RGI-TOPO for RGI 7.0

OGGM was used to generate the topography data used to compute the topographical attributes and the centerlines products for RGI v7.0.

Here we show how to access this data from OGGM.

Input parameters

This notebook can be run as a script with parameters using papermill, but it is not necessary. The following cell contains the parameters you can choose from:

# The RGI-id of the glaciers you want to look for
# Use the original shapefiles or the GLIMS viewer to check for the ID: https://www.glims.org/maps/glims
rgi_id = 'RGI2000-v7.0-G-01-06486'  # Denali

# The default is to test for all sources available for this glacier
# Set to a list of source names to override this
sources = None
# Where to write the plots. Default is in the current working directory
plot_dir = f'outputs/{rgi_id}'
# The RGI version to use
# V62 is an unofficial modification of V6 with only minor, backwards compatible modifications
prepro_rgi_version = 62
# Size of the map around the glacier. Currently only 10 and 40 are available
prepro_border = 10
# Degree of processing level.  Currently only 1 is available.
from_prepro_level = 1

Check input and set up

# The sources can be given as parameters
if sources is not None and isinstance(sources, str):
    sources = sources.split(',')

# Plotting directory as well
if not plot_dir:
    plot_dir = './' + rgi_id
import os
plot_dir = os.path.abspath(plot_dir)

from oggm import cfg, utils, workflow, tasks, graphics, GlacierDirectory
import pandas as pd
import numpy as np
import xarray as xr
import rioxarray as rioxr
import geopandas as gpd
import salem
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import AxesGrid
import itertools

from oggm.utils import DEM_SOURCES
from oggm.workflow import init_glacier_directories

# Make sure the plot directory exists
utils.mkdir(plot_dir);
# Use OGGM to download the data
cfg.initialize()
cfg.PATHS['working_dir'] = utils.gettempdir(dirname='OGGM-RGITOPO-RGI7', reset=True)
cfg.PARAMS['use_intersects'] = False

2026-05-15 17:18:49: oggm.cfg: Reading default parameters from the OGGM `params.cfg` configuration file.
2026-05-15 17:18:49: oggm.cfg: Multiprocessing switched OFF according to the parameter file.
2026-05-15 17:18:49: oggm.cfg: Multiprocessing: using all available processors (N=4)
2026-05-15 17:18:49: oggm.cfg: PARAMS['use_intersects'] changed from `True` to `False`.

Download the data using OGGM utility functions

Note that you could reach the same goal by downloading the data manually from

# URL of the preprocessed GDirs
gdir_url = 'https://cluster.klima.uni-bremen.de/~oggm/gdirs/oggm_v1.6/rgitopo/2026.1/all_dems/'
# We use OGGM to download the data
gdir = init_glacier_directories([rgi_id], from_prepro_level=1, prepro_border=10,  prepro_rgi_version='70G', prepro_base_url=gdir_url)[0]

2026-05-15 17:18:50: oggm.workflow: init_glacier_directories from prepro level 1 on 1 glaciers.
2026-05-15 17:18:50: oggm.workflow: Execute entity tasks [gdir_from_prepro] on 1 glaciers
2026-05-15 17:18:50: oggm.utils: Downloading https://cluster.klima.uni-bremen.de/~oggm/gdirs/oggm_v1.6/rgitopo/2026.1/all_dems/RGI70G/b_010/L1/RGI2000-v7.0-G-01/RGI2000-v7.0-G-01-06.tar to /github/home/OGGM/download_cache/cluster.klima.uni-bremen.de/~oggm/gdirs/oggm_v1.6/rgitopo/2026.1/all_dems/RGI70G/b_010/L1/RGI2000-v7.0-G-01/RGI2000-v7.0-G-01-06.tar...

gdir

<oggm.GlacierDirectory>
  RGI id: RGI2000-v7.0-G-01-06486
  Region: 01: Alaska
  Subregion: 01-02: Alaska Range (Wrangell/Kilbuck)
  Glacier type: Glacier
  Terminus type: Not assigned
  Status: Glacier
  Area: 0.961122833004822 km2
  Lon, Lat: (-151.0094740399913, 63.061062)
  Grid (nx, ny): (70, 88)
  Grid (dx, dy): (24.0, -24.0)

