What is mass balance ?

Regine Hock

Claridenfirn, Switzerland, 1916

1914

Summer School in Glaciology

McCarthy, Alaska, June 2026

• Terminology, Definitions, Units
• Elevation mass-balance feedback
• Conventional and reference surface mass balance
• Firn line, snow line, ELA
• Global mass changes

Alaska Range

PART I

Terminology

1914

Background

• General reference for mass-balance terminology has been Anonymous,1969, J. Glaciology 8(52).
• In practice diverging and inconsistent and confusing use of terminology
• New methods, e.g. remote sensing, require update

Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris.

What is mass balance?

Section 1 in Notes

• SPACE: study volume needs to be defined
• mass balance is often quoted for volumes other than that of the whole glacier, for example a column of unit cross section
• important to report the domain !
• TIME: the time period (esp important for comparison with model results)
• mass change can be studied over any period
• often done over a year or winter/summer seasons --> Annual mass balance � (formerly ‘Net’)

Net gain of mass

Net loss of mass

Accumulation area: acc > abl

Ablation area: acc < abl

Equilibrium line: acc = abl

Firn line

Long-term ELA

Mass balance is the change in the mass of a glacier, or part of the glacier, over a stated span of time:� = mass budget

‘mass imbalance’

What is glacier mass balance ?

ACCUMULATION, (c, C)

• Snow fall
• Deposition of hoar, freezing rain
• Windborne blowing snow/drifting snow
• Avalanching
• Internal accumulation (refreezing)
• Basal freeze-on

Δm

Mass balance components:

It’s more than snowfall and melt

Total mass budget: sum of climatic-basal balance and frontal ablation

Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris.

What is mass balance?

Mass balance of a column

9

What is mass balance?

Change of the mass over a stated span of time

10

Mass balance of a column

Surface internal basal flux divergence

c = accumulation

a = ablation (is negative)

Surface

internal

basal

q_in

q_out

Δm

Terminology ‘mess’

Mass balance of a column

Continuity equation

Surface internal basal flux divergence

Mass balance ?

Thickness change

c = accumulation

a = ablation

Surface

internal

basal

q_in

q_out

SMB ?

Δm

Terminology ‘mess’

Mass balance of a column

Surface internal basal flux divergence

c = accumulation

a = ablation

Climatic-basal balance, b

Climatic balance, b_clim

(Total) mass balance,

Δm

Δm

surface

internal

basal

q_in

q_out

Mass balance in continuity equation

This is not the total mass balance, but the climatic-basal mass balance (balance due to surface, internal and balance accumulation and ablation)

Thickness change

Note: All 3 terms are expressed either in mass or ice equivalent.

surface internal basal frontal ablation

B_sfc

B_i

B_b

A_f

Mass-balance components of marine/lake-terminating glacier

Frequently mixed-up terms

Section 2 in Notes

Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris.

Precipitation Surface accumulation

precipitation includes rain; rain water is not accumulation; water is not considered to be part of the glacier

Terminology: Frequently mixed-up terms

Winter balance <--> winter accumulation

Summer balance <--> summer ablation

Implications for comparison of field measurements with model results?

C, A can be modeled, but what is measured often is B_w, B_s

B_a = B_w+B_s = Acc + Abl

B_w= Acc_w B_s= Abl_w

What is measured in ice cores?

Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris.

Precipitation vs. Surface accumulation

precipitation includes rain; rain water is not accumulation; water is not considered to be part of the glacier

Accumulation vs. �Net accumulation

- Net acc is a balance, acc is not

Melt vs. meltwater runoff

Melt water may refreeze —> does not contribute to meltwater runoff

Meltwater runoff vs. Runoff

Runoff includes rain water

Terminology: Frequently mixed-up terms

What is specific mass balance ?

1. The mass balance at a specific location ?
2. The mass balance of the entire glacier ?
3. The mass balance expressed in m w.e. ?

