they did not include extreme weather conditions.Thus, the yield data of Chinese cabbage grown in extreme weather conditions can be used to improve the accuracy of the developed model.In addition, new varieties of Chinese cabbage are continuously developed by Chinese cabbage breeders from seed companies or research centers.The yield analysis method introduced in this study should be performed periodically considering new or existed varieties that are available in the market.For economic production analysis, data on Chinese cabbage price changes derived by imports and exports should be considered in future studies.

Figure 1 .
Figure 1.Field sites where the morphological characteristics of 24 different fall Chinese cabbage varieties were collected between 2020 and 2021 in six provinces in South Korea.The table shows the number of field sites within each province.Blue circles indicate the field site location in each province, and red circles indicate the simulation sites for the climate change study in Section 2.5.The number above each red circle indicates the weather station site ID.

Figure 1 .
Figure 1.Field sites where the morphological characteristics of 24 different fall Chinese cabbage varieties were collected between 2020 and 2021 in six provinces in South Korea.The table shows the number of field sites within each province.Blue circles indicate the field site location in each province, and red circles indicate the simulation sites for the climate change study in Section 2.5.The number above each red circle indicates the weather station site ID.

18 Figure 2 .
Figure 2. Pseudo code of the k-means clustering for Chinese cabbage segmentation.

18 Figure 3 .
Figure 3. Graph of within-cluster sums of squares (WSS) versus number of potential clusters (k).

Figure 3 .
Figure 3. Graph of within-cluster sums of squares (WSS) versus number of potential clusters (k).

1 : 4 :
Load data set Dk of group k of Chinese cabbages 2: Repeat 3: For  = 1 to n Set the maximum power (L) of  5: Construct a form of   6: Construct  and Y matrices 7: Compute  =     9: Estimate  =  8: Compute R 2 of estimated value of the multivariate polynomial regression

Figure 4 .
Figure 4. Pseudo code of the MPR with the Moore-Penrose pseudoinverse.

6 ) 18 Figure 5 .
Figure 5. Price curve under different production quantities of Chinese cabbage in South Korea.

Figure 5 .
Figure 5. Price curve under different production quantities of Chinese cabbage in South Korea.

Table 1 .
Morphological traits and measurement methods used in this study.

Table 2 .
Mean temperature and total precipitation of September, October, and November in all six provinces in South Korea.The values were averaged over locations conducted in each province, and for the years 2020-2021.

Table 2 .
Mean temperature and total precipitation of September, October, and November in all six provinces in South Korea.The values were averaged over locations conducted in each province, and for the years 2020-2021.

Table 3 .
Names of varieties for each cluster and values of cluster centroids for each cluster.

Table 4 .
Morphological characteristics of height, number of inner leaves and outer leaves, leaf blade width, root length, root diameter, and head weight of the three Chinese cabbage cluster groups created in this study.Chinese Cabbage Yield Model Development and Prediction of Yields in Future Climate Climates

Table 5 .
Maximum, minimum, and average values of mean air temperature, total precipitation from September to November, and average air humidity (%) from September to November in the historical period (2020-2021) and future period (2030-2050) under two climate scenarios, SSP245 and SSP585, among all the simulated sites in all seven provinces, South Korea.

Table 8 .
Total revenue of Chinese cabbage (USD millions) in seven provinces in South Korea under two climate change pathways (SSP245 and SSP 585).