CPSM: A Dynamic Simulation Model for Cucumber Productivity in Solar Greenhouse Based on the Principle of Effective Accumulated Temperature

: The Cucumber Productivity Simulation Model (CPSM) was developed to precisely predict the dynamic process of cucumber productivity in a solar greenhouse. This research conducted a variety of sowing experiments and collected data on cucumber productivity and meteorological conditions from 2013 to 2015 and 2018 to 2020. Employing the principles of least squares, the relationship between cucumber productivity indicators and effective accumulated temperature (EAT) was fitted, determining key crop parameters and constructing the CPSM. Validation of the model was conducted using independent experimental data, evaluating its simulation accuracy. The re-sults indicate that (1) CPSM can dynamically and meticulously simulate the formation process of different productivity indicators in cucumber. Normalized root mean square errors (NRMSE) ranged from 0.44% to 19.64%, and mean relative errors (MRE) ranged from 0.31% to 17.23% across different productivity indicator models. The models for organ water content, maximum root length, specific leaf area, and organ fresh weight distribution index demonstrated high simulation accuracy, while others showed relatively high accuracy. (2) Simulation accuracy varied with indicators and varieties. 19 indicators (34.55%) exhibited high simulation accuracy and 30 indicators (54.55%) showed relatively high accuracy. The JY35 variety (10.44 ± 8.49%) outperformed the JS206 variety (13.44 ± 8.50%) in terms of simulation accuracy. The JY35 variety had 39 superior productivity indicators (70.91%) while the JS206 variety had sixteen (29.09%). CPSM utilizes easily accessible temperature data as its input, allowing for precise and detailed simulation of productivity indicators for cucumber production in solar greenhouses. This research lays a theoretical foundation and provides technical support for guiding intelligent production management, efficient utilization of agricultural resources, and climate change productivity assessment in solar greenhouse cucumber production.


Introduction
Crop models, which are driven by environmental factors such as temperature, light, soil, and water, are used to quantitatively describe and predict crop productivity and quality formation using computer technology and physical-mathematical methods [1,2].These models provide a mechanism for understanding the growth and development processes of crops and have been applied in various areas, including crop productivity forecasting at specific sites and regions [3], quantifying the effects of climate change [4], and decision-making in digital design and field management [5].However, most of these studies have focused on field crops [6][7][8], and there is an urgent need to develop and apply production models for horticultural crops grown in controlled environments.
The accumulating temperature (AT) theory proposed by McMaster et al. states that the accumulated temperature required for crop development is relatively constant [9].This theory offers several advantages, including the simplicity of input data, few measurable model parameters, high accuracy, and strong extrapolation ability.Although scholars have made improvements to crop modeling algorithms, progressing from simple temperature models to more complex integrated models such as light-temperature models and light-thermal-water-fertilizer-soil models [10][11][12], the accumulating temperature model remains a significant component of crop productivity models.Moreover, the algorithms for accumulating temperature models have evolved from simple summation of daily average temperatures to incorporating lower temperature thresholds for active accumulating temperature (AAT) and effective accumulating temperature (EAT) [12,13].Currently, the effective accumulating temperature model has been applied in predicting the productivity of grain crops such as wheat [14,15], maize [16,17], and rice [18,19], horticultural crops like apples [20], cherries [21], citrus [22], walnuts [23], as well as ornamental crops such as tulips [13].These applications have demonstrated high simulation accuracy, indicating the strong extrapolation ability of the effective accumulating temperature model.
Regarding the prediction of productivity in vegetable horticulture, scholars have developed general vegetable horticulture models such as HORTISIM [24] and SIMULSERRE [25], which can quantitatively simulate the processes of developmental stages and phenology, organ generation and completion, photosynthetic production and substance accumulation, assimilate distribution, and yield-quality formation.However, due to the diverse types of vegetable varieties and significant differences in growth characteristics and cultivation management methods, the accuracy of such general models is still in need of improvement.Consequently, researchers have further developed targeted greenhouse tomato production simulation models such as TOMGRO [26] and TOMSIM [27] and have conducted studies on model uncertainty analysis [28], model coupling prediction analysis [29], and parameter sensitivity analysis [30] to enhance the accuracy and universality of the models.However, these models still face challenges such as complex and difficult-toobtain parameters, requiring a large amount of experimental data for parameter localization, which results in such models having poor extrapolation capabilities.Currently, there are few productivity models available for greenhouse cucumber, which has high production and economic benefits.Therefore, it is worth exploring the combination of dynamic simulation of different cucumber varieties' productivity using an effective growing degree day model algorithm.
Based on the conducted variety sowing date experiment and collection of cucumber productivity and meteorological data, this study successfully established the Cucumber Productivity Simulation Model (CPSM) based on the effective accumulated temperature (EAT).By fitting the relationship between productivity indicators and EAT, the model's key crop parameters were determined.Additionally, the model was validated using independent experimental data, and its simulation accuracy was evaluated.The CPSM was developed to precisely predict the dynamic process of cucumber productivity in a solar greenhouse and provide a theoretical basis and technical support for guiding smart production management, efficient utilization of agricultural resources, and productivity assessment in the face of climate change in greenhouse cucumber production.

