Theoretical substantiation of substrate moisture dynamics, hysteresis irrigation and lighting regimes in a multi-tier mini-greenhouse

Abstract

Purpose. The purpose of the article is to develop a mathematical model of substrate moisture dynamics in a multi-tier mini-greenhouse, to analytically justify the parameters of a hysteresis irrigation algorithm, and to quantitatively justify the lighting regime through PPFD and DLI indicators. Methods. The total substrate volume was adopted as the control volume, and a differential water balance equation was derived from the difference between inflow and outflow; transpiration was linked to the lighting signal and vapor pressure deficit; calculations were performed in Python in accordance with the FAO-56 methodology and ANSI/ASABE S640/S642 requirements. Results. Under the adopted parameters, the irrigation cycle period is ≈35.8 h and the dose is ≈4.3 L, with automatic control saving 33% of water compared with timer-based operation. The lighting regime specified in the patent yields DLI = 7.7 mol/(m²·day), below the required 12...17; achieving DLI = 14 requires Py = 56...73 W, while increasing airflow from 33 to 82 m³/h reduces inter-tier VPD non-uniformity from 18% to 7%. Conclusions. A quantitative conflict between lighting and microclimate requirements was identified and a solution combining an extended photoperiod with improved air distribution was substantiated; the derived analytical expressions can be applied in the design of small multi-tier devices.