OGGMAn open source glacier model in Python
https://oggm.org/
Thu, 10 Jun 2021 15:15:44 +0000Thu, 10 Jun 2021 15:15:44 +0000Jekyll v3.9.0New project funded!Some very good news came in the mail last week: a project proposal entitled “A future-ready Open Global Glacier Model” has
been accepted for funding by the German Research Foundation (DFG).
We responded to a specific call entitled “Qualitätssicherung von Forschungssoftware durch ihre nachhaltige Nutzbarmachung”, which is quite tricky to translate. But in short: it seeks to improve the quality of scientific software tools by improving their code to be more sustainable and maintainable. If you are interested in the specifics, you are welcome to have a look at our proposal here (pdf).
We are thrilled by this opportunity, because it will allow us to hire someone to work specifically on OGGM internals, without the usual pressure to produce new results. We will be looking for a new collaborator soon, so watch this space!
Thu, 10 Jun 2021 00:00:00 +0000
https://oggm.org/2021/06/10/software-project/
https://oggm.org/2021/06/10/software-project/workshoptutorialJob announcementAs a mid-size university with 270 professorships and 20.000 students, the University of Bremen maintains a strong and internationally renowned interdisciplinary research focus on oceans and the global climate. The Institute of Geography invites applications for the following academic position (under the condition of job release), starting September 1, 2021 (or as soon as possible thereafter), ending June 30, 2023:
Postdoctoral Researcher
salary grade EG 13 TV-L
full time position
Reference number: A65/21
The postdoc will work in the Climate Lab of the Institute of Geography, in the project “Ice-Ocean Interaction of Peripheral Greenland Glaciers”, funded by the German Ministry of Research and Education (BMBF) within the collaborative project cluster GReenland ice sheet/OCEan Interaction (see https://groce.de/en/).
The postdoc (w/m/d) will focus on regional modelling of peripheral glaciers in north-eastern Greenland within the framework of the Open Global Glacier Model (see http://oggm.org), which will be forced by regional ocean and atmospheric data sets; they will implement a refreezing parameterization in the mass balance module of OGGM, and they will test the sensitivity of OGGM to different boundary conditions. Finally, they will produce projections of freshwater input into the ocean.
Close collaboration is expected with other glaciologists and oceanographers within the project cluster, e.g., to obtain data for calibration and validation, to distribute runoff estimates used as a boundary condition for other models, and to ensure consistency with ice sheet model-based mass change estimates.
To apply successfully, you will:
have a PhD in a field of Earth science with proven, strong mathematical/physical background, or a PhD in physics/mathematics/informatics with previous experience in an Earth science;
have experience in glaciology and/or oceanography;
have a publication record in peer-reviewed, international journals;
have demonstrated skills in scientific programming;
be fluent in English (equivalent to CEFR level C1).
It will be advantageous if you can demonstrate:
working experience in a supercomputing environment;
working experience with Python;
proficiency in German.
Questions regarding the positon should be addressed to Ben Marzeion (ben.marzeion [at] uni-bremen.de).
The University of Bremen is an equal opportunity employer and aims particularly at increasing the share of female faculty members in research and teaching. Thus, qualified women are especially encouraged to apply. International applications and those from candidates with a migration background are explicitly appreciated. Candidates with disabilities will be given preference in case of equal qualifications.
Please submit your application including the reference number (A65/21), a letter of motivation, CV (with copies of certificates), and contact details of two referees until June 9th, 2021 to:
Universität Bremen
Fachbereich 8
FB 8/1 – Reference number A65/21
Universitäts-Boulevard 13
28359 Bremen
or by E-Mail to: fb08.bewerbung [at] uni-bremen.de
Wed, 19 May 2021 00:00:00 +0000
https://oggm.org/2021/05/19/postdoc-position/
https://oggm.org/2021/05/19/postdoc-position/OtherOGGM presentation and tutorial @IGEIn the context of Fabien’s visit to the IGE in Grenoble, we will organize an afternoon tutorial for all lab members interested in OGGM.
When?
Tuesday May 18th!
15H-15H45 (CEST): general presentation and discussion
16H-18H (CEST): online tutorials
Where?
Via zoom, unfortunately. The room link will be shared internally: contact us if you didn’t receive it!
Who?
Anybody from the IGE interested in OGGM and glacier modelling in general! The first part (presentation) will be
very general and tailored for a general audience of glaciologists and glacier modellers. The second
part (tutorials) is for the curious and interested alike, who would like to see how OGGM is built and
run it themselves “on the cloud”.
