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From greenhouse climate to individual leaves: an organ-resolved model of lettuce growth

Md Hasibur Rahman, Faraz Ahmed, Hafiz Muhammad Bilal, Daniel Wells, Dylan Tobin, Tanzeel U. Rehman

arXiv:2609.27118v1cs.CVcs.GR

TL;DR

Greenhouse climate management needs predictions of crop response before conditions change, yet observed growth alone does not show how the same crop would develop under alternative conditions. This paper couples leaf physiology, carbon allocation, and an evolving three-dimensional lettuce canopy; growth and structural traits were reproduced with relative errors of 9.2–13.1%.

  • Problem

    Observed plant measurements describe past development but do not directly predict how the same crop would grow under alternative future environmental conditions.

    Source: §1 · p. 1

  • Method

    A unified framework couples local leaf conditions and physiology to whole-plant carbon balance and an evolving three-dimensional canopy with ray-traced radiation feedback.

    Source: §1 · p. 2

  • Results

    Relative errors were 9.2–13.1% across dry weight, leaf number, canopy diameter, and largest-leaf area, while simulations showed climate and spatial effects on growth.

    Source: §4 · p. 20

  • Takeaways & Limitations

    Environmental and spatial simulations showed how climate and neighboring plants affected carbon assimilation, leaf exposure, and biomass accumulation.

    Source: §4 · p. 20

    The framework used one lettuce cultivar, and its parameters were not updated from observations of the corresponding physical plant during the season.

    Source: §4 · p. 20

Abstract

from arXiv · show

Greenhouse climate management aims to improve crop production while limiting energy use. This requires knowing how a crop will respond before conditions are changed. A crop digital twin can support this decision only if it represents how plant physiology and structure develop together. A unified framework was developed to simulate lettuce growth from the physiology of individual leaves. Each leaf received the conditions at its position in the canopy and contributed carbon through photosynthesis. Part of this carbon was used for maintenance and the remainder supported growth, distributed among leaves by their age, size and local environment. The predicted leaf mass, area and age generated an evolving three-dimensional plant in NVIDIA Isaac Sim. Ray tracing calculated the radiation intercepted by each leaf and returned it to photosynthesis, so structure and growth influenced each other over time. Against greenhouse measurements, the relative root mean square error was 9.5% for total dry weight and 9.2%, 12.7% and 13.1% for leaf number, canopy diameter and largest-leaf area, respectively. A 30% decrease in incident radiation reduced final dry weight by 10.4%, while the same increase raised it by 6.9%, and adding 200 ppm carbon dioxide raised it by 46.1%. Within a simulated 40-plant block, interior plants accumulated 8.6% less dry weight than border plants with identical initial states, and the leaf-specific tipburn index rose in the enclosed leaves over the period in which tipburn appeared on the greenhouse plants. Resolving individual leaves therefore explains how local exposure changes plant growth within the greenhouse. The framework provides the forward plant model needed for a bidirectional digital twin, where observations of the physical plant can update predictions and support greenhouse climate decisions.

1. Introduction

Greenhouse management needs predictions of crop development under alternative conditions, but observations alone describe the trajectory already taken. The paper addresses this gap with a leaf-resolved framework that links local climate, physiology, carbon allocation, and three-dimensional structure.

1. Introduction

  • Observed growth trends do not predict how the same crop would develop under alternative future environmental conditions.The motivation is to compare climate scenarios from the current crop state before applying changes to the physical crop.Source: §1 · p. 1
  • Existing lettuce models separate whole-plant carbon balance from individual-leaf development and ray-traced radiation feedback.The authors identify the missing integration as a model that returns per-leaf radiation to physiology within the same simulation.Source: §1 · p. 2
  • The framework links leaf-level microclimate and physiology to whole-plant carbon balance and an evolving three-dimensional canopy.Leaf carbon remaining after maintenance is allocated by age, size, and local conditions; canopy changes then affect subsequent radiation and growth.Source: §1 · p. 2
  • The study evaluates plant growth and structure against measurements and examines climate, spatial, neighbor, allocation, and tipburn responses.The stated evaluation traits are total dry weight, leaf number, largest-leaf area, and canopy diameter.Source: §1 · pp. 2–3

2. Materials and methods

The methods couple leaf physiology and whole-plant carbon balance to an evolving canopy, so local exposure affects growth and growth changes subsequent light interception.

