Module 3: Photosynthesis & Ripening

Wine quality is at its core a problem of source-sink balance: the canopy must fix enough carbon to load the berries with sugar while still respecting the acid balance and aroma precursors that define varietal identity. This module reviews vineyard training systems (VSP, Scott-Henry, Geneva Double Curtain, sprawl), the Monsi–Saeki canopy light-interception model, Smart’s (1991) leaf-to-fruit-ratio framework for balanced ripening, the biochemistry of phloem sucrose unloading and hexose vacuolar storage, the temperature dependence of malic acid degradation, and the Lakso (2003) VineSim whole-vine carbon-partitioning model.

1. Training Systems and Canopy Architecture

A grapevine trellis defines the three-dimensional geometry of the canopy, which in turn determines how much photosynthetically active radiation (PAR) the vine intercepts and how that light is distributed between fruit-bearing and purely vegetative leaves. Major commercial systems in use today:

Vertical Shoot Position (VSP): single upward curtain of shoots between fixed catch wires. Narrow canopy, easy mechanization; standard for premium V. vinifera in Europe.
Geneva Double Curtain (GDC): twin downward-hanging curtains on a high bilateral cordon. Increases exposed canopy area; suitable for cool, vigorous V. labrusca and hybrid vineyards in New York and Ontario.
Scott-Henry: divided canopy with shoots trained both upward and downward from a middle wire. Doubles the exposed canopy area of VSP without doubling row width.
Sprawl / Californian: unsupported canopy. Cheap and high-vigor-tolerant, but poor light penetration and inconsistent ripening.
Pergola / tendone: overhead horizontal trellis used in Veneto (Italy), Galicia (Spain), and for table grapes. Provides shade and ventilation in hot climates.

Leaf-Area Index (LAI)

Leaf-area index is the ratio of total projected leaf area to ground area. Optimal LAI for V. vinifera is around 1.5–3; above this threshold diminishing returns set in as internal shading begins to limit the marginal leaf. Above LAI ~4 the deepest 30% of leaves are in near-dark sink mode, respiring more than they fix.

\[f_i = 1 - e^{-k\,\text{LAI}},\quad k \approx 0.5\;(\text{spherical leaves})\]

Monsi–Saeki (1953) Lambert–Beer canopy light interception.

2. Photosynthesis: PSII, PSI, and the Chloroplast

The grapevine is a standard C3 plant with no CAM or C4 modifications. Photosynthesis occurs in leaf mesophyll chloroplasts via the canonical two-photosystem Z-scheme: photosystem II (PSII) oxidises water at the oxygen-evolving complex to release O2 and pass electrons to plastoquinone; photosystem I (PSI) re-excites them to reduce ferredoxin and ultimately NADP + H+.

\[\text{H}_2\text{O} \xrightarrow{\text{PSII (680 nm)}} \text{PQ} \xrightarrow{\text{cyt b6f}} \text{PC} \xrightarrow{\text{PSI (700 nm)}} \text{Fd} \xrightarrow{\text{FNR}} \text{NADPH}\]

Pigment Composition

Grape leaves contain roughly 3:1 chlorophyll a:chlorophyll b by mole, plus accessory carotenoids (beta-carotene, lutein, zeaxanthin, violaxanthin, neoxanthin). Carotenoids extend the absorption spectrum into the blue-green gap of chlorophyll and provide photoprotection via the xanthophyll cycle (violaxanthin ↔ antheraxanthin ↔ zeaxanthin), which dissipates excess excitation energy as heat under high-light or drought stress. Post-veraison, these same carotenoids are cleaved by carotenoid cleavage dioxygenases (CCDs) to release C13-norisoprenoid aroma compounds (beta-damascenone, beta-ionone, TDN in Riesling).

Wavelength Dependence

Chlorophyll absorbs maximally at ~430 and ~680 nm; light at 500–580 nm (green) is poorly used and gives leaves their green appearance. PSII has an action-spectrum peak at 680 nm, PSI at 700 nm; when both are stimulated together (the “red drop” phenomenon of Emerson 1958), linear electron transport is maximised. Daylight PAR (400–700 nm) is roughly 45% of total solar irradiance, and this fraction sets the practical ceiling on daily vine carbon assimilation.