Definition:

Mass balance expressed per unit area [M L^–2], � typically kg m^–2 or m w.e.

• The prefix “specific” is not necessary. The units make clear whether or not it is specific.
• Specific mass balance may be reported for a point on the surface (if it is a surface mass balance), a column of unit cross-section, or a larger volume such as the entire glacier.
• Balances reported for a point are always specific.

Mass balance units

Notes: Section 3

Mass-balance units

• Mass [M] kg, Gt (=10¹² kg, 1 billion tonnes)
• mass change per unit area [M L^-2] --> kg m^-2 � (specific unit)
• m or mm water equivalent (w.e.) (specific unit):�-> 1 kg of water (density 1000 kg m^-3) has thickness of 1 mm when distributed over 1 m²�-> kg m^-2 and mm are numerically identical�-> 1 m w.e. = 1000 kg m^-2 / density of water
• m³ w.e. or km³ w.e. (1 km³ w.e. = 1 Gt) � --> important to add w.e. or i.e. (ice equiv.)
• Sea-level equivalent:�kg m^-2 x glacier area /-(density of water x area of the ocean) (362x10⁶ km²)�

Often not included:

• changes in ocean area; any delay and storage in transport of water in the terrestrial water cycle
• isostatic adjustment of the land surface, tectonic movements
• differentiate between grounded and floating ice (floating ice does not contribute to sea-level; grounded ice contributes only to a small fraction since the ice already displaces water)

Mass balance time series look different in different units

Kienholz et al. 2016

Black Rapids Glacier

m w.e. a-1

Gt a^-1

Terminology mess: What is the difference between mass balance and mass change?

Submitted paper to Nature in 2019:

• Mass balance = balance in m w.e.
• Mass change = balance in mass units (Gt)

What do different observations methods measure?

Notes: Section 4

What do different observation methods actually measure?

Berthier et al, 2023

McDonnell et al, 2022

Glaciological method

Geodetic method

Gravimetric method

In-situations measurements of snow depth, density, stake heights

Elevation differencing

• DEMs
• Elevations along satellite or airplane tracks

Repeat measurements of the variations in the Earth´s gravity field

https://www.jpl.nasa.gov/spaceimages/images/largesize/PIA04235_hires.jpg

What do different observation methods actually measure?

Berthier et al, 2023

McDonnell et al, 2022

Glaciological method

Geodetic method

Gravimetric method

In-situations measurements of snow depth, density, stake heights

Elevation differencing

• DEMs
• Elevations along satellite or airplane tracks

Repeat measurements of the variations in the Earth´s gravity field

Terminology !

• Term geodetic method historically used in glaciology to describe surface elevation differencing
• In geodesy = �“suite of techniques to measure (changes in) the Earth´s geometric shape, …”��—> includes both surface elevation-differencing methods and the gravimetric method.

Stake

surface internal basal

flux divergence

GPS

What do different observation methods actually measure?

ice flow

Stake

surface internal basal

flux divergence

GPS

What do different observation methods actually measure?

Stake

surface internal basal

flux divergence

GPS

What do different observation methods actually measure?

Geodetic (elevation differencing) method:

• Elevations are given in relation to a geodetic datum or other standard reference)

Glaciological method:

• Relative to a local reference marker near the surface (e.g. bottom of the stake)

Glaciological method

climatic-basal mass balance

ice flux

densification

bed elevation

subglacia water storage

Processes leading to an elevation change

climatic-basal mass balance

ice flux

densification

bed elevation

subglacial water storage

Processes leading to an elevation change

climatic-basal mass balance

ice flux

densification

bed elevation

subglacial water storage

—> Elevation change can occur without any change in mass

—> Mass change without any elevation change

Elevation change due to mass change

Elevation change without any mass change

850±60

kg/m³

Processes leading to an elevation change

assumed = 0

Glacier-wide balance

At point scale

Elevation change (converted to mass by suitable density) is not the same as the surface mass balance derived from a stake�

but at glacierwide scale, it is the same (assuming last 3 terms are zero), because flux divergence = 0

by M. Huss

assume surface/internal balance=0

total change

not seen

Elevation change

Longitudinal profile

Surface and bed elevations

not seen

Geodetic (elevation change) method: Marine-termination glaciers?