Experimental Design
The experiment was conducted in a solar greenhouse in the agricultural technology innovation base in Wuqing District, Tianjin, China (39°25′48″ N, 116°58′12″ E; the altitude is 8 m) from 2013 to 2015 and from 2018 to 2020.The tested cultivar in the years 2013-2015 was Jinyou 35 (JY 35), while in the years 2018-2020, it was Jinsheng 206 (JS 206).JY35 variety leaves are medium sized and are mainly used for main vine melons.They have a strong ability to produce female flowers, with a fruit-setting rate of less than 10%.They have good early maturity and the length of their waist gourd is between 32 and 34 cm, with a misshapen fruit rate of less than 5%.They are suitable for winter cultivation in sunlight greenhouses and early spring cultivation.JS206 variety leaves are also medium sized.They have a stable early yield and outstanding yield in the middle and later stages.The length of their waist gourd is 34 cm.They are suitable for early spring and summer protected cultivation.In order to improve the annual productivity level of cucumber in a solar greenhouse, the planting was divided into two crops each year-the spring crop and the autumn-winter crop, totaling 7 crops.The experiment was conducted in stages, with each crop divided into 3 transplanting periods, totaling 21 transplanting periods.Early sowing was defined as that which occurred 15 days earlier than the local conventional transplanting date, middle sowing was defined as the local conventional transplanting date (early February for the spring crop and early September for the autumn-winter crop), and late sowing was defined as 15 days later than the local conventional transplanting date.Each transplanting period had 3 replicates, and a randomized complete block design was used.The planting row spacing was 0.67 m, the plant spacing was 0.42 m, and the planting density was 3.555 plants•m −2 .The solar greenhouse was constructed with masonry walls.The rear wall of the greenhouse had a height of 3.7 m and a thickness of 0.5 m.The side wall had a thickness of 0.5 m, while the ridge height was 5.3 m.The rear roof had an elevation angle of 44.0°, while the front roof had an angle of 32.0°.The span of the roof was 10.0 m, its length was 65.0 m, and it occupied a total area of 650.0 m 2 .The soil texture of the experimental site was heavy clay.The total nitrogen content in the cultivation layer (from 0 to 20 cm) was 2.76 g•kg −1 , the hydrolyzed nitrogen content was 227.8 mg•kg −1 , the available phosphorus content was 299.2 mg•kg −1 , the available potassium content was 648.0 mg•kg −1 , the organic matter content was 43.0 g•kg −1 , the pH was 7.61, and the cation exchange capacity was 73.44 cmol•kg −1 .