Read the DEMs and store them all in a dataset

if sources is None:
    sources = [src for src in os.listdir(gdir.dir) if src in utils.DEM_SOURCES]

print('RGI ID:', rgi_id)
print('Available DEM sources:', sources)
print('Plotting directory:', plot_dir)

RGI ID: RGI2000-v7.0-G-01-06486
Available DEM sources: ['TANDEM', 'MAPZEN', 'AW3D30', 'ALASKA', 'ASTER', 'ARCTICDEM', 'DEM3', 'COPDEM90', 'COPDEM30']
Plotting directory: /__w/tutorials/tutorials/notebooks/tutorials/outputs/RGI2000-v7.0-G-01-06486

# We use xarray to store the data
ods = xr.Dataset()
for src in sources:
    demfile = os.path.join(gdir.dir, src) + '/dem.tif'
    with rioxr.open_rasterio(demfile) as ds:
        data = ds.sel(band=1).load() * 1.
        ods[src] = data.where(data > -100, np.nan)

    sy, sx = np.gradient(ods[src], gdir.grid.dx, gdir.grid.dx)
    ods[src + '_slope'] = ('y', 'x'),  np.arctan(np.sqrt(sy**2 + sx**2))

with rioxr.open_rasterio(gdir.get_filepath('glacier_mask')) as ds:
    ods['mask'] = ds.sel(band=1).load()

# Decide on the number of plots and figure size
ns = len(sources)
x_size = 12
n_cols = 3
n_rows = -(-ns // n_cols)
y_size = x_size / n_cols * n_rows

Raw topography data

smap = salem.graphics.Map(gdir.grid, countries=False)
smap.set_shapefile(gdir.read_shapefile('outlines'))
smap.set_plot_params(cmap='topo')
smap.set_lonlat_contours(add_tick_labels=False)
smap.set_plot_params(vmin=np.nanquantile([ods[s].min() for s in sources], 0.25),
                     vmax=np.nanquantile([ods[s].max() for s in sources], 0.75))

fig = plt.figure(figsize=(x_size, y_size))
grid = AxesGrid(fig, 111,
                nrows_ncols=(n_rows, n_cols),
                axes_pad=0.7,
                cbar_mode='each',
                cbar_location='right',
                cbar_pad=0.1
                )

for i, s in enumerate(sources):
    data = ods[s]
    smap.set_data(data)
    ax = grid[i]
    smap.visualize(ax=ax, addcbar=False, title=s)
    if np.isnan(data).all():
        grid[i].cax.remove()
        continue
    cax = grid.cbar_axes[i]
    smap.colorbarbase(cax)

# take care of uneven grids
if ax != grid[-1] and not grid[-1].title.get_text():
    grid[-1].remove()
    grid[-1].cax.remove()
if ax != grid[-2] and not grid[-2].title.get_text():
    grid[-2].remove()
    grid[-2].cax.remove()

plt.savefig(os.path.join(plot_dir, 'dem_topo_color.png'), dpi=150, bbox_inches='tight')

Shaded relief

fig = plt.figure(figsize=(x_size, y_size))
grid = AxesGrid(fig, 111,
                nrows_ncols=(n_rows, n_cols),
                axes_pad=0.7,
                cbar_location='right',
                cbar_pad=0.1
                )
smap.set_plot_params(cmap='Blues')
smap.set_shapefile()
for i, s in enumerate(sources):
    data = ods[s].copy().where(np.isfinite(ods[s]), 0)
    smap.set_data(data * 0)
    ax = grid[i]
    smap.set_topography(data)
    smap.visualize(ax=ax, addcbar=False, title=s)

# take care of uneven grids
if ax != grid[-1] and not grid[-1].title.get_text():
    grid[-1].remove()
    grid[-1].cax.remove()
if ax != grid[-2] and not grid[-2].title.get_text():
    grid[-2].remove()
    grid[-2].cax.remove()

plt.savefig(os.path.join(plot_dir, 'dem_topo_shade.png'), dpi=150, bbox_inches='tight')

