Assigning coords as dimension coordinates
The gridmarthe package use “horizontally reduced” grids, which means that
the spatial dimension is flattened. This is a common practice in geophysical
modeling (meteorology, oceanography, land surface modelling, etc.), where the
grid is often represented as a 1D array of points.
Grids are often 2D in space (or 3D), but here represented as 1D vector of size
Nx*Ny (or Nx*Ny*Nz). Each grid point is associated to an index and a set of
coordinates (and dx, dy).
This is particularly useful and efficient for computing on grids. But as a consequence, it is not straightforward to work with such data, especially when plotting.
This notebooks explore how to move coordinates from variables (1D associated to indices) to coordinates (2D associated to dimensions).
# import package
import gridmarthe as gm
# reading data and storing into Dataset object (with xarray)
ds = gm.load_marthe_grid(
'./data/chasim_hallue.out', 'CHARGE',
fpastp='./data/hallue.pastp',
drop_nan=True
)
# display values and attributes
display(ds)
<xarray.Dataset> Size: 2MB
Dimensions: (time: 205, zone: 927)
Coordinates:
* time (time) datetime64[ns] 2kB 1995-07-31 1995-08-01 ... 2012-07-01
* zone (zone) int32 4kB 255 256 257 258 259 ... 2722 2723 2724 2725 2726
Data variables:
charge (time, zone) float64 2MB 100.0 100.6 101.1 ... 27.0 26.0 26.35
x (zone) float32 4kB 617.8 618.2 618.8 619.2 ... 606.8 607.2 607.8
y (zone) float32 4kB 2.567e+03 2.567e+03 ... 2.543e+03 2.543e+03
dx (zone) float32 4kB 0.5 0.5 0.5 0.5 0.5 0.5 ... 0.5 0.5 0.5 0.5 0.5
dy (zone) float32 4kB 0.5 0.5 0.5 0.5 0.5 0.5 ... 0.5 0.5 0.5 0.5 0.5
izone (zone) int32 4kB 1 2 3 4 5 6 7 8 ... 921 922 923 924 925 926 927
Attributes: (12/17)
conventions: CF-1.10
title: Modélisation du bassin de la SOMME Nappe_Libre
marthe_grid_version: 9.0
original_dimensions: x,y,z [grids]: 53 54 1
crs: {'crs_wkt': 'PROJCRS["NTF (Paris) / Lambert zone II...
lon_resolution: 0.5
... ...
period: 1995-2012
frequency: 30 day(s)
creation_date: Created on 2026-07-16T16:28:41Z UTC
comment: Hydrogeological model created with MARTHE code (Thi...
domain: FR-France
institution: BRGM, French Geological Survey, Orléans, Francexarray.Dataset
- time: 205
- zone: 927
- time(time)datetime64[ns]1995-07-31 ... 2012-07-01
array(['1995-07-31T00:00:00.000000000', '1995-08-01T00:00:00.000000000', '1995-09-01T00:00:00.000000000', ..., '2012-05-01T00:00:00.000000000', '2012-06-01T00:00:00.000000000', '2012-07-01T00:00:00.000000000'], shape=(205,), dtype='datetime64[ns]') - zone(zone)int32255 256 257 258 ... 2724 2725 2726
- compress :
- y x
array([ 255, 256, 257, ..., 2724, 2725, 2726], shape=(927,), dtype=int32)
- charge(time, zone)float64100.0 100.6 101.1 ... 26.0 26.35
- varname :
- CHARGE
- units :
- m
- mart_missing_value :
- 9999.0
- standard_name :
- water_table_level
- long_name :
- groundwater head
array([[100.0473 , 100.6405 , 101.1256 , ..., 26.97066, 26. , 26.29721], [100.0473 , 100.6405 , 101.1256 , ..., 26.97065, 26. , 26.29721], [100.0473 , 100.6405 , 101.1256 , ..., 26.97384, 26. , 26.30182], ..., [100.0473 , 100.6405 , 101.1256 , ..., 26.99997, 26. , 26.36214], [100.0473 , 100.6405 , 101.1256 , ..., 26.99997, 26. , 26.35616], [100.0473 , 100.6405 , 101.1256 , ..., 26.99997, 26. , 26.34742]], shape=(205, 927)) - x(zone)float32617.8 618.2 618.8 ... 607.2 607.8
