modelling Level 4

Glacial Lake Outburst Floods (GLOFs)

What happens when a glacial lake suddenly drains? GLOFs release millions of cubic meters of water in hours, devastating downstream communities. This model derives dam breach equations, implements peak discharge prediction, models flood wave propagation, and shows how to assess GLOF hazards using remote sensing and DEMs.

Prerequisites: dam breach hydraulics, flood routing, peak discharge, energy dissipation

27 Feb 2026 Updated 12 Mar 2026 13 min read

1. The Question

A glacial lake grows behind a moraine dam—when will it fail, and how big will the flood be?

Glacial Lake Outburst Flood (GLOF):

Sudden release of water from ice-dammed or moraine-dammed glacial lakes.

Triggering mechanisms:

Ice dam flotation (buoyancy exceeds ice strength)
Moraine dam overtopping (lake level rises)
Earthquake (dam failure)
Ice/rock avalanche into lake (displacement wave)
Piping through dam (internal erosion)

Characteristics:

Peak discharge: 100-100,000 m³/s (compared to normal flow 1-10 m³/s)
Duration: Hours to days
Sediment content: 30-70% by volume (hyperconcentrated flow)
Highly destructive: Infrastructure, agriculture, lives

Recent examples:

2023: South Lhonak Lake, Sikkim (India) - 40+ deaths
2021: Chamoli disaster, India - 200+ deaths (rock avalanche → lake)
2013: Kedarnath, India - 5,000+ deaths
1941: Huaraz, Peru - 5,000+ deaths (Lake Palcacocha)

2. The Conceptual Model

Lake Types

1. Ice-dammed lakes:

Glacier blocks valley (tributary or main valley)
Lake impounded against ice
Drainage often subglacial (tunnel beneath ice)
Mechanism: Ice dam floats when water pressure exceeds ice overburden

2. Moraine-dammed lakes:

Terminal or lateral moraine forms natural dam
Lake behind unconsolidated sediment/rock debris
Drainage by overtopping or piping
Mechanism: Dam overtops or erodes internally

3. Bedrock-dammed lakes:

Stable, rarely fail
GLOF only if overtopped by displacement wave

Dam Breach Process

Ice dam:

Phase 1 - Tunnel initiation:

Water pressure forces open cracks in ice
Small tunnel grows by melt (frictional heat)

Phase 2 - Tunnel enlargement:

Positive feedback: larger tunnel → more flow → more melt → larger tunnel
Exponential growth

Phase 3 - Peak discharge:

Tunnel diameter = 10s of meters
Discharge peaks when lake lowered to tunnel level

Phase 4 - Recession:

Lake empties, discharge declines
Ice dam may re-seal for next cycle

Moraine dam:

Phase 1 - Overtopping:

Water flows over dam crest
Erosion begins

Phase 2 - Breach initiation:

Channel incises into dam
Headward erosion

Phase 3 - Breach widening:

Rapid enlargement
Dam material highly erodible

Phase 4 - Peak discharge:

Full breach, maximum outflow

Phase 5 - Stabilization:

Bedrock or resistant layer reached
Discharge declines as lake drains

Flood Wave Propagation

Wave travels downstream:

Attenuation:

Peak discharge decreases with distance
Flood duration increases (spreading)

Channel effects:

Narrow valleys: Higher velocity, less attenuation
Wide valleys: Lower velocity, more spreading
Constrictions: Backwater, temporary storage

Sediment bulking:

GLOF erodes channel
Sediment concentration increases
Transforms to debris flow in steep terrain

3. Building the Mathematical Model

Ice Dam Flotation Criterion

Buoyancy condition:

Ice floats when water pressure exceeds ice weight:

\[\rho_w g h_w > \rho_i g h_i\]

Where:

$\rho_w$ = water density (1000 kg/m³)
$\rho_i$ = ice density (900 kg/m³)
$h_w$ = water depth
$h_i$ = ice thickness

Critical water depth:

\[h_w^* = \frac{\rho_i}{\rho_w} h_i = 0.9 h_i\]

Example: Ice dam 100m thick floats when water ≥ 90m deep.

Factor of safety:

\[F = \frac{\rho_i h_i}{\rho_w h_w}\]

Failure: $F < 1$ (lake drains)
Stable: $F > 1$ (lake grows)

Peak Discharge (Clague-Mathews Relation)

Empirical formula for ice-dammed lakes:

\[Q_{\max} = 75 V^{0.67}\]

Where:

$Q_{\max}$ = peak discharge (m³/s)
$V$ = lake volume (10⁶ m³)

Example: Lake volume = 10 million m³

\[Q_{\max} = 75 \times 10^{0.67} = 75 \times 4.64 = 348 \text{ m}^3\text{/s}\]

Uncertainty: Factor of 2-3× (varies with tunnel geometry, ice properties)

Dam Breach (Parametric Model)

