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Nutrient composition, plant chemistry and stock design

Elemental mass balance, real hydroponic N–P–K dose responses, cultivar-by-solution effects on lettuce chemistry and the measurements required to estimate plant nutrient state.

MarkdownJSONRevised 2026-07-29
In brief

How complete elemental recipes, coupled ions, stock compatibility and tissue measurements replace simplistic nutrient-to-taste rules.

Explanation

Adding one fertilizer changes every ion carried by that salt. A KNO₃ dose changes both potassium and nitrate; it is not a pure “sweetness” command.

Mass balance

NUT-1
ni,new=ni,old+∑jνijCjVj−Ui−Lin_{i,\mathrm{new}}=n_{i,\mathrm{old}}+\sum_j\nu_{ij}C_jV_j-U_i-L_i
Ion i changes through stock additions j, stoichiometric coefficients ν, plant uptake U and losses L.

ExplanationThe new amount of one ion equals the previous amount plus stock additions, minus plant uptake and losses.

NUT-2
Ci,new=ni,newVreservoir,newC_{i,\mathrm{new}}=\frac{n_{i,\mathrm{new}}}{V_{\mathrm{reservoir,new}}}
Concentration follows ion amount and the final mixed reservoir volume.

ExplanationFinal concentration is the final ion amount divided by the final mixed solution volume.

Separate N, P and K limitation

The USDA Bibb lettuce dataset changes one target nutrient concentration at a time and reports fresh mass through day 32 after transplant. The day-32 response is not monotonic for every nutrient. Nitrogen rises from 1.16 g at 5 mg·L⁻¹ to 250.73 g at 132 mg·L⁻¹, then falls to 74.11 g at 264 mg·L⁻¹. Phosphorus rises from 9.14 g at 1 mg·L⁻¹ to 250.73 g at 31 mg·L⁻¹. The potassium series contains a wide interval at 42 mg·L⁻¹, so that treatment mean should not be read without its uncertainty.

Figure 16

Fresh mass under separate nitrogen, phosphorus and potassium limitation

Each panel preserves the nutrient's own concentration scale. Points show the authors’ day-32 treatment mean and published 95% interval.

0100200300 Fresh mass at day 32 (g) Nitrogen 5 264 target concentration (mg·L⁻¹) Phosphorus 1 31 target concentration (mg·L⁻¹) Potassium 2 210 target concentration (mg·L⁻¹)
Values
SeriesValueNote
Nitrogen · 5 mg·L⁻¹1.16 ± 0.37 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Nitrogen · 11 mg·L⁻¹32.57 ± 9.22 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Nitrogen · 26 mg·L⁻¹56.62 ± 21.95 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Nitrogen · 33 mg·L⁻¹47.73 ± 7.35 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Nitrogen · 66 mg·L⁻¹100.42 ± 24.14 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Nitrogen · 132 mg·L⁻¹250.73 ± 25.41 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Nitrogen · 264 mg·L⁻¹74.11 ± 10.90 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Phosphorus · 1 mg·L⁻¹9.14 ± 4.57 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Phosphorus · 2 mg·L⁻¹59.23 ± 14.68 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Phosphorus · 5 mg·L⁻¹133.56 ± 18.20 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Phosphorus · 12 mg·L⁻¹176.31 ± 21.98 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Phosphorus · 31 mg·L⁻¹250.73 ± 25.41 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Potassium · 2 mg·L⁻¹22.76 ± 4.89 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Potassium · 13 mg·L⁻¹61.17 ± 6.97 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Potassium · 21 mg·L⁻¹84.91 ± 16.06 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Potassium · 42 mg·L⁻¹128.31 ± 174.63 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Potassium · 105 mg·L⁻¹89.75 ± 30.96 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.
Potassium · 210 mg·L⁻¹128.71 ± 15.45 gTreatment mean fresh mass at day 32 after transplant; ± is the published 95% confidence-interval half-width.

Note. Values reproduced from Sharkey, Chen, and Altman (2025), author-formatted NPK.CrossT.All.xlsx, day 32 after transplant. No curve was fitted and no point was interpolated.

