Analysis of the Rainfall Pattern and Rainfall Utilization Efficiency during the Growth Period of Paddy Rice

: Rainfall is one of the most important water sources for rice production in China. However, its temporal and spatial variability is leading to water shortages. The present study collected a long series of historical rainfall data from research sites during the rice growth period to analyze the characteristics of rainfall distribution and the correlation with rainfall utilization efficiency, aiming to investigate its impact on rice irrigation practices. It is found that the rainfall distribution varied greatly between the different locations and growth periods. The average rainfall of the whole growth period ranges from 135.5 mm to 694.5 mm. The rainfall curve exhibits a typical unimodal pattern with variations in the intensity, duration, and timing of peak precipitation across different growth periods. During the rice growth period, the cases in southern China are more prone to waterlogging for a high probability of continuous rainfall, and the cases in northern China are more prone to drought. The rainfall utilization efficiency of all cases exhibits a significant inter-year fluctuation range, negatively influenced by the rainfall amount and rainfall inhomogeneity. The efficiency in utilizing precipitation is diminished with greater and more uneven rainfall experienced during the growth period. These findings can provide a decision-making basis for optimizing rice irrigation strategies and enhancing rainfall utilization efficiency in diverse regions across China.


Introduction
Paddy rice cultivation holds immense significance in China, serving as a crucial staple food source, with an annual production exceeding 20 million metric tons [1].Commonly, rice is grown in paddy fields that are flooded during specific rice growth periods, thereby facilitating the inherent ability of paddy fields to retain natural rainfall.Cropping seasons in China usually run from March to November, during which the rice-growing areas are usually in the flood season with abundant rainfall.However, a substantial water demand is associated with paddy rice production [2].This is attributed to the highly spatio-temporal variation in rainfall in China, resulting in a significant portion of precipitation being lost as runoff into rivers that ultimately flow into the sea [3].Northern China faces more serious water scarcity than southern China.The total water resources in northern regions are only 19% of the total in China, while cultivated land accounts for approximately 60% of that in China, representing a serious spatial mismatch between productive resource distribution and productive capacity [4].More attention should be paid to preventing drought and yield reduction by improving the rainfall utilization efficiency.However, despite sufficient quantities, southern China experiences water shortages due to extremely uneven rainfall distributions in different years (particularly within a year) [2,5].Thus, the effective use of rainfall to reduce irrigation water in both northern and southern China has become increasingly important in alleviating water shortages.
Engineering measures were developed to improve rainfall utilization efficiency, such as building rain storage facilities, ponds, and small reservoirs, which occupy valuable land resources [6,7].Similar to ponds, paddy fields have a certain function of water storage.Paddy fields are usually blocked by bunds to maintain a ponding water level (i.e., a waterlogging depth) at 20-50 mm during most rice-growing periods [8].Rainwater may be gathered and stored as much as possible in the paddy field to take full advantage of the natural rainwater to improve rainwater utilization.Numerous studies have focused on the methodology of incorporating rainfall into irrigation decision-making, such as the rain-gathering irrigation mode [9,10].However, the analysis of rainfall characteristics during the rice growth period needs to be improved [11][12][13].
Investigating rainfall patterns and their correlation with the rainfall storage capacity in paddy fields (i.e., the rainfall utilization efficiency) during rice growth periods is crucial for making informed irrigation decisions and enhancing the rainfall utilization efficiency.The studies on the relationship between rainfall patterns and rice cultivation focus on analyzing the impact of rainfall patterns, especially seasonal rainfall patterns, on crop production [14][15][16][17][18]. Specifically, the mathematical correlation between rainfall and rice production was established to propose appropriate planting strategies [19,20].Recently, Garbanzo et al. investigated the primary constraints associated with soil salinity and rainfall variability, proposing the Mangrove Swamp Rice Production System as a solution for rice farmers to mitigate the impacts caused by salinity and rainfall fluctuations [21,22].Other scholars place greater emphasis on the impact of rainfall characteristics during specific rice growth periods on rice cultivation [23][24][25].Furthermore, the impact of climate change-induced alterations in rainfall patterns on rice production was investigated, and models were developed to simulate how these changes will influence the growth period and rice production under future climatic scenarios [26][27][28].The studies above primarily concentrate on the correlation between the rainfall and crop yield.Nevertheless, given the escalating water crisis, enhancing the rainfall utilization efficiency for rice irrigation is becoming increasingly imperative.
Numerous studies discuss the relationship between the rainfall mechanism and flood probability.Therefore, most indicator scales for rainfall analysis are hourly or daily scales, such as rainfall intensity, which mainly investigates the characteristics of extreme rainfall in a short period [29].Moreover, previous studies on rainfall patterns during the rice growth period have predominantly focused on indicators such as the annual rainfall amount and the frequency of rainstorms while paying limited attention to indicators closely associated with rainfall patterns, such as continuous rainfall [30] and the concentration degree of rainfall [31,32], for assessing uneven distribution.Given the diverse climatic conditions across different regions and the inherent variability in rainfall patterns, it is crucial to analyze region-specific rainfall patterns.
The present study aimed to investigate the frequency of different rainfall levels and continuous rainfall events throughout the rice growth period at various locations.The rainfall concentration degree and Lorentz curve, commonly employed in other domains, were utilized to examine the spatial and temporal distribution characteristics of rainfall.The specific objectives of this study are (i) to clarify the rainfall characteristics during the rice growth period; (ii) to investigate the spatio-temporal variations in rainfall patterns across different regions of rice cultivation in China; and (iii) to analyze the impact of precipitation on rainfall utilization efficiency during the rice growth period.

Study Area and Data Source
Paddy rice is cultivated in six regions of China, including double-season rice (early rice and late rice) and single-season rice (middle rice) (Figure 1).Six representative stations were selected considering the geographical location, data accessibility, and cropping system.Specifically, Zhangjiang station mainly grows double-season rice, Nanchang grows both double-season rice and single-season rice, and the other four stations mainly grow singleseason rice.There are nine rice production cases in total, namely, Zhanjiang early rice (ZJE), Zhanjiang late rice (ZJL), Nanchang early rice (NCE), Nanchang middle rice (NCM), Nanchang late rice (NCL), Dali middle rice (DLM), Xinxiang middle rice (XXM), Suihua middle rice (SHM), and Yinchuan middle rice (YCM).A meteorological station was located in each case, with detailed information provided in Table 1.