Slope

fig = plt.figure(figsize=(x_size, y_size))
grid = AxesGrid(fig, 111,
                nrows_ncols=(n_rows, n_cols),
                axes_pad=0.7,
                cbar_mode='each',
                cbar_location='right',
                cbar_pad=0.1
                )

smap.set_topography()
smap.set_plot_params(vmin=0, vmax=0.7, cmap='Blues')

for i, s in enumerate(sources):
    data = ods[s + '_slope']
    smap.set_data(data)
    ax = grid[i]
    smap.visualize(ax=ax, addcbar=False, title=s + ' (slope)')
    cax = grid.cbar_axes[i]
    smap.colorbarbase(cax)

# take care of uneven grids
if ax != grid[-1] and not grid[-1].title.get_text():
    grid[-1].remove()
    grid[-1].cax.remove()
if ax != grid[-2] and not grid[-2].title.get_text():
    grid[-2].remove()
    grid[-2].cax.remove()

plt.savefig(os.path.join(plot_dir, 'dem_slope.png'), dpi=150, bbox_inches='tight'):

  Cell In[14], line 29
    plt.savefig(os.path.join(plot_dir, 'dem_slope.png'), dpi=150, bbox_inches='tight'):
                                                                                      ^
SyntaxError: invalid syntax

Some simple statistics about the DEMs

df = pd.DataFrame()
for s in sources:
    df[s] = ods[s].data.flatten()[ods.mask.data.flatten() == 1]

dfs = pd.DataFrame()
for s in sources:
    dfs[s] = ods[s + '_slope'].data.flatten()[ods.mask.data.flatten() == 1]

dfs = df.describe()
dfs.loc['range'] = dfs.loc['max'] - dfs.loc['min']
dfs

	TANDEM	MAPZEN	AW3D30	ALASKA	ASTER	ARCTICDEM	DEM3	COPDEM90	COPDEM30
count	1671.000000	1671.000000	0.0	1671.000000	1671.000000	767.000000	1671.000000	1671.000000	1671.000000
mean	5153.806152	5319.226212	NaN	5316.735352	5295.587672	5529.413086	5328.549372	5277.694824	5277.514160
std	388.357605	350.840381	NaN	351.459656	351.229245	393.222046	351.724101	370.293671	370.142792
min	4497.636719	4622.000000	NaN	4610.906738	4565.000000	4871.422852	4644.000000	4584.852539	4585.657715
25%	4837.172607	5050.000000	NaN	5047.515381	5026.500000	5111.490234	5058.000000	4980.320312	4982.135010
50%	5044.266113	5258.000000	NaN	5255.337402	5250.000000	5613.539551	5259.000000	5231.637207	5231.779785
75%	5441.289551	5578.500000	NaN	5578.190430	5543.000000	5869.918945	5590.000000	5564.726562	5562.813232
max	5975.219727	6111.000000	NaN	6116.865234	6113.000000	6126.963379	6120.000000	6073.276855	6073.898438
range	1477.583008	1489.000000	NaN	1505.958496	1548.000000	1255.540527	1476.000000	1488.424316	1488.240723

Comparison matrix plot

# Table of differences between DEMS
df_diff = pd.DataFrame()
done = []
for s1, s2 in itertools.product(sources, sources):
    if s1 == s2:
        continue
    if (s2, s1) in done:
        continue
    df_diff[s1 + '-' + s2] = df[s1] - df[s2]
    done.append((s1, s2))

# Decide on plot levels
max_diff = df_diff.quantile(0.99).max()
base_levels = np.array([-8, -5, -3, -1.5, -1, -0.5, -0.2, -0.1, 0, 0.1, 0.2, 0.5, 1, 1.5, 3, 5, 8])
if max_diff < 10:
    levels = base_levels
elif max_diff < 100:
    levels = base_levels * 10
elif max_diff < 1000:
    levels = base_levels * 100
else:
    levels = base_levels * 1000
levels = [l for l in levels if abs(l) < max_diff]
if max_diff > 10:
    levels = [int(l) for l in levels]
levels