Light Response of Photosynthesis

Leaf-level CO2 assimilation as a function of incident PAR is well described by the non-rectangular hyperbola (Farquhar 1980):

\[A(I) = \frac{\alpha I + A_{\max} - \sqrt{(\alpha I + A_{\max})^2 - 4\,\theta\,\alpha I\, A_{\max}}}{2\,\theta}\]

\(\alpha\): quantum yield; \(A_{\max}\): light-saturated rate; \(\theta\): convexity.

For a healthy V. vinifera leaf, \(\alpha \approx 0.06\) mol CO2 per mol photon, \(A_{\max} \approx 12\text{--}20\) µmol CO2 m−2 s−1, and light-saturation begins at ~1000 µmol photons m−2 s−1. Full summer sun provides ~2000 µmol m−2 s−1, so sunlit leaves operate near saturation and leaves deeper in the canopy are light-limited.

3. Source-Sink Dynamics and Leaf-to-Fruit Ratio

Balanced ripening requires a match between carbon source (canopy leaves) and sink demand (berry sugar loading). Smart (1991), in Sunlight Into Wine, proposed that an optimum leaf-area to fruit-mass ratio lies around 8–14 cm² leaf per gram of fruit, corresponding to roughly 10–14 leaves per cluster on a balanced VSP canopy.

\[\text{Leaf-to-fruit ratio:}\quad \rho_{LF} = \frac{A_{\text{leaf}}\;(\text{cm}^2)}{M_{\text{fruit}}\;(\text{g})} \approx 8\text{--}14\;\text{cm}^2/\text{g}\]

Smart 1991 balanced-ripening window.

Under-Cropped and Over-Cropped Vines

Vines with \(\rho_{LF} > 14\) (over-leafed, under-cropped) ripen quickly but often lack concentration and may develop “vegetal” character from excessive methoxypyrazine production in the shaded canopy. Vines with \(\rho_{LF} < 8\)(over-cropped) fail to reach target Brix, retain unripe seed and harsh tannins, and produce “thin” wines with elevated green-pepper aroma.

Crop Load and Cluster Thinning

Cluster thinning (“green harvest”) at the lag phase adjusts crop load to the expected canopy photosynthetic capacity. Removing 20–30% of clusters concentrates sugar and phenolics in the remaining clusters and is standard in premium red-wine vineyards.

Lakso 2003 VineSim

Lakso’s (2003) VineSim model is a whole-vine carbon-partitioning simulation that integrates daily photosynthesis, respiration, phloem transport, and organ growth, including explicit representation of (i) canopy light interception by training system, (ii) temperature-dependent respiration (Q10 kinetics), (iii) phenologically triggered sink activation (bud-break, flowering, fruit-set, veraison), and (iv) reserve mobilisation in the perennial woody trunk. VineSim reproduces the empirical yield-Brix trade-off and has been used to model climate-change impacts on wine-grape phenology.

4. Phloem Sugar Loading and Berry Accumulation

Sucrose is the primary translocated carbohydrate in V. vinifera. It is synthesised in source leaves from triose phosphates exported from chloroplasts, actively loaded into the phloem apoplast by SUC/SUT sucrose transporters, and translocated by bulk flow to the berry. Pre-veraison, sucrose is unloaded symplastically and delivered directly to the berry mesocarp cytoplasm; post-veraison (Zhang 2006, see Module 1), plasmodesmata close and unloading switches to the apoplast.

\[\text{sucrose} \xrightarrow{\text{CWINV}} \text{glucose + fructose} \xrightarrow{\text{VvHT}} \text{vacuolar hexose storage}\]

Apoplastic unloading + cell-wall invertase + hexose-transporter vacuolar loading.

Brix: Definition and Measurement

Brix (symbol °Bx) is a refractometric scale defined as percent sucrose by weight in a pure sucrose solution yielding the same refractive index. In grape must it is an approximate proxy for total soluble solids (glucose + fructose + minor acids and cations). For typical premium wines the target is 22–26 °Brix, yielding ethanol of 12–15% v/v after fermentation. Some enologists use specific gravity or the Baumé scale instead.

\[\text{Ethanol (\% v/v)} \approx 0.55 \times \text{Brix}_\text{harvest}\]

Approximate conversion (exact factor depends on yeast efficiency, temperature, and residual sugar target).

Hexose Equilibrium

Glucose and fructose accumulate in near-equimolar ratio in the ripe mesocarp vacuole. Small cultivar-specific biases exist: fructose-dominant in Muscat Blanc, glucose- dominant in Chardonnay. Because glucose and fructose have equivalent ethanol yield but slightly different metabolic paths during yeast fermentation, the ratio can affect fermentation kinetics (fructose is slower to ferment in some yeast strains and is the residual sugar of stuck fermentations).