What will we do?
Part I (15H00-15H45): presentation of the OGGM project.
Objectives of the OGGM project: OGGM as a “modelling framework”
Current developments and future plans (read: the science questions we are trying to address)
What OGGM does not intend to be (and why it is only useful for certain applications)
Open discussion
Part II (16H-18H): online tutorials.
Getting started: building blocks of OGGM, model fundamentals
Hydrological applications (in construction): a fun application of OGGM
Based on interest / demand: projections or ice thickness estimation with OGGM, using your own inventory / bed thickness with OGGM, etc…
Do I need to prepare anything?
No! The tutorials will run online on OGGM-Hub. Some experience with
Python and Jupyter Notebooks is useful, but not mandatory.
Organizers
Nicolas Champollion, Fabien Maussion.
Tue, 27 Apr 2021 00:00:00 +0000
https://oggm.org/2021/04/27/ige-tutorial/
https://oggm.org/2021/04/27/ige-tutorial/workshoptutorial5th OGGM workshop moved (again)Due to the current pandemic situation, the 5th OGGM workshop has been moved (again), this time to September 20 to 24 (Monday to Thursday), and will take place in Neuharlingersiel, Germany, as planned before. Registrations will remain valid. Also note that there are still a few open spots. To register, please contact info@oggm.org.
What is it ?
The original post with all relevant information can be found here
Organisers
Ben Marzeion, Fabien Maussion.
Past workshops
1st OGGM workshop
2nd OGGM workshop
3rd OGGM workshop
4th OGGM workshop
Tue, 13 Apr 2021 00:00:00 +0000
https://oggm.org/2021/04/13/5th-workshop-new-date-again/
https://oggm.org/2021/04/13/5th-workshop-new-date-again/workshopComputing sea-level rise equivalent from glacier mass lossEstimating sea-level rise from glacier mass loss is not as trivial as it might seem. That is not only because there are various (hydrological) processes that can
prevent the meltwater from directly ending up in the oceans (e.g. formation of glacial lakes/dams, percolation, etc.), but due to other
aspects as, e.g., the different densities of ice, freshwater, and ocean water. Another issue is the fact that some of the global glacier ice is situated
below sea-level, which needs to be accounted for in order not to overestimate sea-level changes due to glacier mass loss. Moreover, ice of glaciers
that drain into the ocean is likely to produce icebergs. Because melt-/freshwater has a lower density than the ocean water that is displaced by the iceberg,
a small part of the sea-level rise that is produced by such icebergs will occur with a delay over the time they are melting. This is known as a
halosteric effect. A competing effect is the thermosteric one, which describes the fact that ice melt that is induced by extracting the necessary latent heat from
the ocean will cause a contraction of the ocean water due to the implied cooling (Jenkins, A., and Holland, D., 2007).
In this Jupyter Notebook I compare various approaches to calculating sea-level rise from glacier mass loss,
respecting the density and volume below sea-level issues described above. I put the links to the data and notebook below in case you want to play around with it yourself.
The equations proposed in the Notebook should theoretically be a bit sounder than previously used in Farinotti et al., 2019. Yet, the quantitative differences are
quite small globally (2.4 mm SLR, 0.8%), but can reach 4% regionally.
You can find the data here and the raw notebook here.
References
Farinotti, D., Huss, M., Fürst, J.J. et al. (2019). A consensus estimate for the ice thickness distribution of all glaciers on Earth.
Nat. Geosci., 12, 168–173. doi:10.1038/s41561-019-0300-3.
Jenkins, A., and Holland, D. (2007). Melting of floating ice and sea level rise, Geophys. Res. Lett., 34, doi:10.1029/2007GL030784.
Thu, 04 Mar 2021 00:00:00 +0000
https://oggm.org/2021/03/04/slr-bsl/
https://oggm.org/2021/03/04/slr-bsl/sciencesea-levelRelease of OGGM v1.4We are very proud to announce the new stable release of OGGM, version 1.4.0!
It is the achievement of more than one year of work, with many improvements (and a
bit of struggle) on the way.
This release, more than any other before, reinforces the conversion
of OGGM from a “glacier model” to a “modelling framework”, allowing
multiple workflows and parameterizations to co-exist and be compared, while
still relying, for example, on the same input data for boundary conditions, or on the
same ice dynamics model for glacier evolution simulations.