Study Area and Data Source
Paddy rice is cultivated in six regions of China, including double-season rice (early rice and late rice) and single-season rice (middle rice) (Figure 1).Six representative station were selected considering the geographical location, data accessibility, and cropping sys tem.Specifically, Zhangjiang station mainly grows double-season rice, Nanchang grow both double-season rice and single-season rice, and the other four stations mainly grow single-season rice.There are nine rice production cases in total, namely, Zhanjiang early rice (ZJE), Zhanjiang late rice (ZJL), Nanchang early rice (NCE), Nanchang middle rice (NCM), Nanchang late rice (NCL), Dali middle rice (DLM), Xinxiang middle rice (XXM) Suihua middle rice (SHM), and Yinchuan middle rice (YCM).A meteorological station was located in each case, with detailed information provided in Table 1.
Over 60 years of daily observations for each station were collected from the China Meteorological Data Sharing Service System (http://data.cma.cn,accessed on 1 January 2021), including the minimum temperature, maximum temperature, average tempera ture, average wind speed, sunshine duration, mean relative humidity, and precipitation.Over 60 years of daily observations for each station were collected from the China Meteorological Data Sharing Service System (http://data.cma.cn,accessed on 1 January 2021), including the minimum temperature, maximum temperature, average temperature, average wind speed, sunshine duration, mean relative humidity, and precipitation.
Information on the current agricultural management in each region was collected from the National Irrigation Experiment Results Information Service Platform, field experiments, and previous studies [33][34][35].The growth period of paddy rice is commonly divided into seven stages: the returning green (RG), early tillering (ET), late tillering (LT), jointingbooting (JB), heading-flowering (HF), milk-ripe (MR), and yellow-ripe (YR) stages.In all cases, it was assumed that irrigation would be applied via conventional flooded irrigation, according to the criteria for the field water depth listed in Table 2. Since farmers drain and dry the paddy fields in the sun for a few days at the end of the LT period to control inefficient tillers, the field was fully drained for five days before the end of the LT period in all the simulations.The accumulative and daily precipitation during the rice cultivation period was calculated for the multi-year average, and the frequency and intensity of different rainfall levels were determined.Additionally, the contribution rates of various daily precipitation amounts to the total precipitation were analyzed.Furthermore, the frequency and average daily precipitation during consecutive rainy days and dry days were examined.

Precipitation Concentration Degree and Precipitation Concentration Period
The precipitation concentration degree (PCD) and precipitation concentration period (PCP) were employed to evaluate the non-uniform distribution of weekly rainfall during the rice growth period.Traditionally, PCD and the PCP are determined based on the vector of monthly accumulative precipitation.However, this study specifically focuses on weekly rainfall due to its pronounced influence on rice irrigation management.It can be assumed that weekly total precipitation is a vector quantity with both a magnitude and direction, representing a complete circle (360 • ) during the rice growth period.Then, the PCP and PCD for a specific location can be defined as follows: where R i represents the total precipitation during the rice growth period in the ith year, mm; r ij represents the weekly precipitation in the jth week during the rice growth period in the ith year, mm; and θ j represents the azimuth of the jth week (θ 1 + θ 2 + . ..+θN = 360).PCD i represents the degree to which the total precipitation during the rice growth period in the ith year is concentrated across all weeks, and PCP i indicates the period in which the total precipitation during the rice growth period in the ith year is most concentrated.
The PCD ranges from 0 to 1.A PCD value of 1 indicates concentrated total precipitation during the rice growth period in a specific week, while a PCD value of 0 represents evenly distributed precipitation throughout the rice growth period.

Gini Coefficient and Lorenz Asymmetry Coefficient
The cumulative percentage of days with precipitation was calculated to assess the relative importance of daily rainfall classes, particularly the contribution of different rainfall events.The Lorentz curve, initially proposed by American economic statistician Lorentz, depicts the inequality in the distribution of social wealth [36].It has subsequently been adopted across various disciplines to assess the degree of distribution uniformity [37,38].
In this study, a threshold of 0.1 mm/day was employed to differentiate between rainy and non-rainy days, and a 1 mm interval was used to categorize the precipitation values in ascending order.By counting the number of days within each precipitation range class and computing the corresponding amount of precipitation, the accumulated percentages of days (X) and the corresponding accumulated percentages of precipitation (Y) were obtained.As shown in Figure 2, the Lorenz curve depicts the correlation between X and Y.In the specific scenario of an equal distribution of X/Y, the analytical form of the Lorenz Curve is y = x.In all other cases, assuming that the measured variable remains positive, the Lorenz Curve is convex to the y-axis and never exceeds the line of equality, y = x.
The Gini coefficient (G) quantifies the inequality of the Lorenz Curve by calculating the ratio between the area enclosed by the line of equality and the Lorenz Curve and the triangular area under the line of equality.The Gini coefficient can be evaluated as where G ranges from 0 to 1.If G = 0, the daily precipitation is evenly distributed throughout the rice growth period (i.e., the line of equality), In contrast, if G = 1, the precipitation is distributed unevenly across the rice growth period (i.e., line of inequality).
For the ordered data y 1 ≤ y 2 ≤. ..≤ y i ≤. ..y n , G can be calculated as follows [39]: where y i represents the percentage of accumulated precipitation in the ith rainfall interval, %; I represents the serial number of the rainfall interval; and µ represents the average percentage of accumulated precipitation in the ith rainfall interval, %.The Gini coefficient (G) quantifies the inequality of the Lorenz Curve by calculating the ratio between the area enclosed by the line of equality and the Lorenz Curve and the triangular area under the line of equality.The Gini coefficient can be evaluated as where G ranges from 0 to 1.If G = 0, the daily precipitation is evenly distributed throughout the rice growth period (i.e., the line of equality), In contrast, if G = 1, the precipitation is distributed unevenly across the rice growth period (i.e., line of inequality).
For the ordered data y1 ≤ y2 ≤…≤ yi ≤…yn, G can be calculated as follows [39]: 2 where yi represents the percentage of accumulated precipitation in the ith rainfall interval, %; I represents the serial number of the rainfall interval; and µ represents the average percentage of accumulated precipitation in the ith rainfall interval, %.
When applying the G to evaluate the degree of concentration, it is important to consider that identical G values can derive from different Lorenz Curves.Therefore, the Lorenz asymmetry coefficient (S) was used to evaluate the degree of Lorenz curve asymmetry [39].The S can be calculated as follows: When applying the G to evaluate the degree of concentration, it is important to consider that identical G values can derive from different Lorenz Curves.Therefore, the Lorenz asymmetry coefficient (S) was used to evaluate the degree of Lorenz curve asymmetry [39].The S can be calculated as follows: where m represents the number of rainfall intervals that are less than average; y m represents the percentage of accumulated precipitation in the mth rainfall interval, %; y m+1 represents the percentage of accumulated precipitation in the (m + 1)th rainfall interval, %.As shown in Figure 2, when S = 1, the Lorenz curve exhibits symmetry with respect to the axis of symmetry; when S < 1, the point parallel to the line of equality lies below the symmetry axis, indicating a significant contribution of light rainfall to the overall precipitation; when S > 1, the point parallel to the line of equality is above the symmetry axis, suggesting that a few extreme values account for most of the irregularity in rainfall.