5. Acid Dynamics: Malate, Tartrate, and pH

Grape must is unusual among fruits in the co-dominance of two primary organic acids: L-malic acid (2–9 g/L at harvest, pKa1 = 3.40) and L-(+)-tartaric acid (3–8 g/L, pKa1 = 3.04). Both accumulate during Stage I and reach a joint peak near veraison of ~20 g/L combined. Post-veraison, the two acids diverge dramatically:

Tartaric acid is metabolically stable. Its concentration declines only by dilution as the berry expands; absolute content is roughly constant.
Malic acid is actively respired/decarboxylated by the berry. Rate follows first-order kinetics with strong temperature dependence (Q10 ~ 2.5–3).

Temperature Dependence of Malic Degradation

\[\frac{d[\text{Mal}]}{dt} = -k_m(T)\,[\text{Mal}],\quad k_m(T) = k_m(15^\circ\text{C})\cdot Q_{10}^{(T-15)/10}\]

At 25 °C, malic decay is ~5× faster than at 15 °C (Q10 ~ 2.7).

This temperature sensitivity is the single most important reason why cool-climate wines (Mosel Riesling, Chablis Chardonnay, Marlborough Sauvignon Blanc) have naturally high acidity, while warm-climate wines (Napa Cabernet, southern Rhone Syrah, Barossa Shiraz) require acidulation to maintain freshness.

Titratable Acidity (TA) and pH

Titratable acidity is measured by titration to pH 8.2 (phenolphthalein end-point) with NaOH and expressed in g/L of tartaric-acid equivalent. Typical harvest values: cool climate 8–11 g/L, warm climate 5–7 g/L. Must pH at harvest is empirically related to TA and the malate/tartrate ratio: roughly pH 3.1–3.4 at TA 8 g/L and pH 3.6–3.9 at TA 5 g/L.

Sugar-Acid Trade-Off

Because warmth accelerates both sugar accumulation and malic respiration, warmer seasons produce higher Brix but lower TA. In cool regions this trade-off is an asset—late-harvest styles (Eiswein, Sauternes) depend on residual acidity to balance high residual sugar. In warm regions it is a liability: wines can reach 15% ABV with pH 4.0+ and insufficient structural freshness, requiring acidification with tartaric acid (permitted under most appellation rules).

6. Canopy Management Interventions

Canopy management is the set of in-season manipulations aimed at improving source- sink balance, disease control, and fruit chemistry. Major interventions:

Shoot thinning (post-bud-break): reduce shoot density to target level.
Shoot positioning: tuck shoots into VSP wires for vertical canopy.
Leaf removal / effeuillage: expose cluster zone to sun and air. Reduces methoxypyrazine, increases flavonol, enhances disease control, and warms the cluster microclimate by several degrees.
Shoot topping / hedging: reduces canopy height once target leaf area achieved; diverts assimilates to berry rather than shoot.
Cluster thinning: removes ~20–30% of clusters at lag phase; improves source-sink ratio.
Lateral removal: removes late-season lateral shoots that create canopy shade.

Shade and Vegetal Character

Deep canopy shade delays ripening, retains methoxypyrazines (IBMP, green-pepper note), reduces flavonol and anthocyanin accumulation, and fosters disease pressure (downy/powdery mildew, Botrytis). Excessive leaf removal in hot climates is counter-productive: sunburn damage on exposed skin can denature anthocyanins and oxidise aromatics, producing “cooked” character. The ideal is selective exposure of the cluster-bearing zone with retention of ~1–2 layers of upper canopy leaves.

7. Respiration, Night Temperature, and Climate Niche

Daytime gross photosynthesis is offset by continuous respiration in leaves, shoots, roots, and berries. Leaf respiration follows Q10 ~ 2 kinetics (doubling every 10 °C); at constant daytime carbon gain, a shift from 15 to 25 °C night temperature can reduce net canopy carbon balance by ~25%. This explains the long-observed viticultural wisdom that cool nights produce more structured wines: cool nights preserve both photosynthetic carbon (lower respiration) and malate (lower decay rate).

\[R_{\text{dark}}(T) = R_{\text{ref}}\cdot Q_{10}^{(T - T_{\text{ref}})/10}\]

Arrhenius-like temperature dependence of dark respiration.

