Module 2

Ocean Chemistry & Life

Acidification, deoxygenation, and the unravelling of marine ecosystems

2.1 Ocean Acidification: The Carbonate System

The ocean absorbs approximately 25% of anthropogenic CO$_2$ emissions. When CO$_2$ dissolves in seawater, it initiates a series of chemical reactions that increase acidity. The full carbonate equilibrium chain:

$ \text{CO}_2\text{(g)} \rightleftharpoons \text{CO}_2\text{(aq)} + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^- \rightleftharpoons 2\text{H}^+ + \text{CO}_3^{2-} $

The equilibrium constants governing these reactions (at 25 °C, salinity 35):

$ K_0 = \frac{[\text{CO}_2\text{(aq)}]}{p\text{CO}_2} \approx 3.4 \times 10^{-2}\;\text{mol/(L}\cdot\text{atm)} $

Henry's law solubility (CO$_2$ dissolution)

$ K_1 = \frac{[\text{H}^+][\text{HCO}_3^-]}{[\text{CO}_2\text{(aq)}]} \approx 1.4 \times 10^{-6}\;\text{mol/L} \quad (pK_1 = 5.86) $

First dissociation (carbonic acid to bicarbonate)

$ K_2 = \frac{[\text{H}^+][\text{CO}_3^{2-}]}{[\text{HCO}_3^-]} \approx 1.1 \times 10^{-9}\;\text{mol/L} \quad (pK_2 = 8.92) $

Second dissociation (bicarbonate to carbonate)

The Bjerrum Plot

The Bjerrum plot shows the relative concentrations of the three dissolved inorganic carbon (DIC) species as a function of pH. At seawater pH ($\sim 8.1$), the dominant species is bicarbonate ($\text{HCO}_3^-$,$\sim 90\%$), with carbonate ($\text{CO}_3^{2-}$, $\sim 9\%$) and dissolved CO$_2$ ($\sim 1\%$).

The fractions are derived from the equilibrium constants. Defining total DIC:

$ \text{DIC} = [\text{CO}_2] + [\text{HCO}_3^-] + [\text{CO}_3^{2-}] $

The fraction of each species as a function of $[\text{H}^+]$:

$ \alpha_0 = \frac{[\text{CO}_2]}{\text{DIC}} = \frac{[\text{H}^+]^2}{[\text{H}^+]^2 + K_1[\text{H}^+] + K_1 K_2} $

$ \alpha_1 = \frac{[\text{HCO}_3^-]}{\text{DIC}} = \frac{K_1[\text{H}^+]}{[\text{H}^+]^2 + K_1[\text{H}^+] + K_1 K_2} $

$ \alpha_2 = \frac{[\text{CO}_3^{2-}]}{\text{DIC}} = \frac{K_1 K_2}{[\text{H}^+]^2 + K_1[\text{H}^+] + K_1 K_2} $

pH Change Since Preindustrial

Ocean surface pH has dropped from approximately 8.21 (preindustrial) to 8.10 (present). This 0.11 unit drop corresponds to:

$ \frac{[\text{H}^+]_{\text{now}}}{[\text{H}^+]_{\text{pre}}} = 10^{8.21 - 8.10} = 10^{0.11} \approx 1.29 $

A 29% increase in hydrogen ion concentration — often quoted as “30% more acidic.” Simultaneously, carbonate ion concentration has decreased by approximately 16%:

$ [\text{CO}_3^{2-}] \text{ decreased from } \sim 225\;\mu\text{mol/kg to } \sim 190\;\mu\text{mol/kg} $

Under SSP5-8.5, ocean pH is projected to decline to approximately 7.7 by 2100, representing a 150% increase in H$^+$ concentration — a rate of change unprecedented in at least 66 million years (since the Paleocene-Eocene Thermal Maximum).