2. Materials and methods

  • The Isaac Sim framework returns each leaf’s local radiation and air conditions to physiology, while canopy feedback alters later radiation and growth.The current canopy is ray-traced, and leaf states update the three-dimensional plant for the following interval.Source: §2 · p. 3

2.1.1. Whole-plant growth formulation

  • Leaf carbon enters the whole-plant balance, where maintenance is deducted before net dry-matter growth is divided between shoots and roots.The shoot fraction supplies leaf growth, while leaf assimilation contributes to the plant-level carbon balance.Source: §2.1.1 · p. 3

2.1.2. Leaf appearance and canopy development

  • New leaves are initiated at a temperature- and carbohydrate-dependent rate, then enter growth allocation as their developmental age and activation weight increase.Senescence and organ loss are not included in the simulations.Source: §2.1.2 · p. 3

2.1.3. Individual-leaf allocation and growth

  • Leaf growth shares depend on developmental stage, size, and local carbon supply, with a changing reference area guiding allocation rather than fixing final leaf size.Normalized weights divide the available leaf-growth flux among leaves, and specific leaf area converts dry-matter gain into blade area.Source: §2.1.3 · pp. 3, 5, Figure 1 · p. 4

2.2. Development of the functional-structural plant model

Predicted leaf area and age are converted into a three-dimensional lettuce rosette whose geometry supports radiation-interception calculations.

2.2. Development of the functional-structural plant model

  • Predicted leaf area and age generate a rosette by setting blade dimensions, shaping surfaces, arranging leaves, and scaling canopy diameter.Figure 2 shows the construction sequence and top and side views at 7, 14, 21, and 28 days after transplanting.Source: §2.2 · p. 5, Figure 2 · p. 6
  • Blade width-to-length ratio changes with leaf age, while insertion angle and midrib bend shift leaves from upright young blades to outward-opening mature blades.Young leaves curve inward around the plant heart; mature outer leaves open outward and droop toward the canopy edge.Source: §2.2 · p. 5
  • The mesh is normalized so integrated physiological area matches the growth model, while leaf identity and geometry preserve position and radiation interception.Each modeled leaf surface retains its corresponding physiological leaf identity for returning radiation to that leaf in the next update.Source: §2.2 · p. 7

2.3. Simulation in the NVIDIA Isaac Sim greenhouse environment

The model resolves radiation and greenhouse conditions at leaf and patch positions, linking local exposure to physiology and growth. Leaf-level carbon allocation then reshapes the canopy, while an exploratory index compares enclosed leaves’ expansion demand with transpiration.

2.3.1. Radiation interception by the three-dimensional canopy

  • Ray tracing resolves direct, diffuse, reflected, and scattered radiation across leaf patches, then recalculates exposure as the canopy geometry develops.Patch-level photosynthesis is combined only after calculation, preserving differing responses to light within exposed and shaded parts of a leaf.Source: §2.3.1 · p. 7, §2.3.3 · p. 9

2.3.2. Spatial greenhouse environment

  • Leaf conditions are interpolated from sensor measurements onto a three-dimensional environmental grid and sampled at leaf positions.Leaf temperature and humidity inform energy balance, while humidity also affects expansion; carbon dioxide is evaluated at the plant position.Source: §2.3.2 · p. 7

2.3.3. Leaf physiology and feedback to growth

  • Leaf-level assimilation enters the whole-plant carbon balance, and remaining growth is allocated among leaves according to local carbon supply and developmental and size-related factors.Specific leaf area varies with absorbed light and relative humidity, while the local-supply modifier adjusts allocation without explicitly modeling phloem transport.Source: §2.3.3 · p. 9

2.3.4. Leaf-specific tipburn susceptibility

  • The exploratory tipburn index compares a leaf’s positive relative area-expansion rate with its transpiration latent-heat flux.It supports within-canopy comparisons but does not predict visible injury or represent calcium delivered by root pressure.Source: §2.3.4 · p. 9

2.4. Numerical implementation

The implementation couples evolving leaf states and three-dimensional geometry with repeated radiation and exposure calculations. Greenhouse trials supplied calibration and independent evaluation data, while simulation experiments varied environmental and spatial conditions, tipburn susceptibility, and allocation settings.

