Module 7

Sea Level Rise & Ice Sheet Dynamics

Thermal expansion, Greenland and Antarctic ice sheets, instability mechanisms, and projections

Sea level rise is one of the most consequential impacts of climate change, threatening coastal cities, small island nations, and low-lying deltas housing hundreds of millions of people. Since 1900, global mean sea level has risen ~20 cm, accelerating from ~1.3 mm/yr (20th century) to ~3.7 mm/yr (2006–2018). The physics spans thermodynamics (ocean thermal expansion), glaciology (ice sheet dynamics), and solid-Earth geophysics (isostatic adjustment). Understanding the instability mechanisms in ice sheets is crucial because they could produce sea level rise far exceeding current projections.

7.1 Thermosteric Sea Level Rise

As the ocean absorbs heat, seawater expands. This thermosteric component has contributed roughly 40% of observed sea level rise since 1993. The sea level change from thermal expansion is:

$\Delta h_{\text{thermo}} = \int_0^D \alpha(T, S, p) \cdot \Delta T(z) \, dz$

where $\alpha$ is the thermal expansion coefficient (K$^{-1}$),$\Delta T(z)$ is the temperature change at depth $z$, and$D$ is the ocean depth. The expansion coefficient depends on temperature, salinity, and pressure:

$\alpha = -\frac{1}{\rho}\frac{\partial \rho}{\partial T}\bigg|_{S,p}$

Crucially, $\alpha$ increases with temperature: warm water expands more per degree of warming than cold water. At 5°C, $\alpha \approx 1.0 \times 10^{-4}$ K$^{-1}$; at 25°C, $\alpha \approx 3.0 \times 10^{-4}$ K$^{-1}$. This means tropical oceans contribute disproportionately to thermosteric rise.

From Ocean Heat Content to Sea Level

The ocean has absorbed over 90% of the excess heat from global warming. The ocean heat content (OHC) change is related to thermosteric sea level rise by:

$\Delta h_{\text{thermo}} = \frac{\alpha}{\rho c_p} \cdot \frac{\Delta \text{OHC}}{A_{\text{ocean}}}$

where $\rho \approx 1025$ kg/m$^3$ is the mean seawater density,$c_p \approx 3990$ J/(kg·K) is the specific heat capacity, and$A_{\text{ocean}} \approx 3.6 \times 10^{14}$ m$^2$ is the ocean area. The OHC increase from 1971 to 2018 was ~436 ZJ (0–2000 m), producing ~8 cm of thermosteric rise.

Thermal expansion is a committed process: even if greenhouse gas concentrations stabilized today, the deep ocean would continue warming for centuries as heat diffuses downward, contributing an additional 0.5–1 m of sea level rise over the coming millennium.

7.2 Greenland Ice Sheet

The Greenland Ice Sheet (GrIS) contains enough ice to raise global sea level by ~7.4 m. It has been losing mass at an accelerating rate: ~34 Gt/yr in the 1990s, ~215 Gt/yr in 2012–2017, and ~270 Gt/yr in recent years. The mass balance is determined by the surface mass balance (SMB) and ice discharge:

$\frac{dM}{dt} = \text{SMB} - D = (P - M - R) - D$

where $P$ is precipitation (snowfall), $M$ is surface melt,$R$ is meltwater runoff, and $D$ is dynamic discharge (calving and submarine melt). Currently, about 50% of mass loss is from SMB changes and 50% from dynamic discharge, though SMB is becoming increasingly dominant.

Positive Degree Day Model

Surface melt is commonly estimated using the positive degree day (PDD) approach, which relates melt to the integral of temperatures above a threshold:

$M = f_{\text{PDD}} \cdot \text{PDD} = f_{\text{PDD}} \cdot \int_{\text{year}} \max(T(t) - T_{\text{threshold}}, \, 0) \, dt$

The PDD factor $f_{\text{PDD}}$ differs for snow (~3–5 mm w.e./°C·day) and ice (~8–20 mm w.e./°C·day), reflecting the lower albedo of bare ice. The threshold temperature $T_{\text{threshold}}$ is typically set to 0°C.