Analysis of Rainfall Utilization Efficiency during the Rice Growth Period 2.3.1. Calculation of Rainfall Utilization Efficiency
The rice irrigation schedule was derived using the ACOP-Rice crop model, which is a modified Python version of AquaCrop (AquaCrop-OSPy v1.0.2).This model is based on historical meteorological data and local conventional irrigation modes to calculate the field water balance elements [13].The rainfall utilization efficiency was calculated as follows: where RUE is the rainfall utilization efficiency of the rice growth period; P is the total rainfall of the rice growth period, mm; and D is the total drainage of the rice growth period, mm.

Pearson Correlation Analysis
The Pearson correlation method was employed to analyze the relationship between rainfall utilization efficiency and rainfall characteristics during the rice growth period.This statistical approach is commonly used to quantify the degree of a linear correlation between two variables.For the existing two sets of data (x i , y i ) (i = 1,. ..,n), the correlation coefficient r is calculated as follows: where x avg and y avg are the average values of n samples, respectively; and r is the coefficient of correlation between the two random variables, ranging from −1 to 1.An r value closer to 1 indicates a stronger positive linear correlation, while an r value closer to −1 suggests a stronger negative correlation.If the value is close to 0, it implies a weak or non-linear relationship.The rainfall frequency for nine cases throughout the rice growth period, the frequencies of different rainfall levels, and their corresponding precipitation were computed using daily precipitation data collected from meteorological stations.The rainfall levels were divided into five categories, labeled as light rain, moderate rain, heavy rain, storm, heavy storm, and extraordinary storm, with the corresponding thresholds [0.1, 10), [10,25), [25,50), and [50,100), [100), mm/d.As shown in Table 3, there is a significant variation in total precipitation during the growth period among different rice cases.NCE demonstrates the highest rainfall, while YCM experiences the lowest, resulting in a substantial difference of 559 mm between their respective growth periods.The inconsistent growth periods of rice make it unreasonable to compare differences in precipitation intensity based solely on total precipitation among cases.Therefore, the daily average rainfall for each case was calculated to reflect variations in rainfall intensity accurately.The southern region generally experiences higher rainfall levels than the northern region, as evidenced by the multi-year average daily precipitation during the growing season.Notably, NCE, NCM, ZJE, ZJL, and DLM exhibit relatively high multi-year average daily precipitation levels of 8.6 mm/d, 5.2 mm/d, 4.8 mm/d, 5.7 mm/d, and 5.5 mm/d, respectively.In contrast, the precipitation in NCL, SHM, YCM, and XXM is relatively low, with a multi-year average daily precipitation of 2.7 mm/d,3.5 mm/d, 1.0 mm/d, and 3.3 mm/d, respectively.