2.2 The Calcification Crisis

Many marine organisms build shells and skeletons from calcium carbonate (CaCO$_3$). The ability to do so depends on the saturation state($\Omega$) of seawater with respect to the mineral form used:

$ \Omega_{\text{aragonite}} = \frac{[\text{Ca}^{2+}][\text{CO}_3^{2-}]}{K_{\text{sp,arag}}} $

where:

• $[\text{Ca}^{2+}] \approx 10.3\;\text{mmol/kg}$ — essentially constant in seawater
• $[\text{CO}_3^{2-}]$ — decreases as ocean absorbs CO$_2$
• $K_{\text{sp,arag}} \approx 6.5 \times 10^{-7}\;\text{mol}^2/\text{kg}^2$ (at 25 °C, surface)

When $\Omega > 1$, seawater is supersaturated and calcification is thermodynamically favoured. When $\Omega < 1$, shells and skeletons begin to dissolve. Current surface ocean values:

Tropical surface

Ω ≈ 3.5-4.0

Supersaturated (but declining)

Temperate surface

Ω ≈ 2.0-3.0

Moderately supersaturated

Polar surface

Ω ≈ 1.0-1.5

Near undersaturation

Deep ocean (>2000m)

Ω < 1

Undersaturated (aragonite dissolves)

Deriving $\Omega$ vs Atmospheric CO$_2$

Since $[\text{Ca}^{2+}]$ is constant, the saturation state tracks carbonate ion concentration, which decreases as CO$_2$ is absorbed. The relationship can be derived from the Revelle factor $R$:

$ \frac{\Delta[\text{CO}_3^{2-}]}{[\text{CO}_3^{2-}]} \approx -\frac{\Delta \text{DIC}}{\text{DIC}} \cdot \frac{R-1}{R} \approx -0.016 \cdot \frac{\Delta p\text{CO}_2}{p\text{CO}_2} $

For a doubling of atmospheric CO$_2$ (280 to 560 ppm), carbonate ion concentration decreases by approximately 40%, pushing $\Omega_{\text{arag}}$ from ~4 to ~2.4 in the tropics and below 1 in polar waters.

Organisms at Risk

Pteropods (sea butterflies)

Thin aragonite shells dissolve below Ω = 1.5. Already showing shell thinning in Southern Ocean. Key food for salmon and whales.

Coccolithophores

Calcite plates (coccoliths) affected below Ω_calcite = 2. Major phytoplankton group; decline would alter ocean albedo and carbon export.

Reef-building corals

Calcification rate drops ~30% for each unit decrease in Ω. Below Ω = 3, net reef dissolution exceeds accretion.

Oysters and mussels

Larval stages especially sensitive; hatchery failures already observed in Pacific Northwest (Barton et al. 2012).

2.3 Ocean Deoxygenation

The ocean has lost approximately 2% of its dissolved oxygen since the 1960s, with oxygen minimum zones (OMZs) expanding by 3–8% in volume. Two mechanisms drive this loss:

Solubility Effect (Henry's Law)

Oxygen solubility decreases with temperature. From Henry's law:

$ [\text{O}_2]_{\text{sat}} = K_H(T) \cdot p\text{O}_2 $

The temperature dependence of the Henry's law constant for O$_2$ in seawater can be approximated:

$ \ln K_H = A_1 + \frac{A_2}{T} + A_3 \ln T + A_4 T + S \left(B_1 + \frac{B_2}{T} + B_3 T^2\right) $

where $T$ is absolute temperature and $S$ is salinity. A simpler approximation: O$_2$ solubility decreases by approximately 2% per °C warming. For a 3 °C warming, this alone reduces surface O$_2$ saturation by ~6%.

Stratification Effect

Warming preferentially heats the upper ocean, strengthening density stratification. The stratification parameter:

$ N^2 = -\frac{g}{\rho_0}\frac{\partial \rho}{\partial z} $

where $N$ is the Brunt-Väisälä (buoyancy) frequency. Increased stratification ($N^2$ increasing) reduces vertical mixing, which:

• Reduces ventilation of deep waters (less O$_2$ transported downward)
• Reduces nutrient upwelling (less primary production at surface in some regions)
• Expands oxygen minimum zones (OMZs), compressing habitable depth ranges

Habitat Compression Index

The habitat compression index (HCI) quantifies how the vertical range available to aerobic organisms shrinks as oxygen declines and temperatures rise:

$ \text{HCI} = \frac{z_{\text{oxy}} - z_{\text{therm}}}{z_{\text{oxy,ref}} - z_{\text{therm,ref}}} $

where $z_{\text{oxy}}$ is the depth of the hypoxic boundary ($[\text{O}_2] < 60\;\mu\text{mol/kg}$) and $z_{\text{therm}}$is the depth of the thermal tolerance limit. As OMZs shoal (shallower) and surface waters warm, the habitable vertical range compresses. For tropical tunas, this compression exceeds 15% in some eastern Pacific regions, concentrating fish in a thinner surface layer.