Growing Degree Days

The thermal integral of the growing season is summarised as Growing Degree Days (GDD, Winkler index, base 10 °C). Winkler regions I–V span from <1390 GDD (Region I, Burgundy) to >2220 GDD (Region V, Central Valley). Under climate warming, historic Region I regions (Mosel, Burgundy) are shifting toward Region II, with consequent implications for cultivar and harvest date.

\[\text{GDD}(\text{season}) = \sum_{\text{days}} \max(0,\;\bar T - 10^\circ\text{C})\]

Canopy light interception by training system

8. Vegetative Reserves and Biennial Carry-Over

A grapevine is a long-lived perennial, and the ripening of a year’s crop depends not only on the current season’s canopy but also on reserves accumulated in permanent woody organs (trunk, cordons, roots) in the preceding season. Starch is the primary reserve carbohydrate, stored in ray parenchyma of the trunk and in root cortical cells. Reserves mobilise during bud-break and early shoot growth, when newly expanded leaves are not yet net carbon-fixers.

\[\text{Trunk starch} \xleftrightarrow{\text{beta-amylase}} \text{maltose} \xrightarrow{} \text{sucrose}\]

Reserve mobilisation from stored starch in the trunk.

Biennial Carry-Over and Alternate Bearing

A year of over-cropping depletes reserves and reduces the next year’s bud-fertility and vigour; classical alternate-bearing patterns (every-other-year crop) are mitigated in grape by the long-lived cordon and the flexibility of spur/cane pruning, but are still a real planning concern for commercial growers. The Lakso VineSim model tracks reserve carbon explicitly for multi-year simulations.

8b. Methoxypyrazines and Shade Management

The distinctive “bell-pepper” or “herbaceous” note of underripe Cabernet Sauvignon, Cabernet Franc, and Sauvignon Blanc is produced by 3-isobutyl-2- methoxypyrazine (IBMP) and 3-sec-butyl-2-methoxypyrazine (SBMP). These compounds are exceptionally potent olfactants, detectable at ~2 ng/L and overwhelming at >20 ng/L. They are synthesised from leucine or valine via the enzyme VvOMT3 (O-methyltransferase), and accumulate in skin tissue during Stage I. After veraison, IBMP is degraded photochemically in sun-exposed berries; the degradation follows first-order kinetics with a rate proportional to cumulative UV + visible PAR exposure (Dunlevy 2010, Scheiner 2010).

\[\frac{d[\text{IBMP}]}{dt} = -k_{\text{photo}}\cdot[\text{IBMP}]\cdot I_{\text{UV+PAR}}\]

First-order photochemical IBMP degradation; sun-exposed clusters lose 50–70% of pre-veraison IBMP.

Shade Management in Practice

Leaf removal (“effeuillage”) in the fruiting zone at lag phase is the standard intervention to accelerate IBMP degradation. In Bordeaux and Washington State Cabernet Sauvignon, selective leaf removal of the east-facing (morning sun) side of VSP canopies is preferred to avoid afternoon heat damage. Over-exposure bleaches anthocyanins (sunburn), so the goal is dappled, not full, sunlight on the cluster.

8c. Cluster Thinning and Yield Balance

Cluster thinning (“green harvest”) is the practice of removing a fraction of clusters at lag phase (45–55 DAA) to reduce crop load and concentrate remaining berry chemistry. The intervention is calibrated against the vine’s canopy capacity: thinning a balanced vine wastes potential; thinning an over-cropped vine rescues ripening.

\[\text{Ravaz index} = \frac{\text{yield (kg)}}{\text{pruning weight (kg)}} \approx 5\text{--}10\;\text{balanced}\]

Ravaz 1911 crop-to-vegetative-growth balance; values >12 indicate over-cropping.

Yield vs. Quality Trade-Off

Premium wine estates accept yields of 30–50 hL/ha (2–4 t/ha), versus 80–150 hL/ha (6–12 t/ha) for table wine and 200 hL/ha+ for industrial bulk wine. The yield-quality inverse relationship is driven primarily by source-sink balance: at low yield, each berry receives more carbon and ripens to higher Brix with deeper color and more complex phenolics. Above a cultivar-specific threshold, further yield reduction gives diminishing returns because light interception becomes limiting.