Results and Discussions
Regarding rainfall frequency, DLM exhibited the highest precipitation frequency during the growth period, with an annual average of 57%, while YCM demonstrated the lowest rainfall frequency, averaging only 23%.The ranking of rainfall frequency among different cases generally exhibits a positive correlation with the ranking of average daily rainfall; however, certain variations are observed at specific locations.For instance, DLM demonstrates the highest frequency of rainfall (57%), yet its average daily precipitation (5.5 mm/d) ranks third among nine cases.In contrast, ZJE has a higher rainfall frequency (45%) than ZJL.However, the daily average rainfall in ZJE (4.8 mm/d) is lower than that of ZJL (5.7 mm/d).This observed difference can be attributed to the distribution of varying precipitation levels during the growing season, where DLM and ZJE experience a higher proportion of light and moderate rain.The rainfall intensity exceeding 50 mm/d can surpass the upper limit of the paddy field's storage capacity, leading to a drainage event and reduced rainfall utilization efficiency.Therefore, different rainfall levels are categorized into two levels, below heavy storm (0~50 mm/d) and extreme rainfall (heavy storm and above, >50 mm/d), for the further analysis of the relationship between the rainfall distribution and rainfall utilization efficiency.Regarding the proportion of different rainfall grades, for rainy cases (NCE, NCM, ZJL, ZJE, and DLM), the proportion of extreme rainfall was higher in NCE and ZJL.The frequency of heavy storms or above was 4.4% and 3.0% (9% and 7% of the total rainfall frequency), respectively.NCM and ZJE followed with a frequency of heavy storms or above at 2.4% and 2.3%, representing 7% and 5% of the total rainfall frequency, respectively.The proportion of heavy storms and above in the DLM is significantly lower, accounting for only 1.5% (3% of the total rainfall frequency).Thus, despite frequent rainfall events, the average daily precipitation in DLM does not rank as the highest.Among less rainy cases (NCL, SHM, XXM, and YCM), XXM and NCL exhibited a higher frequency of extreme rainfall, accounting for 1.3% and 1.0%, respectively (equivalent to 4% of the total rainfall frequency).On the other hand, SHM and YCM experienced a lower occurrence of heavy storms or above, with frequencies of 0.6% and 0.1%, respectively (representing 1% and 0.4% of the total rainfall frequency).
The frequency and average daily precipitation of continuous rainfall were computed to investigate the impact of such rainfall on irrigation, as illustrated in Figure 3.The frequency of continuous rainfall at stations other than YCM initially increased, followed by a subsequent decrease as the number of consecutive days increased.In most cases, the highest frequency of continuous rainfall was observed for 2 days, while ZJL recorded the highest frequency for 3 consecutive rainy days.Each case shows a distinct declining trend and variation in peak time.The frequency of continuous rainfall in NCE, ZJE, ZJL, DLM, and SHM has gradually decreased, especially in DLM, where the continuous rainfall lasted for 27 consecutive days.While the frequency of continuous rainfall in NCM, NCL, XXM, and YCM decreased rapidly, continuous rainfall lasting more than 7 days was rare.The frequency of continuous rainfall lasting 2 days or more accounted for 82% of the average rainfall frequency.DLM experienced the highest occurrence at 91%, while YCM had the lowest at 63%.
The average daily rainfall of NCE, NCM, NCL, ZJE, and ZJL showed a significant increase in response to the number of consecutive days with continuous rainfall.However, the average daily rainfall did not exhibit a clear upward trend for long consecutive days due to its infrequent occurrence.This observation suggests that a longer duration of continuous rainfall during the rice growth period is associated with a higher precipitation intensity in these cases.Such extended periods of heavy rainfall are detrimental to the rice cultivation.For instance, in NCE and NCM, there is continuous rainfall for more than 10 days, with an average daily rainfall of 29.6 mm/d and 30.7 mm/d, respectively.This level of precipitation significantly surpasses the water requirement of paddy rice and the field's capacity to retain rainwater, resulting in substantial water displacement.
tinuous rainfall during the rice growth period is associated with a higher precipitation intensity in these cases.Such extended periods of heavy rainfall are detrimental to the rice cultivation.For instance, in NCE and NCM, there is continuous rainfall for more than 10 days, with an average daily rainfall of 29.6 mm/d and 30.7 mm/d, respectively.This level of precipitation significantly surpasses the water requirement of paddy rice and the field's capacity to retain rainwater, resulting in substantial water displacement.The frequency of continuous dry days was computed to investigate its impact on irrigation, as illustrated in Figure 4.Among the four cases (NCE, ZJE, DLM, and SHM), there were rare instances of no rainfall exceeding 15 days.Drought conditions primarily lasted up to 7 consecutive days, indicating a low risk of yield loss.The other 5 cases (NCM, The frequency of continuous dry days was computed to investigate its impact on irrigation, as illustrated in Figure 4.Among the four cases (NCE, ZJE, DLM, and SHM), there were rare instances of no rainfall exceeding 15 days.Drought conditions primarily lasted up to 7 consecutive days, indicating a low risk of yield loss.The other 5 cases (NCM, NCL, ZJL, XXM, and YCM) exhibited a distinct "tail" in Figure 4, indicating a higher frequency of no rainfall for more than 15 days.Notably, the probability of no rainfall for more than 15 days in XXM reached 19.4%.Failing to provide timely irrigation may increase the risk of yield loss.These findings concerning continuous rainfall and continuous dry days are aligned with previous studies showing that the cases in southern China (e.g., NCE and NCM) are more prone to waterlogging and the cases in northern China (e.g., XXM and YCM) are more prone to drought [2,4,5].However, it is worth noting that there are also long periods of no rain in the NC station in southern China due to the uneven distribution of rainfall.

Analysis of Statistical Characteristics of Rainfall during the Whole Growth Period of Paddy Rice
Figure 5 illustrates the rainfall concentration throughout the entire growth period for nine cases.The rainfall distribution varies significantly among different cases for the whole growth period, with the multi-year average PCD ranging from 0.25 to 0.42.In ascending order, the following cases are DLM, NCE, ZJE, SHM, ZJL, YCM, XXM, NCM, and NCL.The Gini coefficient demonstrates a narrower range of variation, averaging from 0.42 to 0.51.The smallest values are observed in NCM, followed by NCE, NCL, XXM, ZJL, ZJE, DLM, SHM, and YCM.The rankings of NCE and YCL showed significant differences due to inconsistencies in the scales used for calculating the rainfall concentration and the Gini coefficient.The concentration of rainfall is determined by weekly precipitation, while the Gini coefficient is computed based on daily precipitation.The rainfall frequency of NCE was significantly high, characterized by a notable occurrence of heavy rain and storm events.However, these events exhibited daily-scale variability while demonstrating a more consistent distribution at the weekly scale.Conversely, the YCM experienced a notably low rainfall frequency, primarily light rain.At the daily scale, this precipitation displayed a higher level of uniformity; however, its distribution became increasingly uneven when observed on a weekly basis.more than 15 days in XXM reached 19.4%.Failing to provide timely irrigation may increase the risk of yield loss.These findings concerning continuous rainfall and continuous dry days are aligned with previous studies showing that the cases in southern China (e.g., NCE and NCM) are more prone to waterlogging and the cases in northern China (e.g., XXM and YCM) are more prone to drought [2,4,5].However, it is worth noting that there are also long periods of no rain in the NC station in southern China due to the uneven distribution of rainfall.