Geodetic (elevation change) method: Marine-termination glaciers?

Hock et al. 2026, J. Glaciol

Elevation change

Longitudinal profile

Surface and bed elevations

Geodetic (elevation change) method: Marine-termination glaciers?

Hock et al. 2026, J. Glaciol

Calving flux

• only includes mass loss due to calving
• BUT: >50% of the mass loss at the glacier front can be due to submarine melting (even if grounded)

Marine/lake terminating glaciers

Time systems

Notes: Section 7

39

• End winter snow probing: What system?
• Stratigraphic system: dates are unknown

Winter

Summer

Winter

• stratigraphic system
• fixed-date system
• floating-date system
• combined system

Stratigraphic system

Time systems for reporting annual/seasonal mass balances

Stratigraphic system

Stratigraphic system

Fixed-date system

Fixed-date system

Fixed-date system

Summer

40

Intellectual break

Time system

Density distribution of glaciological survey dates from WGMS

Out of 8,298 glacier-wide mass-balance records on 516 glaciers, only 57% on 296 glaciers include the start and end dates with the reported annual balance

Hock et al. 2026, J. Glaciol

Intellectual break

Impact of time system on mass balance

Differences of glacier-wide annual and winter mass balance between a fixed annual/winter period (annual: 1 Oct - 30 Sep, winter: 1 Oct - 30 Apr) and the actual measurement period (floating-date system) for 11 Swiss glaciers

Hock et al. 2026, J. Glaciol

--> comparing observations with model results problematic if time system not known

Mass balance (Gt/yr)

Cumulative mass

balance (Gt)

Time systems for reporting annual/seasonal mass balances

Hock et al. 2026, J. Glaciol

Differences between in mass balance over

1. mass balance over a full year and
2. the balance over periods shorter/longer than a full year

as a function of deviation of mass-balance year end date from reference date

1000 kg/m² = 1 m w.e.

Impact of deviating from full year on mass balance

Hock et al. 2026, J. Glaciol

Examples:

• Alaska: 0.09 m w.e. a⁻¹ (∼10%) over 9 yrs; �DEM only 27 days off a full year
• Iceland: 0.4 m w.e. a^-1 over 4-6 years)

Impact of deviating from full year on mass balance

What do glaciers tell us about climate change?

​

Elevation mass-balance feedback

Concept of conventional and reference surface balance

​

Notes: Section 8

Mass-balance feedback: Two opposing effects

Retreat effect Thinning effect

@V. Radic

As the glacier retreats the specific mass balance becomes less negative even if the climate does not change

Mass-balance feedback: Two opposing effects

Retreat effect Thinning effect

@V. Radic

(Bodvardsson, 1955)

Ice cap

As the glacier retreats the specific mass balance becomes less negative even if the climate does not change

As the glacier thins the specific mass balance becomes more negative even if the climate does not change

Mass-balance feedback: Two opposing effects

Retreat effect Thinning effect

@V. Radic

(Bodvardsson, 1955)

Ice cap

Mass balance as climate indicator ?

Step change in climate

B < 0

Glacier retreat

Stable climate

B = 0

Steady-sate

Stable climate

B = 0

Steady-sate

Conventional mass balance

Reference surface mass balance













Balance computed over current glacier area and hypsometry

Glacier area/hypsometry is updated annually

Relevant for hydrological/sea level purposes

Glacier retreated

Balance computed over initial glacier area and hypsometry

Glacier area/hypsometry is kept constant

Year 1 Year 2

Harrison, W., Elsberg, Cox and March, 2005. Different balances for climatic and hydrological applications. J. Glaciol.,�This paper is in your folder !

