Modeling the relationship between water uptake by cucumber and NaCl accumulation in a closed hydroponic system

In a completely closed hydroponic system, Na and Cl commonly accumulate in the root zone, at rates depending on the concentration of NaCl in the irrigation water (rate of Na and Cl inlet) and the Na to water and Cl to water ratios at which they are taken up by the plants (rates of Na and Cl outlet). However, while the concentration of NaCl in the irrigation water is commonly a constant, the Na to water and Cl to water uptake ratios are variables depending on the concentrations of Na and Cl in the root zone and, hence, on the rates of their accumulation. To quantify this feed-back relationship, a differential equation was established, relating the rate of Na (or Cl) accumulation to the rate of water uptake. This equation was solved according to the classical Runge-Kutta numerical method using data originating from a cucumber experiment, which was conducted in a fully automated, closed-loop hydroponic installation. Four different NaCl concentrations in the irrigation water, 0.8, 5, 10 and 15 mm, were applied as experimental treatments. The theoretically calculated curves followed a convex pattern, with an initially rapid increase of the Na and Cl concentrations in the root zone and a gradual leveling out as the cumulative water consumption was rising. This was ascribed to the gradual approaching of the Na to water and Cl to water outlet ratios via plant uptake, which were increasing as NaCl was accumulating in the root zone, to the constant NaCl to water inlet ratio (NaCl concentration in irrigation water). The model could predict the measured Na and Cl concentrations in the drainage water more accurately at 10 and 15 mm NaCl than at 0.8 and 5 mm NaCl in the irrigation water. Possible explanations for these differences are discussed. Plant growth and water uptake were restricted as salinity was increasing, following a reverse pattern to that of Na and Cl accumulation in the root zone. The leaf K, Mg and P concentrations were markedly restricted by the increasing salinity, while that of Ca was less severely affected.