The graph preserves each nutrient's actual concentration scale and the authors' 95% confidence intervals. It demonstrates two practical points: nutrient response can be curved rather than linear, and equal EC values do not imply equal elemental availability.

Nutrient solution and tissue chemistry

El-Nakhel and colleagues tested green and red lettuce with calcium-, magnesium- or potassium-dominant macrocation ratios. The complete design contains three biological replicates in each of six cultivar-by-solution cells. The published measurements include total nitrogen, sulphate, six organic acids and total chlorophyll.

Figure 17

Nutrient-solution composition altered measured lettuce chemistry

Rows combine cultivar and dominant macrocation. Colour is normalised only within each chemical measurement; select a cell for the original unit.

NSulphateMalateChlorophyll Green · Calcium 42.73 1.06 41.35 130 Green · Magnesium 38.76 1.07 34.17 146 Green · Potassium 45.57 1.58 50.18 147 Red · Calcium 42.70 1.81 35.76 276 Red · Magnesium 45.62 1.59 42.81 289 Red · Potassium 46.45 2.26 55.92 233 Colour is scaled separately within each column. Select a cell for its unit, SD and SE.
Values
SeriesValueNote
Green lettuce · Calcium solution · N42.729 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.506 g·kg⁻¹ DW; SE 0.292 g·kg⁻¹ DW.
Green lettuce · Calcium solution · Sulphate1.061 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.014 g·kg⁻¹ DW; SE 0.008 g·kg⁻¹ DW.
Green lettuce · Calcium solution · Malate41.351 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 2.188 g·kg⁻¹ DW; SE 1.263 g·kg⁻¹ DW.
Green lettuce · Calcium solution · Chlorophyll130.271 mg·kg⁻¹ FWMean of n = 3 biological replicates; SD 13.968 mg·kg⁻¹ FW; SE 8.065 mg·kg⁻¹ FW.
Green lettuce · Magnesium solution · N38.760 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.421 g·kg⁻¹ DW; SE 0.243 g·kg⁻¹ DW.
Green lettuce · Magnesium solution · Sulphate1.073 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.113 g·kg⁻¹ DW; SE 0.066 g·kg⁻¹ DW.
Green lettuce · Magnesium solution · Malate34.167 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.832 g·kg⁻¹ DW; SE 0.481 g·kg⁻¹ DW.
Green lettuce · Magnesium solution · Chlorophyll145.958 mg·kg⁻¹ FWMean of n = 3 biological replicates; SD 4.858 mg·kg⁻¹ FW; SE 2.805 mg·kg⁻¹ FW.
Green lettuce · Potassium solution · N45.565 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.155 g·kg⁻¹ DW; SE 0.089 g·kg⁻¹ DW.
Green lettuce · Potassium solution · Sulphate1.578 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.125 g·kg⁻¹ DW; SE 0.072 g·kg⁻¹ DW.
Green lettuce · Potassium solution · Malate50.179 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 1.064 g·kg⁻¹ DW; SE 0.614 g·kg⁻¹ DW.
Green lettuce · Potassium solution · Chlorophyll146.668 mg·kg⁻¹ FWMean of n = 3 biological replicates; SD 8.080 mg·kg⁻¹ FW; SE 4.665 mg·kg⁻¹ FW.
Red lettuce · Calcium solution · N42.696 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.613 g·kg⁻¹ DW; SE 0.354 g·kg⁻¹ DW.
Red lettuce · Calcium solution · Sulphate1.813 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.011 g·kg⁻¹ DW; SE 0.006 g·kg⁻¹ DW.
Red lettuce · Calcium solution · Malate35.763 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 1.308 g·kg⁻¹ DW; SE 0.755 g·kg⁻¹ DW.
Red lettuce · Calcium solution · Chlorophyll275.600 mg·kg⁻¹ FWMean of n = 3 biological replicates; SD 6.060 mg·kg⁻¹ FW; SE 3.499 mg·kg⁻¹ FW.
Red lettuce · Magnesium solution · N45.620 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.498 g·kg⁻¹ DW; SE 0.287 g·kg⁻¹ DW.
Red lettuce · Magnesium solution · Sulphate1.589 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.055 g·kg⁻¹ DW; SE 0.032 g·kg⁻¹ DW.
Red lettuce · Magnesium solution · Malate42.815 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 2.346 g·kg⁻¹ DW; SE 1.354 g·kg⁻¹ DW.
Red lettuce · Magnesium solution · Chlorophyll288.813 mg·kg⁻¹ FWMean of n = 3 biological replicates; SD 1.735 mg·kg⁻¹ FW; SE 1.002 mg·kg⁻¹ FW.
Red lettuce · Potassium solution · N46.449 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.472 g·kg⁻¹ DW; SE 0.273 g·kg⁻¹ DW.
Red lettuce · Potassium solution · Sulphate2.258 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 0.178 g·kg⁻¹ DW; SE 0.103 g·kg⁻¹ DW.
Red lettuce · Potassium solution · Malate55.918 g·kg⁻¹ DWMean of n = 3 biological replicates; SD 3.158 g·kg⁻¹ DW; SE 1.823 g·kg⁻¹ DW.
Red lettuce · Potassium solution · Chlorophyll233.377 mg·kg⁻¹ FWMean of n = 3 biological replicates; SD 8.128 mg·kg⁻¹ FW; SE 4.692 mg·kg⁻¹ FW.