9. Synthesis

Canopy architecture sets the light-intercepting surface; the Monsi–Saeki and Farquhar models translate that surface into daily CO2 assimilation; phloem transport and apoplastic unloading drive sugar into the berry; temperature-dependent malic respiration drains acid; and Smart’s leaf-to-fruit ratio gives the operative rule for balancing the system. Climate drives the whole integrator forward, and the same physical framework that predicts sugar-acid balance in a warm vs. cool vineyard predicts the direction of change as climate warms. Module 4 will ground this framework in water relations; Module 5 will pursue the acid balance to fermentation; and Module 8 will translate the entire system into a climate- change projection for world wine regions.

10. Precision Viticulture and Remote Sensing

Modern vineyards increasingly deploy NDVI (Normalized Difference Vegetation Index) imagery from satellites (Sentinel-2, Landsat) and UAV-mounted multispectral cameras to map within-vineyard variability in canopy vigour, disease pressure, and expected yield. NDVI correlates well with leaf-area index and chlorophyll content, providing a scalable proxy for photosynthetic capacity.

\[\text{NDVI} = \frac{\rho_{\text{NIR}} - \rho_{\text{red}}}{\rho_{\text{NIR}} + \rho_{\text{red}}}\]

NDVI uses the contrast between chlorophyll red absorption and NIR scattering by mesophyll.

Selective Harvest

NDVI-zoned vineyards allow selective harvest of high- and low-vigour zones at different ripeness targets, yielding separately vinified blends. This is standard practice in premium Bordeaux, Napa Cabernet, and Margaret River operations, where within-parcel variability often exceeds between-parcel variability.

Simulation 1: Canopy Light Interception and LAI Optimization

Compute the Monsi–Saeki fractional light interception \(f_i(\text{LAI})\) for four training systems (VSP, Geneva Double Curtain, Scott-Henry, Sprawl), integrate daily canopy CO2 assimilation by the Farquhar non-rectangular hyperbola, and locate the Smart 1991 leaf-to-fruit ratio sweet spot for balanced ripening.

Python

script.py138 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Canopy light interception and photosynthetic production as a function of
# leaf-area index (LAI), training system, and daily photosynthetically active
# radiation (PAR).
#
# Lambert-Beer (Monsi-Saeki 1953) model for fractional light interception:
#
#   I(z) = I_0 * exp(-k * L(z))     (within-canopy irradiance profile)
#   f_i  = 1 - exp(-k * LAI)        (fraction of incoming PAR intercepted)
#
# with canopy extinction coefficient k depending on leaf angle distribution
# (spherical k ~ 0.5; horizontal k ~ 0.8; erectophile k ~ 0.3).
#
# Photosynthesis by canopy-integrated non-rectangular hyperbola (Farquhar 1980):
#
#   A(I) = ( alpha I + A_max - sqrt((alpha I + A_max)^2 - 4 theta alpha I A_max) )
#                                 / (2 theta)
#
# We integrate A over leaf area and over the daylight cycle to obtain daily
# photo-assimilation per vine.

# --- canopy parameters ---
LAI = np.linspace(0.1, 6.0, 80)

# Compare three canopy architectures
systems = {
    'VSP (Vertical Shoot Position)': {'k': 0.55, 'color': '#a855f7'},
    'Geneva Double Curtain':         {'k': 0.42, 'color': '#22d3ee'},
    'Scott-Henry':                   {'k': 0.48, 'color': '#fcd34d'},
    'Sprawl (untrained)':            {'k': 0.70, 'color': '#f43f5e'},
}

# Daily integrated PAR at top of canopy (mol quanta m^-2 d^-1)
PAR_daily = 45.0

# Photosynthetic parameters (C3 leaf)
alpha   = 0.06       # quantum yield (mol CO2 / mol quanta)
A_max   = 16.0       # umol CO2 m^-2 s^-1 (light-saturated)
theta   = 0.85       # curvature
LUE_vin = 0.65       # g dry matter / mol CO2 fixed (Lakso 2003)

# Big-leaf approximation: daily canopy C assimilation scales with
#    f_i * (1 - exp(-eps * (LAI / LAI*))) * LUE_vin * PAR_daily
# where we use Monsi-Saeki's analytical integration.