- axis :
- X
- long_name :
- Easting
- standard_name :
- projection_x_coordinate
- units :
- metre
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- axis :
- Y
- long_name :
- Northing
- standard_name :
- projection_y_coordinate
- units :
- metre
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- conventions :
- CF-1.10
- title :
- Modélisation du bassin de la SOMME Nappe_Libre
- marthe_grid_version :
- 9.0
- original_dimensions :
- x,y,z [grids]: 53 54 1
- crs :
- {'crs_wkt': 'PROJCRS["NTF (Paris) / Lambert zone II",BASEGEOGCRS["NTF (Paris)",DATUM["Nouvelle Triangulation Francaise (Paris)",ELLIPSOID["Clarke 1880 (IGN)",6378249.2,293.466021293627,LENGTHUNIT["metre",1]]],PRIMEM["Paris",2.5969213,ANGLEUNIT["grad",0.0157079632679489]],ID["EPSG",4807]],CONVERSION["Lambert zone II",METHOD["Lambert Conic Conformal (1SP)",ID["EPSG",9801]],PARAMETER["Latitude of natural origin",52,ANGLEUNIT["grad",0.0157079632679489],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",0,ANGLEUNIT["grad",0.0157079632679489],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.99987742,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",600000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",2200000,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["easting (X)",east,ORDER[1],LENGTHUNIT["metre",1]],AXIS["northing (Y)",north,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["Engineering survey, topographic mapping."],AREA["France mainland onshore between 50.5 grads and 53.5 grads North (45°27\'N to 48°09\'N). Also used over all onshore mainland France."],BBOX[42.33,-4.87,51.14,8.23]],ID["EPSG",27572]]', 'semi_major_axis': 6378249.2, 'semi_minor_axis': 6356515.0, 'inverse_flattening': 293.4660212936269, 'reference_ellipsoid_name': 'Clarke 1880 (IGN)', 'longitude_of_prime_meridian': 2.5969213, 'prime_meridian_name': 'Paris', 'geographic_crs_name': 'NTF (Paris)', 'horizontal_datum_name': 'Nouvelle Triangulation Francaise (Paris)', 'projected_crs_name': 'NTF (Paris) / Lambert zone II', 'grid_mapping_name': 'lambert_conformal_conic', 'standard_parallel': 52.0, 'longitude_of_central_meridian': 0.0, 'false_easting': 600000.0, 'false_northing': 2200000.0}
- lon_resolution :
- 0.5
- lat_resolution :
- 0.5
- resolution_units :
- metre
- scale_factor :
- 1.0
- nested_grid :
- False
- extend :
- xymin : 596.75 2542.25; xymax: 622.75 2568.75
- period :
- 1995-2012
- frequency :
- 30 day(s)
- creation_date :
- Created on 2026-07-16T16:28:41Z UTC
- comment :
- Hydrogeological model created with MARTHE code (Thiery, D. 2020. Guidelines for MARTHE v7.8 computer code for hydro-systems modelling. report BRGM/RP-69660-FR).
- domain :
- FR-France
- institution :
- BRGM, French Geological Survey, Orléans, France
We have a time index time (timesteps).
The spatial index is called zone and coordinates variables are:
x(x-coordinate of centre cell),y(y-coordinate of centre cell),z(indice of layer or realz) if present,dx(cell width),dy(cell height)izone(same as zone index, but reset to 1 and incremental only on active cells).
Switch to 2 or 3D grid
To move x,y,z coordinates from variables (depending on zone index) to
array dimensions, and then reshape data from 1D (or 2D with time) to
3 (x,y, time) or 4D (x,y,z,time), use: assign_coords.