🚀 Now let us highlight some of the main improvements you’ll find in OGGM 1.4!
New tutorials website
We are now using jupyter-book to display our
notebook tutorials at http://oggm.org/tutorials.
The main advantage of this new system is that readers can now see the
rendered notebooks (and the expected output) without having to run the
tutorials themselves. It is faster to find a recipe for what you are looking
for, and copy-paste bits of code from the website.
It is also easier than ever to start a notebook in your browser with MyBinder:
New way to compute the glacier flowlines
Glaciers in OGGM are represented as “1.5D flowline glaciers”, which is
a simplified, computationally efficient way to simulate ice flow.
As of v1.4, users can now choose between two different methods to compute the flowlines:
from multiple geometrical centerlines (the default), or (new!) from binned elevation bands
(called “elevation band flowlines” in the model workflow).
Elevation band flowlines are
computed after Huss & Farinotti 2012 and
the algorithm description in Werder et al, 2020 and
are a simpler, non-geometrical but robust way to convert 2D glacier geometries into flowlines.
Cross-sections of the two flowline types for Hintereisferner. Note the different lengths.
Once computed, both representations are programmatically equivalent for OGGM: both can be
used by the model in the exact same way.
Visit our documentation for a
method description and an in-depth discussion of the strengths and weaknesses of both options.
OGGM-Shop
OGGM v1.4 has a new module called shop
(from oggm import shop).
OGGM-Shop
allows user to write a “shopping list” of data that they wish to add to their glacier directories.
“Glacier directories” are the central data structure in OGGM, and contain all kinds of glacier specific data.
With OGGM-Shop, users can now automatically add additional data to their directories, such
as ice velocities from ITS_LIVE or ice thickness data from
the consensus ice thickness estimate.
Ice velocities (left, m yr-1) and ice thickness (right, m), obtained from the OGGM-Shop and the data sources mentioned above.
OGGM-Shop also contains several other datasets, among others
RGI-TOPO or a number
of pre-processed glacier directories, ready to be used by OGGM.
New members of the OGGM ecosystem: PyGEM and OGGM-VAS
PyGEM is a state-of-the art glacier evolution
model developed by David Rounce and colleagues. It has a much more advanced calibration strategy than OGGM, and additional physics in its mass-balance model.
Over the last year, PyGEM and OGGM developers have worked hard to make their models compatible: PyGEM is now able to run
with OGGM’s ice dynamics model! More info on this collaboration will be advertised soon – stay tuned!
OGGM-VAS is a python re-implementation of the
well known Marzeion et al., 2012 model,
based on Volume Area Scaling (hence the name).
This re-implementation is strictly equivalent to the original 2012 model, but adopts “the OGGM workflow”.
This means that both models now also agree on the boundary conditions and climate data. OGGM-VAS has
been developed by Moritz Oberrauch during his master thesis.
Assets & downloads
With OGGM v1.4, we will start to provide more derived products from OGGM
(some of them being around since a long time but not really advertized).
Visit Assets & downloads
for an overview. We will eventually provide glacier projections as well
(when they have been peer-reviewed), but currently we can highlight some
tabular data statistics from glaciers, or shapefiles of the glacier
centerlines available at the global scale (image below).
Shapefile of OGGM’s flowlines and widths for a subset of RGI region 15.
Regional calibration routines
As of OGGM v1.4, users can now calibrate the ice dynamics parameters (Glen A and sliding) to
match other ice thickness products, most notably
the consensus ice thickness estimate.
This can be applied on any number of glaciers, but we recommend to apply this calibration on large number of
glaciers, for example at the regional scale.
Additionally, users can now bias-correct OGGM’s standard mass-balance model to
match regional geodetic estimates,
as provided for example by Zemp et al., 2019.
Visit our documentation for more information!
OGGM-Hub
Welcome screen of https://hub.oggm.org
hub.oggm.org is our own JupyterHub deployment of OGGM
on our servers in Bremen. It works similarly to MyBinder (see try OGGM online) but it is bound to a username (you’ll need an account) and is therefore persistent (your files are saved between sessions). It also gives you access to much more computing resources! It is a great way to learn OGGM online, and even to do simple catchment scale simulations.
In order to be able to log in, you will need to have a (free) user account. It is super easy, just write us an email if you want to try it out!
And much more!
There have been many other changes to the model too numerous to be listed here,
such as the addition of a calving parameterization.