Crop Data
This study divided the growth and development process of cucumbers into 7 key developmental stages: transplanting date (T), stretch tendril period (ST), initial flowering period (IF), fruiting period (F), early harvest period (EH), harvest period (H), and uprooting period (U).The T period begins when the third true leaf emerges and the fourth true leaf appears, which is commonly known as three leaves and one heart.The ST period begins when the fourth true leaf unfolds and the fifth true leaf emerges, known as four leaves and one heart.During this period, the internode length increases and tendrils start to appear in the leaf axils, changing from an upright to a trailing growth habit.The plant transitions from slow growth to rapid growth, marking the end of the seedling stage.The IF period is identified by the emergence of the first female flower.In cultivation management, only flowers above the sixth leaf are retained.The F period is reached when the root squash changes from yellow-green to deep-green, indicating that the squash has settled.After the flowers wither, 2-3 cm immature fruits begin to grow.The EH period is when the root squash reaches maturity, meeting the harvest standards, at which point the fruit length is about 30 cm, and the elongation and thickening process is basically completed, resulting in a crisp and fragrant taste.The H period includes the harvest of waist squash, top squash, back squash, and lateral vine squash when they meet the harvest standards.
The U period is characterized by yellowing stems and leaves, slow maturation of the fruit, and overall plant aging, which is associated with seasonal production capacity, stubble combination and utilization efficiency of photothermal resources.The recording technique used during the developmental period relied on the morphological traits of more than 50% of the experimental population that had reached this stage of development [31].Cucumber was an infinitely growing horticultural plant that underwent multiple pruning and harvesting processes during production [12,31].This study employed a single vine pruning method to promptly prune the functional branches and leaves of pests and illnesses that had diminished photosynthetic capability and excessive nutrient consumption.Typically, in the process of production, plants maintained a range of 13 to 15 fully developed leaves.When establishing the CPSM, only the productivity status of cucumber after pruning management was taken into account.The individual plant yield was calculated based on real-time fruit harvest, without factoring in the productivity status of cucumber after pruning management.The sampling frequency for this experiment was 10 days each.Three representative plants were selected for each treatment during each sampling period.The mean values were ultimately calculated to determine various growth indicators.

Organ Dry and Fresh Weight
Organ fresh weight referred to each the weight of each organ measured on an electronic balance within 3 h after sampling, g.The fresh weight of root, tendril, flower, main stem, petiole, stem, carpopodium, and leaf was recorded as  _ ,  _ ,  _ ,  _ ,  _ ,  _ ,  _ and  _ .Organ dry weight referred to each organ divided into kraft paper bags and placed in an oven.First, it was sterilized at 105 °C for 0.5 h, then dried at 80 °C to a constant weight, and finally the weight of each organ was determined using an electronic balance, which relayed the weight in g.The dry weight of root, tendril, flower, main stem, petiole, stem, carpopodium, and leaf was recorded as  _ ,  _ ,  _ ,  _ ,  _ ,  _ ,  _ and  _ .The weight of stem was the sum of the weight of the main stem and petiole (Formula (1)).The plant overground weight was the sum of the weights of the tendril, flower, main stem, petiole, carpopodium, and leaf (Formula (2)), and the plant overground fresh weight was recorded as  _ ; the plant overground dry weight was recorded as  _ .The weight of whole plant was the sum of the weight of the root, tendril, flower, main stem, petiole, carpopodium, and leaf (Formula (3)), and the fresh weight of whole plant was recorded as  _ , the dry weight of whole plant was recorded as  _ .The yield referred to the cumulative weight of harvested fruit, which was divided into fresh weight yield ( _ ) and dry weight yield ( _ ).

𝑊 𝑠 = 𝑊 𝑚 + 𝑊 𝑝
(1) =   +   (3) where   was the dry and fresh weight of the stem in g.   was the dry and fresh weight of the main stem in g.   was the dry and fresh weight of the petiole in g.   was the dry and fresh weight of plant overground in g.   was the dry and fresh weight of the tendril in g.   was the dry and fresh weight of the flower in g.   was the dry and fresh weight of the stem in g.   was the dry and fresh weight of the leaf in g.   was the dry and fresh weight of the root in g.