2.4 Fisheries Under Warming

Marine fisheries are being reorganised by warming. The two standard stock-recruitment models show how warming affects sustainable yield.

Ricker Model

The Ricker model describes spawner-recruit dynamics with density-dependent mortality:

$ R = \alpha S \, e^{-\beta S} $

where $R$ is recruitment, $S$ is spawning stock biomass,$\alpha$ is productivity (recruits per spawner at low density), and$\beta$ controls density dependence. The maximum sustainable yield (MSY) occurs at:

$ S_{\text{MSY}} = \frac{1}{\beta}, \quad \text{MSY} = \frac{\alpha}{\beta e} $

Beverton-Holt Model

The Beverton-Holt model assumes compensatory (not overcompensatory) density dependence:

$ R = \frac{\alpha S}{1 + \beta S} $

Temperature Effect on MSY

Productivity $\alpha$ depends on temperature through metabolic scaling. For species near their thermal optimum, further warming decreases $\alpha$:

$ \alpha(T) = \alpha_{\text{opt}} \cdot \exp\!\left[-\frac{(T - T_{\text{opt}})^2}{2\sigma_T^2}\right] $

This gives a temperature-dependent MSY. Global analyses (Free et al. 2019) estimate that warming has already reduced maximum sustainable yield of assessed populations by 4.1% on average since 1930. Tropical fisheries show the largest declines (up to 35%), while some high-latitude stocks have temporarily benefited.

Poleward Redistribution

Marine species are shifting poleward at a rate of approximately 70 km per decade (Poloczanska et al. 2013), far faster than terrestrial species (~17 km/decade). This has profound geopolitical implications:

• Winners: High-latitude nations (Norway, Iceland, Russia) gaining species and productivity
• Losers: Tropical nations (many developing countries) losing catch potential by 40–60% under SSP5-8.5
• Conflict zones: Transboundary stocks crossing national EEZ boundaries create disputes

2.5 Deep Ocean Carbon Storage

The ocean stores approximately 38,000 GtC — 50 times the atmosphere. Two major mechanisms transport carbon to the deep ocean:

The Biological Pump

Photosynthesis in the surface ocean fixes CO$_2$ into organic matter. A fraction (the export ratio, typically 5–25%) sinks below the mixed layer as dead organisms, faecal pellets, and marine snow. The Martin curve describes the attenuation of sinking particulate organic carbon (POC) with depth:

$ F(z) = F_{100} \left(\frac{z}{100}\right)^{-b} $

where $F_{100}$ is the flux at 100 m depth, $z$ is depth in metres, and $b \approx 0.86$ (Martin et al. 1987). This means approximately 90% of exported organic carbon is remineralised (converted back to CO$_2$) in the upper 1000 m.

Thermohaline Circulation

The solubility pump works through the thermohaline (overturning) circulation. Cold, dense water forming at high latitudes is enriched in CO$_2$ (higher solubility) and sinks to the abyss. The residence time of deep ocean carbon:

$ \tau_{\text{deep}} = \frac{V_{\text{deep}} \cdot [\text{DIC}]_{\text{deep}}}{F_{\text{overturning}}} \approx \frac{1.0 \times 10^{18}\;\text{m}^3 \times 2.3\;\text{mol/m}^3}{20\;\text{Sv}} \approx 800{-}1200\;\text{years} $

where 1 Sv = $10^6\;\text{m}^3/\text{s}$. This long residence time means that anthropogenic CO$_2$ absorbed today will influence ocean chemistry for centuries to millennia.

Climate change weakens both pumps: warming reduces solubility (less CO$_2$ absorbed), stratification reduces both mixing and nutrient supply (weakening the biological pump), and potential slowdown of the Atlantic Meridional Overturning Circulation (AMOC) reduces deep water formation. These feedbacks could reduce the ocean carbon sink by 20–40% by 2100 under high-emission scenarios.

Bjerrum Plot: Carbonate Species vs pH

The relative abundance of dissolved inorganic carbon species as a function of seawater pH:

Bjerrum plot for the seawater carbonate system at 25 °C, salinity 35. At seawater pH (~8.1), bicarbonate dominates (~90%). The shift from pH 8.2 to 7.7 dramatically reduces carbonate ion availability for shell-building organisms.