Analysis of Statistical Characteristics of Rainfall during the Whole Growth Period of Paddy Rice
Figure 5 illustrates the rainfall concentration throughout the entire growth period for nine cases.The rainfall distribution varies significantly among different cases for the whole growth period, with the multi-year average PCD ranging from 0.25 to 0.42.In ascending order, the following cases are DLM, NCE, ZJE, SHM, ZJL, YCM, XXM, NCM, and NCL.The Gini coefficient demonstrates a narrower range of variation, averaging from 0.42 to 0.51.The smallest values are observed in NCM, followed by NCE, NCL, XXM, ZJL, ZJE, DLM, SHM, and YCM.The rankings of NCE and YCL showed significant differences due to inconsistencies in the scales used for calculating the rainfall concentration and the Gini coefficient.The concentration of rainfall is determined by weekly precipitation, while the Gini coefficient is computed based on daily precipitation.The rainfall frequency of NCE was significantly high, characterized by a notable occurrence of heavy rain and storm events.However, these events exhibited daily-scale variability while demonstrating a more consistent distribution at the weekly scale.Conversely, the YCM experienced a notably low rainfall frequency, primarily light rain.At the daily scale, this precipitation displayed a higher level of uniformity; however, its distribution became increasingly uneven when observed on a weekly basis.
The rainfall concentration of different cases exhibited substantial interannual variability across various years.For instance, the PCD of NCL displayed significant fluctuations, ranging from 0.03 to 0.95.Conversely, the interannual variation in PCD for DLM was relatively limited, ranging from 0.06 to 0.48.Furthermore, based on the data distribution, it is evident that, in most years, the PCD of NCE and NCM was predominantly skewed towards lower values.In comparison, the PCD of ZJL tended to demonstrate a tendency towards higher values.As for the Gini coefficient, NCE and NCM exhibit a greater concentration in the lower values.The distribution pattern of other cases demonstrated greater evenness.
To summarize, the rainfall distribution in NCE and NCM exhibits unevenness, characterized by a higher amount of precipitation.Conversely, the rainfall distribution in NCL and XXM is also uneven but at a lower level.On the other hand, ZJE, ZJL, and DLM display a uniform distribution pattern accompanied by a greater volume of rain.Lastly, SHM and YCM demonstrate a more uniform distribution with a lower level of precipitation. Figure 6 shows the PCP during the whole growth period of nine cases, and Table 4 gives the specific dates of characteristic values.The annual distribution of PCP among different cases exhibits significant variations across different years.With the exception of SHM, XXM, and YCM, which experience a deficiency in rainfall during the late growth period, the PCP for other cases is almost distributed throughout the growth period.For a specific case, the PCP still varies in different years.The PCP of ZJE and DLM is primarily concentrated in the latter half of the rice growth period.In contrast, the PCP of NCM, NCL, and ZJL is primarily observed during the early half of the rice growth period, while in The rainfall concentration of different cases exhibited substantial interannual variability across various years.For instance, the PCD of NCL displayed significant fluctuations, ranging from 0.03 to 0.95.Conversely, the interannual variation in PCD for DLM was relatively limited, ranging from 0.06 to 0.48.Furthermore, based on the data distribution, it is evident that, in most years, the PCD of NCE and NCM was predominantly skewed towards lower values.In comparison, the PCD of ZJL tended to demonstrate a tendency towards higher values.As for the Gini coefficient, NCE and NCM exhibit a greater concentration in the lower values.The distribution pattern of other cases demonstrated greater evenness.
To summarize, the rainfall distribution in NCE and NCM exhibits unevenness, characterized by a higher amount of precipitation.Conversely, the rainfall distribution in NCL and XXM is also uneven but at a lower level.On the other hand, ZJE, ZJL, and DLM display a uniform distribution pattern accompanied by a greater volume of rain.Lastly, SHM and YCM demonstrate a more uniform distribution with a lower level of precipitation.
Figure 6 shows the PCP during the whole growth period of nine cases, and Table 4 gives the specific dates of characteristic values.The annual distribution of PCP among different cases exhibits significant variations across different years.With the exception of SHM, XXM, and YCM, which experience a deficiency in rainfall during the late growth period, the PCP for other cases is almost distributed throughout the growth period.For a specific case, the PCP still varies in different years.The PCP of ZJE and DLM is primarily concentrated in the latter half of the rice growth period.In contrast, the PCP of NCM, NCL, and ZJL is primarily observed during the early half of the rice growth period, while in other cases, it shows a more even distribution.Based on the median value, the average PCP of different stations was observed in the early tillering period (NCM), the late tillering stage (NCL, ZJL, and XXM), the jointing-booting stage (SHM), the heading-flowering stage (DLM and YCM), and the milk-ripe stage (ZJE).According to the previous study [32], it is typically observed that the peak of water demand occurs during the middle and later stages of the paddy rice growth period, while the PCP of NCM is located in the early growth period.It did not align with the water demand, leading to drainage events and reducing the utilization efficiency of rainfall.
Agronomy 2024, 14, x FOR PEER REVIEW 12 of 22 stage (NCL, ZJL, and XXM), the jointing-booting stage (SHM), the heading-flowering stage (DLM and YCM), and the milk-ripe stage (ZJE).According to the previous study [32], it is typically observed that the peak of water demand occurs during the middle and later stages of the paddy rice growth period, while the PCP of NCM is located in the early growth period.It did not align with the water demand, leading to drainage events and reducing the utilization efficiency of rainfall.The distribution of the Lorentz asymmetry coefficient (S) for each case is shown in Figure 7, with an average range of 0.84 to 0.93.For rainy cases, the S remained below 1 throughout all years, except for a few instances of NCM.In cases with lower levels of rainfall, there were a few years where the value of S was greater than 1, while in the remaining years, it was less than 1.YCM and NCL demonstrated the highest frequency of years with S > 1, 9, and 10, respectively, accounting for approximately 15% and 13% of the total years.These years, the uneven rainfall distribution during the growth period was primarily attributed to the days with intense precipitation.In conjunction with the average daily rainfall during the growth period, the findings revealed a positive correlation between lower precipitation levels and an increased occurrence of S > 1 in rice cultivation.
Overall, the frequency of S > 1 is significantly lower than that of S < 1, suggesting that the uneven rainfall distribution during the rice growth period primarily stems from days with less rainfall.

Distribution Characteristics of Rainfall for the Specific Growth Period of Paddy Ric
The distribution of various rainfall levels during each growth period for th cations considered in the study is shown in Figure 8.The rainfall distribution significant variation across different locations and growth periods.The rainfall most cases demonstrates a typical unimodal pattern during various growth per playing variations in the amplitude, duration, and timing of the peak rainfall.Th the rainfall distribution for most stations occurred during the heading-flowerin However, the peak of rainfall distribution for XXM and ZJL was in the early till riod; for NCE, it was in the returning green; and for NCL, it was in the first thre periods.In addition, storms or above occurred more frequently in the periods most rainfall, such as in the heading-flowering period of NCE, the returning NCM, the returning green and the late-tillering of NCL, the heading-flowering and the early tillering of XXM.