# add coordinates to transform the 2D Dataset into 3D
ds_3d = gm.assign_coords(ds)
display(ds_3d) # check new coordinates
<xarray.Dataset> Size: 3MB
Dimensions: (y: 48, x: 44, time: 205)
Coordinates:
* y (y) float32 192B 2.567e+03 2.566e+03 ... 2.544e+03 2.543e+03
* x (x) float32 176B 599.2 599.8 600.2 600.8 ... 619.8 620.2 620.8
* time (time) datetime64[ns] 2kB 1995-07-31 1995-08-01 ... 2012-07-01
Data variables:
charge (time, y, x) float64 3MB nan nan nan nan nan ... nan nan nan nan
dx (y, x) float32 8kB nan nan nan nan nan nan ... nan nan nan nan nan
dy (y, x) float32 8kB nan nan nan nan nan nan ... nan nan nan nan nan
izone (y, x) float64 17kB nan nan nan nan nan nan ... nan nan nan nan nan
Attributes: (12/17)
conventions: CF-1.10
title: Modélisation du bassin de la SOMME Nappe_Libre
marthe_grid_version: 9.0
original_dimensions: x,y,z [grids]: 53 54 1
crs: {'crs_wkt': 'PROJCRS["NTF (Paris) / Lambert zone II...
lon_resolution: 0.5
... ...
period: 1995-2012
frequency: 30 day(s)
creation_date: Created on 2026-07-16T16:28:41Z UTC
comment: Hydrogeological model created with MARTHE code (Thi...
domain: FR-France
institution: BRGM, French Geological Survey, Orléans, Francexarray.Dataset
- y: 48
- x: 44
- time: 205
- y(y)float322.567e+03 2.566e+03 ... 2.543e+03
- axis :
- Y
- long_name :
- Northing
- standard_name :
- projection_y_coordinate
- units :
- metre
array([2566.75, 2566.25, 2565.75, 2565.25, 2564.75, 2564.25, 2563.75, 2563.25, 2562.75, 2562.25, 2561.75, 2561.25, 2560.75, 2560.25, 2559.75, 2559.25, 2558.75, 2558.25, 2557.75, 2557.25, 2556.75, 2556.25, 2555.75, 2555.25, 2554.75, 2554.25, 2553.75, 2553.25, 2552.75, 2552.25, 2551.75, 2551.25, 2550.75, 2550.25, 2549.75, 2549.25, 2548.75, 2548.25, 2547.75, 2547.25, 2546.75, 2546.25, 2545.75, 2545.25, 2544.75, 2544.25, 2543.75, 2543.25], dtype=float32) - x(x)float32599.2 599.8 600.2 ... 620.2 620.8
- axis :
- X
- long_name :
- Easting
- standard_name :
- projection_x_coordinate
- units :
- metre
array([599.25, 599.75, 600.25, 600.75, 601.25, 601.75, 602.25, 602.75, 603.25, 603.75, 604.25, 604.75, 605.25, 605.75, 606.25, 606.75, 607.25, 607.75, 608.25, 608.75, 609.25, 609.75, 610.25, 610.75, 611.25, 611.75, 612.25, 612.75, 613.25, 613.75, 614.25, 614.75, 615.25, 615.75, 616.25, 616.75, 617.25, 617.75, 618.25, 618.75, 619.25, 619.75, 620.25, 620.75], dtype=float32) - time(time)datetime64[ns]1995-07-31 ... 2012-07-01
array(['1995-07-31T00:00:00.000000000', '1995-08-01T00:00:00.000000000', '1995-09-01T00:00:00.000000000', ..., '2012-05-01T00:00:00.000000000', '2012-06-01T00:00:00.000000000', '2012-07-01T00:00:00.000000000'], shape=(205,), dtype='datetime64[ns]')
- charge(time, y, x)float64nan nan nan nan ... nan nan nan nan
- varname :
- CHARGE
- units :
- m
- mart_missing_value :
- 9999.0
- standard_name :
- water_table_level
- long_name :
- groundwater head
array([[[ nan, nan, nan, ..., 102.6527 , 103.3882 , 103.5225 ], [ nan, nan, nan, ..., 100.3159 , 100.7368 , nan], [ nan, nan, nan, ..., 98.134 , 98.3761 , nan], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[ nan, nan, nan, ..., 102.6527 , 103.3882 , 103.5225 ], [ nan, nan, nan, ..., 100.3159 , 100.7368 , nan], [ nan, nan, nan, ..., 98.134 , 98.3761 , nan], ... [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]], [[ nan, nan, nan, ..., 102.6527 , 103.3882 , 103.5225 ], [ nan, nan, nan, ..., 100.5129 , 100.941 , nan], [ nan, nan, nan, ..., 98.5106 , 98.77482, nan], ..., [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan], [ nan, nan, nan, ..., nan, nan, nan]]], shape=(205, 48, 44)) - dx(y, x)float32nan nan nan nan ... nan nan nan nan