Organ Dry and Fresh Weight Distribution Index
The organ dry and fresh weight distribution index referred to the ratio of the dry and fresh matter weight of each organ to the dry and fresh weight of the whole plant (Formula (4)).The fresh weight distribution index for the root, tendril, flower, main stem, petiole, stem, carpopodium, and leaf were denoted as  _ ,  _ ,  _ ,  _ ,  _ ,  _ ,  _ and  _ .The dry weight distribution index for the root, tendril, flower, main stem, petiole, stem, carpopodium, and leaf were denoted as  _ ,  _ ,  _ ,  _ ,  _ ,  _ ,  _ and  _ .The dry and fresh weight distribution index of the stem was the sum of the dry and fresh weight distribution index of the main stem and petiole (Formula ( 5)).Therefore, the sum of the dry and fresh weight distribution index of the root, tendril, flower, petiole, carpopodium, and leaf was equal to the sum of the dry and fresh weight distribution indices of the root, tendril, flower, stem, carpopodium, and leaf, which were 100% (Formula ( 6)).
=   +   (5)   +   +   +   +   +   = 100% (6) where j = 1, 2, ..., 8, respectively, represented the root, tendril, flower, main stem, petiole, stem, carpopodium, and leaf.  represented the dry and fresh weight distribution index of organ j, %.   represented the weight of fresh and dry substances in organ j in g.   represented the dry and fresh weight of the whole plant in g.   was the dry and fresh weight distribution index of organ stems, %.   was the dry and fresh weight distribution index of the main stem, %.   was the dry and fresh weight distribution index of the petiole, %.   was the dry and fresh weight distribution index of the root, %.   was the dry and fresh weight distribution index of the tendril, %.   was the dry and fresh weight distribution index of the flower, %.   was the distribution index of the dry and fresh weight of the stem, %.   was the dry and fresh weight distribution index of leaf, %.

Organ Water Content
Organ water content referred to the ratio of organ water weight to organ fresh weight (Formula ( 7)).The relative water content of the root, tendril, flower, main stem, petiole, stem, carpopodium, and leaf was denoted as   ,   ,   ,   ,   ,   ,   and   .
= ( _ −  _ )/ _ * 100% where   was the relative water content of organ j, %.  _ was the fresh weight of organ j in g.  _ was the dry weight of organ j in g.

Stem Volume
This study only considered the volume of stem and assumed that the organ stems were cylindrical.Therefore, the stem volume could be calculated using the stem length and diameter (Formula ( 8)).The volume of the main stem, petiole, and stem was denoted as   ,   , and   .
where i = 1, 2, and 3, respectively, represented the main stem, petiole, and stem.  was the volume of organ i in cm 3 .  is the diameter of organ i in mm.  was the length of organ i in cm.The root to shoot ratio was the ratio of the dry and fresh weight between the plant underground and overground (Formula ( 9)) [32], which was divided into fresh weight root to shoot ratio (  ) and dry weight root to shoot ratio (  ).The plant height was the distance between the top of root and the top of the plant [33], denoted as H, in cm.The maximum root length was the distance from the bottom of root to the bottom of the stem [33], denoted as   , in cm.Leaf rea was observed using the coordinate paper method [33], denoted as LA.The leaves were placed flat on the coordinate paper and calculated each leaf area in a numerical grid manner.If the leaf edge exceeded half a grid, it was calculated as 1.If it was less than half a grid, it was calculated as 0. The leaf area index was calculated as the product of the leaf area and planting density (Formula ( 10)) [34], denoted as LAI.The specific leaf area was the ratio of the leaf area to leaf dry weight (Formula ( 11)) [35], denoted as SLA. =   /  (9)  =  * /10 4 (10)  = / _ (11) where  was the ratio of dry and fresh root to shoot of the plant in g•g −1 . was the leaf area index in m 2 •m −2 . was the leaf area per plant in cm 2 ,  was the planting density (3.555 plant•m −2 ) and 10 4 was the unit conversion coefficient between cm 2 and m 2 . was the specific leaf area in cm 2 •g −1 .