2.4. Numerical implementation

  • Plant geometry was regenerated every six hours from updated leaf states, after which radiation and local environmental exposure were recalculated for the next growth interval.Plant states used a fourth-order Runge-Kutta scheme with a 300-s time step; radiation and batched plant operations were GPU accelerated.Source: §2.4 · p. 9

2.5.1. Plant materials and greenhouse experiment

  • Auburn greenhouse measurements tracked dry weight and structural traits at transplanting and 7, 14, 21, and 28 days after transplanting, using destructive samples from different plants.One trial was used for calibration and a separate trial was reserved for evaluation.Source: §2.5.1 · p. 10

2.5.2. Model parameters and environmental inputs

  • Sensor records supplied the simulations’ environmental inputs, and each trial’s PAR record drove incident light before ray tracing calculated leaf-level absorbed radiation.Parameters estimated from one Auburn trial were fixed before evaluation on a separate trial without refitting.Source: §2.5.2 · p. 10

2.5.3. Simulation experiments

  • Simulation experiments varied temperature, radiation, carbon dioxide, plant position, neighboring plants, allocation, and tipburn conditions while holding initial states and parameters fixed in each comparison.Allocation sensitivity compared paired runs with λ = 0.5 and λ = 0 under the same initial and environmental conditions.Source: §2.5.3 · pp. 10–11

3. Results and discussion

The leaf-resolved model reproduced measured lettuce growth and structural development, then simulated responses to altered climate and position within a planted block. Its results also show how leaf-level light exposure and enclosure relate to growth and tipburn susceptibility.

3.1. Simulated and measured plant growth

  • 9.5% RRMSE for total dry weight: simulated values at all four sampling dates were within one standard deviation of measured values.The model underestimated the day-28 measured mean by 0.59 g plant−1 (6.8%).Source: §3.1 · p. 11, Figure 4 · p. 12

3.2. Simulated and measured structural development

  • Structural RRMSEs were 9.2% for leaf number, 12.7% for canopy diameter and 13.1% for largest-leaf area.The rosette became narrower than measured later in development, while the largest blade was underestimated from day 21 onward.Source: §3.2 · p. 13, Figure 5 · p. 14

3.3. Plant response to sustained environmental changes

  • Across sustained scenarios, 30% less radiation lowered day-30 dry weight 10.4%, 30% more raised it 6.9%, and 200 ppm added CO2 raised it 46.1%.A 2 °C decrease raised dry weight 2.1%, while a 2 °C increase lowered it 4.5%; CO2 enrichment also increased leaf number and total leaf area.Source: §3.3 · pp. 13–14, Figure 6 · p. 15

3.4. Growth and leaf exposure in a planted block

  • With the prescribed air field and each identical plant traced alone (S5), mean dry weight increased to 8.25 g plant−1, 27.3% above S1; adding neighbors reduced weight by an amount equivalent to 22.4% of S1.Source: §3.4 · p. 17
  • In the simulated block, interior plants accumulated 8.6% less dry weight than border plants with identical initial states, and absorbed radiation tracked position-specific dry weight.Across individual leaves, neighboring plants reduced radiation by 34–84% on the interior plant’s five oldest outer leaves, while ranks 10–18 changed by only +0.2 to −9.1%.Source: §3.4 · p. 17, Figure 8 · p. 18, Figure 9 · p. 19

3.5. Tipburn susceptibility and allocation sensitivity

  • The enclosed-leaf tipburn index rose as the head closed during the same period that tipburn appeared on greenhouse plants, though timing alone was weak evidence.On day 28, the enclosed-leaf index was approximately twenty times the outer-leaf index; turning off the allocation rule’s local carbon-supply term changed no plant trait by more than 0.4%.Source: §3.5 · pp. 17, 20

4. Conclusion

The framework couples leaf-level physiology with an evolving 3D lettuce canopy, and its predictions tracked measured biomass and structural development. Its current configuration is limited to one cultivar and does not update parameters from physical-plant observations.

