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Expand Up @@ -46,10 +46,14 @@ See `antarcticglaciers.org (mass-balance)`_
for an introduction about glacier mass-balance and the ELA, or our
:ref:`glacier_basics` graphics for an illustration.

**In "beginner mode", start by setting the ELA to 3000m a.s.l**, and note
on a piece of paper: the equilibrium volume of the glacier,
its length and maximal thickness. **Now choose the "wider top" glacier shape**
and run the model again. Is the new glacier larger or smaller than before? Why?
**Experiment:**

- In "Beginner mode", start by setting the ELA to 3000m a.s.l, and note on a piece of paper: the equilibrium volume of the glacier, its length and maximal thickness.
- Now choose the "wider top" glacier shape and run the model again.

**Question to answer:**

- Is the new glacier larger or smaller than before? Why?

.. admonition:: Take home messages
:class: toggle
Expand Down Expand Up @@ -79,17 +83,17 @@ for an introduction about glacier mass-balance and the ELA, or our

We are going to show that the ELA is determinant in shaping glaciers.

**In "beginner mode", start by setting the ELA to 2500m a.s.l**, and note
on a piece of paper: the equilibrium volume of the glacier,
its length and maximal thickness.
**Experiment:**

**Now change the ELA up to 3500m a.s.l in 200m increments** and, at each
step, note the equilibrium volume of the glacier, its length and maximal thickness.
- In "Beginner mode", start by setting the ELA to 2500m a.s.l, and note on a piece of paper: the equilibrium volume of the glacier, its length and maximal thickness.
- Now change the ELA up to 3500m a.s.l in 200m increments and, at each step, note the equilibrium volume of the glacier, its length and maximal thickness.
- Next draw these variables on a graph, as a function of the ELA.

**Now draw these variables on a graph, as a function of the ELA.**
How does glacier volume change with ELA? Can you explain why?
What about glacier length and thickness? Are these changes linear, or more
complex?
**Questions to answer:**

- How does glacier volume change with ELA? Can you explain why?
- What about glacier length and thickness?
- Are these changes linear, or more complex?

.. admonition:: Take home messages
:class: toggle
Expand Down Expand Up @@ -119,21 +123,25 @@ The along-slope component "pulls" the glacier downwards and the perpendicular co

**Experiments:**

- *Beginner*: Use beginner mode with standard settings (constant width, mass
balance gradient of 4 and ELA of 3000) and run the model with all different
settings for the slope and use the geometry plot for inspection.
Take note on a piece of paper of the ice thickness, volume, area and length
at the end of each model run.
- *Advanced*: Conduct the same experiment as for Beginner, but additionally
switch on the timeseries plot. Also take notes of the velocity and look how
the parameters change with time in the timeseries plot.
*Beginner*:

- Use beginner mode with standard settings (constant width, mass balance gradient of 4 and ELA of 3000) and run the model with all different settings for the slope and use the geometry plot for inspection.
- Take note on a piece of paper of the ice thickness, volume, area and length at the end of each model run.

*Advanced*:

- Conduct the same experiment as for Beginner, but additionally take notes of the velocity and look how the parameters change with time in the timeseries plot.

**Questions to answer:**

- *Beginner*: which glaciers are thicker? Steep or flat ones? And why?
- *Advanced*: which glaciers are faster? Steep or flat ones? How and why does
the velocity change with time?
*Beginner*:

- Which glaciers are thicker? Steep or flat ones? And why?

*Advanced*:

- Which glaciers are faster? Steep or flat ones? How and why does
the velocity change with time?

.. admonition:: Take home messages
:class: toggle
Expand All @@ -160,27 +168,17 @@ We will use the simulator app to explore the characteristics of a surging glacie

**Experiment:**

Use the "beginner mode" with standard settings (constant width, mass balance gradient of 4 and ELA of 3000) and run the
model to create a glacier in equilibrium.
This glacier should now experience a surge which lasts for ten years:
Switch into the "advanced mode". Turn on "sliding", i.e. the glacier will "slip" on the
bedrock, and let the model advance for 10 years. Between surge events long periods of
quiescence happen: simulate one by advancing your glacier without sliding for 100 years.
Repeat the surge event and the period of quiescence. Use the timeseries plots and the
timeseries options to show the maximum velocity as well as the maximum thickness.
- Use the "beginner mode" with standard settings (constant width, mass balance gradient of 4 and ELA of 3000) and run the model to create a glacier in equilibrium.
- This glacier should now experience a surge which lasts for ten years: Switch into the "advanced mode". Turn on "sliding", i.e. the glacier will "slip" on the bedrock, and let the model advance for 10 years.
- Between surge events long periods of quiescence happen: simulate one by advancing your glacier without sliding for 100 years.
- Repeat the surge event and the period of quiescence. Use the timeseries plots and the timeseries options to show the maximum velocity as well as the maximum thickness.