Elevation–Melt Feedback

A critical positive feedback in Greenland: as the ice sheet thins, its surface reaches lower elevations where temperatures are warmer (lapse rate ~6.5°C/km). This increases melt, which further lowers the surface — a self-amplifying cycle. The feedback implies a threshold: once sufficient thinning occurs, the ice sheet cannot regrow even if temperatures return to pre-industrial levels. Current estimates place this threshold at ~1.5–3°C global warming above pre-industrial.

7.3 Antarctic Ice Sheet & Marine Instabilities

The Antarctic Ice Sheet (AIS) holds enough ice to raise sea level by ~58 m. While East Antarctica is mostly stable (grounded above sea level), West Antarctica (WAIS) is a marine ice sheet — much of it grounded below sea level on a bed that slopes inward (retrograde slope). This geometry makes it vulnerable to an instability mechanism first identified by Weertman (1974) and formalized by Schoof (2007).

Marine Ice Sheet Instability (MISI)

At the grounding line — where the ice sheet transitions from grounded to floating — the ice flux is a strong function of ice thickness. Schoof (2007) showed that for a power-law rheology, the flux at the grounding line scales as:

$Q_g = C \cdot h_g^{n+2} \quad \text{where } n \approx 3 \text{ (Glen's flow law exponent)}$

The key result: since $n + 2 \approx 5$, the flux increases very steeply with ice thickness. On a retrograde bed (bed deepening inland), if the grounding line retreats slightly, it encounters thicker ice. Thicker ice means higher flux, which causes further thinning and retreat. This creates a positive feedback — retreat on a retrograde bed is inherently unstable.

The full Schoof (2007) boundary condition at the grounding line is:

$Q_g = \left(\frac{A(\rho_i g)^{n+1}(1 - \rho_i/\rho_w)^n}{4^n C_b}\right)^{\frac{1}{n+1}} h_g^{\frac{n(n+2)}{n+1}}$

where $A$ is the ice softness parameter (Glen’s law), $\rho_i$ and$\rho_w$ are ice and water densities, $g$ is gravitational acceleration, and $C_b$ is the basal friction coefficient. The stability criterion is that the bed must slope seaward (prograde) for the grounding line to be stable; retrograde slopes are unconditionally unstable.

Thwaites Glacier

Thwaites Glacier (“Doomsday Glacier”) drains a basin containing ~65 cm of potential sea level rise. Its grounding line sits on a retrograde bed, and observations show it has retreated ~14 km since the late 1990s. Warm Circumpolar Deep Water reaching the grounding line triggers submarine melting at ~40–80 m/yr, driving grounding line retreat. The International Thwaites Glacier Collaboration (ITGC) has found that unstable retreat may already be underway.

Marine Ice Cliff Instability (MICI)

If an ice shelf disintegrates (as Larsen B did in 2002), it can expose a tall ice cliff at the grounding line. If the cliff exceeds a critical height, the tensile stress from the ice’s own weight exceeds its strength, causing structural collapse. We can derive the maximum stable cliff height:

$\sigma_{\text{tensile}} = \rho_i g H_{\text{cliff}} / 2 \quad \Rightarrow \quad H_{\max} = \frac{2\sigma_T}{\rho_i g}$

With the tensile strength of ice $\sigma_T \approx 0.5\text{--}1$ MPa and $\rho_i = 917$ kg/m$^3$:

$H_{\max} = \frac{2 \times 10^6}{917 \times 9.81} \approx 220 \text{ m (upper bound)}$

More realistic estimates accounting for crevassing and fatigue give $H_{\max} \sim 90\text{--}100$ m. In West Antarctica, bed depths reach 1–2 km below sea level, so ice thicknesses at the grounding line can exceed 1 km (cliff heights ~800 m above waterline). If ice shelves are lost, MICI could drive rapid, cascading retreat. However, MICI remains debated — some models suggest meltwater slurries and ice mélange may buttress cliffs sufficiently.