4. Conclusion

  • The model couples leaf-level carbon assimilation and allocation, maintenance, and 3D canopy development, with changing canopy structure affecting later radiation interception and growth.Source: §4 · p. 20
  • Relative errors were 9.2–13.1% for dry weight, leaf number, canopy diameter and largest-leaf area.Environmental and spatial simulations also linked climate and neighboring plants with leaf exposure and biomass, while the leaf-specific tipburn index rose during the period when greenhouse tipburn appeared.Source: §4 · p. 20
  • The framework was configured for one lettuce cultivar, with parameters fixed during the season rather than updated from observations of the physical plant.Future work will extend it to multiple cultivars and add learnable parameters and an observation-driven update pass.Source: §4 · p. 20

Declaration of generative AI and AI-assisted technologies in the writing process

The authors used Grammarly and ChatGPT to improve the manuscript’s grammar, readability and flow, then reviewed and edited the content and retained responsibility for the publication.

Declaration of generative AI and AI-assisted technologies in the writing process

Appendix A.1. Protocol of the simulation experiments

The spatial simulations compared prescribed air, neighboring plants and individual variation across 40 occupied positions over 30 days. The protocol paired scenarios and specified the air field and how plant and tipburn outcomes were summarized.

Appendix A.1. Protocol of the simulation experiments

  • The 40-position block was simulated for 30 days at 0.2032 m spacing, with 22 border and 18 interior plants and empty remaining table positions.Five scenarios separated the prescribed air field, neighboring plants and assigned individual variation; paired differences used the same positions and contrasts were normalized by the uniform-air, identical-plant reference.Source: Appendix A.1 · p. 24
  • The prescribed air field used a 0.1 °C m−1 temperature gradient, humidity derived at common vapor pressure, 20 ppm carbon dioxide depletion over 0.4 m, and 0.09 m s−1 air speed.Season-mean absorbed irradiance per leaf area and final-week, 24-hour mean absorbed power per plant were reported separately.Source: Appendix A.1 · p. 24
  • The local carbon-supply modifier was tested with paired runs at λ = 0.5 and λ = 0, holding initial states, positions, identities, forcing and numerical settings fixed without refitting parameters.Each run evolved its own geometry; day-30 trait changes used λ = 0.5 as the denominator, and leaf profiles were paired by persistent leaf identity.Source: Appendix A.1 · p. 24

Appendix A.2. Spatial scenarios and carbon balance

The appendix separates air-field, neighbor, identity and interaction contrasts across the 40-plant scenarios. It reports that the air-field advantage emerged late, after leaf area and absorbed power increased.

Appendix A.2. Spatial scenarios and carbon balance

  • The five scenarios used the same 40 occupied positions; plants traced alone retained self-shading but excluded other plants, while plants traced with neighbors included their evolving geometry.Individual variation was assigned deterministically, with individuals paired between S2 and S4.Source: Appendix A.2 · p. 24
  • Adding neighbors reduced mean day-30 weight by 17.6% relative to S5; the identity contrast averaged −2.1% of S1, and the interaction averaged −0.36 percentage points.The identity contrast ranged from −47.2 to +39.3%, with a mean absolute interaction magnitude of 2.26 percentage points.Source: Appendix A.2 · p. 24
  • S5 remained below S1 for 20 of 30 days, first exceeded it on day 20.5, and S3 crossed S1 on day 22.5.Plants first developed more leaf area, then more dry matter; S5 had the largest leaf area and absorbed power.Source: Appendix A.2 · p. 24

Appendix A.3. Diagnostic evaluation of the prescribed air-field response

The prescribed air field altered leaf-level humidity and radiation conditions, with a much larger growth response in the leaf-resolved than the plant-level model. In the diagnostic plant, leaf-area expansion preceded the biomass advantage.