**Questions to answer:**

*Beginner:*

During a surge event:

- How much faster is the glacier during a surge in comparison to a "normal" (quiescence) period?
- How much gains the glacier in length?

After a surge event:

- How can you explain the glacier retreat?
- During a surge event: How much faster is the glacier during a surge in comparison to a "normal" (quiescence) period? How much gains the glacier in length?
- After a surge event: How can you explain the glacier retreat?

*Advanced:*

Expand All @@ -192,12 +190,12 @@ After a surge event:
.. admonition:: Take home messages
:class: toggle

- during a surge event: The glacier flows faster and reaches lower in the valley.
- During a surge event: The glacier flows faster and reaches lower in the valley.
In the upper parts the accumulation of snow does change, but not much
(accumulation is slightly less since the glacier is thinner: a process called mass-balance / elevation feedback).
At the same time, a much larger area than usual of the glacier is exposed to melt below
the ELA. Therefore the glacier thins and looses volume, although it is still advancing.
- after a surge event: The glacier flow recovers its usual "slow" velocity. The glacier
- After a surge event: The glacier flow recovers its usual "slow" velocity. The glacier
will retreat until it accumulated enough ice to advance again.

**Going further:**
Expand All @@ -209,30 +207,37 @@ Velocity and thickness along the glacier

**Experiments:**

- *Beginner*: Use "Beginner mode" to simulate a glacier in equilibrium with *Width* = *Constant*, *ELA* = 3000, *Mass-balance gradient* = 4 and *Slope* = 11°.
- *Advanced*: Use "Beginner mode" to simulate a glacier with *Width* = *Wide top, narrow bottom*, *ELA* = 3500, *Mass-balance gradient* = 4 and *Slope* = 11°.
*Beginner*:

- Use "Beginner mode" to simulate a glacier in equilibrium with *Width* = *Constant*, *ELA* = 3000, *Mass-balance gradient* = 4 and *Slope* = 11°.

*Advanced*:

- Use "Beginner mode" to simulate a glacier with *Width* = *Wide top, narrow bottom*, *ELA* = 3500, *Mass-balance gradient* = 4 and *Slope* = 11°.

**Questions to answer:**

- Make a guess as to where the ice velocity along the glacier is largest?
- When you made your guess, go to "Geometry opt." and tick the box *Ice velocity (top left)* and *Ice thickness (bottom left)*.
Now the red/blue colors are showing the velocity/thickness distribution along the glacier. Did you guess correctly?
- *Advanced*: what is the influence of the glacier bed bottleneck (narrowing) on ice thickness and velocity? Why?
*Beginner:*

- Make a guess as to where the ice velocity along the glacier is largest?
- When you made your guess, go to "Geometry opt." and tick the box *Ice velocity (top left)* and *Ice thickness (bottom left)*. Now the red/blue colors are showing the velocity/thickness distribution along the glacier. Did you guess correctly?

*Advanced*:

- What is the influence of the glacier bed bottleneck (narrowing) on ice thickness and velocity? Why?

.. admonition:: Take home messages
:class: toggle

- *Beginner*:
- mass is accumulated from the top of the glacier down to the ELA (areas of positive mass-balance): all this mass must be
transported downwards, and so the ice flux at equilibrium is largest at the ELA. Larger ice flux means thicker ice
and faster glacier flow.
- below the ELA, mass is constantly ablated and the ice flux decreases: lower ice flux means thinner ice and reduced glacier flow
velocity.
- *Advanced*:
- a narrowing of glacier widths means that the same amount of ice needs to be transported through a smaller door: this
means that we have both the creation of a "traffic jam" (thickening) and an increase of ice velocity in order to transport
more mass downwards.
- in this case, the maximum velocity is no longer located around the ELA but further down (at the bottleneck)
*Beginner*:

- mass is accumulated from the top of the glacier down to the ELA (areas of positive mass-balance): all this mass must be transported downwards, and so the ice flux at equilibrium is largest at the ELA. Larger ice flux means thicker ice and faster glacier flow.
- below the ELA, mass is constantly ablated and the ice flux decreases: lower ice flux means thinner ice and reduced glacier flow velocity.