Meteorological Data
The greenhouse microclimate was monitored using a microclimate observation instrument called CAWS2000 (Beijing Huayun Shangtong Technology Co., Ltd., Beijing, China).This instrument automatically collected meteorological data, including air temperature, humidity, CO2 concentration, and total solar radiation, at 10 min intervals.The encrypted auxiliary observation employed a small climate observation instrument called Hobo (ONSET Technology Co., Ltd., Cape Cod, MA, USA), which autonomously logged meteorological data, including the air temperature, humidity, and total solar radiation, at 5 min intervals.
This study made the assumption that there is a direct relationship between the rate of growth and development of cucumbers and temperature.The effective accumulated temperature (EAT) was determined by calculating the difference between the average temperature and the biological lower limit temperature (Formula ( 12)) [12].

𝐸𝐴𝑇 = {
∑( ave −   ) ,  ave ≥   0,  ave <   (12) where  ave was the daily average temperature in °C.  was the biological lower limit temperature, °C, which was related to the developmental stage, with the T to ST stage valued at 13 °C, ST to IF valued at 14 °C, and IF to U valued at 16 °C [12].
where X obs was the experimental observation.X sim was the experimental simulation.X ̅ obs was the average of experimental observations.N was the number of samples.This study comprehensively evaluated the accuracy of the model by calculating the average of NRMSE and MRE (A  ).If A  was less than 10%, this illustrated that the simulation accuracy was extremely high.If 10% < A  < 20%, this illustrated that the simulation accuracy was high.If 20% < A  < 30%, this illustrated that the simulation accuracy was general.If A  was greater than 30%, this illustrated that the simulation accuracy was poor.The advantage productivity indicator was defined as a productivity indicator where the mean RMSE, NRMSE, MAE, and MRE statistics proportion was less than 50%, otherwise, it was considered a disadvantage productivity indicator.

Establishing Model
The present study utilizes early sowing and late sowing data for model construction.By applying the principle of least squares, the relationship between cucumber productivity index and effective accumulated temperature (EAT) is fitted.The fitting forms mainly include mean type (Formula ( 18)), linear type (Formula ( 19)), logarithmic type (Formula (20)), and logistic type (Formula ( 21)), resulting in the CPSM's initial parameters.The model's final parameters are obtained through parameter tuning (Table 1).