[-300, -150, -100, -50, -20, -10, 0, 10, 20, 50, 100, 150, 300]

smap.set_plot_params(levels=levels, cmap='PuOr', extend='both')
smap.set_shapefile(gdir.read_shapefile('outlines'))

fig = plt.figure(figsize=(14, 14))
grid = AxesGrid(fig, 111,
                nrows_ncols=(ns - 1, ns - 1),
                axes_pad=0.3,
                cbar_mode='single',
                cbar_location='right',
                cbar_pad=0.1
                )
done = []
for ax in grid:
    ax.set_axis_off()
for s1, s2 in itertools.product(sources, sources):
    if s1 == s2:
        continue
    if (s2, s1) in done:
        continue
    data = ods[s1] - ods[s2]
    ax = grid[sources.index(s1) * (ns - 1) + sources[1:].index(s2)]
    ax.set_axis_on()
    smap.set_data(data)
    smap.visualize(ax=ax, addcbar=False)
    done.append((s1, s2))
    ax.set_title(s1 + '-' + s2, fontsize=8)

cax = grid.cbar_axes[0]
smap.colorbarbase(cax);

plt.savefig(os.path.join(plot_dir, 'dem_diffs.png'), dpi=150, bbox_inches='tight')

Comparison scatter plot

import seaborn as sns
sns.set(style="ticks")

l1, l2 = (utils.nicenumber(df.min().min(), binsize=50, lower=True),
          utils.nicenumber(df.max().max(), binsize=50, lower=False))

def plot_unity():
    points = np.linspace(l1, l2, 100)
    plt.gca().plot(points, points, color='k', marker=None,
                   linestyle=':', linewidth=3.0)

g = sns.pairplot(df.dropna(how='all', axis=1).dropna(), plot_kws=dict(s=50, edgecolor="C0", linewidth=1));
g.map_offdiag(plot_unity)
for asx in g.axes:
    for ax in asx:
        ax.set_xlim((l1, l2))
        ax.set_ylim((l1, l2))

plt.savefig(os.path.join(plot_dir, 'dem_scatter.png'), dpi=150, bbox_inches='tight')

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[20], line 13
      9     plt.gca().plot(points, points, color='k', marker=None,
     10                    linestyle=':', linewidth=3.0)
     11 
     12 g = sns.pairplot(df.dropna(how='all', axis=1).dropna(), plot_kws=dict(s=50, edgecolor="C0", linewidth=1));
---> 13 g.map_offdiag(plot_unity)
     14 for asx in g.axes:
     15     for ax in asx:
     16         ax.set_xlim((l1, l2))

File /usr/local/pyenv/versions/3.13.13/lib/python3.13/site-packages/seaborn/axisgrid.py:1425, in PairGrid.map_offdiag(self, func, **kwargs)
   1414 """Plot with a bivariate function on the off-diagonal subplots.
   1415 
   1416 Parameters
   (...)   1422 
   1423 """
   1424 if self.square_grid:
-> 1425     self.map_lower(func, **kwargs)
   1426     if not self._corner:
   1427         self.map_upper(func, **kwargs)

File /usr/local/pyenv/versions/3.13.13/lib/python3.13/site-packages/seaborn/axisgrid.py:1395, in PairGrid.map_lower(self, func, **kwargs)
   1384 """Plot with a bivariate function on the lower diagonal subplots.
   1385 
   1386 Parameters
   (...)   1392 
   1393 """
   1394 indices = zip(*np.tril_indices_from(self.axes, -1))
-> 1395 self._map_bivariate(func, indices, **kwargs)
   1396 return self

File /usr/local/pyenv/versions/3.13.13/lib/python3.13/site-packages/seaborn/axisgrid.py:1574, in PairGrid._map_bivariate(self, func, indices, **kwargs)
   1572     if ax is None:  # i.e. we are in corner mode
   1573         continue
-> 1574     self._plot_bivariate(x_var, y_var, ax, func, **kws)
   1575 self._add_axis_labels()
   1577 if "hue" in signature(func).parameters:

File /usr/local/pyenv/versions/3.13.13/lib/python3.13/site-packages/seaborn/axisgrid.py:1583, in PairGrid._plot_bivariate(self, x_var, y_var, ax, func, **kwargs)
   1581 """Draw a bivariate plot on the specified axes."""
   1582 if "hue" not in signature(func).parameters:
-> 1583     self._plot_bivariate_iter_hue(x_var, y_var, ax, func, **kwargs)
   1584     return
   1586 kwargs = kwargs.copy()

File /usr/local/pyenv/versions/3.13.13/lib/python3.13/site-packages/seaborn/axisgrid.py:1659, in PairGrid._plot_bivariate_iter_hue(self, x_var, y_var, ax, func, **kwargs)
   1657         func(x=x, y=y, **kws)
   1658     else:
-> 1659         func(x, y, **kws)
   1661 self._update_legend_data(ax)

