tlabgum.rst - pism - [fork] customized build of PISM, the parallel ice sheet model (tillflux branch)
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tlabgum.rst (6228B)
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1 .. include:: ../../global.txt
2
3 .. _sec-labgum:
4
5 An SIA flow model for a table-top laboratory experiment
6 -------------------------------------------------------
7
8 Though there are additional complexities to the flow of real ice sheets, an ice sheet is a
9 shear-thinning fluid with a free surface. PISM ought to be able to model such flows in
10 some generality. We test that ability here by comparing PISM's isothermal SIA numerical
11 model to a laboratory observations of a 1% Xanthan gum suspension in water in a
12 table-top, moving-margin experiment by R. Sayag and M. Worster
13 :cite:`SayagWorster2013`, :cite:`SayagPeglerWorster2012`. The "gum" fluid is more shear-thinning
14 than ice, and it has much lower absolute viscosity values, but it has the same density.
15 This flow has total mass `\sim 1` kg, compared to `\sim 10^{18}` kg for the Greenland ice
16 sheet.
17
18 We compare our numerical results to the "constant-flux" experiment from
19 :cite:`SayagWorster2013`. :numref:`fig-labgumexperiment` shows the experimental setup by
20 reproducing Figures 2(c) and 2(d) from that reference. A pump pushes the translucent
21 blue-dyed fluid through a round 8 mm hole in the middle of a clear table-top at a mass
22 rate of about 3 gm/s. The downward-pointing camera, which produced the right-hand figure,
23 allows measurement of the location of margin of the "ice cap", and in particular of its
24 radius. The measured radii data are the black dots in :numref:`fig-labgumresult`.
25
26 .. figure:: figures/labgumexperiment.png
27 :name: fig-labgumexperiment
28
29 Reproduction of Figures 2(c) and 2(d) from :cite:`SayagWorster2013`. Left: experimental
30 apparatus used for "constant-flux release" experiment. Right: snapshot of constant-flux
31 experiment (plan view), showing an axisymmetric front.
32
33 The closest glaciological analog would be an ice sheet on a flat bed fed by positive basal
34 mass balance (i.e. "refreeze") underneath the dome, but with zero mass balance elsewhere
35 on the lower and upper surfaces. However, noting that the mass-continuity equation is
36 vertically-integrated, we may model the input flux (mass balance) as arriving at the
37 *top* of the ice sheet, to use PISM's climate-input mechanisms. The flow though the
38 input hole is simply modeled as constant across the hole, so the input "climate" uses
39 ``-surface given`` with a field ``climatic_mass_balance``, in the bootstrapping
40 file, which is a positive constant in the hole and zero outside. While our replacement of
41 flow into the base by mass balance at the top represents a very large change in the
42 vertical component of the velocity field, we still see good agreement in the overall shape
43 of the "ice sheet", and specifically in the rate of margin advance.
44
45 Sayag & Worster estimate Glen exponent `n = 5.9` and a softness coefficient `A = 9.7
46 \times 10^{-9}\,\text{Pa}^{-5.9}\,\text{s}^{-1}` for the flow law of their gum suspension,
47 using regression of laboratory measurements of the radius. (Compare PISM defaults `n=3`
48 and `A\approx 4\times 10^{-25}\,\text{Pa}^{-3}\,\text{s}^{-1}` for ice.) Setting the Sayag
49 \& Worster values is one of several changes to the configuration parameters, compared to
50 PISM ice sheet defaults, which are done in part by overriding parameters at run time by
51 using the ``-config_override`` option. See ``examples/labgum/preprocess.py`` for
52 the generation of a configuration ``.nc`` file with these settings.
53
54 To run the example on the default 10 mm grid, first do
55
56 .. code-block:: none
57
58 ./preprocess.py
59
60
61 and then do a run for 746 model seconds :cite:`SayagWorster2013` on the 10 mm grid on a
62 `520\,\text{mm}\,\times 520\,\text{mm}` square domain using 4 processors:
63
64 .. code-block:: none
65
66 ./rungum.sh 4 52 &> out.lab52 &
67
68 This run generates text file ``out.lab52``, diagnostic files ``ts_lab52.nc`` and
69 ``ex_lab52.nc``, and final output ``lab52.nc``. This run took about 5 minutes on
70 a 2013 laptop, thus roughly real time! When it is done, you can compare the modeled radius
71 to the experimental data:
72
73 .. code-block:: none
74
75 ./showradius.py -o r52.png -d constantflux3.txt ts_lab52.nc
76
77 You can also redo the whole thing on higher resolution grids (here: 5 and 2.5 mm), here
78 using 6 MPI processes if the runs are done simultaneously, and when it is done after
79 several hours, make a combined figure just like :numref:`fig-labgumresult`:
80
81 .. code-block:: none
82
83 ./preprocess.py -Mx 104 -o initlab104.nc
84 ./preprocess.py -Mx 208 -o initlab208.nc
85 ./rungum.sh 2 104 &> out.lab104 &
86 ./rungum.sh 4 208 &> out.lab208 &
87 ./showradius.py -o foo.png -d constantflux3.txt ts_lab*.nc
88
89 .. figure:: figures/labgumradius.png
90 :name: fig-labgumresult
91
92 Radius `r_N(t)` for runs with 10 mm (``ts_lab52.nc``), 5 mm (``ts_lab104.nc``), and 2.5
93 mm (``ts_lab208.nc``) grids, compared to observations from Sayag & Worster's
94 :cite:`SayagWorster2013` table-top "ice cap" (gravity current) made from a 1% Xanthan
95 gum suspension, as shown in Figure :numref:`fig-labgumexperiment`.
96
97 We see that on the coarsest grid the modeled volume has "steps" because the margin
98 advances discretely. Note we are computing the radius by first computing the fluid-covered
99 area `a` on the cartesian grid, and then using `a=\pi r^2` to compute the radius.
100
101 Results are better on finer grids, especially at small times, because the input hole has
102 radius of only 8 mm. Furthermore this "ice cap" has radius comparable to the hole for the
103 first few model seconds. The early evolution is thus distinctly non-shallow, but we see
104 that increasing the model resolution reduces most of the observation-model difference. In
105 fact there is little need for "higher-order" stresses because the exact similarity
106 solution of the shallow continuum equations, used by Sayag & Worster, closely-fits the
107 data even for small radius and time (see :cite:`SayagWorster2013`, Figure 4).
108
109 In any case, the large-time observations are very closely-fit by the numerical results at
110 all grid resolutions. We have used the Glen-law parameters `n,A` as calculated by Sayag &
111 Worster, but one could do parameter-fitting to get the "best" values if desired. In
112 particular, roughly speaking, `n` controls the slope of the results in
113 :numref:`fig-labgumresult` and `A` controls their vertical displacement.