Results
This study obtained a comparison validation diagram that illustrated the measured and simulated values of the CPSM model based on EAT (Figure 1).In Figure 1, the solid line represents a 1:1 line, while the dashed line represents the error range.The close proximity of the simulated and measured values to the 1:1 line, within the error range, suggest a high level of consistency between the two.As shown in Figure 1, R 2 was between 0.34 and 0.99, NRMSE was between 0.44% and 19.64%, MRE was between 0.31% and 17.23%, and D value was between 0.71 and 1.00.Therefore, the CPSM model based on EAT had high simulation accuracy.According to NRMSE, the simulation accuracy of productivity indicators was in the order of ,   , fresh weight distribution index (  ), SLA, dry weight distribution index (  ) , H, LAI,  _ , stem volume (  ),  _ , organ fresh weight (  ), , and organ dry weight (  ).According to MRE, the simulation accuracy of productivity indicators was in the order of ,   , SLA,   , LAI,   , H, ,   ,   ,  _ ,  _ , and   .In summary, the simulation accuracy of CPSM model for  ,   , SLA, and   was extremely high, while the simulation accuracy of other productivity index models was high.This study further analyzed the indicators and varieties of differences in CPSM model simulation accuracy.In terms of indicator differences, the NRMSE was between 0.12% and 37.79% and the MRE was between 0.11% and 32.67%.Based on the comprehensive analysis of NRMSE and MRE, the simulation accuracy of productivity indicators was in the order of WCp, WCs, WCm, WCc, WCr, WCl, WCt, WCf, DIf_s, DId_l, DIf_l, DId_s, DIf_m, Lr, DId_m, SLA, DId_p, DIf_p, Wf_o (A  = 9.83%), Wf_w (A  = 10.56%),LAI, Wd_o, Wd_w, Wf_s, H, Vp, Wf_m, RSd, DIf_r, DId_r, Wf_r, Wf_p, Vs, RSf, Vm, Wf_l, Yd_f, Wd_p, Yf_f, Wd_s, Wd_m, Wf_c, Wd_l, DIf_t, DIf_c, DId_c, Wd_r, Wf_f, DId_f (A  = 19.59%),DId_t (A  = 21.48%),DIf_f, Wd_c, Wf_t, Wd_f (A  = 24.35%)and Wd_t (A  = 35.23%).There were, respectively 19 indicators (accounting for 34.55%), 30 indicators (accounting for 54.55%), 5 indicators (accounting for 9.09%), and 1 indicator (accounting for 1.82%) with extremely high, high, general, and poor model simulation accuracy.In terms of variety differences, the NRMSE of the JY35 variety was between 0.12% and 56.65% and the MRE was between 0.10% and 50.19%; the NRMSE of the JS206 variety was between 0.12% and 35.86% and the MRE was between 0.11% and 36.18%.The JY35 variety (A  = 10.44 ± 8.49%) had higher simulation accuracy than the JS206 variety (A  = 13.44 ± 8.50%).The advantageous productivity index model of JY35 variety included   ,  _ ,   ,   ,   , ,   , ,   , H, and LAI, and the advantageous productivity index model of JS206 variety included  _ and SLA.In the   model, the advantageous productivity index of JY206 variety was  _ ,  _ ,  _ and  _ .In the   model, the advantageous productivity index of JY206 variety was  _ ,  _ and  _ .In   model, the advantageous productivity index of JY206 variety was  _ and  _ .In   model, the advantageous productivity index of JY206 variety was  _ ,  _ and  _ .In  model, the advantageous productivity index of JY206 variety was   .In summary, CPSM model simulation accuracy had the indicators and varieties differences (Table 2).
Table 2. Statistics of measured and simulated values of CPSM model, where * indicates that the model had an extremely high simulation effect, # indicates that the model had a high simulation effect, $ indicates that the model had a general simulation effect, !indicates that the model had a poor simulation effect, and @ indicates the disadvantageous variety of the model.This study further comprehensively analyzed the interaction between indicators and variety factors differences of CPSM model simulation accuracy.As shown in Figure 2, the statistical proportions of RMSE, NRMSE, MAE, and MRE were, respectively, from 9.48% to 90.52%, from15.34% to 84.66%, from 8.91% to 91.09%, and from 16.28% to 83.73%.The statistical proportions of JY35 and JS206 varieties were, respectively, from 16.10% to 80.65% and from 19.35% to 83.90%.Among them, the number of superior productivity indicators for JY35 variety was 39 (accounting for 70.