For moraine dams, breach geometry:

Breach width:

\[B = k_w h_d^a\]

Where:

$h_d$ = dam height (m)
$k_w$ = width coefficient (~2-5)
$a$ = exponent (~1.0-1.4)

Typical: $B \approx 3h_d$ (breach width 3× dam height)

Breach formation time:

\[t_f = \frac{V_d}{C}\]

Where:

$V_d$ = volume of eroded dam material (m³)
$C$ = erosion coefficient (m³/s)

Peak discharge (broad-crested weir):

\[Q_{\max} = C_d B h_b^{1.5}\]

Where:

$C_d$ = discharge coefficient (~1.7)
$B$ = breach width (m)
$h_b$ = breach flow depth (m)

Flood Routing (Kinematic Wave)

Flood wave velocity:

\[c = \frac{dQ}{dA} = \frac{5}{3} v\]

Where:

$c$ = wave celerity (m/s)
$v$ = flow velocity (m/s)
5/3 factor from Manning equation

Travel time:

\[t_{\text{travel}} = \int_0^L \frac{dx}{c(x)}\]

Peak attenuation:

\[Q_{\text{downstream}} = Q_{\text{upstream}} \times e^{-\alpha x}\]

Where $\alpha$ = attenuation coefficient (depends on channel geometry, roughness)

Typical: Peak reduces 30-50% per 10 km in mountain valleys.

4. Worked Example by Hand

Problem: Estimate GLOF peak discharge and travel time.

Glacial lake:

Surface area: 0.5 km² = 500,000 m²
Average depth: 50 m
Volume: $V = 0.5 \times 10^6 \times 50 = 25 \times 10^6$ m³
Ice dam thickness: 80 m
Water depth at dam: 75 m

Downstream:

Village 15 km downstream
Channel slope: 0.05 (5%)
Manning’s n: 0.045 (boulder bed)

Solution

Step 1: Check flotation

\[F = \frac{0.9 \times 80}{75} = \frac{72}{75} = 0.96 < 1\]

Dam will float (marginal stability, likely to fail)

Step 2: Peak discharge (Clague-Mathews)

\[Q_{\max} = 75 \times 25^{0.67} = 75 \times 8.55 = 641 \text{ m}^3\text{/s}\]

Step 3: Flood velocity

Using Manning equation for wide channel:

\[v = \frac{1}{n} R^{2/3} S^{1/2}\]

Assume depth $h = 5$ m (during peak):

\[R \approx h = 5 \text{ m}\] \[v = \frac{1}{0.045} \times 5^{2/3} \times 0.05^{1/2} = 22.2 \times 2.92 \times 0.224 = 14.5 \text{ m/s}\]

Step 4: Wave celerity

\[c = \frac{5}{3} \times 14.5 = 24.2 \text{ m/s}\]

Step 5: Travel time

\[t = \frac{15000}{24.2} = 620 \text{ seconds} = 10.3 \text{ minutes}\]

Step 6: Attenuation

Assume $\alpha = 0.03$ km⁻¹:

\[Q_{15\text{km}} = 641 \times e^{-0.03 \times 15} = 641 \times e^{-0.45} = 641 \times 0.64 = 410 \text{ m}^3\text{/s}\]

Summary:

Peak discharge at source: 641 m³/s
Peak discharge at village: 410 m³/s (36% reduction)
Travel time: 10 minutes (very little warning!)
Flow depth: 5 m (catastrophic)

Hazard assessment: EXTREME - village would be destroyed with <15 min warning.

5. Computational Implementation

Below is an interactive GLOF simulator.

Lake volume (million m³): 25 Ice dam thickness (m): 80 Water depth (m): 75 Distance downstream (km): 15

Safety factor: --

Peak discharge: -- m³/s

Travel time: -- min

Downstream peak: -- m³/s

Hazard: --

Try this:

Increase water depth: Safety factor drops below 1.0 → dam fails!
Larger lake: Higher peak discharge (exponential relationship)
Increase distance: Peak attenuates, delayed arrival
Red hydrograph: At source (lake breach)
Blue hydrograph: Downstream (lower peak, delayed, wider)
Safety factor < 1.0: Dam flotation imminent
Watch hazard level change from Low → Extreme
Notice: Even 15 km away, travel time < 20 minutes!

Key insight: GLOFs give minimal warning time—early detection and evacuation planning critical!

6. Interpretation

Early Warning Systems

Remote sensing monitoring:

Satellite optical (Landsat, Sentinel-2):

Lake area change (monthly)
Ice dam position
Freeboard (water to dam crest)

SAR (Sentinel-1, ALOS-2):

All-weather monitoring
Dam deformation (InSAR)

On-site monitoring:

Water level sensors
Seismometers (ice cracking, dam failure)
Discharge gauges downstream
Automated cameras

Warning threshold:

Lake level rising + dam deformation → evacuate!