TypeError: plot_unity() got an unexpected keyword argument 'color'

Table statistics

df.describe()

	TANDEM	MAPZEN	AW3D30	ALASKA	ASTER	ARCTICDEM	DEM3	COPDEM90	COPDEM30
count	1671.000000	1671.000000	0.0	1671.000000	1671.000000	767.000000	1671.000000	1671.000000	1671.000000
mean	5153.806152	5319.226212	NaN	5316.735352	5295.587672	5529.413086	5328.549372	5277.694824	5277.514160
std	388.357605	350.840381	NaN	351.459656	351.229245	393.222046	351.724101	370.293671	370.142792
min	4497.636719	4622.000000	NaN	4610.906738	4565.000000	4871.422852	4644.000000	4584.852539	4585.657715
25%	4837.172607	5050.000000	NaN	5047.515381	5026.500000	5111.490234	5058.000000	4980.320312	4982.135010
50%	5044.266113	5258.000000	NaN	5255.337402	5250.000000	5613.539551	5259.000000	5231.637207	5231.779785
75%	5441.289551	5578.500000	NaN	5578.190430	5543.000000	5869.918945	5590.000000	5564.726562	5562.813232
max	5975.219727	6111.000000	NaN	6116.865234	6113.000000	6126.963379	6120.000000	6073.276855	6073.898438

df.corr()

	TANDEM	MAPZEN	AW3D30	ALASKA	ASTER	ARCTICDEM	DEM3	COPDEM90	COPDEM30
TANDEM	1.000000	0.930963	NaN	0.930687	0.923299	0.858754	0.934220	0.928387	0.928303
MAPZEN	0.930963	1.000000	NaN	0.999929	0.997390	0.957611	0.998911	0.996033	0.995645
AW3D30	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
ALASKA	0.930687	0.999929	NaN	1.000000	0.997280	0.957513	0.998666	0.996075	0.995697
ASTER	0.923299	0.997390	NaN	0.997280	1.000000	0.960869	0.997277	0.995702	0.995283
ARCTICDEM	0.858754	0.957611	NaN	0.957513	0.960869	1.000000	0.957046	0.957821	0.957143
DEM3	0.934220	0.998911	NaN	0.998666	0.997277	0.957046	1.000000	0.995559	0.995141
COPDEM90	0.928387	0.996033	NaN	0.996075	0.995702	0.957821	0.995559	1.000000	0.999891
COPDEM30	0.928303	0.995645	NaN	0.995697	0.995283	0.957143	0.995141	0.999891	1.000000

df_diff.describe()

	TANDEM-MAPZEN	TANDEM-AW3D30	TANDEM-ALASKA	TANDEM-ASTER	TANDEM-ARCTICDEM	TANDEM-DEM3	TANDEM-COPDEM90	TANDEM-COPDEM30	MAPZEN-AW3D30	MAPZEN-ALASKA	...	ASTER-ARCTICDEM	ASTER-DEM3	ASTER-COPDEM90	ASTER-COPDEM30	ARCTICDEM-DEM3	ARCTICDEM-COPDEM90	ARCTICDEM-COPDEM30	DEM3-COPDEM90	DEM3-COPDEM30	COPDEM90-COPDEM30
count	1671.000000	0.0	1671.000000	1671.000000	767.000000	1671.000000	1671.000000	1671.000000	0.0	1671.000000	...	767.000000	1671.000000	1671.000000	1671.000000	767.000000	767.000000	767.000000	1671.000000	1671.000000	1671.000000
mean	-165.419989	NaN	-162.929626	-141.781450	-251.653717	-174.743149	-123.888710	-123.708183	NaN	2.490369	...	-102.185113	-32.961700	17.892747	18.073272	76.316795	110.184074	110.319916	50.854447	51.034972	0.180525
std	142.198023	NaN	142.417313	149.341491	224.423676	138.969170	144.647827	144.721756	NaN	4.234587	...	108.948818	25.941984	38.488241	39.801988	114.381777	113.430321	114.278862	38.750864	40.056016	5.457573
min	-851.888672	NaN	-848.312500	-829.932129	-1085.924805	-872.888672	-812.890137	-812.099121	NaN	-14.705078	...	-428.646973	-128.000000	-111.338867	-123.904297	-151.276367	-131.313965	-136.359863	-17.004395	-26.395508	-17.572266
25%	-214.740479	NaN	-212.847412	-193.438232	-358.547607	-217.682861	-179.401855	-178.104980	NaN	0.054199	...	-171.116211	-48.000000	-7.423828	-8.449463	-1.839355	36.502441	35.619141	23.536377	22.958496	-2.751221
50%	-123.718750	NaN	-120.674805	-100.195801	-170.058594	-133.516602	-95.284180	-95.392578	NaN	2.204590	...	-71.489746	-29.000000	12.738770	13.353027	38.955078	81.454102	82.882324	39.517090	39.264160	0.013672
75%	-71.849121	NaN	-67.788818	-44.948730	-111.032227	-84.589355	-17.190430	-18.154541	NaN	5.209473	...	-28.157715	-19.000000	40.641357	42.359863	139.544922	158.221924	158.155029	74.026611	73.800049	3.210938
max	16.507324	NaN	15.732910	85.662109	48.799805	14.181152	78.665039	84.786133	NaN	20.434082	...	121.276367	52.000000	124.032227	128.154297	399.646973	452.215332	459.774902	163.009766	173.853027	18.569824