def daily_A(LAI, k):
    # Light absorbed by canopy
    fi = 1 - np.exp(-k * LAI)
    # Average leaf PAR: absorbed * canopy
    # Saeki (1960) analytical integrated photosynthesis:
    # A_day = A_max * ln( (A_max + alpha k I0) / (A_max + alpha k I0 e^{-k LAI}) ) / k
    I0 = PAR_daily / 12.0 * 1e6 / 3600  # convert mol/d to umol/m^2/s (rough daylight average)
    numer = A_max + alpha * k * I0
    denom = A_max + alpha * k * I0 * np.exp(-k * LAI)
    A_day_integral = A_max / k * np.log(numer / denom)
    # Convert to daily mol CO2 (per m^2 ground) over 12 h daylight
    A_total = A_day_integral * 3600 * 12 * 1e-6  # mol CO2 m^-2 d^-1
    return fi, A_total

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(15, 11))
fig.patch.set_facecolor('#0a0a1a')
for ax in [ax1, ax2, ax3, ax4]:
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#e9d5ff')
    for spine in ax.spines.values():
        spine.set_color('#581c87')
    ax.grid(True, color='#3b0764', alpha=0.35)

# Panel 1: light interception fraction f_i(LAI) by system
for name, p in systems.items():
    fi, _ = daily_A(LAI, p['k'])
    ax1.plot(LAI, fi, color=p['color'], linewidth=2.3, label=f"{name} (k={p['k']})")
ax1.axvline(2.0, color='#e9d5ff', linestyle=':', alpha=0.7, label='Target LAI 2.0')
ax1.set_xlabel('Leaf-area index (LAI)', color='#e9d5ff', fontsize=11)
ax1.set_ylabel('Fraction PAR intercepted', color='#e9d5ff', fontsize=11)
ax1.set_title('Monsi-Saeki light interception by training system',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax1.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 2: daily CO2 assimilation rate
for name, p in systems.items():
    _, A_tot = daily_A(LAI, p['k'])
    ax2.plot(LAI, A_tot, color=p['color'], linewidth=2.3, label=name)
ax2.set_xlabel('Leaf-area index (LAI)', color='#e9d5ff', fontsize=11)
ax2.set_ylabel('Daily canopy A (mol CO2 m^-2 d^-1)', color='#e9d5ff', fontsize=11)
ax2.set_title('Integrated canopy photosynthesis',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax2.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 3: diminishing-returns: marginal A per unit LAI
k = 0.5
_, A_ref = daily_A(LAI, k)
dA_dLAI = np.gradient(A_ref, LAI)
ax3.plot(LAI, dA_dLAI, color='#c084fc', linewidth=2.4)
ax3.fill_between(LAI, dA_dLAI, alpha=0.3, color='#c084fc')
ax3.axhline(0.05 * dA_dLAI.max(), color='#fcd34d', linestyle='--', label='5% of max: diminishing-return LAI')
ax3.set_xlabel('LAI', color='#e9d5ff', fontsize=11)
ax3.set_ylabel('dA / dLAI (mol CO2 m^-2 d^-1 / LAI)', color='#e9d5ff', fontsize=11)
ax3.set_title('Marginal light interception per unit leaf',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax3.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=9)

# Panel 4: leaf-to-fruit ratio sweet-spot (Smart 1991)
LF_ratio = np.linspace(4, 20, 100)
# Empirical quality index: parabolic around optimum at 10 cm^2/g
quality = 1.0 - 0.015 * (LF_ratio - 11.0)**2
quality = np.clip(quality, 0, 1)
yield_ratio = 1.0 - 0.018 * (LF_ratio - 7.0)**2
yield_ratio = np.clip(yield_ratio, 0, 1)
balanced = quality * 0.6 + yield_ratio * 0.4

ax4.plot(LF_ratio, quality,     color='#fcd34d', linewidth=2.2, label='Wine quality index')
ax4.plot(LF_ratio, yield_ratio, color='#22d3ee', linewidth=2.2, label='Yield index')
ax4.plot(LF_ratio, balanced,    color='#a855f7', linewidth=2.5, label='Balanced Smart 1991')
ax4.axvspan(8, 14, color='#fb7185', alpha=0.18, label='Smart optimal band 8-14 cm^2/g')
ax4.set_xlabel('Leaf-to-fruit ratio (cm^2/g)', color='#e9d5ff', fontsize=11)
ax4.set_ylabel('Normalized index', color='#e9d5ff', fontsize=11)
ax4.set_title('Smart 1991 leaf-to-fruit ratio optimization',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax4.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=9)