Case study - Tsho Rolpa, Nepal:

1990s: Lake expanded rapidly
2000: Dam lowering project (-3m lake level)
Ongoing monitoring
Evacuation plan for 10,000 people downstream

Risk Reduction

Engineering solutions:

1. Lake lowering:

Pump water out
Construct outlet channel
Reduces volume → reduces potential discharge

2. Dam reinforcement:

Add rock fill
Armoring (concrete blocks)
Improve drainage

3. Early warning:

Sensor networks
Sirens
Communication systems

Cost-benefit:

Lake lowering: $1-10 million
Lives saved: 100s-1000s
Infrastructure protected: $10s-100s millions

Climate Change Impacts

Glacier retreat:

More lakes forming (number increased 50% since 1990)
Larger lakes (less ice to stabilize)
Higher lakes (closer to steep terrain)

Permafrost thaw:

Moraine dams less stable
Increased piping potential

Extreme precipitation:

Overtopping events more frequent
Displacement waves from landslides

Projection: GLOF risk increasing 2-3× by 2050 in many regions.

7. What Could Go Wrong?

Underestimating Peak Discharge

Clague-Mathews empirical:

Derived from ~20 events, mostly small lakes.

Large lakes (>50 million m³): May exceed formula by 2-5×

Moraine dams: Often higher peaks than ice dams (sudden full breach vs. gradual tunnel growth)

Solution: Use multiple methods, uncertainty ranges, worst-case scenarios.

Ignoring Sediment Bulking

GLOF erodes channel:

Entrains sediment → increases volume by 30-70%

Debris flow transformation:

In steep channels (>10% slope), GLOF becomes debris flow:

Higher velocity
Greater impact forces
Overtops bends
Deposits thick debris fans

Solution: Model sediment entrainment, debris flow mechanics.

Cascade Effects

GLOF triggers downstream GLOFs:

Example - Chamoli 2021:

Rock avalanche into lake
GLOF released
Eroded valley
Triggered secondary failures
Compound flood wave

modelling challenge: Must simulate entire cascade.

False Alarms

Lake level fluctuates naturally:

Seasonal melt, rainfall

Dam deformation: Gradual vs. pre-failure

Balance: Sensitivity (detect real events) vs. specificity (avoid false alarms)

Solution: Multi-parameter thresholds, expert review.

8. Extension: GLOF Hazard Mapping

Combine:

1. Lake inventory:

Satellite mapping of all glacial lakes
Size, growth rate, dam type

2. Susceptibility assessment:

For each lake:

\[S = w_1 V + w_2 F + w_3 G + w_4 D\]

Where:

$V$ = volume score
$F$ = flotation/freeboard score
$G$ = growth rate score
$D$ = dam condition score
$w_i$ = weights

3. Downstream vulnerability:

Population density
Infrastructure value
Evacuation capacity

4. Flood modelling:

HEC-RAS or similar:

Dam breach → hydrograph
Route through DEM
Inundation mapping

Output: GLOF hazard map (high/medium/low risk zones)

9. Math Refresher: Dam Breach Hydraulics

Broad-Crested Weir Flow

Critical flow over weir:

\[Q = C_d B h^{3/2} \sqrt{2g}\]

Where:

$C_d$ = discharge coefficient (~0.5-0.6)
$B$ = breach width (m)
$h$ = flow depth above weir crest (m)
$g$ = 9.81 m/s²

Simplified: $Q \approx 1.7 B h^{1.5}$

Energy Conservation

Total energy (Bernoulli):

\[H = z + \frac{v^2}{2g} + \frac{p}{\rho g}\]

Where:

$z$ = elevation
$v$ = velocity
$p$ = pressure

For free surface: $p = p_{\text{atm}}$ (gauge pressure = 0)

\[H = z + \frac{v^2}{2g}\]

Energy loss (friction):

\[\Delta H = f \frac{L}{D} \frac{v^2}{2g}\]

Where $f$ = Darcy-Weisbach friction factor.

Summary

GLOFs: Catastrophic floods from sudden glacial lake drainage
Triggers: Ice flotation, dam overtopping, avalanches, earthquakes, piping
Ice dam flotation: Occurs when water pressure > ice weight (F < 1.0)
Peak discharge: Clague-Mathews $Q_{max} = 75V^{0.67}$ for ice-dammed lakes
Travel time: Minutes to hours in steep terrain (minimal warning)
Attenuation: Peak reduces 30-50% per 10 km but still catastrophic
Moraine dams: Often fail more suddenly than ice dams (full breach)
Climate change: GLOF risk increasing (more lakes, less stable dams)
Mitigation: Lake lowering, dam reinforcement, early warning systems
Monitoring: Satellite remote sensing + ground sensors + flood modelling
Critical for mountain communities in Peru, Nepal, Bhutan, Pakistan, China