Distribution Characteristics of Rainfall for the Specific Growth Period of Paddy Rice
The distribution of various rainfall levels during each growth period for the nine locations considered in the study is shown in Figure 8.The rainfall distribution showed significant variation across different locations and growth periods.The rainfall curve in most cases demonstrates a typical unimodal pattern during various growth periods, displaying variations in the amplitude, duration, and timing of the peak rainfall.The peak of the rainfall distribution for most stations occurred during the heading-flowering period.However, the peak of rainfall distribution for XXM and ZJL was in the early tillering period; for NCE, it was in the returning green; and for NCL, it was in the first three growth periods.In addition, storms or above occurred more frequently in the periods with the most rainfall, such as in the heading-flowering period of NCE, the returning green of NCM, the returning green and the late-tillering of NCL, the heading-flowering of SHM, and the early tillering of XXM.
However, the peak of rainfall distribution for XXM and ZJL was in the early tillering period; for NCE, it was in the returning green; and for NCL, it was in the first three growth periods.In addition, storms or above occurred more frequently in the periods with the most rainfall, such as in the heading-flowering period of NCE, the returning green of NCM, the returning green and the late-tillering of NCL, the heading-flowering of SHM, and the early tillering of XXM.The highly spatiotemporal variation in rainfall distribution significantly impacts paddy rice production.Production measures should be adjusted in time according to the characteristics of rainfall distribution, such as early and late rice in Zhanjiang station (ZJE and ZJL).For ZJE, the rainfall in the early growth periods was minimal, with an average precipitation of 2.0 mm/d in the returning green (RG) period, consisting mainly of light rain, with a low frequency of rainstorms (Figure 8).Previous results revealed that the number of tillers and rice plant diets increased with the positive impact of rainfall at the tillering stage [25].During these periods of ZJE, attention should be paid to adjusting the water depth of the paddy field and using natural rainfall as much as possible.After the tillering stage of ZJE, the frequency of heavy rain increased (Figure 8), with rainfall becoming more concentrated in the later periods (Figure 5).The heading-flowering (HF) and the milk-ripe (MR) periods are important for enriching rice grain.Heavy rain during these periods can lead to waterlogging in paddy fields located in low-lying areas with poor soil permeability.This condition hinders root respiration and fertility absorption, leading to the slow or even complete growth of rice and a significant reduction in the rice yield.During these periods of ZJE, waterlogging should be prevented to keep the soil in the field free of water to facilitate rice ripening.For ZJL, the rainfall peak occurred in the first two growth periods, mainly due to the rainstorm caused by a typhoon landing in southern China [24].Therefore, during the early growth periods of ZJL, it is important to closely monitor typhoon updates and promptly drain excess water after heavy rainfall to promote rice tillering, enhance the rate of tiller heading, and ultimately achieve a high yield.
The distribution of the Gini coefficients for nine rice cases at different growth stages is presented in Figure 9.In comparison to the Gini coefficient for the whole growth period, the range of variation in the Gini coefficient for each growth stage exhibits a greater magnitude, indicating a more pronounced variability in rainfall distribution within a growing season.All cases exhibit growth stages with G = 1 in specific years, indicating concentrated rainfall on particular days during these stages.This phenomenon is particularly evident during the returning green stage and heading-flowering stage of NCL, the returning green stage of ZJE, the yellow-ripe stage of ZJL, the returning green stage of DLM, and the returning green stage of YCM.Notably, the frequency of G = 1 during these growth stages exceeds 25%.The Gini coefficient of the same case at different growth stages exhibited negligible variations compared to the distributions of various rainfall levels (Figure 8).

Rainfall Utilization Efficiency during the Rice Growth Period
The variation characteristics of the rainfall utilization efficiency during the rice growth period were analyzed, and a box diagram illustrating the rainfall utilization efficiency for each case is presented in Figure 10.The rainfall utilization efficiency of all cases exhibits a significant inter-year fluctuation range.The lowest observed rainfall utilization efficiency is in NCE, while the highest is observed in SHM, reaching 0.92.The average rainfall utilization efficiency for all cases shows a difference of 0.49 between the highest and lowest values, with the DLM consistently displaying the most miniature fluctuation range from 0.35 to 0.70.On average, NCE, NCM, and NCL exhibited a low rainfall utilization efficiency, falling within the range of 0.15 to 0.70, followed by ZJE, ZJL, DLM, XXM, and YCM, which exhibited a moderate rainfall utilization efficiency within the range of 0.25 to 0.87.SHM demonstrated the highest rainfall utilization efficiency, with values ranging from 0.45 to 0.92.The data distribution indicates that, in most years, NCL, ZJE, and ZJL tend to exhibit closer proximity to the lower end of the spectrum regarding rainfall utilization efficiency.Conversely, SHM and YCM show a tendency towards higher values over multiple years, while other cases display a more evenly distributed pattern.