Computational Simulations

Ocean pH and Aragonite Saturation Projections

Python

script.py179 lines

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

fig, axes = plt.subplots(2, 2, figsize=(14, 11))
fig.patch.set_facecolor('#0a0a1a')
for ax in axes.flatten():
    ax.set_facecolor('#0a0a1a')

# Panel 1: Bjerrum plot (computed)
ax1 = axes[0, 0]
pK1 = 5.86
pK2 = 8.92
K1 = 10**(-pK1)
K2 = 10**(-pK2)

pH_range = np.linspace(4, 12, 500)
H = 10**(-pH_range)

denom = H**2 + K1*H + K1*K2
alpha_CO2 = H**2 / denom
alpha_HCO3 = K1*H / denom
alpha_CO3 = K1*K2 / denom

ax1.plot(pH_range, alpha_CO2, color='#ef4444', linewidth=2.5, label='CO$_2$(aq)')
ax1.plot(pH_range, alpha_HCO3, color='#22c55e', linewidth=2.5, label='HCO$_3^-$')
ax1.plot(pH_range, alpha_CO3, color='#3b82f6', linewidth=2.5, label='CO$_3^{2-}$')

# Mark current and projected pH
ax1.axvline(x=8.2, color='#22d3ee', linestyle='--', alpha=0.7, linewidth=1.5)
ax1.axvline(x=8.1, color='#f97316', linestyle='--', alpha=0.7, linewidth=1.5)
ax1.axvline(x=7.7, color='#ef4444', linestyle='--', alpha=0.7, linewidth=1.5)
ax1.text(8.25, 0.85, 'Pre-industrial', color='#22d3ee', fontsize=8, rotation=90)
ax1.text(7.85, 0.85, 'Current', color='#f97316', fontsize=8, rotation=90)
ax1.text(7.45, 0.85, '2100 (RCP8.5)', color='#ef4444', fontsize=8, rotation=90)

ax1.set_xlabel('pH', color='white', fontsize=11)
ax1.set_ylabel('Fraction of DIC', color='white', fontsize=11)
ax1.set_title('Bjerrum Plot: Carbonate Speciation', color='white', fontsize=13, fontweight='bold')
ax1.legend(fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')
ax1.set_xlim(4, 12)

# Panel 2: Ocean pH projections under 3 scenarios
ax2 = axes[0, 1]
years = np.arange(1850, 2101)

def ocean_ph(yr, scenario):
    if scenario == 'SSP1-2.6':
        if yr < 1960: return 8.21 - (yr-1850)*0.0001
        elif yr < 2020: return 8.20 - (yr-1960)*0.0018
        elif yr < 2050: return 8.09 - (yr-2020)*0.001
        else: return 8.06 - (yr-2050)*0.0002
    elif scenario == 'SSP2-4.5':
        if yr < 1960: return 8.21 - (yr-1850)*0.0001
        elif yr < 2020: return 8.20 - (yr-1960)*0.0018
        else: return 8.09 - (yr-2020)*0.003
    else:  # SSP5-8.5
        if yr < 1960: return 8.21 - (yr-1850)*0.0001
        elif yr < 2020: return 8.20 - (yr-1960)*0.0018
        else: return 8.09 - (yr-2020)*0.005

scenarios_ph = {'SSP1-2.6': '#22c55e', 'SSP2-4.5': '#eab308', 'SSP5-8.5': '#ef4444'}
for scen, col in scenarios_ph.items():
    ph = [ocean_ph(yr, scen) for yr in years]
    ax2.plot(years, ph, color=col, linewidth=2.5, label=scen)

ax2.axhline(y=8.0, color='#94a3b8', linestyle=':', alpha=0.4)
ax2.set_xlabel('Year', color='white', fontsize=11)
ax2.set_ylabel('Surface Ocean pH', color='white', fontsize=11)
ax2.set_title('Ocean pH Projections', color='white', fontsize=13, fontweight='bold')
ax2.legend(fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')

# Panel 3: Aragonite saturation vs CO2
ax3 = axes[1, 0]
co2_levels = np.linspace(280, 1200, 500)

# Simplified model: Omega decreases roughly logarithmically with CO2
# Omega_arag ~ 4.0 at 280 ppm, drops following carbonate chemistry
omega_ref = 4.0
# Approximate: each doubling reduces omega by ~40%
omega = omega_ref * (280 / co2_levels)**0.5