array([[nan, nan, nan, ..., 0.5, 0.5, 0.5], [nan, nan, nan, ..., 0.5, 0.5, nan], [nan, nan, nan, ..., 0.5, 0.5, nan], ..., [nan, nan, nan, ..., nan, nan, nan], [nan, nan, nan, ..., nan, nan, nan], [nan, nan, nan, ..., nan, nan, nan]], shape=(48, 44), dtype=float32) - dy(y, x)float32nan nan nan nan ... nan nan nan nan
array([[nan, nan, nan, ..., 0.5, 0.5, 0.5], [nan, nan, nan, ..., 0.5, 0.5, nan], [nan, nan, nan, ..., 0.5, 0.5, nan], ..., [nan, nan, nan, ..., nan, nan, nan], [nan, nan, nan, ..., nan, nan, nan], [nan, nan, nan, ..., nan, nan, nan]], shape=(48, 44), dtype=float32) - izone(y, x)float64nan nan nan nan ... nan nan nan nan
array([[nan, nan, nan, ..., 5., 6., 7.], [nan, nan, nan, ..., 12., 13., nan], [nan, nan, nan, ..., 19., 20., nan], ..., [nan, nan, nan, ..., nan, nan, nan], [nan, nan, nan, ..., nan, nan, nan], [nan, nan, nan, ..., nan, nan, nan]], shape=(48, 44))
- conventions :
- CF-1.10
- title :
- Modélisation du bassin de la SOMME Nappe_Libre
- marthe_grid_version :
- 9.0
- original_dimensions :
- x,y,z [grids]: 53 54 1
- crs :
- {'crs_wkt': 'PROJCRS["NTF (Paris) / Lambert zone II",BASEGEOGCRS["NTF (Paris)",DATUM["Nouvelle Triangulation Francaise (Paris)",ELLIPSOID["Clarke 1880 (IGN)",6378249.2,293.466021293627,LENGTHUNIT["metre",1]]],PRIMEM["Paris",2.5969213,ANGLEUNIT["grad",0.0157079632679489]],ID["EPSG",4807]],CONVERSION["Lambert zone II",METHOD["Lambert Conic Conformal (1SP)",ID["EPSG",9801]],PARAMETER["Latitude of natural origin",52,ANGLEUNIT["grad",0.0157079632679489],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",0,ANGLEUNIT["grad",0.0157079632679489],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.99987742,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",600000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",2200000,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["easting (X)",east,ORDER[1],LENGTHUNIT["metre",1]],AXIS["northing (Y)",north,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["Engineering survey, topographic mapping."],AREA["France mainland onshore between 50.5 grads and 53.5 grads North (45°27\'N to 48°09\'N). Also used over all onshore mainland France."],BBOX[42.33,-4.87,51.14,8.23]],ID["EPSG",27572]]', 'semi_major_axis': 6378249.2, 'semi_minor_axis': 6356515.0, 'inverse_flattening': 293.4660212936269, 'reference_ellipsoid_name': 'Clarke 1880 (IGN)', 'longitude_of_prime_meridian': 2.5969213, 'prime_meridian_name': 'Paris', 'geographic_crs_name': 'NTF (Paris)', 'horizontal_datum_name': 'Nouvelle Triangulation Francaise (Paris)', 'projected_crs_name': 'NTF (Paris) / Lambert zone II', 'grid_mapping_name': 'lambert_conformal_conic', 'standard_parallel': 52.0, 'longitude_of_central_meridian': 0.0, 'false_easting': 600000.0, 'false_northing': 2200000.0}
- lon_resolution :
- 0.5
- lat_resolution :
- 0.5
- resolution_units :
- metre
- scale_factor :
- 1.0
- nested_grid :
- False
- extend :
- xymin : 596.75 2542.25; xymax: 622.75 2568.75
- period :
- 1995-2012
- frequency :
- 30 day(s)
- creation_date :
- Created on 2026-07-16T16:28:41Z UTC
- comment :
- Hydrogeological model created with MARTHE code (Thiery, D. 2020. Guidelines for MARTHE v7.8 computer code for hydro-systems modelling. report BRGM/RP-69660-FR).
