Growth model for vertical towers in greenhouse based on use efficiency of radiation and plant position

Shade projection of crops in vertical towers significantly affects yield productivity and quality. Inside a greenhouse, plants at lower positions receive less radiation than those at higher levels. This uneven distribution of light results in higher and faster growth in plants located at higher levels than at lower ones. Stepwise harvesting can offer a simple and practical solution to improve the viability of vertical systems under low-tech greenhouses in urban and peri-urban areas. However, determining the optimal time for harvest at each crop level requires using predictive crop modelling tools. This study aimed to develop a growth model for vertical hydroponic crops under greenhouse conditions, which estimates the variation in dry biomass accumulation plant positions along the tower. The model is based on Heuvelink's radiation-driven growth equation. Dry matter production is a function of radiation use efficiency (RUE), leaf area index (LAI), extinction coefficient (k), and incident photosynthetically active radiation (PAR). Each vertical tower was a closed system with a 20L lower tank and a 1.6 m high vertical pipe, with 45 holes for plants at 25 plants·m² of density. For model validation, Swiss chard (Beta vulgaris L. 'Ford Hook Giant') was grown in autumn 2024 with Steiner's nutrient solution in vertical towers inside a tunnel greenhouse. Radiation was measured daily at three levels of the canopy, upper (U), middle (M), and lower (L) using a lux meter. The extinction coefficients for each position were estimated using nonlinear GRG optimization, from the Excel® Solver tool. The results show an extinction coefficient between 0.06 and 0.09, which decreased as plant position increased in height. The RUE ranged from 1.12 to 1.79 g·MJ^-1, with the U level being the most efficient. Since R² ranged from 0.88 to 0.95, this indicates that the proposed model shows a good predictive capacity throughout the canopy and could be applicable for scheduling staggered harvests in vertical systems within a greenhouse. Defining the commercial weights of desirable plants, the optimal time of harvest at each level of the tower can be easily predicted.