# integrated daily C assimilation from LAI=0 to LAI=3 for VSP canopy
_, A_VSP = daily_A(LAI, systems['VSP (Vertical Shoot Position)']['k'])
C_vintegral = np.trapezoid(A_VSP[LAI<=3.0], LAI[LAI<=3.0])
print(f"Integrated VSP assimilation from LAI 0.1 -> 3.0 (trapezoid): {C_vintegral:.2f} mol CO2 / (LAI * m^2 * d)")

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')

print(f"Peak daily A at LAI=3: VSP {daily_A(3, 0.55)[1]:.2f} mol m^-2 d^-1")
print(f"Peak daily A at LAI=3: Geneva {daily_A(3, 0.42)[1]:.2f} mol m^-2 d^-1")
print(f"Light interception at LAI=3, VSP: {daily_A(3, 0.55)[0]*100:.1f}%")
print(f"Smart 1991: leaf-to-fruit ratio optimum 8-14 cm^2/g for balanced ripening")
print(f"Lakso 2003 VineSim: above LAI ~3 diminishing returns (self-shading)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation 2: Coupled Sugar-Acid Dynamics During Ripening

Integrate the coupled ODE for Brix (sugar approach-to-saturation) and malic acid (first-order temperature-dependent decay) at four vineyard temperatures (15/20/25/30 °C). Overlay the resulting pH trajectory and the Brix–malate phase plane to visualise the warm-climate low-acid wine pathology.

Python

script.py125 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy.integrate import odeint

# Sugar-acid coupled dynamics during ripening:
#
#   dBrix/dt = f_sugar(t) * S_max * (1 - Brix/S_max)   (approach to saturation)
#   dMal/dt  = -k_m(T) * Mal                           (first-order decay)
#   dTart/dt = 0                                       (tartrate stable)
#   pH       = pKa1(tart) - log10(TA/A)                (titratable-acid model)
#
# Temperature dependence of malic decay (Q10 approach):
#   k_m(T) = k_m(15 C) * Q10^((T - 15)/10),    Q10 ~ 2.5-3
# At 25 C malic decays ~5x faster than at 15 C -> warm-climate low-acid wines.

days = np.linspace(0, 45, 800)   # days post-veraison

# Three temperature scenarios
T_cases = {
    'Cool (15 C mean)': 15.0,
    'Temperate (20 C)': 20.0,
    'Warm (25 C)':      25.0,
    'Hot (30 C)':       30.0,
}
colors = {'Cool (15 C mean)': '#22d3ee',
          'Temperate (20 C)': '#a855f7',
          'Warm (25 C)':      '#fcd34d',
          'Hot (30 C)':       '#f43f5e'}

# Base parameters
Brix_max = 26.0
Mal0     = 22.0      # g/L at veraison
Tart     = 8.5       # g/L stable
k_sugar  = 0.18      # d^-1 approach rate to max

# Malic acid rate at reference T=15 C
km_ref = 0.015       # d^-1 (slow at 15 C)
Q10 = 2.7

def km_of_T(T):
    return km_ref * Q10**((T - 15.0)/10.0)

def model(y, t, T):
    Brix, Mal = y
    dB = k_sugar * (Brix_max - Brix)
    dM = -km_of_T(T) * Mal
    return [dB, dM]

# Panel 1: Brix trajectory (identical across T for this simple model)
for label, T in T_cases.items():
    sol = odeint(model, [4.0, Mal0], days, args=(T,))
    ax1.plot(days, sol[:,0], color=colors[label], linewidth=2.2, label=label)
ax1.axhline(24, color='#fde68a', linestyle='--', label='Typical harvest Brix 24')
ax1.set_xlabel('Days post-veraison', color='#e9d5ff', fontsize=11)
ax1.set_ylabel('Brix (%w/w)', color='#e9d5ff', fontsize=11)
ax1.set_title('Sugar accumulation curve',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax1.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=9)