Ice Sheet Cross-Section & MISI

This diagram shows a marine ice sheet in cross-section, illustrating the grounding line, ice shelf, retrograde bed slope, and the mechanism of marine ice sheet instability.

Figure 7.1: Marine ice sheet cross-section showing grounding line, ice shelf, calving front, and the mechanism of MISI on a retrograde bed. Warm Circumpolar Deep Water (CDW) drives submarine melting at the grounding line.

7.4 Glacial Isostatic Adjustment

When ice sheets melt, the underlying bedrock — previously depressed by the ice load — rebounds viscously. This glacial isostatic adjustment (GIA) continues for thousands of years after deglaciation and affects relative sea level measurements, gravity field observations (GRACE), and even ice sheet stability.

The relaxation time for isostatic rebound depends on mantle viscosity and the wavelength of the load:

$\tau = \frac{2\eta}{\rho_m g \lambda / (2\pi)} = \frac{4\pi \eta}{\rho_m g \lambda}$

where $\eta \approx 10^{21}$ Pa·s is the upper mantle viscosity,$\rho_m \approx 3300$ kg/m$^3$ is the mantle density,$g = 9.81$ m/s$^2$, and $\lambda$ is the characteristic wavelength of the ice load. For the Laurentide ice sheet ($\lambda \sim 3000$ km),$\tau \sim 4000$ years. Scandinavia is still rebounding at ~1 cm/yr from the last deglaciation ~10,000 years ago.

GIA complicates sea level measurements: regions formerly covered by ice sheets experience apparent sea level fall (land rising), while regions at the periphery (forebulge collapse) experience apparent sea level rise. This is why tide gauge records must be corrected for GIA before interpreting climate-driven sea level trends.

In West Antarctica, GIA may provide a stabilizing feedback: as ice melts and the bed rebounds, it can reduce water depth at the grounding line, potentially slowing MISI retreat. However, the timescale of rebound (~10$^3$–10$^4$ years) is much longer than the timescale of projected ice loss (~10$^2$ years), so this stabilization is likely too slow to prevent significant near-term retreat.

Thermal Expansion & Surface Melt Simulation

This simulation computes thermosteric sea level rise from an ocean temperature profile and applies the PDD melt model to compute Greenland surface melt under different warming scenarios.

Thermal Expansion Model & PDD Surface Melt

Python

script.py139 lines

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

fig, axes = plt.subplots(2, 2, figsize=(14, 10))

# ======== Panel 1: Thermal expansion coefficient ========
ax1 = axes[0, 0]
T_range = np.linspace(0, 30, 200)
# Approximate thermal expansion coefficient (simplified UNESCO equation)
alpha = (0.5 + 0.095 * T_range) * 1e-4  # K^-1, increases with T

ax1.plot(T_range, alpha * 1e4, color='#60a5fa', linewidth=2.5)
ax1.fill_between(T_range, alpha * 1e4, alpha=0.15, color='#60a5fa')
ax1.set_xlabel('Temperature (°C)', color='white')
ax1.set_ylabel(r'$\alpha$ ($\times 10^{-4}$ K$^{-1}$)', color='white')
ax1.set_title('Thermal Expansion Coefficient vs Temperature', color='white', fontsize=14)
ax1.set_facecolor('#0a0a1a')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.2)
ax1.annotate('Warm water expands\nmore per degree', xy=(20, 2.4), fontsize=11,
             color='#60a5fa', bbox=dict(boxstyle='round,pad=0.3', facecolor='#0c2461', edgecolor='#60a5fa'))