Visit our what’s new section if you want to know more, or join us on our slack channel (write us an email to register)!
List of contributors
Thanks to all who have contributed to this release!
Anouk Vlug
Beatriz Recinos
David Rounce*
Julia Eis
Li Fei*
Lilian Schuster*
Lizz Ultee*
Matthias Dusch
Nicolas Champollion
Sarah Hanus*
Timo Rothenpieler
(first time contributors are indicated with a *)
Thu, 18 Feb 2021 00:00:00 +0000
https://oggm.org/2021/02/18/oggm-v140/
https://oggm.org/2021/02/18/oggm-v140/releasetutorialmodelTwo PhD graduations in the OGGM teamCongratulations to the OGGM team members Dr. Julia Eis and Dr. Beatriz Recinos for their successful PhD defense!
The entire OGGM team is proud of you, and we are extremely thankful for your contributions to the model.
I passed my Kolloquium today 😆 ... a hard journey indeed but one that I wouldn't have imagined myself completing it if it wasn't for all those people that helped me out! all @OGGM_org #team @IRTG_ArcTrain @no1benjones and family&friends #GlaciologosSalvadoreños (how many?) pic.twitter.com/ndF1QaftaP— Beatriz Recinos (@bmrocean) December 21, 2020
That is probably the best thing I've ever made possible, but please don't forget: YOU are my makers 🙏Congrats @eis_julia on your successful thesis defence and looking forward to see all the things you will do next! https://t.co/0jvhQFFClz— OGGM (@OGGM_org) November 26, 2020
Mon, 21 Dec 2020 00:00:00 +0000
https://oggm.org/2020/12/21/phd-theses/
https://oggm.org/2020/12/21/phd-theses/sciencepublicationsphdNew publications outside of the OGGM core teamTwo publications making use of the OGGM model came out recently:
Khadka, M., Kayastha, R. B. and Kayastha, R.: Future projection of cryospheric and hydrologic regimes in Koshi River basin, Central Himalaya, using coupled glacier dynamics and glacio-hydrological models, J. Glaciol., 1–15, doi:10.1017/jog.2020.51, 2020.
Parkes, D. and Goosse, H.: Modelling regional glacier length changes over the last millennium using the Open Global Glacier Model, The Cryosphere, 14, 3135–3153, doi:10.5194/tc-14-3135-2020, 2020.
What makes these publications very special to us is that, for the first time that we are aware of, the authors of these publications were able to use and apply the OGGM model without any involvement of the OGGM core team, and without any technical support from us.
This is a big step for OGGM, and a fantastic reward for all the work that went into documenting and making OGGM useful and user friendly.
We still have a lot of work to do to make the model even more user friendly of course, but we are proud of what we achieved. We are also seeking funding to make the OGGM codebase even better and cleaner, but it turns out to be quite difficult using traditional funding schemes. If you are aware of software oriented research funds that we could apply for, let us know!
Fri, 25 Sep 2020 00:00:00 +0000
https://oggm.org/2020/09/25/new-publications/
https://oggm.org/2020/09/25/new-publications/sciencepublicationsNumerics in OGGM's ice dynamics modelOne of the recent blog posts discussed the OGGM time stepping scheme. In short, it explains that OGGM still uses an ad-hoc CFL condition to determine the time step. An “optimal” value, currently in use, was determined through many empirical tests, making a compromise between speed and error growth. However, since this value was not determined by a rigorous mathematical treatment:
it does not ensure numerical stability for all glaciers: some would need a lower CFL condition to prevent error growth,
it is not optimal: for some glaciers, we could possibly use a higher CFL value and thus reduce the computation time.
So why don’t we just crunch the numbers and determine the optimal (rigorously speaking) CFL value? Well, it’s because stability analysis of our time stepping scheme is not that easy. In this blog post we will look at why that is.
Some math & physics basics
As so many other simple glaciological models, OGGM is also based on the shallow ice approximation. In this formulation, the building blocks of glaciers are vertical columns of ice, each moving with a velocity dependent on the ice thickness and the inclination (gradient) of the ice surface (a bit more detail can be found e.g. in a textbook by Hutter, K. (1983).
To model the movement of the ice, we have some flexibility in how we formulate the governing equations. Shallow ice models usually solve diffusion-type equations - this is because generally, these cause fewer numerical issues than advection-type equations.