Appendix A.3. Diagnostic evaluation of the prescribed air-field response

  • For diagnostic plant 1, the field lowered mean local air temperature by 1.09 ◦C and raised expansion-weighted relative humidity from 0.675 to 0.755.The expansion-weighted humidity factor increased by 7.26% and the radiation factor by 1.34%.Source: Appendix A.3 · p. 24
  • In plant 1, leaf-area difference between S5 and S1 grew from +0.86% on day 1 to +61.13% on day 30, while dry weight stayed below S1 for the first 19 days.The leaf-area difference was +13.07% on day 11.Source: Appendix A.3 · p. 24
  • The leaf-resolved model’s day-30 dry weight rose 27.3% under sampled air-field forcing, versus +0.153% in the plant-level model.The spatial scenario comparison is shown in Figure A.1.Source: Appendix A.3 · p. 24, Figure A.1 · p. 25

Appendix A.4. Measured tipburn and spatial index comparisons

The simulated enclosed-leaf index rose during the period when tipburn appeared on greenhouse plants, while spatial comparisons associated its spread with canopy development rather than absorbed light alone.

Appendix A.4. Measured tipburn and spatial index comparisons

  • Real tipburn appeared between day-14 and day-21 sampling, while the variable block’s median enclosed-leaf index climbed from 0.47 on day 7 to 3.70 ×10−6 m2 J−1 on day 28.The median was 1.78 and 2.14 ×10−6 m2 J−1 on days 14 and 21; identical plants rose from 0.41 to 3.35 over the same days.Source: Appendix A.4 · p. 26
  • Heavier plants tended to have more severe injury, with shoot-weight correlations of +0.41 on day 21 and +0.37 on day 28; one retained day-21 record shifted the area correlation from −0.22 to +0.41 when omitted.Leaf number was available for only one of 23 late-stage scored plants and was not used.Source: Appendix A.4 · p. 26
  • At day 28, index–absorbed-light Spearman correlations were +0.27 in S3 and −0.07 in S4, while identical-plant block CVs were 3.2% and 9.0% on days 14 and 21.The index spread appeared across the block as canopies developed.Source: Appendix A.4 · p. 26
  • 66 of 114 scored measured plants fell outside the simulated shoot-weight range, so the comparison emphasized timing and which leaves carried risk rather than matched plant sizes.The measured plants were heavier than simulated plants on the same day.Source: Appendix A.4 · p. 26

Appendix A.5. Paired allocation ablation and leaf-profile sensitivity

Removing the local carbon-supply term left whole-plant traits nearly unchanged, though leaf-profile differences were larger in the interior and concentrated in small shaded leaves.

Appendix A.5. Paired allocation ablation and leaf-profile sensitivity

  • The ablation paired five-plant and 40-plant cases, changed λ from 0.5 to zero, and held all 45 initial states and positions identical; geometry evolved independently in each run.No parameter was refitted; Figure A.5 distinguishes case-average traits from plant-1 profile RMS annotations.Source: Appendix A.5 · p. 26, Figure A.5 · p. 29
  • Mean leaf-profile difference was higher in interior than border plants (2.24% against 1.24%), despite similar mean absolute dry-weight differences (0.098% and 0.100%).The interior contained more small leaves in shade.Source: Appendix A.5 · p. 26, Table A.5 · p. 30
  • The largest block profile value was 11.82%, from a leaf declining from 2.936 to 1.239 cm2, a 57.8% change on 1.696 cm2 of area.The profile statistic gives each included leaf equal weight, so percentage changes in small leaves can dominate it.Source: Appendix A.5 · p. 26
  • Dry weight, largest-leaf area and total leaf area were insensitive to removing the local carbon-supply modifier in both cases; area offset was 0.05 to 0.07% of reference area.Table A.4 reports paired day-30 changes for λ = 0 minus λ = 0.5.Source: Appendix A.5 · p. 26, Table A.4 · p. 30
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