Simulating cucumber plant heights using optimized growth functions driven by water and accumulated temperature in a solar greenhouse

Plant height is the main agronomic character used to measure the vertical growth and developmental abilities of plant. Cucumber is a popular greenhouse vegetable in Northwest China, and its production is principally limited by water and temperature. However, few studies have simulated water- and temperature-driven cucumber heights in solar greenhouses; in this paper, we explored these optimum growth functions to simulate cucumber height dynamics under different irrigation upper limits by conducting experiments between 2017 and 2019 in Wuzhong, Ningxia, China. First, we calculated the accumulated temperature during the growth period by measuring growth-stage base temperatures.We then calculated water impact factor parameters based on the per-day plant height growth rate. We constructed functions (DWSTR(i)) of the factors affecting cucumber plant heights at different growth stages, then used these functions as multipliers; the accumulated temperature was taken as an independent variable in four functions (i.e., the Bertalanffy, Gompertz, Logistic and Mischerlich functions) to describe the water- and temperature-driven cucumber plant height growth dynamics. Consequently, an optimal function was selected among the four simulated functions defined as Mo-B, Mo-G, Mo-L and Mo-M. Impact factor functions were established with 2018 experimental data as y = 0.1753e0.0177x, y = 0.6332e0.0046x and y = 0.7241e0.0031x in the stretch-tendril period, initial flowering period, and early harvest period, respectively; the corresponding correlation coefficients were 0.9604, 0.9937 and 0.9191. These data were then used to assess the function-associated parameters. The models were calibrated with the 2017 and 2019 experimental data, and the Mo-L model obtained the best IA (0.993 and 0.998 in 2017 and 2019) and NRMSE (10.27 and 4.97 in 2017 and 2019) values among the four models. Further, the mean IA (0.995) and NRMSE (9.20) values of the Mo-L model were significantly higher than those of the Mo-B and Mo-M models between 2017 and 2019. The Mo-L model could be optimal for simulating the physiological cucumber height growth insolar greenhouses, and the model calibration showed good agreement between the simulated and measured results.