Simulation and validation of extinction coefficient at different positions of cucumber and celery in solar greenhouse

Extinction coefficient (k) in a photosynthetic action is an important parameter in a growth model of crops. If the extinction coefficients of a crop at the different positions are accurately evaluated, the photosynthetic rate of crop canopy can be accurately simulated, thereby to improve the simulation accuracy of crop model. The purpose of this study is to simulate the extinction coefficient of cucumber (Cucumis sativus L.) and celery (Apium graveolens L.) in a solar greenhouse. A 2-year greenhouse experiment was carried out from 2018 to 2020 in the Agricultural Science and Technology Innovation Base, in Wuqing, Tianjin, China (116°58′ E, 39°26′ N, altitude 8 m). There were two or three transplanting dates for each stubble, particularly on the early transplanting date (EP, about 15 to 20 days earlier than the local conventional planting date), the medium transplanting date (MP local conventional transplanting date), where the spring stubble was transplanted in late March, while, the autumn and winter crops were transplanted in middle October, and the late planting (LP, about 15 to 20 days later than the local conventional transplanting date). The planting density, varieties and management methods were consistent with the similar vegetable cultivation methods in North China, providing that the yield and quality can reach the best level. Three replicates were set for each transplanting date, while the random block group design was adopted. The cucumber variety was Jinsheng 206, and celery variety was Juventus. The cucumber was divided into 7 development stages, namely, the transplanting date (T), stretch tendril period (ST), initial flowering period (IF), fruiting period (F), the early harvest period (EH), harvest period (H), and uprooting period (U). The celery was divided into 5 development stages, namely, the transplanting date (T), outer leaf growth period (OLG), cardiac hypertrophy period (CH), early wither period (EW), and late wither period (LW). The radiation data of cucumber and celery was collected at various height positions (Bottom of Crop (BC), 1/3 Height of Crop (1/3HC) and 2/3 Height of Crop (2/3HC)), where the crop height of celery was equal to the plant height, but that of cucumber was not exactly equal. A simulation model of extinction coefficient was established for a greenhouse crops, according to the value of extinction coefficient at noon (12 o 'clock), using the experimental observation data of 11 transplanting dates. The model parameters were used to verify the rationality and accuracy of modules, representing by the statistical indicators. The results showed: 1) In the change of k value at noon (12 o 'clock), the cucumber presented a trend of decline first and then rise during the autumn and winter crop (AW) stubble, while, the spring crop (SC) stubble presented an opposite trend, where the AW stubble was higher than that of SC. The k value was greater as the increase in the height of position. In the growing season of celery, the k value was the process of the first increase and then decrease. As the increase in the height of position, the k value first decreased and then increased. 2) In the daily change of k value, the cucumber and celery showed a change trend of the first rising and then falling. 3) In the change of k value in each development stage, the k value of cucumber increased gradually with the rise of height in the same stage of development. The celery showed a trend of the first decline and then rise. At the same position level, the mean value of cucumber k at each position showed a trend of decreasing first and then increasing, while, that of celery at each stage decreased gradually. 4) The relationship between k value at time and at noon, the height parameters, and the number of time decreased linearly, indicating that the model parameters were related to the crop types and height position. The Root Mean Square Error (RMSE) of simulated and measured k value in the cucumber and the celery were 0.45 and 0.06, and the Normalized Root Mean Square Error (NRMSE) was 18.34% and 13.35%, respectively. The RMSE of simulated and measured k value at different heights (BC, 1/3HC, and 2/3HC) were 0.47, 0.36 and 0.33, and the NRMSE were 17.91%, 19.69% and 23.85%, respectively, indicating a high accuracy of the model. The findings can provide a theoretical foundation and a scientific application for the simulation accuracy and rationality of vegetable growth and development model.