# Different regions
omega_tropical = omega * 1.0
omega_temperate = omega * 0.65
omega_polar = omega * 0.35

ax3.plot(co2_levels, omega_tropical, color='#ef4444', linewidth=2.5, label='Tropical')
ax3.plot(co2_levels, omega_temperate, color='#eab308', linewidth=2.5, label='Temperate')
ax3.plot(co2_levels, omega_polar, color='#06b6d4', linewidth=2.5, label='Polar')

ax3.axhline(y=1.0, color='#ef4444', linestyle='--', alpha=0.7, linewidth=1.5)
ax3.text(290, 1.1, 'Dissolution threshold (\u03a9 = 1)', color='#ef4444', fontsize=9)
ax3.axhline(y=3.0, color='#f97316', linestyle='--', alpha=0.5, linewidth=1)
ax3.text(290, 3.1, 'Coral reef threshold (\u03a9 ~ 3)', color='#f97316', fontsize=9)

ax3.axvline(x=420, color='#94a3b8', linestyle=':', alpha=0.5)
ax3.text(425, 3.5, 'Current\n(~420 ppm)', color='#94a3b8', fontsize=8)

ax3.set_xlabel('Atmospheric CO\u2082 (ppm)', color='white', fontsize=11)
ax3.set_ylabel('\u03a9 aragonite', color='white', fontsize=11)
ax3.set_title('Aragonite Saturation vs CO\u2082', color='white', fontsize=13, fontweight='bold')
ax3.legend(fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')

# Panel 4: O2 solubility vs temperature + fisheries MSY shift
ax4 = axes[1, 1]
temp_c = np.linspace(0, 35, 200)
# O2 saturation in seawater (Garcia & Gordon 1992, simplified)
# Using Weiss (1970) approximation
temp_k = temp_c + 273.15
# Simplified: O2_sat ~ 14.6 - 0.4*T + 0.007*T^2 - 0.00006*T^3 (mg/L, freshwater approx)
o2_sat = 14.6 - 0.4*temp_c + 0.007*temp_c**2 - 0.00006*temp_c**3
# Convert to umol/kg (approx: mg/L * 31.25)
o2_umol = o2_sat * 31.25

ax4_twin = ax4.twinx()

ax4.plot(temp_c, o2_umol, color='#06b6d4', linewidth=2.5, label='O\u2082 solubility')
ax4.fill_between(temp_c, o2_umol, 0, color='#06b6d4', alpha=0.1)

# Hypoxia threshold
ax4.axhline(y=60, color='#ef4444', linestyle='--', alpha=0.7, linewidth=1.5)
ax4.text(26, 65, 'Hypoxia threshold', color='#ef4444', fontsize=9)

# MSY relative change on twin axis
msy_rel = np.exp(-0.03 * (temp_c - 15)**2 / (2 * 5**2))  # Gaussian around 15C
msy_rel = msy_rel / np.max(msy_rel) * 100
ax4_twin.plot(temp_c, msy_rel, color='#f97316', linewidth=2, linestyle='--', label='Relative MSY')
ax4_twin.set_ylabel('Relative MSY (%)', color='#f97316', fontsize=11)
ax4_twin.tick_params(axis='y', colors='#f97316')

ax4.set_xlabel('Temperature (\u00b0C)', color='white', fontsize=11)
ax4.set_ylabel('O\u2082 saturation (\u03bcmol/kg)', color='#06b6d4', fontsize=11)
ax4.set_title('O\u2082 Solubility and Fisheries MSY', color='white', fontsize=13, fontweight='bold')
ax4.tick_params(axis='y', colors='#06b6d4')

# Combined legend
lines1, labels1 = ax4.get_legend_handles_labels()
lines2, labels2 = ax4_twin.get_legend_handles_labels()
ax4.legend(lines1 + lines2, labels1 + labels2, fontsize=9,
           facecolor='#1e293b', edgecolor='#334155', labelcolor='white', loc='upper right')

for ax in axes.flatten():
    ax.tick_params(colors='white')
    ax.spines['bottom'].set_color('#334155')
    ax.spines['left'].set_color('#334155')
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.grid(True, alpha=0.15, color='#334155')
ax4_twin.spines['top'].set_visible(False)
ax4_twin.spines['right'].set_color('#f97316')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight')

print("Ocean Chemistry Analysis")
print("=" * 50)
print("\nCarbonate Species at Different pH Values:")
for ph_val in [8.2, 8.1, 7.7]:
    h = 10**(-ph_val)
    d = h**2 + K1*h + K1*K2
    a0 = h**2 / d
    a1 = K1*h / d
    a2 = K1*K2 / d
    print(f"  pH {ph_val}: CO2={a0*100:.1f}%, HCO3-={a1*100:.1f}%, CO3^2-={a2*100:.1f}%")