Rainfall Utilization Efficiency during the Rice Growth Period
The variation characteristics of the rainfall utilization efficiency during the rice growth period were analyzed, and a box diagram illustrating the rainfall utilization efficiency for each case is presented in Figure 10.The rainfall utilization efficiency of all cases exhibits a significant inter-year fluctuation range.The lowest observed rainfall utilization efficiency is in NCE, while the highest is observed in SHM, reaching 0.92.The average rainfall utilization efficiency for all cases shows a difference of 0.49 between the highest and lowest values, with the DLM consistently displaying the most miniature fluctuation range from 0.35 to 0.70.On average, NCE, NCM, and NCL exhibited a low rainfall utilization efficiency, falling within the range of 0.15 to 0.70, followed by ZJE, ZJL, DLM, XXM, and YCM, which exhibited a moderate rainfall utilization efficiency within the range of 0.25 to 0.87.SHM demonstrated the highest rainfall utilization efficiency, with values ranging from 0.45 to 0.92.The data distribution indicates that, in most years, NCL, ZJE, and ZJL tend to exhibit closer proximity to the lower end of the spectrum regarding rainfall utilization efficiency.Conversely, SHM and YCM show a tendency towards higher values over multiple years, while other cases display a more evenly distributed pattern.The box diagram in Figure 11 illustrates the variations in rainfall utilization e at different growth stages of rice.The rainfall utilization efficiency was occasion ative during the LT and YR periods, primarily due to compulsive drainage even tionally, in certain years, the limited rainfall experienced during these growth pe sulted in a greater displacement than precipitation within a specific growth pe rainfall utilization efficiency during the growth stages, other than the LT and YR is related to the rainfall distribution, as corroborated by the analysis presented 8.The higher and more variable the rainfall, the lower the efficiency of rainfall u during the growth stage.In addition, there are significant differences in the me mean values of certain cases, such as the RG period of NCE, the HF period of N the ET and JT periods of NCL.The uneven rainfall during these growth stages years results in extreme values that have a significant impact on the calculation values.The median of most growth periods in all cases exceeded the average.F growth periods, the median was 1, indicating that RUE = 1 in over 50% of ye suggests that rainfall could be fully utilized in most years during the growth peri ever, a few exceptional years experienced excessive rainfall, leading to water wa The box diagram in Figure 11 illustrates the variations in rainfall utilization efficiency at different growth stages of rice.The rainfall utilization efficiency was occasionally negative during the LT and YR periods, primarily due to compulsive drainage events.Additionally, in certain years, the limited rainfall experienced during these growth periods resulted in a greater displacement than precipitation within a specific growth period.The rainfall utilization efficiency during the growth stages, other than the LT and YR periods, is related to the rainfall distribution, as corroborated by the analysis presented in Figure 8.The higher and more variable the rainfall, the lower the efficiency of rainfall utilization during the growth stage.In addition, there are significant differences in the median and mean values of certain cases, such as the RG period of NCE, the HF period of NCM, and the ET and JT periods of NCL.The uneven rainfall during these growth stages between years results in extreme values that have a significant impact on the calculation of mean values.The median of most growth periods in all cases exceeded the average.For some growth periods, the median was 1, indicating that RUE = 1 in over 50% of years.This suggests that rainfall could be fully utilized in most years during the growth period; however, a few exceptional years experienced excessive rainfall, leading to water wastage.
The analysis of the correlation between rainfall and rainfall utilization efficiency revealed that, with the exception of NCL and YCM, the remaining cases demonstrated a diminishing trend in rainfall utilization efficiency as precipitation increased (Figure 12).This is attributed to the positive correlation between rainfall intensity and the likelihood of surpassing the water storage capacity in paddy fields, leading to drainage events and subsequently reducing the rainfall utilization efficiency.However, NCL and YCM experienced comparatively lower rainfall, with multi-year average daily precipitation of 2.7 mm/d and 1.0 mm/d, respectively, resulting in a reduced likelihood of drainage issues caused by excessive precipitation.As a result, there is a weak association between the rainfall utilization efficiency and the precipitation of NCL and YCM.The correlation coefficient suggests that the relationship between rainfall and rainfall utilization efficiency is not statistically significant, as the highest correlation coefficient observed was only 0.6976 in DLM.The analysis of the correlation between rainfall and rainfall utilization efficiency revealed that, with the exception of NCL and YCM, the remaining cases demonstrated a diminishing trend in rainfall utilization efficiency as precipitation increased (Figure 12).This is attributed to the positive correlation between rainfall intensity and the likelihood of surpassing the water storage capacity in paddy fields, leading to drainage events and subsequently reducing the rainfall utilization efficiency.However, NCL and YCM experienced comparatively lower rainfall, with multi-year average daily precipitation of 2.7 mm/d and 1.0 mm/d, respectively, resulting in a reduced likelihood of drainage issues caused by excessive precipitation.As a result, there is a weak association between the rainfall utilization efficiency and the precipitation of NCL and YCM.The correlation coefficient suggests that the relationship between rainfall and rainfall utilization efficiency is not statistically significant, as the highest correlation coefficient observed was only 0.6976 in DLM.The correlation between the Gini coefficient, rainfall concentration, and rainfall utilization efficiency was calculated to explore the relationship between rainfall inhomogeneity and rainfall utilization efficiency (Figures 13 and 14).A negative correlation between G and PCD with rainfall utilization efficiency was observed in all cases except for the PCD of DLM.Moreover, it was found that such correlation became stronger as the cases exhibited more uneven rainfall distributions (i.e., larger G and PCD values), highlighting the significant influence of rainfall distribution on the rainfall utilization efficiency during the growth period.The correlation coefficient suggests that the negative correlation between G and rainfall utilization efficiency is equally as significant as the negative correlation between precipitation and rainfall utilization efficiency, but it exceeds the correlation ob- The correlation between the Gini coefficient, rainfall concentration, and rainfall utilization efficiency was calculated to explore the relationship between rainfall inhomogeneity and rainfall utilization efficiency (Figures 13 and 14).A negative correlation between G and PCD with rainfall utilization efficiency was observed in all cases except for the PCD of DLM.Moreover, it was found that such correlation became stronger as the cases exhibited more uneven rainfall distributions (i.e., larger G and PCD values), highlighting the significant influence of rainfall distribution on the rainfall utilization efficiency during the growth period.The correlation coefficient suggests that the negative correlation between G and rainfall utilization efficiency is equally as significant as the negative correlation between precipitation and rainfall utilization efficiency, but it exceeds the correlation observed between PCD and rainfall utilization efficiency.Nevertheless, its significance remains limited.Unlike the relationship between rainfall and flood discharge probabilities, the rainfall-runoff model was widely applied in engineering practice to estimate a hydrograph with a given peak discharge probability [40].Rainfall is a random process with significantly uncertain frequency and uncontrollable amounts [41,42].Rainfall utilization efficiency is influenced not only by the rainfall amount (Figure 12) and rainfall inhomogeneity (Figures 13 and 14) but also by other factors, such as the matching degree of the rainfall distribution and the crop water demand [32].Previous studies on the effect of rainfall on paddy rice mainly focused on inundation and yield reduction.However, the effect of rainfall utilization still needs to be analyzed.Flooded paddy fields are capable of maintaining a water depth of 5-10 cm.In this case, paddy fields, similar to small reservoirs, can collect and retain water from natural rainfall rather than completely relying on artificial water management.Therefore, the reservoirlike function provides great opportunities for water-saving in rice production [23].This paper mainly analyzed the rainfall distribution during rice growth and its relationship with rainfall utilization efficiency in six typical stations within rice-growing areas in China, focusing on using different statistical indicators to clarify the characteristics of rice rainfall distribution and the impact of rainfall distribution on rainfall use efficiency.These results assist farmers in making irrigation decisions based on rainfall distribution characteristics [4].Further research is necessary to achieve the smart irrigation of rice active-adapting to rainfall, such as better coupling the information of the water balance models, field sensors, and weather forecasts.When adopting strategies for managing the irrigation demand in the rice areas, the spatial and temporal distribution characteristics of local rainfall should be considered first, and rice irrigation should be changed from passive-waiting irrigation to active-adapting to rainfall.Previous studies on the effect of rainfall on paddy rice mainly focused on inundation and yield reduction.However, the effect of rainfall utilization still needs to be analyzed.Flooded paddy fields are capable of maintaining a water depth of 5-10 cm.In this case, paddy fields, similar to small reservoirs, can collect and retain water from natural rainfall rather than completely relying on artificial water management.Therefore, the reservoirlike function provides great opportunities for water-saving in rice production [23].This