Discussion
The Cucumber Productivity Simulation Model (CPSM), based on effective accumulated temperature (EAT), was developed in this study to accurately simulate the dynamic process of cucumber productivity in a solar greenhouse.It was compared to general vegetable horticultural crop growth models such as HORTISIM [24], SIMULSERRE [25], TOMGRO [26] and TOMSIM [27].Although these models can quantitatively simulate the development and phenological stages of horticultural crops, organ initiation and growth, photosynthesis and biomass accumulation, assimilate allocation and yield quality formation, there are challenges related to their adoption due to the complexity and availability of the parameters involved.For instance, the process parameters of photosynthesis and respiration need to be considered.Therefore, prior to using these models, extensive experimental data collection is necessary for parameter localization.CPSM utilizes easily accessible temperature data as its input, allowing for precise and detailed simulation of productivity indicators for cucumber production in a solar greenhouse.This research lays a theoretical foundation and provides technical support to guide intelligent production management, efficient utilization of agricultural resources, and climate change productivity assessment in solar greenhouse cucumber production.The distinctive feature of this study lies in the quantitative and detailed description of the dynamic changes in cucumber productivity indicators based on EAT.These indicators primarily include   ,   ,  _ ,  _ ,   ,   , ,   , , LA, LAI, SLA,   and H. Furthermore, key crop parameters for different cucumber varieties were determined and the differences in simulation accuracy, variety, and interactive were analyzed.
The simulated values of different productivity indicators in the productivity model constructed in this study show an NRMSE ranging from 0.44% to 19.64% and an MRE ranging from 0.31% to 17.23%.These results demonstrate that the CPSM, based on EAT, has a high level of simulation accuracy.The model takes into consideration the impact of crop variety and temperature on crop productivity.The simulation accuracy of the CPSM is generally consistent with other crop productivity models based on EAT in previous studies [13,20,22,23].Furthermore, our analysis reveals that the NRMSE of simulated values compared to measured values ranging from 0.12% to 37.79% in terms of indicatorbased differences, and the MRE ranges from 0.11% to 32.67%.In terms of variety-based differences, the JY35 variety (10.44 ± 8.49%) shows higher simulation accuracy than the JS206 variety (13.44 ± 8.50%), indicating that the CPSM exhibits variability in simulation accuracy for different indicators and varieties.The CPSM has advantages such as easily obtainable input data and high extrapolation ability.However, the CPSM constructed based on EAT has some limitations in modeling principles.Firstly, it only considers temperature as a single factor in simulating the process of productivity, which may cause simulation distortion and model errors.Secondly, the statistical EAT is based on daily average temperature and does not consider the daily temperature variations.This neglects the impact of time periods where temperatures may exceed or fall below the biological lower temperature limit but still contribute to accumulated temperature values, which may affect productivity.Thirdly, different crop varieties have different threshold temperatures, and this study lacks the determination of baseline temperature indicators for the developmental stages of the tested varieties.This could lead to inaccurate estimation of accumulated temperatures and, consequently, result in errors in CPSM simulation.Lastly, there are multiple factors that influence the productivity process, including biological factors such as species and variety types, physiological controls [12,13], as well as environmental factors such as light [12,33], water [37], fertilizer [37], pests and diseases [38], natural disasters [39], and growth regulators [40].These factors could affect the effectiveness and reliability of the CPSM in practical applications of crop production.In conclusion, while the CPSM based on EAT demonstrates high simulation accuracy and certain advantages, it also has limitations in its modeling principles, which may introduce errors in simulation results.Consideration of additional factors and improvements in determining baseline temperature indicators for different variety development stages could enhance the validity and reliability of the CPSM in practical crop production applications.

Conclusions
(1) The Cucumber Productivity Simulation Model (CPSM) can dynamically and meticulously simulate the formation process of different productivity indicators in cucumber.There is a significant correlation between productivity indicators and effective accumulated temperature (EAT).The normalized root mean square error (NRMSE) of the CPSM model varied between 0.44% and 19.64%, while the mean relative error (MRE) ranged from 0.31% to 17.23%.The productivity indicator models for organ water content, maximum root length, specific leaf area, and organ fresh weight distribution index exhibited exceptional simulation accuracy.The simulation accuracy of other productivity indicator models was high.
Regarding the future research and application directions of the CPSM, several aspects can be explored.Firstly, it is important to deepen the coupling mechanism and methods between the model and "3S" technologies [41] in order to enhance the productivity simulation accuracy in extreme climate environments and different production management modes.Secondly, there is a need to investigate estimation methods for crop genetic parameters based on functional gene physiological effects and genetic regulations.This should include exploring the interaction mechanisms and quantitative methods between major trait gene effects and environmental effects [42], leading to the development of an integrated simulation model covering "gene effects-genetic parameters-phenotypic characteristics-productivity formation".Thirdly, integrating relevant algorithms from artificial intelligence decision-making and crop phenotypic monitoring technologies [43], it is essential to construct an intelligent agricultural production management decision support system.This system can provide intelligent tools like optimized crop canopy design.Lastly, developing a productivity model support system that incorporates multiple algorithms is necessary to reduce the uncertainty caused by model parameters and structure on simulation results [12].

Figure 1 .
Figure 1.Comparison between measured and simulated values of CPSM model, including fresh weight (a), fresh yield per plant (b), dry weight (c), dry yield per plant (d), fresh weight distribution index (e), dry weight distribution index (f), water content (g), stem volume (h), root to shoot ratio (i), maximum root length (j), plant height (k), leaf area index (l) and specific leaf area (m).

Table 1 .
CPSM model parameters, where a, b, and c are model parameters that are related to the productivity characteristics of the variety, and R 2 represents the coefficient of determination, which can reflect the significance of the relationship between productivity indicators and effective accumulated temperature.