A short reminder: in the diffusion equation, the time derivative of a variable $\psi$ depends on the divergence of its gradient. On the other hand, in the advection equation, the time derivative of a variable depends on its flux divergence:
Diffusion: $~~ \frac{\partial \psi}{\partial t} \propto \nabla \cdot \left(D\nabla \psi \right)\qquad $ Advection: $~~\frac{\partial \psi}{\partial t} \propto \nabla \cdot \left(u \psi \right) $ ,
where $\psi$ is the variable of interest, $D$ is a diffusion coefficient and $u$ is velocity of the flow. In diffusion-based models $\psi$ is the surface elevation.
However, a diffusion formulation does not provide enough flexibility for OGGM; we want to allow for changing widths of the glaciers and various bed shapes (rectangular, trapezoidal or parabolic). Thus, in the OGGM model we choose to solve an advection-type equation, which gives us a bit more flexibility in this regard. In OGGM, the advected variable is the glacier cross-section (denoted by uppercase $S$):
$\frac{\partial S}{\partial t} = w\dot{m} - \nabla \cdot \left(uS \right)$
where $w$ is the width of the glacier at its surface, $\dot{m}$ is the mass balance and $u$ is the column integrated velocity. In short, the model advects the glacier cross section (and thus mass) along the flow. This formulation allows us to solve the same equation for each bed shape. More details about this formulation can be found in the OGGM documentation.
Since other models use different formulations and solve other equations, we can’t just save ourselves the work and look up the stability conditions. And so we will have to try and tackle this by ourselves.
The usual approach: von Neumann stability analysis
The most common and basic method for determining the CFL criterion is the so-called von Neumann analysis. This approach requires first decomposing the variable of interest into a discrete Fourier series, and then mathematically determining the conditions under which the amplitude of each separate Fourier mode does not grow over time. However, this method can be used only under certain conditions ([Wesseling, P. (2009)], Sec. 5.8).
The first limitation is that this method works only for linear equations with constant coefficients (in our case, that would mean that $u$ is constant in space); in non-linear equations, there is an interaction between various Fourier modes, and thus the modes cannot be each treated separately. Second, again because of the Fourier decomposition, we require either a periodic boundary condition, or an infinite spatial domain. The third requirement is constant grid spacing. Let’s look at all these conditions one by one.
Linearity
In the shallow ice equation, the velocity $u$ depends among others on the ice thickness $h$ and the surface inclination $\alpha$ (defined as $\alpha = -\frac{\partial s}{\partial x} = -\frac{\partial}{\partial x}(h+b)$, where lowercase $s$ is the ice surface elevation, and $b$ is the bedrock elevation). Thus, the velocity is variable in space:
$ u = f_d (\alpha \rho g)^{n} h^{n+1} + f_s (\alpha \rho gh)^{n} h^{n-1} . $
(Again, for more details and definitions, go here.)
Furthermore, for all bed shapes, the cross section $S$ is a function of the ice thickness $h$:
$S = wh$ (rectangular)
$\qquad S = w_0h + \frac{\lambda h^2}{2}$ (trapezoidal)
$\qquad S = \frac{2}{3}wh=\frac{4h^{3/2}}{3P^{1/2}} $ (parabolic)
Here, the width $w$ of a rectangular bed is a given constant. For the trapezoidal bed, $w_0$ is the bed width at the valley floor and $\lambda$ determines the wall angle. The bed shape of a parabolic glacier is further determined by a shape parameter $P_s = \frac{4h}{w^2}$, so that the cross section is again determined only by one constant parameter and the ice thickness.
For each bed shape we can invert this relationship between the cross-section and the ice thickness, and say that $h=h(S)$:
$h = \frac{S}{w}$ (rectangular)
$\qquad h = \frac{\sqrt{w_0^2 + 2 \lambda S}-w_0}{\lambda}$ (trapezoidal)
$\qquad h = \left( \frac{3}{4}P_s^{1/2}S \right)^{2/3}$ (parabolic)
Because of the linearity condition, it is important to stress again that cross-section and ice thickness are not independent for any bed shape. Then, when the shallow ice equation is written out in full, it is easy to see that the term $\nabla \cdot (uS) $ is indeed pretty complicated and non-linear because of the dependence of $u$ on $\alpha$ and $h$ and thus also indirectly on $S$:
$ \frac{\partial S}{\partial t} = w\dot{m} - \nabla \cdot \left[ \left(f_d (\alpha \rho g)^{n} h^{n+1} + f_s (\alpha \rho gh)^{n} h^{n-1} \right) S \right] $
For now, basal slipping is ignored in the model (i.e. $f_s = 0 $), but the first term still remains non-linear: the linearity condition is not fulfilled. This fact is based purely on the differential equation we’re solving and has nothing to do with its numerical implementation.