# ======== Panel 2: Thermosteric sea level rise ========
ax2 = axes[0, 1]

# Ocean temperature profile with warming
depth = np.linspace(0, 4000, 500)  # meters

# Pre-industrial temperature profile
T_preindustrial = 1.5 + 15 * np.exp(-depth / 300)

# Warming scenarios: surface warming penetrating to different depths
warming_scenarios = {
    '+1°C surface': {'dT_surface': 1.0, 'penetration': 300, 'color': '#4ade80'},
    '+2°C surface': {'dT_surface': 2.0, 'penetration': 500, 'color': '#fbbf24'},
    '+4°C surface': {'dT_surface': 4.0, 'penetration': 700, 'color': '#f87171'},
}

for name, params in warming_scenarios.items():
    dT = params['dT_surface'] * np.exp(-depth / params['penetration'])
    T_new = T_preindustrial + dT
    alpha_profile = (0.5 + 0.095 * T_new) * 1e-4
    # Thermosteric rise = integral of alpha * dT * dz
    dh = np.trapezoid(alpha_profile * dT, depth) * 100  # convert m to cm
    ax2.plot(depth, np.cumsum(alpha_profile * dT * (depth[1] - depth[0])) * 100,
             color=params['color'], linewidth=2, label=f'{name}: {dh:.1f} cm')

ax2.set_xlabel('Depth (m)', color='white')
ax2.set_ylabel('Cumulative thermosteric rise (cm)', color='white')
ax2.set_title('Thermosteric Sea Level Rise by Depth', color='white', fontsize=14)
ax2.legend(fontsize=9)
ax2.set_facecolor('#0a0a1a')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.2)
ax2.invert_xaxis()

# ======== Panel 3: PDD melt model ========
ax3 = axes[1, 0]

# Monthly temperatures at Greenland ice sheet margin (baseline)
months = np.arange(1, 13)
T_baseline = np.array([-18, -17, -12, -5, 2, 7, 10, 8, 3, -5, -12, -16])

warming_levels = [0, 1, 2, 3, 4, 5]
f_pdd_snow = 4.0   # mm w.e. / degree-day (snow)
f_pdd_ice = 12.0   # mm w.e. / degree-day (ice)

melt_rates = []
for dT_global in warming_levels:
    # Arctic amplification ~2x
    dT_arctic = dT_global * 2.0
    T_warm = T_baseline + dT_arctic
    # PDD per month (approximate: each month has ~30 days)
    pdd_monthly = np.maximum(T_warm, 0) * 30  # degree-days
    total_pdd = np.sum(pdd_monthly)
    # Melt: first melt snow (limited by snowfall), then ice
    snowfall_pdd = 200  # equivalent PDD that snowfall can absorb
    melt_snow = min(total_pdd, snowfall_pdd) * f_pdd_snow  # mm w.e.
    melt_ice = max(total_pdd - snowfall_pdd, 0) * f_pdd_ice  # mm w.e.
    melt_total = (melt_snow + melt_ice) / 1000  # m w.e.
    melt_rates.append(melt_total)

colors_bar = ['#60a5fa', '#4ade80', '#a3e635', '#fbbf24', '#fb923c', '#f87171']
bars = ax3.bar([f'+{w}°C' for w in warming_levels], melt_rates, color=colors_bar,
               edgecolor='white', linewidth=0.5)
for bar, val in zip(bars, melt_rates):
    ax3.text(bar.get_x() + bar.get_width()/2, val + 0.1, f'{val:.1f}',
             ha='center', color='white', fontsize=11)

ax3.set_xlabel('Global warming above pre-industrial', color='white')
ax3.set_ylabel('Annual surface melt (m w.e.)', color='white')
ax3.set_title('Greenland Surface Melt (PDD Model)', color='white', fontsize=14)
ax3.set_facecolor('#0a0a1a')
ax3.tick_params(colors='white')
ax3.grid(True, alpha=0.2, axis='y')