Note. Means calculated from the complete 2 × 3 × 3 design published by El-Nakhel et al. (2020). The downloadable table includes each replicate, standard deviation, standard error and two-way ANOVA output.

A balanced two-way fixed-effects ANOVA was recomputed from all 18 published observations. For malate, the nutrient-solution effect was F(2, 12) = 106.39 with Holm-adjusted p = 3.94 × 10⁻⁷, and the cultivar-by-solution interaction was F(2, 12) = 21.40 with adjusted p = 9.93 × 10⁻⁴. For total chlorophyll, the interaction was F(2, 12) = 25.38 with adjusted p = 4.89 × 10⁻⁴. The interaction means the solution effect changes with cultivar; one universal nutrient-to-chemistry coefficient would discard that structure.

Estimating plant nutrient state

Visible colour is useful but not chemically specific. Nitrogen limitation, water stress, senescence, exposure error and disease can all alter RGB appearance. FlavoRotor therefore joins four records at the same plant and time: the delivered elemental formulation, pH and EC history, the repeated image, and a reference measurement such as tissue mineral composition or chlorophyll. A supervised model predicts a declared laboratory endpoint, not an undefined label such as “nutrient health”.

NUT-STATE
x^t=f ⁣(It−k:t,ut−k:t,st−k:t,g,d)\hat{\mathbf{x}}_t=f\!\left(\mathbf{I}_{t-k:t},\mathbf{u}_{t-k:t},\mathbf{s}_{t-k:t},g,d\right)
Estimated plant state uses an image sequence I, delivered nutrient and light inputs u, measured environmental state s, cultivar g and day after transplant d over a defined history window.

ExplanationEstimated plant state combines a recent image sequence, delivered treatments, measured environmental conditions, cultivar and day after transplant.

Evaluation keeps all observations from one plant or cultivation cycle in the same fold. The report includes MAE for continuous chemistry, balanced accuracy for declared deficiency classes, calibration of uncertainty and performance for each cultivar and growth stage.

Why EC is insufficient

EC is an indirect bulk response to all dissolved ions. Closed systems can maintain a target EC while individual nutrients become deficient or excessive.

Four-channel implication

The four FlavoRotor channels must be assigned to chemically defined and compatible fluids. Channel labels describe the liquid, not an expected flavour. The formulation must account for coupled ions, precipitation risk, source-water composition and the limited degrees of freedom available with four reservoirs.

Validation

Recipe trials report the full elemental formulation, source water, pH, EC, solution replacement, delivered stock volumes and tissue composition. Sensory conclusions are made only after chemical and blinded sensory measurements.

Article bibliography

Sources used on this page