Conclusions
In this study, over 60 years of historical rainfall records in six rice-growing regions in China were collected, and the statistical indices were calculated during the growth period of the research stations to analyze the rainfall distribution pattern of the rice growth period.The correlation between rainfall utilization efficiency and both the rainfall amount and heterogeneity was analyzed, and the potential impact of rainfall distribution on rice irrigation was explored.
The results show that the rainfall distribution varied greatly between locations and growth periods.The rainfall distribution in nine cases can be divided into four types: uneven with more rain in NCE and NCM, uneven with less rain in NCL and XXM, even with more rain in ZJE, ZJL, and DLM, and even with less rain in SHM and YCM.During the rice growth period, the cases in southern China are more prone to waterlogging for a high probability of continuous rainfall, and the cases in northern China are more prone to drought.For different growth periods, the rainfall curve is the typical unimodal sort but with differences in the amplitude, duration, and time of the maximum rainfall.The range of variation in the Gini coefficient during specific growth periods was greater than that observed over the entire growth period, indicating a higher level of heterogeneity within a year.The rainfall utilization efficiency of all cases exhibits a significant inter-year fluctuation range.The negative correlations between rainfall utilization efficiency and both rainfall amount and distribution were observed at all stations.The greater and more uneven the rainfall experienced during the growth period, the more diminished the efficiency in utilizing precipitation.

Figure 1 .
Figure 1.Geographical distribution of study stations.The red dots indicate the locations of six study stations.

Figure 1 .
Figure 1.Geographical distribution of study stations.The red dots indicate the locations of six study stations.

3 . 1 .
Distribution Characteristics of Rainfall during the Whole Growth Period of Paddy Rice 3.1.1.Analysis of the Statistical Characteristics of Rainfall during the Whole Growth Period of Paddy Rice

Figure 3 .
Figure 3.The frequency of continuous rainfall and the average daily rainfall during continuous rainfall.

Figure 3 .
Figure 3.The frequency of continuous rainfall and the average daily rainfall during continuous rainfall.

Figure 4 .
Figure 4.The frequency of continuous dry days.

Figure 4 .
Figure 4.The frequency of continuous dry days.

Figure 5 .
Figure 5.The precipitation concentration degree (PCD) and Gini coefficient during the rice growth period of all cases.

Figure 5 .
Figure 5.The precipitation concentration degree (PCD) and Gini coefficient during the rice growth period of all cases.

Figure 6 .
Figure 6.The precipitation concentrate period (PCP) during the rice growth period of all cases.

Figure 7 .
Figure 7.The Lorenz asymmetry coefficient (S) of all cases during the rice growth period

Figure 7 .
Figure 7.The Lorenz asymmetry coefficient (S) of all cases during the rice growth period.

Figure 8 .Figure 8 .
Figure 8.The multiyear average daily rainfall distribution in each of the seven growth periods and the average of the rice season for the nine cases included in the study.RG, ET, LT, JB, HF, MR, and

Agronomy 2024 , 22 Figure 9 .
Figure 9. Gini coefficient (G) of the different growth periods of all cases.RG, ET, LT, JB, HF, MR, and YR represent the growth stages of the returning green, early tillering, late tillering, jointing-booting, heading-flowering, milk-ripe, and yellow-ripe, respectively.

Figure 9 .
Figure 9. Gini coefficient (G) of the different growth periods of all cases.RG, ET, LT, JB, HF, MR, and YR represent the growth stages of the returning green, early tillering, late tillering, jointing-booting, heading-flowering, milk-ripe, and yellow-ripe, respectively.

Figure 10 .
Figure 10.Rainfall utilization efficiency (RUE) during the rice growth period of all cases.

Figure 10 .
Figure 10.Rainfall utilization efficiency (RUE) during the rice growth period of all cases.

Figure 11 .
Figure 11.Rainfall utilization efficiency (RUE) of each growth period of all cases.RG, ET, LT, JB, HF, MR, and YR represent the growth stages of the returning green, early tillering, late tillering, jointing-booting, heading-flowering, milk-ripe, and yellow-ripe, respectively.

Figure 12 .
Figure 12.Scatter plot of rainfall and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Figure 12 .
Figure 12.Scatter plot of rainfall and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Agronomy 2024 , 22 Figure 13 .
Figure 13.Scatter plot of the Gini coefficient (G) and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Figure 14 .
Figure 14.Scatter plot of the precipitation concentration degree (PCD) and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Figure 13 .
Figure 13.Scatter plot of the Gini coefficient (G) and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Figure 13 .
Figure 13.Scatter plot of the Gini coefficient (G) and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Figure 14 .
Figure 14.Scatter plot of the precipitation concentration degree (PCD) and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Figure 14 .
Figure 14.Scatter plot of the precipitation concentration degree (PCD) and rainfall utilization efficiency (RUE) during the rice growth period.The red lines represent the fitted linear curve.y = ax + b is the fitted linear equation, and r means the correlation coefficient.

Table 1 .
Basic information about the study stations.

Table 1 .
Basic information about the study stations.

Table 2 .
Duration and current recommended thresholds of field water depth for each growth stage of rice for all cases.RG, ET, LT, JB, HF, MR, and YR represent the growth stages of the returning green, early tillering, late tillering, jointing-booting, heading-flowering, milk-ripe, and yellowripe, respectively.

Table 3 .
Rainfall statistics during the whole growth period.LR, MR, HR, ST, and HS represent light rain, moderate rain, heavy rain, storm, and heavy storm, respectively.

Table 4 .
Distribution characteristic values during the rice growth period of all cases.ET, LT, JB, HF, and MR represent the growth stages of early tillering, late tillering, jointing-booting, heading-flowering, and milk-ripe, respectively.PCP means the precipitation concentrate period.
The distribution of the Lorentz asymmetry coefficient (S) for each case is shown in Fig-CasesFigure 6.The precipitation concentrate period (PCP) during the rice growth period of all cases.

Table 4 .
Distribution characteristic values during the rice growth period of all cases.ET, LT, JB, HF, and MR represent the growth stages of early tillering, late tillering, jointing-booting, heading-flowering, and milk-ripe, respectively.PCP means the precipitation concentrate period.