The soilless culture system simulation roughly consisted of irrigation control based on the integrated solar radiation, changes in the water content of the substrate by irrigation and transpiration, and nutrient uptake (

Figure 1a). The dynamic changes in incoming solar radiation were modeled by the total cloud cover model based on solar elevation [

28,

29]:

where

${K}^{+}$ is the reduced solar radiation by the total cloud cover;

${K}_{0}^{+}$ is the incoming solar radiation at ground level under clear skies, which is determined by solar elevation over seasonal time changes;

${b}_{1}$ and

${b}_{2}$ are the empirical coefficients; and

$N$ is the total cloud cover.

$N$ is a value between 0 and 1; closer to 0 corresponds to a clear day, and closer to 1 corresponds to a cloudy day. In simulation analysis, dynamic weather changes were simulated by moving

$N$ between 0 to 1 in a random walk process. The irrigation of the soilless culture system was controlled based on the integrated value of solar radiation

${K}^{+}$ for simulating the general greenhouse irrigation automation method [

9]. The transport of nutrients and water in a soilless culture system was simulated by the soilless culture system model of Ahn and Son [

30] based on the nutrient transport model in a substrate condition [

31,

32]. For the absorption of nutrients, according to the concentration of nutrients in the substrate, the Michaelis–Menten equation was used. A nutrient absorption rate model incorporating the root surface area reflecting the absorption capacity of plants was used:

where

${P}_{RSA}$ is the root surface area (m

^{2}),

${J}_{max}^{I}$ (mmol m

^{−2} min

^{−1}) is the maximum absorption rate of nutrient I,

${K}_{m}^{I}$ (mM) is the Michaelis–Menten constant, and

${C}_{min}^{I}$ (mM) is the minimal concentration at which

${J}^{I}$ = 0. The types of plant nutrients included in the simulation were K, Ca, Mg, NO

_{3}, and P. In this simulation, a stochastic coefficient was applied to the nutrient absorption capacity of plants to detect changes in the rate of nutrient absorption under various conditions:

where

${S}_{cof}$ acts as a nutrient absorption factor and corresponds to a random walk process that increases or stops with a probability of

λ from the initial value of an absorption factor and decreases with a probability of 1 −

λ. For the transpiration model, the empirical version of the Penman–Monteith equation was used [

33,

34]:

where

${Q}_{trs}$ is the transpiration rate (L min

^{−1}),

$a$ and

$b$ are empirical coefficients,

$k$ is the extinction coefficient in the plant canopy,

${P}_{LAI}$ is the leaf area index (LAI), and

${P}_{VPD}$ is the vapor pressure deficit (VPD). For the LAI used in the simulation, a fixed measured value was used. The leaf area of the tomato (

Solanum lycopersicum) used in the LAI calculation was estimated by measuring the leaf area of the tomato in the cultivation experiment (measured at 2 January 2020). A non-destructive method was used for the leaf area estimation by measuring leaf width and length [

35]. VPD was simulated to move in a random walk process between 0.5 and 2.0 kPa during simulation analysis to apply the stochastic fluctuation of transpiration in the simulation analysis. For simulation of the EC-based nutrient solution supply method, the EC of the nutrient solution was calculated by converting the molar concentration of the nutrients into an equivalent concentration, and then the total equivalent concentration was converted to EC by the empirical conversion equation [

36]. Calculation of the index related to nutrient absorption was conducted by summation of the difference between the nutrient inflow into the substrate and the nutrient outflow from the substrate:

where

$E{C}_{i}^{Sup}$ and

${V}_{i}^{Sup}$ are daily EC and volume of irrigated nutrient solution, respectively, and

$E{C}_{i}^{Drg}$ and

${V}_{i}^{Drg}$ are daily EC and volume of drained nutrient solution, respectively. Through simulation, various changes were made to the rate of nutrient absorption and drainage ratio of the soilless culture system, and the effect on the correlation between Day Nutrient Absorption Index (DNAI) and nutrient absorption was analyzed. Additionally, we compared the correlation between nutrient absorption and major indicators in nutrient and water management, such as irrigation amount, drainage ratio, leaching fraction, drainage EC, and transpiration. These indicators are available for direct data collection in the soilless culture system online and affect the growth of plants.