# ======== Panel 4: Schoof grounding line flux ========
ax4 = axes[1, 1]

# Schoof (2007): Q_g proportional to h_g^(n+2)
n_glen = 3
exponent = n_glen + 2  # = 5

h_g = np.linspace(100, 2000, 200)  # ice thickness at grounding line (m)
# Normalized flux
Q_g = (h_g / 1000) ** exponent  # normalized

ax4.plot(h_g, Q_g, color='#818cf8', linewidth=2.5)
ax4.fill_between(h_g, Q_g, alpha=0.1, color='#818cf8')

# Mark typical values
for h_val, label in [(500, 'Typical shelf'), (1000, 'Pine Island'), (1500, 'Thwaites')]:
    q_val = (h_val / 1000) ** exponent
    ax4.plot(h_val, q_val, 'o', color='#fbbf24', markersize=8, zorder=5)
    ax4.annotate(f'{label}\nh_g = {h_val} m', xy=(h_val, q_val),
                 xytext=(h_val + 80, q_val + 0.5),
                 color='#fde68a', fontsize=9,
                 arrowprops=dict(arrowstyle='->', color='#fbbf24'))

ax4.set_xlabel('Ice thickness at grounding line h$_g$ (m)', color='white')
ax4.set_ylabel('Grounding line flux Q$_g$ (normalized)', color='white')
ax4.set_title('Schoof Grounding Line Flux: Q $\\propto$ h$_g^5$', color='white', fontsize=14)
ax4.set_facecolor('#0a0a1a')
ax4.tick_params(colors='white')
ax4.grid(True, alpha=0.2)
ax4.annotate('Steep power law (n=5)\nmeans small thickness\nchanges cause large\nflux changes', xy=(300, 5),
             fontsize=10, color='#818cf8',
             bbox=dict(boxstyle='round,pad=0.3', facecolor='#1e1b4b', edgecolor='#818cf8', alpha=0.8))

fig.patch.set_facecolor('#0a0a1a')
plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
plt.close()
print("Thermal expansion and PDD simulation complete.")
print(f"Thermosteric rise for +2C surface warming: ~{melt_rates[2]:.1f} m w.e. melt at +2C global")
print(f"Schoof exponent (n+2): {exponent}")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

7.5 Sea Level Projections

The IPCC AR6 projects global mean sea level rise by 2100 relative to 1995–2014:

SSP1-2.6: 0.32–0.62 m (likely range), median 0.44 m
SSP2-4.5: 0.44–0.76 m, median 0.56 m
SSP3-7.0: 0.55–0.90 m, median 0.68 m
SSP5-8.5: 0.63–1.01 m, median 0.77 m

These projections assume no large-scale ice sheet instabilities (MISI/MICI). Low-confidence, high-impact scenarios including ice sheet dynamics could add an additional 0.5 m or more by 2100. Under such scenarios, 2 m of sea level rise by 2100 cannot be ruled out, with implications for coastal adaptation planning (see Climate & Biodiversity for adaptation strategies).

Beyond 2100, committed sea level rise is much larger. For 2°C of warming sustained for centuries, total sea level rise could reach 2–6 m (primarily from Greenland and West Antarctic contributions). For 4°C, 6–12 m is plausible over millennia.

Sea Level Projection Fan Chart

This simulation generates sea level projection fan charts for different SSP scenarios, decomposing contributions from thermal expansion, glaciers, Greenland, and Antarctica.