Relevant for climatological purposes

Mass-balance feedback: Two opposing effects

Retreat effect Thinning effect

@V. Radic

(Bodvardsson, 1955)

Ice cap

As the glacier retreats the specific mass balance becomes less negative even if the climate does not change

As the glacier thins the specific mass balance becomes more negative even if the climate does not change

Reference surface mass balance eliminates the effect of retreat & thinning on specific mass balance —> true climate signal

52

Harrison et al. 2009, Ann. Glaciol.

Which one is the conventional / reference balance?

Firn line, equilibrium line, snow line ...

Notes: Section 9

Snow line

• Boundary separating snow from ice or firn at any time t
• Transient - Annual

FIRN LINE

FIRN = Wetted snow that has survived one summer � without being transformed to ice

FIRN

ICE

The set of points on the surface of a glacier delineating the firn area and, at the end of the mass-balance year, separating firn (usually above) from glacier ice (usually below).

Mass balance

Snow surface

FIRN LINE can be seen on radar profiles

Snow line

• Boundary separating snow from ice or firn at any time t
• Transient - Annual

Equilibrium line

• The set of points on the surface of the glacier where the climatic mass balance is zero at a given moment. �The equilibrium line separates the accumulation zone from the ablation zone.
• Transient - Annual

Equilibrium line vs. equilibrium line altitude (ELA)

Approximate ELA

ELAs from space: Remote sensing

Landsat image of

Vatnajoekull (Iceland)

Ablation zone

Accumulation zone

Where is the firn line,

ELA?

Where are the firn line, equilibrium line, snow line relative to each other?

firn?

snow

Vatnajoekull (Iceland)

Assuming no superimposed ice

Federico Covi: The pictures were taken August 31, 2015, which luckily happen to be just 2 days before the end of the melting season. The first one is from Vedretta Lunga a small glacier in my beloved Italian central alps and the second one is from Hintereisferner a well monitored glacier in Austrian alps.

Langenferner

Hintereisferner

snow

snow

firn

firn

ice

ice

Why do we care about snow/firn/equilibrium lines?

62

Hintereisferner 2017, @G. Kaser

• Indicator of glacier health � (ELA inversely correlated with mass balance)
• Impact on energy balance� (distinctly different albedos)
• Impact runoff generation � (Water flow through firn slower than over ice)

What is glacier runoff ?

​

Not in Notes

What is glacier runoff?

1.) All runoff from glacierized area

Q = M - R

- discharge a gauging station would measure

�

​

2.) Runoff from glacier net mass loss

Q = M - R + P

​

3.) Runoff only from bare ice area

Q = M_ice

• happens always, i.e. also in year where annual balance is zero
• glacier in balance has no effect on annual runoff (but seasonal effects)
• relevant for hydrologists

​

• relevant for sea-level, streamflow
• ‘extra’ water from long-term glacier storage�

Radic V. and R.Hock, 2014. Glaciers in the Earth’s hydrological cycle. Assessments of glacier mass and runoff changes on global and regional scales. Survey of Geophysics 35, 813-837.

melt runoff

annual mass loss

Response to warming

Short-term�time scale

Period of negative mass balances

Balanced mass budget

How does runoff change as it becomes warmer?