# Panel 2: Malic acid decay
for label, T in T_cases.items():
    sol = odeint(model, [4.0, Mal0], days, args=(T,))
    ax2.plot(days, sol[:,1], color=colors[label], linewidth=2.2, label=label + f'  (k={km_of_T(T):.3f}/d)')
ax2.axhline(3.5, color='#fde68a', linestyle='--', label='Typical harvest malate 3.5 g/L')
ax2.set_xlabel('Days post-veraison', color='#e9d5ff', fontsize=11)
ax2.set_ylabel('Malic acid (g/L)', color='#e9d5ff', fontsize=11)
ax2.set_title('Temperature-dependent malate decay (Q10=2.7)',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax2.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 3: titratable acidity and pH
# TA = 1.5 * Mal + Tart (g/L tartrate-equivalent, simplified)
# pH = 2.9 - 0.18 * log10(TA / 7.5)
#     (empirical relationship near grape must)
for label, T in T_cases.items():
    sol = odeint(model, [4.0, Mal0], days, args=(T,))
    TA = sol[:,1] + Tart
    pH = 2.95 + 0.20 * np.log10(9.0 / np.maximum(TA, 3.0))
    ax3.plot(days, pH, color=colors[label], linewidth=2.3, label=f'{label}  pH final {pH[-1]:.2f}')
ax3.axhline(3.3, color='#fcd34d', linestyle='--', label='pH 3.3 (crisp/fresh)')
ax3.axhline(3.8, color='#f43f5e', linestyle='--', label='pH 3.8 (soft/warm)')
ax3.set_xlabel('Days post-veraison', color='#e9d5ff', fontsize=11)
ax3.set_ylabel('Must pH', color='#e9d5ff', fontsize=11)
ax3.set_title('pH trajectory during ripening',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax3.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=8)

# Panel 4: climate phase plane Brix vs Malic
for label, T in T_cases.items():
    sol = odeint(model, [4.0, Mal0], days, args=(T,))
    ax4.plot(sol[:,0], sol[:,1], color=colors[label], linewidth=2.4, label=label)
    ax4.scatter([sol[-1,0]], [sol[-1,1]], color=colors[label], s=90,
                edgecolor='#f3e8ff', zorder=5)
ax4.set_xlabel('Brix', color='#e9d5ff', fontsize=11)
ax4.set_ylabel('Malic acid (g/L)', color='#e9d5ff', fontsize=11)
ax4.set_title('Ripening phase plane (Brix, Malate)',
              color='#f3e8ff', fontsize=12, fontweight='bold')
ax4.legend(facecolor='#1e1b4b', edgecolor='#581c87', labelcolor='#e9d5ff', fontsize=9)

# Integrate cumulative degree-days of warm ripening in the 25 C case
T = 25.0
dd = np.trapezoid(np.full_like(days, max(T - 10, 0)), days)
print(f"Cumulative growing degree-days (trapezoid, base 10 C, {T} C, 45 d): {dd:.1f} GDD")

# Malic acid half-life at each temperature
for label, T in T_cases.items():
    t_half = np.log(2) / km_of_T(T)
    print(f"  {label}: Malic half-life = {t_half:.1f} d")

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print("Malic acid decay is ~5x faster at 25 C than at 15 C (Q10=2.7)")
print("Warm-climate low-acid wines: high pH, less structure")
print("Cool-climate wines: high malate/TA, low pH, more structure")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Key References

• Smart, R. & Robinson, M. (1991). Sunlight Into Wine: A Handbook for Winegrape Canopy Management. Winetitles, Adelaide.

• Monsi, M. & Saeki, T. (1953). “Uber den Lichtfaktor in den Pflanzengesellschaften.” Japanese Journal of Botany, 14, 22–52.

• Farquhar, G. D., von Caemmerer, S. & Berry, J. A. (1980). “A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species.” Planta, 149, 78–90.

• Lakso, A. N. & Poni, S. (2003). “VineSim: a process-based vine growth and yield model.” Acta Horticulturae, 707, 307–316.

• Kliewer, W. M. & Dokoozlian, N. K. (2005). “Leaf area/crop weight ratios of grapevines: influence on fruit composition and wine quality.” American Journal of Enology and Viticulture, 56, 170–181.

• Jackson, D. I. & Lombard, P. B. (1993). “Environmental and management practices affecting grape composition and wine quality - a review.” American Journal of Enology and Viticulture, 44, 409–430.

• Winkler, A. J., Cook, J. A., Kliewer, W. M. & Lider, L. A. (1974). General Viticulture. University of California Press.

• Keller, M. (2020). The Science of Grapevines, 3rd edition. Academic Press.

• Ruffner, H. P. (1982). “Metabolism of tartaric and malic acids in Vitis: a review, part A.” Vitis, 21, 247–259.

• Sweetman, C., Deluc, L. G., Cramer, G. R., Ford, C. M. & Soole, K. L. (2009). “Regulation of malate metabolism in grape berry and other developing fruits.” Phytochemistry, 70, 1329–1344.

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