Sea Level Projections: Fan Chart & Component Decomposition

Python

script.py161 lines

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

np.random.seed(42)

years = np.arange(2020, 2101)
n_years = len(years)

# ======== SSP scenario parameters ========
scenarios = {
    'SSP1-2.6': {
        'thermal': {'rate': 1.5, 'accel': -0.005},
        'glaciers': {'rate': 0.8, 'peak': 2060},
        'greenland': {'rate': 0.5, 'accel': 0.01},
        'antarctica': {'rate': 0.3, 'accel': 0.005},
        'color': '#4ade80', 'median_2100': 44,
    },
    'SSP2-4.5': {
        'thermal': {'rate': 2.0, 'accel': 0.005},
        'glaciers': {'rate': 1.0, 'peak': 2070},
        'greenland': {'rate': 0.8, 'accel': 0.02},
        'antarctica': {'rate': 0.5, 'accel': 0.01},
        'color': '#fbbf24', 'median_2100': 56,
    },
    'SSP5-8.5': {
        'thermal': {'rate': 3.0, 'accel': 0.02},
        'glaciers': {'rate': 1.5, 'peak': 2060},
        'greenland': {'rate': 1.5, 'accel': 0.04},
        'antarctica': {'rate': 1.0, 'accel': 0.03},
        'color': '#f87171', 'median_2100': 77,
    },
}

fig, axes = plt.subplots(2, 2, figsize=(14, 10))

# ======== Panel 1: Fan chart ========
ax1 = axes[0, 0]

for name, params in scenarios.items():
    dt = years - 2020
    # Simple parametric model for total SLR
    median = params['median_2100'] * (dt / 80)**1.3
    # Uncertainty grows with time
    sigma = 5 + 0.15 * dt * (params['median_2100'] / 50)

p5 = median - 1.65 * sigma
    p17 = median - sigma
    p83 = median + sigma
    p95 = median + 1.65 * sigma

ax1.fill_between(years, p5, p95, alpha=0.1, color=params['color'])
    ax1.fill_between(years, p17, p83, alpha=0.25, color=params['color'])
    ax1.plot(years, median, color=params['color'], linewidth=2.5, label=name)

ax1.axhline(y=0, color='white', linewidth=0.5, alpha=0.3)
ax1.set_xlabel('Year', color='white')
ax1.set_ylabel('Sea level rise (cm)', color='white')
ax1.set_title('Sea Level Projections (Fan Chart)', color='white', fontsize=14)
ax1.legend(fontsize=9)
ax1.set_facecolor('#0a0a1a')
ax1.tick_params(colors='white')
ax1.grid(True, alpha=0.2)

# ======== Panel 2: Component decomposition (SSP5-8.5) ========
ax2 = axes[0, 1]
dt = years - 2020
p = scenarios['SSP5-8.5']

thermal = p['thermal']['rate'] * dt + 0.5 * p['thermal']['accel'] * dt**2
thermal = thermal / thermal[-1] * 30  # normalize to ~30 cm

glaciers = p['glaciers']['rate'] * dt * np.exp(-0.5 * ((years - p['glaciers']['peak']) / 30)**2)
glaciers = np.cumsum(glaciers) / np.sum(glaciers) * 15  # ~15 cm

greenland_rate = p['greenland']['rate'] + p['greenland']['accel'] * dt
greenland = np.cumsum(greenland_rate) / np.sum(greenland_rate) * 18  # ~18 cm

antarctica_rate = p['antarctica']['rate'] + p['antarctica']['accel'] * dt
antarctica = np.cumsum(antarctica_rate) / np.sum(antarctica_rate) * 14  # ~14 cm

ax2.fill_between(years, 0, thermal, alpha=0.6, color='#60a5fa', label='Thermal expansion')
ax2.fill_between(years, thermal, thermal + glaciers, alpha=0.6, color='#a78bfa', label='Glaciers')
ax2.fill_between(years, thermal + glaciers, thermal + glaciers + greenland,
                 alpha=0.6, color='#4ade80', label='Greenland')
ax2.fill_between(years, thermal + glaciers + greenland,
                 thermal + glaciers + greenland + antarctica,
                 alpha=0.6, color='#818cf8', label='Antarctica')

ax2.set_xlabel('Year', color='white')
ax2.set_ylabel('Sea level rise (cm)', color='white')
ax2.set_title('SLR Components (SSP5-8.5)', color='white', fontsize=14)
ax2.legend(fontsize=9, loc='upper left')
ax2.set_facecolor('#0a0a1a')
ax2.tick_params(colors='white')
ax2.grid(True, alpha=0.2)