Boundary conditions
This condition for the von Neumann analysis is also not fulfilled in our model - we do not use periodic boundary conditions. At the uppermost point of the glacier, we do not allow flow into the numerical domain.
Grid spacing
This requirement is the only one fulfilled - the grid spacing indeed does not change over the spatial domain in the OGGM numerical model.
Thus, even not taking the numerical implementation into account, the basic von Neumann method is not usable for determining the CFL condition for our numerical scheme.
Perturbation method
The next thing to try would be to perform the stability analysis using the perturbation approach.
This method is nicely illustrated by [Budd, W. F., and Jenssen, D. (1975)], who apply it to an advection equation similar to ours (albeit less complicated). The central assumption of this method is that the glacier is in steady state - to analyze stability, we then introduce a small perturbation in the variable of interest (ice thickness in the case of Budd and Jenssen, or the glacier cross-section in the case of OGGM) and see under what circumstances this perturbation grows in time, and under what circumstances it decays.
The first step is to separate the variable of interest into a steady state part and a perturbation, and to determine the linearized differential equation for the perturbation growth in time. This step is still independent of the numerical scheme. However, we need to consider the interplay between various variables - a perturbation in the cross-section $S$ will of course lead to perturbations in both the ice thickness $h$ and the surface gradient $\alpha$. Thus, we have to express both $h$ and $\alpha$ in terms of the cross-section. Because of the different relationships between $S$ and $h$ for various bed shapes (see the section above), already at this stage of analysis we can see that the linearized equation and thus also the CFL condition will vary between the three cases.
Once we have the linearized differential equations for error growth, the numerical scheme comes into play and von Neumann analysis can be used to determine the stability condition. In principle, this is doable - however, even for a simpler case considered by Budd and Jenssen, the math is already quite complicated, and the resulting expression for a stability condition needs further assumptions and simplifications to be practically usable. With our equation, the analysis would be very challenging for the parabolic and trapezoidal bed shapes.
Furthermore, even if we did find the CFL condition for our equation and the numerical scheme with this approach, we would have to keep in mind the central assumption (i.e. that the glacier is in steady state), which is rarely fulfilled.
Other ways to perform stability analysis
Or, some of the dead ends I found on the way
In literature on numerical modeling you can find a few more ways of performing stability analysis than just the ones mentioned above. However, whether we can actually use the methods is restricted by the equation we’re solving as well as by the numerical implementation of it. For completeness, I would like to briefly mention some of the methods that I stumbled upon, and explain how they work and why we cannot apply them to our problem.
Local von Neumann analysis
A very well written textbook by [Hirsch, C. (2007)] discusses this method under the section “Stability analysis for non-linear problems” (Ch. 8).
When the coefficients are variable ($u \neq$ const.), this method can be used to determine the necessary (but not sufficient) conditions for stability. This method freezes the coefficient in space, and determines the stability conditions locally. The most stringent requirement are then chosen and applied to the entire domain.
However, this method could be used only if we solved an equation of the form
$ \frac{\partial S}{\partial t} = u(x)\frac{\partial S}{\partial x} $
where $u$ is variable is space, but it is independent of $S$. However, in our case we have an equation of the form
$ \frac{\partial S}{\partial t} = \frac{\partial \left( u(S)S \right)}{\partial x}, $
and so we cannot apply this method. As Hirsch states, this method is only applicable “for linear problems with non-constant coefficients”.
Matrix/eigenvalue method
I read about this method before I realized that I have to look for methods that work with non-linear equations - I found it relevant because it can be used for problems with non-periodic boundary conditions. And although we can’t use this method, I decided to mention it here because it seems to be pretty widely used. (If we wanted to use this method, we would have to linearize our equation first again.)
As the name already implies, the method relies on linear algebra to find stability conditions. We start with the linear initial boundary value problem
$ \frac{\partial u}{\partial t} = L(u), $
where $u$ is some variable of interest, and $L$ is a space differential operator acting on $u$. This equation can be discretized and reformulated as a system of differential equations, one for each grid point:
$\frac{dU}{dt} = SU + Q. $
Here, $U$ is the vector of $u$-values at grid points, and $S$ is a space discretization matrix - it determines how these values are combined to form spatial derivatives at each point. Finally, $Q$ contains the non-homogeneous terms and boundary values. The structure of $S$ depends on the chosen numerical scheme.