- domain :
- FR-France
- institution :
- BRGM, French Geological Survey, Orléans, France
Data are now 3D for the charge (head) variable: y and x are now coordinates
dimensions, with time.
This dataset can now be plot easily as show in the previous notebook.
Return to 1D grid
It can still be useful to return to a 1D grid. To do so, use stack_coords function:
ds1d = gm.stack_coords(ds_3d, dropna=True)
display(ds1d)
<xarray.Dataset> Size: 2MB
Dimensions: (time: 205, zone: 927)
Coordinates:
* time (time) datetime64[ns] 2kB 1995-07-31 1995-08-01 ... 2012-07-01
* zone (zone) int64 7kB 38 39 40 41 42 43 ... 2082 2083 2084 2085 2086
Data variables:
charge (time, zone) float64 2MB 100.0 100.6 101.1 ... 27.0 26.0 26.35
dx (zone) float32 4kB 0.5 0.5 0.5 0.5 0.5 0.5 ... 0.5 0.5 0.5 0.5 0.5
dy (zone) float32 4kB 0.5 0.5 0.5 0.5 0.5 0.5 ... 0.5 0.5 0.5 0.5 0.5
izone (zone) float64 7kB 1.0 2.0 3.0 4.0 5.0 ... 924.0 925.0 926.0 927.0
y (zone) float32 4kB 2.567e+03 2.567e+03 ... 2.543e+03 2.543e+03
x (zone) float32 4kB 617.8 618.2 618.8 619.2 ... 606.8 607.2 607.8
Attributes: (12/17)
conventions: CF-1.10
title: Modélisation du bassin de la SOMME Nappe_Libre
marthe_grid_version: 9.0
original_dimensions: x,y,z [grids]: 53 54 1
crs: {'crs_wkt': 'PROJCRS["NTF (Paris) / Lambert zone II...
lon_resolution: 0.5
... ...
period: 1995-2012
frequency: 30 day(s)
creation_date: Created on 2026-07-16T16:28:41Z UTC
comment: Hydrogeological model created with MARTHE code (Thi...