# ======== Panel 3: Rate of SLR ========
ax3 = axes[1, 0]

for name, params in scenarios.items():
    dt = years - 2020
    median = params['median_2100'] * (dt / 80)**1.3
    rate = np.gradient(median, years)  # cm/yr
    rate_mm = rate * 10  # mm/yr
    ax3.plot(years, rate_mm, color=params['color'], linewidth=2, label=name)

ax3.axhline(y=3.7, color='white', linestyle=':', linewidth=1.5, alpha=0.5, label='Current rate (3.7 mm/yr)')
ax3.set_xlabel('Year', color='white')
ax3.set_ylabel('Rate of SLR (mm/yr)', color='white')
ax3.set_title('Rate of Sea Level Rise', color='white', fontsize=14)
ax3.legend(fontsize=9)
ax3.set_facecolor('#0a0a1a')
ax3.tick_params(colors='white')
ax3.grid(True, alpha=0.2)

# ======== Panel 4: Committed SLR (multi-century) ========
ax4 = axes[1, 1]

warming_levels = np.linspace(1, 5, 50)
# Multi-century committed SLR (meters)
committed_thermal = 0.4 * warming_levels  # ~0.4 m/K thermal
committed_glaciers = 0.1 * warming_levels  # ~0.1 m/K glaciers
committed_greenland = np.where(warming_levels < 1.5, 0.05 * warming_levels,
                                0.05 * 1.5 + 1.5 * (warming_levels - 1.5))  # threshold at 1.5K
committed_antarctica = np.where(warming_levels < 3, 0.1 * warming_levels,
                                 0.1 * 3 + 2.0 * (warming_levels - 3))  # threshold at 3K

total_committed = committed_thermal + committed_glaciers + committed_greenland + committed_antarctica

ax4.fill_between(warming_levels, 0, committed_thermal, alpha=0.6, color='#60a5fa', label='Thermal')
ax4.fill_between(warming_levels, committed_thermal,
                 committed_thermal + committed_glaciers, alpha=0.6, color='#a78bfa', label='Glaciers')
ax4.fill_between(warming_levels, committed_thermal + committed_glaciers,
                 committed_thermal + committed_glaciers + committed_greenland,
                 alpha=0.6, color='#4ade80', label='Greenland')
ax4.fill_between(warming_levels,
                 committed_thermal + committed_glaciers + committed_greenland,
                 total_committed, alpha=0.6, color='#818cf8', label='Antarctica')

ax4.axvline(x=1.5, color='#fbbf24', linestyle=':', linewidth=1.5, label='1.5°C target')
ax4.axvline(x=2.0, color='#fb923c', linestyle=':', linewidth=1.5, label='2.0°C target')

ax4.set_xlabel('Global warming (°C above pre-industrial)', color='white')
ax4.set_ylabel('Committed SLR (meters, multi-century)', color='white')
ax4.set_title('Committed Sea Level Rise', color='white', fontsize=14)
ax4.legend(fontsize=8, loc='upper left')
ax4.set_facecolor('#0a0a1a')
ax4.tick_params(colors='white')
ax4.grid(True, alpha=0.2)

fig.patch.set_facecolor('#0a0a1a')
plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
plt.close()
print("Sea level projection complete.")
for name, params in scenarios.items():
    print(f"{name} median 2100: {params['median_2100']} cm")
print(f"Committed SLR at 2.0C: {total_committed[np.argmin(np.abs(warming_levels-2))]:.1f} m (multi-century)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

Fox-Kemper, B. et al. (2021). Ocean, Cryosphere and Sea Level Change. In: Climate Change 2021: The Physical Science Basis. IPCC AR6 WG1, Chapter 9.
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M6. Carbon Cycle & Feedbacks M8. Projections & Scenarios