Global glacier mass changes

Not in Notes

Yakutat Glacier, Alaska 2011; photo: B. Truessel

Global glacier volume

Sea-Level Equivalent (SLE)

~65 m

57.4 m Antarctica

7.4 m Greenland

0.5 m mountain glaciers

• ~200,000 glaciers
• 705 km² including glaciers in the periphery of Greenland (89,700 km² ) and Antarctica (133,200 km²)

Mountain glaciers and ice caps

Yakutat Glacier, Alaska 2011; photo: B. Truessel

- inventoried glacierized area (WGI)

- NOT inventoried glacierized area before 2012

RGI 7.0

Yakutat Glacier, Alaska 2011; photo: B. Truessel

Global glacier mass changes 2000 - 2019

• Photogrammetry: Stereo-images from ASTER
• Elevation changes at 1/2 billion 100 m resolution pixels during 2000-2019

Hugonnet et al., 2021, Nature

Global glacier mass changes 1960-2019

Fox-Kemper et al. 2021, IPCC AR6, Chapter 9

based on Hugonnet et al., 2021, and other studies

1960 1980 2000 2020

50-60

cm w.e. /yr

All glaciers (except those in Greenland/ Antarctica)

Mass balance (m w.e yr^-1)

0.5

-0.5

-1.0

North Asia

New Zealand

Central Europe

Low Latitudes

Caucasus

Scandinavia

Iceland

Global

Russian Arctic

Arctic Canada S

Sval-bard

Alaska

Arctic Canada N

Greenland

South Asia W

Southern Andes

Central Asia

Antarctica

RCP2.6

RCP4.5

RCP6.0

RCP8.5

W Canada/USA

South Asia E

Marzeion et al 2020

RCP = Representative Concentration Pathways

Regions are sorted by relative mass losses

1

0.6

0

0.4

0.8

0.2

Glacier mass remaining at 2100 (rel. to 2015)

Regional glacier projections

2015 - 2100

2015

2100

279 simulations from 11 glacier models

RCP2.6

RCP4.5

RCP6.0

RCP8.5

North Asia

New Zealand

Central Europe

Caucasus

Scandinavia

Iceland

Global

Russian Arctic

Arctic Canada S

Svalbard

Alaska

Arctic Canada N

Greenland

South Asia W

Southern Andes

Central Asia

Antarctica

Specific mass changes (kg m^-2 yr^-1)

Marzeion et al. (2020), Earth's Future

W Canada/USA

South Asia E

1000 kg m^-2 yr^-1 = 1 m w.e. yr^-1

RCP2.6

- Constant mass loss rates in highly glacierized regions

- Decreasing mass loss rates (approaching zero) in less glacierized regions

North Asia

New Zealand

Central Europe

Caucasus

Scandinavia

Iceland

Global

Russian Arctic

Arctic Canada S

Svalbard

Alaska

Arctic Canada N

Greenland

South Asia W

Southern Andes

Central Asia

Antarctica

Specific mass changes (kg m^-2 yr^-1)

RCP2.8

RCP4.5

RCP6.0

RCP8.5

Marzeion et al. (2020), Earth's Future

W Canada/USA

South Asia E

1000 kg m^-2 yr^-1 = 1 m w.e. yr^-1

RCP8.5

Greater mass loss rates in highly glacierized regions than in regions with little ice

Global mass loss by 2100 increases linearly with�global warming above pre-industrial

Area loss (%)

Rounce et al, 2023, Science

Mass loss (%)

Regions sorted by glacier area

Ice lost

5%

85%

40%

Zellari & Schuster et al., 2025, Science

Mass balance: Main conclusions

• Reporting mass balance: always report
• domain to which the balance refers (and area)
• time period a balance refers to
• if annual balance is reported report the dates and/or the time system (--> essential to compare to model results)
• report which mass balance component is measured/modeled; use proper terminology

• Elevation change can occur without mass change and vice versa: Conversion factor between elevaation/volume change can range from -infinity to +infinity

Summary

• Specific mass balance: mass per area
• surface mass balance: strictly speaking only balance at the surface -> climatic balance if internal accumulation included
• annual balance instead of previous term net balance
• Accumulation is not identical to net accumulation
• Runoff is not identical to melt or meltwater runoff
• Frontal ablation includes calving flux and submarine melting
• Reporting of time systems and glacier area (area-elevation distribution) is crucial
• Conventional balance (area, elevation updated)�reference surface mass balance (kept constant)

Terminology

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