print(f"\nH+ increase from pH 8.2 to 8.1: {10**(8.2-8.1)*100-100:.0f}%")
print(f"H+ increase from pH 8.2 to 7.7: {10**(8.2-7.7)*100-100:.0f}%")

print("\nAragonite saturation (tropical surface):")
for co2 in [280, 420, 560, 800, 1100]:
    om = 4.0 * (280/co2)**0.5
    print(f"  CO2 = {co2} ppm: Omega_arag = {om:.2f} ({'OK' if om > 3 else 'STRESS' if om > 1 else 'DISSOLUTION'})")

print("\nO2 solubility decrease with warming:")
for t in [5, 15, 25, 30]:
    o2 = (14.6 - 0.4*t + 0.007*t**2 - 0.00006*t**3) * 31.25
    print(f"  T={t}C: O2_sat = {o2:.0f} umol/kg")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Fisheries Stock-Recruitment Under Warming

Python

script.py107 lines

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

fig, axes = plt.subplots(1, 3, figsize=(16, 5.5))
fig.patch.set_facecolor('#0a0a1a')
for ax in axes:
    ax.set_facecolor('#0a0a1a')

# Panel 1: Ricker model at different temperatures
ax1 = axes[0]
S = np.linspace(0, 10, 500)
beta = 0.3

temps_fish = [10, 15, 20, 25, 30]
colors_fish = ['#06b6d4', '#22c55e', '#eab308', '#f97316', '#ef4444']
T_opt = 15  # optimal temperature for this species

for T, col in zip(temps_fish, colors_fish):
    # Temperature-dependent alpha
    alpha = 3.0 * np.exp(-(T - T_opt)**2 / (2 * 7**2))
    R = alpha * S * np.exp(-beta * S)
    ax1.plot(S, R, color=col, linewidth=2, label=f'T = {T}\u00b0C')

# MSY point
    S_msy = 1 / beta
    R_msy = alpha * S_msy * np.exp(-1)
    ax1.plot(S_msy, R_msy, 'o', color=col, markersize=6)

ax1.plot(S, S, color='#94a3b8', linestyle=':', alpha=0.5, linewidth=1)
ax1.text(8.5, 8, 'R = S', color='#94a3b8', fontsize=9)
ax1.set_xlabel('Spawning Stock (S)', color='white', fontsize=11)
ax1.set_ylabel('Recruitment (R)', color='white', fontsize=11)
ax1.set_title('Ricker Model vs Temperature', color='white', fontsize=13, fontweight='bold')
ax1.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='white')

# Panel 2: MSY vs temperature
ax2 = axes[1]
T_range = np.linspace(0, 35, 200)
alpha_T = 3.0 * np.exp(-(T_range - T_opt)**2 / (2 * 7**2))
MSY = alpha_T / (beta * np.e)

ax2.fill_between(T_range, MSY, 0, color='#06b6d4', alpha=0.15)
ax2.plot(T_range, MSY, color='#06b6d4', linewidth=2.5)
ax2.axvline(x=T_opt, color='#22c55e', linestyle='--', alpha=0.7, linewidth=1.5)
ax2.text(T_opt + 0.5, np.max(MSY) * 0.95, f'T_opt = {T_opt}\u00b0C', color='#22c55e', fontsize=10)

# Mark warming impact
for dT, col in [(0, '#22c55e'), (2, '#eab308'), (4, '#f97316'), (6, '#ef4444')]:
    T_cur = T_opt + dT
    msy_cur = 3.0 * np.exp(-(T_cur - T_opt)**2 / (2 * 7**2)) / (beta * np.e)
    ax2.plot(T_cur, msy_cur, 'o', color=col, markersize=8, zorder=5)
    pct_loss = (1 - msy_cur / np.max(MSY)) * 100
    if dT > 0:
        ax2.annotate(f'+{dT}\u00b0C\n-{pct_loss:.0f}%', (T_cur, msy_cur),
                     textcoords='offset points', xytext=(12, 5),
                     fontsize=9, color=col)

ax2.set_xlabel('Temperature (\u00b0C)', color='white', fontsize=11)
ax2.set_ylabel('Maximum Sustainable Yield', color='white', fontsize=11)
ax2.set_title('MSY Shift With Warming', color='white', fontsize=13, fontweight='bold')