*Advanced*:

- a narrowing of glacier widths means that the same amount of ice needs to be transported through a smaller door: this means that we have both the creation of a "traffic jam" (thickening) and an increase of ice velocity in order to transport more mass downwards.
- in this case, the maximum velocity is no longer located around the ELA but further down (at the bottleneck)

Mass-balance gradient
~~~~~~~~~~~~~~~~~~~~~
Expand All @@ -255,13 +260,15 @@ around the world. Here, we will now discover how different mass-balance gradient

**Questions to answer:**

- *Beginner*:
- Which of the two glaciers (maritime or continental) is thicker (*Max ice thickness*)?
- Which is flowing faster (*Max ice velocity*)?
- Which reaches the equilibrium faster (*Time*)?
*Beginner*:

- *Advanced*:
- How are *Length*, *Area* and *Volume* affected?
- Which of the two glaciers (maritime or continental) is thicker (*Max ice thickness*)?
- Which is flowing faster (*Max ice velocity*)?
- Which reaches the equilibrium faster (*Time*)?

*Advanced*:

- How are *Length*, *Area* and *Volume* affected?

.. admonition:: Take home messages
:class: toggle
Expand Down Expand Up @@ -290,51 +297,46 @@ of the experiments, note that the total ice gain/loss at a certain elevation equ

**Experiments:**

- *Beginner*: Use "Beginner mode" and conduct runs with *Width* = *Constant* and *Width* = *Wide top, narrow bottom*,
*Beginner*:

- Use "Beginner mode" and conduct runs with *Width* = *Constant* and *Width* = *Wide top, narrow bottom*,
and note down the different AAR-eq (*ELA* = 3300, *Mass-balance gradient* = 4, *Slope* = 11°).
- *Advanced*: Conduct experiments with *Constant* width and different mass-balance gradients

*Advanced*:

- Conduct experiments with *Constant* width and different mass-balance gradients
(e.g. *Mass-balance gradient below ELA* = 4, *Mass-balance gradient above ELA* = 2 and vice versa)
in "Advanced mode". Note down the different AAR-eq.

**Questions to answer:**

- *Beginner*:
- Explain the observed AAR-eq for *Constant* width and for *Wide top, narrow bottom*.
- For *Constant width*, what values of AAR-t (below or above 0.5) do you expect for an
*Beginner*:

- Explain the observed AAR-eq for *Constant* width and for *Wide top, narrow bottom*.
- For *Constant width*, what values of AAR-t (below or above 0.5) do you expect for an
advancing and a retreating glacier? Can you confirm by looking at the AAR during the
simulation, or using the timeseries plots.

- *Advanced*:
- How is AAR-eq changing with a different mass-balance gradients below and above the ELA?
- What can you conclude from the experiments about real-world glaciers which have a typical AAR-eq
*Advanced*:

- How is AAR-eq changing with a different mass-balance gradients below and above the ELA?
- What can you conclude from the experiments about real-world glaciers which have a typical AAR-eq
between 0.5 and 0.8? (see for example
`Hawkins, 1985 <https://www.cambridge.org/core/journals/journal-of-glaciology/article/equilibriumline-altitudes-and-paleoenvironment-in-the-merchants-bay-area-baffin-island-nwt-canada/21991E0893BCCF88D611103F397D73D1>`_)

.. admonition:: Take home messages
:class: toggle

- *Beginner*:
- In the *Constant width* case and a linear mass-balance, the AAR is around 0.5.
The total ice gain/loss at a certain height is only determined by the distance away from
the ELA (e.g. the same amount of mass is accumulated 100 m above the ELA as there is mass
ablated 100 m below the ELA) and so the glacier area above the ELA equals the glacier area below (approximately).
- In the *Wide top, narrow bottom* case and a linear mass-balance, the AAR is around 0.6.
In this case the total ice gain/loss at a certain height is not only determined by the distance
away from the ELA but also from the width at a certain height (e.g. if the width 100 m above the ELA is double the width
of 100 m below the ELA, so the total ice gain is double of the total ice loss at 100 m from the ELA).
In this case the glacier length is longer compared with the case of constant width and in the lower altitudes
the more negative mass-balance leads to more ice melt. Overall, the ablation area (area below ELA) stays smaller
than the accumulation area, even with a longer glacier.
- For an advancing glacier with constant width the AAR-t is well above 0.5 (mass gain),
and in the retreating case well below 0.5 (mass loss).
- *Advanced*:
- With a mass-balance gradient below the ELA twice the gradient above the ELA, the total ice loss
is twice the total ice gain going the same distance away from the ELA. Therefore, the ablation area
(area below the ELA) only needs to be half of the accumulation area at equilibrium. For the AAR-eq
this means a value of approx. 0.6 (AAR = Ablation Area / Total Area = Ablation Area / (Accumulation Area + Ablation Area) =
Ablation Area / (0.5 * Ablation Area + Ablation Area) = 1 / 1.5 = 2 / 3).