The stability analysis is then based on the eigenvalue structure of the matrix S - if all the eigenvalues don’t fall below a certain value, the scheme is unstable. However, finding the eigenvalues in the first place can be pretty challenging. A good detailed explanation can again be found in Hirsch (Ch. 10).
Take home points
Stability analysis for non-linear problems with non-periodic boundary conditions is hard.
The only usable analysis approach that I found is the perturbation method - however, until we do this, the CFL will stay ad hoc.
References
Hutter, K. (1983). Theoretical Glaciology, Mathematical Approaches to Geophysics, D. D. Reidel.
Wesseling, P. (2009). Principles of computational fluid dynamics (Vol. 29). Springer Science & Business Media.
Budd, W. F., & Jenssen, D. (1975). Numerical modelling of glacier systems. IAHS publ, 104, 257-291.
Hirsch, C. (2007). Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics. Elsevier.
Wed, 08 Jul 2020 00:00:00 +0000
https://oggm.org/2020/07/08/numerics/
https://oggm.org/2020/07/08/numerics/sciencemodelnumericsJob announcementAs a mid-size university with 270 professorships and 20.000 students, the University of Bremen maintains a strong and internationally renowned interdisciplinary research focus on oceans and the global climate.
The Institute of Geography, University of Bremen, invites applications for the following academic position (under the condition of job release), starting September 1, 2020, for the duration of three years:
Postdoctoral Researcher (f/m/d)
salary grade EG 13 TV-L
full time position
Reference number: A131/20
The postdoc will work in the Climate Lab of the Institute of Geography.
This postdoctoral position is funded by the European Commission through the PROTECT H2020 project (Sept. 2020 - Aug. 2024, duration of the postdoc: Sept. 2020 to Aug. 2023). PROTECT gathers 26 international partners and aims to project the glaciers’ and ice sheets’ contributions to sea-level rise, and to assess local implications. More details on PROTECT can be found here.
In our work package we will - jointly with partners at the ETH Zurich and the University of Zurich - improve projections of the glaciers’ contribution to global sea level. The postdoc to be employed at the University of Bremen will develop and implement a parameterization of the effects of debris cover on glacier mass change on the global scale. The performance of the parameterization will be evaluated using the global glacier models GloGEM and OGGM, using calibration and cross-validation tools based on large-scale observations of glaciers from remote sensing.
The postdoc will also contribute to the coordination of the Glacier Model Intercomparison Project, in order to advance large-ensemble projections of the glaciers’ contribution to sea-level rise during the 21st century.
To apply successfully, you will:
have a PhD in a field of Earth science, physics, or mathematics with a background in numerical modeling of glaciers;
have experience with advanced glacier model evaluation methods and/or effects of debris cover on mass balance;
be a proficient user of Python for scientific computing;
have a publication record in peer-reviewed, international journals;
be fluent in English (equivalent to CEFR level C1).
It will be advantageous if you can demonstrate experience in:
collaborating in large, international research collaborations;
applying for competitive, external funding;
working in a supercomputing environment.
Proficiency in German is not necessary, but may be helpful for everyday life in Bremen.
The University of Bremen is an equal opportunity employer and aims particularly at increasing the share of female scientists employed in research and teaching. Thus, qualified women are especially encouraged to apply. International applications and those from candidates with a migration background are explicitly appreciated. Candidates with disabilities will be given preference in case of equal qualifications.
Questions regarding the position should be addressed to Ben Marzeion (ben.marzeion [at] uni-bremen.de).
Please submit your application including the reference number, a letter of motivation, CV (with copies of certificates), and contact details of two referees until June 24, 2020 to:
Universität Bremen
Fachbereich 8
FB8/3 – Reference number A131/20
Universitäts-Boulevard 13
28359 Bremen
or by E-Mail to: fb08.bewerbung [at] uni-bremen.de
All applications received before June 24, 2020 will be considered, thereafter review will continue until the position is filled.
Tue, 02 Jun 2020 00:00:00 +0000
https://oggm.org/2020/06/02/postdoc-position/
https://oggm.org/2020/06/02/postdoc-position/Other