8 rows × 36 columns

df_diff.abs().describe()

	TANDEM-MAPZEN	TANDEM-AW3D30	TANDEM-ALASKA	TANDEM-ASTER	TANDEM-ARCTICDEM	TANDEM-DEM3	TANDEM-COPDEM90	TANDEM-COPDEM30	MAPZEN-AW3D30	MAPZEN-ALASKA	...	ASTER-ARCTICDEM	ASTER-DEM3	ASTER-COPDEM90	ASTER-COPDEM30	ARCTICDEM-DEM3	ARCTICDEM-COPDEM90	ARCTICDEM-COPDEM30	DEM3-COPDEM90	DEM3-COPDEM30	COPDEM90-COPDEM30
count	1671.000000	0.0	1671.000000	1671.000000	767.000000	1671.000000	1671.000000	1671.000000	0.0	1671.000000	...	767.000000	1671.000000	1671.000000	1671.000000	767.000000	767.000000	767.000000	1671.000000	1671.000000	1671.000000
mean	165.650691	NaN	163.309280	147.605664	253.502304	174.815853	134.962799	135.184494	NaN	3.799071	...	112.711556	35.226212	31.869296	32.801881	95.275925	117.711647	118.163139	51.431971	52.023959	4.060298
std	141.929044	NaN	141.981552	143.584187	222.330780	138.877648	134.367798	134.057739	NaN	3.113807	...	98.004051	22.770194	28.025463	28.886490	99.124644	105.587395	106.137970	37.980538	38.762088	3.649907
min	0.151367	NaN	0.070801	0.175293	0.293457	0.848633	0.050781	0.002441	NaN	0.002930	...	0.155762	0.000000	0.000000	0.005371	0.184570	0.624512	0.650879	0.002441	0.012207	0.000488
25%	71.849121	NaN	67.788818	49.170898	111.032227	84.589355	38.032227	38.805664	NaN	1.328125	...	41.791260	20.000000	10.204102	11.155762	21.433594	41.026611	41.187012	23.536377	23.231689	1.359131
50%	123.718750	NaN	120.674805	100.195801	170.058594	133.516602	95.284180	95.392578	NaN	3.072266	...	73.289062	29.000000	22.945801	23.466309	52.738770	82.970215	84.257812	39.517090	39.264160	2.911621
75%	214.740479	NaN	212.847412	193.438232	358.547607	217.682861	179.401855	178.104980	NaN	5.534912	...	171.116211	48.000000	46.310059	47.615723	141.093506	158.221924	158.155029	74.026611	73.800049	5.748779
max	851.888672	NaN	848.312500	829.932129	1085.924805	872.888672	812.890137	812.099121	NaN	20.434082	...	428.646973	128.000000	124.032227	128.154297	399.646973	452.215332	459.774902	163.009766	173.853027	18.569824

8 rows × 36 columns

What’s next?

• return to the OGGM documentation

• back to the table of contents