- For real glaciers in equilibrium with AAR between 0.5 and 0.8, we can assume wider tops and larger
mass-balance gradients below the ELA.
*Beginner*:

- In the *Constant width* case and a linear mass-balance, the AAR is around 0.5.The total ice gain/loss at a certain height is only determined by the distance away from the ELA (e.g. the same amount of mass is accumulated 100 m above the ELA as there is mass ablated 100 m below the ELA) and so the glacier area above the ELA equals the glacier area below (approximately).
- In the *Wide top, narrow bottom* case and a linear mass-balance, the AAR is around 0.6. In this case the total ice gain/loss at a certain height is not only determined by the distance away from the ELA but also from the width at a certain height (e.g. if the width 100 m above the ELA is double the width of 100 m below the ELA, so the total ice gain is double of the total ice loss at 100 m from the ELA). In this case the glacier length is longer compared with the case of constant width and in the lower altitudes the more negative mass-balance leads to more ice melt. Overall, the ablation area (area below ELA) stays smaller than the accumulation area, even with a longer glacier.
- For an advancing glacier with constant width the AAR-t is well above 0.5 (mass gain), and in the retreating case well below 0.5 (mass loss).

*Advanced*:

- With a mass-balance gradient below the ELA twice the gradient above the ELA, the total ice loss is twice the total ice gain going the same distance away from the ELA. Therefore, the ablation area (area below the ELA) only needs to be half of the accumulation area at equilibrium. For the AAR-eq this means a value of approx. 0.6 (AAR = Ablation Area / Total Area = Ablation Area / (Accumulation Area + Ablation Area) = Ablation Area / (0.5 * Ablation Area + Ablation Area) = 1 / 1.5 = 2 / 3).
- For real glaciers in equilibrium with AAR between 0.5 and 0.8, we can assume wider tops and larger mass-balance gradients below the ELA.


Balance Ratio, in the footsteps of a paleo-glaciologist
Expand All @@ -352,22 +354,17 @@ the ELA is increasing.

**Experiment:**

- You made expeditions to the European Alps and Kamchatka to find two glacier areas of the last glaciological maximum,
by using landmarks (e.g. abrasive erosion, moraines, ...). You want to use this information to approximate the
ELA height and compare the past climates at these locations (note that this experiment is only fictional).
- For the European Alps glacier you found an approximated past area of 3 km². The glacier geometry
is a *Linear* bedrock profile with a slope of 11° and *wide top, narrow bottom* width along the glacier (typical shape for a glacier).
- For the Kamchatka glacier the past area was also approx. 3 km². This glacier is *getting flatter* (bedrock profile)
and *getting narrower* (width along glacier).
- You know that a typical Balance Ratio for the European Alps is around 1.5 and for the Kamchatka around 3
(e.g. `Rea, 2009 <https://www.sciencedirect.com/science/article/abs/pii/S0277379108002989?via%3Dihub>`_).
- You made expeditions to the European Alps and Kamchatka to find two glacier areas of the last glaciological maximum, by using landmarks (e.g. abrasive erosion, moraines, ...). You want to use this information to approximate the ELA height and compare the past climates at these locations (note that this experiment is only fictional).
- For the European Alps glacier you found an approximated past area of 3 km². The glacier geometry is a *Linear* bedrock profile with a slope of 11° and *wide top, narrow bottom* width along the glacier (typical shape for a glacier).
- For the Kamchatka glacier the past area was also approx. 3 km². This glacier is *getting flatter* (bedrock profile) and *getting narrower* (width along glacier).
- You know that a typical Balance Ratio for the European Alps is around 1.5 and for the Kamchatka around 3 (e.g. `Rea, 2009 <https://www.sciencedirect.com/science/article/abs/pii/S0277379108002989?via%3Dihub>`_).

**Questions:**
- Use the simulator and change its parameters in a "try and error" approach to find the corresponding past ELAs.
- Which of the two glaciers was located in a warmer environment at that time?
- How do different absolute values of the mass-balance gradients change your results?
- What additional information would be useful to know about our past glaciers in order to determine the absolute
values of the mass-balance gradients?

- Use the simulator and change its parameters in a "try and error" approach to find the corresponding past ELAs.
- Which of the two glaciers was located in a warmer environment at that time?
- How do different absolute values of the mass-balance gradients change your results?
- What additional information would be useful to know about our past glaciers in order to determine the absolute values of the mass-balance gradients?

.. admonition:: Take home messages
:class: toggle
Expand Down

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