domain: FR-France
institution: BRGM, French Geological Survey, Orléans, Francexarray.Dataset
- time: 205
- zone: 927
- time(time)datetime64[ns]1995-07-31 ... 2012-07-01
array(['1995-07-31T00:00:00.000000000', '1995-08-01T00:00:00.000000000', '1995-09-01T00:00:00.000000000', ..., '2012-05-01T00:00:00.000000000', '2012-06-01T00:00:00.000000000', '2012-07-01T00:00:00.000000000'], shape=(205,), dtype='datetime64[ns]') - zone(zone)int6438 39 40 41 ... 2083 2084 2085 2086
array([ 38, 39, 40, ..., 2084, 2085, 2086], shape=(927,))
- charge(time, zone)float64100.0 100.6 101.1 ... 26.0 26.35
- varname :
- CHARGE
- units :
- m
- mart_missing_value :
- 9999.0
- standard_name :
- water_table_level
- long_name :
- groundwater head
array([[100.0473 , 100.6405 , 101.1256 , ..., 26.97066, 26. , 26.29721], [100.0473 , 100.6405 , 101.1256 , ..., 26.97065, 26. , 26.29721], [100.0473 , 100.6405 , 101.1256 , ..., 26.97384, 26. , 26.30182], ..., [100.0473 , 100.6405 , 101.1256 , ..., 26.99997, 26. , 26.36214], [100.0473 , 100.6405 , 101.1256 , ..., 26.99997, 26. , 26.35616], [100.0473 , 100.6405 , 101.1256 , ..., 26.99997, 26. , 26.34742]], shape=(205, 927)) - dx(zone)float320.5 0.5 0.5 0.5 ... 0.5 0.5 0.5 0.5
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- conventions :
- CF-1.10
- title :
- Modélisation du bassin de la SOMME Nappe_Libre
- marthe_grid_version :
- 9.0
- original_dimensions :
- x,y,z [grids]: 53 54 1
- crs :
- {'crs_wkt': 'PROJCRS["NTF (Paris) / Lambert zone II",BASEGEOGCRS["NTF (Paris)",DATUM["Nouvelle Triangulation Francaise (Paris)",ELLIPSOID["Clarke 1880 (IGN)",6378249.2,293.466021293627,LENGTHUNIT["metre",1]]],PRIMEM["Paris",2.5969213,ANGLEUNIT["grad",0.0157079632679489]],ID["EPSG",4807]],CONVERSION["Lambert zone II",METHOD["Lambert Conic Conformal (1SP)",ID["EPSG",9801]],PARAMETER["Latitude of natural origin",52,ANGLEUNIT["grad",0.0157079632679489],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",0,ANGLEUNIT["grad",0.0157079632679489],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.99987742,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",600000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",2200000,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["easting (X)",east,ORDER[1],LENGTHUNIT["metre",1]],AXIS["northing (Y)",north,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["Engineering survey, topographic mapping."],AREA["France mainland onshore between 50.5 grads and 53.5 grads North (45°27\'N to 48°09\'N). Also used over all onshore mainland France."],BBOX[42.33,-4.87,51.14,8.23]],ID["EPSG",27572]]', 'semi_major_axis': 6378249.2, 'semi_minor_axis': 6356515.0, 'inverse_flattening': 293.4660212936269, 'reference_ellipsoid_name': 'Clarke 1880 (IGN)', 'longitude_of_prime_meridian': 2.5969213, 'prime_meridian_name': 'Paris', 'geographic_crs_name': 'NTF (Paris)', 'horizontal_datum_name': 'Nouvelle Triangulation Francaise (Paris)', 'projected_crs_name': 'NTF (Paris) / Lambert zone II', 'grid_mapping_name': 'lambert_conformal_conic', 'standard_parallel': 52.0, 'longitude_of_central_meridian': 0.0, 'false_easting': 600000.0, 'false_northing': 2200000.0}
- lon_resolution :
- 0.5
- lat_resolution :
- 0.5
- resolution_units :
- metre
- scale_factor :
- 1.0
- nested_grid :
- False
- extend :
- xymin : 596.75 2542.25; xymax: 622.75 2568.75
- period :
- 1995-2012
- frequency :
- 30 day(s)
- creation_date :
- Created on 2026-07-16T16:28:41Z UTC
- comment :
- Hydrogeological model created with MARTHE code (Thiery, D. 2020. Guidelines for MARTHE v7.8 computer code for hydro-systems modelling. report BRGM/RP-69660-FR).
- domain :
- FR-France
- institution :
- BRGM, French Geological Survey, Orléans, France
Warning: Mind that in the previous operation (stack_coords) the zone
index is not consistent anymore. New index are generated.