# Panel 3: Poleward shift of fisheries
ax3 = axes[2]
decades = np.arange(1970, 2060, 10)
# Stylized catch data by latitude band (relative units)
tropical = [40, 38, 35, 30, 25, 20, 15, 12, 10]
temperate = [30, 32, 33, 35, 34, 33, 30, 28, 25]
polar = [5, 6, 8, 12, 18, 25, 32, 38, 42]

ax3.stackplot(decades, tropical, temperate, polar,
              colors=['#ef4444', '#eab308', '#06b6d4'],
              labels=['Tropical', 'Temperate', 'Polar/Subpolar'],
              alpha=0.7)
ax3.set_xlabel('Decade', color='white', fontsize=11)
ax3.set_ylabel('Relative Catch Potential', color='white', fontsize=11)
ax3.set_title('Fisheries Redistribution', color='white', fontsize=13, fontweight='bold')
ax3.legend(fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='white', loc='upper left')

for ax in axes:
    ax.tick_params(colors='white')
    ax.spines['bottom'].set_color('#334155')
    ax.spines['left'].set_color('#334155')
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.grid(True, alpha=0.15, color='#334155')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight')

print("Fisheries Under Climate Change")
print("=" * 50)
print("\nRicker Model MSY = alpha / (beta * e)")
print(f"  beta = {beta}, T_opt = {T_opt}\u00b0C")
print("\nMSY loss with warming above T_opt:")
for dT in [0, 1, 2, 3, 4, 5, 6]:
    alpha_val = 3.0 * np.exp(-(dT)**2 / (2 * 7**2))
    msy_val = alpha_val / (beta * np.e)
    msy_ref = 3.0 / (beta * np.e)
    loss = (1 - msy_val/msy_ref) * 100
    print(f"  +{dT}\u00b0C: MSY = {msy_val:.2f} ({loss:.1f}% loss)")

print("\nGlobal fisheries redistribution:")
print("  Tropical catch potential: declining 40-60% by 2100 (SSP5-8.5)")
print("  Polar catch potential: increasing, new species arriving")
print("  Shift rate: ~70 km/decade poleward for marine species")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

• Doney, S.C. et al. (2009). Ocean acidification: The other CO$_2$ problem. Annual Review of Marine Science, 1, 169–192.
• Orr, J.C. et al. (2005). Anthropogenic ocean acidification over the twenty-first century and its impact on calcifying organisms. Nature, 437, 681–686.
• Keeling, R.F., Körtzinger, A. & Gruber, N. (2010). Ocean deoxygenation in a warming world. Annual Review of Marine Science, 2, 199–229.
• Free, C.M. et al. (2019). Impacts of historical warming on marine fisheries production. Science, 363(6430), 979–983.
• Poloczanska, E.S. et al. (2013). Global imprint of climate change on marine life. Nature Climate Change, 3, 919–925.
• Martin, J.H. et al. (1987). VERTEX: Carbon cycling in the northeast Pacific. Deep Sea Research, 34(2), 267–285.
• Barton, A. et al. (2012). The Pacific oyster, Crassostrea gigas, shows negative correlation to naturally elevated carbon dioxide levels. Limnology and Oceanography, 57(3), 698–710.
• Zeebe, R.E. & Wolf-Gladrow, D. (2001). CO$_2$ in Seawater: Equilibrium, Kinetics, Isotopes. Elsevier Oceanography Series.
• IPCC, 2019: Special Report on the Ocean and Cryosphere in a Changing Climate.

Ocean Chemistry & Life

2.1 Ocean Acidification: The Carbonate System

The Bjerrum Plot

pH Change Since Preindustrial

2.2 The Calcification Crisis

Deriving \(\Omega\) vs Atmospheric CO\(_2\)

Organisms at Risk

2.3 Ocean Deoxygenation

Solubility Effect (Henry's Law)

Stratification Effect

Habitat Compression Index

2.4 Fisheries Under Warming

Ricker Model

Beverton-Holt Model

Temperature Effect on MSY

Poleward Redistribution

2.5 Deep Ocean Carbon Storage

The Biological Pump

Thermohaline Circulation

Bjerrum Plot: Carbonate Species vs pH

Computational Simulations

Ocean pH and Aragonite Saturation Projections

Fisheries Stock-Recruitment Under Warming

References